HDTenEightyP/NetNews huggingface dataset:
From: scip1061@nuscc.nus.sg (Marc Paul Jozef)
Subject: Re: How do you draw a straight line?
Organization: National University of Singapore
Date: Tue, 13 Oct 1992 14:17:30 GMT

jbaez@riesz.mit.edu (John C. Baez) writes:
: In article <1992Oct12.083128.29023@nuscc.nus.sg> scip1061@nuscc.nus.sg (Marc Paul Jozef) writes:
: >jbaez@riesz.mit.edu (John C. Baez) writes:
: >: In article <1992Oct8.115013.2533@nuscc.nus.sg> scip1061@nuscc.nus.sg (Marc Paul Jozef) writes:
: >: >
: >: > The spacetime metric of GR defines geodesics
: >: >in spacetime. A string or a rod or whatever
: >: >define world*sheets* in spacetime; `straightness'
: >: >of a line has nothing to do with geodesics of GR.
: >: 
: >: While it's true that over time a rod covers a 2-dimensional surface
: >: in spacetime, the closest thing there is to a straight (spacelike) line
: >: in GR is a spacelike geodesic.
: 
: >    So what? 
: >    The correspondence may be `close', but it can
: >    never be precise (except in static spacetimes
: >    which have a unique timelike Killing-field,
: >    so that there is a unique 3+1 splitting of
: >    spacetime).
: 
: So what?  Close is the best you can do when it comes to trying to 
: find a reasonable notion of straight lines on a curved spacetime.
: Close is good enough when it comes to the everyday notion of a "straight
: line", which assumes that line is not too long compared to
: characteristic length scale of the curvature.


       As there is no natural mathematical curve corresponding
       to a physical line, the best you can do is to forget
       about the correspondence :-)
       As you say, spaceTIME is curved, but that is trivial:
       the worldcurves of two satelites traversing the same geo-stationary
       orbit in opposite directions cross more than
       once. What does this have to do with spatial curvature?
       (spacetime remains just as curved when you
        have euclidean frames all over the place).
From: rgep@emu.pmms.cam.ac.uk (Richard Pinch)
Newsgroups: sci.math
Subject: Re: Topological Question
Date: 12 Oct 92 17:35:06 GMT
Organization: DPMMS University of Cambridge

In article <1992Oct12.163249.1@vmsa.technion.ac.il> chr09tk@vmsa.technion.ac.il writes:
>Is there a connected and locally connected topological space which is not path
>connected? 
>Is there such a space which is also compact?

I hope this isn't homework!

The cofinite topology (closed <=> finite) on a countable set is
compact, hyperconnected, hence connected and locally connected, 
but not path connected or locally path connected.

Such questions can usually be resolved by reference to that
splendid work "Counteraxamples in Topology" by L.A. Steen and
J.A. Seebach jr, Springer-Verlag, 1978.

Richard Pinch,  Dept of Pure Mathematics,  University of Cambridge
Newsgroups: sci.math
From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: consequences of the Axiom of Choice
Organization: Boise State University
Date: Thu, 8 Oct 1992 18:30:47 GMT

In article <92147@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P Wiener) writes:
>In article <1992Oct6.214824.4955@guinness.idbsu.edu>, holmes@opal (Randall Holmes) writes:
>>And, alas, the prime ideal theorem is false in Solovay's model (it
>>implies the existence of non-measurable sets).
>
>I've never quite understood the philosophy behind this "alas".  People
>who don't like AC usually do so because they like constructive proofs.
>Most constructive work keeps one within the realm of the measurable.
>The only exception that I know of, where knowledge and sometimes even
>use of PCA say exists, is probability.
>-- 
>-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)

The "alas" was somewhat ironic in intent.  The mere existence of
Solovay's model shows that _all_ constructive work can be assumed to
keep one in the realm of the measurable, does it not?  I don't think
that applications of the prime ideal theorem are really needed for
classical measure theory!  The interesting thing is that Solovay's
result requires consistency strength more than that of ZFC; the
assumption that all sets of reals are Lebesgue measurable enables one
to intepret ZFC + "there is an inaccessible"; ZF + "all sets are
measurable" is stronger than ZFC!


