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matheducators | Why can an easily graphable definite integral, be labyrinthine to evaluate? | How can I explain to 16-year-olds, who just started calculus, why it's so nettlesome and tricky to symbolically integrate definite integrals, when their graphs look so unremarkable and straightforward?
I used Desmos to graph $\int_0^{\pi/2}\frac{x^2\log^2{(\sin{x})}}{\sin^2x} \, dx$ below. u/camelCaseCondition's comment reaffirms that the solution is knotty and effortful, but not why:
The extent of math that this involves (beyond standard integration techniques usually taught in Calc II, just applied on a large scale) is a significant bit of Complex Analysis (the residue theorem, etc.). In general, everything in his derivation should at least be understandable had you taken Calc I-III and Complex Analysis.
However, eyeballing those substitutions and thinking of how to put them all together (and tricks like the mapping from 1/t) to do this is something that probably comes from years of experience using all these techniques and an exceptional cleverness. I can only be in awe when I see the whole thing put together[.]
My question is more specific than Why do statements which appear elementary have complicated proofs? and Why are mathematical proofs so hard?, because I'm asking especially about definite integrals with uneventful graphs, but that high schoolers can effortlessly graph without software.
| VQAonline_00043909.png | Integration is tricky in general because it is like trying to find the question given an answer. For differentiation, we have a set of rules that work, and if we are systematic and careful enough, we can symbolically compute any derivative using those rules. Integration is tougher because you are trying to undo those rules to arrive back at the starting point. Furthermore, since many functions have equivalent forms (before and after simplification for instance), it can be very tricky to determine which rules were applied as two functions may look similar but have very different integrals.
Going back to the question-answer analogy, think of this way. Suppose you know the answer to a question is five, and you are interested in determining the question. From this information alone, it is pretty much impossible to determine the original question. Why? We're missing a lot of context. Maybe the five represents dollars and is the amount we spent on lunch today. Maybe the five represents shoes and the question is how many shoes do we have. Now, suppose we knew the answer is five years. We would have a better chance of knowing what the question is here and can rule out some of the previous options, but again, the lack of context makes it hard to know precisely what that question is.
The same thing happens in integration. You are given an answer (a function to integrate), and you are asked to determine the question (the integral) that the answer corresponds to. This integrand is usually given in a simplified form meaning it's akin to knowing the answer is five; the simplifications make us lose contextual information useful for solving the integral. As you apply your integration rules, you regain more and more of the context for the answer until you know enough to arrive at the question.
Last note: the graphing is easier because ultimately, the graph does not have to be perfect. It can be a very good approximation, but due to human error or finiteness (of computer arithmetic), it is never a perfect. Making the graph is like being in the right ballpark; you are super close, but you might miss the mark by a smidge. Symbolic computations on the other hand are perfect; they do not discard any information; therefore, they are harder to arrive at.
| https://matheducators.stackexchange.com/questions/21010 |
matheducators | How should I grade true-or-false questions if the student's writing is unclear? | See the attached image:
I am having a difficult time grading this paper as I am not sure if the student intentionally wrote the answers in such a way that each answer looks like both "T" (or "t") and "F" (or "f") or if it is just his normal style of writing. He did a terrible job in answering other questions, if this information is even relevant.
Questions:
How should I grade this student's answer? (The correct answers are "F", "T", "T", "T", and "F".) If the student intentionally wrote ambiguously, should I give him zero for all these five questions? If yes, how to prove that he did this intentionally?
How should I design my questions to prevent this from happening in the future?
Edit 2022-03-04. Mystery solved! I have talked to the student and he admits that he wrote his answers in frustration. His intended answers are TTTFT. Many thanks to everyone for your input.
| VQAonline_00043912.png | I read them as TTTFT. But the fourth is very hard to tell, the first somewhat hard to tell, and all show poor writing, perhaps indicating a lack of engagement. You could tell him that such terrible penmanship will get him zeroes in the future (not even the 50/50 chance he has going now).
You could also print the T and F and have the kids circle one. I actually find this quicker and easier to scan when grading. (But don't feel like you have to change.) E.g.
Circle one answer, T true or F false:
Choice
Question
T F
y=x^4 is the equation of a parabola.
T F
x/5 + y/3.1415 =0 is the equation of a line.
FWIW, I wouldn't be so worried about static from the kid, unless you've had squabbles before. He's going to get crushed on the test, overall, and will probably just take it on the chin.
Edit: I disagree with the comment that you should only have essay style (long answer) problems. You should do a mix. T/F is effective for checking tricky things, like the (very mildly) tricky questions I mentioned. On the other hand, you should probably have more standard questions (sans tricks) for the long answer, worked problems. In other words, have a blend of problem types.
Edit: I disagree with the suggestion to orally quiz the kid. You don't have the time for that, especially if you have to initiate it yourself, versus the kid coming to you. Plus he could have reviewed the materials, now. If he actually meant something different, tough...this is a lesson to write more precisely in the future. He will learn that harsh lesson much better from losing the points, than from pleas to write better. And, we need to be a little sanguine about the possibility that at some point a student gets misgraded. School is a practical process, not a theorem of Euclid.
| https://matheducators.stackexchange.com/questions/24985 |
matheducators | Solving a Polar set of equations algebraically? | I was coaching a student on how to approach this problem. 2 equations given and the question was where they intersect.
Now, with a bit of practice on polar coordinates, producing the graph by hand wasn't too tough. I was able to point out the petal in the first quadrant wan't going to intersect the vertical line unless rotated 30 degrees clockwise.
The student said the result was expected to be algebraic, i.e. set the 2 equal, manipulate and show no solution. I wasn't able to do this after about 10 minutes of manipulation, I just would up with sine to the 3rd power along with a number of sine*cos terms.
I'm not so much looking for this single solution as I am a process how to approach this style of problem. (This is for a pre-calc class, typically with high school juniors)
| VQAonline_00043884.png | This might not quite be an "algebraic" solution in the sense the student was looking for, but I think a more reasonable approach to this sort of problem is using bounds, not setting things equal from the outset.
The general strategy is to notice that one curve is entirely inside a circle of radius 4, while the other is entirely outside that circle, so any intersection must occur on the boundary. This is often a good strategy for showing two objects don't intersect: bound them inside larger, simpler regions that can be shown to intersect only in certain very limited ways.
More precisely, since $\sec(\theta) = 1/\cos(\theta)$, we have
$$\lvert 4\sec(\theta) \rvert \geq 4$$
with equality if and only if $\lvert \cos(\theta) \rvert = 1$. However,
$$\lvert 4 \sin(3 \theta) \rvert \leq 4,$$
so if $4 \sec(\theta) = 4 \sin(3\theta)$, then $\lvert \cos(\theta) \rvert = 1$, which means $\theta$ is an integer multiple of $\pi$. But that implies $4 \sin(3\theta) = 0$, a contradiction.
| https://matheducators.stackexchange.com/questions/11721 |
matheducators | An alternative to "two column" geometry proofs | I'm a high school teacher in New York State (US), starting in on my first year of teaching Geometry. One of the things that really intrigues me is that the Regents exam (the state-mandated final exam) accepts a graphic organizer for proofs that is different than the traditional two column Statement-Reason style that I learned. Here, for instance, is a fully correct model response in a recent exam.
My colleagues and I are really intrigued with this style and the potential that it has to make the "flow" of a proof more visually intuitive for students. However, I'm afraid that I don't even know what this style is named, much less research on whether it helps students master skills in proof-writing and strategies for teaching it in a class. Does anyone have any leads that could point me in the right direction?
| VQAonline_00043903.png | This is an example of what is usually called a flowchart proof (or sometimes a flow proof for short). A quick Google search for "flowchart proof" or "flow proof" shows many, many contemporary examples of the form, including a whole genre of YouTube videos teaching this style of presentation.
This style of proof has been promoted at various points since the 1960s. As it happens, way back in 2006 (when I was a grad student) I once prepared an annotated bibliography of articles from The Mathematics Teacher on proof and proving; one section of that bibliography was about "Articles proposing alternatives / modifications to the 2-Column Form", and a subsection of that was "II. Articles about 'Flow Proofs'". I am reproducing the entirety of that section below (with a few minor edits and elisions for clarity). (In what follows, MT is an abbreviation for Mathematics Teacher.)
It seems that the "Flow Proof" gets rediscovered every eight years or so:
Ness, H. (1962). "A method of proof for high school geometry". MT, 55, 567-569.
Thorsen, C. (1963). "Structure diagrams for geometry proofs." MT, 56, 608-609.
Hallerberg, A. (1971). "A form of proof." MT, 64, 203-214.
McMurray, R. (1978). "Flow proofs in geometry." MT, 71, 592-595.
Basinger, D. (1979). "More on flow proofs in geometry." MT, 72, 434-436.
Brandell, J. (1994). "Helping students write paragraph proofs in geometry." MT, 87, 498-502.
A few words about the articles above: Ness (1962) introduces (is this
the first reported case of it?) the flow proof. He begins with a
concise summary of the drawbacks of the 2CF, and then goes on to say:
"The School Mathematics Study Group, in its geometry course,
introduces the paragraph type of proof presumably to eliminate some of
the objections listed above. However, in my opinion, the paragraph
type of proof would be extremely difficult for sophomore geometry
students, and these proofs are often vague and lack precision. I
would like to introduce a method of proof that we tried last year as
an experiment... that I believe eliminates the difficulties of the
two-column proof without introducing the vagueness and lack of
precision of the paragraph proof."
Ness then goes on to give an example of the same proof, done both in 2CF and as a flow proof (although
he does not name his 'method'). Curiously, his flow proof consists
solely of what are normally called "statements"; there is no space in
his diagram for the "reasons". Curiously, he seems not to notice this
– at least he makes no mention of it.
Thorsen (1963) is a response to
Ness (1962). Apparently Thorsen had also been using an essentially
identical format, the only difference being that Thorsen's statements
are enclosed in boxes ("balloons"). Like Ness, Thorsen does not
include reasons in his flow proofs, which he calls "structure
diagrams". Thorsen cautions against using structure diagrams instead
of a 2CF; rather, he uses them as a planning tool, to help understand
the logic of an argument, which still needs to be written as a 2CF
"which includes 'authorities'" (i.e. reasons). The structure diagram
thus serves as a scaffolding device only.
Hallerberg (1971)
re-discovers the flow proof independently (?) eight years later. His
flow proofs are extremely formal in nature; nodes in the proof
correspond to implications (of the form P -> Q), with incoming edges
representing known assertions (P) and outgoing edges representing
deduced conclusions (Q). Thus Hallerberg, like Berger, Schacht, and
Shields, makes the law of modus ponens the central feature of his
format. Hallerberg's flow proofs lack the readability of Thorsen's
and Ness's, largely because his diagrams consist solely of code labels
($S_n$, $G_k$, etc.) with a "legend" alongside the diagram decoding the
symbols. The result might please a logician but is manifestly
classroom –unfriendly.
Two remarkable features of Hallerberg's
article are that he makes no claim that this has worked well in the
classroom (I believe his article is unique in not making this claim),
and that he offers examples of non-geometric proofs as well. He also
addresses using the flow proof with indirect proofs.
Flow proofs
are rediscovered once again in McMurray (1978). It is here that the
name "flow proof" is first (?) used. McMurray's flow proofs consist
of statements, joined by arrows; each arrow is labelled with a number,
and under the flow proof the numbers are associated with "reasons".
As in Hallerberg, McMurray stresses that the law of modus ponens
(which he calls the "law of detachment") is made manifest through this
representation.
Basinger (1979) is a response to McMurray (1978).
Basinger reports that he has also used flow proofs, with a few key
superficial differences in notation. Interestingly, Basinger writes
"The flow proof format does seem to show graphically the 'flow of
logic' in complicated proofs. But overemphasis of this proof format
may be just as bad as over-emphasis on the traditional formats... It
may be better to use several proof formats, with near-equal emphasis
on each of them... And certainly the paragraph proof should not be
left out."
My final paper in this section is Brandell (1994). Despite its title ("Helping
students write paragraph proofs in
geometry") the paper has much more to say about flow proofs than about
paragraph proofs. In fact, Brandell's approach to teaching paragraph
proofs seems to be: (1) First, make a flow proof. (2) Then, turn
the flow proof into sentences and paragraphs. This approach seems
amazingly backwards to me. The whole point of paragraph proof is that
it's less rigorously formal, more like natural language. (Isn't it?)
To teach paragraph proof as just a highly-condensed form of flow proof
is just weird. Brandell's flow proofs have statements in boxes,
linked by arrows, with the reasons labelling the arrows.
Interestingly, he suggests as a learning tool that unnecessary
statements could be included in the flow diagram; when the paragraph
is finally written, those extraneous statements are jettisoned.
| https://matheducators.stackexchange.com/questions/16989 |
matheducators | Is induction or recursion easier to understand? | This is not really a new question, more a revisiting of @vonbrand's "Any suggestions on how to approach recursion and induction?" In an introductory programming class this past year, I asked the students to create a Mondrian-like image
via recursion.
Here is a typical submission:
These 1st-yr college students had little difficulty understanding
the recursion necessary to produce such images. Most of them had
little beyond US high-school mathematics—maybe calculus, no discrete math, no proofs.
And yet at the same time I taught more advanced students induction in the
theory of computation, and it was a mental hurdle for most of them.
Despite the informative answers to "Why are induction proofs so challenging for students?," I am still
uncertain. The Mondrian experience has made me wonder if it might not be
better pedagogically to introduce recursion first, nail that down thoroughly, and then teach
induction—the apparently more difficult concept—by connecting to
and building upon their
understanding of recursion. This may work even for students who have no programming experience, and are taught recursion "theoretically."
| VQAonline_00043888.png | One thing that you have to keep in mind here, is that you don't need to understand recursion to implement it. There is a big difference between "we were taught to do it like that, I implement it and it works" and really understanding the concepts and why it works as it does. With induction, on the other hand, you are supposed to write down a complete, formal proof, so you need at least better understanding of the concepts, if possible you should understand completely why it works.
Regarding your question if you should teach recursion or induction first, I would suggest this order:
Teach recursion and let the students program recursive functions.
After the students saw that it worked, focus on the theoretical concepts. For example give them a short recursive program and ask them to prove what it computes on a given input. Or go back to the problems programmed before and ask the students to prove that they really do what they are supposed to.
Show the students that for such proofs, it is easier to build them up from the bottom, i.e. not showing "on input $n$, we do this and that and use the function on $n-1$. Here, on input $n-1$, we do..." but rather starting with $n=1$.
Let them train induction and recursion parallel. For example assume that the students should show
$$\sum_{i=1}^n i = \frac{n(n+1)}{2}.$$
Let them write a recursive program, computing the left hand side (that should be a rather easy program...), then apply the methods learned above to show that this program actually computes the right hand side.
Gradually drop the programing tasks and focus more on the proofs.
In this way, the students don't just get induction as a strange, abstract concept, they have a practical component in learning it. They can learn that a proof is not something strange, it's just a formalized way to show something (in this case: "my program does what I claim it does"), show them that this formalism is not something to fear but is rather making it easier to show the correctness of their recursive programs and statements. In this way, you might actually be able to get them to understand that a formal proof is something good; this knowledge will be useful far beyond your course on induction.
Disclaimer: I am assuming an optimal class. In practice, some of these things might not work so well due to time limits or unmotivated students.
| https://matheducators.stackexchange.com/questions/12421 |
matheducators | Explanation for cutting a Möbius strip at one-third its width | Can anyone offer a concise, convincing explanation for why cutting
a Möbius strip along a line, not midway but rather one-third of the width of
the strip, and eventually joining back to itself, produces two linked, twisted
loops, one long, one short:
(Image from this web site.)
I am not seeking a proof, but rather an explanation that could convince
essentially anyone paying sufficient attention.
Especially the lack of symmetry in the result can be surprising.
Consider it a teaching challenge. :-)
| VQAonline_00043875.png | The middle third is obtained by trimming the edges off the original möbius loop. It is therefore simply a thinner möbius loop (the short loop).
The outside thirds of the möbius loop are obtained by cutting the loop in half and trimming 1/3 off the edge that was not originally the outside edge. It is the same as cutting the strip in half: as the outside edges are linked by a twist, the edge is a single loop twice as long as the original.
Imagining that a wire runs along the centre of the original möbius loop, one can follow the path of the outside edge as you trace along the wire. The edge slowly twists around the inside loop, so that after following the wire for 2 rotations, the edge has made a complete loop around the centre of the Möbius strip, going through the middle of the wire loop. As the wire becomes the small Möbius strip, and edge becomes the long Möbius strip, the long strip loops itself once around the small strip.
| https://matheducators.stackexchange.com/questions/7392 |
mathoverflow.net | Extending a map from $S^n\to M^n$ to a nice map from $B^{n+1}\to M^n$ | Let $S^n$ and $B^{n+1}$ be the unit sphere and unit ball in $\mathbb{R}^{n+1}$, and let $M^n$ be a contractible space of dimension $n$.
If necessary, assume that $M^n$ is a contractible simplicial $n$-complex.
Let $\sigma\colon S^n\to M^n$ be a continuous map.
Question
Does there exist a continuous map $\beta\colon B^{n+1}\to M^n$ such that for any $b\in B^{n+1}$, the point $b\in\mathbb{R}^{n+1}$ lies in the convex hull of the preimage $\sigma^{-1}(\beta(b))$?
Edit
The following stronger statement is false already if $n=1$.
There exists a continuous map $\beta\colon B^{n+1}\to M^n$ and an involution $f$ on $S^n$ with $\sigma=\sigma\circ f$, such that for any $b\in B^{n+1}$ there exists some $x\in S^n$ such that $\sigma(x)=\beta(b)$, and $b$ lies on the line segment between $x$ and $f(x)$ in $\mathbb{R}^{n+1}$.
The figure below illustrates a counter example to this stronger claim.
$Y$ is a star graph with three edges, and $\sigma$ is indicated by the dashed lines. None of the points interior to the white triangle lie between any pair of points that map to the same point on $Y$.
| VQAonline_00044467.png | The answer is no, essentially since higher homotopy groups of spheres are nontrivial.
For example, in the $n=3$ case let $M=B^3$ and let $\sigma\colon S^3 \to M$ be the Hopf map from $S^3$ to the boundary sphere $\partial M$ of $M$. Viewing $S^3$ as the unit sphere in $\mathbb{C}^2$, the group $U(1)$ of unit complex numbers acts on $S^3$ by scalar multiplication, and the preimage of each point in $\partial M$ is a great circle in $S^3$ which is an orbit under the action of $U(1)$.
Now suppose $\beta\colon B^4\to M$ is any map satisfying the given conditions. Note that $\sigma^{-1}(\beta(b))$ will be empty if $\beta(b)\notin \partial M$, so it must be the case that $\beta(b)\in \partial M$ for all $b\in B^4$, i.e. $\beta$ maps $B^4$ to $S^2=\partial M$. Note that each $\sigma^{-1}(\beta(b))$ is one of the circles described above, and the associated convex hull is a disk through the origin.
Now, if $b$ is any point on the sphere $S^3\subset B^4$, then $b$ lies in the convex hull of $\sigma^{-1}(\beta(b))$ if and only if $b$ lies on the circle $\sigma^{-1}(\beta(b))$, which occurs if and only if $\beta(b)=\sigma(b)$. Thus $\beta$ restricts to $\sigma$ on the boundary sphere $S^3$. But this is impossible since $\beta$ maps $B^4$ into the $2$-sphere $\partial M$ and the Hopf map is not nullhomotopic.
| https://mathoverflow.net.stackexchange.com/questions/344039 |
mathoverflow.net | Is it a new method to construction of a conic, how can prove? | There are some methods to construct a conic, example: Based on Pascal theorem, Steiner construction, .....I propose a method to construct a conic as follows:
Let $L_1, L_2$ be two parallel lines, let $A, B, C, D$ be four points in the plane. Let $E$ be a point lie on the line $L_1$, $F$ be the point lie on line $L_2$ such that $EF \parallel AB$. Let circle $(E, ED)$ meets the circle $(F, FC)$ at two points $H$, $G$.
My question: I am looking for a proof that locus of $H, G$ is a conic section when $E$ be moved on line $L_1$.
See also:
A chain of six circles associated with a conic
| VQAonline_00044408.png | Without loss of generality, let $L_1$ be the x-axis and $t$ be a parameter. Denote $C,D,E,F$ by $$C(x_1,y_1),D(x_2,y_2),E(t,0),F(t+a,b)$$ such that the vector $<a,b>$ is in the same direction as $\overrightarrow{AB}$ and $x_1,y_1,x_2,y_2,a,b$ are constants. Then the locus of $H$ (or $G$) satisfies $$\frac{PE}{ED}=\frac{PF}{FC}=1,$$ where $P(x,y)$ represents $H$ (or $G$). In terms of equations, one has $$(x-t)^2+y^2=(x_2-t)^2+y_2^2\qquad (1)$$ and $$(x-t-a)^2+(y-b)^2=(x_1-t-a)^2+(y_1-b)^2\qquad (2)$$ Then from (1), one gets $$t=\frac{x^2+y^2-x_2^2-y_2^2}{2(x-x_2)}\qquad (3)$$ Subtracting (2) from (1) gives $$(2x-2t-a)(a)+(2y-b)(b)=(x_1+x_2-2t-a)(x_2-x_1+a)+(y_2+y_1-b)(y_2-y_1+b)\quad (4)$$ Now substituting (3) into (4) and clearing denominator, one gets a quadratic equation in $x$ and $y$, so it gives an equation for a conic.
| https://mathoverflow.net.stackexchange.com/questions/316857 |
mathoverflow.net | Shape whose translated and scaled copies are closed under intersection | The translated and scaled copies of an equilateral triangle with fixed orientation are closed under intersection - the intersection is again an equilateral triangle with the same orientation.
What other convex shapes in 2D have this property?
| VQAonline_00044253.png | I think triangles (degenerated ones included) are the only such convex shapes. The idea is: If $C$ is such a convex shape, let $p_i\in\partial C$ for $i=1,2,3$ be three smooth points. One can obtain an approximate triangle as an intersection of three large copies $C$, say $m(C-p_i)+p_i$ for large $m$. Since these intersections are similar to $C$, and converge to a triangle as $m\to\infty$, $C$ itself is a triangle.
| https://mathoverflow.net.stackexchange.com/questions/232791 |
mathoverflow.net | Car movement - differential geometry interpretation. | I've posted this on Math Stack Exchange and I didn't get any answer in a couple of days, so I'll try and post it here too.
