HDTenEightyP/NetNews huggingface dataset:
From: rryan@panix.com (Rob Ryan)
Subject: Re: Three-sided coin
Date: Mon, 23 Nov 1992 14:35:29 GMT
Organization: Panix, NYC

In <1992Nov23.012622.14231@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:

>In article <1992Nov20.191504.17650@husc15.harvard.edu> blom@husc15.harvard.edu writes:
>>I came late to this thread, but it sounds like you are looking for a coin
>>that would land 1/3 of the time on either face and 1/3 of the time would
>>stabilize on its side.  For this to be so the width of the coin should
>>equal its radius.  
>
>Prove it.

Yeah.  That would guarantee that the surface area of the edge was the same as
surface area of the two sides (added together), but is that sufficient?  It
seems like other factors would play (like average distance from the center of
gravity) into the equation.
-- 
 Rob Ryan
    Internet:   rryan@panix.com or Robert_Ryan@brown.edu
    Bitnet:     ROBR@BROWNVM
    Compu$erve: 70324.227@compuserve.com
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: ok, i'll bite.
Organization: Computer Science Department,  Stanford University.
Date: Mon, 16 Nov 1992 19:04:32 GMT

In article <92320.214859RVESTERM@vma.cc.nd.edu> <RVESTERM@vma.cc.nd.edu> writes:
>i understand "cryptography".  i understand "np".  someone please
>explain the connection.

NP is the class of problems whose instances encrypt or hide their
easily seen solution.  For example the set of composites is in NP:
hidden in every composite pq is a factor between 2 and pq-1, an easily
recognized key giving away the secret of pq's compositeness.

Cryptography is not defined as formally as NP, so one cannot hope for
an exact correspondence.  For example the one-time-pad cryptosystem
does not have a corresponding NP notion.  Here one makes up a random
bitstring R of length that of the message M, and sends R and R+M (their
XOR) by two different routes.  Each of R and R+M by themselves looks
completely random, but R+(R+M) = M.  Even exponentially much work
cannot extract M from either R or R+M by itself, showing that the full
resources of cryptography go beyond mere complexity obstacles of the
kind posed by problems in NP-P.

(Around 1978 Adi Shamir found a neat generalization of this to n
messages sent by that many routes, such that one must intercept at
least m of them to read the message.  If m = n/2 the adversary must
catch at least half the couriers to read the message, and block at
least half to stop it getting through.  With only m-1 couriers the
message remains completely hidden.  Other applications: shifty-eyed
couriers, infiltrated cells, etc.  Technique: make the parts of the
message the values of a degree m-1 polynomial at 1,2,...,n where the
message itself is the value at 0.)

However as a corollary of plausible assumptions about channels,
computing time, and application details, many practical cryptosystems
turn out to be no harder to crack than to decide membership for some
set in NP.  Cracking RSA for example reduces to factoring; it is in NP
(but not known to be NP-hard) to decide whether the i-th bit of the
larger factor of pq in the published key is 1.  (The converse
reduction, from factoring to cracking, is not known for RSA, but it is
known for a variant of RSA due to Michael Rabin, which is as hard to
crack as to factor integers.)
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.
Newsgroups: sci.math
From: qye@next7 (QIAN YE)
Subject: HELP!WEAK_CONVERGENCE_PROBABILITY.
Keywords: weak convergence, probability.
Organization: Michigan Technological University
Date: Wed, 18 Nov 1992 00:52:38 GMT

Hi. Do anyone know an example that a r.v. sequence converge weakly but not  
converge in probability? The sequence is supposed to converge to a  
constant.

My E.Mail:qye@mathlab.mtu.edu.
Thanks a lot.
Qian.
Xref: sparky sci.math:15091 sci.physics:19020
From: butler@rschp2.anu.edu.au (Brent Butler)
Newsgroups: sci.math,sci.physics
Subject: Re: 3-sided coin
Date: 16 Nov 1992 22:46:00 GMT
Organization: Australian National University
NNTP-Posting-Host: 150.203.35.27
Summary: Gravitational Potential energy!

The solution to this problem is simple.  When a coin is flipped it
will *come to rest* in a position that represents a minimum in its
(gravitational) potential energy.  For a real coin this means one
of its two faces with equal probability - it will never *come to
rest* on its edge even though it has a finite area because this is
a metastable state.

Our three sided coin, therefor, should be 1 coin diameter thick. This 
is where the center of mass is at equal heights in each of the three
states and so each configuration represents an equally likely
stable state for the coin to *come to rest* after a toss.

