HDTenEightyP/NetNews huggingface dataset:
From: guckes@math.fu-berlin.de (Sven Guckes)
Subject: Re: Einstein's Erdos number
Summary: And the question is : "Where is Erdos now?"
Originator: guckes@medusa
Organization: Free University of Berlin, Germany
Date: Wed, 2 Sep 1992 11:00:15 GMT

gerry@macadam.mpce.mq.edu.au (Gerry Myerson) writes:

>In article <Btwt5H.A6n@watserv1.uwaterloo.ca>, shallit@graceland.uwaterloo.ca (Jeffrey Shallit) writes:
>[...]
>> In the preface to "A Tribute to Paul Erdos", Cambridge University Press,
>> 1990, it is stated that Einstein's Erdos number is 2.

Erdos has just been to our faculty here in Berlin.
He said that he's improved the "Erdos distance function (EDF)" a little bit:
For those persons who have published with him more than once it is

	EDF(person) := 1/(#co-published papers)

I understand that Erdos thus wants to acknowledge for more than one co-work. 

Sven

>> That means there exists a person who has written a paper with Einstein,
>> and a paper with Erdos.  Anybody know who it is?

>Just a guess, but Ernst Straus was an assistant to Einstein in the late 40s, 
>and surely a co-author of Erdos'. 
Newsgroups: sci.math,sci.philosophy.tech
From: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Subject: Re: Proof of God's Existence
Organization: Indiana University
Date: Tue, 1 Sep 1992 21:37:11 GMT

In article <1992Sep1.135132.5195@dcs.glasgow.ac.uk> jack@dcs.glasgow.ac.uk (Jack Campin) writes:

>What you might have in mind is Robert K. Meyer's "God Exists!", published
>in the American philosophical journal "Nous" around 1980.  It uses Zorn's
>lemma in a version of Aquinas's "first cause" argument.  Meyer is a serious
>and reputable (if idiosyncratic) logician, and a Christian; the paper isn't
>a leg-pull like the Ian Stewart item mentioned here before.

Well, it seems to me that the paper is not entirely serious.  The abstract
certainly seems to have tongue firmly ensconced in cheek:

 Meyer, Robert K.  God exists. Nous 21, 345-361 S 87.

 Building on a suggestion communicated in conversation by Hilary Putnam, this
 article provides a definite answer to a previously disputed question of
 philosophy by establishing the existence of God. In outline the argument
 (which the reader may find somewhat familiar) goes as follows: Everything has
 a cause; therefore there is a First Cause, namely God.  Objections to the
 effect that the argument is refuted because causal sequences can descend
 forever are themselves refuted by a timely appeal to Zorn's Lemma.

Particularly nice touches in this send-up of philosophical pretensions
include the "definite answer to a previously disputed question", along
with the "somewhat familiar" and the name-dropping.  (Thanks to Calvin
Ostrum for pointing out this abstract to me.)

The paper itself is quite fun, although it does rest on some dubious
assumptions, viz: (1) to get the upper bounds required for the
application of Zorn's Lemma, one must postulate that there is something
causally anterior to every item in a given causal sequence; (2) to
establish the uniqueness of God (who is, of course, a First Cause), one
must assume that for any two events, there is some item that is
causally anterior to both.

It follows as a simple corollary that the existence of God is equivalent
to the axiom of choice (to get the converse implication, just let
God do the choosing).  Meyer notes that this immediately rules out
the possibility of a constructive proof of God's existence (i.e. one
that doesn't appeal to Choice), as such a proof would imply that
the axiom of choice was not independent of the other axioms, contra
Cohen.  He also suggests that given the equivalence of the axiom of
choice and the existence of God, AC should hereafter be ascribed to
Aquinas rather than Zermelo.

-- 
Dave Chalmers                            (dave@cogsci.indiana.edu)      
Center for Research on Concepts and Cognition, Indiana University.
"It is not the least charm of a theory that it is refutable."
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: coskeleton
Date: 3 Sep 92 01:10:22 GMT
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.


