HDTenEightyP/NetNews huggingface dataset:
From: mcfarlan@corona.math.washington.edu (Thomas J. McFarlane)
Newsgroups: sci.math
Subject: Re: Report on Philosophies of Physicists
Date: 11 Sep 92 01:08:31 GMT
Article-I.D.: u.1992Sep11.010831.17124
Organization: University of Washington, Mathematics, Seattle

pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>
>The problem with Platonism is that the entities discovered by
>mathematicians depend for their existence on which axioms one assumes.
>...
>So Platonism is on very shaky ground.  It only seems firm because we
>are trained to believe it is firm, and because we walk on it all the
>time without noticing any tremors, reinforcing our lifelong belief in
>the absoluteness of mathematics.  But in reality the reality of
>mathematics is an illusion.
>======================================================| God found the positive
>Vaughan Pratt   pratt@cs.Stanford.EDU   415-494-2545  | integers, zero was
>======================================================| there when He arrived.
                                                         ^^^^^^^^^^^^^^^^^^^^
I think your signature is very interesting in light of your views on Platonism!

Regarding the dependence of mathematical entities on our assumptions,
this happens all over the place, and not just at the set-theoretic level.
It is only when we assume a subgroup H is normal in G that we can assert
the existence of the factor group G/H, for example.  Even after we are 
given a set of axioms for set theory, we still continue to make assumptions
about things in order to talk or prove anything.  It all rests on what
domain of discourse we have chosen for the moment.  The choice of axioms
for set theory don't strike me as fundamentally different.  Nor would
this seem to bother the Platonist very much, I think.  The Platonist
shouldn't be any more concerned that certain results depend on the axiomatic
base for set theory than that they depend on any other assumptions one makes.

The point, it seems, is that certain things necessarily follow once one
choses certain assumptions.  Is there reason to consider one choice real and
another unreal?  The Platonist, it seems to me, would consider them all
equally real.  And there would be no conflict between the different entities
because they exist in different contexts.  The neo-Platonist Proclus
wrote, "For all the highest Ideas are unified with one another and created
in common, even those that would seem to be the antithesis of each other...
This is the peculiar property of the bodiless Ideas.  They penetrate one
another without being confused and are distinguished from one another
without being separated."  (Commentary on Plato's Parmenides)

A Platonism of this form doesn't seem to be on shaky ground at all, at
least not because of what is now known from work in foundations of math.
But a Platonism that considers one axiomatic foundation more real than
another seems to be in need of justification, as you pointed out.

Tom McFarlane
From: kriman@acsu.buffalo.edu (Alfred M. Kriman)
Newsgroups: sci.math
Subject: Re: Abel's proof of the insolubility of the quintic
Summary: Maybe you're not looking at the best original paper.
Date: 9 Sep 92 20:11:21 GMT
Organization: UB = University at Buffalo = SUNYAB = State U of NY at B

In article <1992Sep2.204229.12330@news.cs.brandeis.edu>,
ruberman@binah.cc.brandeis.edu writes:
>Does anyone know a reference for a modern treatment of Abel's
>proof of the insolubility of the quintic?  A high-school student 
>recently came to me, having learnt the solutions to the lower degree
>equations, and hoping to understand the higher degree case as well.
>He tried to read Abel's memoir (translated into English in the venerable
>Source book in Mathematics).  Understandably, he didn't get too far
>since Abel's paper is rather dense and obscure to an untutored reader.
                              ^^^^^ indeed:
   I don't have convenient access to the "venerable source book," so
excuse me if I'm therefore missing something relevant.
   Abel's original paper on the subject (the no-go proof, not the earlier,
rejected paper, which claimed to have a solution) he had published at his
own expense.  To save money, he compressed this me'moire down to six pages.
Later, he published a more complete paper in Crelle's Journal (Journal fuer
die reine und angewandte Mathematik).  At this time he still didn't know
about Ruffini's work.  He did eventually learn of it, but found it so hard
to understand that he would not accept that he'd been anticipated.  (I have
no opinion.)
   By the way, I presume that the "venerable source book" you refer to is
D. E. Smith's.  Perhaps H. O. Midonick's has something.
Newsgroups: sci.math
From: steves@truevision.com (Steve Spicklemire)
Subject: e-mail based discussion groups?
Organization: Truevision Inc., Indianapolis, IN
Date: Sat, 05 Sep 1992 02:45:20 GMT


Hi,
	I am posting this for a friend who does not have access to
news, but *does* have access to e-mail.