-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu
Newsgroups: sci.math
From: wiawkph@dutrun2.tudelft.nl (K.P. Hart)
Subject: Re: Well-known people who majored in math (other than mathematicians)
Organization: Delft University of Technology
Date: Wed, 14 Oct 1992 10:20:25 GMT

Davey Johnson, former New York Mets manager has a `degree in math'
according to an old Baseball Yearbook.

-- 
KP. Hart                         PAPER: dept of math and comp sc
E-MAIL:  wiawkph@dutrun2.tudelft.nl      TU Delft
         hart@dutiaw3.twi.tudelft.nl     Postbus 5031
PHONE    +31-15-784572               NL-2600 GA  Delft
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Looking for a slick proof
Date: Fri, 9 Oct 1992 13:23:04 GMT
Organization: University Of Kentucky, Dept. of Math Sciences

In article <1aterkINNj4f@matt.ksu.ksu.edu> bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:
>Hi,
>
>How does one prove that 2^n divides n*(n+1)*(n+2)*......*(2n) without     
>having to resort to the 'odd' and 'even' induction? Any ideas?

It looks to me like half of those 2n numbers are even.

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu
Newsgroups: sci.math
Subject: Re: Linearity question
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 12 Oct 92 21:01:37 GMT
Organization: Beckman Instruments, Inc.

In <105268@siemens.siemens.com> kostas@siemens.com. (Konstantinos Diamantaras) writes:

>Hi netters,

>in the course of my research I came up with the following,
>I think iteresting question

>Suppose I have a continuous real function f(x) of a single
>real parameter x. I want to "design" two functions which
>I will call "addition" (+) and "multiplication" (*)
>(clearly not the usual ones) such that f is linear in them

>f(x+y)=f(x)+f(y), f(a*x)=a*f(x)

>In addition, I would like these functions to have some of the
>standard addition and multiplication properties. In particular,

>(a) I want both functions to be smooth
>    (first derivative exists is enough for the moment)
>(b) I want both to be abelian groups (with respect to the real
>    numbers)
>(c) I want them to have the property
>    (x+y)*z = (x*z)+(y*z)

Are you trying to say, in (b) that:

(R,+) forms a group with identity z.
(R - {z},*) forms a group with identity e.

?

Or equivalently, that (b) and (c) state that (R,'+','*') forms a field?

If so, I have a partial solution:

f(x) = f(e '*' x) = x '*' f(e)

Conversely, if we assume we have "+" and "*", then writing f(x) = x '*' q,

f(x '+' y) = (x '+' y) '*' q = (x '*' q) '+' (y '* 'q) = f(x) '+' f(y), and
f(a '*' x) = (a '*' x) '*' q = a '*' (x '*' q) = a '*' f(x).

If we assume, as I  believe must be the case, that (R,'+','*') must be
isomorphic to (R,+,*), there is a 1-1 function k such that:

k(x '+' y) = k(x) + k(y), and
k(x '*' y) = k(x) * k(y), and, finally,

k(f(x)) = k(x '*' q) = k(x) k(q).

I don't want to work out the necessary conditions for k to exist here, but
it is clear that if f has a first derivative, f(0) = 0 < f'(0) ~= 1, 
0 < f'(x), f has no other fixed points, and f maps R onto R, then we can
choose a smooth k with k'(0) = 1 such that k(f(x)) = k(x) f'(0).



