OpenLLM-France/wikimedia huggingface dataset:
# Introduction to Philosophy/Logic/Building More Complicated Formulas

Introduction to Philosophy > Logic > Building More Complicated Formulas
    'I need a hammer and nails or a screwdriver and screws.'
Though we know what is meant by the above statement, it is technically ambiguous - imagine saying it to a not very bright apprentice. In this case no harm would be done and the apprentice might fetch an unnecessary tool. One could think of other situations where such ambiguity could be lethal.
In propositional calculus we use brackets to prevent any ambiguity:
    'I need (a hammer and nails) or (a screwdriver and screws).'
This is just like the usual mathematical use of brackets: you evaluate the contents first.
We don't use brackets around ¬ symbols -- it binds tightly onto whatever is following it.
# Introduction to Philosophy/Logic/Modal Logic

Introduction to Philosophy > Logic > Modal Logic

## Modality

   Still holding the copy of The Grasshopper Lies Heavy, Robert said, 'What sort of alternate present does this book describe?' Betty, after a moment, said, 'One in which Germany and Japan lost the war.' They were all silent. (Philip K. Dick, The Man in the High Castle)
This is the basic premise of modal logic: some things could have been otherwise. In our everyday reasoning, we distinguish between necessary truths and statements that just happen to be true but could have been false. We say that the latter are contingently true, or that their negation is possible. The concepts of necessary, contingent, possible and impossible are very closely related: something is necessary if it is impossible for it to be false, and something is possible if its falsehood is not necessary. Contingency is the negation of necessity, and impossibility the negation of possibility. Modal logic attempts to include the notions of modality (necessary, contingent, possible and impossible, among others) into the structure of classical logic (propositional logic and predicate calculus) and is therefore an extension of classical logic.

## Modal propositional calculus
### Syntax

Modal logic introduces three new symbols into classical logic: $\Box$(necessary),$\Diamond$ (possible) and $\Rightarrow$ (if, then). Formulae are constructed in the usual way, with the following rules added before the closure clause (see the rules for Well-Formed Formulae in propositional calculus):
* If $\alpha$ is a well-formed formula, then $\Box \alpha$ and $\Diamond \alpha$ are also well-formed formulae.
* If $\alpha$ and $\beta$ are well-formed formulae, then $\alpha \Rightarrow \beta$ is also a well formed formula.
Actually, one can define the modal propositional calculus axiomatically using just $\Box$ or $\Diamond$. For example, if we wish to define $\Diamond$ and $\Rightarrow$ in terms of $\Box$, $\Diamond \alpha$ can be defined simply as a abbreviated notation for $\neg \Box \neg \alpha$ and $\alpha \Rightarrow \beta$ as another way of writing $\Box (\alpha \rightarrow \beta )$.

### Rules of inference
## Bibliography

* Hughes, G. E., & Cresswell, M. J.: An Introduction to Modal Logic, Methuen and Co Ltd, London (1972).
* Hughes, G. E., & Cresswell, M. J.: A Companion to Modal Logic, Methuen and Co Ltd, London (1984).
* Smullyan, R.: Forever Undecided (1987). Part IX: Possible Worlds.
Up: Logic Table of Contents
# Introduction to Philosophy/Logic/Nand and Nor

Introduction to Philosophy > Logic > Nand and Nor
Our connectives ¬, ∧, ∨, →, fit easily with our every day way of reasoning about things. For the reductionists out there, it turns out that we can get a single connective to do all the work of our familiar connectives. Indeed there are two ways we can do this.
The first way is using joint denial, known in electronics circles as nand. Its truth table is as follows:
We can see that ¬p is the same as p nand p. etc. ...
The other candidate is alternative denial or nor.
Electronics people like nand and nor. I think it is because it gives them a one-size-fits-all chip, which they can connect up how they like to get the other connectives.
Is there are an advanced civilization on some distant planet that does all its reasoning using nand or nor? If so, would cause and effect ever have become a big issue for them?
# Introduction to Philosophy/Logic/Bibliography

