HDTenEightyP/NetNews huggingface dataset:
From: news@sbil.co.uk
Newsgroups: sci.math.stat
Subject: Re: Let's Make a Deal!
Date: 29 Sep 92 08:27:06 GMT
Organization: Salomon Brothers International Limited

In article 7583@u.washington.edu, rons@hardy.u.washington.edu (Ronald Schoenberg) writes:
>My view, and probably Savant's view, is that the discussion about the
>problem being ill-posed is really a way of avoiding admitting that a
>lot of mathematicians and statisticians screwed up a problem that she
>got right.  Did all those Ph.D. mathematicians and statisticians who
>sent the wrong answers while patronizing her and treating her like a
>child because she didn't have a Ph.D. (or possibly also because she
>was a woman) get the problem wrong because it was ill-posed?  No, they
>got it wrong because they screwed up in spite of their Ph.D.'s.  And
>now they want to deny that they screwed up by saying that it was
>ill-posed.  Maybe a few got it wrong because they saw a different
>problem, but I don't think very many.  And I think the proper response
>to Savant should have been a little respect instead of some technical
>diversion to slake some male egos.


I tend to agree with this ; lots of people get the wrong answer, then
cry "ill-posed" when the correct reasoning is presented.

Of course, Savant is a very, very bright woman. But even she has been 
known to slip up. Try this one out :

"Brain Power" Page 105, M. Vos Savant and L.Fleischer

<< Here's an example of a number series:

	4   9   25   49   81   ?

The correct answer is 121, that is , 11 * 11. And here is how to arrive at
that solution.
	The first successful step you take in your scanning process -
your first insight into solving the problem - is noticing that the above
numbers are all squares: 4 is 2 * 2 ; 9 is 3 * 3 ; 25 is 5 * 5 ;
49 is 7 * 7 ; 81 is 9 * 9 . Therefore, the square root number series
would read :

	2   3   5   7   9   (?)

Scan _that_ series and your second insight will be that the above are all
prime numbers, numbers which can be evenly divided _only_ by themselves
and by 1. Logically, then, the next number in that series would have to be 
the sixth prime number, 11. Going back to the original series, the answer
would be 11 squared or 121 . >>

Whoops. Never mind, we all make mistakes. This is NOT a flame of
Ms. Savant of course : her intellectual powers are beyond dispute.
( According to the Guinness Book of Records, she has an IQ of around 
230 ). The book is well worth reading, incidentally.

	The usual disclaimers apply.

	PB
Newsgroups: sci.math.stat
From: jsvrc@rc.rit.edu (J A Stephen Viggiano)
Subject: Re: Generating Cauchy deviates
Organization: RIT Research Corp
Date: Tue, 29 Sep 1992 14:42:29 GMT

In article <38663@sdcc12.ucsd.edu> whart@cs.ucsd.edu (Bill Hart) writes:
>Can anyone point me to some code for generating samples with the Cauchy 
>distribution?  I've browsed through statlib, but I didn't see anything
>that had this distribution?

1. Generate a uniformly-distributed random variable between -pi and pi.

2. Take the tangent of this quantity.

The result will be distributed with a Cauchy distribution with a median of
zero and a first-to-third quartile range of two. (Both the mean and variance
are undefined.) You can adjust these two quantities by multiplying or dividing
(to adjust the first-to-third quartile range) and then adding or subtracting
(which adjusts the median).
From: fsmgs@camelot.acf-lab.alaska.edu (Michael Schmahl [Black-Robe Mage])
Newsgroups: sci.math.stat
Subject: Re: Let's Make a Deal!
Date: 29 Sep 92 00:09:17 GMT
Article-I.D.: raven.1992Sep29.000917.4917
Organization: University of Alaska Computer Network

