HDTenEightyP/NetNews huggingface dataset:
From: seal@leonardo.Jpl.Nasa.Gov (David Seal)
Subject: How do I get the FAQ?
Keywords: FAQ
Organization: Jet Propulsion Laboratory
Date: Tue, 13 Oct 1992 22:39:21 GMT

see the subject line.  thanks!
--
-----------------------------------------------------------------------------
David Seal                 |  Jet Propulsion Laboratory  |     sunset: 7:54pm
seal@leonardo.Jpl.Nasa.Gov |       Mission Design        |   temp: 82 degrees
Xref: sparky sci.math:13314 sci.physics:16648
Newsgroups: sci.math,sci.physics
Subject: Refining the Crackpot Index
From: bob@1776.COM (Robert Coe)
Date: Fri, 16 Oct 92 08:44:17 EDT
Distribution: world
Organization: 1776 Enterprises, Sudbury MA

jbaez@riesz.mit.edu (John C. Baez) writes:
> >Expressing disdain for the elitism of "fancy mathematics" must surely
> >merit extra credit on the Crackpot Index.
>
> I would certainly like to include this one, but as a strong proponent of
> "fancy mathematics" myself I fear I am hopelessly biased.  Many good
> physicists, including Feynman, Phil Morrison and Steve Weinberg, have at
> times expressed their disdain for mathematics that is too "fancy".  I have
> always regarded this as childishness comparable to the mathematicians' 
> occaisional cracks at physics.

Yes, but it's worth remembering that the fanciness of the mathematics re-
quired to describe a phenomenon can constitute a warning that there is an
underlying simplification waiting to be discovered.  Kepler's mathematical
formulation of planetary motion, for example, was a lot simpler than Tycho 
Brahe's.

   ___            _                                           -  Bob
   /__) _   /    / ) _   _
(_/__) (_)_(_)  (___(_)_(/_______________________________________ bob@1776.COM
Robert K. Coe ** 14 Churchill St, Sudbury, Massachusetts 01776 ** 508-443-3265
Newsgroups: sci.math
From: wft@math.canterbury.ac.nz (Bill Taylor)
Subject: Another chocolate fish problem.
Organization: Department of Mathematics, University of Canterbury
Date: Wed, 14 Oct 1992 03:41:12 GMT

I'm glad to see that among all the religious proselytizing, requests for
medical costs handouts, wood-duck comments, and *endless* debating about
Barbie dolls,  there is *still* some actual math happening in this newsgroup.

Let me add to this majority interest with an easy-ish problem. As always,
first fully correct answer may claim a chocolate fish off me personally, on
any visit to Christchurch, New Zealand.
----

Define  u(n) = number of ordered partitions of n into 1's & 2's only.

e.g. u(4) = |{ 1111 , 112 , 121 , 211 , 22 }| = 5 .

Define  v(n) = number of ordered partitions of n into 2's & above.

e.g. v(6) =  | { 6 , 42 , 24 , 33 , 222 } |  = 5 .

PROBLEM: prove u(n) = v(n+2) for all n.
------------------------------------------------------------------------------
             Bill Taylor              wft@math.canterbury.ac.nz
------------------------------------------------------------------------------
      This sentence does not have the property it claims to be lacking.
------------------------------------------------------------------------------
From: kibler@turing.ICS.UCI.EDU (Dennis Kibler)
Newsgroups: sci.math
Subject: NxN tile puzzle
Date: 15 Oct 92 23:56:51 GMT


 I assume that the NxN tile sliding puzzle
has been solved, although possible not optimally.
I would appreciate a reference to any  algorithmic solution.
Thanks
Xref: sparky sci.math:13280 sci.physics:16609
From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Newsgroups: sci.math,sci.physics
Subject: Re: "The Universe of MOTION" (crackpot index)
Date: 16 Oct 92 00:08:47 GMT
Organization: University of Virginia

In article <1bkpg2INNmt1@smaug.West.Sun.COM> Richard.Mathews@West.Sun.COM (Richard M. Mathews) writes:
>jbaez@riesz.mit.edu (John C. Baez) writes:
>
>>I want the index to be easy to compute.  In fact, what I'd really like
>>would be an index that could be computed automatically.
>
>Ask and ye shall receive.  Just before reading your posting, I completed
>just such a program.  My simplified rules are:
...