Introduction to Philosophy > Logic > Bibliography
I have difficulty recommending any books on logic. Perhaps that indicates the need for the present work. Perhaps you can recommend one to me. You might want to look at:
Wilfred Hodges, Logic Penguin Books, 1977 ISBN 0140219854
The next two books on the list are definitely rather mathematical:
       The word 'introduction' in the title needs to be taken with a pinch of salt.
Up: Logic Table of Contents
# Introduction to Philosophy/Logic/Formal Logic

Logicians describe various formal systems of logic which are intended to match a precise but limited range of reasoning. Each such system defines a formal language. A scope of such a system—and the corresponding expressability of its formal language—matches the range of reasoning it is supposed to describe.
# Introduction to Philosophy/Logic/Fault Diagnosis

Introduction to Philosophy > Logic > Fault Diagnosis
Our propositional calculus can be quite useful for descriptions of systems and fault diagnoses. Here are some propositions regarding part of a fairly simple plumbing system:
* If there is an overflow in the upper tank, then the buzzer is sounding or there is an electrical problem.
* If there is water dripping from the ceiling, then there is an overflow in the upper tank.
* The buzzer is not sounding.
* There is water dripping from the ceiling.
____________________________________________
As with many things the propositions could be divided into:
* observations, e.g. 'the buzzer is sounding';
* hypothetical if-then statements;
* diagnoses.
Anyway, to show that the argument above is valid, we first assign letters to all the elementary propositions:
* p - there is an overflow in the upper tank;
* q - the buzzer is sounding;
* r - there is an electrical problem;
* s - water is dripping from the ceiling.
Then we can write our propositions out using symbols:
* P → (q ∨ r)
* s → p
* ¬ q
* s
With fairly simple systems, one's intuition usually provides the correct answer fairly quickly. If you think of a chemical plant or a power station, the chains of inference can get quite complicated, yet swift action may be required in the case of a fault. In this case automated reasoning in the form of 'expert systems' can be quite useful. (Of course then there is the problem that the expert system could be faulty. Here we encounter the problem of infinite regress.) When the reasoning gets complicated, the kind of analysis we have done here becomes useful.
If this kind of thing interests you, then perhaps you should study artificial intelligence.
# Introduction to Philosophy/Logic/Mini TOC

Part 1: Logic and Reason · Part 2: Truth and Validity · Part 3: Paradoxes
Introduction · Chapter 1: Logic · Chapter 2: Epistemology · Chapter 3: Metaphysics · Chapter 4: Ethics · Single page print version
# Introduction to Philosophy/Logic/Informal Logic

Introduction to Philosophy > Logic > Informal Logic
For now, see Informal Logic.
# Introduction to Philosophy/Logic/Modes

Introduction to Philosophy > Logic > Modes
   There can be no smoke without fire.
          —old proverb
You will need to know about at least two 'modes' before skipping to propositional calculus.

## modus ponens

First premise: If you drive too fast, you will have an accident. Second premise: You drive too fast. ___________________________________________ Conclusion: you will have an accident.
Well, that was pretty obvious. Here is another example:
smoke implies fire smoke __________________
fire
Generally: 'From the premises "p implies q" and "p", we can infer "q".'

## modus tollens

Sometimes we want to reason backwards:
First premise: If you drive too fast, you will have an accident. Second premise: You will not have an accident. ________________________________________________________________ Conclusion: You do not drive too fast.
The second premise is in the future tense. Only a clairvoyant would assert such a thing in real life. The argument is valid, though it is not possible to know in advance the truth of the second premise.
Here is another example:
smoke implies fire no fire __________________ no smoke
Generally: 'From the premises "p implies q" and "not q", we can infer "not p".