--
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: travis@binah.cc.brandeis.edu (Leopold Travis)
Newsgroups: sci.math
Subject: Re: Another GRE question for you folks
Date: 15 Oct 92 19:55:39 GMT
Reply-To: travis@binah.cc.brandeis.edu
Organization: Brandeis University

In article <1992Oct12.221420.19382@galois.mit.edu>, jbaez@riesz.mit.edu 
(John C. Baez) writes:
>In article <SMITH.92Oct12141247@gramian.harvard.edu> smith@gramian.harvard.edu
>(Steven Smith) writes:
>
>>Did the test really say ``the square root of 2,'' or did it use a
>>surd, i.e.,       _
>>                \/2 ?
>>
>>By convention, the surd notation denotes the positive real root of a
>>positive number.  If the ETS used a surd, their answer is correct, and
>>they can avoid yet another damaging article on the front page of the
>>Wall Street Journal.
>>
>>If they said ``the square root of 2'' or ``2^(1/2),'' they are
>>referring to a number x such that x^2 = 2, and the correct answer is D
>>by the reasons you stated.
>
>Surely if they say THE square root of 2 they are hinting that they believe
>there is a unique one, i.e., that they are forgetting the negative one.

Absolutely.  If they were referring to some number x such that x^2=2,
they would have said _a_ square root of 2.

--
Leopold Travis                 |  It's just not within the scheme of things
travis@binah.cc.brandeis.edu   |  To give up your life so easily
		               |  That's not the way you're meant to be
			       |  What a waste of time and energy
			       |    -Erasure
From: davep@paladin.corp.sgi.com (David Packer)
Newsgroups: sci.math,sci.physics
Subject: Re: "The Universe of MOTION" (crackpot index)
Date: 16 Oct 92 17:14:29 GMT
Organization: Silicon Graphics, Inc.  Mountain View, CA
NNTP-Posting-Host: paladin.corp.sgi.com


What about those who become crackpots over time? should there
be a special weighted index based on mental collapse over time??

i.e.:

I've read about ALBERT einstein (capitalization, it's starting to happen)
        weight 1.1

I'VE met ALBERT EinStien (increasingly worse)
        weight 1.5

I AM albert EINSTEINs' GHOST I was Wrong about Relativity (gross neglect of
        the brain during formidable years!!)
	weight 2.0



I would imagine the program would have to keep a file of most common
abusers. As the index increased, so would the weight.  This way just in
case someone like Hannu came back and said something normal(not likely),
then he would still score higher than if Dale had said something.
(maybe not?). 

 
Dave Packer
Silicon Graphics Inc.

---

My opinions are mine,....I think?

"Imagination is more important than knowledge"
			- Albert Einstein -
From: litow@csd4.csd.uwm.edu (Bruce E Litow)
Newsgroups: sci.math
Subject: prime factor question
Date: 8 Oct 1992 15:10:22 GMT
Organization: Computing Services Division, University of Wisconsin - Milwaukee
Distribution: world
NNTP-Posting-Host: 129.89.7.4
Originator: litow@csd4.csd.uwm.edu

Let p_1,...,p_n be the first n primes. Are there, say, n^(1/2) distinct
prime factors among p_1 - 1, p_2 - 1,..., p_n - 1 ?
-- 
Bruce Litow
Computing Services Division
P.O.Box 413, University of Wisconsin-Milwaukee, 53201
414 229 6431    litow@csd4.csd.uwm.edu
Date: Monday, 12 Oct 1992 20:33:04 EST
From: <RVESTERM@vma.cc.nd.edu>
Newsgroups: sci.math
Subject: Re: Another GRE question for you folks
Distribution: world
 <1bcao2INN8c8@fido.asd.sgi.com> <92286.195223RVESTERM@vma.cc.nd.edu>

whoops.  make that "a line segment AB and a line segment CD," not "a line
segment AB and a line segment BD."  but you probably figured that out
anyway.