Duncan Murdoch writes
> In article <1992Sep24.144902.15458@galileo.cc.rochester.edu>  
em@finch.cvs.rochester.edu (Ethan Montag) writes:
> >Hall also talked
> >about how he could manipulate peoples' choices by what he says and the way
> >he presents the choices in ways that don't change the probabilities.
> 
> But what he says *does* affect how one should judge the probabilities.  
> Monty is making a choice; the probabilities depend on how he makes it.  If 
> he is free to do whatever he wants (e.g. not open any door, open the door 
> with the big prize behind it, cancel the game), then you've got 
> insufficient information to judge whether to switch.  At the other extreme,
> if he's constrained to always choose a bogus door, and to flip a coin to 
> pick which one in case there are two available, then you've got a clear 
> probabilistic basis for a decision to switch.
> 
> What he says in the pitch leading up to your choice is going to affect your 
> mental model of Monty and how he is making his decision.  Of course
> he can manipulate peoples' choices.
> 
> 
> Duncan Murdoch
> dmurdoch@mast.queensu.ca

But it doesn't matter what he >always< does.  It only matters what he >did< do.   
He >did< pick a bogus door to reveal to you.  Therefore the odds are in favor of  
switching.

Period.
Newsgroups: sci.math.stat
From: rhh@alice.att.com (r hardin)
Newsgroups: sci.math.stat
Subject: Re: margin of error
Date: 4 Oct 92 00:56:05 GMT
Article-I.D.: alice.23792
Organization: AT&T Bell Laboratories, Murray Hill NJ



>         "The margin of error for this poll was +/- 3 percent."

>I'd like to know what such a statement means in precise terms.  The
>Chebyshev inequality allows us to make statements like, "the
>probability that the measured value differs from the "true" value by
>more than D, is less than P."

It's worse that that, you can only say ``if thus and such has a
so and so distribution, then the probability ... etc''

You can't get a probability without a leading if, no matter how
much sampling you do.
Newsgroups: sci.math.stat
From: rich@boreas.whoi.edu
Subject: Robust Spectral Estimation of Gappy Series
Organization: Woods Hole Oceanographic Institution
Date: Tue, 29 Sep 92 23:41:00 GMT


I am trying to generate spectral estimates from time series which have
2 problems:

   1) dropouts, i.e. gaps in the time series (perhaps 20% of the values)
   2) error spikes (perhaps 2% of the values)

The time series is a geophysical one (i.e. reddish spectrum), with
perhaps a few small peaks (tides and what-not).

The standard window-fft-and-average techniques seem to be inadequate
for this - I can't think of a good way to handle the gaps (other than
ignoring them by removing them from the series), and the spikes tend to
give a lot of "white" energy.

Median filtering can get rid of some of the spikiness, but it does bad
things to some of the other parts of the signal.


Can anyone help me with some good references?


Email or post, I will summarize.




--
Rich Pawlowicz ----------------- INTERNET: rich@boreas.whoi.edu
Woods Hole Oceanographic Institution
"Home of the 99 cent squid burger (cheese extra)"
--------------------------------------------------------------
Newsgroups: sci.math,sci.math.num-analysis
From: rcpshdb@dutrun2.tudelft.nl (Han de Bruijn)
Subject: Re: What is BLAS? And where can I get it?
Originator: rcpshdb@dutrun2.tudelft.nl
Reply-To: rcpshdb@dutrun2.tudelft.nl (Han de Bruijn)
Organization: Delft University of Technology
Date: Thu, 1 Oct 1992 09:42:41 GMT

Thanks to everybody who responded. Well, now I remember everything again,
and I've decided not to waste further bandwidth on this elementary question.

Frederick W. Chapman posted an exellent summary in "sci.math.num-analysis".
-- 
* Han de Bruijn; Applications&Graphics | "A little bit of Physics * No
* TUD Computing Centre; P.O. Box 354   | would be NO idleness in  * Oil
* 2600 AJ  Delft; The Netherlands.     | Mathematics" (HdB).      * for
* E-mail: Han.deBruijn@RC.TUDelft.NL --| Fax: +31 15 78 37 87 ----* Blood
Newsgroups: sci.math
From: torkel@sics.se (Torkel Franzen)
Subject: Re: consequences of the Axiom of Choice
Organization: Swedish Institute of Computer Science, Kista
	<TORKEL.92Oct5044312@lludd.sics.se>
	<BvMu6n.1Hp@cantua.canterbury.ac.nz>
Date: Mon, 5 Oct 1992 08:57:21 GMT

In article <BvMu6n.1Hp@cantua.canterbury.ac.nz> wft@math.canterbury.ac.nz 
(Bill Taylor) writes:

 >I don't think this will really work, will it ?  The first ordinal definable
 >set (of the type given) is some specific set given by a class formula with no
 >free variables; at least that's the first definable set.