	Are there any e-mail based mathematical discussion groups?
Any ideas would be appreciated!

please respond via e-mail to

	swett@gandlf.uindy.edu

please *don't* respond to me!

thanks!
-steve

-- 
Steve Spicklemire
steves@truevision.com (daily)	spicklemire@gandlf.uindy.edu (sometimes)
Dept. of Mathematics and Physics, Univ of Indianapolis 
(317) 788-3313
Newsgroups: sci.math
From: dchatham@utkvx1.utk.edu (Chatham, Doug)
Subject: Re: Foundational issues
News-Software: VAX/VMS VNEWS 1.41    
Organization: University of Tennessee Computing Center
Distribution: na
Date: Sat, 12 Sep 1992 19:51:00 GMT

In article <92Sep12.101940edt.47512@neat.cs.toronto.edu>,
 arnold@cs.toronto.edu (Arnold Rosenbloom) writes...
[Introduction and signature deleted]

>First the number theory text assumes the Peano Axioms, now if we
>view these axioms as the specification of a particular set, how
>do we know that we have a well defined system. For example, the Peano
>axioms assume the existence of a successor function that behaves in a certain
>way. How do we know there is a subset of NxN which has the required properties.
> 
>The other side (set theory) of the coin also presents some problems. 
>THat is, the natural
>numbers are 'defined' as 0={}, 1={0}, 2={0,1}, ... , n+1={0,...,n}.
>But this looks like an inductive definition. So how can you make an inductive
>definition (and hope it makes sense) without the natural number system already
>there to prove that you have actually defined something?

	I'm not sure what you mean by "well defined system."  However, the 
reason we "know" the existence of a successor function is that we ASSUMED it. 
Unfortunately, according to Godel we cannot prove the consistency of a
number theory including the Peano axioms [without bringing in some larger
formal system whose consistency would be unprovable without . . .ad nauseaum,
ad infinitum].  So we can't prove the successor function won't cause a 
contradiction somehow.
	Secondly, to make inductive definitions we need to ASSUME the 
existence of at least one inductive set.  ZF (Zermelo-Frankel?) set theory
makes this assumption an explicit axiom.
	I hope this helps.

			Sincerely,
			Doug Chatham
From: kriman@acsu.buffalo.edu (Alfred M. Kriman)
Newsgroups: sci.math
Subject: Re: Einstein's Erdos number
Summary: A.E. had >20 coauthors on journal articles.
Date: 7 Sep 92 23:38:06 GMT
Organization: UB = University at Buffalo = SUNYAB = State U. of NY At B.

------
Continuing a thread on Einstein's Erdos number in
<NIALL.92Sep2220055@scheria.nmsu.edu> (I guess),
niall@nmsu.edu (Niall Graham) writes:
>  [. . .]  Einstein's co-authors were 
>Ehrenfest, Lorentz, Minkowski, Somerfeld, Straus, Weyl.
>Straus' co-authors include Erdos and Cantor.
>Source: From Figure 1 of "On properties of a well-known graph or
>what is your ramsey number?"  Annals of the New York Academy of
>Sciences, Vol. 328. The author calls himself Tom Odda of Xanadu University.

------
In article <2aa7a8a2wnr070@ark.abg.sub.org>
ralf@ark.abg.sub.org (Ralf Stephan) asks:
>and Rosen, Podolsky ?
 
------
In article <1992Sep7.181616.24038@cs.mcgill.ca>
prakash@cs.mcgill.ca (Prakash Panangaden) writes:
>Yes what about Podolsky and Rosen?  What about Leopold Infeld?  I have read
>both these papers so I am certain that they were co-authors of Einstein.
>Also I am very surprised to see that Lorentz and Minkowski are listed as
>co-authors of Einstein.  Is it possible that this is an error stemming from
>the fact that there is a collection of early papers on relativity that 
>includes papers by Einstein, Lorentz and Minkowski (all solo authored).
>I have this book and noticed that the authors are listed as Einstein,
>Lorentz, Minkowski,...  I am also curious about papers that he may have
>written with Weyl since I have another collection of papers that includes
>solo authored papers by Einstein and by Weyl.  Of course I am not saying that
>Einstein did not write papers with all these people only that it is 
>surprising especially since he said once how much he disliked Minkowski's
>work!

