HDTenEightyP/NetNews huggingface dataset:
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: What is catastrophe theory?
Date: 12 Nov 92 15:15:30 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: gokhman@ring05.cs.utsa.EDU (Dmitry Gokhman)

In article <1992Nov12.054448.26967@ringer.cs.utsa.edu>, gokhman@ring05 (Dmitry Gokhman) writes:
>It's not a theory of everything, it's a theory of dynamical systems
>producing discontinuous results from continuous input.  It is not at
>all clear to me what the so-called controversy is all about.  The
>theorems come with proofs.  Somebody please enlighten me.

The controversy came because the models were frequently applied with
no evidence regarding any underlying dynamical systems.  This is in
contrast to good chunks of the chaos fad, where the dynamics is often
explicit.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
Xref: sparky sci.math:14684 sci.physics:18563
From: aalpern@hamp.hampshire.edu
Newsgroups: sci.math,sci.physics
Subject: Info? on Fractal and Chaotic music, et al...
Date: 9 Nov 92 21:18:46 GMT
Organization: Hampshire College

Does anyone know of where one can obtain information, or find discussions,
concerning musical applications of fractals, the 1/f nature of music, source
code(preferably C, but anything will do), random number generation using
fractal principles, chaos theory, and musical applications of chaotic systems?
I would particularly like to know if there are any source code examples of
anything related to any of these topics.

Thanks for your help!
        -Adam Alpern



-- 
Adam Alpern			* "All that is gold does not glitter, not all  *AAlpern@hamp.hampshire.edu	* those who wander are lost." - JRR Tolkien    *				* "When I look in the mirror I see the days to *				* come, and my face is just a trace of where   *				* I'm coming from." - Ani DiFranco	       *
Newsgroups: sci.math
From: harper@kauri.vuw.ac.nz (John Harper)
Subject: Re: Relatives with Crackpot Proofs
Organization: Victoria University of Wellington
Date: Wed, 11 Nov 1992 01:59:06 GMT

In article <1992Nov10.144053.100358@watson.ibm.com> platt@watson.ibm.com (Daniel E. Platt) writes:
>I think it depends on your relative.  Some people will hear it,
>some people won't.  If they won't, it doesn't much matter what
>you say.
True,and well known long ago. Proverbs 9:8 says "Reprove not a scorner,  
lest he hate thee: rebuke a wise man, and he will love thee." 

John Harper Mathematics Dept. Victoria University Wellington New Zealand
Newsgroups: sci.math
From: platt@watson.ibm.com (Daniel E. Platt)
Subject: Re: Relatives with Crackpot Proofs
Date: Tue, 10 Nov 1992 14:40:53 GMT
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: IBM T.J. Watson Research Center

In article <2105@celia.UUCP>, keith@celia.UUCP (Keith Goldfarb) writes:
|> Does anybody have any good suggestions about how to deal with
|> crackpot "proof"s from relatives and friends?  A relative of
|> mine cornered me at a party recently and gave me a copy of
|> his "proof" of FLT.  He'd like me to give him some feedback.
|> I told him that he should just mail away a few copies to some
|> real experts (trying my hardest to get out of it) and he said
|> that he had done that, but he wanted my feedback as well.
|> 
|> Of course, his document had no value at all, it was a classic
|> case of a crackpot proof as we've all see them.  Now, I don't
|> want to start another discussion about crackpot proofs in general,
|> but rather what should be done when the person pushing the proof
|> is personally known, and known well.  When I next see this guy,
|> he's going to ask me what I thought, and I really don't know how
|> I should deal with it.
|> 
|> Maybe Dear Abby would have some suggestions?

Reminds me of a situation like that I was in.  A friend was very
stubborn about having a trisection construction.  I pointed out
that the general reason you cannot trisect an angle was that
it required a cube root somewhere (the cos(theta) is a cubic
in cos(theta/3)), and you can only get square roots at most
out of a straight-edge and compass (you can get itterative
square-roots as well... what I've seen described as a 'surd'
field ['surd' is the name of the square-root radical sign]).
That wasn't good enough.  I then went on and calculated the
actual angles for him, and showed him explicitly that they
had not trisected the angle.  That didn't work either.  He
has since gone onto graduate school in mathematics.... I wouldn't
have thought he had the real disposition for it given his
stubborness in being wrong, and not being interested in how
the actual arguments for trisection worked.