  I think I see how you're thinking here, so let me make my suggestion
clearer. We can put aside the general concept of ordinal definability
and consider a special case.

  We are interested in the following property P of sets:

      X is a countably infinite set of pairs of infinite sets of
      real numbers

Let us introduce a further property Q of sets:

      X has property P, and moreover, there is a formula A(x) with
      one free variable, such that X is the one and only set
      satisfying A(x) in V(omega+omega). (In other words: X is
      definable over V(omega+omega).)

Here V(omega+omega) is the ordinary cumulative hierarchy up to omega+omega.
That X satisfies A(x) in this universe means that A(x) is true of X when
all quantifiers in the formula are restricted to V(omega+omega). Note
that it is not assumed that A(x) is a formula of the form "x is the
set of y such that...".

  Now let S be the set defined by

      S has property Q, and S is definable over V(omega+omega) by
      a smaller formula (according to some ordering of formulas)
      than any other set with property Q.

(This is a definition of S in ZF, although not a definition over
V(omega+omega).)

  Now, do we have any reason to believe that there is a definable
choice function for S? Your idea seems to be that we should get such
a choice function from inspection of the minimal formula defining
S over V(omega+omega). However, a priori it is not at all clear that
we can even prove in ZF that the minimal formula does in fact define
S. Given a formula A(x), whether or not it defines, over V(omega+omega),
a set with property P is not in general decidable in ZF.
Newsgroups: sci.math,rec.puzzles,comp.theory
From: torkel@sics.se (Torkel Franzen)
Subject: Re: more on .999... = 10.0
Organization: Swedish Institute of Computer Science, Kista
	<1992Sep29.035048.4747@cs.cornell.edu> <1a9qi2INN898@uwm.edu>
Distribution: inet
Date: Wed, 30 Sep 1992 08:51:06 GMT

In article <1a9qi2INN898@uwm.edu> markh@csd4.csd.uwm.edu (Mark) writes:

 >For that matter, it's an open question whether there even EXISTS a model of
 >the real number system without infinitesimals in it.  As far as anyone knows,
 >they all have infinitesimals in them.

  This remark is based on some misunderstanding. By definition, the real
field contains no infinitesimals. By the way, "model of the real number
system" is not standard terminology; only theories have models.
Newsgroups: sci.math
Subject: Full Radix Complement in base 10
From: sbrack@jupiter (Steven S. Brack)
Date: 26 Sep 92 21:56:45 EST
Distribution: world  
Keywords: help, radix, base 10, base, complement, HELP!!!!!!!!  8)
Summary: SOS!  
X-Newsreader: Tin 1.1 PL4


	I have beaten my head against the problem of taking 10's complements
	of numbers, but cannot seem to grasp the concept. 

	Could someone post or (preferrably) email a worked out step-by-step 
	10's complement of some number, like 012398.

	Also, if someone could explain how to determine how many digits must
	be kept to maintain accuracy when converting numbers with integral &
	fractional components from one radix to another?