What was all that talk about honey anyway :^) 

-Brent Butler (butler@rschp2.anu.edu.au)
Newsgroups: sci.math
From: mueller@schaefer.math.wisc.edu (Carl Douglas Mueller)
Subject: Re: Square root of a number
Reply-To: mueller@schaefer.UUCP (Carl Douglas Mueller)
Organization: Univ. of Wisconsin Dept. of Mathematics
Distribution: na
Date: Wed, 18 Nov 92 14:29:32 GMT

>In article <1992Nov15.194049.1@woods.ulowell.edu> buxamusaa@woods.ulowell.edu writes:
>>Please could someone help me with an assignment that I have to do.
>>It is a very general question, though the answer could be quite lengthy.
>>"Discuss methods for finding the square root of a number."
>>What I am looking for are all possible methods/alogrithms for this.
                            ^^^^^^^^^^^^^^^^^^^^

There are MANY methods.  For example to find the square root of x.
1) Pick a random number r.
2) Compute r*r.  
3) if r*r <> x goto 1.

(OK, so this isn't an efficient method.  It is a method.   :-)  )
Newsgroups: sci.math
From: avatarp@well.sf.ca.us (Peter Rothman)
Subject: RSA Encryption
Summary: Algorithms to rapidly find prime factors
Keywords: cryptography, primes
Organization: Whole Earth 'Lectronic Link
Date: Sat, 21 Nov 1992 16:32:56 GMT


Although I am clearly not an expert on the subject, I believe the whole
debate regarding P=NP and RSA encryption security maybe moot.  In a recent
study I was messing around  with a pattern recognition algorithm and
attempting to find hard test cases for this algorithm.  One we tried was
predicting the digits of the next prime number.

Originally, I had supposed that algorithm would perform poorly on this  data
set, but in fact we found that we were able to predict the digits of prime
numbers with a success rate much greater than chance.  Although this work
was not taken any  further, I suspect that similar techniques could be used
to develop statistical algorithms which could make RSA useless.

In essence this type of algorithm would relax the problem of finding the key
to the problem of "probably" finding the key.  In otherwords, the algorithm
wouldn't be guaranteed to find any given key, but the probability of failure
could be controlled.

Once again I am not a mathematician (although I do have a BS in math) and my
idea maybe fatally flawed.  I welcome your comments...

Peter Rothman
avatarp@well.sf.ca.us

"The squirming facts exceed the squamous mind, if one may say so.  And yet
relation appears..."  Wallace Stevens
Newsgroups: sci.math,sci.physics
From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: Three-sided coin
Organization: ORA Corporation
Date: Tue, 17 Nov 1992 13:01:47 GMT

bhoughto@sedona.intel.com (Blair P. Houghton) writes:

>Summary: probability is distributed according to entropy, not energy

If we are talking about a flipped coin, I don't think it is
distributed according to either. The probability distribution on coins
depends on the way the coin is flipped and the initial orientation.
For example, if my coin is a cylinder (three sides), and flipping
consists of rolling it, then it has essentially zero probability of
landing on either of its two ends.

Perhaps there is a way to flip a cylinder so that the ends are given a
fair chance, but certainly it depends on the flipping mechanism. You
can't say that probability depends on energy, or surface area, or
entropy, independently of some model for how the flipping is done. And
different models will give different answers.

Daryl McCullough
ORA Corp.
Ithaca, NY
From: hrubin@mentor.cc.purdue.edu (Herman Rubin)
Newsgroups: sci.math
Subject: Re: Cryptography and P=NP
Date: 16 Nov 92 01:51:05 GMT
Article-I.D.: mentor.BxsD57.5MH
Organization: Purdue University Statistics Department

In article <1e6hraINNdui@manuel.anu.edu.au> des@thrain.anu.edu.au (David Stewart 249-4502 room 134) writes:
>
>If P=NP then **every** public key cryptosystem is in trouble!
>
>(Computing the private key given the public key is in NP -- given the private key
>the point is that the public key is easy to compute, but not vice-versa.)