>2.14634 Paul Budnik
>2.56065 Steve Carlip
>3.18687 Benjamin Weiner
>3.81494 RING, DAVID WAYNE
>4.23726 Cameron Randale Bass
>5.13109 Douglas G. Danforth
>5.66667 Tom Van Flandern
>5.79702 Robert Firth
>6.61422 Leigh Palmer
>6.66667 Dr. Norman J. LaFave <lafave@ial4.jsc.nasa.gov>
>7.21700 Ric Peregrino
>7.60326 Mcirvin
>7.89399 Matt Austern
>8.72341 Bronis Vidugiris
>8.75751 Daryl McCullough
>9.08969 Hartmut Frommert
>9.80049 Jim Carr
>10.4906 John C. Baez
>10.5006 hporopudas@tnclus.tele.nokia.fi
>10.6189 Richard M. Mathews
>11.1111 snarfy@cruzio.santa-cruz.ca.us
>11.8265 SCOTT I CHASE
>15.0000 Matthew P Wiener
>15.4365 Blair P. Houghton
>18.1966 Mcinnes B T (Dr)
>20.1698 Terry Bollinger
>25.6695 Jack Sarfatti

     Obviously, word choice and simple syntactic considerations are not 
     sufficient to discern true crackpots.

                                  dale bass
-- 
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926
From: torbenm@diku.dk (Torben AEgidius Mogensen)
Newsgroups: sci.math
Subject: Re: Looking for a slick proof
Date: 9 Oct 92 15:53:36 GMT
Organization: Department of Computer Science, U of Copenhagen

cyeomans@ms.uky.edu (Charles Yeomans) writes:

>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.

Yes, but that only proves that 2^(n/2) divides the product. However,
you can use that 4 divides every fourth number etc. Thus we have

(n+1) div 2 numbers where 2 is a divisor
(n+1) div 4 numbers where 4 is a divisor
(n+1) div 8 numbers where 8 is a divisor
etc.

All divisions round down. The numbers that divide by 2 also divide by
4 etc., so we get only one power of two for each number in each list.
Now,

n <= (n+1) div 2 + (n+1) div 4 + (n+1) div 8 + ... + (n+1) div log2(n)
  <= n+1-log2(n+1)

so 2^n divides the product above.

In order to see that the sum is at least n, consider how we round the
fractions. In the worst case, we round every fraction down, so we lose

1/2 + 1/4 + 1/8 + ... 1/log2(n+1) = 1-log2(n+1)

from the best case, where we always have exact divisions (when (n+1)
is a power of 2), so at worst we get

n+1-log2(n+1) - (1-log2(n+1)) = n

Q.E.D.

	Torben Mogensen (torbenm@diku.dk)
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: consequences of the Axiom of Choice
Date: 8 Oct 92 14:58:07 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: holmes@opal.idbsu.edu (Randall Holmes)

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)
From: P.Samet@cs.ucl.ac.uk (Paul Samet)
Newsgroups: sci.math
Subject: Re: Polya Question
Date: 7 Oct 92 10:31:15 GMT

Polya died on 7 September 1985, at Palo Alto, following a stroke.

There is a very comprehensive obituary of him, with a description and
assessment of his work in "Bulletin of the London Mathematical Society", Vol
19, part 6, number 81, November 1987, pages 559-608.

The LMS established a prize in his honour, with money donated by his widow, in
1986.  The first holder of the prize, in 1987, was J. H. Conway.