						

--
Steven S. Brack        | B0 w+f s+k+c+v a!v |   sbrack@jupiter.cse.utoledo.edu
2021 Roanwood Drive    \____________________/  STU0061@uoft01.utoledo.edu
Toledo, OH  43613-1605 /                    \    brack@uoftcse.cse.utoledo.edu 
+1 419 GR4 1010        |  MY OWN  OPINIONS  |   sbrack@maine.cse.utoledo.edu
From: rgep@emu.pmms.cam.ac.uk (Richard Pinch)
Newsgroups: sci.math
Subject: Re: consequences of the Axiom of Choice
Keywords: Axiom of choice; Cartesian product
Date: 1 Oct 92 08:48:36 GMT
Organization: DPMMS University of Cambridge

As an elementary equivalent of the Axiom of Choice, how about
  " The product of non-empty sets is non-empty "

Richard Pinch, Department of Pure Mathematics, University of Cambridge
From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math
Subject: Re: Most important event in the history of mathematics
Date: 1 Oct 92 17:28:40 GMT
Organization: Univ. of South Florida, Math Department

In article <1992Sep28.204734.3601@Princeton.EDU> tao@potato.princeton.edu (Terry Tao) writes:
>In article <1992Sep28.174237.26784@Cookie.secapl.com>, frank@Cookie.secapl.com (Frank Adams) writes:
>|> In article <1992Sep28.145025.4059@guinness.idbsu.edu> holmes@opal.idbsu.edu (Randall Holmes) writes:
>|> >In article <1992Sep25.201622.40255@Cookie.secapl.com> frank@Cookie.secapl.com (Frank Adams) writes:
>|> >>[the proof of the inconsistency of naive set theory]
>|> >>was nevertheless probably the most [important] event in the history of
>|> >>mathematics.
>|> >
>|> > It was not the most important
>|> >event in the history of math by a long shot.
>|> 
>|> All right; what was the most important event in the history of mathematics?
>|> My vote is in; what do the rest of you think?
>
>Feynman said that in his HO Tartagalia's solving of the cubic.  Not because
>that this was really important in itself, but because it showed that we could
>beat the ancient Greeks.
>


The discovery of noncommensurables, undermining the 
first foundation of mathematics (number theory) and 
the discovery of nonEuclidean geometry, undermining 
the second foundation of mathematics (geometry) were 
both more important than Russell's paradox (which 
I gather is what is meant by "the inconsistency of 
naive set theory").  Despite the paradox, the third 
foundation of mathematics (set theory) still stands 
and is still accepted.

-----Greg McColm
Xref: sparky sci.math:12549 sci.math.num-analysis:2883 sci.math.symbolic:2595
From: mccoyje@wkuvx1.bitnet
Newsgroups: sci.math,sci.math.num-analysis,sci.math.symbolic
Subject: Fermat's Last Theorem Solved!(right...)
Date: 1 Oct 92 02:11:29 GMT
Organization: Western Kentucky University, Bowling Green, KY

> In article <MCGRANT.92Sep28100407@rascals.stanford.edu> mcgrant@rascals.stanford.edu (Michael C. Grant) writes:

>>I have discovered a most unique proof to this Theorem but in the interest
>>of saving bandwith I must not post it here.

Gee, would you send me this "proof" via e-mail. I would find it (and
the trust fund that goes to the prover) very interesting.

"Sleep -- those little slices of death -- how I loathe them!"
					-- Edgar A. Poe
"I am the way!"
	-- Pinhead
From: wilson@web.ctron.com (David Wilson)
Newsgroups: sci.math
Subject: Function problem
Date: 5 Oct 92 16:07:13 GMT
Reply-To: wilson@web.ctron.com (David Wilson)
Organization: Cabletron Systems INc.


-- 
David W. Wilson (wilson@web.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."
From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: Topos theory for mere mortals (?)
Date: 28 Sep 92 15:13:15 GMT
Organization: Computer Science Dept, QMW, University of London

zeleny@husc9.harvard.edu (Michael Zeleny) writes:

>[...]  However, I wish to go on record as stating that,
>though it probably is a sociological fact that most realists who bother
>thinking about it, think that there is exactly one universe of all sets,
>and that, conversely, some people have gone on record announcing their
>conversion to formalism on the grounds of their loss of belief in the
>unique existence of such a universe, I do not myself believe that a realist
>philosophy of mathematics cannot accomodate a multiplicity of set-theoretic
>(or type-theoretic) universes possessed of different size and structural
>properties. 