Newsgroups: sci.math
From: wjcastre@magnus.acs.ohio-state.edu (W.Jose Castrellon G.)
Subject: Re: Order -> Algebraic Structure
Keywords: Rationals,Dense Ordering,Algebraic Structure
Organization: The Ohio State University,Math.Dept.(studnt)
Date: Sat, 10 Oct 1992 18:28:14 GMT

In article <1992Oct10.161042.19021@magnus.acs.ohio-state.edu> I write:

>In article <BvvuD8.I26@world.std.com> rjk@world.std.com (robert j kolker)
>writes:
>
>>Let H be a denumerable completely ordered set, where the ordering is
>>dense, and there are no maximum or minumum elements. It is well known that
>>any two sets having these properties are order isomorphic. 
>>
>>The set of rationals Q is a fortiori this set (up to an isomorphism).
>>Clearly the seemingly innocent densely ordered set inherits its algebraic
>>properties via this isomorphism or does it? 
>>
>>Is there someway of showing independent of this coincidental isomorphism ,
>>that denumerable,densely ordered -> the algebraic structure of Q, i.e. Q
>>is a denumerable field or characteristic 0.
>>
>>Your input would be appreciated.
>>
>
>I think it is not possible to prove a statement along those lines, as one
>can cook up examples of denumerable densely ordered fields of characteris-
>tic zero that dont have the same global properties of Q ; for example Q is
>an Archimedean field (i.e given any positive element  x, and an arbitrary 
>positive  y, one of  x, x+x, x+x+x, ... will be greater than y) : one field 
>that doesn't have that property is the set of quotients of polynomials 
>in one variable, with rational coefficients, where you say that p(x)/q(x)
>is positive if the limit as x goes to infinity is positive. It is not hard
                    
This is incorrect, here I should have written: if p(x)/q(x) eventually becomes
positive. Sorry about that.

>to see that this is a densely denumerable non-Archimedean field of char 0.
                              ^^ordered                  
>It looks like an interesting question, IMO to ask what additional hypotheses
>could characterize the structure of Q, or of other fields.
From: kwhyte@dent.uchicago.edu (Kevin Whyte)
Newsgroups: sci.math
Subject: Spectum of a Lie group ...
Date: 7 Oct 92 20:10:58 GMT
Organization: Dept. of Mathematics, U. of Chicago



  Let G be a compact semi-simple Lie group.  The killing
form gives a canonical Riemannian metric, and hence a 
laplacian acting on smooth functions.  What are the eigen-values
of this laplacian?

  L (the laplacian) is a G invariant elliptic operator, on, say
L2(G).  Hence the eigenspaces  are finite dimensional and G invariant.
Peter-Weyl then tells us that each one of these is just some sum
of irreduciple reps. of G (each of which occurs as many times as
its weight).  Thus, given an irreducible rep. of G, it occurs in at
most n such eigenspaces (if G is an n dimensional rep.), so it
should have n positive real numbers associated to it. What are they?

-Kevin
kwhyte@math.uchicago.edu
Newsgroups: sci.math
From: rz@mips.complang.tuwien.ac.at (Richard Zach)
Subject: Re: famous non-mathematicians who majored in math
Reply-To: zach@csdec1.tuwien.ac.at
Organization: Technische Universit"at Wien
Date: Thu, 15 Oct 1992 16:29:29 GMT

> >>>         So the question is, do you know of any well-known people who 
|> >>> majored in math but aren't known as mathematicians?

Robert Musil (Austrian writer: _The Man without Qualities_)

-- 
Richard Zach                         Technische Universitaet Wien
[zach@csdec1.tuwien.ac.at]     Abteilung fuer Formale Logik 185.2
Newsgroups: sci.math
From: ssmithap@cc.curtin.edu.au
Subject: Root Solver Program
Organization: Curtin University of Technology
Date: Mon, 12 Oct 1992 05:45:43 GMT


  Hi!

  Could anyone tell me a name of a program for an MSDOS based machine
  that can find the roots of an equation up to the nth order. (ideally
  up to 10th order or better).  Where abouts would I be able to ftp 
  such a program from.

  Could you please e-mail me your replies.