Let C be a category and let X be a simplicial object of C. How do I
construct the coskeleton kth coskeleton of X? What assumptions are
needed on the category C for the k-th coskeleton to exist for all X and
all k ?

Where is this written down?

Allan Adler
ara@altdorf.ai.mit.edu
From: Madeleine Thomas
Subject: HELP!! Inscribed Circle Problem
Organization: Bell-Northern Research
Date: Thu, 27 Aug 1992 13:03:27 GMT

HELP! HELP! HELP!

Surely one of you math whizzes can assist me?

I'm writing a computer program that needs to do
the following: given two points on earth, call them 'a' and 'b';
 each point being in lat/long coordinates, 

a) find the shortest distance between the points;
b) given point 'b' and a distance 'R', what is the quickest method of
determining 
whether another point 'c' is in the circle defined by radius R around point
'b'. 

I have over 6 million data points to search through.

or, stated another way;

I know that Jane lives in Washington, DC, at Lat X, Long Y.  I have a list of
all
the K-Marts in the entire world (with their respective Lat-Long coordinates). 

a) what is the closest one to her? How far is it?
b) list all K-Marts within distance R from Jane.

All suggestions/answers appreciated!

Thanks in advance!!!

Madeleine Thomas

P.S. I have to write this thing today...for some VP that the boss promised it
too!
Newsgroups: sci.math
From: jacek@tut.fi (Nieweglowski Jacek)
Subject: Re: Psuedo Random sequences   Help needed
Organization: Finnish University and Research Network FUNET
Date: Mon, 31 Aug 1992 07:43:18 GMT


To generate pseudo random sequences you need
a shift register, which you described. The
connections in the register are described by
so called PRIMITIVE POLYNOMIALS. If you
want to use 12-bit register use following polynomial

y = x^12 + x^6 + x^4 + x + 1

This effectively means that the output (shifted out)
has to be EX-ORed with bit '1', the result of this
EX-ORed with bit '4' and the result of that with bit
'6' and the result fed back into the highest bit of
the register. So the register should look like

 ________________________+_____+___________
|			 ^     ^           ^
|			 |     |           |
 -> 12--11--10--9--8--7--6--5--4--3--2--1----> bits out

the register should be initialized with any 
nonzero bit pattern and will generate pseudo
random sequence of lenght 2^12-1.
Below are the primitive polynomials for other
number of bits. They are represented as 
polynomial coefficients 
1,0,1,1 represents x^3 + x + 1

Note that primitive polynomials are not unique.
There can be thus alternative polynomial and
what follows register architecture.

int
  primpol3[]={1,0,1,1},
  primpol4[]={1,0,0,1,1},
  primpol5[]={1,0,0,1,0,1},
  primpol6[]={1,0,0,0,0,1,1},
  primpol7[]={1,0,0,0,1,0,0,1},
  primpol8[]={1,0,0,0,1,1,1,0,1},
  primpol9[]={1,0,0,0,0,1,0,0,0,1},
  primpol10[]={1,0,0,0,0,0,0,1,0,0,1},
  primpol11[]={1,0,0,0,0,0,0,0,0,1,0,1},
  primpol12[]={1,0,0,0,0,0,1,0,1,0,0,1,1},
  primpol13[]={1,0,0,0,0,0,0,0,0,1,1,0,1,1};


Jacek
-----------------------

Jacek Nieweglowski
Signal Processing Laboratory
Tampere University of Technology
P.O. Box 553
SF 33-101 Tampere, Finland

jacek@cs.tut.fi
--
From: matt@amsaa-cleo.brl.mil (Matt Rosenblatt)
Newsgroups: sci.math
Subject: Minimizing waste when cutting fabric.
Summary: Algorithm or computer program wanted.
Keywords: Waste; Fabric
Date: 2 Sep 92 15:35:02 GMT
Organization: U.S. ARMY MATERIEL SYSTEMS ANALYSIS ACTIVITY (AMSAA), APG, MD.