------
   I think P.P. scored a direct hit:  Probably Tom Odda based himself on
book authorships only.
   Bram Pais's scientific biography of Einstein [1] contains an appendix
about A.E.'s scientific collaborators (chap. 29).  Thirty-two are listed,
including those previously attested on the net (Straus, Podolsky, Rosen,
Infeld) on the basis of actual papers.  The following footnote describes
the selection: "I believe but cannot certify that the list of collaborators
given in what follows is complete.  I do not include men such as Besso,
with whom Einstein had important scientific discussions not accompanied or
followed by a joint enterprise."  The publication of a jointly-authored
paper was not a sine qua non for inclusion in the list.  In some cases
including Szilard (unless you count the letter to FDR), the only joint
publications were patent disclosures.  Some other collaborations also
did not lead to joint papers.  Perhaps the most notable of these was a
one-year interaction with C. Lanczos.

[1] _'Subtle is the Lord...': The Science and the Life of Albert Einstein_,
by Abraham Pais (Oxford Univ. Press, 1982).
Newsgroups: sci.math
From: moorthy@cs.rpi.edu (Moorthy)
Subject: Re: D^k f^n ?
Keywords: differentiation, combinatorics
Date: Mon, 14 Sep 1992 16:57:59 GMT

Ofcourse, Knuth Vol One, Pages 50, exercise 21. There are additional
citations there.
Newsgroups: sci.math
From: herve@nttcvg.NTT.JP (Herve Delingette)
Newsgroups: sci.math
Subject: Functional Equation
Date: 14 Sep 92 08:14:47 GMT
Distribution: sci.math
Organization: NTT Human Interface Laboratories, Yokosuka, Japan.


I would like to find all the functions f C1 continuous such that :

f'(x)= [f(x+ x0)-f(x-x0)]/2x0 where f'(x) is the derivative of f
and where x0 is a real number ..

I am pretty sure that the only solutions are the linear functions 
f(x)=ax+b but I am not sure.

Please answer at herve@nttcvg.ntt.jp

Thanks in advance.

**Herve**
From: voros@vaxc.cc.monash.edu.au (Joe Voros)
Newsgroups: sci.math
Subject: Re: Warm and Fuzzy?  Koalas vs. Math
Date: 14 Sep 92 11:28:20 +1000
Organization: Physics Department, Monash University, Australia.


Trying to work out the attribution is impossible, so...
SomeOne once said:  

>>>If you want something warm and fuzzy, raise koala bears.

Since this is sci.math, which is noted for its pedantic tone, I must
state that koalas are *not* bears.  

:)

-- 
Joe Voros
Department of Physics, Monash University, Clayton, VIC, 3168, Australia.
voros@physics.monash.edu.au
Quantum Mechanics is God's way of telling you to mind your P_i's and Q_j's.
From: bennett@math.ksu.edu (Andy Bennett)
Newsgroups: sci.math
Subject: Re: Lebesgue integral (was: Couple of questions
Date: 15 Sep 92 15:29:53 GMT
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu

ramsay@unixg.ubc.ca (Keith Ramsay) writes:

]I've heard that much (nearly all, perhaps) of what is done with L^2,
]regarded as Lebesgue square-integrable functions, modulo functions
]supported on sets of measure zero, is just as nicely done (if not
]better) by regarding L^2 as the formal completion (relative to the L^2
]norm) of a convenient dense subset (where the Lebesgue measure theory
]is not needed). I'm not enough of an analyst to confirm this.

You can certainly produce an acceptable theory of integration this way. See
Chapter 13, The Daniell Integral in Royden's Real Analysis. I've never seen
the advantage though. You seem to end up doing just as much technical work
as developing the Lebesgue integral. 

-- 
Andrew G. Bennett         bennett@math.ksu.edu         If you count too
Dept. of Mathematics      Voice: (913) 532-6750        much you turn
Kansas State University   Fax:   (913) 532-7004        purple.  -  SARAH
Manhattan, KS 66502       STRICTLY MY OWN OPINIONS
From: goodman@bright.uoregon.edu (Albert Goodman)
Newsgroups: sci.math
Subject: Tiling sphere by triangles (Re: 3 space terahedron-packing)
Date: 11 Sep 92 18:27:27 GMT
Article-I.D.: nntp.1992Sep11.182727.28044
Organization: Dept. of Mathematics, University of Oregon, Eugene OR 97403-1222

In article <f#tng3h.spworley@netcom.com> spworley@netcom.com (Steven) writes:
>I am trying to implement an interpolation algorthim over 3D space by
>using a "grid" of tetrahedrons. What I need to compute is a complete
>tiling of 3-space with unit length tetrahedrons: ie, given an XYZ
>location, identify the four points of the tetrahedron that encloses
>that location in this "packed" space.   [...]

This reminds me very much of something someone asked me about
recently, although really I think it's an unrelated question.