  Your help would be greatly appreciated

  Thanks

   Andrew
   ssmithap@cc.curtin.edu.au

Newsgroups: sci.math
From: holmes@garnet.idbsu.edu (Randall Holmes)
Subject: Re: consequences of the Axiom of Choice
Keywords: Axiom of choice; Cartesian product
Organization: Boise State University
Date: Wed, 14 Oct 1992 18:10:13 GMT

In article <1992Oct9.192054.11140@ariel.ec.usf.edu> mccolm@darwin.math.usf.edu. (Gregory McColm) writes:
>In article <1af9g6INN6d2@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
>>In article <1992Oct1.152704.16387@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>>>Bertrand Russell used to explain choice this way.  Imagine you are
>>>blessed with infinitely many pairs of shoes and socks.  You wish to
>>>choose one of each pair.  With the shoes it is easy:  you could take
>>>all the left ones, or all the right ones.  But can you choose one sock
>>>from each pair?  To claim that you can is to assert the axiom of
>>>choice.
>>
>>So, let's try to find a good mathematical example to illustrate Russel's
>>explanation.  Explicitly find a countably infinite set S of (unordered) pairs,
>>for which a choice function is not obvious.  [More technical details.
>>The set S should be explicitly and uniquely specified in the language of ZF.
>>It should be provable in ZF that it is a countable set of pairs.]
>>
>>An UNCOUNTABLE set of pairs with no obvious choice function is
>>easy: take the set of ALL pairs of sets of real numbers.
>>-- 
>
>
>Won't work:  given any pair {r,s}, choose the smaller one.  
>In fact, no set with a constructible linear order will work, 
>and an infinite set with no constructible linear ordering 
>will be a strange beast indeed.
>
>-----Greg McColm

On the contrary, the set of equivalence classes of real numbers of
real numbers under tail equivalence of decimal expansions (eventual
equivalence of some decimal expansion) can fail to have a
constructible linear ordering, I believe.  Of course, under V = L, it
does, but the order is not natural...  The identical consideration
applies to the set of equivalence classes of sets of natural numbers
under the relation of having finite symmetric difference (essentially
the same example).  These may be "strange beasts", of course...


-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu
From: buyskes@lafcol.lafayette.edu (Steve Buyske)
Newsgroups: sci.math
Subject: Well-known people who majored in math (other than mathematicians)
Date: 8 Oct 92 19:12:30 GMT
Organization: Lafayette College, Easton PA



	Some time ago on this group there was a discussion of well-known 
people who had some kind of math background but weren't known as 
mathematicians. I've had most of the names from that discussion posted 
on more door, and now I'm hoping to add some more. I'm especially 
interested in adding some women to the  list.

	So the question is, do you know of any well-known people who 
majored in math but aren't known as mathematicians?

Steve Buyske
buyskes@lafcol.lafayette.edu
buyskes@lafvax.lafayette.edu

Here's my list::