Suppose I am an upholsterer who buys fabric in rolls.  Each roll is
54 inches wide, and I can assume it is infinitely long:

                               Y
            -------------------------------------------
           |                                          /
           |                                         /
        X  |                                        |   . . .
           |                                         \
           |                                         /
            -----------------------------------------

Suppose I need to cut  n  pieces  P_i,  where  P_i  is to be a 
rectangle  x_i  inches wide in the  X  direction, and  y_i  inches 
long in the  Y  direction.  (Because of the pattern in the fabric,
a rectangle  x" wide by  y"  long is not equivalent to a rectangle
y"  wide by  x"  long.)  I can start at the beginning of the roll,
cutting a few rectangles whose combined width  w  does not exceed 
54".  When I can no longer fit any more rectangles at the beginning, 
I can start cutting rectangles out of the as-yet-unused material.
Once I start doing this, a strip of fabric  (54" - w) wide will
have to be wasted.  I want to cut the  n  pieces in such a way
as to minimize this waste.

This must be a basic version of a much more general problem where
the pieces to be cut can take all sorts of shapes.  Surely there
have been algorithms designed for the more general case.  What kind
of algorithms are they, and where can I find them?

					-- Matt Rosenblatt
					(matt@amsaa-cleo.brl.mil)
Newsgroups: sci.math,sci.physics
From: phew@mullet.gu.uwa.edu.au (Phew)
Subject: Re: math and physics degrees
Organization: University Computer Club --- Perth, Western Australia
Date: Wed, 26 Aug 1992 10:07:29 GMT

This is at a slight tangent, but anyway...

I am an undergraduate, planning to do a double major in Maths and Physics.
At our university, it is possible to be admitted to Masters of Engineering
directly from honours in Science.
 Is this a good way to go (Has anyone actually done this?). I also plan
to go on and get a Ph.D ASAP, and so have a similar problem to that being
discussed here - Ph.D in Maths, Physics or Engineering.
 Note - I don't intend to be responsible for a flame war between the merits
of the fields, but I want to go into research at NASA or some similar place
and want to maximize my options.

Thanks in advance.

Patrick Hew
1st Year Science/ Engineering
University of Western Australia
From: holmes@opal.idbsu.edu (Randall Holmes)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
Date: 4 Sep 92 19:25:28 GMT
Organization: Boise State University Math Dept.

In article <1992Sep1.090011.1@tnclus.tele.nokia.fi> hporopudas@tnclus.tele.nokia.fi writes:
>
>In article <17ui6kINNsft@matt.ksu.ksu.edu>, bubai@matt.ksu.ksu.edu
>(P.Chatterjee) writes:
>> I was told by somebody that there is a mathematical proof of God's existence;
>> was wondering if somebody could shed some light on the same.
>>
>> Thanks. Looking forward to the response.
>
>   I think that God's existence is an axiom. He says in the Holy Bible (Second
> book of Moses 3:14-15 in Old Testament and also in Johannes 8:28-29 in New
> Testament) that He is "Existence Himself".
>   If someone is arguing that "Existence Himself" does not exist, I think that
> at the same time he/she is arguing that he/she himself/herself does not exist.
>
>              Hannu.

This reminds me of the student who responded to my (true) assertion
that we can prove in ZF that the universe does not exist (i.e., there
is no set containing everything) by asking why we were bothering with
the course (or anything) if there were a mathematical proof that
nothing exists.  It is not a prerequisite for the existence of
individual objects that the abstract object "existence" exist.
-- 
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: jmarlan@titan.nmt.edu (Jon Marlan)
Subject: Re: Math Legend: Who Is This Story About?
Organization: New Mexico Tech
Date: Tue, 25 Aug 1992 14:31:28 GMT


Concerning Karl Friedrich Gauss:

Howard Anton's "Calculus" 3rd ed. (pp. 1172-1173) lists yet
another astonishing story about Gauss.  When he was not yet
3, Gauss surprised his parents with his genius.  One day when
his father was computing the weekly payroll for workers under
his charge, young Gauss spotted a mistake in his calculation and
gave the correct sum.  His parents rechecked the sum to find
that little Gauss was correct!