The problem presented below is from my differential geometry course. The initial reference is Nelson, Tensor Analysis 1967. The car is modelled as follows:
Denote by $C(x,y)$ the center of the back wheel line, $\theta$ the angle of the direction of the car with the horizontal direction, $\phi$ the angle made by the front wheels with the direction of the car and $L$ the length of the car.
The possible movements of the car are denoted as follows:
steering: $S=\displaystyle\frac{\partial}{\partial \phi}$;
drive: $D=\displaystyle\cos \theta \frac{\partial}{\partial x}+\sin\theta \frac{\partial}{\partial y}+\frac{\tan \phi}{L}\frac{\partial}{\partial \theta}$;
rotation: $R=[S,D]=\displaystyle\frac{1}{L\cos^2 \phi}\frac{\partial }{\partial \theta}$;
translation: $T=[R,D]=\displaystyle\frac{\cos \theta}{L\cos^2 \phi}\frac{\partial}{\partial y}-\frac{\sin\theta}{L\cos^2\phi}\frac{\partial}{\partial x}$
Where $[X,Y]=XY-YX$ (I can't remember the English word now). All these transformations seem very logical. My question is:
How can we justify the mathematical interpretation made above, especially the part with the rotations and translations?
The interpretations are quite interesting:
from the expression of $D$, when the car is shorter, you can change the orientation of the car very easily, but when it is longer, like a truck, you it is not that easy ( see the term with $\frac{\partial}{\partial \theta}$)
the rotation is faster for smaller cars, and for greater steering angle
translation is easier for smaller cars.
| VQAonline_00043975.png | I'm not sure what you mean by "justify", but one way of looking at this is through the Chow theorem.
You've calculated that $R = [S, D]$. This is a statement about vector fields, which are infinitesimal flows. So if you steer by a small amount, followed by driving over a small amount, followed by turning the wheel back into the original position and driving backward, you end up performing a small rotation. You can interpret $T = [R, D]$ in the same way: if you want to parallel park the car (performing a translation), you turn ($R$), drive forward ($D$), turn back ($-R$) and drive backward ($-D$).
A normal car has four degrees of freedom, the angles $\theta$ and $\phi$ on your figure and the coordinates $x, y$ of the center of mass. However, you as the driver can only be drive and steer the car, you can't just translate the car or rotate it around its axis. So you can only control $S$ and $D$. We say that this system is underactuated, meaning that you have less control inputs than there are degrees of freedom in the system.
However, differential geometry comes to the rescue: if you consider the distribution spanned by $S$ and $D$, you'll find that it is totally nonholonomic, meaning that you can create any possible motion (any linear combination of $R$, $D$, $T$ and $S$) by a linear combination of $S$ and $D$ and their (iterated) commutators. Physically, this means that you can perform any motion with the car by driving and steering, although you will sometimes have to execute a nontrivial motion in $S$ and $D$ (look up "control by sinusoids")
If now you have a metric on the distribution spanned by $S$ and $D$ (telling you, for instance, how much it costs to steer resp. drive the car) you have an instance of what is called a sub-Riemannian geometry. (I hope this will entice Richard Montgomery to comment on this question).
I can polish/extend this answer a great deal, so please feel free to ask follow-up questions.
| https://mathoverflow.net.stackexchange.com/questions/66578 |
mathoverflow.net | Highest weight representations of Kac—Moody algebras: what is inside the weight spaces? | Let $V(\lambda)$ be the unique irreducible representation of a Kac—Moody algebra $\mathfrak{g}$ with the highest weight $\lambda$. If $\mathfrak{g}$ is not of finite type, then even for $\lambda$ one of the fundamental weights the weights of $V(\lambda)$ usually have multiplicities $\geqslant2$.
Is there a nice way to pick a basis in each of the weight spaces $V(\lambda)_\mu$?
Here "nice" means that there is an explicit description of the action of the standard generators of $\mathfrak{g}$, so one could actually write (infinite) matrices for the Lie algebra elements. I have checked some sources including Lie Algebras of Finite and Affine Type by R. Carter and Affine Lie Algebras, Weight Multiplicities and Branching Rules by Kass, Moody, Patera and Slansky, but none contains such details even for the smallest cases like $\tilde{A}_1$. Here is a picture from the second:
As you can see, this diagram gives no hint to how exactly the generators act inside the weight spaces. I guess this can be reconstructed from the desription of $V(\lambda)$ as a quotient of the Verma module, but this seems quite computationaly extensive, so I was wondering whether someone has already done it in some cases (say, for the untwisted affine KM algebras for some particular choice of $\lambda$)?
| VQAonline_00044335.png | The key word you're looking for is Littelmann path model, which gives a nice geometric description for the basis of a weight space of a highest-weight representation of a symmetrisable Kac-Moody algebra (see e.g. http://people.bath.ac.uk/lpah20/GeomSemNP.pdf for an introduction), and gives a fairly explicit algebraic description of this basis (see http://www.mi.uni-koeln.de/~littelma/montreal.pdf Theorem 5.2), from which it is possible to calculate the action of the standard generators.
While I don't know of a precise reference where this is written up, it is a good exercise to calculate these things for, say, $\tilde A_1$ and $\tilde A_2$.
| https://mathoverflow.net.stackexchange.com/questions/279170 |
mathoverflow.net | Random Diophantine polynomials: Percent solvable? | Suppose one generates a random polynomial
of degree $d$ with integer coefficients
uniformly distributed within $[-c_\max,c_\max]$.
For example, for
$d=8$, $|c_\max|=100$, here is one random polynomial:
$$
-46 x^8-19 x^7+14 x^6-75
x^5+94 x^4+18 x^3-48 x^2+29
x-61=0
\;.
$$
Q. What is the probability that such
a random $(d,c_\max)$-polynomial has at least one
integer solution?
Here is a bit of data, based on $10^5$ polynomials for each $d=1,\ldots,10$
with $|c_\max|=100$:
I.e., For $d=1$, about $5.5$% have integer solutions,
while for $d=10$, about $0.8$% have integer solutions.
The above displayed degree-$8$ example has the solution $x=-1$,
and in addition these $7$ non-integer roots:
$$
-1.54767,\\ -0.0337862 \pm 0.794431 i,\\
0.196632 \pm 1.19591 i,\\
0.904467 \pm 0.323333 i
\;.
$$
If the constant coefficient is $0$, then of course $x=0$ is a solution.
So $\frac{1}{2 c_\max+1}$ is a lower bound,
in the above chart, $\frac{1}{201} \approx 0.5$%.
| VQAonline_00044175.png | The case of degree $1$ has been handled by quid. This turns out to be an exceptional case, and for all degrees $d\ge 2$ one can show that there is a constant $K(d)$ such that the number of degree $d$ polynomials with coefficient bounded by $C$ and having an integer root is
$$
\sim K(d) (2C+1)^d.
$$
Moreover, for large $d$, the constant $K(d)$ is approximately equal to
$$
1+ 2 \frac{\sqrt{6}}{\sqrt{\pi d}}.
$$
In this approximation, the term $1$ gives the contribution of polynomials having $0$ as a root, and the second term $\sqrt{6/\pi d}$ accounts for polynomials having a root at $1$ (and another similar contribution from those having a root at $-1$). For large $d$, the effect of having roots at integers larger than $1$ in size is substantially smaller.
For $d=10$ and $C=100$ this approximation is about $0.93\%$ which is a little higher than your data, but for $d=9$ it is much closer (the approximation being $0.96\%$). Perhaps the Monte-Carlo simulations haven't fully stabilized?
Clearly the number of polynomials having a root at $0$ is $(2C+1)^d$. Now suppose that $k\ge 1$ is a positive integer, and consider polynomials having a root at $k$ (naturally the same holds for $-k$). Write $f(x)=a_dx^d+\ldots+a_0 = (x-k) (b_{d-1}x^{d-1} + \ldots +b_0)$. Note that $kb_0$ must lie in $[-C,C]$ giving us about $(2C+1)/k$ choices for $b_0$. Next if $b_0$ is fixed, then $-kb_1+b_0$ must lie in $[-C,C]$ giving us about $(2C+1)/k$ choices for $b_1$. Proceeding in this manner, we get at most $(2C+1)/k$ choices for each $b_j$, with the additional constraint that the final $b_{d-1}$ must also be constrained to be in $[-C,C]$. It follows that there are at most $(2C+1)^d/k^d$ possible polynomials having a root at $k$. This upper bound summed over $k$ converges for $d\ge 2$ (but not for $d=1$), and shows that the proportion of polynomials having a large integer root is very small. Thus at any rate the number of polynomials having an integer root is at most $(1+2\zeta(d)) (2C+1)^d$, and by similar reasoning we may see that the number of polynomials having two integer roots is at most $O((2C+1)^{d-1+\epsilon})$.
By our work above, the number of polynomials having an integer root is essentially the sum of those polynomials having a root at $k$ over integers $|k|\le K$ for some slowly growing $K$. Now for a given $k\ge 1$, for the polynomial to have a root at $k$ means that given $a_1$, $\ldots$, $a_d$ (all chosen in $[-C,C]$) we must have the sum $a_1k+a_2k^2+\ldots +a_d k^d$ lying in $[-C,C]$ (which then uniquely determines $a_0$). But now we may write $a_j=Cx_j$, and then the $x_j$ behave like independent random variables chosen uniformly from $[-1,1]$ and then we are asking for the probability that $x_1 k+x_2k^2+\ldots +x_d k^d$ also lies in $[-1,1]$. Clearly this probability must be some constant $K(d,k)$ (which by our earlier work is at most $1/k^d$), and therefore our claimed asymptotic holds with
$$
K(d) = 1+ 2\sum_{k=1}^{\infty} K(d,k).
$$
Lastly we come to the approximation for $K(d)$ for large $d$. Note that the contribution of terms $k\ge 2$ is $O(2^{-d})$ is extremely small. It remains to understand $K(d,1)$ -- the probability that the sum of $d$ independent random variables chosen uniformly from $[-1,1]$ also lies in $[-1,1]$. For large $d$, the sum of $d$ independent random variables is approximately normal with mean $0$, and variance $d/3$. From this our approximation follows. By using Parseval, one can also see that
$$
K(d,1) = \int_{-\infty}^{\infty} \Big(\frac{\sin (\pi x)}{\pi x}\Big)^{d+1} dx,
$$
from which we can calculate, for example, that $K(10,1)=0.4109\ldots$ which is pretty close to the approximation $0.437\ldots$.
| https://mathoverflow.net.stackexchange.com/questions/203981 |
mathoverflow.net | Special version of $\Delta$-system Lemma for singular cardinals | In his article "Remarks on cardinal invariants in topology" (you can get the paper here: Where can I find the following S. Shelah's paper?), Saharon Shelah states the following claim:
(A) is simply the classic version of the $\Delta$-system Lemma. I have been trying to prove (B) and have not succeeded; also, I've looked in the usual set theory books to see if it's written somewhere, but I haven't had any luck here either. I can prove 2) and 3) by assuming that the cardinals $\lambda_\alpha$ are regular and uncountable (which is fairly reasonable since $\lambda>cf(\lambda)>\omega$), but I have failed to argue that 1) is also possible.
In this case, any help is welcome: an argument for 1) or any reference would be great.
| VQAonline_00044696.png | I'll assume that you already have Clauses (B)(2)-(3). We need to thin down once more to get (1). WLOG, we can assume each $\lambda_{\alpha}$ is a successor cardinal strictly above $\max(\mu^+, \sup_{\beta < \alpha} \lambda_{\beta})$. Put $\mu = cf(\lambda) > \aleph_0$. First apply (A) to the family $\{A_{\alpha}: \alpha < \mu\}$ to get $A$ and $X \in [\mu]^{\mu}$ such that for every $\alpha \neq \beta$ in $X$, $A_{\alpha} \cap A_{\beta} = A$. WLOG, $X = \mu$.
Fix $\alpha < \mu$. Put $W_{\alpha} = \bigcup \{A_{\beta}: \beta < \mu\} \cup \bigcup \{A_{\beta, \gamma}: \beta < \alpha, \gamma < \lambda_{\beta}\}$. Then $|W_{\alpha}| < \lambda_{\alpha}$. Observe that for each $\alpha < \mu$, $\{A_{\alpha, \beta} \setminus A_{\alpha}: \beta < \lambda_{\alpha}\}$ is a family of pairwise disjoint sets. So fewer than $\lambda_{\alpha}$ of these intersect $W_{\alpha}$. Throw these away and check that (1) holds.
Edit: I have added the union of the $A_{\alpha}$'s to $W_{\alpha}$. (1) should hold now.
| https://mathoverflow.net.stackexchange.com/questions/419304 |
mechanics | Help setting up Bi-Xenon lights with h4 wiring | I am doing one of the oh-so controversial HID retrofits - I got myself I nice pair of projectors and bulbs (I am using cheep ballasts until I have the money for some nice OEM ones). The projectors I bought have solenoids to open up the high beam. I would like to use the lights with my Jeep's current light switch on the steering column. My halogen lights are h4 and the low beams are not on when the high beams are. If I want to wire a bi-xenon solenoid I will need to find some way of getting the light to stay on and have the solenoid open when the high beam is on.
I have an idea that will work, but it involves a relay which means the lights will momentarily be off when I switch from low to high beam (as the relay changes from closed to open). Here is my drawing, will this be good enough, or will I need to make sure the voltage does not get cutoff when opening the solenoids?
| VQAonline_00044786.png | Cycling HID lamps the way you propose will reduce the lifespan of the bulbs, they aren't made to be turned back on shortly after being turned off.
Also, I'm having trouble making sense of your schematic - the oval labeled "LIGHTS" - is that supposed to represent the ballast? I don't know that I'd power that directly from your H4, seems like I'd want a new fused run from the battery through a relay powering the ballasts.
I am not affiliated with them, but http://www.theretrofitsource.com/ sells kits that comes with a ballast controller module that can be interfaced directly to your factory H4 connector. I have one in my Subaru. It takes care of the things you appear to be overlooking - like keeping the ballast and bulbs powered while switching from low to high beams (on HID's all that should happen is the solenoid to move the shield should be powered), or implementing a time-delay so that the ballast does not fire, die, and fire again in rapid succession while turning the key from off through accessory to run, temporarily to start, and back to run.
| https://mechanics.stackexchange.com/questions/4979 |
mechanics | 1990 Suburban exhaust system replacement | I recently purchased a 1990 Suburban - and it has a Chevy 350. The exhaust merges and exits on the left side.
I am unable to locate a replacement which is a direct fit. Also, almost all y-pipes online merge on the right.
Anyone has any experience with this - or knows a cross reference with another model?
Update - based on accepted answer - found the rest of the part numbers on the WALKER website
| VQAonline_00045425.png | If you looking under the "V" series Suburban (ie: V1500), the WALKER 40317 Y Pipe drops on the left side. It is probably what you'd need for a 4x4. If memory serves me correctly, the front drive shaft of the transfer case drops on the right side, so they had to route it down the left side. Usually, GM used the "K" designation for 4x4's, so the V is tossing me around a little bit. I would suggest you ensure this is the part you need for your truck before purchase.
On how to find other parts you might need ... you just have to look. Online searches are probably the best. Now that you might have the a better designation for your Suburban, you might be able to find it easier. Secondarily, you should consider just taking it to a shop and having them build one for you or find the parts for you. It'd be done right and you wouldn't have to worry about the outcome.
If you're still heck-bent on doing it yourself, a resource I use is rockauto.com (no affiliation). They have a very extensive parts list, which means you can pick and choose. If you find what you need there, you can take the part numbers and shop it wherever you need to to find the parts.
| https://mechanics.stackexchange.com/questions/87740 |
mechanics | Trim repair on a 2003 Ford Focus | The door trim on the drivers side door of my 2003 Ford Focus has come loose at the front:
I'm guessing that a proper repair would require the interior door panel to be removed, and this seems like a lot of work for such an old car. I would be happy with a "bodge job" repair if that could be guaranteed to last the few years the car has left to live. Can anyone suggest the best way to do this?
I was thinking that double sided tape would do but the usual domestic double sided tape is too thin and I think it would come loose very quickly. Some sort of tape or other adhesive that is thicker and with more "give" would be needed. Can anyone suggest something like this that is easily obtainable?
| VQAonline_00044888.png | Get something like 3M Super Weatherstrip Adhesive or Permatex Super Weatherstrip Adhesive. Follow the directions on the product. You'll probably want to use some painter's tape (the blue stuff) to keep the trim in place while it cures. If it's a leading edge (appears to be so), make sure you have the tape covering the point of the trim so the wind won't try to screw up your job (if you are planning on using the vehicle while it is curing).
You'll want to leave the tape in place for probably 24 hours at least to ensure good bonding of the adhesive. The reason I suggest to use the blue tape is that it shouldn't leave a residue behind when you pull it off. Whatever you use will look ugly in the mean time, but have no fear, it's the end result you want.
Oh, one last thing ... ensure you clean the area where you want to apply the adhesive before you apply or your fix will not last. Pull up the trim the best you can and get all of the old glue off. It doesn't have to be perfect, but you should do the best you can on it. Make sure you have plenty of painted area to put the adhesive on. (EDIT NOTE: Leave the small piece of plastic on the door if it is firmly affixed as it would be a good point for adhesion between the trim and the door.)
| https://mechanics.stackexchange.com/questions/18693 |
mechanics | 06 Solstice LE5 DTCs | My love-to-hate-it relationship with the Solstice continues.
I was having some issues with apparently-random warnings (ABS light, weird DTC, gas cap warning when the gas cap was not loose). The issues temporarily (for a few days) disappeared. Since an autocross last Sunday, I hadn't seen any weird behavior. (However, even though the ABS light was not on at the autocross, the brakes locked up a few times.)
Today, my CEL came back on. I hooked up the scanner:
0x7E8: P0171 - System Too Lean (Bank 1) (Pending, Current, History)
0x7E8: P0420 - Catalyst System Efficiency Below Threshold (Bank 1) (Pending, Current)
0x7E8: P0455 - Evaporative Emission System Leak Detected (gross leak/no flow) (Pending, Current, History)
0x7E8: P0507 - Idle Air Control System RPM Higher Than Expected (Current)
0x7E8: P0563 - System Voltage High (Pending, Current)
0x7E8: P0621 - Generator Lamp Terminal Circuit
I suspect a bad ECU. Even the alternator warning (P0563, P0621) appear to be harmless, since the battery is definitely getting charged. The car starts right up.
Oh, and I noticed yesterday that the tach doesn't really work for about the first 10 seconds after start. The needle just sort of bobs up and down about 5ish degrees.
Definitely some sort of electrical gremlin. :/ All the grounds I've checked have been fine, but there are a lot of them so it's possible I've missed one.
Update
I pulled the alternator yesterday, and saw this. Not sure how I missed this when I pulled it off of the old engine. It's worth noting that the previous motor threw a rod from the #1 cylinder. I think the rod grazed the alternator.
Looks like there's a short in the coil.
| VQAonline_00044972.png | Oh wow, there's definitely something funky going on with the electrical system.
With regards to the P0563 and P0621, have you tried getting a live reading of the voltage from your scan tool or a multimeter when the car is running?
My advice - get a decent automotive electrician on the case. Your run of the mill mechanic isn't the right person for the job
| https://mechanics.stackexchange.com/questions/27948 |
mechanics | How can I rectify Replacement filler cap? | Civic coupe vti 1999.
I have just received my replacement filler cap off eBay and it does fit!
However I noticed some white stuff around a bit the outer part of the rubber seal and thought it was dirt. Trying to remove it with some tissue the whole seal came off then I realised it’s actually underlying glue which wasn’t covered by the seal. The seal coming off so easily shows it was a poor manufacturing job I guess.
Anyway im tired of this filler cap issue. Right now to remove the seal u really need to poke with your nails so I could just at least temporarily use car by manually put seal into place and every time I remove the cap just ensure the rubber is still in place as it’s not moving easily even without glue.
I could also dab a little bit of super glue(?) Where existing glue is.
What do you recommenced?If the existing or super glue sticks out a little either side of the rubber will that matter as the original glue did will that matter in which case I’ll need to clean and glue until I get it right?
I imagine I could send it back but would rather avoid it. They may also argue I shouldn’t have picked at the visible glue but of course I would how do I know of it is dirt that just needed picking out or glue. Plus the glue job was obviously poor to begin with.
Thanks
| VQAonline_00045408.png | Usually "super glue" type adhesives don't stick well to materials like that gasket is made of. It should stay put in the groove for it without any glue. If not, then it's not the right size or you stretched it out messing with it.
Go to a local hardware or auto parts store and see if you can find a suitable o-ring that will fit properly.
If you have to, just put the o-ring on and tighten the cap as intended. Over time the o-ring will tend to stick to either the cap or the valve cover.
| https://mechanics.stackexchange.com/questions/85534 |
mechanics | Honda Odyssey alignment results in camber out of spec? Normal? | I splurged on an alignment after getting new tires for my 2018 Odyssey. It was done by the my Honda dealership that has done all service on the vehicle, except the recently installed Costco tires.
Looking at the report, it looks like Front Right Toe was out of spec before alignment, and in spec after. But then Rear Right Camber went from in spec to out of spec? (1.2 deg vs -1.0 deg to 0.0 deg?)
Is this normal for an alignment result? I see the Toe on the same tire was almost out of spec before and is now in the middle of desired range. I was just surprised the alignment resulted in something going from being in spec to out of spec. Should I be concerned at all? Here's the alignment report:
| VQAonline_00045436.png | Most vehicles do not have a rear alignment adjustment. What you have is what you get. It is not uncommon for the rear alignment to go a little out of spec during an alignment procedure. Even so, looking at the report, the cross camber is within spec and the total toe became even better. You shouldn't have an issue with this alignment. The rear tires are pulled, which as the rear alignment isn't completely wonky, won't make much of a difference. If the toe was out of whack, you'd probably see a difference in fuel mileage as well as tracking issues.
The reason you might be seeing a little more camber that is there might be a little wear on the bushings which support the rear. Again, nothing to worry about.
As far as "splurging" for an alignment, it is my opinion you should ALWAYS get an alignment with fresh tires. You just laid down a fairly large chunk of change on those black donuts. Getting an alignment will help ensure they'll last longer and stay healthier throughout their lifetime. IOW: It is money well spent.
| https://mechanics.stackexchange.com/questions/88917 |
mechanics | Why do diesel fuel lines have to be bled? | Background
I've had a couple of situations with diesels. One in particular where I swapped a Ford F350 Powerstroke 7.8 transmission. When I was done. The truck wouldn't start. It was a painful troubleshooting situation for me because of my diesel ignorance. It turned out that the fuel lines needed to be bled.