Paul Samet
Newsgroups: sci.math
From: niall@nmsu.edu (Niall Graham)
Subject: Re: a graph problem
Organization: Computing Research Lab
Distribution: sci.math
Date: Thu, 8 Oct 1992 02:36:00 GMT


>What is the maximum number of nodes possible in a graph if all nodes have
>degree at most d (in my case d=16) and the distance between any two nodes
>is at most dist (i.m.c. dist=4) ??

Naturally, this is called the degree-diameter problem.
One of the papers in the second last issue of Discrete Applied Math.
(spceial issue on networks) contains the latest table of values.  
I've heard a rumor that a few of these values have recently been
surpassed though.   The recent flurry of new values has been due to
the use of Cayley coset graphs (& supercomputers) in the construction 
of new examples.  
I've mislaid my copy of the Table, so I can't
give you the latest "bid" on entry (16,4).

--

Niall Graham     "We live in an age that reads too much to be wise,
Los Alamos            and that thinks too much to be beautiful"
                                                        Oscar Wilde
From: rehman@math.bu.edu (Naved Rehman)
Newsgroups: sci.math
Subject: FAREY
Date: 15 Oct 92 00:07:38 GMT
Organization: Department of Mathematics, Boston University, Boston
Originator: rehman@math.bu.edu



are there any applications of FAREY SEQUENCE?
From: whorf@vnet.ibm.com
Newsgroups: sci.math
Subject: Egyptian Fractions
Date: 15 Oct 1992 07:08:59 -0500
Organization: UTexas Mail-to-News Gateway
NNTP-Posting-Host: cs.utexas.edu

For all integer fractions a/n (GCD = 1) with a fix nominator a > 1 there exist
(depend. from a) n0 > 0 in such a way that for all n >= n0 the fraction can be
written in egyptian form as the sum of max. of 3 unit fractions 1/x + 1/y + 1/z
(egyptian fractions). For a = 2 only 2 fractions are sufficient, for a = 3
3 unit fractions are necessary. The first nontrivial case with a = 4 is a
conjecture by Erdoes/Straus (1950). There is now the general conjecture for
a >= 4 (Schinzel/Sierpinski). Is this the latest state of the art or are
there more recent results? What are the newest algorithms for building
egyptian fractions (perhaps computer programs)?
Newsgroups: sci.math
From: rickert@mp.cs.niu.edu (Neil Rickert)
Subject: Re: What a weird group!!!
Organization: Northern Illinois University
Date: Thu, 15 Oct 1992 20:27:38 GMT

In article <1992Oct15.045312.13089@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>
>From an exercise in a book:  The Bohr compactification of the real
>numbers is a compact topological group which contains the real numbers
>as a dense set.  The embedding of the reals into the Bohr group is not a
>homeomorphism.
>
>Well, actually that in itself is not so weird now that I think of it.
>One can embed the real numbers in the torus as a subgroup, namely a line
>of irrational slope, and then it's dense but the image of the reals in
>the torus with the induced topology is not homeomorphic to the reals
>with their usual topology.  (I think this is what was meant by the
>exercise above, by the way.)  
>
>But I bet the Bohr group is a lot weirder than the torus.  
>
>Here's how you get it. ...

I believe this amounts to the same as the following:

  Start with the real numbers as a discrete group (i.e. every point is
  both open and closed.  Now take the dual group.  That group is the
  compact, since the dual of a discrete group is compact.  The dual
  group is just the group of continuous characters (i.e. representations
  into the circle group).

  The continuous reals are self dual, with the characters w(t) = exp(iwt).
  Every such character is also a character on the discrete reals, which
  gives the embedding.

Yes, it is a little weirder than a torus.