I think it depends on your relative.  Some people will hear it,
some people won't.  If they won't, it doesn't much matter what
you say.

Dan


-- 
-------------------------------------------------------------------------------
Daniel E. Platt                                      platt@watson.ibm.com
The views expressed here do not necessarily reflect those of my employer.
-------------------------------------------------------------------------------
Newsgroups: sci.math
From: groak@cayley.mit.edu (Paul Gunnells)
Subject: Soccer Ball Problem
Organization: MIT Department of Mathematics
Date: Fri, 6 Nov 92 00:28:39 GMT


Hello all.  Forgive me if this is a FAQ.

What's the ratio of a side of a soccer ball to the radius of the 
circumscribed sphere?

Please eMail an answer if you can, because I don't read this group very
often.  Just a bit of curiosity on my part.


Paul
From: fogel@ragu.berkeley.edu (Micah E. Fogel)
Newsgroups: sci.math
Subject: Re: What's a knot? (inspired by "What's a manifold?")
Date: 7 Nov 1992 00:58:11 GMT
Organization: U.C. Berkeley Math. Department.
Distribution: world
NNTP-Posting-Host: ragu.berkeley.edu


In article <COLUMBUS.92Nov6105242@strident.think.com> columbus@strident.think.com (Michael Weiss) writes:
>...
>This suggests that whenever we have a definition of the form
>
>	"widgets are equivalence classes of wadgets under the boff
>    	equivalence relation"
>
>we should look for a definition of a widget that doesn't mention wadgets or
>boff...
>
>How would one define a (tame) knot, intrinsically?  Definitions I am
>familiar with either involve modding out by ambient isotopy (in fact there
>are subtle points here, I believe-- perhaps someone more knowledgeable
>would like to post), or by Reidemeister moves.
>
>Is the field just too young to have a suitably slick and (on first
>encounter) unintuitive definition?

	When working with tame knots of S^1 in S^3, we now know that the
knot (upto isotopy, and disregarding orientation information) is determined
by the homeomorphism type of its exterior (or complement, whichever you
prefer).  Thus if you take manifold to be defined without using wadgets,
so is a knot.  Just "define" a knot as a 3-manifold with torus boundary
that sits inside S^3.
					Micah Fogel
					fogel@math.berkeley.edu
Newsgroups: sci.math
Subject: Re: What's a knot? (inspired by "What's a manifold?")
Summary: 
Expires: 
Followup-To: 
Distribution: sci
Organization: U.C. Berkeley Math. Department.
Keywords: 

In article <COLUMBUS.92Nov6105242@strident.think.com> columbus@strident.think.com (Michael Weiss) writes:
>...
>This suggests that whenever we have a definition of the form
>
>	"widgets are equivalence classes of wadgets under the boff
>    	equivalence relation"
>
>we should look for a definition of a widget that doesn't mention wadgets or
>boff...
>
>How would one define a (tame) knot, intrinsically?  Definitions I am

	When working with tame knots of S^1 in S^3, we now know that the
knot (upto isotopy, and disregarding orientation information) is determined
by the homeomorphism type of its exterior (or complement, whichever you
prefer).  Thus if you take manifold to be defined without using wadgets,
so is a knot.  Just "define" a knot as a 3-manifold with torus boundary
that sits inside S^3.
					Micah Fogel
					fogel@math.berkeley.edu
Newsgroups: sci.math
Subject: Mercator Projection
From: kfree@netlink.cts.com (Kenneth Freeman)
Date: Sat, 07 Nov 92 01:26:09 PST
Organization: NetLink Online Communications, San Diego CA

My Mercator projection goes 'up' to only 84 degrees, ~the northern
tip of the classically huge Greenland. I'd like to know three things.
1) For a given area, what is its apparent increase in size for a 
given latitude? I.e., what is the rate of increase the closer you
get a pole (and infinity)? 2) Is there a program out there for showing
the Mercator projection with the Earth shifting around an axis? I'd like
a larger Fiji. 3) Are there any commerical Mercator projections which
put the Equator in the middle and which get closer than five degrees
to both poles? 

--                    
INTERNET:  kfree@netlink.cts.com (Kenneth Freeman)
UUCP:   ...!ryptyde!netlink!kfree
NetLink Online Communications * Public Access in San Diego, CA (619) 453-1115
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Newsgroups: sci.math
Subject: Re: Simple Diff Eq
Date: 9 Nov 92 17:46:30 GMT
Organization: Beckman Instruments, Inc.

