HDTenEightyP/NetNews huggingface dataset:
From: zeleny@husc10.harvard.edu (Michael Zeleny)
Newsgroups: sci.math,sci.philosophy.tech
Subject: Re: Numbers and sets
Date: 3 Jan 93 03:36:34 GMT
Organization: The Phallogocentric Cabal

In article <1992Dec28.165203.402@guinness.idbsu.edu>
holmes@opal.idbsu.edu (Randall Holmes) writes:

>I'm avoiding nested quotations here.
>
>On "purports to mean"; that was a slip of the metaphorical tongue.
>Zeleny certainly did succeed in meaning what he said.

Thank you.

>Certainly Foundation asserts that a _nonempty_ set is disjoint from
>one of its elements :-(   Sorry about that.

No sweat.

>My profession is relevant; Zeleny is claiming that the _definition_ of
>a concept within the sphere of my work implies certain things.  Zeleny
>undermines his own position by pointing out an alternate approach to
>the notion of "set", that which regards sets as extensions of
>predicates.  Obviously, I regard stratified comprehension (the
>comprehension axiom of NF or NFU) as an acceptable version of the
>latter approach; the mere existence of the alternate approach casts
>doubt on the claim that Foundation is an analytic property of sets.
>
>It is quite true that if one regards "set" as being defined in terms
>of the iterative hierarchy, Foundation becomes analytic.  Well-founded
>sets are well-founded for the same sort of reason that bachelors are
>unmarried.  But Choice remains open to doubt (I don't doubt it,
>myself, but I don't regard it as analytically true of sets, either).

Randall, you are conveniently neglecting the history of the matter.
Cantor, Dedekind, and Zermelo were there long before Quine and Jensen;
moreover, their use of the term is overwhelmingly prevalent among set
theoreticians.  Your professional entitlement in no way absolves you
from the responsibility for usurping a term possessed of a well-defined
conventional meaning.  You have acknowledged that your reference to
"sets" involves a radically unorthodox conception of the same; surely
you do not fancy that there remains a practical chance that it would
prevail over the Cantorian one.  Indeed, even with the Axiom of Choice,
where one may cite genuine mathematical motivations for alternative
assumptions (vs. the extramathematical considerations adduced by Aczel
and Co in favor of rejecting the Axiom of Foundation), the consensus is
that the descriptive set theorists who adopt the Axiom of Determinacy,
are really investigating a *deviant* set theory.  Thus, inasmuch as I am
conducting this discussion in accordance with the social conventions of
the English language, I am perfectly well justified in assuming that
sets are characterized as members of the cumulative hierarchy, and so
likewise -- in claiming that Foundation and Choice are analytically true
of sets.

>-- 
>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

cordially,
mikhail zeleny@husc.harvard.edu
"Le cul des femmes est monotone comme l'esprit des hommes."
From: mnewman@comlab.ox.ac.uk (Matthew Newman)
Newsgroups: sci.math
Subject: After brackets
Date: 22 Dec 92 11:18:37 GMT
Organization: Oxford University Computing Laboratory, UK
Originator: mnewman@client40.comlab

Was it on this news group that someone asked what comes after curly
braces, and someone replied that you can use an overscore to denote
priority ?

If so, then you might like to know that it's called vinculum (pl.
vincula) from the Latin vincire "to bind". It's amazing what you
pick up doing crosswords.
Newsgroups: sci.math
From: steve@hubcap.clemson.edu ("Steve" Stevenson)
Subject: Re: Rounding Rules
Organization: Clemson University
Date: Wed, 23 Dec 1992 14:01:48 GMT

In article <1992Dec20.003018.14325@sol.ctr.columbia.edu> shaw@toadflax.UCDavis.EDU (Rob Shaw) writes:
>
>What is the rationale behind the following rounding rule?
>
>when dealing with 5's followed by all zero's, check the
>next digit to the left. If it's even, round down; odd,
>round up.
>
>For example both 1.13500 and 1.14500 are 1.14 to 3 places.
>What is the advantage of having the interval closed at both
>ends around even digits, and open at both ends around odds?
>

The problem with many of the "rounding rules" is that they are biased.
In the IEEE round of rules, an attempt is made to make rounding as unbiased
as possible. Round to even is specified as the rule of choice, since it
avoids many of the problems of "round to infinity" or "round towards zero".