Even if we modestly bow to the apparent inevitability of having to
face the existence of a plurality of "universes" of "sets", then,
unless we give up the use of our rational faculties altogether,
we are forced (aren't we?) to develop a "theory of universes", with
pretensions to absolute truth.

What sort of thing do people mean by the phrase "a universe"? How do
we reason about such things? Are they mathematical objects?

Perhaps the common noun "universe" here can be replaced by "topos", and
perhaps it can't; either way,I'm not technically qualified to say.
Be that as it may, my (non-technical) question is whether there is any 
way of understanding this word (in the sort of context in which you have
just used it) as referring to anything other than a structured set. If
there is, my whole argument collapses. (Of course, merely replacing the
word "set" here by "class" or "collection" makes no semantic difference.)

>There is, after all, no good reason to suppose that everything
>in the mathematical universe is a set [...]

Naively, I just can't see how the human mind could possibly manage
without some such concept of "*the* universe" as you have just
appealed to (without irony, I take it).

--
Angus H. Rodgers  (PhD student), | arodgers@dcs.qmw.ac.uk  
Dept. of Computer Science, Queen | [ +44 | 0 ] 71 975 5241   
Mary & Westfield College,  Mile  | This space has not been left blank,
End Rd., London E1 4NS, England  | intentionally or otherwise.
Newsgroups: sci.math
From: cs202144@umbc8.umbc.edu (cs202144)
Subject: Roman Numerals
Organization: University of Maryland, Baltimore County Campus
Date: Sun, 4 Oct 1992 20:31:59 GMT

This may be a dumb question, but I am curious...How are roman numerals larger
than 3999 expressed? Is there an extended symbology or are the existing symbols
altered in some way to express larger values?

Newsgroups: sci.math
From: lew@cbnewsd.cb.att.com (lewis.h.mammel..jr)
Subject: Re: Logarithms - how did they start/
Organization: AT&T
Date: Fri, 2 Oct 1992 02:20:18 GMT
Summary: Napier's log base

In article <BvG62w.IJs@mentor.cc.purdue.edu>, hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
> In article <1992Oct1.011035.59324@cc.usu.edu> sl870@uranus.ee.usu.edu (Ullas Gargi) writes:
> >A sitter from a netter:
> >
> >How did the first guys (Napier et al) calculate the logs of numbers?
> >If I wanted to sit down and manually calculate the log of a non-trivial no.
> >(like 10), how would I do it? A Taylor expansion formula?
> 
> There is nothing obscure about this.  Napier originally used a base
> 1 + 10^(-7) and used multiplication to get the antilogarithms.  ......

Actually, 1 - 10^-7 :

	Hence, if from the radius with seven cyphers added you
	subtract its 10000000th part, and from the number thence
	arising its 10000000th part, and so on ...

		from Struik's SOURCE BOOK IN MATHEMATICS

Lew Mammel, Jr.
Xref: sparky sci.math:12252 sci.math.symbolic:2542
From: fateman@peoplesparc.Berkeley.EDU (Richard Fateman)
Newsgroups: sci.math,sci.math.symbolic
Subject: Risch algorithm
Date: 26 Sep 1992 18:41:53 GMT
Organization: University of California at Berkeley
NNTP-Posting-Host: peoplesparc.berkeley.edu

There seems to be some problem understanding what the Risch algorithm might
do, versus what it actually does in the context of a symbolic math system.

Let's take the simplest problem imaginable,  integrate(0,x).  The answer
we would expect from the Risch algorithm is 0  (plus a constant, as they say).

Let us say that someone offers you another algorithm A that is alleged
to compute indefinite integrals just like the Risch algorithm.
Being a skeptic, you
test the A algorithm, starting with the simplest example, integrate(0,x).

Say  A  gives for an answer, f(x):=arctan(x)+arctan(1/x).   You say that
is absurd, it should be 0 (plus a constant).   Try evaluating f(x) though.
f(1.0) = f(2.0) = f(3.0) ---  IT IS ZERO PLUS A CONSTANT  (pi/2).