It made no real sense to me but it was the solution. The fact that air was in the system at all didn't make sense to me.
My Question
Why do diesel fuel lines have to be bled?
Here's a generic diesel fuel system image
| VQAonline_00044932.png | Not all Diesels are the same.
My former car, a 1994 VW Passat 1.9 TDI had only one fuel pump in the engine bay. This pump was responsible for several things:
bring fuel from the fuel tank
raise the pressure to the injection pressure (approximately 600 bar)
distribute pressured fuel to each injector in the correct order
There was no electric pump to "push", it was just the main pump which had to "suck" fuel from the tank and sucking is worse (in terms of efficiency) than pushing (no pun intended). Therefore whenever I had to change the fuel filter I had to carefully fill it up with fuel before installing it.
Newer Diesels (be it common-rail or unit-injector system) usually have at least one electric fuel pump (my current common-rail TDI has two electric pumps and a mechanical high pressure pump) which aid this task a lot more.
But still they don't fix things completely. They still need to be activated using a diagnostic tool (for VW, TDIs there's a VCDS software pack along with an OBD-2 interface which can be used to prime the whole circuit).
Either way, even if the pump is activated shortly using the ignition, this won't be enough to fill an empty fuel filter, or even push out a lot of air in the circuit. You will need to activate them using the diagnostic tool, or, some might connect them directly to a 12 V battery (I don't recommend).
The reasons for this necessity stand in a few things:
Diesel fuel is a bit "thicker" than gasoline
The fuel filter is larger and having it emptied requires more effort to refill
The high pressure pump is usually lubricated with the Diesel fuel itself and it is much more sensitive to lack of lubrication (i.e. running dry)
| https://mechanics.stackexchange.com/questions/24844 |
money | As a young kid should I spend my time learning value investing or should I just chuck all my money into IVW/VOO | I have a genuine question, I am a noob at stocks. from what I have been reading value investors get higher returns than growth investors but then how come the growth etf IVW gets much higher returns than the value index fund VTV. I've looked at other value ETF's but they sucked even more. Is value investing worth the hype or are these ETF's just bad. If professionals can't do good value investing what chance do we have? Is this a skill worth spending my time in?
| VQAonline_00045799.png | "Value investing" is essentially looking for stocks that are cheaper than they "should be" by some measure. That ETF tracks an index of large cap value stocks,
which may skew the results somewhat, since there may be more smaller "value" stocks that perform better than larger ones.
Also note that the two were largely in sync until mid-2018 and mid-2020, where large tech stocks (which are more "growth" than value) dominated from COVID lockdowns (there are many other factors, but that's a significant one).
And note that this year, VTV has outperformed IVW - the value fund is only down 5% while the growth fund is down 18%. So it may be an anomaly that growth has outperformed over the period you're looking at.
If you're a "noob at stocks" then it's best to stick with very broad index funds until you understand more the risks associated with different styles of funds, and slowly move to individual stocks. There's no way to ensure that you pick the "best fund" or even the best strategy going forward.
As a young kid, you have plenty of time to make mistakes and learn from them. Don't try to "get rich young" (you might get lucky and do that, but more than likely you'll lose more than you win). Play the long game, save as much as you can, watch it grow, and as you grow you can set aside portions of your portfolio (say 10%) to experiment with individual stocks or other strategies.
| https://money.stackexchange.com/questions/152286 |
money | I'm trying to setup my 401k with 5% match from my employer | I am newbie and I need help setting up my 401k. Basically, I just want to avail my employer's maximum match, and 5% is the minimum needed to reach it. But I'm not sure if I am doing it right. Here's the screenshot of my current setting:
| VQAonline_00045585.png | Based on the numbers on the screen, it looks like your income is in the range of $9,325 to $37,950 per year. This puts you in the 15% tax bracket. I personally would recommend you move the slider all the way to the right and put your entire contribution into the 401K Roth (so you'll have 0% pre tax and 100% post tax.) The reasoning here is that you'll pay the 15% tax now which is on the low side, but you'll never pay tax on the money's growth for the rest of your life, including when you take it out at retirement. If you do this your take home will be approximately $9 less per paycheck (or a little higher depending on your state income tax).
Note that the company match will go into a traditional 401K so you'll likely see two separate accounts on your 401K statements.
The choice to go with traditional vs roth 401k is complicated and there are many variables. As a rule of thumb, the lower your current tax rate, the more likely you should be to lean towards the roth. Some exceptions might be if you are close to retirement age and you don't have much saved for retirement, or if you live in a state with a high income tax rate and you don't think you'll still live there when you retire, or if you are living paycheck to paycheck and the slight difference in take home pay would make a difference to you.
| https://money.stackexchange.com/questions/83267 |
money | What is the strategy to gain profit from an option which has less volatility? | The following is the chart of Delta Airlines. The stock moved between the price of $52 and $62 for the last 6 months or so. Looking at this chart, someone who bought a PUT or CALL at the strike price $57 for $2 per option may not make much profit because the price has not moved much on either side.
Being less volatile is good, but what strategies can be used to make profit for such stocks that don't move much on either side?
| VQAonline_00045687.png | In your 6 month chart, Delta went from $56 to $63 to $56 to $60 to $52 to $57. That certainly presented a number of opportunities to double your option money or better if you had the magical ability to figure out when to be directionally long or when to be short as well as how to avoid being long or short during August/September when DAL range traded between $56 and $59. Good luck with that :->)
To answer your question, low risk neutral option strategies include calendar spreads, butterflies, iron condors, calendar straddles.
There are a number of other strategies that can be employed when you have a neutral outlook but they are by no means low risk: covered calls, covered puts, short calls, short puts, short strangles, short straddles.
In all cases, you're selling short term premium in the hope that price doesn't move against you and time decay works its magic.
| https://money.stackexchange.com/questions/117618 |
money | Why is the highest quintile the only quintile whose wealth exceeds its income? | Based on this study, the highest quintile of the population is the only group whose wealth is greater than its income. Why might this be?
Is it because they are more likely to inherit wealth from their parents?
Is it because they invest more money so they generate more wealth faster?
I am simply speculating without any proof, can anyone help?
| VQAonline_00045554.png | I think you came up with a worthy Masters/PhD research project, it is a great question.
This is in Australia so it is difficult for me to have complete perspective. However, I can speak about the US of A.
To your first point relatively few people inherit their wealth. According to a brief web search about 38% of billionaires, and 20% of millionaires inherited their wealth. The rest are self-made.
Again, in the US, income mobility is very common. Some act like high level earners are just born that way, but studies have shown that a great deal of income mobility exists. I personally know people that have grown up without indoor plumbing, and extremely poor but now earn in the top 5% of wage earners.
Quid's points are valid. For example a Starbucks, new I-Phone, and a brake job on your car are somewhat catastrophic if your income is 50K/year, hurts if your income is 100K, and an inconvenience if you make 250K/year. These situations are normal and happen regularly. The first person may have to take a pay day loan to pay for these items, the second credit card interest, the third probably has the money in the bank. All of this exaggerates the effect of an "emergency" on one's net worth.
To me there is also a chicken-and-egg effect in wealth building and income. How does one build wealth? By investing wisely, planning ahead, budgeting, delaying gratification, finding opportunities, etc... Now if you take those same skills to your workplace isn't it likely you will receive more responsibility, promotions and raises? I believe so. And this too exaggerates the effect on one's net worth. If investing helps you to earn more, then you will have more to invest.
To me one of the untold stories of this graph is not just investing, but first building a stable financial base. Having a sufficient emergency fund, having enough and the right kind of insurance, keeping loans to a minimum. Without doing those things first investments might need to be withdrawn, often at an inopportune time, for emergency purposes.
Thanks for asking this!
| https://money.stackexchange.com/questions/70246 |
money | What does it mean for the price of oil to be negative? |
The New York Times website currently has this graph, showing that the price of "West Texas Intermediate, May contract" is $-13.10. Does it literally mean that someone's offering $13.10 to take a barrel of oil off their hands, or is it a quirk of the financial market such as a trader trying desperately to make an upcoming event somebody else's problem?
| VQAonline_00045718.png | These are futures contracts that expire on 4/21, which means that if you hold a futures contract at the end of the trading day tomorrow (April 21st), then you are obligated to "purchase" 1,000 barrels (per contract) of oil for -$13 (effectively you get paid $13/barrel to take the oil).
But that also means that you will need the means to transport and store the oil. Which is why prices went negative - storage is full and there's no practical way for anyone to take the oil that's being produced. So speculators that were holding these futures contracts are pressured to sell them, otherwise they'll have to take ownership of the actual oil. But no one is looking to buy these contracts, so there is enormous downward pressure on price, which ultimately leads to negative prices. They are actually paying to get rid of these contracts.
| https://money.stackexchange.com/questions/124269 |
money | How can Volume be greater than Open Interest? |
Notice how at the strike price of 30 and 35 for Puts, you have volume at 22 and 7, but Open Interest at 0.
If volume is the number of trades made a day, and Open Interest is the number of contracts held by people, how on earth can Volume be greater than Open Interest? It doesn't make sense.
| VQAonline_00045583.png | Volume tells you how many trades occurred over the course of the day. Open interest is how many contracts are outstanding at that moment. So your question essentially asks how the open interest on an option can decrease---what can cause liquidation of an option? There are a few ways. These are the ones I could think of:
Open interest decreases when options are exercised. If this is not the settlement date, and if it's an American-style option, you may be looking at an early exercise situation.
Open interest can decrease via an offsetting trade. For example, if the option writer (creator) no longer wants to be on the hook for this option, they can basically purchase the option from the option holder and get out of their obligation. That is, if the option writer also owns the option, then the option disappears and is removed from open interest.
Options may disappear when the option writer violates their margin agreement and gets forced liquidation of their position.
My guess is that one of these situations (or something similar) occurred after some trades happened. My money is on #2.
| https://money.stackexchange.com/questions/81453 |
money | How AAPL is keeping the EPS close to Analysts expectations? | The below chart shows that AAPL from 2017 beat the analysts expectations. I assume that the AAPL Financials are not public for Analysts to analyze, neither AAPL CFO knows how the Analysts figure out an expectation. But both of their results are a few points apart. How the Analysts figure the EPS out and how AAPL achieve a few points above the Analysts expectations of EPS?
| VQAonline_00045691.png | Most companies beat earnings estimates most of the time. So Apple isn't terribly unusual in this regard.
Why do companies generally beat earnings?
Expectations management. Public companies regularly release guidance to analysts (both in terms of their own earnings target and in terms of qualitative and quantitative factors). As with any goal, a company's earnings target is generally something that they expect they will able to meet or exceed. If a company sees that analysts have set the target too high, they're likely to provide some sort of guidance (i.e. "ongoing trade issues are creating some supply chain issues and may reduce sales") that cause analysts to lower their targets. Then the company can beat the revised targets when they release earnings. Note that the company isn't lying, they're just being conservative in the guidance they provide. Regulators, for example, take a much harder look at a company that regularly misses guidance than one that regularly meets or exceeds their targets. If companies are excessively optimistic, it's usually because management is trying to keep the stock price up (so that management can dump shares at inflate prices) or so that they can borrow money from the bond market at lower rates (which potentially defrauds those buying the bonds).
Earnings management. Accounting standards exist so that companies have less flexibility to "massage" earnings and that two similarly situated companies account for similar transactions in the same way. In practice, though, companies still have some amount of flexibility about how and when to recognize certain charges or how to structure certain transactions. Generally, companies use that flexibility to help ensure they beat earnings targets most of the time. If they're going to have a bad quarter, they usually use that opportunity to recognize a bunch of charges so that they have one really bad quarter that sets them up for a bunch of good quarters later.
Analysts, like companies, are conservative about earnings. Some of that is a result of the information analysts can acquire-- an Apple analyst may be able to get figures from some of the factories that supply iPhone screens and use that to estimate iPhone production for the year. Generally, they're going to be conservative when they extrapolate a final number from those estimates, however, to account for things that they don't know (i.e. has the market share of the factories they have numbers for shrunk from last quarter). Some is the result of market incentives-- most investors are going to be a lot more upset at an analyst whose predictions are generally a few pennies a share high than low. And some is the result of analysts getting talked down by companies when the company isn't sure they can meet the expectations.
| https://money.stackexchange.com/questions/118055 |
movies | Is "The Architect" in The Matrix actually a program? | We have confirmation that The Oracle is a program (in The Matrix Reloaded). So it's clear that some programs are allowed to interact with humans.
But I wonder whether The Architect is also a program? All the available evidence suggests so but is there any hard confirmation?
This also raises a related question: Are machines programming other machines as well as an artificial world for humans? And if so, then have machines reached a level of consciousness at least equivalent to (if not beyond) that of humans? And if so, are they in fact a totally independent life form? Could this be the actual future of the human race given the potential of AI?
Edit: Also, who programmed the program who programmed the program and so on? Did this ability to program themselves spontaneously emerge or did humans somehow make this happen? Is there any evidence to support a theory on this?
| VQAonline_00046406.png | Yes, The Architect Is A Program
From its article on the Matrix Wikia:
The Architect is a highly specialized, humorless program of the Machine world as well as the creator of the Matrix. As the chief administrator of the system, he is possibly a collective manifestation, or at the very least a virtual representation of the entire Machine mainframe.
While his history is unclear, he appears to have been created by the AI behind the machine systems, and given the task of creating the Matrix - the human-like virtual world where the coppertops believe they live.
As for your second question (which should really be a separate question), humans were the ones who created the AI. It was this AI, who learned exponentially, that created the machines, waged war on, and eventually enslaved humanity. In order to keep its batteries happy, this AI created the Architect, who in turn created the Matrix, etc.
Neo meets a representation of the controlling AI in the third film.
| https://movies.stackexchange.com/questions/80336 |
movies | Okay, I'm gonna go eat this steak in the bathroom - why is it funny? | From Family Guy - Turban Cowboy [S11E15], why is Okay, I'm gonna go eat this steak in the bathroom funny?
I imagine that I am missing a cultural refernce, but internet search does not help.
| VQAonline_00046664.png | I don't think it's about race, at least not directly. It could be implying and related to them eating at a cheap steak house with poorly trained chefs. Apparently eating improperly cooked steak is known to cause diarrhea, so the joke could very well be related to eating a cheap steak making the person eating it have to use the toilet immediately.
If there is a racial component to the joke, it could be that there's a stereotype that the demographic in question might be likely to order steak at low quality restaurants where they are likely to cook it incorrectly. I'm not familiar with such a stereotype, but it's a possibility.
See: https://www.livestrong.com/article/473861-steak-and-diarrhea/
Note: This episode was removed from all streaming services after the Boston Marathon bombing because it contains a cutaway joke where Peter drives a van over some marathon runners to "win" the Boston Marathon. There is a transcript of the episode available, but I don't think linking to it is appropriate since it is probably not properly licensed.
| https://movies.stackexchange.com/questions/112374 |
movies | How to they film walk on glass scenes in movie? | Like below image, walk on glass intro scene of mass hero is very common in Indian film.
Like this kind of scenes, how to they use cameras?
| VQAonline_00046440.png | Whenever scene like this are needed to shoot, They usually uses a glass panel placed above the camera.
Actor walks on the glass panel. possible it could be a hardened glass. So actor walks on the glass, camera is located at below the glass, Not touching the glass. Then scene can be shot as normal one. No other special effects used.
| https://movies.stackexchange.com/questions/85761 |
movies | Why was David's happiness so important to the Mecha descendants? | At the end of the movie Artificial Intelligence: A.I, the young protagonist David is found by the Mecha after 2000 years encased in ice.
According to their representation of the blue fairie, there was no detail too small that David didn't store for them, yet they do everything in their power to fulfill his wishes - but why?
| VQAonline_00046295.png | David was of great historical interest to the future A.I.s, since he had actual memories of human beings, who are apparently long extinct by their time. Beyond that, he was actually built by humans, where they are undoubtedly built by other A.I.s. Studying him would help them understand their own past. They wanted to preserve him, and although they are not organic, seem to have a morality which prevents them from simply taking him apart or locking him in a cage.
| https://movies.stackexchange.com/questions/68913 |
movies | What are these letters at the end of closing credits? | In 20th Century Women, I find some letters at the end of the closing credits.
What are these?
| VQAonline_00046356.png |
JM = Janet Meyer/Jan Mills, his mom
KM = Most likely his oldest sister, but I can't find confirmation on her first name
MA = Megan Ace, his older sister
MJ = Miranda July, his wife
HM = Hopper Mills, his son
Source for names: http://www.newyorker.com/magazine/2017/01/09/mike-mills-anti-hollywood-family-films
| https://movies.stackexchange.com/questions/73705 |
movies | Did Vin MoCap the Dance? | We all know Vin Diesel is famous for his silky moves...
Is there anything to substantiate the claim that Vin Diesel was himself the model for the Motion Capture of Groot's already infamous pre-credit jive in Guardians of the Galaxy?
| VQAonline_00046008.png | I messaged Jesse Hildreth, the ILM animator who was responsible for that sublime little dancing Groot at the end and he told me that Vin Diesel definitely did not perform mo-cap for that shot, and in fact it was James Gunn who performed it for the reference footage!
Jesse was also responsible for most of Star-Lord's helmet shots, some close-ups on Rocket's hands and a couple of Milano shots - all cool stuff!
UPDATE: Jesse just sent me a link with the following quote:
"I'm not motion-captured, but I'm motion-referenced and that is 100%
me dancing..."
James Gunn
Read more at http://www.comicbookmovie.com/fansites/MarvelFreshman/news/?a=105173#1ZQTzc6HS9QULsvb.99
| https://movies.stackexchange.com/questions/23593 |
movies | Can't the Time Stone be touched with bare hands? | So throughout Infinity War and in the current Endgame, the Time Stone was never touched with bare hands, it seemed to be surrounded by a certain aura and gets transferred from person to person untouched.
Is there a special reason behind it?
| VQAonline_00046566.png | There are no official sources for this, just some theories and speculations:
One speculation says it can be touched, but just like the power stone, you will suffer the effects of touching an infinity stone (Maybe it kills you, vaporizes you, etc).
And that's why the Eye of Agamotto was created:
The Eye was created by Agamotto, using the Time Stone as a component to allow the user to safely wield it without directly touching it and suffering the adverse effects of touching an infinity stone. The container was created in the shape of an eye, hence its name. The mystical properties of the relic, as well as the spells and gestures necessary to use it
One other theory that I really like is that the stone represents Time, and time isn't really a physical thing that you can touch it.
| https://movies.stackexchange.com/questions/101270 |
music | Is there a typo in this exercise, or am I not counting correctly? | I have this set of right hand open string exercises for classical guitar. Many are in 4/4 but some are in 6/8 (see pic below). The notes are grouped in 6 but there is no tuple notation. Reading as straight 6/8 I expect 12 16th notes per measure. Lines 1 and 2 show 24 16th notes per measure. My question is am I reading it wrong or is there a missing bar in each line separating each into 2 groups of 12 16th notes. Thanks.
| VQAonline_00047403.png | It's incorrect. Either it's in 12/8, or there's a barline missing, or they should be demi-semiquavers.
| https://music.stackexchange.com/questions/72566 |
music | How do you identify a key signature's name? | Normally, I'm really bad with key signatures. The thing is, I cannot memorize their names associated with their look. Is there an easy method/technique to recognizing the name of a key signature upon sight? For example, if I had a key signature that looked like this:
How would I find that key signature's name?
| VQAonline_00047554.png | The way I learned it, for flats you look at the second flat in the signature from the right. Here, it's A♭ (B♭-E♭-A♭-D♭).
For sharps, take the last sharp and raise it by a half-step. If you had F♯, C♯, and G♯ in the key signature, the last sharp is G♯. Up a half step from G♯ is A.
No sharps is C major, one flat is F major. You absolutely need to know those two by sight.
Note that this is for major keys. For minor, convert however you normally do from major. In this case, the minor key would be F minor.
I highly recommend that you devote some effort to being able to recognise key signatures on sight. You don't want to spend 30 seconds figuring out that you're playing in D major during a sight-reading gig (Actually, this skill sort of comes with practice itself, but certainly don't neglect it).
User Dom found this site, and it has a specific exercise for this. I really like this site, and I think you'll find this useful, especially if you want to memorise them: (The Exercise)
EDIT: If you need help with finding the minor key signatures, just find the major one (A♭), then find its sixth scale degree (A♭-B♭-C-D♭-E♭-F-G), et voilà, you know it's F minor. That, or memorization.
| https://music.stackexchange.com/questions/82415 |
music | Are all modes relative to Ionian (major) in Roman numeral analysis? | I saw in this Wikipedia article that there are a lot of flats and sharps in the modal natural chords. And I was wondering if it's because they all refer to Ionian.
So in Aeolian the "bIII" chord is read "take the 3rd chord from Ionian, and flatten its root; then use this flattened root and make a major chord from it since the roman numerals are capitalized". Does that sound right?
Borrowing chords from a parallel mode then is just a matter of picking chords from this table (I saw this video on modal interchange). So the resulting non-diatonic chord progression, for example I bVII IV bII, is still always in reference to Ionian (?). Meaning, bVII in this progression is read "take the 7th chord from Ionian, flatten its root, use it to make a major chord".
| VQAonline_00047490.png | Yes, you're correct! (One might say that it's actually relative to major instead of Ionian, but that's being pretty fussy.)
The only thing to watch out for is the accidentals that are "hidden" in some of the Roman numerals. Imagine you're in D and you want to add in the II chord that's borrowed from Lydian. There's no accidental with that II Roman numeral, so you might just think we have a regular supertonic chord in D. But remember that the ii chord is typically minor in major/Ionian, and this II chord is major, thus requiring a G♯. Another way to think of this is that Lydian has the raised fourth scale degree, which would again result in that G♯.
| https://music.stackexchange.com/questions/78844 |
music | How do I know what pattern to strum based on chords alone? | I find a lot of music with only chords:
They don't tell me the pattern I should strum. How can I know when to strum up or strum down?
| VQAonline_00046741.png | For this, you can either go by ear by listening to the recorded song, or by feel (i.e. how do you WANT to play it?). As far as up and down strumming, a general rule of thumb is that - regardless of the actual strumming pattern - you should maintain a steady up/down rhythm. Then you will simply hit the strings when you want sound and not hit them when you don't.