Consider, that the discrete reals is an infinite direct sum of copies of
the discrete rationals.  When we go to the dual group, the Bohr group is
an infinite product of copies of the dual of the rationals.  Now if it
were an infinite product of copies of the dual of the integers it would
be an infinite dimensional torus.  So, in some ways, the weirdness comes
in going from the dual of the integers (the circle group, or reals mod 1)
to the dual of the discrete rationals.

The rationals have, as a subgroup, the integers.  The quotient group is
one in which every element is of finite order (some multiple of a fraction
is an integer).  This means that in the dual group there is a subgroup
which is a totally disconnected compact group (topologically much like
the cantor set), such that the quotient group is the circle group.  Look
at it this way - take the line, and wrap it around (mod 1) to get the
circle group.  Now instead wrap it (mod 2) to get another circle group,
which contains the first circle as a quotient.  Do the same (mod 2*3).
Keep going using factorial n in the nth step.  In the limit, you have
the dual of the discrete rationals.
From: proberts@informix.com (Paul Roberts)
Newsgroups: sci.math
Subject: Re: Mattel on women
Date: 8 Oct 92 23:40:11 GMT
Organization: Informix Software, Inc.

In article <1b1h8oINNgl@master.cs.rose-hulman.edu> goddard@NeXTwork.Rose-Hulman.Edu (Bart Goddard) writes:
>
>I think our opinions depend on how we imagine Barbie's quote.  It makes
>a difference whether she says "Ooooh!  Math class is sooooooo haaaard!

Quite right. Barbie may be being quoted quite out of context! Where are
those investigative journalists when we really need them?
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Barbie update
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Thu, 8 Oct 92 04:15:06 GMT

I just found this on another newsgroup and thought it might provide
some more facts for our little quarrel about Barbie.

          WASHINGTON (AP) _ Girls aren't good at math! That's the
message that Mattel Toys is sending out with its newest Barbie Dolls,
complains a national women's group.
           The American Association of University Women on Thursday
demanded the immediate recall of all Teen Talk Barbie Dolls,
claiming the dolls' words perpetuate sexist stereotypes.
           One of the doll's phrases: ``Math class is tough!''
           ``Barbie has been criticized in the past for presenting girls
with an unobtainable model of female physical perfection,'' said
Sharon Schuster, the association's president.
           ``By reinforcing the dated stereotype that math is too hard
for girls, Barbie can undermine girls' confidence in their mental
ability to do math,'' Schuster added. ``Why can't Barbie say `I'm
good at math,' or `Math class is fun'?
           Mattel, based in El Segundo, Calif., never intended to send
the wrong message, said Mattel spokeswoman Donna Gibbs.
           Gibbs said the dolls also say many positive things like
``Let's start a business,'' ``I love school, don't you?'' and ``I'm going
to be a veterinarian.''
           ``Mattel in no way meant to discourage girls from pursuing
education in the math and science fields,'' she said. ``If Barbie
talks in the future, we will take into account these concerns.''
           Each talking Barbie utters four phrases, randomly selected
during production from a list of 270. The idea said is to make each
Barbie doll unique.
           The talking Barbie hit the stores in July and contains a
microchip that prompts the doll to speak at the push of a button.
The doll retails for about $25.


"If Barbie talks in the future..." - so perhaps she will just shut up
and avoid controversy.  :-)

I would like to see the list of 270 phrases to see what the average
Barbie is like.  Presumably there aren't contradictory pairs of phrases,
since randomly picking *both* would yield a split personality Barbie.