See any good (and recent) text on architecture or see

@article{ goldberg,
 author={David Goldberg},
 title={What every computer scientist should know about floating-point
        arithmetic},
 journal={Computing Surveys},volume=23,number=1,year=1991,
 pages={5--48}
}

-- 
===============================================================================
Steve (really "D. E.") Stevenson           steve@hubcap.clemson.edu
Department of Computer Science,            (803)656-5880.mabell
Clemson University, Clemson, SC 29634-1906
Newsgroups: sci.math,comp.edu,misc.education
From: thomasd@tps.COM (Thomas W. Day)
Subject: Re: Education crisis (was RE: how much math...)
Organization: TPS
Date: Wed, 30 Dec 1992 15:12:03 GMT

In article <PRENER.92Dec30022205@prener.watson.ibm.com> prener@watson.ibm.com (Dan Prener) writes:

>   > Little kids learn much faster. ...
>   > But the fact that little kids' learning capacity is so much greater
>   > than that of older people ...
>   Is there any evidence for this?  It goes against my experience.
>Of course, there are those who believe that young childrens' superiority
>at learning language is so dramatic that there must be some other
>mechanism at work beyond general learning ability, some switch that 
>shuts off the ability to learn languages after a certain age.
 
How about the complexity of life, in general?  A child only has that one 
task to accomplish, assuming a fairly normal home life.  Children don't have 
to look for practical applications for the things they learn, they just 
absorb the good and the bad with barely any discrimination.  Later, adults 
have to justify the effort because they are juggling many other complex 
tasks.  A friend of mine, with a photographic memory, told me that memory 
was a function of how complex you life is: the more complex, the less you 
can learn.  He felt he was his own evidence.  As he grew older, he saw his 
concentration fade as outside interference increased.

>So, for another example, less often cited but more dramatic, consider how
>much an infant learns in the first year or two of life.  Most of the
>informal physics one knows, about the effects of gravity, light, sound,
>heat, etc., is learned in that period.  In addition, the complex skills
>of hand-eye coordination, upright locomotion, controlled voice production,
>are learned then.  So are the philosophical distinctions between self and
>other, and the social complexities of communication, even ignoring language.
>And on, and on.

I think you are still keeping the kind of information learned very simple.  
As a person ages, the information becomes more complex.  Can you really 
equate learning child-observed physics with learning a programming 
language?  I can't.  

>Think about the amount one learns as a child not measured in terms of the
>number of equivalent academic courses, but in pure information-theoretic
>terms: the number of bits of information.  Can you suggest another age
>at which that bit rate is higher?

The unemployed age?  When an educated person finds himself obsolete, one 
option is to learn a whole new technology and find a new life.  Many people 
do this, encumbered by a complex daily life.  I think this overwhelms the 
rate that a child accumulates *complex* knowledge.
Newsgroups: sci.math
From: ted@nmsu.edu (Ted Dunning)
Subject: Re: Bayes' theorem and QM
Reply-To: ted@nmsu.edu
Organization: Computing Research Lab
	<449@mtnmath.UUCP> <1992Dec26.080126.12238@monu6.cc.monash.edu.au>
Date: Sun, 27 Dec 1992 21:58:45 GMT


In article <1992Dec26.080126.12238@monu6.cc.monash.edu.au> darice@yoyo.cc.monash.edu.au (Fred Rice) writes:

   >It seems likely
   >to me that some form of deterministic chaos also underlys the seemingly
   >fundamental nature of probability in quantum mechanics.

   Interesting... I have had the same thought of this possibility too.  Does 
   anyone know if any work on how chaos and fundamental QM might relate has 
   been done?  If so, can anyone give any helpful references or names?


this is called the hidden variable interpretation of quantum
mechanics.

it has been shown to be incompatible with experiments.  the basic
problem is that of correlation of wave functions and whether or not
correlated wave functions can communicate faster than the speed of
light. 

basically, you have to either give up the hidden variables or
causality.  (you pick which one you prefer).

Newsgroups: sci.math,sci.physics
From: charlie@umnstat.stat.umn.edu (Charles Geyer)
Subject: Re: Banach-Tarski (_NOT_ Re: Bayes' theorem and QM)
Organization: School of Statistics, University of Minnesota
Date: Thu, 31 Dec 1992 19:59:31 GMT

In article <1hu8buINN8ve@gap.caltech.edu> allenk@ugcs.caltech.edu (Allen Knutson) writes:
>charlie@umnstat.stat.umn.edu (Charles Geyer) writes, under a wholly
>inappropriate subject line:

Wow, a subject line flame.  Happy holidays to you too, buddy.  This subject
line is also inappropriate.  You missed the point.