Not necessarily.  Numerical  integration formulas of the type used in one
dimension extend polynomially to any number of dimensions.  But this makes
them so expensive that they are not even used too often in 3 dimensions.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
From: kosowsky@minerva.harvard.edu (Jeffrey J. Kosowsky)
Newsgroups: sci.math
Subject: Borel product measures
Date: 17 Nov 92 16:53:47 GMT
Organization: Harvard Robotics Lab, Harvard University


Suppose X and Y are topological spaces. Let E and F be their
respective Borel sigma-algebras. I am interested in knowing when the
product sigma-algebra ExF is itself Borel.
I know the following facts:

1] If the topologies on X and Y are second countable, then clearly ExF
is Borel.

2] In general ExF is not Borel.

3] Let u and v be Borel measures on (X,E) and (Y,F) respectively. Then
the completion (ExF)* with respect to uxv is not in general Borel.

3] If (X, E, u) and (Y, F, v) are locally compact, sigma-compact,
sigma-finite Borel regular measure spaces, the (XxY, (ExF)*, uxv) is a
locally compact, sigma-compact, sigma-finite *Borel* regular measure
space.
(This follows from a construction using the Riesz representation
xtheorem)

So I am interested in knowing under what conditions the completion
(ExF)* with respect to uxv contains all Borel sets.
Now, (3) shows that locally compact, sigma-compact, sigma-finite Borel
regular measures are sufficient to insure a Borel product
sigma-algebra. Can these conditions be relaxed. e.g. are sigma-finite
Borel regular measures sufficient?

Please provide a proof and/or reference for your suggested sufficient
conditions. Thank you!

Jeff Kosowsky
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: a first year grad student freaks out.
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 16 Nov 92 21:41:10 GMT

In article <1333@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>In article <1992Nov11.223722.29808@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>>
>>>In article <92314.170255RVESTERM@vma.cc.nd.edu> <RVESTERM@vma.cc.nd.edu> writes:
>>You think *you've* got it bad!  I'm a mathematics professor with nobody
>>to assign me things to prove!
>
>I can fix this for you in no time, John.

Sorry, I prefer to torture myself.

Newsgroups: sci.math
From: rkaivola@mits.mdata.fi (Risto Kaivola)
Subject: Re: Prime test algorithm
Organization: Microdata Oy
Date: Tue, 17 Nov 1992 16:26:06 GMT

[ I'm sorry if this appears twice. ]

rkinder@iat.holonet.net (Robert J. Kinder) writes:

>blom@husc15.harvard.edu writes:
> [asks information on C-language packages for doing big number arithmetics
   and some special things]
>: 
>: --Eric Blom

>The best package seems to be Arjen Lenstra's arbitrary precision
>arithmethic package written in C, based on what I've read.

>Try anonymous FTP from cl-next2.cl.msu.edu and look for lenstra_3.c in the
>BigNum directory.  The file should be about 91KB in size.  This package
>has -, +, *, /, mod, primality testing, and exponentiation plus other
>functions.
>-- 
>// Robert J. Kinder, Jr.                             Boca Raton, Florida  -

I tried to access the site, and it seems that it does permit access from
sites outside of North America.  Could you point me to some other sites
where the package might be located, or, alternatively, give me the exact
names of the files in package (including full paths)?  In the latter case,
I might be able to use DECFTP, which is presumably located in the USA.
 

--
Risto Kaivola
(Internet address:   rkaivola@mits.mdata.fi)
Newsgroups: sci.math
From: f88-ali@nada.kth.se (Anders Lindstrm)
Subject: Ramsey theory applications wanted!
Keywords: Ramsey 
Organization: Royal Institute of Technology, Stockholm, Sweden
Date: Wed, 18 Nov 1992 15:57:50 GMT

* QUESTION:
  --------
  Have you heard of any applications of Ramsey theory?
  If yes, which of the theorems are used, and which problems do they solve?

* BACKGROUND:
  -----------
  The reason for my interest is that I am preparing a lecture in Ramsey theory.
  To make the subject more interesting I need to give some examples of
  applications of the theory. 

  All I know about applications of Ramsey theory is that it could be used to
  build better communications networks, information transmission and retrieval   systems. But how? Which are the questions Ramsey theory answers in these 
  contexts?