## some bad reasoning

smoke implies fire no smoke __________________ no fire
Someone who reasons like this could end up being burned alive in an accident involving smokeless fuel. Whereas modus ponens and modus tollens are examples of deduction, our last example is an example of abduction. It works some of the time, it can suggest what might be the case, but it is unreliable. This logical fallacy is known as denying the antecedent.
We used to have a safety officer who would come from head office and say 'if it is tidy, it is safe'. He concluded things were safe if they were tidy. This did not impress the computer programmers in the department since to be a programmer you need to have a bit of sensitivity to logic. To conclude things were safe if they were tidy, he would have more correctly said 'if it is untidy, it is unsafe', or 'if it is safe, it is tidy'.
The Wikipedia has a long list of different kinds of logical fallacy. I suggest you have a look at it, and read some of the entries. Not only will you find it amusing, it could stop you from being duped by bad arguments.
Up: Logic Table of Contents
# Celestia/Celx Scripting/CELX Lua Methods/CEL command select
### select

select { object <string> }
Selects the specified object <string> in order to perform other commands on it.
Arguments:

#### object <string>

    The name of a planet, moon, asteroid, comet, galaxy, spacecraft, etc.. No default. If you are currently positioned outside of our Solar System, and want to select an object inside of our Solar System, you must include "Sol/" (our sun's name) in the <string>.
CELX equivalent:
Based on the celestia:select method;
* Find an object with name <string> which must be selected and store in "objectname".
* Use celestia:select method to select "objectname".
Summarized:
Example-1: Select the star Aldebaran.
CEL:
CELX with the celestia:select method:
Example-2: Select planet Mars when in our Solar System:
CEL:
CELX with the celestia:select method:
Example-3: Select planet Mars when in or outside our Solar System:
CEL:
CELX with the celestia:select method:
Back to CEL command index
# High School Engineering/Science and Math in Engineering

Engineering is the application of the principles of mathematics and science to the creation or modification of components, systems, and processes (which are often referred to as a product or an artifact) for the benefit of society. Engineers use a series of logical steps (the engineering design process) to create such artifacts which represent a balance between quality, performance, and cost. This chapter explores and examines the role and connections of math and science to engineering and the need to succeed in the study of those subjects for a professional career in engineering.

#### Learning Objectives

After working through this chapter, you should be able to do the following:
* Explain the goals and the nature of the fields of science, mathematics, and engineering and the differences between them.
* Explain generally how the fields of math and science and engineering benefit from one another as well as need one another.
* Explain what engineers in different disciplines do and the math and science they use.
* Explain the role of science and math in each step of the engineering design process.
* Describe the types of science and math that might be used by engineers in the different engineering disciplines along with an example for the design of a product or a process.

#### Lessons

* How Math, Science, and Engineering Led to the First Pocket Radio
* Role of Science and Math in Engineering
* Connecting Math and Science with Engineering in High School and College
* Connecting Engineering Career Fields with Science and Engineering
* Connecting Math and Science to the Engineering Design Process
← The Design Process in Action · Role of Science and Math in Engineering →
This material was adapted from the original CK-12 book that can be found here. This work is licensed under the Creative Commons Attribution-Share Alike 3.0 United States License
# Jet Propulsion/Intakes

Air enters a jet engine via the intake or inlet, which is a shaped duct connecting the streamtube (approaching the inlet) to the compressor face. A major objective is to lose as little total (or stagnation) pressure as possible in the process and to act as pre-compressor, whilst minimizing any distortion to the flow entering the compressor. Supersonic intakes often employ cones or ramps to create conical/oblique shock waves to help improve pressure recovery at supersonic flight speeds.

## Functional requirements

Intakes are matched to the jet engine to provide maximum performance. This imposes different requirements on the intake depending upon the operating regime.
* Brake release: maximize mass flow by accelerating the static surrounding air without raising entropy.
* Takeoff & climb: Maximize pressure recovery while minimizing flow distortions due to off angle conditions
* Subsonic: maximize pressure recovery at speed and altitude
* Maneuver: Maximize mass throughput for given speed
* Supersonic: maximize pressure recovery at speed and altitude without suffering unstarts
* Hover (VTOL): Maximum mass flow with minimal hot gas reingestion

### Pressure recovery

The incoming air flow is diffused. For subsonic flows a divergent duct is commonly used and for supersonic flows a convergent divergent duct is used. Supersonic intakes usually require movable structures to perform well. Without such measures lower performance results.