Corazon  Aquino, former President of the Phillipines.
Harry Blackmun, Associate Justice of the US Supreme Court, AB in        
	Mathematics at Harvard around 1940. 
Pierre Boulez, composer.
Clifford Brown, 50's jazz trumpeter.
Lewis Carroll,  author of Alice in Wonderland, Through the Looking 
	Glass, and other works.
David Dinkins, mayor of New York.
Milton Glasser, head of the American Civil Liberties Union.
Edmund Husserl, philosopher.
Michael Jordan (into his junior year).
John Maynard Keynes, economist. BA in Mathematics, Cambridge .
Ommar Khayyam, author of The Robaiyat. 
Evelyn Fox Keller, social theorist.
Emanuel Lasker, chess player.
Tom Lehrer, songwriter-parodist. Ph.D. in Math. at Harvard
Huey Lewis (of Huey Lewis and the News). 
J. Pierpont Morgan, the billionaire banker He had enough talent that 
	the Harvard math faculty tried to convince him to become a 
	professional  mathematician.
Paul Painlev, President of France in the early 20th century.  
David Robinson, basketball star. B.S. in math, Annapolis.
Frank Ryan, former professional football player and current science-
	technology adviser to Congress. Ph.D. in Math.  
Stephen Sondheim, songwriter.
Alexander Solzhenitsyn, novelist, degree in math and physics from the   
	University of Rostov.
Laurence H. Tribe, Professor at Harvard Law School, generally regarded 
	as one of the most outstanding authorities on Constitutional Law. 
	Both an AB  and an MA in Math from Harvard circa 1962. 
Leon Trotsky He registered to read Pure Mathematics at Odessa in 1897, 
	but imprisonment and exile in Siberia seem to have disturbed his    
	concentration. 
Eamon de Valera, first President of the Republic of Ireland. 
	Professor of Mathematics at Our Lady of Mercy, Carysfort, 
	Blackrock, Ireland. 
Virginia Wade, Wimbledon champion, Math degree from Sussex.
James Woods, actor.
Frank Zane, a two-time Mr. Olympia (as in bodybuilding).
James Moriarty, former Professor of Mathematics, author of  The 
	Dynamics of an Asteroid, whose essay on the binomial theorem is 
	reported to have  enjoyed a continental vogue, became the leader 
	of the most sinister criminal conspiracy in Victorian England.  He 
	has been called 'the Napoleon of  Crime.'
From: leverge@irisa.fr (Herve Leverge)
Newsgroups: sci.math
Subject: Re: Permutation Polytopes
Keywords: Extreme points
Date: 12 Oct 92 18:16:38 GMT
Organization: Irisa, Rennes(FR)


In article <97468@bu.edu>, mike@park.bu.edu (Michael Cohen) writes:
|> 
|> Treat the orderings on n letters as permutations.
|> For each ordering a, define a point in n X n-1/2
|> space as follows.
|> 
|> U_a(i,j) = 1 if i a j
|> U_a(i,j) = -1 otherwise.
|> 
|> Consider the convex polytope U which is a convex combination of these
|> extreme points.  Question:  What is the polar polyhedron.  i.e. the
|> extreme points of the the of elements <l, u> <= 1. for all u in U.
|>             -mike
|> 
|> 
|> 
|> -- 
|> Boston University (617-353-7857) Email: mike@park.bu.edu
|> Smail: Michael Cohen                     111 Cummington Street, RM 242
|>        Center for Adaptive Systems        Boston, Mass 02215
|>        Boston University

A slight variant of this problem has been studied extensively by
G. Reinelt. For this case :

U_a(i,j)=1 if i a j
        =0 otherwise
         ^

You might have a look in :

@Book{Reinelt85,
  author =      {{Reinelt}, Gerhard},
  title =       {The Linear Ordering Problem: Algorithms and Applications},
  publisher =   {Heldermann Verlag Berlin},
  year =        {1985}
}


@TechReport{Reinelt91,
  author =      {Gerhard Reinelt},
  title =       {A Note on Small Linear Ordering Polytopes},
  institution = {Institut f\"{u}r Mathematik, Universit\"{a}t Augsburg,B}
  year =        {1991},
  type =        {Research Report},
  number =      {329},
  address =     {Universit\"{a}tsstra{\ss}e 8, D-8900 Augsburg},
  month =       {November}
}


@Article{Grotschel84,
  author =      {{Gr\"{o}tschel}, Martin and {J\"{u}nger}, Michael and
                 {Reinelt}, Gerhard},
  title =       {A {C}utting {P}lane {A}lgorithm for the {L}inear {O}rdering
                 {P}roblem},
  journal =     {Operations Research},
  year =        {1984},
  volume =      {32},
  number =      {6},
  pages =       {1195-1220},
  month =       {November-December},
  OPTnote =     ""
}

The corresponding polytope is only known until n=7, whose
full description appears in the above report.

Hope this helps!

RV.
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Electronic math notation
Date: 12 Oct 92 14:54:28 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Oct9.094353.23555@rcvie.co.at> se_karne@rcvie.co.at (Georg Karner) writes:
>If you use TeX notation, probably most people on the net will understand

Some of us will object strenuously to any increase in this lamentable idea.

Later,
Andrew Mullhaupt