For most basic strumming patterns, consider down-strumming every quarter note and up-strumming on the eighth notes in-between.
| https://music.stackexchange.com/questions/5459 |
music | What is meant by setting semi-tone on Guitar Tuner? | On a guitar tuner there’s a setting to set semi-tone. Options are Off, b, bb. What do these options mean? While I understand that semi-tone means interval of half-tone (one fret), I need some understanding of how b & bb are related in terms of Tuner setup.
Thanks.
| VQAonline_00047168.png | Tuners are generally set at A=440Hz. Concert pitch. With so many guitarists tuning down these days, the tuner can be reset so that the whole guitar is one semitone low,(b) as in Eb for top and bottom, or down to D, (bb),where the guitar is one tone lower than standard.
So, your tuner has 3 settings - standard, one semitone flat, or one tone flat.
| https://music.stackexchange.com/questions/51372 |
music | Meaning of dots below note heads | I’m learning music theory and I found a music sheet that I attach one part in a picture. If you see in the Treble Cleff, there are 8 eighth dotted notes and is a 4/4 signature. Like is a 4/4 is not supposed to be only the eighth notes alone without be dotted? Or why are dotted? It’s supposed 2 eighth notes make 1 quarter note and 4 quarter notes fill the 4/4 signature no? But why are dotted, is not required the dot no?
| VQAonline_00047413.png | The notes in the treble clef are not dotted eighth notes, but just plain eighth notes. The dots beneath the note heads are articulation marks which mean that the notes should be played staccato. If the stems were down instead of up the dots would be probably be above the note heads in your example, but articulation marks may in general be placed either above or below the note with the goal of maximizing legibility.
| https://music.stackexchange.com/questions/73390 |
music | How to determine which inversion a chord is? | Say I'm given the notes like this.
How do I determine whether it's already in root, 1st, 3rd, or 7th inversion?
| VQAonline_00046870.png | This is an F dominant seventh chord. The inversion is determined entirely by the lowest note, so here it would be first inversion.
How I identified the chord: I recognised F-A-C as an F Major chord. But even if we ignore that, when going up from A (A-C-E♭-F), C (C-E♭-F-A) or E♭ (E♭-F-A-C) we get a major second every time. A chord, by definition, is a stack of thirds, so you have to reorder them until you get rid of the second. (Exception: incomplete chords skip thirds.)
To find out the inversion, we just have to list the notes in the order in which they are all a third apart: F-A-C-E♭. Then we just count these notes, starting at zero:
F-A-C-E♭
0 1 2 3
And we see A maps to 1 for first inversion.
| https://music.stackexchange.com/questions/20372 |
musicfans | Help finding this older pop song | I am looking for a famous older pop song. This is the approximate melody of the chorus as sung by a woman, I think in spanish.
| VQAonline_00048224.png | I have found it : Porque te vas sung by Jeannette. Apparently, it is Spanish and from 1974.
| https://musicfans.stackexchange.com/questions/7949 |
musicfans | Identify the music on Australian advertisement for Sidchrome spanners | Back in the 1980s or 90s, there was an advertisement on Australian TV for Sidchrome spanners. It showed a collection of spanners being made, starting with red hot metal being stamped out, then cleaned up, filed down, washed, and finally presented. At the end a voiceover said in a broad Australian accent "Sidchrome. Ya canna hand a man a grander spanner."
Behind all this there was quite a cheerful, flowing piece of classical music. I have never heard it anywhere else and I have no idea what it's called or who wrote it. Does anyone else remember this ad and know what the music was?
I went looking on youtube and found a couple of old Sidchrome ads and lot of Australian ads from the period, but not this one. I will update if I can find a clip.
Update: I wrote down the first couple of bars in musical notation. Take this with a grain of salt, because I can't read or write music; I sounded it out on a musical score site and took a screenshot. I couldn't make the tempo sound quite right, but I think the notes are correct relative to each other. I'll add more when I get a chance.
| VQAonline_00048225.png | I found it on youtube by accident. Not the advertisement, but the actual piece.
It's Bach's Violin Concerto in A Minor, BWV 1041. Here's a recording, with the musical score scrolling as it goes so you can see that my version was far from perfect.
It's a good piece. Go listen even if you never saw the ad.
| https://musicfans.stackexchange.com/questions/8027 |
musicfans | What prejudices could neighbors have when they see a Rammstein flag on the house? | I've been listening to Rammstein since I was a teenager, and I've listened to all their songs an infinite number of times. Also the new band "Lindemann", inspires me.
What prejudices could neighbors have if they see a Rammstein flag on the house?
| VQAonline_00048242.png | Having a quick look at the Controversies section of Wikipedia's article on the band suggests that neighbors might have any prejudice on seeing that flag. The band courts controversy actively, and their taste for using sarcasm and satire has caused many people to misconstrue the band's message.
Someone unfamiliar with the band, therefore, is more likely to think that the flag represents right-wing nationalistic views. Someone familiar with the band is more likely to see it as an endorsement of left-leaning anti-establishment views. Furthermore, those familiar with the band because of one of the many controversies they have sparked might associate the flag with that controversy.
Whether any person harboring any of these prejudices views you more or less favorably as a result will, of course, depend on what that person thinks of nationalism, the establishment, or the particular controversy.
| https://musicfans.stackexchange.com/questions/12083 |
musicfans | Who was the guy in the B-52's video "Roam"? | In the music video Roam by the B-52's there appears to be an African American B-52 with large hair (not really an Afro but similarly large).
Upon seeing that I though "Oh, cool, the B-52s were more diverse than I thought" but then when I checked out the Wikipedia article to find out who he was I didn't see any African-American B-52 listed.
Who was that guy?
| VQAonline_00048208.png | It Iooks like its Zachary 'Zack' Alford, a professional drummer known for his work in the Saturday Night Live Band, as well as with Bruce Springsteen and David Bowie.
According to the biography on his website, zachalford.com, he played for the B52s in 1989. This was the year the B52s album 'Cosmic Thing' was produced, from which the single Roam was taken.
| https://musicfans.stackexchange.com/questions/5476 |
musicfans | Did Jimi Hendrix's reverted Stratocaster influence his sound? | Jimi Hendrix was left-handed and at the time he started to play the guitar, left-handed ones may have been hard to find, so he strung his guitar upside down.
Then, even he became rich enough to have access to any left-handed guitar he wanted, he kept playing on his reverted guitar. Was it just for personal visual style reasons or did it influence his playing, his sound on a way that he wanted to keep it?
The only thing I can see is with a reverted Strat, higher frets are harder to access.
| VQAonline_00048211.png | There are many ways it would have affected his sound.
A few points about the interaction of pickups and strings changes.
The angle of the bridge pickup is backwards. This will cause his higher strings to be further away from the bridge where they pass over the pickup and his lower strings closer to the bridge where they pass over it. This will have caused his high strings to sound more mellow and his low strings to sound more sharp and biting.
On the headstock side, there is longer string travel on the bass strings and shorter string travel for the high strings between the nut and the tuners, as compared to a regularly Strat. The longer the strings travel the 'floppier' the string will sound. This one is more likely felt than heard but can definitely influence the player's technique.
The pole pieces which are staggered for certain strings sizes will be different and change the way individual strings sound.
A couple of points about the upside down body contour.
On a normally worn Strat the upper horn, which is the longer one, will have the strap attached to it. Wearing it upside down will bring the the fretboard further away from one's body. This will make fretting open chords and notes lower down on the fretboard harder to get to and notes higher up will be easier to get to.
The cutaways of the two horns are not equal. The lower horn on a regularly worn Strat has a deeper cut into the body to allow easier access to upper frets. Wearing it upside down will make access to upper frets harder and the player will have to adjust his fingering technique to reach them. This needing to work hard for upper frets is something many players of Gibson Les Pauls say influences their playing.
These two points sound contradictory and one might think they cancel each other out, but in reality it doesn't work like that.
| https://musicfans.stackexchange.com/questions/5842 |
musicfans | Sheet music puzzle from the Church of Higher Truth website | I got this piece of sheet music as part of an online game[?], called the Church of Higher Truth can you identify it for me?
It was presented as a puzzle to solve, along with this text:
"Name this song, and give me its meaning. This song is a prelude to the things to come, and it's important to know what to expect. Sing it, play it, and dream it."
The overarching context of the game (or is it not a game?) is that reality is not what we think, and those in power have been lying to us and we need to wake up.
| VQAonline_00048210.png | This is the opening to Richard Wagner's Götterdämmerung ("Twilight of the Gods"), the fourth and final music drama of Der Ring des Nibelungen.
Excerpt #388 begins right at m. 1 of the Prelude to Act I; #389 begins at m. 17.
If this is a "sign of things to come," it's probably a reference to the ominous outcome of the end of Götterdämmerung, where the gods are overthrown, the world burns, is immersed in water, and is reborn anew. It fits with your interpretation that "those in power have been lying to us and we need to wake up" and overthrow those in charge.
(And, as an aside meant for The Church of Higher Truth: it's not a "song." Songs have words, which these two excerpts do not.)
Edit: If anyone is curious to hear the music for the end of the world, here you go.
| https://musicfans.stackexchange.com/questions/5772 |
musicfans | Identifying an excerpt by Beethoven (Ddim7ㅡAbm/EbㅡEbㅡAbm) | While working on an assignment based on secondary leading-tone chords, I found this excerpt that I am not quite familiar with:
I see a secondary leading-tone seventh chord to the dominant, then a cadential six-four, repeated Ebs which represent the V, and then the tonic chord. The key is Ab minor.
Can someone identify this piece?
| VQAonline_00048232.png | It's the third movement of Beethoven's Piano Sonata no.31 in A flat (op.110) - III. Adagio ma non troppo.
| https://musicfans.stackexchange.com/questions/9914 |
mythology | The Enchantress and the blue rose tree | Does anyone know the title of this story and where it was translated from?
Source: the Golden Bough
| VQAonline_00048256.png | Sir James George Frazer cited this story from the 1873 book Russian Folk-Tales by William Ralston Shedden-Ralston. Ralston, in turn, translated it from Ivan Khudyakov's 1861 collection Russian Fairy Tales, where it was numbered 109. Clearly the story is Russian in origin.
Ralston did not give the story a title, which probably indicates that neither did Khudyakov (but I can't read Russian, so someone else would have to confirm this). Traditional folk tales rarely come with names, or rather, only one widely accepted name. Hence many fairy tale collections use numbering instead. So we could reasonably say, there isn't a title.
On the other hand, in his The Golden Bouch, Frazier gave the paragrap containing the story the subtitle, "Death in the blue-rose tree". You could treat this as a title - it's as close to a name as there is for this story, in English at least.
| https://mythology.stackexchange.com/questions/3312 |
mythology | What is that on Athena's chest? |
In this statue there is something what looks like a face on Athena's chest. I have seen it on some other statues of Athena.
What is it? Is there a myth behind it?
| VQAonline_00048261.png | It's not clear from your picture, but the face is most probably a Gorgoneion, a recurring element of Athena's iconography:
In Ancient Greece, the Gorgoneion (Greek: Γοργόνειον) was a special apotropaic amulet showing the Gorgon head, used most famously by the Olympian deities Athena and Zeus: both are said to have worn the gorgoneion as a protective pendant. It was assumed, among other godlike attributes, as a royal aegis to imply divine birth or protection, by rulers of the Hellenistic age, as shown, for instance, on the Alexander Mosaic and the Gonzaga Cameo.
Source: Wikipedia contributors. (2018, June 16). Gorgoneion. In Wikipedia, The Free Encyclopedia. Retrieved 21:22, February 5, 2019, from https://en.wikipedia.org/w/index.php?title=Gorgoneion&oldid=846161112
The ever-so-helpful theoi.com has tons of information on the mythology of the Gorgons, if you wish to know more about them. We also happen to host some very interesting questions about Medusa and her sisters on this site.
| https://mythology.stackexchange.com/questions/5436 |
mythology | What is the origin of a common Christmas tree quotation concerning an old Babylonish fable about an evergreen tree? | Searching for "evergreen tree which sprang out of a dead tree stump" gets nearly 3000 hits.
The Seed of the Woman and the Power of Darkness - Donbor Syiemlieh - Google Books is an example:
"An old Babylonish fable told of an evergreen tree which sprang out of a dead tree stump.
The old stump symbolized the dead Nimrod, the new evergreen tree symbolized that Nimrod had come to life again in Tammuz!
Among the Druids the oak was sacred, among the Egyptians it was the palm, and in Rome it was the fir, which was decorated with red berries
during the Saturnalia!" (Walsh, Curiosities of Popular Customs, p. 242).
Obviously I didn't check all results, but those that I did check contain that same quotation, and almost all give the same attribution.
The problem is, while page 242 of that book does talk about Christmas trees, and the writing style is similar, it doesn't include the above quotation or anything like it:
The quotation doesn't appear elsewhere in that section or anywhere else in the book.
So what is its origin?
| VQAonline_00048264.png | This question has now been answered:
quote identification — Literature Stack Exchange
TL;DR:
… those who attribute the quotation to Walsh are misattributing and/or misquoting.
The direct quotation originates with Ralph Woodrow, who paraphrases and cites, but does not quote, Walsh.
… page 152 in chapter 20 of Woodrow's Babylon Mystery Religion.
| https://mythology.stackexchange.com/questions/7757 |
mythology | How many Great Gods did the Sumerians have? | How many Great Gods did the Sumerians have?
Was it twelve, as counted on Wikipedia, or it's just a coincidence? Does the number of Great Gods have any meaning?
For example in this article it's suggested:
Department of Oriental Antiquities at the British Museum - describes a pantheon of 'twelve great gods' who despite having been given somewhat different names
See The Sumerian Pantheon (the family tree) below:
Does it indicate that the twelve was some special number? Similar to Greek pantheon (The Pantheon of Twelve)?
This source: “Assembly of the Gods” – 12 Members reads:
There are 6 male deities and 6 female deities among the ruling twelve positions in the “Assembly of the Gods“.
| VQAonline_00048245.png | The source of the claim of twelve great gods comes from a book titled "The Chaldean Account of Genesis" by George Smith, written in 1876. You can see the list in Chapter 4, here:
http://wisdomlib.org/mesopotamian/book/the-chaldean-account-of-genesis/d/doc2816.html
I'm not really sure whether I buy the "twelve great gods" claim entirely, but nevermind that. I'll call it plausible.
In some remote age there appear to have been three great cities in the country, Erech, Eridu, and Nipur, and their divinities Anu, Hea, and Bel were considered the "great gods" of the country. Subsequent changes led to the decline of these cities, but their deities still retained their position at the head of the Babylonian system.
Smith claims that gods became "great" as a function of the growth of their cities, so the list of great gods would grow naturally as cities rise and fall. Which leads, once again, to the number twelve is likely coincidental.
More recent resources have claimed a pantheon of 7 "gods who decree" and 50 "great gods" (from "The Sumerians. Their History, Culture and Character", by Samuel Noah Kramer, 1963)
| https://mythology.stackexchange.com/questions/206 |
mythology | Why is Aether shown battling a lion-headed giant? | In this picture, the primordial god of the upper air, Aether, is depicted wrestling a lion-headed giant.
Is there a myth/story for this anywhere?
| VQAonline_00048255.png | The lion-headed giant apparently is Leon, who, according to Ptolemy Hephaestion was slain by Herakles during the Gigantomachy:
Herakles did not wear the skin of the Nemean lion, but that of a certain Leon (Lion), one of the Gigantes (Giants) killed by Herakles whom he had challenged to single combat.
Source: Ptolemy Hephaestion, New History Book 5 (summary from Photius, Myriobiblon 190) (trans. Pearse) (Greek mythographer C1st to C2nd A.D.)
Unfortunately, I do not think a tale of Leon battling Aether survive.
| https://mythology.stackexchange.com/questions/3128 |
mythology | Who are the twelve gods of the underworld of the Hittites? | The west wall of Chamber B in the Yazilikaya sanctuary, near the Hittite capital Hattusa, depicts - according to Wikipedia - twelve gods of the underworld:
Who are these twelve gods? Do they have names, and what is their function? How do they relate to other gods of the Hittite pantheon? Do they feature in any story?
| VQAonline_00048263.png | Thanks for the question. Very interesting search along the way to coming to the following info.
https://www.heroicage.org/issues/15/malcor.php
Excerpt:
The Twelve Companions
§18. As Macqueen (1986, 58) pointed out, "The principle weapon
employed [from Hittite chariots] was the stabbing spear," but the
Hittite soldiers of the Anatolian hills wielded a slashing-sword,
which was replaced by "a long cutting-weapon with a straight blade by
"the end of the second millennium" (Macqueen 1986, 59–60). The swords
carried by the twelve runners in Chamber B resemble the short,
crescent-shaped sword, decorated with animal heads which was carried
by Hittite warriors in ceremonies rather than in battle (Macqueen
1986, 59–60). The Hittite axe born by Sarruma has "ribbing round the
shaft-hole [that] is a feature" from, among other places, the northern
Caucasus area (Macqueen 1986, 61), while the axe's blade "is of a type
which can be paralleled only in the Caucasus region" (Macqueen 1986,
61).19 Although the gods carry the swords in this image, recall that
in the texts the swords are embedded.
§19. The steppe war god himself was not the celestial Ram, but he was
represented by the story of the ram, just as Jason can be represented
by a reference to the Golden Fleece. This raises the possibility that
he was not the sign of Aries but another sign that appeared in the sky
along with—or at the same time as—Aries. The twelve figures
associated with the sword god, then, may have nothing at all to do
with Underworld deities. Instead, they may represent the twelve signs
of the Zodiac, and the crossroads the Hittites associated with them
might not be underground at all, but rather in the sky.
Conclusion
§20. The Hittite version of the Sword in the Stone story has several
elements in common with the Arthurian variant. Both feature a sword in
a graveyard. Both swords are associated with a king. The twelve
runners in the Hittite variant parallel the Twelve Knights of the
Round Table in Arthurian tradition. Also, the anvil of the Arthurian
variant preserves the connection between the forging of iron and the
story of the god who planted a sword in a stone. The tales are clearly
part of the same tradition, yet, by placing the image of the sword god
in conjunction with celestial deities at Yazilikaya, the Hittites
retained an association that the Arthurian variant has lost: the tale
of the Sword in the Stone had something to do with the stars.
Historical Dictionary of the Hittites By Charles Burney
(Note: Any typos are mine.)
The clearest, most familiar manifestation of the Underworld in Hittite
religion, or more accurately in the Hurrian cult, occurs in Chamber B
of the Yazilikaya sanctuary outside the city of Hattusa, with the
remarkable and indeed unique Sword-God, a god in human form emerging
from the hilt of a dagger, its blade too shortened to be termed a
sword. This has long been recognized as identifiable with Nergal, the
god of the Underworld, one of the Mesopotamian deities imported by the
Hurrians into Anatolia. From a magical ritual going far to explain the
Sword-God of Chamber B at Yazilikaya come the words: “He makes them as
swords and fixes them in the ground.” In another text “the bronze
swords of Nergal” and “the twelve gods of the crossroads” are
mentioned together: hence the twelve running gods, not soldiers as
once supposed, facing the Sword-God and likewise appearing in the
larger Chamber A at Yazilikaya at the rear of the procession….
| https://mythology.stackexchange.com/questions/5894 |
mythology | Why is rape featured so prominently in Greek mythology? | This question may be a little controversial so try to keep your answers as academically as possible. (take an example from @DukeZhou )
If on the subject general answers are also accepted
I am familiar with the fact that this happened in pretty much every mythology, but Greek mythology seems to utilize it a lot. And I was wondering if there was a special reason for this behaviour apart from being the "go-to deed" for the writers of antiquity.
While reading up on some Greek myths I started to notice a recurring pattern in the act of rape.
Is there a reason for the writers in a considerable amount of Greek mythologies epics and poems to resort to rape?
Why is rape featured so prominently and what is the (if any) hidden meaning behind the rapes?
This is the list I put together as defined by Wikipedia:
list 1. list 2
Aethra (mother of Theseus); was raped by Poseidon
Antiope; raped by Zeus.
Apemosyne; raped by Hermes
Callisto; raped by Zeus.
Cassandra; raped by Ajax the Lesser, and later forced into
concubinage by Ἀgamémnōn.
Chrysippus; raped by his tutor Laius.
Demeter; according to an Arcadian myth, Demeter was
being pursued by Poseidon and she changed into a horse to escape
him. Poseidon, however, transformed himself into a horse and,
after cornering Demeter, raped her, resulting in her giving
birth to Despoina, a maiden goddess, and Arion, a divine
horse.
Europa; raped by Zeus after he abducted her in the form of
a bull.(as seen on the Greek €2 coin)
Ganymede, son of Tros of Dardania; taken up to Mount
Olympus by Zeus in the form of an eagle.
Leda, raped by Zeus in the form of a swan.
The daughters of Leucippus, Phoebe and Hilaeira,
were abducted, raped and later married by Castor and Pollux. In
return, Idas and Lynceus, nephews of Leucippus and
rival suitors, killed Castor.
Medusa; raped by Poseidon in Athena's temple.
Odysseus; raped by Calypso on the island of Ogygia
in his seven year stay.
Persephone; raped by Hades and, in some versions, raped by
her father, Zeus.
Philomela; raped by her brother-in-law Tereus.
| VQAonline_00048262.png | Preface: This subject is complicated by changing social standards. Forced marriage has been routinely practiced around the world into the contemporary era, depending on the society. (This is a major theme of Game of Thrones, as is the condition of women in pre-modern societies in general.) The Rape of the Sabine Women can provide some context.
I see three main reasons, lurid appeal, ritual, and humanism.
Mythology and folklore serve many functions. They are form of entertainment (appeal), a commemoration of religious events (ritual), and, in the case of the Classical period in Greece, it is one of the vehicles for the birth of humanism.
Lurid Appeal
This rationale is easy. "Sex sells", and violence as well. You find everywhere from the very earliest myths to contemporary media. (Gilgamesh starts out with a prostitute and a fist fight. The Osiris myth involves murder, dismemberment, and necrophilia.) Rape combines the two (see: "sexual violence") and provides a titillation.
Storytellers have to support themselves and to do that they need to hold the attention of an audience. One of the central rules of fiction is high stakes = high audience engagement. The more transgressive the better. (Kill Bill and The Girl With The Dragon Tattoo are contemporary exemplars, and both can be seen as forms of Philomel, which was a female-centered revenge story involving rape.) Rape is widely used in modern entertainment as a pretext for revenge, so this phenomenon is in no way restricted to Greek mythology.