  The litterature I have come across so far are:
 
  * 'Ramsey theory' by Graham, Rotschild and Spencer, Wiley 1990
  * Scientific American July 1990, 'Ramsey Theory' p.80-85, by Graham and
	 Spencer

* MY EMAIL-ADDRESS: 
  -----------------
  Please send your answers to f88-ali@nada.kth.se

  / Anders Lindstrom,
      student at The Royal Institute of Technology, Stockholm, Sweden
    


Xref: sparky sci.math:15112 comp.theory.dynamic-sys:351
From: wut@acf3.NYU.EDU (Tom Wu)
Newsgroups: sci.math
Subject: Re: Looking for Time Series Analysis software
Date: 16 Nov 92 16:07:00 GMT
Article-I.D.: acf3.8400003
Organization: New York University


 
	There is a package called RATS (Regression Analysis of
Time Series) that is very popular among academics. I have seen 
it being used by Columbia's Business School research center and
Citicorp's internal research dept. It is basically a high level
programming language that's capable of doing regrssions, ARIMA
model fitting and lots of Stat functions that I don't understand.
I think that it's distributed by VAR. I could check on that if
you are interested. The version I have is very old, and I am
not sure if they are making new versions of it.


			---Tom
 
Newsgroups: sci.math
From: drobot@sjsumcs.sjsu.edu (Vladimir Drobot)
Subject: Re: 1+1/2+1/3+1/4+...+1/n
Organization: San Jose State University - Math/CS Dept.
Date: Sat, 21 Nov 1992 04:02:20 GMT

1+1/2+1/3+1/4+. . . +1/n != an integer for any n != 1 actually

See Polya-Szego
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: confidentiality
Date: 23 Nov 92 01:49:27 GMT
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.


There are a number of circumstances in which one is expected to trust
people in positions of responsibility to treat information as 
confidential. My impression of how this works is that there is no
confidentiality at all, except that an individual normally does not
have access to his/her own records.

How is one suppposed to deal with a system that tells people to expect
confidentiality and at the same time routinely diffuses confidential
information?

The way confidential information diffuses in universities is probably not
through leaks to the press. More likely, it is through the following 
mechanisms:
(1) gossip, to trusted individuals (who in turn have their own people they 
    trust)
(2) the perception that a story is too good to treat confidentially
(3) individual interpretation of the word "confidentiality" as meaning anything
    from "only those with a need to know" to "just make sure so and so doesn't
    find out".
(4) Rebellion against having to comply with procedures. For example, 
    I know of one individual who works for a government granting agency and
    who sent me unsolicited materials marked confidential simply because
    he hated being told not to distribute them.

I seriously question whether this half-hearted pretense at confidentiality
serves a useful purpose and I would be interested in hearing other opinions
about it. Would it really be so terrible if people had to take responsibility
for their professional opinions?

One reason for "protecting" them with confidentiality is the fear that they
will be the object of retribution. I think it would be useful to examine in
detail the ways in which such retribution are possible and to examine whether
these constitute abuses of authority and whether they are a good focus for
reform.

It should be possible for everyone to speak his/her mind freely and openly
without fear of retribution. And when this is possible, it will be possible
to have dialogue on these matters of opinion, instead of treating the subjects
of these opinions as dangerous animals. The US constitution provides that
one has the right to know one's accusers. Let that right extend to the
workplace as well.


Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Re: 1+1/2+1/3+...+1/n > x (SOLUTION)
Date: 20 Nov 92 22:39:36 GMT
Organization: The University of British Columbia
NNTP-Posting-Host: unixg.ubc.ca

In <1992Nov20.101643.17628@husc15.harvard.edu> blom@husc15.harvard.edu writes:

>              n   1                            1    inf  BERNOULLI (k) 
>             SUM --- = LN (n) + euler_gamma + --- - SUM ---------------
>             k=1  k                           2 n   k=2           k
>                                                             k (n)



>By expanding the above sequence, we can find the sum of the first n
>reciprocals quickly and easily.  My computer gives anomalous results
>for n in the range in which the sum > 100, but maybe someone else could
>use this formula to verify the exact value for which we are looking.
>The greatest integer less than

>              100 - euler_gamma
>             e

>is a good estimate, but it might be a little off.

Actually, you don't need to be quite so sophisticated.

The answer is N=15092688622113788323693563264538101449859497 which is the
integer part of exp(100 - gamma).