In <13390031@hpspdla.spd.HP.COM> ric@hpspdla.spd.HP.COM (Ric Peregrino) writes:


>Hello sci.math,

>I've come by a simple differential equation that I'm interested in:

>df(x)/dx - 1/f(x) = 0

Mathematica 2.0 for HP Apollo Domain/OS
Copyright 1988-91 Wolfram Research, Inc.
 -- Display Manager graphics initialized -- 

In[1]:= DSolve[f'[x] == 1/f[x],f[x],x]

Out[1]= {{f[x] -> Sqrt[2 x + 2 C[1]]}, {f[x] -> -Sqrt[2 x + 2 C[1]]}}

With that information, you should be able to construct a proof.  (And
Mathematica's answer, is, for once, correct and complete.)


--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
My interaction with our news system is unstable; please mail anything important.
From: joel@math.toronto.edu (Joel Chan)
Newsgroups: sci.math
Subject: Re: Michael Spivak
Date: 5 Nov 92 07:42:21 GMT
Organization: Department of Mathematics, University of Toronto

In article <74LSBVY5@cc.swarthmore.edu> rbrown1@cc.swarthmore.edu (Randolph Gregory Brown) writes:
>mpl3@midway.uchicago.edu writes:
>> Is there anywhere as good a calculus text as Spivak?
>
>I loved using Spivak's caluculus book, and I've never seen a better
>one.  As for the pig to which the book is dedicated, I think that it
>is that little one on the outside cover, which I've guessed is the
>symbol for Publish or Perish, Inc., the publisher of the book.
>
>BTW, look at what "Grin and bear it" refers to in the index.  My
>opinion exactly.

Rumour has it that before Calculus was written, Spivak was writing a
book that he had spent a long time on.  His colleagues noticed that
he would always bring his writings around, so he would actually have
to lug tons of paper.  Since the sheets of paper were yellow, his
colleagues called it the "Yellow Pig."

Here's where my memory gets very shaky.  I think his proposed book
eventually got rejected and was never published and so when he
wrote "Calculus," he dedicated the book to his Yellow Pig.
(Someone tells me that the Yellow Pig was actually the text of
"Calculus," but I'm not sure.)

For more references, check out the dedication in the front of the book
and also the index (under "pig").

I used Spivak's book in my freshman year and I loved it, despite the
errors that still exist in the second edition. (Anyone notice that the
partial fractions problem is really messed up?  The question is posed
twice, but *both* of them have different typos.)  


Cheers!

Joel
-- 
Joel Chan, Department of Mathematics	  	 joel@math.toronto.edu
Toronto Blue Jays: 1992 World Series Champions
"History: Those who ignore it are condemned to repeat it.  Math, too."
				    -From the comic strip "Betty"
Newsgroups: sci.math,alt.politics.kibo,alt.magnus.and.ketil
From: magnus@bark-fddi.ii.uib.no (Magnus Alvestad)
Subject: Re: three sided coin
Reply-To: magnus@ii.uib.no
Organization: UVBS -> SFK/T-DSA / SOPS - HOS / RNoN
	<1992Nov3.094443.10479@impmh.uucp> <1d6ti8INN976@CAUCHY.MATH.YALE.EDU>
	<Bx85Hn.6Cz@world.std.com>
Date: 6 Nov 92 16:53:34

Over here in Norway, the land of the bold and the strong, most of us
measure our heights in meters. I guess it's just the viking heritage.

-Magnus (!kibo)
From: A.M.Wall@newcastle.ac.uk (A.M.Wall)
Newsgroups: sci.math
Subject: Re: Apology about f'(g(x))
Date: 12 Nov 92 13:09:04 GMT
Organization: University of Newcastle upon Tyne, UK NE1 7RU

So you are all arguing about the following:

                             df 
Is f' a function, with value --, or does f'(y) mean "take f and differentiate 
                             dx
wrt y"? The answer is probably that both are perfectly good interpretations, 
but that the former is more widely accepted. If you need to use the latter, 
                       df(g(x))                  
then the full notation -------- is less confusing (whether or not you actually 
                        dg(x)
prefer it).
Newsgroups: sci.math
From: gedgar@magnus.acs.ohio-state.edu (Gerald A Edgar)
Subject: Re: who should teach calculus?
Organization: The Ohio State University, Dept. of Math.
Date: Thu, 12 Nov 1992 20:39:23 GMT


How about: "should algebraists teach calculus?"
Are they the ones who say, "I have never used hyperbolic functions,
so we can skip that section"??
-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
Newsgroups: sci.math
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: definition of topological space
Keywords: Topology; Open sets; Continuity
Date: 8 Nov 92 15:51:23 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)

In article <1992Nov7.044233.28977@CSD-NewsHost.Stanford.EDU>, pratt@Sunburn (Vaughan R. Pratt) writes:
>No circularity, these are alternative definitions.  Let me collect
>three of them here in the one place to make this clearer.