Jon
From: bwallet@apssgi.nswc.navy.mil (Brad Wallet)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
Date: 2 Sep 92 12:50:20 GMT
Organization: Naval Surface Warfare Center

In article <1992Sep2.084837.1@tnclus.tele.nokia.fi>, hporopudas@tnclus.tele.nokia.fi writes:
|> 
|> In article <1992Sep1.123533.14058@relay.nswc.navy.mil>,
|> bwallet@apssgi.nswc.navy.mil (Brad Wallet) writes:
|> > In article <1992Sep1.090011.1@tnclus.tele.nokia.fi>,
|> hporopudas@tnclus.tele.nokia.fi writes:
|> > |>
|> > |> In article <17ui6kINNsft@matt.ksu.ksu.edu>, bubai@matt.ksu.ksu.edu
|> > |> (P.Chatterjee) writes:
|> > |> > I was told by somebody that there is a mathematical proof of God's existence;
|> > |> > was wondering if somebody could shed some light on the same.
|> > |> >
|> > |> > Thanks. Looking forward to the response.
|> > |>
|> > |>    I think that God's existence is an axiom. He says in the Holy Bible (Second
|> > |>  book of Moses 3:14-15 in Old Testament and also in Johannes 8:28-29 in New
|> > |>  Testament) that He is "Existence Himself".
|> > |>    If someone is arguing that "Existence Himself" does not exist, I think that
|> > |>  at the same time he/she is arguing that he/she himself/herself does not exist.
|> > |>
|> > |>               Hannu.
|> >
|> > Mr. Space Potato has left/was run off sci.physics and has found a new home.
|> > Please, before this gets started, take it to alt.talk.does.not.belong.here.
|> 
|>   Can't we ever get rid of these unbusinesslike comments.
|> 
|>                    Hannu.


I don't know a thing about business so I can't help you there.  I am after
all a mathematician and consider myself entirely technical.  I defended
your write to freedom of speech in the sci.physics channel.  Now, well, I
don't know anymore.  I want to discuss math.  The original poster was
looking for a mathematical proof.  I won't comment on that, but let us 
just say that I am skeptical God's existance can be proved by just using
math.

One reason I supported you was I didn't think you were serious.  I thought
your point was a six year old child is as likely to come up with a correct
theory of time/space as a theoretical physicist sitting alone in his office.
Now, if you are trying to demonstrate an example of a circular arguement,
let me know, and I will support you again.

Brad
From: jake@skatter.usask.ca
Newsgroups: sci.math
Subject: Royal Road of Caratheodory
Date: 28 Aug 92 03:13:52 GMT
Organization: University of Saskatchewan

Hello everyone.

A few years ago while still an undergrad I happened upon a conversation in
which a technique for solving differential equations called the "Royal
Road of Caratheodory".  This is supposed to be some way to obtain a test
function which you then ram back through the DE to fine-tune.
I have been meaning to look further into the matter, but as usual it got
put on the back burner.  Waay back.

Anyway, I would appreciate finding out more about this "Royal road",if 
anyone has any information, references, etc.  please mail them to me.