I like that pickup line: "Hey, babe, let's start a business."
From: mbk@jacobi.ucsd.edu (Matt Kennel)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Date: 15 Oct 1992 00:35:28 GMT
Organization: Institute For Nonlinear Science, UCSD
NNTP-Posting-Host: jacobi.ucsd.edu
X-Newsreader: Tin 1.1 PL3

joe@astro.as.utexas.edu (Joe Wang) writes:
: In article <1992Oct5.144142.2182@alchemy.chem.utoronto.ca> mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
: >     Every year in my physical chemistry class, I find bright women who
: >are terrified of math.  (This is far more common than male mathphobes.)
: 
: I get exactly the same experience in my astronomy class.
: 
: >Since their performance in this course (and indeed their past
: >performance in calculus and physics) indicates that they can use
: >mathematically phrased ideas if simultaneously pushed and properly
: >tutored, why are they so afraid? 
: 
: That's been my experience too.  There don't seem to be any sex-linked
: differences in how difficult males and females find the math in the
: class or how well they can do it.  The problem is that a large
: fraction of people in the class have this psychological block against
: believing that they can do math, and a disproportionate number of
: these people are female.

There's the social aspect of taking science and math classes.  Specifically,
working on the problem sets.  Typically men will get together in study
groups and work out the problems togther.  They learn from each other and
when they face difficulties they attribute it to "The professor didn't
explain this clearly, the T/A didn't go over that, the book is written in
ancient Chinese, the problems are ridiculous and vague, etc".  Some of that
may be justified and other parts simple arrogance, but it helps people to
stick with it.

Women often have fewer friends in the class, are more likely
to end up working alone, and when they can't do all the problems themselves
without help (which men don't usually attempt to do) they think that they
must be stupid, and maybe women really are intrinsically inferior.



Note that this is in contrast to the usual pop-psych generalization that
men are competitive loners vs cooperative social women, but appears to be 
true.


Perhaps then, a good solutions, would be for teachers and TA's to specifically
organize problem sessions and encourage full participation by all students,
especially those who seem to be out of the social mainstream in the
class.

--
-Matt Kennel  		mbk@inls1.ucsd.edu
-Institute for Nonlinear Science, University of California, San Diego
-*** AD: Archive for nonlinear dynamics papers & programs: FTP to
-***     lyapunov.ucsd.edu, username "anonymous".
From: mstemper@ems.cdc.com (Michael Stemper)
Newsgroups: sci.math
Subject: Re: 'Perfect' numbers
Date: 12 Oct 92 21:43:35 GMT
Reply-To: mstemper@ems.cdc.com
Organization: Empros Systems International, a division of Ceridian

dagjo@ifi.uio.no (Dag Espolin Johnson) writes:
>Does someone have a list of the first numbers (as many as possible) that are
>'perfect'?

This is taken from a post by Julien Cassaigne (Ecole Normale
Supe'rieure) back in February. It probably should be in the
FAQ, as this is the second time this month that I've answered it.

	6
	28
	496
	8128
	33550336
	8589869056
	137438691328
	2305843008139952128
	2658455991569831744654692615953842176

[from Sloane's Handbook of Integer Sequences, sequence #1744]

-- 
#include <Standard_Disclaimer.h>
Michael F. Stemper
Power Systems Consultant
mstemper@ems.cdc.com
Newsgroups: sci.math
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: 'Perfect' numbers
Date: Mon, 12 Oct 1992 17:22:35 GMT
Organization: Security APL, Inc.

In article <Bvzsy7.B9E@ux1.cso.uiuc.edu> simms@ux1.cso.uiuc.edu (dan) writes:
>guckes@math.fu-berlin.de (Sven Guckes) writes:
>>If I remember correctly then the following are perfect numbers, too:
>
>>496
>>2128
>
>>Unfortunately I don't have a reference at hand.
>
>496 is, but 2128 isn't or at least the program I wrote says it isn't..
>..it has chugged out past 10,000 without finding one

You're both wrong.  2128 is not a perfect number, but 8128 is.
Newsgroups: sci.math
From: fokp@bray1b.its.rpi.edu (Pingtao (Ben) Fok)
Subject: Math and Society
Keywords: Math and Society
Reply-To: fokp@rpi.edu
Organization: Rensselaer Polytechnic Institute, Troy, NY.
Date: Fri, 16 Oct 1992 00:19:32 GMT