Let h_N = sum_{n=1}^N 1/n.
Note that h_N_ - ln(N+1) = sum_{n=1}^N (1/n - ln((n+1)/n)).
The limit as N -> infinity is Euler's constant gamma.  So 
  h_N - ln(N+1) - gamma = - sum_{n=N+1}^infinity (1/n - ln((n+1)/n)).
We can expand f(t) = 1/t - ln((t+1)/t) = 1/(2 t^2) - 1/(3 t^3) + ...,
an alternating series (for t > 1).  So 1/(2 t^2) - 1/(3 t^3) < f(t) < 1/(2 t^2),
and  h_N - ln(N+1) - gamma < - int_N^infinity (1/(2 t^2)) dt = - 1/(2 N)
while h_N - ln(N+1) - gamma > - int_(N+1)^infinity (1/(2 t^2) - 1/(3 t^3) dt
                                  = - 1/(2(N+1)) + 1/(6(N+1)^2).
So, if u(N) = ln(N+1) + gamma - 1/(2N) 
and    v(N) = ln(N+1) + gamma - 1/(2(N+1)) + 1/(6(N+1)^2)
we want u(N-1) < 100 (to ensure h_(N-1) < 100) and v(N) > 100
(to ensure h_N > 100).  Since the difference between u(N) and v(N) is
of order 1/N^2, we have an excellent chance that this will be true for
some N.

Now, I checked using both Maple and Mathematica:

exp(100 - gamma) = 15092688622113788323693563264538101449859497.30...
Taking N as the integer part of this,
u(N-1) = 99.999999999999999999999999999999999999999999942747
v(N) =  100.00000000000000000000000000000000000000000000900



-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: What is catastrophe theory?
Date: 13 Nov 92 22:22:43 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Nov11.180552.14797@progress.com> neil@progress.COM (Neil Galarneau) writes:
>I have heard of something called catastrophe theory.
>
>I am looking for recommendations on articles/books (in English!) readable by a
>non-math major.

Please read as much as possible of V. I. Arnold's book: _Catastrophe Theory_.
The introduction should be accessible to the mathematically naive. Read this
_first_ before anything else on the subject.

Later,
Andrew Mullhaupt
From: herlihy@crl.dec.com (Maurice Herlihy)
Newsgroups: sci.math
Subject: another trivial homology question
Date: 23 Nov 92 15:03:44 GMT
Organization: DEC Cambridge Research Lab

Let D be an n-dimensional simplicial complex that is connected with trivial
homology groups above dimension 0.  Is D necessarily homeomorphic to an n-disk?
Newsgroups: sci.math,sci.physics
From: voros@physics.monash.edu.au (Joe Voros)
Subject: Re: SU(4), SO(6)
Organization: Physics Dept, Monash Uni, Melbourne, Australia.
Date: Tue, 24 Nov 1992 02:45:46 GMT

columbus@strident.think.com (Michael Weiss) writes:
> SU(4) is the double cover of SO(6).  Has nature made use of this delightful
> fact?

Hmmm.  SU(4) is the starting point of the twistor formalism, I believe,
and is isomorphic to Spin(0,6), the special clifford group based upon a
six dimensional metric which may be reduced to all -1's along the
diagonal.  Therein may lie the connection with rotations in six
dimensions :) 

-- 
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: maj@waikato.ac.nz
Newsgroups: sci.math
Subject: Re: Counterfactuals.
Date: 24 Nov 92 17:19:06 +1300
Organization: University of Waikato, Hamilton, New Zealand

In article <By7BIB.Jwt@cantua.canterbury.ac.nz>, wft@math.canterbury.ac.nz (Bill Taylor) writes:
[stuff deleted]
> 
> So what happens to these results of the "wrong" sort, when and if the 
> conditioning result is decided.  Do they suddenly become uninteresting ? Do
> they suddenly lose all their information content, or do they still retain
> some ?
> 
> ( Perhaps they should be solemnly excised from all copies ofjournals, like
> the Stalinesque instructions to encyclopaedia owners when a politician
> suddenly fell from favor...... ).
> 
> Well, it's a pretty vague question; but perhaps someone can think of a pretty
> vague but sensible answer ?
> 
Not to answer you, but to add a [possibly related] question.
I have often wondered about the possibility of a system of
statements being inconsistent, but _almost consistent_ in
the sense that the shortest proof of a contradiction is
very, very, long. This might be vaguely related to a concept
of the _value_ of a statement, being the average factor by
which proofs of a set of key theorems are shortened when the
statement is assumed.

> ------------------------------------------------------------------------------
>               Bill Taylor              wft@math.canterbury.ac.nz
> ------------------------------------------------------------------------------
>                    There's no future in living in the past. 
> ------------------------------------------------------------------------------
-- 
Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
Department of Mathematics and Statistics     Hamilton, New Zealand      
__________________________________________________________________
'Tis the song of the Jubjub! the proof is complete,
if only I've stated it thrice.'
Newsgroups: sci.math