Thank you very much and have a good day.

jake@skatter.usask.ca
From: soeren@cse.ucsc.edu (Soren Soe)
Newsgroups: sci.math
Subject: x 2^x = 2^n ?
Date: 26 Aug 92 20:01:30 GMT
Organization: University of California, Santa Cruz (CE/CIS Boards)
NNTP-Posting-Host: arapaho.ucsc.edu

Can anyone tell me what `x' is in this equation:

	x 2^x = 2^n

Is there a general solution, or do I have to approximate `x' to something like
x = n - lg n + a_little_more ?
In fact I can do with an approximation to x, iff 
		floor(x) <= app(x) <= x

I need the "floor" of `x' to solve the following summation, where k 
would be equal to floor(x):

	i=n-1
	SUM   min(2^i, 2^2^(n-i))
	i=0

	i=k	     i=n-1
    =   SUM  2^i  +  SUM   2^2^(n-i)
	i=0	     i=k+1

--soeren

Soren Soe,
soeren@ce.ucsc.edu
Newsgroups: sci.math
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: dividing 100 digit nos.?
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Wed, 26 Aug 1992 14:56:00 GMT

In article <17g3f1INN220@hilbert.math.ksu.edu> bennett@math.ksu.edu (Andy Bennett) writes:
>comptec91065@camins.camosun.bc.ca writes:
>
>>	Can you help me locate the easiest method of dividing
>>	integers of at least 100 digits (possibly up to 4300 digits) ?
>
>Use UBASIC. This is a public domain basic developed by Yuji Kida in Japan
>with full support for integers up to about 2500 digits. It also comes with
>state of the art number theory algorithms already coded (for primality
 
With all due respect: [this is not a flame]

I do not believe that you answered the question that was asked, although
you may have answered what the poster *meant to ask*.

What was asked about was the easiest *method* for doing division on 100
digit integers. That information can be found in Knuth Vol. 2
The poster may have wanted to know how it is done, rather than wanted
a black box to do it.

I may be wrong, in that the poster was really asking where he could
find software to perform what he wanted, but in absence of other information
I answer what is asked, rather than try to fathom what is *meant*.
 
Also, while UBASIC is an EXCELLENT piece of software, it isn't quite
state-of-the art. [at least the version I have isn't.]
 
If I am off base here, please tell me.
--
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
From: morgan@math.psu.edu (Ilene Morgan)
Subject: Re: Solitaire games
Organization: Penn State Department of Mathematics
Date: Wed, 2 Sep 1992 17:20:22 GMT

In article <4906@balrog.ctron.com> wilson@web.ctron.com (David Wilson) writes:
>
>
>    I used to put three hours a day on the road to and from work.  My
>    game was to factor license plate numbers in my head (preferably
>    before I lost sight of the car).  A simpler game was to try to
>    break the numbers on the license plate into two groups whose sum is
>    the same. 
>
>
>
>-- 
>David W. Wilson (wilson@ctron.com)
>
>Disclaimer: "Truth is just truth...You can't have opinions about truth."
>- Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."

My game with license plates is to try to find a word that contains the
letters of the license plate in order, not necessarily consecutively.
For example, XPV -> expressive.  My license plate used to have XPF; I never
did think of one for that.

Ilene
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Newsgroups: sci.math
Subject: Re: A matrix anti-derivative puzzle
Date: 31 Aug 92 19:19:51 GMT
Distribution: usa

In <52675@dime.cs.umass.edu> bradtke@greed.cs.umass.edu writes:


>I have a problem involving the anti-derivative of a matrix function.
>I would like to find a function F such that 

>dF/dw = - G'w

>or

>dF/dw = (G - G')w,

>where G is a nonsymmetric matrix, and w is a vector.
>The quadratic form F = w'Gw gives, of course, dF/dw = (G+G')w.

The equation d^2F/dw_i/dw_j = d^2F/dw_j/dw_i gives us that if G is a constant
matrix, and 

     dF/dw = G' w, 

then G is symmetric.