Ritual
Burkert, Eliade, and Frazer have written extensively on this subject. At a very high level, there is archeological evidence of human sacrifice in ancient Europe and other ancient cultures. Human sacrifice is a central element of several of Euripides' plays, but by the time of Euripides, these sacrifices of legend have been ritualized in the form of drama. (The Festivals of Dionysus were religious festivals, and the play The Bacchae is, at its core, a commemoration of the death of the god.)
There is an original religious function to mythology. It covers everything from the creation of the universe to the acts of the gods. In the case of the Greek gods, these acts are often lurid. The behavior of the gods is commemorated in stories, rituals (re-enactments), and in the acts of humans. Cronus swallows his own children, as do Tereus and Thyestes. Just as Cronus overthrows Ouranos, Zeus overthrows Cronus.
Persephone, in the ancient context especially, is a coming-of-age story. Her abduction and forced marriage to Hades explain the cycle of life and the seasons. It's also symbolic of death and rebirth. [See: Kore & Persephone]
Persephone's is a central myth, explaining winter, and the Kore is an archetype--in some sense, her story is the story of almost all women. Abductions and forced marriage in Greek myth may be reflections of her story.
There also the factor that Zeus is a serial rapist and so it's not surprising rape becomes a staple of Greek Mythology. A key difference is that what is permissible for the gods is not necessarily permissible for man--Zeus marries his own sister. So human rapists in Greek mythology are generally villains (Tereus and Thyestes) and, unlike the gods, typically come to bad ends, even in the case of the hero little Ajax.
In his Agamemnon, Aeschylus makes the king's concubinage of Cassandra Clytaemestra's main motivation for killing her husband (jealousy and fear of being supplanted). Although Aeschylus was quite sympathetic to Agamemnon, Euripides is significantly less so, citing Agamemnon's murder of her infant from her previous marriage, and sacrifice of their daughter, Iphigenia, at Aulis, as Clytaemestra's motivations, which leads to the next element:
Humanism
The humanism wiki doesn't give the full story because the undermining of divine authority begins with works like the Iliad, which has many functions, including subversive. In this great poem the dignity of the gods is undermined while the dignity of man is elevated through Achilles and Hector. It also evokes tremendous pity, for Hector in particular--the poem, which begins with the "rage of Achilles", ends with "the funeral of Hector, the breaker of horses."
Unlike the storytellers, thinkers like Plato used mythology to explicate philosophical inquiry. (In the sense of the Iliad as a subversive text, Zeus may be said to not have escaped the prophecy on Thetis in being ultimately diminished by her son, ironically in a rare case where he forgoes having sex;)
Catharsis (pity and dread) was a central element of Greek Drama. These plays rarely commemorate the travails of the gods, instead celebrating the ordeals of humans. In the Bacchae, it is Pentheus who serves as tanist for Dionysus. Aeschylus writes of the sufferings of Prometheus in service of mankind, but also writes of the trials, and vindication, of Orestes. Sophocles most famous heroine is Antigone, who dies in service of a principle. Euripides can be viewed as strongly feminist, through plays such as Hecuba, The Trojan Women, and Iphigenia at Aulis. (Humanism is rooted in the agency of humans, and feminism in the agency of women, both central elements of Greek Drama.)
An aspect of Shakespeare that makes the works such standouts is the creation of multi-dimensional female characters, whether villains or heroines. So with Euripides.
Like The Rape of Lucrece, Ovid's account of Philomela evokes tremendous pity. Empathy is a key to seeing the other as human. Andromache is play about Hector's wife, and her life as slave, after the fall of Troy. It can argued that by creating strong, believable female characters, and in generating sympathy for their travails, authors like Euripides, Ovid and Shakespeare put a spotlight on the condition and plight of women. In an indirect sense, this supports the idea of women's rights.
Political Uses
There can also be a political component, as in the myth of Lucrece, which casts her abuser, Tarquin, as a tyrant to be overthrown. This is the rationale for the establishment of the Roman Republic. Exploring the meaning of the Latin răpĭo, rooted in abduction and seizure by force, women, as prizes of war, were "booty" in both senses of the word. The abduction of Helen is the pretext for the Trojan War, but, if there was such a war, it was surely fought over the trade route connecting Asia & Europe and the Euxine & Aegean.
Notes:
Rape, in the modern conception, seems, in pre-modern times, only considered transgressive in regard to wives and daughters specifically in an extra-marital context--i.e. only a crime when involving "free women", or, women of status, as opposed to chattel, and only outside the bounds of marriage.
Modern statistics on rape can be controversial, but under-reporting is definitely an issue. Regardless of the precise numbers, sexual violence is still common, and rape is still used as an instrument of warfare. The prevalence of rape in stories and mythology may be a reflection of how often it occurs in the real world.
I tried to keep this concise in that any one of these aspects could fill a dissertation, so I apologize if everything is not fully explicated. I can provide more details in comments. I also recognize this is a potentially charged subject and have attempted to approach it as academically as possible.
| https://mythology.stackexchange.com/questions/5461 |
opensource | Is Linux Mint's version of Firefox really Free software? Is it compliant with the MPL? | Trying to keep this as short as possible... In a VM, to test a problem of someone else, I installed a fresh Linux Mint 17.3 and opened Firefox. The search bar (right of the address bar) didn't include Google as an option, as I'm used to. Proceeding to the option to add search providers, I finally found it, along with a "reason" it wasn't there by default.
A little put off by that, but not too worried about it, (they need money too, right?) I found the link for Google and enabled it. Now it was available, and all was good. Except that it wasn't.
Normally, as I type in the search box I get suggestions that lend themselves to what's been typed so far. Often this shortens my typing significantly. Now, it wasn't doing that. I switched back to Yahoo, and it work as normal. Back to Google, no such luck. Not unfamiliar with about:config I poked around, then dug around, and did some comparisons with settings between Yahoo and Google. No dice, can't find what triggers the difference in behavior.
"Ok," says I to self, I'm just go to the repository and drop the Mint custom version, and install the Mozilla original version. Into software manager and drill down to Firefox. No options to upgrade, downgrade, switch versions, or anything else, just "Remove" which, after doing that, only gives the option to "Install." Shows what version will be installed, but no options to change it.
I'm not a Mint user, so I don't know if there's other options for controlling software or not. I'm sure that a source install is likely to be available somehow. But.. Is that the point.
As I understand "Free" software, it's about choice, and not having someone, disto author in this case, dictate what I can use. The option to add Google seemed to fulfill that promise, until I found it only half-worked. Making it difficult, maybe prohibitively so, to replace the restrictive version with an unrestricted version was the icing on the cake.
Edit
So, Linux Mint, Linux kernel and all, is, or is not, Free software? BTW: The source is available, so it's probably "Open source" at least.
The proper question relates only to the version of Firefox, firefox_51.0.1+linuxmint1+rosa, supplied in the repos of Mint, not to the distro itself, or to any other package in the disto, including the kernel. As such, the question should have been, "Does the version of Firefox supplied with Linux Mint 17.3 comply with the MPL and is it still free within the FSF concept?"
Notes:
In re: the "crippling" of the software: I don't know how long I've been using Mozilla products, or Firefox in general, but as their product have evolved, and as I've moved from one distro to another, between OSs, and between platforms, I have become accustomed to features behaving consistently across them all.
I'll not argue, here or in comments, as to whether or not that version is "crippled." I do know that it is modified, and that it does not work the same as every other release of Firefox that I have available to me for testing. The modified source code is available, to anyone who wants it, and according to the accepted answer, modified or not it does comply with the FSF's four freedoms. That was the question, and that is the answer.
I have been replying to comments that go beyond the scope of the question, and I probably shouldn't have been. By my rep, even across SE as a whole, you can see that I'm learning the Stack Exchange way. Comments about the real question will be replied to, while my crippled phrase, my improper scope to include the distro, and related debates won't be fueled by me. Further insights, or explanations that are germane to the OS topic are welcomed and encouraged. That's how others like me can learn.
| VQAonline_00048268.png | Software is free (as defined by the FSF) if it gives you the four freedoms:
The freedom to run the program as you wish, for any purpose (freedom 0).
The freedom to study how the program works, and change it so it does your computing as you wish (freedom 1). Access to the source code is a precondition for this.
The freedom to redistribute copies so you can help your neighbor (freedom 2).
The freedom to distribute copies of your modified versions to others (freedom 3). By doing this you can give the whole community a chance to benefit from your changes. Access to the source code is a precondition for this.
It could have bad usability, it could have bugs, it could spy on you, it could technically restrict browsing to certain sites or installation of certain software, it could intentionally delete your music – as long as it gives you the four freedoms, it qualifies as free software.
Thanks to these freedoms, you are allowed and enabled to change the things you don’t like, and to share the changed software with others. Note that this doesn’t mean that you need to be able to change it e.g. within the GUI, or that is has to be easy – it just has to be allowed (legally) and possible (source code provided).
So the issue you mention doesn’t affect whether or not Linux Mint is free software.
Is it free software? Well, this depends on what is meant with "it", as a GNU/Linux distribution consists of many different parts, and could come with separate but pre-installed software.
If we talk about the ISO that can be downloaded (so not taking any packages into account that can be installed from their repository): According to Linux Mint’s FAQ Does Linux Mint include proprietary drivers?, it doesn’t contain any proprietary software (but note that this applies to the current release; it seems that this was not the case for older releases). So yes, Linux Mint is free software.
| https://opensource.stackexchange.com/questions/5168 |
opensource | Can I "Override" a licensing policy? | On many sites, especially Stack Overflow, I can't help but notice such amazing code snippets. However, they come with a "catch" designed by the author.
With user contributions being licensed with the Creative Commons ShareAlike 3.0 License, many users try and "override" this by stating how they license the work on their profile page. For example:
All contributions that I make to this site shall be licensed under the Apache 2.0 License
This surprises me, because it seems to violate the policy of licensing, if not the Terms of Use that are present as well.
Is this acceptable? Are users allowed to essentially "override" and decide their own licenses, against what has been standardized by the organization?
| VQAonline_00048265.png | It depends. For Stack Exchange: yes.
When you write something, you own the copyright, and have the right to do whatever you want with it (from a copyright perspective at least).
When you post something to some site, you usually give a license to use that material on that site, through the terms and services, or you transfer the copyright to them.
If the terms are to transfer the copyright to them, you no longer own the copyright, and you can't grant additional licenses.
If you grant them a license, it's either an exclusive license, or a non-exclusive license. If it is an exclusive license, you can't grant anyone else a license anymore.
If it is a non-exclusive license, you may still dual license your content, and make it available under some other license as well.
In the case of Stack Exchange, the terms read
You agree that all Subscriber Content that You contribute to the
Network is perpetually and irrevocably licensed to Stack Exchange
under the Creative Commons Attribution Share Alike license.
This means it is a non-exclusive license, and you can release your content to others under a different license as well. This seems to be the most common scenario for other sites as well, but you should always double check.
Note that this doesn't override the license. You are dual licensing your content. Per the terms and services, you have no choice but to license your work under CC-BY-SA. But you have no restriction to also license it under a different license of your choosing.
These licenses don't have to be compatible. Anyone can choose under which license they use your work, the standard StackExchange one (CC-BY-SA), or another you offer personally.
| https://opensource.stackexchange.com/questions/504 |
opensource | How to handle a pattern of GitHub volunteers wanting to work on an issue then disappearing | Since I registered my project on Up For Grabs, I get a lot of novice volunteers, which is great as I like both the ideas of 1) improving the app 2) introducing novices to open source collaboration.
But I have a management+social+technical problem, illustrated by this example today:
As you can see, one after the other, 3 volunteers have taken the issue under their responsibility then become silent, with a month's interval between each.
They are volunteer novices, so the problem is not them. I fully expect that they might give up, and hold no grudge against them.
On the technical side, GitHub is not helping, as I can not assign an issue to someone who is not a member of the project. And I don't think making them a GitHub project member is a good idea at this step (or is it?). I created the "assigned" label to work around this problem, but it is not optimal as it does not say to whom the issue is assigned. I want to continue to use GitHub for issue tracking, though, as it has become a de facto standard.
I hesitate between spending more time spoonfeeding newcomers, or spending less time so that I dedicate my time to other aspects of the project.
Before we had a policy of "First pull request wins", that lead to frustration as we had some real cases of novices posting nearly the same pull request at the same time for something non-trivial that they that obviously had dedicated a lot of time to. Not a pleasant situation, and a very traumatic first experience for some of them, which is something I really want to avoid.
How can I improve my handling of the situation? Be it via behavior, project guidelines, technical solutions, or anything else.
| VQAonline_00048270.png | EDIT: while the content of this answer may still be interesting, the limitation of GitHub that is discussed is no longer relevant, as this is now possible to assign an issue to anyone who comments it.
On the technical side, Github is not helping, as I can not assign an issue to someone who is not a member of the project. And I don't think making them a Github project member is a good idea at this step (or is it?). I created the "assigned" label to work around this problem, but it is not optimal as it does not say to whom the issue is assigned. I want to continue to use Github for issue tracking, though, as it has become a de facto standard.
While agreeing completely with Philippe's answer, I will try to answer to the technical sub-question here: indeed GitHub does not make it easy to assign issues to new contributors but there are workarounds.
If your project is part of an organization (and only in this case), you may create a team in your organization (call it "External" or "New contributors" for instance) and give it "Read access" to your repository (see this screenshot of the repository settings). When your repository is already public, giving read access basically amounts to giving no privileges, but it will allow you assigning issues to people in the team (they have first to accept the invitation though).
If you use this to assign issues to newcomers, you should have a clear rule in your contributing guidelines that not communicating for a week (or any other predefined period) amounts to losing the issue.
The rest of this answer is drifting away from the original question but it might still be of interest to you: you can use "Write access" as the next level of privileges for people who have already contributed usefully a few times. If, at the same time, you protect your branches and activate the "Review requested" feature and restrict merging to a subset of contributors (possibly only administrators), then "Write access" will mean privilege to label / milestone / close / reopen / assign issues (and edit / delete comments), to mark a pull request as approved, but not to commit anything directly to a branch nor to merge pull requests. Then the next level of privilege can be permission to merge approved pull requests (leaving pushing on branches directly or merging unapproved pull requests to repo admins only).
| https://opensource.stackexchange.com/questions/6121 |
opensource | Can code licensed under AGPL also be (re)licensed under LGPL by its contributor? | I have a puzzling question:
Somebody contributed to a AGPL licensed project (he is not the owner). Now this code could also be applied to a different project licensed under LGPL. Could the author of this code part (he is listed in the license header of the AGPL code as (c) ) give permission to use that code in the other LGPL project? The contributor thinks that he can not because he signed some contributor agreement with the AGPL project but I wanted to ask this here and maybe someone has some insight...
Update: I think I found the CLA, so here is the interesting part:
| VQAonline_00048281.png | What this author has signed in not a Contributor License Agreement, giving the project additional (non-exclusive) rights in addition to what they get under the AGPL, but a transfer of copyrights (CTA, Copyright Transfer Agreement).
This means that the AGPL project owns the copyrights on the contribution and the author has just as many rights as anyone else who obtained a copy1.
1: This is not entirely true, depending on the view on moral rights in the author's jurisdiction, but that does not make a difference when it comes to re-using the code in a different project.
| https://opensource.stackexchange.com/questions/10136 |
opensource | Mixing GPL v3 and Proprietary library | My application has two parts GUI and a backend algorithm module. I have used a library under GPLv3 to write my GUI. In the GUI we can create a workflow of different digital signal processing units so I thought to share this GUI to the community under GPL, but I wish to keep my some algorithm modules as proprietary, what are the possible approaches?
| VQAonline_00048269.png | That's easy. Make sure you don't compile your GUI and your algorithms together statically as a single executable. If you do that, you don't have any GPL obligation for your algorithms.
Run your algorithms as a command-line tool and use inter-process communication in your GUI. This is a very common implementation in computer chess engines.
Run your algorithms as an internal web server and use internal web connection
Example from computer chess (use process communication):
https://gamedev.stackexchange.com/questions/136434/how-can-i-use-gpl-software-like-stockfish-chess-engine-in-my-unity-game
To do this validly, you must make sure that the free and non-free programs communicate at arms length, that they are not combined in a way that would make them effectively a single program.
| https://opensource.stackexchange.com/questions/6044 |
opensource | Interference of Software Patents with Free & Open Source Software | While visiting wikipedia page on Free and open-source software, I noticed the challenges from the template at bottom:
In which Digital rights management and Software patents seems considerable to me.
So, I want to know interference/interaction of Software patents with Free & Open Source Software
In other words how do we interact with it?
Note: This question is split off from this to be specific on Software patents.
| VQAonline_00048266.png | Why is it a problem?
Patents are dangerous because they can put an additional restriction on the use and distribution of software which is not mentioned in the license.
A company can freely contribute to an open source project and license their work under an open source license, but in the meantime file a patent on some aspect of their contribution. Later they can then use that patent to collect license fees from distributors and users of the allegedly free software. All of this is completely legal because licenses usually only deal with copyright law, and patent law is a completely different beast, even though the outcome is usually the same.
This can also be done by companies which were not involved in the development at all but own a similar patent filed before the project was published. The patent doesn't even need to be enforceable. The threat alone that it might apply can be enough to stunt the adoption of free software, because patent lawsuits are expensive. Companies fear that they might lack the resources to fight a patent lawsuit, even when they could win with enough money.
Patents can also be used to prevent someone from creating a free alternative for a proprietary product. A good example for this is the H.264 video encoding algorithm, also known as MPEG-4. The algorithm was developed as proprietary software, but how to implement it is no secret. An algorithm can not be copyrighted, only a specific implementation can. So as far as copyright is concerned, anyone could create a free implementation for everyone to use. But unfortunately there are various companies which hold several software patents which apply (or might apply) to this algorithm. This allows them to collect royalties from anyone implementing the algorithm, free or not.
Advocates of free software thus recommend to use different algorithms like OGG Vorbis which was specifically designed to circumvent any known patents on video encoding. But video encoding is such a minefield of patents that some people believe that there might still be some less known patents out there which could also be applied to Vorbis and fear that wide adoption of Vorbis could prompt the holders of these patents to surface and start to demand money.
Patent law is an area which is not internationally homogenized. Different countries have different laws regarding what can be patented and which laws apply. Software patents in particular is a shaky area which is handled differently in different jurisdictions. This can lead to the situation that a certain piece of free software is only free in some parts of the world and not in others, violating the right to free distribution without discrimination of certain groups.
How can we deal with it?
Demand patent licensing in licenses. The GPLv3 for example has a section on patents which says that any contributors must license any patents which apply to their work for free. However, this does not help against 3rd party patent claims.
Work around the patents. When you have an open source project, do your research about which patents might apply to the area and try to not violate them. Release early, because after you released a product, any applications for new patents which apply to the product are invalid due to prior art.
Bust the patents. When prior art can be proven for a patent, it can be declared invalid. A good medium for crowdsourcing potential prior art is the stackexchange site Ask Patents which has a specific tag for prior art requests. The Electronic Frontier Foundation also has a patent busting project.
Build a defensive pool of patents. Just play the same game the patent trolls play. Register patents yourself, and then pledge that you will only enforce them against those who also try to press their own patent claims. This is the strategy many large companies use to protect themselves from frivolous patent claims. Unfortunately this only works against people who actually implement their patents in products and are not just in the business of filing lawsuits. Also, the strategy of fighting fire with fire might not sit well with the more ideological parts of the free software community.
Political lobbying against software patents. Software patents have already be declared unenforceable in large parts of the world. But there are still countries which have not yet understood how bad they are for innovation and the international competitiveness of the countries IT economy. Support organizations which try to convince politicians to change the local patent laws for the better. When you live in such a country, try to convince your local politicians yourself and consider their opinions about software patents when casting your vote in the next election.
| https://opensource.stackexchange.com/questions/1088 |
opensource | Can I use separate license for commercial use? |
I would like to create a REST API in my server that internally use a GPL library. As far as I know the GPL license affects the 'distribution' not the 'usage'.
-So whoever calls(uses) my REST API shouldn't be affected by the GPL license right ?
Am I obliged to distribute the API code that uses the GPL library?
So must I Distribute Code server and make it under GPL?
| VQAonline_00048275.png | This boils down to “what is a derivative work?” and the answer is “we don't really know”.
However, there seems to be general industry consensus that a server program and a client program that behave as separate programs and just communicate over some IPC mechanism such as HTTP messages are separate works, not derivative works of each other. If that is the case, distributing the client cannot trigger any GPL requirements in the server code.
This means your understanding seems correct.
As long as you don't distribute/convey your server software you do not have to disclose the source code.
You are correct that the GPL does not trigger when merely running the software.
Exception: if you include modified AGPL-covered software then that already triggers when users can interact with that software, i.e. when you publicly perform the software.
| https://opensource.stackexchange.com/questions/8047 |
or | Why isn't $x_2+x_3+x_4\le 2$ a cutting plane? |
In my textbook, to generate cutting planes, they tell you to proceed as follows:
A procedure for generating cutting planes:
Select a ($\le$) constraint that has only nonnegative coefficients.
Find a group of variables such that
a) The constraint is violated when all variables in the group equals 1
and the remaining variables equal to 0.
b) But the constraint is satisfied if any one of the variables in the
group is changed from 1 to 0.
Suppose there are $K$ variables in the group add the following
constraint as a new cutting plane:
Sum of variables in the group $\le − 1$
My Question: Why isn't $x_2+x_3+x_4\le 2$ a cutting plane? Since if we go by 2a) , and put $x_2=1 , x_3=1 , x_4=1$ and $x_1=0$ , then it violates the inequality? Since $11>7$
| VQAonline_00048299.png | It is a cutting plane, but it is implied by $x_2+x_4\le 1$ and $x_3\le 1$ so not very useful.
| https://or.stackexchange.com/questions/3267 |
or | Can I apply decomposition methods for this scheduling problem | I have a centralized optimization problem for a residential area in the context of a smart grid and load flexibility. So let's say I have 10 buildings and each of them has an electric heating device. Further each building has a photovoltaic PV system that generates renewable energy. Now the goal of the centralized optimization problem is to schedule the heating activities of all buildings such that the overall usage of the total reneable energy (sum of all the PV generation of all buildings) is maximized.
Basically every building has 24 decision variables (one for each hour): x_1, ..., x_24
The quantiy the (continious) power consumption of the electric heating device in each hour. Of course we also have some thermal constraints for the room temperature such that it is not possible to heat with full power during all hours. Moreover, each building has a PV generation that is given exogeneously meaning that this is a parameter: PV_1, ..., PV_24
So the goal of the centralized optimizer is to choose x_1, ..., x_24 for all 10 buildings such that the PV self consumption rate, is maximized. The total electrical power P_total for the residential area for one timeslot is just the sum of the x_1s, ..., x_24s for all buildings. The same is valid for the total PV generation PV_total of the residential area. Now we want to minimize the sum of PV_total - P_total over all 24 hours of the day (this maximizes the self-consumption rate of PV).