>>If you think that every "real world" set should be measurable, and hence
>>Lebesgue theory is a waste of time, then you object to more of classical
>>mathematics than just the axiom of choice.
>
>>Not so?
>
>Not so. Solovay proved in 1970 that the axiom "All subsets of the reals are
>measurable" is consistent with ZF (obviously not with ZFC), under some
>standard large cardinal assumption. I think I have this right... Allen K.

So?  Does this mean I should burn all of the measure theory texts on my
bookshelf?  The question is what kind of integration theory does that leave
you with?

-- 
Charles Geyer
School of Statistics
University of Minnesota
charlie@umnstat.stat.umn.edu
Xref: sparky sci.math:17441 alt.books.technical:396
From: erik@naggum.no (Erik Naggum)
Newsgroups: sci.math,alt.books.technical
Subject: Re: High Prices of Math Books. I am pissed.
Date: 27 Dec 92 21:39:54 GMT
Reply-To: Erik Naggum <enag@ifi.uio.no>

Joseph Fortt <jfortt@dorsai.com> writes:
|
|   More important Dover has a nonreturn policy; once a bookstore buys
|   the book from Dover it is stuck with it (unlike most publishers who
|   have to deal constant returns).

This is not the problem it appears to be.  Dover books are classics in
their field.  Euclid: The Elements is not going to come in an updated
edition any time soon, for instance.

The bookstore can just hold on to the copy, and accumulate interest on
the initial investment in it, add "shelf rent" and sell it when a buyer
eventually comes around asking for it.

Dover does a very good job, and deserve credit for their long-range
publishing policies in a market where other publishers go bananas if
they can't recover their costs in the first three months after release.

Best regards,
</Erik>
--
Erik Naggum                 ISO  8879 SGML                    +47 295 0313
                            ISO 10744 HyTime
<erik@naggum.no>            ISO  9899 C                 Memento, terrigena
<SGML@ifi.uio.no>           ISO 10646 UCS             Memento, vita brevis
Newsgroups: sci.math.research
From: agw@ground.cs.columbia.edu (Art Werschulz)
Subject: Multivariate Legendre polynomials
Originator: dan@symcom.math.uiuc.edu
Reply-To: agw@cs.columbia.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: CS Dept, University of Texas at Austin
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 28 Dec 1992 17:04:03 GMT

Does anybody have references about multidimensional Legendre
polynomials defined over simplexes in $d$-dimensional space?  

Thanks.

      Art Werschulz
      InterNet:  agw@cs.columbia.edu
      ATTnet:    Columbia University (212) 939-7061
                 Fordham University  (212) 636-6325

Newsgroups: sci.math.research
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Variational Problem
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Wed, 23 Dec 1992 17:11:31 GMT

It seems these days that calculus of variations is a lost art. I have
talked to a number of top-flight mathematicians about the following
problem and none of them could help in solving it. (I can't solve it
either). Can anyone help?

Let  L(x) be an unknown function, let u be a parameter to be optimized,
let F be an known integer, and let P(a,b) be a known (but messy!) function.

Find L(x) and u to minimize

	u
       ---
       \
	\   L(b)
	/
       /
       ---
       b=1

subject to:


	u	L(b)
       ---     -----
       \       \
	\       \       P(a,b)   >= F
	/       /
       /       /
       ---     -----
       b=1    a= -L(b)

I know how to compute P(a,b), but dealing with it analytically is
intractable. It is the product of two Dickman's rho functions.

Can anyone help? How do I solve the above problem?
 
Notes:

(1) One can, of course, turn the above discrete problem into a continuous
    one by changing the sums into Stieltje's integrals.

(2) P(a,b) is as follows:

Let rho(t) be Dickman's rho function, given by the differential-delay
equation   t rho'(t) = rho(t-1).  Let FB and M be integers.  Then, P(a,b) is:

mu(a,b) mu'(a,b)

where

mu(a,b) = integral from  beta-alpha to beta-1 of  rho(t)/(beta-alpha) dt

where  alpha = log(FB)/log(a + bM)
       beta = 2*alpha

mu'(a,b) = integral from beta'-alpha' to beta'-1 of rho(t)/(beta'-alpha') dt

where	alpha' = log(FB)/log(a^d - k b^d)      d,k known
	beta' = 2 alpha'

mu and mu' are respectively the probability that a+bM  and a^d-kb^d factor
into the product of primes up to FB, with possibly a single additional factor
between FB and FB^2.
 