Instead of 3-space, consider the surface of a sphere (such as [an
approximation to] the surface of the earth), and suppose we want to
find a tiling or "grid" of triangles which divide up the surface of
the sphere into many small pieces all of the same area (and preferably
all the same shape, i.e. congruent triangles).  (Actually the original
question didn't have to use triangles, just some constant shape, but
triangles seems perhaps a nice choice; trying to use squares, as would
be the obvious solution on a flat surface, doesn't seem to work on the
sphere to get all of the same area.)

I think I already know a way to do this (suggested by someone I
mentioned this to privately), but I haven't worked out the details
yet (in particular an algorithm for finding which triangle contains
any specified point).  So first I'm wondering if anyone has considered
such a thing before.
			-- Albert Goodman  (goodman@math.uoregon.edu)
Newsgroups: sci.math
From: torkel@sics.se (Torkel Franzen)
Subject: Re: ZFC etc. (was Re: Report on Philosophies of Physicists)
Organization: Swedish Institute of Computer Science, Kista
Date: Tue, 15 Sep 1992 05:33:08 GMT

In article <716501145.10401@minster.york.ac.uk> cjhs@minster.york.ac.uk writes:

   >We all know that ZFC is consistent (or maybe just those of us who
   >are sufficiently naive): I want to know why we have this confidence.
   >It just the case that lots of very intelligent people have failed
   >to find an inconsistency? Or are there informal arguments (as there
   >are for Church's thesis) to suggest consistency.

  Some people suggest that that there are "statistical" reasons for taking
ZFC to be consistent. That is, no inconsistency has been found in spite
of the theory having been used a lot, so it is reasonable to think that
no inconsistency exists. In my opinion this argument is worthless.

  Others hold that we have good grounds for believing the theory to be
consistent, namely that we know or "can imagine" that all the axioms are
true. I belong, more or less, to this category, but I would also want
to emphasize that this argument implies a lot more. Consistency, after all,
isn't all that interesting in itself. For example, the consistency of ZFC
implies that every theorem of ZFC of the form "the Diophantine equation ...
has no solution" is true, but it does not imply that every theorem of
ZFC of the form "the Diophantine equation ... has a solution" is true.
Taking the axioms of ZFC to be true or "possibly true" in the sense here
at issue implies, for one thing, taking every arithmetical consequence of
ZFC to be true.

  Yet others are frankly dubious about even the consistency of ZFC. I don't
think there is any compelling argument to convince any of these people that
ZFC is consistent.

   >Are the proofs by Cohen and Godel are formal proofs? (I would think
   >so.) Can we identify the formal system in which the proofs were
   >performed?

  The proofs you are talking about are as formal as anything in mathematics.
On logical grounds, it is known that the statement "if ZFC is consistent,
CH is undecidable in ZFC" is provable by an elementary combinatorial proof.
From: greil@guug.de (Anton Greil)
Newsgroups: sci.math
Subject: incompletness of arithmetic, conjugacy problem
Date: 14 Sep 92 19:12:24 GMT
Organization: Technical University of Munich, Germany

Many number-theoretical problems can be embedded into the context of
discrete subgroups of Moebius transformations.

In 1971 C.F. Miller has shown that the conjugacy problem is unsolvable for 
finitely generated linear groups, like e.g. the modular group or the Picard
group. Has it ever happened to a researcher, that the solution of an arithmetic
problem would have needed necessarily the solution of the conjugacy problem and
that thus the incompletness of arithmetic (Goedel) came to light ?

Toni
Newsgroups: sci.math
From: Oliver Schoett <schoett@informatik.tu-muenchen.de>
Subject: Re: Springer Verlag server
Organization: Inst. fuer Informatik, Technische Univ. Muenchen, Germany
Date: Tue, 15 Sep 1992 10:15:10 GMT

In article <stephen.715640509@mont> stephen@mont.cs.missouri.edu
(Stephen Montgomery-Smith) writes:

 > Does anyone know if it is possible to get the Springer-Verlag files for
 > submitting articles via ftp?

They have a mail server: send mail with the line 'HELP' in the body to
svserv@dhdspri6.bitnet


Oliver Schoett     Inst. f. Informatik (H2), Technische Univ. M"unchen
                   Postfach 20 24 20,     8000 M"unchen 2,     Germany
schoett@informatik.tu-muenchen.de    phone +49 89 2105-2399  fax -8207
Newsgroups: sci.math
From: hporopudas@tnclus.tele.nokia.fi
Subject: Re: Proof of God's Existence
Organization: Nokia Telecommunications.
Date: Sun, 6 Sep 1992 15:51:24 GMT


In article <ARA.92Sep4201537@camelot.ai.mit.edu>,
ara@zurich.ai.mit.edu (Allan Adler) writes:
> Hannu writes:
>
>>Definition: God is Existence.
>>Theorem: Existence exists.
>
>
> This is not a defintion. Even if I knew what "existence" was, I would
> still have to figure out what "Existence" is.
>
> Allan Adler
> ara@altdorf.ai.mit.edu

    As I said earlier I think that we humans can never define "Existence"
  completely, this is partly due to the point of view that there may exist
  several unknown dimensions in very small scale about which we don't know
  anything at the moment and about which we perhaps will never know anything.
  And "Existence Himself" is possibly capable to choose the form and scale of
  His manifestation as He likes. These are the main reasons why it seems to
  me that it is senseless try to define "Existence" completely.