### Distortion avoidance

The intake straightens the flow at high angles of attack and sideslip conditions. Using flow splitters, the low energy boundary layers next to fuselages can also be removed to provide uniform flow at the compressor face.

### Noise suppression

Intakes usually have noise suppression surface treatments to reduce forward noise transmission.

### EMF suppression

Compressor faces have a distinct dignature that can be suppressed by appropriately shaped screens, intake surface treatments and intake vanes.

## Types
### Pitot

A diverging forward facing duct is most often used. The length of the duct is governed by the flow straightening, boundary layer development and diffusion requirements.

### 3D compression (Conical centrebody)

For supersonic applications. Conical shockwaves from the central conical ramp are used to progressively compress the supersonic flow till a terminating normal shockwave makes the flow subsonic. From that shock wave onwards a divergent duct is used to diffuse the subsonic flow.
The cone can be moved depending upon the speed of operation although the cone angle cannot easily be changed.

### 2D compression (ramp)

A ramp is used to generate the inclined shockwaves to provide compression. The ramp angle is varied depending upon speed of operation. At low speeds the ramp can be oriented to provide minimal acceleration of the flow.
# Jet Propulsion/Euler turbine equation

The energy added to a stream of fluid flowing through the blades in a blade row:
$(h_{2}+u_{2}^{2}/2)-(h_{1}+u_{1}^{2}/2)=\omega (r_{2}v_{2}-r_{1}v_{1})$
where
1 is upstream and 2 is downstream
ω is the rotor angular velocity
r is the distance from the axis of the stream tube upstream and downstream
v is the swirl (tangential) velocity component of the fluid velocity upstream and downstream
u is the impeller tip speed, which is defined as, u = (diameter in inches X RPM)/229.18
# Jet Propulsion/Gas turbine energy exchange

In a gas turbine processes energy is converted from one form to another.
Kinetic energy to fluid temperature
Changing the velocity of the fluid by pressure changes simultaneously changes the temperature. Compression work raises the apparent temperature of the fluid. We can relate Mach number to the internal energy of the fluid:
$M^{2}={\frac {2}{\gamma -1}}{\frac {u^{2}}{c_{P}T}}$
... more gas dynamics
Work addition to the fluid by blades
Combustion energy addition
Heat transfer to and from walls
# Jet Propulsion/Free stream

The properties of the fluid far enough away from the body in motion that the body's effect is negligible.
# Jet Propulsion/Glossary/Stagnation temperature

The temperature at a stagnation point in a fluid flow. See gas dynamics.
# Jet Propulsion/General cascade analysis

The total enthalpy h_t of the fluid flowing at velocity u is
$h_{t}=c_{p}T_{t}=c_{p}T+u^{2}/2=h+u^{2}/2$
Euler turbine equation
stage temperature ratio
# Jet Propulsion/History

Jet propulsion had its beginnings in the turbo superchargers devised by Dr. Sanford Moss in 1918. These were used to improve the performance of reciprocating engines at high altitude.
Frank Whittle received the patent in 1930 for a jet engine. Hans von Ohain received the German patent in 1935. The first jet aircraft was the Heinkel He 178 flown in 1939 with a von Ohain engine producing 4.9kN of thrust.
The first American jet was the Bell P-59 Airacomet flown in 1942.
The first combat jet was the Gloster Meteor which entered service with 616 Squadron Royal Air Force in May 1944. They were initially deployed against V1 flying bombs and specifically prohibited from flying over Germany. The germans also had a jet fighter in operational service before the end of the war the Messerschmitt Me 262. A large number of these were built toward the end of the war but supply of engines was so limited that less than 30 were in service at any one time.
The first American civil jet engine was the General Electric J47 certified in 1949. The first civil jet aircraft was the De Havilland Comet flown in 1949. Three of the nine initially built exploded because of fatigue problems in the pressurised fuselage.
The first civil American jet was the Boeing 707 flown in 1954, powered by the JT3C turbojet.
The first high bypass turbofan was the General Electric TF39 used on the Lockheed C-5A which first flew in 1968 and paved the way for the engines used in the 747 and other widebody aircraft in use today.
# Circuit Idea/Slowing Circuit Processes