I hope you have understood the basics of this problem (if not I can give you more information). My fundamental question now is, whether I can use one of the following decomposition methods to transform this centralized large optimization problem into distributed smaller problems that could be solved by the buildings themselves. Basically I would like to know if I can use one of these methods:
ADMM: Alternating methods of multipliers
Dual decomposition
Dantzig-Wolfe decomposition
Benders decomposition
I'd appreciate every comment.
Update: Here is the complete optimization problem
x_t_b and y_t_b are the decision variables for all timeslots t and all buildings b. The objective is to minimize the surplus power in the residential area. The surplus power is calculated by subtracting the total electrical deamand of the area from the total PV geneartion. But only the positive surplus power should be minimized. I use the Big-M approach to incorporate this into the model with the two big M parameters and an auxillary binary variable h^positive. I have two thermal storage systems (modelled by T^UFH and V^DHWuse) which have upper and lower limits. x_t_b is the decision variable for heating up the T^UFH_b and y_t_b the decision variables for heating up the V^DHWuse_b. Only on of them can be heated up at one time slot. To model this I use a binary auxilliary variable h^Aux for each building and each time slot. The total demand P^total comprises the electrical demand of the heat pumps and the inflexible demand P^Demand that is a parameter.
| VQAonline_00048313.png | Thank you for adding the formulation. Assuming $\Delta t$ is a nonnegative coefficient, you can simplify the formulation by omitting $h_t^\text{positive}$, $P_t^{\text{Surplus}^-}$, and the associated constraints. Instead, you need only impose
$$P_t^{\text{Surplus}^+} \ge P_t^\text{PVtotal} - P_t^\text{total} \quad \text{for all $t$} \tag 1$$
to get the desired behavior of minimizing the positive surplus.
It looks like you still need some constraints to enforce the relationships between $T$ and $V$ and the rest of the model. Currently, $T$ and $V$ appear by themselves.
If you substitute the expressions for $P_t^\text{PVtotal}$ and $P_t^\text{total}$ (or use implicit/defined variables) and treat $(1)$ as the linking/complicating constraints, the rest of the problem decomposes by building, so you might benefit from applying Dantzig-Wolfe decomposition with one block per building.
Update to answer your additional questions:
By substitution, I meant replacing $(1)$ with
$$P_t^{\text{Surplus}^+} \ge \sum_{b=1}^B P_{t,b}^\text{PV} - \sum_{b=1}^B \left((x_{t,b}+y_{t,b})P_b^\text{HPmax}+P_{t,b}^\text{Demand}\right) \quad \text{for all $t$} \tag{1$'$}$$
To treat $(1)$ or $(1')$ as linking constraints, some automated Dantzig-Wolfe implementations allow you to specify the block-angular structure by using constraint attributes. For example, see this Getting Started example from the SAS documentation.
Dantzig-Wolfe decomposition applies when you have a set of linking/complicating constraints whose omission makes the resulting problem much easier.
In contrast, Benders decomposition applies when you have a set of linking/complicating variables such that fixing the values of these variables makes the problem much easier. In principle, either decomposition algorithm can be used for any subset you choose, but the best performance is obtained when your problem has some structure where only a small percentage of constraints or variables are complicating. The Dantzig-Wolfe decomposition I suggested seems the most natural for your problem, and it matches your intuition of wanting to solve the buildings separately.
| https://or.stackexchange.com/questions/4395 |
or | A variant of weighted perfect bipartite matching | I am currently working on weighted perfect bipartite matching, i.e., assignment problem.
Formally speaking, it could be formulated as follows:
$$
min \sum\limits_{i=1}^{N}\sum_{j=1}^{N}c_{ij}x_{ij}
$$
, where
$$
\sum\limits_{j=1}^{N}x_{ij} = 1 (i=1...N),\\
\sum\limits_{i=1}^{N}x_{ij} = 1 (j=1...N),\\
x_{ij}\in \{0,1\}
$$
Here, $c_{ij}\in R$ is given as the cost matrix.
But now, my problem has an additional constraint on it : $c_{ij} < c_{ij'}$ if $j < j'$.
That is, each row of the cost matrix is monotonically increasing. For example, the following cost matrix:
(By analogy with workers and jobs, it is like that jobs in right is more difficult so every workers needs more time to get it done.)
The classic Kuhn-Munkres algorithm can be used to solve assignment problem and it can be applied to this surely. But I wonder if any faster algorithm (or related research) exists. I have tried some greedy approaches but it doesn't seem to work.
Thanks!!
| VQAonline_00048332.png | I don't think the monotonicity will help much, for the following reason. Start with any arbitrary assignment problem. Add a constant amount $K$ to $c_{i2}$ for all $i$, with $K$ sufficiently large to make $c_{i2} > c_{i1}$ for all $i$. Since someone has to be assigned to sink 2, this effectively adds a constant amount $K$ to the objective function, and so any optimal solution to the modified problem will be optimal in the original problem (and vice versa). Now repeat, adding a (different) constant amount to each column of the cost matrix to make it bigger than the previous column, until the monotonicity condition is satisfied.
What this shows is that every assignment problem is equivalent (in the sense of having exactly the same feasible region and exactly the same set of optimal solutions) to an assignment problem satisfying the monotonicity condition. If someone had found a way to exploit monotonicity, it would be used for all assignment problems. As far as I know, there is no such algorithm for the general assignment problem.
| https://or.stackexchange.com/questions/6945 |
or | Transforming a Quadratic constraint to SOCP | I have a problem similar to Markowitz portfolio optimization that I would like to transform into second-order cone programming. I have a linear objective function with a quadratic constraint (assuming that I can take the square on both sides of the constraint to make it quadratic).
Assume that $X$ is a vector of decision variables. The objective function and the constraint are below. How can I transform it into a second-order cone constraint? \begin{align}\min&\quad c^\top X\\\text{s.t.}&\quad\sqrt{\sum_{i,j}^n(W_i\cdot X)^2+(W_j\cdot X)^2+2\rho_{i,j}(W_i\cdot X)\cdot(W_j\cdot X)}\le b\end{align} where
$W_i$ and $W_j$ are matrices of constant values of the same dimension as $c^\top$
$\rho_{i,j}$ are correlation coefficients, the matrix generated by it can be assumed to be positive semi-definite
$b$ is a constant.
For example, when $n=2$, the constraint is given by $$\sqrt{(W_1\cdot X)^2+(W_2\cdot X)^2+2\rho_{1,2}(W_1\cdot X)\cdot(W_2\cdot X)}\le b.$$
I would like to understand this both when it is expressed in a more compact matrix form and also when written in the more simplified summation form (as in the question).
For example,
| VQAonline_00048303.png | Revamp of my answer given the example now provided.
Let there be $n$ VaR factors. Let $R$ = $n$ by $n$ matrix of correlations (the 2nd matrix in your example) of the VaR factors.
Let $W$ = $n$ by $1$ vector whose ith element is $W_i$.
The VaR portfolio constraint can be expressed as $$W^TRW \le b^2.$$
This constraint can be rewritten in terms of $X$ as follows:
Let $M$ be the 1st matrix in your example. Then it is the case that $$W = MX.$$ Using that, the VaR portfolio constraint can then be expressed as a convex quadratic inequality constraint in terms of $X$ (resulting in QCQP, or actually, QCLP)
$$X^T(M^TRM)X \le b^2.$$
Let $F$ be the upper triangular Cholesky factor of $M^TRM$. I.e., $M^TRM = F^\top F$. Then the quadratic inequality constraint can alternatively be expressed as a Second Order Cone Constraint
$$\|FX\|_2 \le b.$$
That is because $X^\top M^TRMX = X^\top F^\top FX = (FX)^\top(FX) = \|FX\|^2_2$.
Alternatively, if $G$ is the upper triangular Choelsky factor of $R$, the Second Order Cone constraint can be expressed as $$\|GMX\|_2 \le b.$$
| https://or.stackexchange.com/questions/3737 |
or | How to formulate problems in the language of mathematical programming? | The question says it all. I am having difficulties formulating general problems (meaning no numbers just variables). When I read the solution, I understand but I can't figure how to formulate myself in new problems. I need some tips or what to look for, some guidance in general. By formulation I mean finding the objective to be minimized/maximized and the constraints. Here is an example with the solution (you can just look at the solution to understand what I mean):
Formulate the problem of finding an optimal timetable for a school. The timetable is represented by variables $x_{i,j,k} \in \{0,1\}$. The index $i\in \{1, ...,6\}$ stands for the timeslot (with the duration of one lesson) on a day from the morning to the late afternoon. The index $j=\{1, ...,5\}$ stands for a weekday. The index $k\in \{1, ...,6\}$ stands for the subject. The index $\in \{1,2,3\}$ stands for the classroom.The decision variable $x_{i,j,k}$ is set equal to 1 if subject $k$ is given in timeslot $i$ on day $j$. Otherwise $x_{i,j,k}$ is set equal to 0. Formulate the mathematical program under the following constraints: (C1) Subject 1,2 and 3 are given 6 timeslots per week, subjects 4, 5 and 6 only 3 timeslots per week. (C2) At every time, a classroom can be used only for one subject. (C3) The same subject cannot be taught in parallel at the same time. (C4) the same subject should not be taught more than two times per day. Moreover, the total number of lessons taught in timeslots 1, 5 and 6 should be minimized.
(The image has the solution)
| VQAonline_00048300.png | This is quite a broad question, and I'm not sure you'll get the answers you need here. To learn how to formulate mathematical optimization problems takes learning and practice, and there's no concrete answer that we can provide on a Q&A site like this. Your best bet is to take a class that teaches or uses optimization modeling, or to learn from a good book.
Having said that, there are some relevant Q&As on this site that might help you:
What are good reference books for introduction to operations research?
Recommended books/materials for practical applications of Operations Research in industry
I've formulated my optimization model; now what?
You can also check out the questions tagged modeling. Good luck!
| https://or.stackexchange.com/questions/3438 |
or | When using column generation, can I delete a node with negative reduced cost from my subproblem? | I am solving a minimization problem with a column generation procedure. The master problem is of the form
$$
\min \sum_{i\in \Omega}c_i \lambda_i
$$
subject to
$$
\sum_{i\in \Omega \mid v \in i } \lambda_i = 1 \quad \forall v \in V
$$
Columns $\lambda_i$ represent paths with nodes belonging to set $V$.
Let $\pi_v$ denote the dual variable associated with each constraint. In my subproblem, I am looking for columns that have smallest marginal cost :
$$
\hat{c}_i = c_i - \sum_{v\in V, v \in i} \pi_v
$$
My question is, if $\pi_v <0$, can I safely delete node $v$ from the subproblem (as passing through $v$ will increase the global cost) ? Or do I have to keep it, in case passing through $v$ is the only way to access other nodes that together have a potential negative reduced cost ?
More generally, is there a strategy to delete useless nodes or edges from the subproblem to speed up computation ?
In this article by Francois Soumis et al (a VRP variant solved with column generation), edges and nodes are eliminated heuristically from the sunproblem: [p.15, section 4.3]
They refer the reader to another paper ([14]) for the details of these "heuristics," but the paper is nowhere to be found. I am interested in such techniques as my problem is also a VRP variant (my subproblem also consists in finding some sort of shortest path).
| VQAonline_00048306.png | If your sub-problem is a shortest path problem on a complete graph, without resource constraints, you can delete vertices which don't decrease the reduced cost. Indeed, for any path containing such a vertex, removing the vertex gives another path which is both feasible for the sub-problem and which corresponds to a master problem column with smaller reduced cost.
If the graph is not complete, in general you cannot delete vertices because you might even disconnect the graph. Analogously, if you have resource constraints, removing a vertex might (in the extreme case) disallow the only resource-feasible paths. Whether you can do vertex removal under special circumstances is, I think, problem-dependent.
From my experience, heuristic vertex or arc removal can give good results. Especially if your sub-problem has high complexity, say pseudo-polynomial or worse. Just make sure that you solve the sub-problem exactly (i.e., with no heuristics) at the end of the exploration of each node, to make sure that there are no more negative-reduced-cost columns.
| https://or.stackexchange.com/questions/3993 |
or | Safety stock for lumpy demand |
I have a product for which the monthly demand pattern for the last year looks like the following. The product is ordered only 22 days out of 366 days in batch sizes of 272 kgs. Since there are so many months with 0 demand, the demand distribution is heavily skewed. The mean and standard deviation come out to be 634 and 1167 (rounded off), respectively. I have been using this formula (which is the most widely used, I believe) for calculating the safety stock-
$$SS = z_\alpha\sigma_{LTD} $$
where-
$$\sigma^2_{LTD} = \mu_L\sigma_D^2$$
Taking a lead time of 2.8 months and z = 2.33 (99% Service Level), I get SS = 4550 kgs. Now it doesn't make sense to hold 4550 kgs of inventory when the demand is so lumpy. I know that the above formula is best suited for demands that are approximately normally distributed and understandably results in really high SS values. This is a problem I have been facing with multiple products for which there are several months with very little demand or 0 demand. What is the best way to optimize the inventory for items with lumpy/erratic demand and calculate the safety stock and reorder points for the future?
| VQAonline_00048312.png | Just like any other demand distribution (e.g., this one), you want to set the base-stock level ($S$) equal to $F^{-1}(\alpha)$, where $F(\cdot)$ is the cdf of the lead-time demand distribution and $\alpha$ is the desired service level; and then the safety stock is given by $SS = S - \mu_{LTD}$.
(In the case of normal demand, as in your question, $F^{-1}(\alpha) = \mu_{LTD} + z_\alpha\sigma_{LTD}$, so $SS = z_\alpha\sigma_{LTD}$, as you said.)
So, my recommendation is to fit a distribution $\hat{F}$ to your demand data and then set $S = \hat{F}^{-1}(\alpha)$ and $SS = S - \mu_{LTD}$. In your case, the demand distribution will have a point mass at 0.
You can set $\mu_{LTD} = L \mu_D$ and $\sigma_{LTD}^2 = L\sigma^2_D$ (where $\mu_D$ and $\sigma_D$ are the mean and SD of the demand per period and $L$ is the lead time). But you could also try to estimate these directly from the data, e.g., estimate the mean and SD of the demand over an $L$-period stretch.
By the way, there is some literature on this topic. A Google search for "inventory optimization lumpy demand" or something similar will turn up some hits that are probably more rigorous and general than my approach.
| https://or.stackexchange.com/questions/4267 |
outdoors | Water filters: is there always a tradeoff between longevity and safety | My research thus far has acquainted me with a kind of trade-off: one can try to minimize the amount of contamination (from bacteria/parasites) or one can try to minimize the amount of particulates that could clog the filter. I concede there are many factors to consider, but it essentially boils down to this:
faster moving water has less contamination risk from bacteria/viruses as it's constantly being diluted, however faster water tends kick up more sand/silt particulates which over time can pose a legitimate clog hazard to the filter.
Other things to consider would be depth and temperature. If we go too deep we would encounter contamination from bacteria living on the nutrient rich bottom, but if we go too high, the higher temperatures enable bacteria/parasites to grow. Here is a cool picture illustrating this:
Source
Question
Is there any way to have the best of both worlds; such that we both minimize the risk of contamination and clogging? I would imagine we'd have to put more effort in to it, so an assessment of whether or not it's worth the effort might be informative too.
| VQAonline_00048583.png | If the water is muddy or there are swimmers, then the usual solution is to prefilter before treating.
A handkerchief is usually sufficient for filtering out all of the visible swimming bugs and sand/dirt although it won't filter out any of the things that will make you sick. Then you can treat/filter to kill the giardia/bacteria.
Of course, the precautions necessary depend on the area you are in and how severe the risks are.
| https://outdoors.stackexchange.com/questions/20644 |
outdoors | Why are common grackles standing on our bird feeders with their heads pointed straight up? | I live in Northeastern United States, where it's spring at the moment. We keep bird-feeders throughout the year, so those that over-winter always have something to eat.
As is usual at this time of year, a massive group of common grackles (Quiscalus quiscula) recently arrived, along with other birds of similar size and color, including starlings and red-winged blackbirds. There were hundreds of them, quite a magnificent sight. Some have already dispersed, especially the red-wings, but a large number will stay until the late fall migration.
Over the last few weeks, we've been witnessing a behavior we don't remember having seen before. At least five grackles perch near each other on top of a grouping of bird feeders or, less often, on the ground. They stop eating and stare straight up into the sky. Some puff up their bodies and flap their wings. They screech at each other, but it doesn't sound like the usual grackle call we're used to hearing.
After a minute or so, some fly off to join the groups scattered in the yard or trees, and the others will continue eating. When they all leave, it's only for a few minutes, and then it happens again. It could be the same group returning or a different group altogether, as we can't strictly identify them. We've seen it a few times over the course of a few hours on a number of different days.
At first we thought they were on the lookout for some kind of predator up high in the trees or in the sky. However, because they only see out of the sides of their eyes, if their heads are straight up they can't be watching the sky, or even the tall branches above them, so we've pretty much ruled out that theory.
Does anyone know what this behavior means?
Unfortunately, they're quite skittish, so every time we try to take a picture, they fly off. They very much resemble the picture below.
Picture Source
| VQAonline_00048512.png | Those grackles are engaged in a courting behavior, most frequently called “bill tilt.” It's also been called “head up” or “head up threat.” While establishing pairs for mating, males vie for the attention of the females. Usually as the birds arrive, a group of males will chase the females. Gradually the males drop off until there are fewer males vying for the attention of each female. Once they settle in at the feeding and nesting areas, the males begin the process of establishing dominance, thus increasing their chance of attracting the specific female who'll become his mate. The males won't do the head tilt unless at least one other male and one female is present. The females may also do the head tilt, but once the pair is established, they both discontinue it. In each group, the male who can tilt his head farthest back and hold it the longest is considered dominant and the other males respect that.
Although the grackles may engage in some physical sparring behavior to establish dominance, much of that is avoided by this behavior.
From page 208 of Stokes Backyard Bird Book: The Complete Guide to Attracting, Identifying and understanding the birds in your back yard.:
Watch the common grackles at your bird feeder. Every once in a while they'll look up as if they were looking at the sky. (They are not really looking at the sky; when birds do that they tilt their head to one side.) This display, called “bill tilt”, is part of their language. It is usually done between two males or two females when they are competing for dominance over a mate or at a feeding site. The display is held for several seconds, and then the birds resume feeding. Bill tilting is especially likely to occur when new birds arrive on the scene.
From Pennsylvania State University
Groups of grackles foraging in a common feeding area frequently display dominance and aggression behaviors toward each other. One of these behaviors is the “bill-tilt.” Interacting birds tilt their heads upward and point their bills toward the sky. The more dominant the bird, the more upwardly tilted their heads!
The ruffling of feathers is also a courting or nesting behavior.
Males put on a display for females by fanning their wings and tail, ruffling feathers and tilting their bills. Females quiver their wings in response.
Source
World-renowned ornithologist, Arthur Cleveland Bent, compiled a large group of studies and visual reports of grackles and their behavior dating back to the late 1800s. The following is a quote from Witmer Stone in 1937, published by Mr. Bent:
As early as March 5, I have seen evidence of mating and sometimes two males have been in pursuit of a single female, resting near her in the tree tops, where they adopted a curious posture with neck stretched up and bill held vertically.
As early as March 13, many of the Grackles are flying in pairs, the male just behind the female and at a slightly lower level. They are noisy, too, about the nest trees and there is a constant chorus of harsh alarm calls, 'chuck, chuck, chuck,' like the sound produced by drawing the side of the tongue away from the teeth, interspersed with an occasional long drawn 'seeek,' these calls being uttered by birds on the wing as well as those that are perching. Then at intervals from a perching male comes the explosive rasping "song" 'chu-seeeek' accompanied by the characteristic lifting of the shoulders, spreading of the wings and tail, and swelling up of the entire plumage.
The sounds are described and Illustrated in Peterson's Field Guide to Bird Sounds of North America
Interestingly, the specific calls will be used between males and females or males and males while in a group. Much like the head tilt, the male uses it only in the presence of other males. Once he has found a mate, he doesn't use either again, and neither does she.
| https://outdoors.stackexchange.com/questions/15838 |
outdoors | What is this tree with a spiral shaped trunk in Massachusetts? | On a recent hike at the Audubon Wildlife Sanctuary in Princeton, Massachusetts, my husband came across this tree.
The trunk is twisted in a spiral/curly fashion. It was in a forest of many other trees, but this was the only one that looked like that.
What is the name of the tree? Is that just the way it grows, or an indication of something wrong with it?
| VQAonline_00048524.png | I suspect that tree grew with something else twined around it. That something else has meanwhile died or been removed. Bittersweet is a likely candidate for what might have wound around the tree earlier in its life. There is more information on bittersweet in this question.
I can't tell exactly what type of tree it is without seeing the leaves. However, it is a hardwood. The leaves we can see appear to be maple, but it's hard to tell, and they don't look like they are from the tree in question.
| https://outdoors.stackexchange.com/questions/16867 |
outdoors | Do golden color pine trees associate with the name of Fluffy? | I went to a nursery over the weekend and purchased a golden colored pine tree. The nursery was calling them Fluffy Trees (picture below). This tree name really makes me laugh and smile but I am having a hard time believing that is what it is actually called. In fact I went online and found that the name could be Wate's Golden Pine. Would someone be able to identify this tree and confirm if the word Fluffy is appropriately associated with this specie of tree?
| VQAonline_00048612.png | What you have there is almost certainly a variety of Chameacyparis lawsoniana. These trees are characterized by the flattened scale-like leaves in a fairly dense branching cluster. Wate's golden pine is a Pinus species, all of which have needles for leaves, like you might see on a classic christmas tree.
As to which variety it is - there are lots of them, some of them are yellow (it'll turn green in the middle, retaining yellow on the new foliage), so I can't tell from a photo, and for some it takes some aging to see the true colours and size come through.
I have never heard of them called "Fluffy" trees before, though the foliage is described as fluffy by a few places, based on a quick google search.
| https://outdoors.stackexchange.com/questions/25170 |
outdoors | is it a good idea to cover a tent with a tarp to protect for heavy rainfall? | Last summer, I went camping with my family for the first time. We bought a second hand tent, similar to the one on the picture below. We had a great time, but after a rainstorm that went on for 24 hours, the tent started leaking at the seams at the top, causing the rain to drip down at the inside and soaking our sleeping bags. More rain was coming for the next day, so we were forced to pack up our wet tent and return back home a few days earlier than planned.