An excellent book in this regard as Thron TOPOLOGICAL STRUCTURES.  He
goes through the abstract shenanigans involved in innumerable approaches
to topology.  Sort of like Edmund Landau FOUNDATIONS OF ANALYSIS, but at
a higher level.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
Newsgroups: sci.math
From: hofbauer@csri.toronto.edu (John Hofbauer)
Subject: Looking for Henri Poincare quote
Organization: CSRI, University of Toronto
Date: 9 Nov 92 05:06:35 GMT

Poincare compared science (and mathematics) to art.  The quote goes
something like this:  A scientist, especially a mathematician, should
feel about what his work the same way as an artist feels about his art.

BTW, over the years I've heard quite a few pithy observations by him.
He strikes me as a true philospher/mathematician and a fascinating
character.  Can anyone recommend a biography on him?
Newsgroups: sci.math,sci.math.symbolic
From: uds@trace.eng.wayne.edu (Seetamraju Udaybhaskar)
Subject: ......  examples of voronoi/dirichlet tesselations ....
Reply-To: uds@trace.eng.wayne.edu (Seetamraju Udaybhaskar)
Organization: Wayne State University, Detroit
Date: Tue, 10 Nov 1992 03:12:48 GMT


qn.1  :	What is a piece of a region that has been `effected' by a (voronoi) tessellation ?
	Is it called a `tessel' ?

qn.2  : Are there any other type of tesselations or equivalent terms ?

qn.3  : Could someone please give me a few `one-line' examples where voronoi
	tesselations are popularly used.   I shall look up further on that.


reasons for asking : I want to use the word tessellation to describe a feature
			in my PhD oral exam `report'.  I was asked for specific
reasos for the use of that word.  Well, I am a computer engineer, and completely
lack a math background.  I saw an application ( cant think of a better word) of
the voronoi/dirichlet tessellation in the book Krogh,et al.. on neural networks
(1991).  From the description in that book, I thought it perfectly fitted the
features I have ...

I would really appreciate it, if U could email me.  But such topics would
be interest to the usenet community in general too, so make Ur own choice...


Seetamraju Udaya Bhaskar Sarma
(email : seetam @ ece7 . eng . wayne . edu)

Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: definition of topological space
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Thu, 5 Nov 92 21:14:26 GMT

In article <1992Nov5.033835.5180@leland.Stanford.EDU> ledwards@leland.Stanford.EDU (Laurence James Edwards) writes:
>The definition of a topological space is:
>
>    :a set with a collection of subsets satisfying the conditions that 
>    both the empty set and the set itself belong to the collection, the 
>    union of any number of the subsets is also an element of the collection, 
>    and the intersection of a finite number of the subsets is an element 
>    of the collection
>
>What is the purpose of this definition? To the naive reader (such as myself)
>it would seem that just about any set along with one of its subsets and the
>empty set would be a topological space, e.g. it would semm to me that:
>
>{1,2,3} {} {1}
>
>is a topological space. What am I missing here? In one math dictionary
>it is stated that this definition allows one to establish the notion of
>continuity as it applies to functions between topological spaces ...
>I don't see how. Can anyone clue me in?

Yup, that's a topological space, albeit a small and dull one.   A better
example is to take R (the real numbers) and define a set S to be open if
given x in S, all points within some small distance of x are also in S.
This is the usual topology on R.

A function f from one topological space X to another Y is defined to be
continuous if given any open set O in Y, f^{-1}O is open in X.  Here
f^{-1}O means the set of all points in X which are sent by f to points
in Y.

Now for the payoff: this definition of continuity, when applied to the
example of the real numbers given above, is equivalent to the usual
epsilon/delta definition of continuity.  That is, a function f from R to R
is continuous iff for all x and all epsilon > 0 there is a delta > 0
such that if |x-y| < delta, then |f(x) - f(y)| < epsilon.  