The cause is delayed, albeit for a moment, relative to the effect - first the cause (input signal) appears, and then the effect (output signal) changes. Therefore, in order to introduce causality into inertialess, proportional electronic devices, they must be deliberately made slow, inertial, integral. By slowing down the action of the studied devices many times over, it becomes commensurable with the speed of human thinking and allows to "peek" into the transition process, where there is a hidden valuable information about the circuit operation.
This heuristic approach can be applied to op-amp circuits with negative feedback. How op-amp works is a key point to understanding op-amp circuits. Reading classical formsl explanations, we could not understand what and how an op-amp really does in op-amp circuits with negative feedback. We gradually realize a paradoxical fact: although an op-amp is really a proportional and, as they consider, an almost "non-inertial" device, in order to understand how op-amp circuits work, we have to think of it as of an integrating, inertial device what it actually is. Figuratively speaking, we have to think of the op-amp as of a "being" that "observes" continuously its input voltage and changes its output voltage until it manages to zero the input voltage. If we think of the op-amp in terms of Vout = A.Vin (i.e., Vin and Uout change simultaneously), we fall into a vicious circle traveling the feedback loop and we can never understand circuit operation. We have to assume that the output voltage stays late regarding the input voltage. More philosophically speaking, we have to see the causality in the op-amp operation; to think of the input voltage as of a cause and of the output voltage as of a result.
We can find this concept in the H&H The Art of Electronics, "The golden rules" section (p. 177): What the op-amp does is "look" at its input terminals and swing its output terminal around so that the external feedback network brings the input differential to zero (if possible). As you can see, Horowitz & Hill have also animated the inanimate op-amp with the sole purpose of showing what it actually does in negative feedback circuits.

## See also

Op amp myths (Integrator Inside section) by Barrie Gilbert
# Circuit Idea/Reinventing the Common-Source Amplifier
## The rule of understanding

It is an interesting fact that things in life are understood through similar but simpler things. The paradox is that they are not understood as things themselves but through other things. For example, no matter how much you study the transistor device in Semiconductor engineering, it is not enough to understand transistor circuits. There is a need for something else that is not learned there, but long before that in electrical circuits and in life.

## Building the common-source stage

Perhaps it is best to reinvent step by step the most elementary transistor amplifier stage to understand the meaning of things.

### Converting the voltage into resistance

Regardless of all the complexities of the (MOS) transistor, generally speaking, it does one simple thing in amplifier circuits - introduces adjustable losses in the form of a voltage drop. So does the much simpler variable resistor in electrical circuits. They both do it the same way - by inserting resistance into the circuit and changing it. So the simple functional idea of a transistor is as a voltage controlled variable resistor (voltage-to-resistance converter). Indeed, there is a "small" difference - a resistor is a linear element with a constant resistance, whereas a transistor is a non-linear element with a "self-changing" (dynamic) resistance, but this is not essential to understanding the basic idea of the transistor amplifier stage. It is a concept, and details get in the way of understanding concepts.

### Converting the resistance into current

Variable resistor: The resistance is only a parameter that can control some "true" electrical quantity, most simply the current. For this purpose, we (the "input voltage source":-) supply the variable resistor Rds with a voltage source Vdd and by changing the resistance we adjust the current Id = Vdd/Rds = 10 mA (Ohm's law) looking at the "ideal" ammeter.
To get a better idea of the resistor's behavior, let's measure and plot its IV curves for three resistance values - 1 kΩ, 2 kΩ and 10 kΩ. As you can see from the graphs, at 10 V the corresponding currents are 10 mA, 5 mA and 1 mA.

## Web resources

A similar story from an answer to a related StackExchange EE question
# Circuit Idea/Simplest Transistor Amplifier

It doesn't get much simpler