Back home, we discovered that the rubbery sealing of the seams had worn out, so we have repaired this, but it might not provide enough protection for heavy rainfall during a next camping trip.
So I was thinking to bring a large tarpaulin and use that to cover the tent at the top.
Is this a good idea ? Or might this get dangerous if heavy wind gets under the tarp ? And should I tighten the tarp directly over the tent (like this) or keep some distance using cords (like this) ?
| VQAonline_00048423.png | First of all
You might need to look into getting a new impregnation for your second hand tent. This can be done either yourself using sprays or wash-in-products (and in your case a probably huge washing machine) or by giving the tent for re-impregnation to professionals, i.e. your local outdoor/tent supplier (this can be expensive though). In any case it might be a good idea to get their professional opinion on if and how you could re-impregnate the tent.
As for the tarp idea
This is totally feasible and also quite cheap. The main disadvantage is the added weight and packing space. But looking at the size of your tent it seems you're likely not carrying it for any significant distance, so the additional weight of a tarp (and the needed additional tent pegs/cords) shouldn't be much of a problem.
I's also possible to just directly tighten the tarp over your tent. This will actually make the entire construction quite a bit more stable I'd guess, as there will be less area of attack for wind. Just make sure to tie the entire thing down well enough and you should have no worries.
Note:
As correctly mentioned by @mattnz draping a tarp directly onto your fly sheet can lower its life expectancy, as friction between the two (cause by wind for example) can degrade the impregnation a bit. But seeing as your fly sheet is not currently rain-proof in the first place I think you'll still be better off with an additional tarp than without: that way at least you should have a working (read: rain-proof) construction for the time being.
| https://outdoors.stackexchange.com/questions/8793 |
outdoors | What's inside this fishing reel? | I saw a teardown of a reel and noticed a part inside the spool:
https://youtu.be/_NKVN9fRD4k?t=327
Does anyone know what the spring does?
| VQAonline_00048632.png | The metal tab is called the click tongue, and the spring holds the click tongue against a sprocket on the reel spindle. Together they are responsible for the clicking sound a reel makes when line is pulled off against the drag, for example, when fighting a large fish. If a fish removes line rapidly, the individual clicks sound more like a continuous whine, a coveted sound to anglers known as a screaming drag.
There are other mechanisms in use in some reels, but I've seen this on Penn reels before. This image search link shows a number of variations.
| https://outdoors.stackexchange.com/questions/28057 |
outdoors | Are these tracks in the mud tortoise/turtle tracks? | I was having a nice evening walk near one of the nature reservations in Andover MA, close to Tewksbury, when I've found such a footprint. I'm really sorry for image quality, though. So it's a wet, bog-like, piece of ground, two lanes of deep small holes (probably the actual footprints) - the distance between them is like 25-30 centimeters (10-12 inches) - and the ground in the middle looks like something was dragged. In the top left corner of a picture the ground seems to be pushed below, and the hole is filled with water.
I'm not from US, and have almost no idea about Massachusetts fauna, but to me it looks like a tortoise. It was lying on the ground, thinking it's slow thoughts - that's how the hole filled with water appeared - then it decided to do some action, got up and moved, dragging it's plastron upon the ground.
That's the best idea I have. But it should be pretty big tortoise, 10-12 inches wide. I wonder if there are any in MA. Does anyone recognize this footprint?
| VQAonline_00048473.png | This does look like some sort of turtle. Snapping turtles can easily get to the size you mention, and are fairly common. The picture doesn't give the impression the tracks are really 10 inches apart. They seem narrower than that, which would open the possibility for a number of other turtles. Box turtles get to a reasonable size, and then there are a list of other more rare possibilities.
| https://outdoors.stackexchange.com/questions/13067 |
parenting | How can my toddler learn to stay under the blanket at night? | My 2yo son slept in a sleeping bag (see image below) until around 1½ years old, then he didn't like that anymore so we switched to using a blanket. He moves around so much while sleeping that the blanket usually isn't covering him at all. This hasn't been a problem so far during summer, but now the cold season is coming and we think he'll get too cold at night. He's already rather cold in the mornings -- with cold hands and cold feet -- so the current mode of operation won't do.
We're not tucking him in "English style" with the blanket going under the mattress, but average "European style" where it's just draped over him. He's very active and dislikes being restrained, so "English style" is not an option.
I've learned to stay underneath my blanket during sleep, but I have no recollection how I learned it -- can we somehow "teach" him, or does it only come naturally with age? How can we keep him under the blanket?
What we're already trying:
We are re-covering him several times during the evening until we go to bed ourselves, and sometimes again during the night if we're up for any reason.
We are dressing him in warmer pajamas and socks to keep him from getting cold at night, but we can't comfortably dress him warm enough in winter. If we dress him warmly (so that he wouldn't become too cold without the blanket) then the blanket makes him too warm and he wakes in a sweat, so we avoid that.
We are trying to find a sleeping bag that fits his current size (92cm) but seem to be rare in these sizes; apparently they're only popular for infants but not so for toddlers. Even if we find one, there's a risk that he'll reject it, just like he ended up doing half a year ago.
| VQAonline_00048642.png | Until she was 5, my daughter would sleep on top of her blanket with her pillow on her feet. She knew about sleeping under the blankets (having seen us doing it), but just wasn't interested.
Dress them warmly and let them figure it out on their own.
| https://parenting.stackexchange.com/questions/3098 |
parenting | How long does breast milk last after taken from the fridge? | There's a lot of information available about how long pumped breast milk can be kept for, generally citing different temperature ranges.
From the CDC (though the same reference is also cited by the Canadian Pediatric Society):
It's cited that milk thawed from the freezer should be used within 24 hours in the fridge, or 1 hour at room temperature.
The Mayo Clinic has an article saying "Other studies have shown that refrigeration beyond two days might reduce the bacteria-killing properties of breast milk", but no references to where this comes from or any further information.
My wife is exclusively pumping, and so there is a lot of milk cycling in and out of the fridge. She is always concerned about using milk taken out of the fridge (generally +/- 1 day old) within an hour or two. We often talk milk out (and let it warm up to room temperature), only to have baby fall back asleep. Is there a basis to how long fridge-temperature milk (stored at 3 degrees C for a day or two) can be out of the fridge for before it has to be used/tossed?
| VQAonline_00048652.png | The Short Answer
Breast milk can be safely consumed if it has been at room temperature for no more than 6 to 8 hours total, which includes all of the time the milk spends above refrigerated temperature. So, if you heat it up to room temperature, then put it back in the fridge after half a period of time, you to account for:
The time it takes to heat up the milk
The time the milk spends outside of the fridge
The time it takes for the milk to cool back down, once back inside the fridge. Depending on the initial temp, the bottle size, and the fridge temp, this could take another 30+ minutes.
The longer the breast milk stays above refrigerated temperatures, the less time it will be viable in the fridge. Guidelines say that milk in the fridge can last 5-8 days, but that time will be considerably less if the milk isn't properly placed in the refrigerator immediately after pumping. Conversely, the longer the milk stays in the fridge, the less time it will be viable at room temperature. Continue reading for more explanation and details.
The Long Answer
In food service, temperatures that are ideal for breeding micro-organisms are called the Danger Zone or something similar. Different foods have different amounts of time they can spend in the danger zone based on the types of bacteria/organisms that grow on/in them.
Once a food has been taken into the danger zone, you also shorten its refrigerated expiration date. While fresh breast milk that's immediately put in the fridge may last 5-8 days, a bottle that's spent 2 hours at room temp may only last 3-4 days instead.
I don't think you'll find any hard data about how many more days a bottle will last in the fridge based on how long it spent at room temperature. That would have to be some very controlled experiments that, in the end, wouldn't serve much usefulness.
To answer your question, we must make some inferences with the data we do have.
For instance, we also know that if you freeze the expressed milk at all, then after you thaw it out it must be consumed within 24 hours or thrown out.
So, we know:
Keeping milk at higher temperatures decreases how long it will last at lower temperatures
Keeping milk at lower temperatures does not necessarily preserve the initial maximum safe time at higher temperatures
Putting that together, and some general assumptions:
The longer the milk has been in the fridge, the sooner it will go bad. If it's only been refrigerator for a day, then it should still be okay for about 6 hours. If it's been in there for 5 days, I'd only give it 2 hours.
Your wife shouldn't have to worry about using day-old milk within two hours. I'd be surprised if you didn't get at least four hours. However, if the room/milk temperature is greater than 77 F/25 C, then it will last significantly less than the noted 6 hours.
Other factors to keep in mind that will affect how long milk last:
The cleanliness of the nipple area before/during pumping
How well sanitized the storage containers are if they're reusable
How well sanitized and maintained the pieces of the pump that contact the milk are
Whether or not you store it in the back of the fridge (because the front meets warmer air every time the fridge door is open)
How much you warm up the milk, if "serving" it above room temperature
Personal Experience
We never had problems with refrigerated milk spoiling within 1-2 hours. When my son was under 1 year old we'd often leave a bottle in his crib with him at night. The ones he didn't finish would still be okay 4-6 hours later. We usually didn't give it to him again, but if he woke up and decided to finish the bottle before we had a chance to take it there were never any problems. Rarely, if ever, did the milk stay in the fridge for longer than 2 days.
However, we did have times when milk stored in an insulated cooler bag with ice packs would spoil much faster than we expected, which made some of our longer car trips surprisingly more difficult.
| https://parenting.stackexchange.com/questions/18263 |
parenting | When is a child ready to start playing with bricks? | Just out of curiosity: at what age is a child ready to play with its first bricks? The light, large, colored wooden ones, like these below?
By playing I mean actually creating something of of them: a structure of sorts, animals, corridors, or whatever the imagination suggests.
| VQAonline_00048649.png | When they can grasp them is the short answer.
There are various stages of play but as a first starting point as soon as they have the coordination to pick them up one by one to begin exploring colour, shape texture and (of course) taste!
Creating structures requires the ability to do imaginative play and is a considerably later developmental stage so I wouldn't expect to see that until much later around 3 years or so based on articles from the LEGO® DUPLO® page.
| https://parenting.stackexchange.com/questions/10882 |
parenting | food feeders can be used for baby lead weaning? | Can food feeders be used as first steps to baby lead weaning (6-7 m.o baby)? Or there is really no connection?
If not, is there any benefit in food feeders over puréed foods?
I mean food feeders like Kidsme Feeder or Munchkin Fresh food feeder
This award-winning product allows your baby to enjoy lots of delicious foods without the choking risk. Simply put a piece of fruit, vegetables or meat into the mesh bag and snap shut. Your baby can chew, suck and enjoy all the whole food goodness and taste, with only the tiniest, digestible pieces coming through. Your baby gets great flavor and you get great peace of mind.
| VQAonline_00048650.png | I'm not an expert (we did BLW but not in a terribly organized manner), but I would tend to say, not very much. Baby-led weaning, from what I know, is mostly about teaching the baby to learn how to eat; and while feeders are nice to use for teething (which is what we used them for), they don't really teach the baby how to eat very well.
To the extent that they do help with baby led weaning, they probably are most useful early on when the baby is first learning how to move the gums/jaw to chew as an alternative to soft foods. Once that has been learned, they don't really offer very much in terms of help in that regard. In addition, it would be better to learn to chew on bananas or other soft foods so that the baby can get used to swallowing chewed food.
| https://parenting.stackexchange.com/questions/12069 |
parenting | Toddler's head falling back in car seat | My 2.5 year old is in a forward-facing Maxi Cosi Pria 85 carseat. The problem is, if he falls asleep while we're driving somewhere, his head falls back. Every site that mentions bad sleeping positions in the carseat fails to mention what to do for heads that fall BACK. Even if I stop and reposition him, his head goes right back to where it was. His face is parallel to the roof of the car. I've also tried keeping it to the most reclined position for forward-facing but that does not help.
I would like to know if this is safe and if not, what can be done about it.
EDIT: I added a picture to show what I'm talking about. I tried adjusting the back part so each picture shows it in a different position. It happens in both positions. The strap is tight and the chest clip is in proper position.
| VQAonline_00048656.png | Without seeing it's hard to say anything for sure, but based on how every car seat I have encountered is constructed I am inclined to ask whether your boy's belt straps are sufficiently tight.
For his head to be that far back the seat would either need to
Not have sufficient padding/bracing behind his head, which is a problem in and of itself
Be letting his chest move forward and away from the back of the seat so that his head can move back that far
Have a lot of padding around his torso that doesn't exist behind his head.
The last could be possible if you're strapping him in while still wearing a very puffy coat (but in August?) but the recommendations are that you don't leave kids in thick coats when strapping them down anyway, precisely because then you can't tighten the straps sufficiently tight.
Make sure he's in tight enough and that the chest strap/buckle is high enough up on his chest to keep it firmly back against the seat.
| https://parenting.stackexchange.com/questions/26687 |
parenting | Is it ok to play a computer game with a 3yo | My 3yo daughter has recently noticed me playing Craft the World, a game which is (mostly) about dwarves working and building their home, with hardly any violence. She wanted to know what it's about, I started explaining, and after a while we've started playing together.
She really enjoyed building dwarves their home, furnishing it, dressing dwarves and giving them tools to work better, etc. etc.
So far, over the last week or so, we've played 3 or 4 times for 15 minutes max each time. I'm doing most of the clicking but decisions are made together. I encouraged her to use the mouse, but with little success.
I'm having doubts about this. While I'm against giving a child a phone or tablet to get rid of them, I didn't really feel bad playing this game with her. I had the opportunity to talk about some things she never heard about before, explain with a good example that one has to work to have something.
Should I let her play with me at all? Do you think that this activity, as I have described it, is acceptable for a 3 yo?
four-years-later edit, 2020.08.22
Our daughter did not develop an unhealthy attachment to computer games. She is now 7 and is allowed to play age-appropriate nintendo DS, tablet or PS4 games, but on an ask-first basis. She does ask a few days a week and plays 30-45 min at a time. Whenever we ask her to stop gaming, she does it without protest - we do agree to "let me finish it" or "one more minute" and she does not abuse the permission. I'll try to write in a few years, because we apply the same strategy to our now 3-yo son.
| VQAonline_00048658.png | The primary reason "screen time" is considered bad for children is that, even when somewhat interactive as games are, it does not stimulate their brain as much as other things do. Kids need all sorts of different activities - physical ones to help develop coordination and strength, social ones to help develop social awareness and social skills, they need to talk to people and hear them talk in order to develop vocabulary and comprehension.
Playing a computer game with you, in a highly interactive way, is to me comparable to reading with a child. If it is a way for you to give her attention and to give you a chance to bond, then it's a perfectly fine option in my opinion, so long as it is reasonably limited; it shouldn't be the main thing she does, but a half hour or so won't be a problem. It's a great way to help her learn problem solving skills, and if she is moving the mouse she's also developing her fine motor control (as opposed to a tablet which tends towards more simple, large areas to select).
The thing to be wary about is the game turning into the only thing she wants to do. You'll want to have a set amount of time that it can be played per day, and stick to that. You'll probably also want to limit yourself in the same fashion, and do so obviously, so that the child understands this is something you need to learn to do, as opposed to this being a hypocritical "do what I say not what I do" type of thing. If you're playing the game 4 hours a day and she's only allowed 1, it'll be hard for her to understand why.
I play Pokémon with my five year old, for example, and while he enjoys it quite a lot, it can be a struggle to limit the time effectively. I only play when he's playing (or when he's asleep); and the asleep-time I limit sufficiently so that we are at roughly the same stage in the game (he often plays when I don't). This has worked fairly well, and I don't think it's had a negative effect on him; but it has led to him wanting to play constantly, and needing to keep hard limits on his play, so be aware of that.
All in all, though, I think gaming as a social activity is a great thing for even younger children, as long as it's in moderation and age-appropriate of course. Getting your undivided attention, and getting to learn things with you, is a great thing for your daughter.
| https://parenting.stackexchange.com/questions/28264 |
parenting | The teacher erased 3 pages of my 5 year old's completed homework | I have a 5-year-old smart child. He does his homework as neat as he can. Yesterday, he stayed up for an hour doing 3 pages of homework as good as he can and today when checking his copy-book, I found that his teacher had erased all the 3 pages and wrote a note on each page (do your homework neatly).
Is this the right way of checking a small kid's homework, and if not, how am I supposed to act?
I attached one of the pages.
In response to comments: The teacher replied that he has to write on the lines not off lines. I went to the school and tried to meet her, but they said it's not allowed during school time, so I had a meeting with the coordinator and the school principal who both insisted that this is the right way of correcting the homework and said that it is better than marking all the homework with red and crossing it out for him. I certainly believe that erasing a kid's homework will cause a negative impact which already happened, he cried when he found it erased and asked "why do I have to do it all again?"
| VQAonline_00048661.png | This teacher is carefully producing a future math-hater. I've worked with enough high school students to know.
I've also worked with enough people in personal counseling to know that whether you care to face it or not, this sort of work is NOT accidental. This is a deliberate, even if unconscious, effort to sabotage your child's learning.
At that age the MOST important asset your child has school-wise is a love of learning. Nothing can substitute for that. A teacher who will destroy a love of learning in pursuit of a perfectly written piece of homework—entirely invalidating the careful hours your son put in to do a good job—is valuing form over content to the point of insanity. One could also say it is valuing mechanics over purpose; whatever you call it, it is totally counter-productive.
Personally, I value my son highly, and I respect his rights and dignity as a person. I would remove him immediately from the influence and power of this teacher.
When I was very young (about 8 years old), my parents sent me to a new school. It was supposed to be an excellent school, with an excellent curriculum, etc., etc. I only went for a semester, and then (to my relief) I went to another, smaller school where I enjoyed myself much more and where, even though the curriculum wasn't as jammed with "high value subjects," I learned a lot more a lot faster. And had more fun. I subsequently finished 4th, 5th and 6th grades in the same year, and went on to graduate High School (12 grades) by the age of 13.
Years later, talking to my mother, I found out why she had taken me out of that prestigious new school after only one semester. It was because she found out I didn't like going there. That was the only reason.
(Thank you, mom.)
You know your child. You care more for your child than anyone else on the planet, and you know what is best for your child. Don't let anyone tell you otherwise. If you don't like the approach used by that school, don't let your child be subjected to it.
| https://parenting.stackexchange.com/questions/30013 |
pets | Is this kind of puppy's stool normal? | Is it normal that 13 days old puppy's stool is liquid and with foam (little bubbles) ?
Today I notice that one of the 4 puppies made that kind of stool and at the same time the puppy screamed loudly like if someone were hurting the puppy. So the puppy felt pain while doing it.
Why?
Should I take the puppy to the vet? Or is something passenger?
| VQAonline_00048772.png | I never had contact with such young puppy as the fastest you can get one is 8(or 7) weeks old, but if it's stool is different from the rest of puppies, I would contact vet, just because of how young the dog is.
But for older dog, that kind of stool is not normal. My puppy got that kind of runny stool after 3rd dose of vaccines, but we gave him overcooked rice, with a little bit of coal, and next day, overcooked rice,chicken and carrot, and it went back to normal. Though he was 12 weeks old. And I'm not sure what kind of food very young puppies can eat.
| https://pets.stackexchange.com/questions/20911 |
pets | Can cats identifiy specific tones/frequencies? | I have a cat who lost her eyesight due to blood-pressure complications when she was about 6 years old (she is 8 now). She adapted very well to living without eyesight, to the point where it would almost seem as if she wasn't blind at all.
She obviously uses her hearing and sense of smell to navigate to food, water and toilet successfully, but she is currently sick with a flu and has lost her sense of smell, and to my understanding some loss of her hearing too (blockages from flu). Because of this, she is having some difficulty finding things.
My question is - can cats identify specific tones or frequencies generated by something like an Arduino & piezo buzzer, and then associate that tone to something, such as food?
I'm looking to create beacon-like devices which emit a specific frequency for a certain duration that a blind cat can potentially use as a reverse-echolocator, and just wanted to validate whether this is probably a waste of time, or something worth exploring?
Update (1/28/2020):
Thank you for all your suggestions. Unfortunately before I could complete a beacon POC, she had to be put to sleep due to a number of pre-existing issues that having flu/not eating catalyzed.
If you're reading this, and you have a blind cat, please ensure that they can wayfind without their sense of smell should they get sick.
RIP Katja, 2011-2020.
| VQAonline_00048800.png | Short answer: yes.
What you intend to do is Classical Conditioning and works just like clicker training. Your cat will probably need a few days to learn that a certain frequency means food, but it will surely learn.
Long answer:
I really like your idea, but I think you need to adapt it to the physiology and needs of a cat. Cats hear better than humans, especially high frequencies. A piezo buzzer emitting a high beep in the "normal" loudness for a human might be uncomfortably loud for a cat. Please keep in mind that cats hunt rodents by listening to their faint sounds in the grass and even underground.
As a rule of thump, I would try the following configuration:
Make the piezo buzzer as quiet as possible
Choose a frequency you can hear
If you cannot make it very quiet, go for a lower frequency and emit the sound for only 100 - 200 milliseconds
A simple piece of soft foam or thick fabric wrapped around the piezo buzzer can help reducing the loudness as well.
If the sound beacon is close to the sleeping place of your cat, either tune the loudness down during late night or deactivate it if you cannot tune it very quiet.
Start with only 1 beacon and see how your cat reacts. If it seems to work and you want to add another beacon for another place, choose a frequency you can distinguish from the first one. Your cat will be able to distinguish it as well.
Since you simply want to mark certain locations with the sounds, it will be enough to place the beacons in the intended location and let your cat get used to them. Hiding them between walls or behind furniture might confuse your cat because of echos.
| https://pets.stackexchange.com/questions/26883 |
pets | Cat looks wounded, what is wrong with it? |
I found this stray cat outside my home with yellowish liquid running down its eyes. I'm not sure if it's pus from an infection or a bad wound from a fight. Tried to offer it some food but it didn't seem interested.
Does anybody have an idea what's afflicting it? I'd like to know if it is serious and what can I do immediately to help it. Thanks
| VQAonline_00048795.png | This is definitely serious, looks like it could be a major infection and there are definite signs of fleas. Bring it to the vet if you can.
| https://pets.stackexchange.com/questions/26372 |
pets | Found this skink in my tomato plant bucket. Is he trapped? Or could he leave if he wanted? | I've been growing some tomatoes in a 5 gallon bucket. About 4 days ago, I found this skink sitting there in the dirt. .