--
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; if you want to be sure I see a post, mail it.
Newsgroups: sci.math
From: jrickard@eoe.co.uk (John Rickard)
Newsgroups: sci.math
Subject: Re: Elementary solution needed: harmonic bi-sequences
Date: 31 Aug 92 15:57:25 GMT
Organization: EO Europe Limited, Cambridge, UK
X-Newsreader: Tin 1.1 PL3

ap@levangerhs.no (Andrei Prasolov) writes:
: 
:    There is a problem which seems to have a very simple solution.
: I remember that I heard one in my youth. That solution used
: the epsilon-delta language only. However, I cannot recall that.
: 
: DEF. Let`s call a bi-sequence (a(i,j), i,j from Z) HARMONIC if for all i,j
: 
: (*)       a(i,j) = 1/4 (a(i,j+1) + a(i,j-1) + a(i+1,j) + a(i-1,j)).
: 
: PROBLEM. Prove that any bounded (|a(i,j)| < C) harmonic bi-sequence is
: constant.

Rewrite (*) as:

     a(i,j) = (1/8) a(i,j+1) + (1/8) a(i,j-1) + (1/8) a(i+1,j)
                      + (1/8) a(i-1,j) + (1/2) a(i,j)            (1)

By substituting (1) in itself and repeating a number of times we get,
for each N >= 0:
                    (N)
     a(i,j) = sum  B  (m,n) a(i+m,j+n)                           (2)
              m,n

where
      (0)
     B  (m,n)  =  (  1,    if m=n=0
                  (  0,    otherwise

      (N+1)                (N)                (N)
     B    (m,n)  =  (1/8) B  (m,n+1) + (1/8) B  (m,n-1)

                             (N)                (N)
                    + (1/8) B  (m+1,n) + (1/8) B  (m-1,n)

                             (N)
                    + (1/2) B  (m,n)                             (3)

We have (proofs left as exercise for the reader):

                      (N)
     For fixed N, n, B  (m,n) is monotonically increasing for m < 0,
     reaches its maximum at m = 0, and is monotonically decreasing
     for m > 0.  It is 0 for m sufficiently far from 0.          (4)

          (N)
     sum B  (0,n) -> 0 as N -> infinity.                         (5)
      n

From (2):
                                    (N)        (N)
     | a(0,0) - a(1,0) | = | sum ( B  (m,n) - B  (m-1,n) ) a(m,n) |
                             m,n
                                    (N)        (N)
                         < C sum | B  (m,n) - B  (m-1,n) |       (6)
                             m,n

From (4) we have:

            (N)        (N)                (N)
     sum | B  (m,n) - B  (m-1,n) |  =  2 B  (0,n)                (7)
      m

Combining (6) and (7):
                                    (N)
    | a(0,0) - a(1,0) |  <  2C sum B  (0,n)                      (8)
                                n

By (5), the RHS of (8) tends to 0 as N -> infinity, so a(0,0) and
a(1,0) must be equal.  Similarly any two adjacent values of a(i,j)
must be equal, so a(i,j) is constant.
From: chaas@coe.drexel.edu (Chuck Haas)
Newsgroups: sci.math
Subject: Re: Additional info on "trends" question
Date: 28 Aug 92 17:55:38 GMT
Organization: Drexel University
X-Useragent: Nuntius v1.1b2

Use of Mann's test for trend (see Kotz and Johnson, Ency. of
Statistical Sciences, vol5, p 207).

sort paired observations (Xi, Yi) according to X (in your case, year)

compute sign(Yj-Yi) for all i<j;  sign(arg) = arg/absolute value(arg)

define S* = sum of sign(Yj-Yi)

For large samples, S* null distribution is normal with zero mean and
variance given by:

(1/18) [n(n-1)(2n+5)- SIGMA u(u-1)(2u+5)]

where n = number of observations
           u = multiplicity of ties (if two observations Y are equal,
u=2; if three are equal
                 then u=3, etc.) for each "tuple"

Reject null hypothesis (i.e. trend is statistically significant) based on
comparison
to tables of the standard normal distribution.

Comment:
	This test obviously neglects the information contained in your year
intervals, however does not require many assumptions that exist for
example in regression analysis.

Perhaps someone else would have information on the relative power of this
test to  regression.

==============
Charles N. Haas
Betz Chair Professor of Environmental Engineering
Drexel University
Philadelphia PA
Xref: sparky sci.math:10959 sci.psychology:3635