I am writing a journal on Math and Society.  I am trying to understand
the relationship between Mathematics and Society.  Is there a way to 
think society in terms of mathematics idea?  Please feel free to send 
me Email and post you opinion.  That would be very very helpful.
Thanks
Ben
fokp@rpi.edu    (how much you got to know before you know how little
you know)
From: Frederick.A.Ringwald@dartmouth.edu (Frederick A. Ringwald)
Newsgroups: sci.math
Subject: Re: Calculating pi: help!
Date: 15 Oct 92 03:44:05 GMT
Organization: Dartmouth College, Hanover, NH
X-Posted-From: InterNews1.0a5@newshost.dartmouth.edu

Below is a repost from sci.astro, which I hope is helpful. I now have a
calculation to 50,000 places, which took about 2.5 hours (as I was
saying, it isn't the fastest machine in town). If you want it, please
e-mail, although keep in mind it's over 100K long.

Newsgroups: sci.space
From: Frederick.A.Ringwald@dartmouth.edu (Fred Ringwald)
Subject: Re: Math programs with arbitrary precision for the Mac?
X-Posted-From: InterNews1.0a5@newshost.dartmouth.edu
Organization: Dartmouth College, Hanover, NH
Date: Wed, 14 Oct 1992 01:27:10 GMT

In article <seal.719016011@leonardo>
seal@leonardo.Jpl.Nasa.Gov (David Seal) writes:

>  other mac programs or ways of computing pi?

You mean like this?

N[Pi, 1000]
3.1415926535897932384626433832795028841971693993751058209749\
 
  4459230781640628620899862803482534211706798214808651328230\
 
  6647093844609550582231725359408128481117450284102701938521\
 
  1055596446229489549303819644288109756659334461284756482337\
 
  8678316527120190914564856692346034861045432664821339360726\
 
  0249141273724587006606315588174881520920962829254091715364\
 
  3678925903600113305305488204665213841469519415116094330572\
 
  7036575959195309218611738193261179310511854807446237996274\
 
  9567351885752724891227938183011949129833673362440656643086\
 
  0213949463952247371907021798609437027705392171762931767523\
 
  8467481846766940513200056812714526356082778577134275778960\
 
  9173637178721468440901224953430146549585371050792279689258\
 
  9235420199561121290219608640344181598136297747713099605187\
 
  0721134999999837297804995105973173281609631859502445945534\
 
  6908302642522308253344685035261931188171010003137838752886\
 
  5875332083814206171776691473035982534904287554687311595628\
 
  6388235378759375195778185778053217122680661300192787661119\
 
  590921642

This was done in about 4 seconds just now, read by me from a clock
on-screen, so it might be better, on a Mac II with 5 Megs of RAM, a
68030 chip with a 68881 coprocessor (which I'm not sure is even used),
under System 7.0.0 with virtual memory disabled, because it has never
worked on this machine - i.e., not the greatest Mac around, probably
slower than a new Classic II - with Mathematica 2.0.3 Enhanced. 

It's no wonder Mathematica is rapidly emerging as the standard, at
least in academia. Not only was I able to redo all the math I had in
all of high school, college, and grad school in an afternoon (my
favorite command is still InverseLaplaceTransform[expr, s, t]), but
it's also frighteningly easy to use. Pricey, but well worth it, and no,
Steven Wolfram didn't pay me to write this. (Perhaps he should...)

E-mail me if you're interested in 10,000 or more places,
fred.ringwald@dartmouth.edu
From: gagibson@grad07.math.ncsu.edu (Gregory A. Gibson)
Newsgroups: sci.math
Subject: Re: Question on real numbers
Date: 8 Oct 92 22:13:25 GMT
Organization: NCSU Mathematics Dept.


       In the previous post I should have said that the extensions need to
   be finite extensions for something of this sort to work in a computer to
   solve say, a linear system where all of the numbers involved are in the
   finite extension field.

        -- Greg Gibson