Basically what is happening is that we want to find a function bounding an
area so as to minimize that area, subject to a (joint) density function 
over that area summing to at least F.
--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"

Newsgroups: sci.math.research
From: Allan Adler <ara@zurich.ai.mit.edu>
Subject: points
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: M.I.T. Artificial Intelligence Lab.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 25 Dec 1992 06:58:34 GMT


Let X be a scheme. There are various toposes associated to X, more than
I can name here. These include the Zariski topos, the etale topos,
the flat topos, the fppf topos, the fpqc topos, the crystalline topos,
etc.

There is a notion of a point of a topos. A point of a topos T is a morphism
of toposes p:Ens-->T, where Ens is the topos of sets. I think that in the case 
of the Zariski topos, one recovers X as the set of points of the Zariski topos,
as least if X is Noetherian and separated, but I could easily be mistaken.

At any rate, I would be interested in knowing what are the points of the
various toposes associated to X. Is it known in all these cases?

I know that in Artin's book Algebraic Spaces, he considers a scheme over
an algebraically closed field and at each point x of the scheme, considers
the ring of algebraic functions defined at x, while in SGA 4.5 one
talks about strictly henselian local rings containing the local rings of 
X (if I remember correctly). So maybe these are the points of the etale topos,
the rings of algebraic functions being a sufficient family of points.

Thus, for the Zariski and etale toposes, I have a fraction of an idea, possibly
wrong. For the other toposes associated to X, I have no idea. 


Allan Adler
ara@altdorf.ai.mit.edu

Newsgroups: sci.math.research
From: dvf@kepler.unh.edu (David V Feldman)
Subject: Exposition of Riemann Surfaces
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of New Hampshire  -  Durham, NH
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 25 Dec 1992 04:13:28 GMT

I am wondering if anyone has ever given an exposition of the
basic theory of Riemann surfaces that systematically did everything
on the universal covering space.  The idea would be that having
global coordinates would allow all objects such as differentials
of various sorts to be viewed as functions with appropriate
transformation properties, and theorems like Riemann-Roch, Serre
Duality, Abel-Jacobi might be accessible, in some guise, to readers
with only a basic knowledge of complex variables, but no significant
background in topology, sheaves, cohomology and the like.  I am
especially thinking here of compact Riemann surfaces of genus greater
than 2.

If no such exposition exists, in part, or in whole, I am interested
in opinions on what parts of the theory would be awkward from this
point of view.

David Feldman


Newsgroups: sci.math.research
From: asimov@nas.nasa.gov (Daniel A. Asimov)
Subject:  Critical Points of Gaussian Curvature
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: NAS, NASA Ames Research Center, Moffett Field, California
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 22 Dec 1992 00:49:10 GMT

The Four-Vertex Theorem states that the curvature function on a smooth 
simple closed curve in the plane has at least 4 critical points.

Now consider a closed hypersurface M^n smoothly embedded in R^(n+1). 

Let "Gaussian curvature" K denote the determinant of the Jacobian of the
Gauss map G: M -> S^n (obtained by setting G(x) =  the outward unit normal 
to M at x).

QUESTION:
	Is there some generalization of the Four-Vertex Theorem for the 
	Gaussian curvature of such hypersurfaces in R^(n+1) ?

	Intuitively, if M were a non-degenerate ellipsoid, it would apparently
	have 2n critical points of its Gaussian curvature K: M -> R.  So, is 
	there evidence for or against the possibility that

		The Gaussian curvature K: M -> R of an 
		arbitrary smooth hypersurface 
		M^n in R^(n+1) must have at least 2n critical points.
	?

	Possible cases to consider:	a)	M is convex 
					b)	M is topologically S^n 
					c)	M is arbitrary.


Dan Asimov
Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000

asimov@nas.nasa.gov
(415) 604-4799

P.S.  To avoid questions of differentiability I have assumed that everything
in sight is smooth, although a finite number of derivatives would almost
certainly suffice.