The REAL payoff is that the definition of continuity involving abstract
topological spaces is much more general and applies to many interesting
situations in which the epsilon/delta definition does not apply.  It
even applies to rather weird topological spaces like the one you
invented.  By the way, to visualize your space, think of the points 2
and 3 as sitting right on top of each other (since no open set contains
one but not the other), and the point 1 as sitting off to the side.
From: brihut@pro-palmtree.socal.com (Brian Hutchings)
Newsgroups: sci.math
Subject: Bozos Synonymous
Date: Fri, 6 Nov 92 19:49:22 PST
Organization: The Palmtree BBS - 310/453-8726 - Santa Monica, CA

the Int'l E-cafe, that hosts the board (Pro-Palmtree)
that I'm posting this at, will be be hosting a showing of Richard Hoagland's
second video in a series about the "face on Mars" and
other nearby geological stuff, there, as well as about geometry
as it relates to planetology & physics (what he calls "tetrahedral math."),
(Hoagland's formerly of NASA)....  that's on 18th Street,
just north of Olympic Boulevard, in Santa Monica (get-off the I-10
at 20th, and turn north) this Sunday at 7:30pm, $10.
 
note that I'm not promoting this.  my concern has to do
with the apparent (I only saw the first video) linkage
of the Martian stuff with the recent appearance of agrocycles,
or crop-circles, in Druidland, UK -- yes;
the land of the old, Celtic tree-worshippers/agriculturists.
 
now, the supposedly wonderous geometrical forms, that these things take,
are just the sort of thing that you'll find *in abundance*
in the "exercises" section of many texts *on* geometry, although
I know of no new, profound "laws" of math being embodied, there,
as one researcher had thought (reported in Science News) -- that is, *if*
they're not just pictograms, as most of`em are, nowadays, or
amateurishly-drawn Mandelbrot-sets....  that's the part
that belongs under "sci.math".
 
speculation about the nature of such agricultural stuff
--with emphasis on, cult--should perhaps go elsewhere, but
this board is rather small, so ... look:
why go overboard (or outerspace) in attributing these things, when
some of the (earlier) circular ones could well have been
of fungal origin (as in, faerycircles -- rings of mushrooms
that generally grow in lawns (cultivated grasses) -- why not ask,
why not?
 
what possible need is their to invoke a couple of old buffoons,
dragging a log around at night, or flame-brained ETs, when
a small, ritually-dedicated group of latter-day Druids could do it,
systematically, after the harvest, when the grass is down
and the sun is up?...  I mean, let's face it:
no modern-day mechanized farmer spends much time gaurding his fields.
what needs to be manipulated, folks, is not the stalks of wheat (or
rapeseed, or what ever), themselves, but the *soil*, and
that could be done e.g.fungally, with gravelflour, with NPK or (God
forbid it) herbicides -- applied at any particular time
o`the year.
 
Hoagland, get a grip on it!...  that one guy
that's been promoting the agro-cycles/-grams, Colin Andrews,
himself said that he'd been working with the British Psychical Society --
I heard'im on Roy Tuckman (who's co-hosting this)'s show on KPFK, but
I *also* thought that I'd heard another gentleman on Roy's show,
Dave Emory ("archivist in audio") say that the BPS (or
some thing that sounds like it, that's British, psychological & organized;
it's late-night radio, zzzzzzz) was originally an arm
of the Brit's Psych.War department.
 
or, did you just remember that, Roy?
 
y`all go back to bed,
now.
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: Relatives with Crackpot Proofs
Date: 10 Nov 1992 21:20:26 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

In article <2105@celia.UUCP> keith@celia.UUCP (Keith Goldfarb) writes:
> Does anybody have any good suggestions about how to deal with
> crackpot "proof"s from relatives and friends?  > 
> K.
> -- 


This is considered horribly rude behavior when the expert is a 
medical doctor.  If your relative is an MD or a plummer, say, be sure  
and get some free work out of him in return.  

At family reunions, I am always called on to do such difficult math as
counting heads and 2-digit multiplication.  I always lie.  The best way  
to lie is to have a pre-defined way of generating a wrong answer.  I  
usually just concatenate all the digits in their question into one big  
number:  "Hey, Bart, what's 34 times 51?"  "3 thousand 4 hundred and
fifty-one".  Since I don't have to think, I can give the "answer"
so quickly and effortlessly, that their awe of my mathematical prowess  
(which they think is a birth defect) increases.  

Bart
Newsgroups: sci.math