Try differentiating f(x).  You get a rational function that is equivalent to
zero... so it has the right derivative...f(x) is an anti-derivative of zero,
so maybe it is right???

Look again (maybe graph f(x))... and you notice that
f(-1.0) = f(-2.0) = ...  for negative arguments f(x) is ZERO PLUS A CONSTANT...
BUT IT IS A DIFFERENT CONSTANT  (-pi/2).  oops...

And what about f(0) ?  It too is a constant, though we don't know which...

Is this answer f(x) correct?  According to the Risch rules, f(x) IS AN
ANTIDERIVATIVE of 0.

Now this may seem to you rather ridiculous -- why return f(x) when a perfectly
good alternative representation  (namely 0) is a much better answer?  The
answer f(x) is discontinuous, it has a singularity at zero (and another at
infinity, but that you may not have noticed).

The fact of the matter is, the Risch algorithm may return answers that are
just as ridiculous as A's f(x).  They may not be defined everywhere you want
them to be defined and they may be discontinuous. They may even be
defined nowhere.

You might not notice these problems because the answer would be more
complicated that atan(x)+atan(1/x).  Systems like Mathematica (especially)
would not notice these problems either.  That's been shown over and over
again.  Maple and Macsyma may be more careful, but they are not careful
enough.  (Some research here at Berkeley is pursuing how to be careful.)

In a nutshell, any algorithm that only guarantees algebraic
"closed-form antiderivatives",  like the Risch algorithm, is perfectly
entitled to give you f(x) instead of 0  for an answer to the "antiderivative
of 0".  If you don't like this answer, it is not the fault of the Risch
algorithm.  If Mathematica (etc.) gives you the wrong integral (indefinite
or definite) because it uses the Risch algorithm, then don't complain to
Robert Risch.  He solved Liouville's conjecture on "integrability in
terms of elementary functions" in part by restating it in terms of
differential fields. He didn't tell anyone to write a program.



-- 
Richard J. Fateman
fateman@cs.berkeley.edu   510 642-1879
Newsgroups: sci.math
From:  jvr@or.math.lgu.spb.su (Joseph Romanovsky)
Subject: Number Theory 
Reply-To: jvr@or.math.lgu.spb.su
Organization: University of St-Petersburg
Date: Wed, 30 Sep 1992 18:14:42 GMT

1. For every prime number P of the form 4k+1 there exists a unique pair of
positive integers x and y such that P = x^2+y^2.
2. For every prime number P of the form 6k+1 there exists a unique pair of
positive integers x and y such that P = x^2+3y^2.
3. The same as 2. but with P = x^2+xy+y^2 = (x+y)^2-xy.
4. For every prime number P of the form 10k+-1 there exists a unique pair of
positive integers x and y such that P = x^2+3xy+y^2 = (x+y)^2+xy.

 Statement #1 is Fermat's Christmas theorem of 1640. Statement #2 also is by
Fermat. Many people know about statement #3 but nobody seems to know the
author. ( Who? ) Is statement #4 somebody's theorem or is this only my unproved
conjecture? I've found elegant algorithms for statement #1, #3 and #4 that
generate primes P with their corresponding x and y but have no more idea than
a golf ball why they work. I give the algorithm for Fermat's Christmas theorem
for comment or proof. r,P,w,x and y are positive integers. gpd(n) stands for
greatest prime divisor of the integer n. ( n > 1 of course )

 Step #1. r:= 1
 Step #2. r:= r+1; P:= gpd(r^2+1)
 Step #3. if 2r > P then repeat step #2
 Step #4. x:= P; y:= r
 Step #5. w:= x; x:= y; y:= w mod x
 Step #6. if x^2 > P then repeat step #5
 Step #7. Print (P,x,y) and return to step #2

 At step #7 we have P = x^2+y^2. Every prime of the form 4k+1 is generated with
it's corresponding x,y pair once and only once but not in strictly ascending
order.

- Bernon Mitchell c/o Joseph Romanovsky