Since he's been there, he's been happily just burrowing around in the dirt and (probably) eating some bugs. He's totally welcome to stay as long as he wants, I think he's pretty neat. My concern is, I read skinks aren't that great at climbing, unlike geckos. If he wanted to leave the bucket, would he be able to? Or do I need to catch him and set him free?
| VQAonline_00048788.png | I think it needs some help getting out of there,maybe you can put some thing in there for it to climb on.
They do an important job eating bugs and snails protecting your tomato plant(s).
Try not to use any pestecides where it lives.
It is best if you try to avoid catching him it can have a negative effect on him some of them are known to drop their tail if they get scared.I do not know the exact type you have there https://en.wikipedia.org/wiki/Skink
| https://pets.stackexchange.com/questions/24273 |
pets | Can I locate my cats' feeding maze close to their litter-box? | I have two cats. We feed them wet food daily (in the kitchen far from the litter-box,) and we provide them free access to dry kibble all day long.
The litter-box and the feeding zone are located in the "no-dog" part of the house and are in the same room.
We've never had any (apparent) problem with that setup: both cats are using the litter-box with no issue, and both cats are eating a few times a day.
I know this is not the ideal situation, but we've never had any problem, and I'm trying to find a balance between the theoretical ideal setup (2+1 litter-boxes, feeding in another room, etc.). Should I worry about that?
I'm also planning to change their bowl with a feeding maze (see picture). Would it be acceptable for them to "play" close to their litterbox? Should I just try and, if they use it, conclude that it is OK with them?
| VQAonline_00048692.png | Many cats are very fussy about their litter box and food proximity, bearing in mind that their sense of smell is substantially better than ours, but not all cats are that particularly bothered by it. So, short answer is "yes" you can do that if the cat(s) tolerate it. Some things to consider:
Keep the boxes clean, scooped daily (or more frequent) and washed weekly.
Keep the boxes in good shape, scratched/old boxes are more likely to hold odors in them.
Keep an eye on the feeding habits. If they start to show signs of food avoidance, look to separate the food from the litter boxes. Mind you, if it's just one cat, then this may be an indication of something else.
Keep an eye on litter usage. If they start going outside of the boxes, away from the food, then this a sign that they don't like this arrangement.
Anecdotally, I had a cat many years ago where the food and litter box were side by side and he never fussed about it, always ate his food, always used the box. On the other hand, our current cats won't tolerate that, at all, so we have the boxes and food in different rooms. It's going to depend on the cat.
| https://pets.stackexchange.com/questions/3037 |
pets | Something is wrong with my cockatiel - she is missing feathers | I have two cockatiels and four budgies. Since I got my second cockatiel, I noticed that she doesn't have feathers under her crest. I thought that the reason for it is that she is really submissive and lets herself to be pecked all the time. This was far from true, because now she got worse (see picture). She is 4 years old.
Please help me, I need some group knowledge about this topic, because I have never even encountered such issue with my parrots so far, so I really don't know what to do next.
The bald spot is reddened by her blood - others pecked the feathers out. But I noticed black base of quill (maybe blood in it?).
| VQAonline_00048798.png | There seem to be basically 2 possibilities:
Another bird pecks her and plucks her feathers
She scratches or plucks herself, which can indicate anything from stress or boredom to malnutrition or parasites.
The first thing to do is getting the bird examined by a vet to rule out any skin condition, malnutrition, allergy, fungal infection or parasites.
Then you need to observe what or who caused the wound. If she plucks herself and the behavior started before you adopted her, she might have been very stressed by her former living conditions. Since it's gotten worse since you adopted her, the change in her environment could have intensified her plucking. Since self-plucking is unfortunately quite common in birds, you can find many resources online, like this video, this article on PetMD or this article on petco and many more.
If another birds plucks her, you'll need to separate them for a while. But this honestly sounds and looks a lot like self-plucking.
| https://pets.stackexchange.com/questions/26806 |
pets | Hostile hamster - Biting hands whilst holding | I recently got a Syrian hamster at the age of seven weeks. Now, at the age of three months, he is not curiously nibbling me, but actually biting until I am bleeding (three times already). What am I supposed to do?
Background story: We had a rather unpleasant first day: he desperately attempted to escape his cardboard box we got him in (see also the opening scene of Jurassic Park). Later that night I tried to reconcile and have him on my hand. Unfortunately he jumped of and we had a chase. Short story, lot of poo, lot of screaming and a trauma for the both of us.
Weeks passed and things got better. I gave him food out of my hand, gave him treats after being in the big ball and all, and I could even pet him while he was eating. This was the moment where I thought I could try to hold him (with one hand covering him a bit), so I could have him in my hands out of the cage. But this is the point where it all changed. He became very vicious when I held him and bit me very hard. From that point on, I couldn't even put my hand in the cage without the hamster biting me.
Is there a chance that he stops this behavior, or is the possibility to bond gone?
| VQAonline_00048761.png | I wouldn't say the possibility of bond is gone. I hate to say this, because I want to be as positive as possible, but when I worked at a pet store there were 2 things we for sure ALWAYS recommended when taking a hamster home: 1) don't hold him on the first night, so he/she doesn't associate you with the stress or become more stressed and 2) don't hand feed him because he'll associate your hand with food, nibbling and biting, and may expect the food- as he would expect food in his bowl- since that's where he's seen food before. BUT, with all that's said I think you can try a fresh start.
Maybe give him a week with little to no handling, give him a break, in a sense. Move things around in his cage so he has a change in scenery and routine, so he doesn't expect his environment to always be the same. Next time you do handle him, maybe try sitting on the floor with him with your legs forming a border and let him explore you and your scent without your hands as part of the equation (except to take him out and put him down) but try to let him know that you two can co-exist without food in hand and so he's free to move around. Anytime you hold him or interact, don't push- simply let it go if he squirms, it's a sign he's had enough and will likely bite if you fight it, just gently place him back in his cage. After testing the floor theory maybe let him on your lap and explore other parts of you- one of my hammies I had, loved to just chill in my hoodie pocket or in the hood. A dark hiding place makes them feel safe.
When you change his bedding and give him fresh food and water, do it with him outside of the cage, in a separate box and in between feedings remove the bowl and fill it outside of the cage and place it back instead of putting your hand in and the food coming from you.
After some time of doing this regularly, from time to time just rest your hand in his cage and see how he takes it. If he runs from your hand, don't chase him, just leave it still so it's non-threatening, and encourage him to explore without picking him up, after a few times of doing this you can pick him up by keeping your hand flat and gently lifting up when he gets on your hand. Keep these visits brief and eventually you'll be able to make each time a little longer until he's used to you taking him out and NOT getting food until he's back in the cage.
Always wash your hands well before handling him, and before it becomes a habit try Keeping a bottle of hand sanitizer near the cage as a reminder to clean off smells and residue from your day. They have a great sense of smell and you want to keep smells from food, other environments and other people off your hands so he doesn't smell you and get freaked out by a threatening or Yummy smell.
Good luck and update us on how things go in the coming weeks.
Also, there will be more bites in the future, when he does, put him back in the cage and wait until the next day to try again, to give him time to calm down and disassociate.
| https://pets.stackexchange.com/questions/18707 |
philosophy | Authors who think Culture is power? | The USA is leading country in military expenditure in the world. To match what the USA spends you have to add up the budget of the next 11 countries on the list combined. ref here
The USA is not just the most militaristic nation on earth but also the first world cultural superpower. The whole world is flooded American films, music, news, fashion, architecture, foods, etc. Even American English is the international language nowadays. In most mainstream literature and art this country is generally portrayed as the hero country of the world givers of freedom and capitalistic prosperity. It's rare to find cases in which the Americans are portrayed as villains not even in non-American films.
In history American culture (mainly Hollywood) has tried to offer an unrealistic vision of the world through art and propaganda which antagonises those considered enemies or apathetic to their Anglo-capitalistic agenda whose distortion of reality still remains up until today. ex. (Native Indians, African slavery, Socialism, Communism, Spanish-American war, The Japanese during WWII, the Vietnam war, The Russians, The Iraqis, The Iranians, etc.)
The relationship between culture and military power is nothing new. The Romans took a great deal of culture from the Greeks and the Roman Empire influenced culturally not just their colonies but neighbouring areas.
Are there any books, films authors etc who ponder on how culture is power and vice-versa?
Sid Meier's Civilization® is an strategy game about world domination. In this game you can also achieve a cultural victory
| VQAonline_00048886.png | America's Danger of Imperial Overstretch Bloomberg News. https://www.bloomberg.com/opinion/articles/2016-07-13/america-s-in-danger-of-imperial-overstretch
Books by the American historian Chalmers Johnson. http://americanempireproject.com/authors/chalmers-johnson/
| https://philosophy.stackexchange.com/questions/65208 |
philosophy | Can inductive arguments be made in first order logic and, if not, why not? | After reading a question by rus9384 Why is faulty generalization called an informal fallacy? I wondered whether induction can be part of any argument in first order logic (FOL).
rus9384 symbolized an example of an inductive argument: ∃x: F(x) ∴ ∀x: F(x)
Given the rules for existential elimination and universal introduction, I don't think this argument can even get started, but I may be wrong.
Clearly, we can go in the opposite direction. Here is a proof of going from a universally quantified sentence to an existentially quantified one: ∀x: F(x) ∴ ∃x: F(x)
I am not concerned with whether induction is a fallacy, formal or informal, but to what extent induction arguments can be symbolized or made at all in FOL.
QUESTION: Can inductive arguments be made in FOL and, if not, why not? If they can, an example of their use would be helpful.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
| VQAonline_00048870.png | You can formalize inductive logic, but it is usually though to require the introduction of an ambient Bayesian probability theory. The reason first-order logic alone doesn't work is because first-order logic examines whether an argument is valid or invalid. An argument is valid if and only if the truth of the premises guarantees the truth of the conclusion. By contrast, an inductive argument provides probable support for the conclusion. To evaluate inductive arguments you need a way to evaluate the degree of support a set of premises provide for the conclusion. First-order logic makes no such provision. Hence to formalize inductive logic probability theory is used. Intuitively, what you want to know is how probable a state of affairs P is given the premises.
As a corollary, the argument form you cite (∃x: F(x) ∴ ∀x: F(x)) does not really capture the form of inductive reasoning. First, the existential quantification requires only one entity that is F to be satisfied. Almost no inductive arguments have that form, and usually involve a large number of observations. In fact, in the sciences, inductive arguments typically make testable hypotheses relative to background hypotheses from other scientific domains (This, by the way, is another reason first-order logic cannot really "formalize" inductive reasoning adequately). Hence the form you list here is at best a highly idealized way of thinking about inductive reasoning that is so divorced from inductive reasoning in practice as to be useless. Secondly, inductive arguments most often have the form of predictions about what our future observations will likely be, and don't require a universal quantification over a domain. For example, if you argue, "I've tasted thousands of lemons and every single one has been sour. Therefore, the very next one I taste will likely be sour." This is a perfectly cogent inductive argument that does not require a universal quantification over a domain.
Check out the following page if you want to know more: https://plato.stanford.edu/entries/logic-inductive/
| https://philosophy.stackexchange.com/questions/54112 |
philosophy | What are the conditions for RAA? | My textbook states that:
In this case, however, what about situations where we can get Q ^ ~Q (sorry, unfamiliar with this formatting) without depending on P? For instance, the proof of EFQ:
1 (1) P A
2 (2) ~P A
3 (3) ~Q A
1,2 (4) P ^ ~P 1^2
1,2 (5) ~~Q 3,4 RAA
1,2 (6) Q 5 DN
Why isn't it a problem that line 5 does not depend on line 3, when it is the negation of line 3 that we are proving? If we take the above definition of RAA to be true, don't we need 3 to be a dependency of P ^ ~P?
| VQAonline_00048884.png | It only seems like a problem if we think the set Γ is consistent, in which case we feel like it's P which "makes" the premises inconsistent, and so must be used in the proof. But if Γ is already inconsistent, then we don't need to use P at all. Think about it in cases:
If Γ is consistent, and Γ, P ⊢ Q ∧ ¬Q, then {Γ, P} is inconsistent, so that Γ ⊢ ¬P
If, on the other hand, Γ is already inconsistent (as in your example proof), then Γ ⊢ ¬P anyways (since inconsistent sets of statements can prove anything).
| https://philosophy.stackexchange.com/questions/63571 |
philosophy | Logical Consequence and Tarski's World | I found this question in an old exam paper. I have no idea what is expected from a question like this.
Consider the Tarski's world below. This world illustrates that ¬∃xTet(x) is NOT a logical consequence of the premises below. Explain why/
1. ∀x∀y [LeftOf(x, y] → Larger(x, y)]
2. ∀x∀y [Smaller(y, x) → (Cube(x) ∧ Dodec(y))]
This is worth 6 marks.
I think the obvious things are that you cannot infer ¬∃xTet(x) from the premisses.
Maybe I just don't really understand the question
| VQAonline_00048836.png | In order to show that the conclusion is not a logical consequence of the premises, we have to find a counter-example, i.e. a "world" were the premsies are ture and the conclusion is not.
After having checked that the two premises are satisfied in the "world" depicted, we can conlude that ¬∃xTet(x) it is not true, simply because there are two tetrahedra.
| https://philosophy.stackexchange.com/questions/17857 |
philosophy | Why does negation reverse order of strength? |
1. It is the negation that does the trick. Think of a "condition" as a restriction on the class of things that satisfy it, the stronger the restriction the narrower the class. Normally NC are weaker than SC, but [2.] negation always reverses the order of strength: [End of 2.]
¬{a weaker condition} is always stronger than ¬{a stronger condition}.
I already saw these pictures, but the following (created by me) depict 1: P ⊆ Q ⟺ QC ⊆ PC.
But I still sense that I can delve more into 1: why is 2 true intuitively?
| VQAonline_00048858.png | Consider splitting a set in two based, one subset of which the elements satisfy the predicate, and one subset of which the elements don't satisfy the predicate. If the predicate is stronger, the Yes-set will be smaller ("the stronger the restriction, the narrower the class"). Therefore, the No-set will be bigger. And since it works both ways, this means that the negation of the predicate is now weaker.
This does not only work for predicates that become stronger or weaker. If we have a strong predicate, that means the Yes-set is small. Since the No-set is the complement of the Yes-set, it has to be big, and therefore the negation of the original predicate (that is, the predicate of the No-set) has to be weak.
The same, mathematically.
Suppose we have a set X and a predicate P. Then Y = {x ∈ X ∣ P x} and N = {x ∈ X | ¬P x} partition X, that is, Y ∪ N = X and Y ∩ N = ∅.
Since "the stronger the restriction, the narrower the class", Y will be smaller when P is stronger. And since N = X ∖ Y, this means that N will be greater, therefore, ¬P will be weaker. A similar argument can be made when P gets weaker: Y will be greater, so N smaller, therefore, ¬P will be stronger.
| https://philosophy.stackexchange.com/questions/36995 |
philosophy | What is the justification for closing a whole branch in a modal truth tree diagram if there is a contradiction in only one world? | I am watching "Modal logic 1.2 - truth trees for system K" presented through Kane B's channel.
The standard propositional truth tree diagrams are not a problem. Where I am having trouble is opening worlds in the tree diagram and closing branches with these opened worlds. I don't see why I am justified in closing a whole branch if some worlds in that branch do not have a contradiction in them.
At about 14:00 in the video the presenter states, "If we derive a contradiction in either of these worlds the whole branch closes."
Shouldn't we close all worlds prior to closing the whole branch?
Here is a screenshot of the tree:
I don't see why stacking the worlds justifies the step. Creating world "w2" was not permitted without the stacking.
| VQAonline_00048877.png | Up to the branch in w0, we have only propositional logic rules.
Then we go on on the right branch first : □¬p.
We apply the modal rule for ◊ with ◊p: we need a new world w1 such that w1 ⊩ p.
But from w0 ⊩ □¬p it follows that w1 ⊩ ¬p and we have the contradiction closing the right branch.
Now for the left one with □q; we apply again the modal rule for ◊ to ◊¬q.
This step needs a new world w2 such that w2 ⊩ ¬q.
But from w0 ⊩ □q it follows that w2 ⊩ q and we have the contradiction closing also this branch.
"Worlds" behave exactly as the "single universe" of classical logic : they cannot tolerate contradictions.
The basic rule for Kripke semantics for Modal logic is :
v(□A,w)=T iff for every world w′ in W we have : v(A,w′)=T.
The rule states that □A is true (at a world w) exactly when A is true in all possible worlds.
From it, we have the corresponding one for ◊ :
v(◊A,w)=T iff for some world w′ in W we have : v(A,w′)=T.
The rule insures that ◊A is true just in case A is true in some possible world.
| https://philosophy.stackexchange.com/questions/57135 |
philosophy | Who does Wil Wheaton represent in "Big Bang Theory"? | Following the aesthetics-challenge my first question on this site:
In several episodes of "The Big Bang Theory" Wil Wheaton appears.
In the credits it is stated that he plays "himself". But I have problems with that statement. It seems to me that there are two different entities: The A-ctor on the set of Big Bang Theory and the C-haracter he portrays. They must be different entities because they have different properties: A has no friend named Sheldon Cooper. C was never actor in a show named "The Big Bang Theory". So following Leibniz A and C cannot be the same entity.
But there are very strange consequences of this. For one the character he plays is said to be Wil Wheaton. If someone asks me, which character is played by Liam Neeson in "Schindler's List" I would answer "He plays Oskar Schindler, a historic person of the third Reich". Accordingly if someone asks me which character is played by Wil Wheaton in "The Big Bang Theory" I'd answer "He plays Wil Wheaton, an actor known from Star Trek". I would not answer "He plays a character very familiar to Wil Wheaton". If a character in a show is introduced as Mr. So-and-so he is Mr. So-and-so, not a character very similar to Mr. So-and-so. If we need to drop this "rule", we were also forced to say: "In Skyfall Daniel Craig plays a character similar to James Bond." That sounds most weird to me. And it feels wrong.
Also with this approach we create a whole new set of entities: To every C there is also an A then, and that's not exactly ontological parsimony.
Are there any theories dealing with cameo-problem? And if so: How is it dealt with?
| VQAonline_00048834.png | I generally take characters on shows to be a different instance of the same person, that is, the name doesn't matter, but in the context of the show the actor is that same actor but in the context of the parallel universe developed for the show.
Let's use object orientated because that is freakishly easy notation for this problem.
(Consensus Reality).(Wil Wheaton) portrays (The Big Bang Theory).(Wil Wheaton).
So if someone asked me what character Wil Wheaton plays in the The Big Bang Theory, I would say "He plays Wil Wheaton" which is the verbal representation of the statement above in OO notation because context is reasonably clear from the discussion.
For example, my name is Calvin. Moreover, the protagonist of my perception of reality is Calvin. So I have two Calvins.
(Consensus Reality).Calvin and (Calvin's Perception).Calvin.
In Consensus Reality, Calvin is portrayed by the same Calvin as in Calvin's Perception, so I would say that the credits of Consensus Reality could list Calvin as played by himself.
However, there are certain differences. For example, (Calvin's Perception).Calvin was not born, but just slowly emerged into consciousness over time (due to the nature of memory). However, this difference can be reconciled by viewing these different Calvins as different instances of the same Calvin across multiple abstractions of reality.
Or at least, that makes sense to me.
| https://philosophy.stackexchange.com/questions/15551 |
photo | What does the Gamma histogram represents? | I do not understand what does the Gamma Adjustment histogram represents, as it differs a lot from the regular brightness histogram. Would very much appreciate an explanation :)
Here taken from Canon's Digital Photo Professional:
| VQAonline_00049686.png | I found the answer I was looking for here:
https://www.cambridgeincolour.com/tutorials/histograms2.htm
Basically, it says that the RGB histogram displays the summation of the three Red, Blue, Green histograms, while the Gamma histogram displays the luminosity histogram, which gives different weight to different colors, as the human-eye is more sensitive to green than red.
| https://photo.stackexchange.com/questions/108068 |
photo | How can I photograph bright lights properly? | I built a toy light saber, and I'd really like to get a good picture of it. This is what it looks like when I try to take a picture:
The blade is not actually that color. With my own eyes, it looks red, but through cell phones and digital cameras, it always looks bright orange. Is there a good way to correct the way lights look through a camera?
| VQAonline_00049404.png | There are two issues at play here.
The first is exposure. If your camera completely blows out (oversaturated) the light from the "blade" of the model because the rest of the scene is much darker then it doesn't matter what color the "blade" is, it will show up white in the photo. Why? Because even though there may be more red than blue or green light in the "blade", if there's enough blue and green in there for them to be completely saturated on your camera's sensor at the exposure selected by the camera, the (R, G, B) values on a scale of 0-255 will be (255, 255, 255). Even though there is ten times as much red as there is green or blue, the camera can only count the red up to 255, not 2550! When viewing the image this area will appear white, since all three color channels have the same numerical value. In your case it appears the red and green channel may both be oversaturated but the blue channel is not, thus you get orange as a result.
The second is white balance. If your camera is set to "auto" white balance it tries to determine what color temperature and tint values to use when interpreting the data from the sensor based on the brightest parts in the picture that aren't oversaturated. If the brightest non-saturated part of your picture is not actually white, then the camera will fail to set white balance correctly.
So, what can you do to correct this? If possible with the camera you are using dial in some negative exposure compensation or use manual exposure to reduce the overall exposure. When the light from the "blade" is no longer blown out it will appear more red if that is the actual color of the light from the "blade". You can also attempt to adjust the white balance to match the lighting conditions in the room. Since you haven't told us what type of light is illuminating the "blade" from the inside, you might need to experiment until you find a preset WB setting that works best.
| https://photo.stackexchange.com/questions/71780 |
photo | Can a cheap DX battery damage my camera? | I would like to purchase a spare battery for my new Canon EOS 550D\Rebel T2i for a trip abroad.
I've found this battery on DealExtreme. It costs 6.90$ (with shippment), a small fraction from the street price.
What are the chances this battery will damage my camera?
| VQAonline_00048994.png | The chances are high. Nikon started putting holograms on their batteries so they would be recognized as originals because some fakes burst into flames after some use.
Most importantly, is why are you even considering this? You paid good money for a nice camera and you want to risk it by saving some money on a cheap battery? If the one you have is not enough, even one more will give you at least another 400-shots per charge unless you use the flash more than you should.
| https://photo.stackexchange.com/questions/15277 |