            Hannu.

 "Good is one, pleasant is an another matter. These two lead man to very
  different goals. Who chooses good, will become happy. Who keeps pleasant
  better, will loose his goal. Wises let never pleasant delude themself.
  They choose good. Mads become entangled only in pleasant's toils and they
  get lost.

  Thrown to ignorance man gives himself to work and employment and by
  keeping himself sensible and learned he steggers without goal like
  blind lead by blinds.
       ...

  Body is like a waggon, in front of which sences are harnessesed like horses.
  Mind is like bridle, with aid of which driver, in other words, brains keeps
  horses, in other words sences, holds in check. Soul controls waggon, and
  the road is matter's world, where sences are working. If bridles are not
  kept firmly and wisely, then sences get on the loose like refractory horses,
  and waggon does not get to the destination. If man is wise and holds
  his mind in check, then his sences are like good horses, controlled
  by a good driver.
       ...
  When knots of heart are undone and man is free from earthly attachments,
  man becomes immortal."

              (Indian wisdom, Kat'ha upanisad, roughly translated)
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: 2n = difference of primes?
Date: 6 Sep 92 13:13:58 GMT
Organization: U of Cambridge, England

Er, it's not an open problem to prove that 2 is the difference of SOME pair of
primes...
-- 
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Couple of questions
Date: Fri, 11 Sep 1992 13:22:13 GMT
Organization: University Of Kentucky, Dept. of Math Sciences

In article <1992Sep9.102457.15049@news.columbia.edu> pvl2@cunixb.cc.columbia.edu (Priscilla V Loanzon) writes:
>Could someone please explain to me a few basic things:
>
>What is the logic used to answer questions of the below type?
>
>1) If the finite group G contains a subgroup of order 7 but no element
>(other than the identity) is its own inverse then the order of group G
>could be (a)27   (b)28   (c)35   (d)37   (e)42.
>
>It says that the correct anwer is (c). I know why we can eliminate (a)
>and (d) but don't know how to proceed further.
>
>
>
SInce G contains a subgroup of order 7,Lagrange's theorem tells us that
the order of G is divisible by 7.  This rules out (a) and (d).  THe other
hypothesis tells us that G has no element of order 2; thus the order of G
can not be divisible by 2 (use Sylow theorem here).  This eliminates (b)
and (e).

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu


Newsgroups: sci.math
From: rairan@ecf.toronto.edu (RAI Ranjan)
Subject: Chess Problem
Organization: University of Toronto, Engineering Computing Facility
Date: Fri, 11 Sep 1992 22:10:37 GMT

In celebration(?) of the Fischer-Spasky rematch in Yugoslavia, I thought I'd post
a little chess problem I encountered in high school.
 
Chess Problem:
     Eight rooks are placed at random on a chessboard.  What is the probability that
   no two rooks can attack one another?
        
-- 
Ranjan Rai                             <rairan@ecf.toronto.edu> 
Engineering Science 9T3                <rairan@eecg.toronto.edu>
University of Toronto                      
Newsgroups: sci.math
From: west@symcom.math.uiuc.edu (Douglas West)
Subject: Re: Graph Problem
Organization: University of Illinois at Urbana
Date: Tue, 15 Sep 1992 04:59:18 GMT
Keywords: Combinatorial problem, bipartite graphs.

The original poster asked for bounds on the number of complete matchings in a
bipartite graph with partite sets V,U, where |V|<=|U| and each vertex in V has
degree l<=|V|, and where the graph satisfies Philip Hall's marriage condition
and therefore has a complete matching (saturating |V|, that is).

The best possible upper bound is l^l.
The best possible lower bound is l!, which is a special case
of a 1948 theorem of Marshall Hall.

In general, if d is the minimum degree of vertices in V, M. Hall's theorem
states that there are at least d(d-1)...(d-k+1) matchings,
where k is the minimum of d and |V|.  This is proved by induction on |V|.
Newsgroups: sci.math