Newsgroups: sci.math.research
From: burchard@horizon.math.utah.edu (Paul Burchard)
Subject: Re:  Critical Points of Gaussian Curvature
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Minnesota
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 22 Dec 1992 09:47:10 GMT

In article <1992Dec22.004910.20943@nas.nasa.gov> asimov@nas.nasa.gov (Daniel A.  
Asimov) writes:
> QUESTION:
> 	Is there some generalization of the Four-Vertex Theorem for the 
> 	Gaussian curvature of such hypersurfaces in R^(n+1) ?
> 
> 	Intuitively, if M were a non-degenerate ellipsoid, it would apparently
> 	have 2n critical points of its Gaussian curvature K: M -> R.  So, is 
> 	there evidence for or against the possibility that
> 
> 		The Gaussian curvature K: M -> R of an 
> 		arbitrary smooth hypersurface 
> 		M^n in R^(n+1) must have at least 2n critical points.
> 	?
> 
> 	Possible cases to consider:	a)	M is convex 
> 					b)	M is topologically S^n 
> 					c)	M is arbitrary.
> 
[The ellipsoid would have 2(n+1) critical points...I am responding to that
conjecture here.] 

I proposed this same problem (in the case of topological spheres) to the crew
here at the Geometry Center.  Ken Brakke found a very neat and simple
counterexample, namely a BANANA!  This has only four critical points.  By
slightly "banana-izing" a sphere, you can also get convex counterexamples
with just four critical points.

Still, I would expect that the minimum number of critical points for the
curvature will always be greater than the trivial minimum of 2.

P.S. Ken won $10 for his ingenuity...
--
--------------------------------------------------------------------
Paul Burchard	<burchard@geom.umn.edu>
``I'm still learning how to count backwards from infinity...''
--------------------------------------------------------------------

Newsgroups: sci.math.research
From: Alejandro <rivero@cc.unizar.es>
Subject: Re: points
Originator: dan@symcom.math.uiuc.edu
X-Xxdate: Tue, 29 Dec 92 14:06:58 GMT
X-Useragent: Nuntius v1.1.1d12
X-Submissions-To: sci-math-research@uiuc.edu
Organization: ftuz
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Date: Tue, 29 Dec 1992 13:09:30 GMT
X-Xxmessage-Id: <A7660C0281039318@m14724.unizar.es>

I had one or two questions to add to Adler ones, perhaps
some naughty cathegorist there can answer easily.

First, is the category of conmutative C*-algebras a topos?
Being as it is the dual (or it was the antiequivalente?) of the
category of compact topological spaces, it would be a  topos or sort of, am I
correct?

Second, what about the category of all C* algebras, this is, including the no
conmmutative algebras? Following Connes, you can use ANY C* algebra to make
diferential geometry. And you have "points" and "arcs" (R-->M or dually
C(M)-->R). This would have a categorial counterpart.

Third, which is the difference  from the categorial point of view of the two
categories? This would be: Which is the correct categorial formulation of
conmuttativity? But I m not sure if there are more diffs.

I dont know if categorists are or not in the side of Connes but I think they
would have something to say about all this stuff of non conmutative geometry,
manifolds etc...

Alejandro Rivero
rivero@cc.unizar.es

Newsgroups: sci.math.research
From: hammond@csc.albany.edu (William F. Hammond)
Subject: Re: Exposition of Riemann Surfaces
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Dept of Math & Stat, SUNYA, Albany, NY
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Sat, 26 Dec 1992 22:16:54 GMT

In article <1he1p8INNlh0@mozz.unh.edu> dvf@kepler.unh.edu
(David V Feldman) writes:

> I am wondering if anyone has ever given an exposition of the
> basic theory of Riemann surfaces that systematically did everything
> on the universal covering space.  The idea would be that having
> global coordinates would allow all objects such as differentials
> of various sorts to be viewed as functions with appropriate
> transformation properties,  . . .

This is the theory of "automorphic functions" in dimension 1.
For a first reference I would suggest:  C. L. Siegel, Topics in
Complex Function Theory, volume II (Automorphic Functions and Abelian
Integrals), English translation by A. Shenitzer & M. Tretkoff,
Interscience Tracts in Pure & Appl. Math., No. 25, Wiley-Interscience,
1971.

----------------------------------------------------------------------
William F. Hammond                   Dept. of Mathematics & Statistics
518-442-4625                         SUNYA, Albany, NY 12222 (U.S.A.)
hammond@csc.albany.edu               FAX: 518-442-4731
----------------------------------------------------------------------

Newsgroups: sci.math.research