Newsgroup sci.logic 18926

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In article <56afd6$10cu@pulp.ucs.ualberta.ca>, Bingham  writes:
|> The logical way to create a time machine is to accually cause one to
|> create itself.  Simply look in you filing cabinet under the heading of
|> Time machine.  There you will find all the plans you need to build a
|> time machine.  Just make sure that when you have made it, go back in
|> time five minutes before you looked into your filing cabinet and deposit
|> the plans under a heading called Time machine.
This is what you call a perpetuo mobile: creating order out of disorder.
-- 
"You will _wish_ you only had hordes chasing you" -Groo the Wanderer

This is a reply. I have not chosen the header newsgroups this thread is found in.
I have added alt.religion.christian to share with them, however if you
are a christian reading this in alt.religion please do stick to the C-14 topic.
I have difficulty working a scanner.
(Need advise for best scan dpi , format, lineart [?] etc.)
However, I will be posting the C-14 of trees from a published Nobel convention.
A list of dendrochronology dates BP~BC along with C-14 dates BP~BC.
In the list is revealed the fact that trees having C-14 from 2300 BC are being
claimed by dendrochronology as 3000 BC trees favoring Egyptology.
Of course, you are claiming them to be trees from 3000 BC containing
C-14 from that era in larger amounts which falsely produce 2300 BC dates.
I believe the real Egyptology is proven by the Hebrew Genesis back to
2370 BC and not the Turin Papyrus (Septuagint Genesis) back to 3090 BC.
Thus the C-14 is my testimony from God as the truth or word of God,
and not the dendrochronology you worship as the word of God.
http://www.execpc.com/~elijah/c14TPC.gif
forgive me, when I scanned, I clipped the Pharaohs names off the bottom
(not being able to read them in the GIF until I looked back at the book)
I will change it, but clearly you require more charted evidence so I will
spend my time scanning more charts than waste time on just one.
These other Egyptology C-14 chart readings reveal that it is closer to
round the C-14 down to biblical centuries (minus 500 years) believing there
was LESS C-14 and that decades from the Flood were increasing in C-14 to the present,
than to presume the C-14 error as 720 years by claiming that 3000 BC carbon-14
was higher and so now dates younger as 2300 BC. I am presenting
these C-14 charts to declare the current INTERPRETATION of dendrochronology
as a fraud based on a fraudulent Egypt.
Moses did not know Ramses. But when you choose the Turin Papyrus chronology,
you choose 1290 BC Ramses. When I choose the Bible Genesis, I choose
Moses who was bold enough to face all Egypt's scholars twice as being wrong
1554 / 1514 BC. A unanimous group system can save society, it can also
exercise its power to cause total destruction of society by its bold claims of truth
when it is DEAD wrong. You have known little guys before to show up as
correct. But you will not give in whenever the word Bible is mentioned.
I have sent letters off to many institutes, and when I say it is for the Bible,
I get told they're busy, but when that word isnt used, I get a reply.
I think this serves well to indicate the feelings inside of those leading society.
Kerry A. Northrop wrote:
> I take offense at that.  I do not charge people to hear what I have to
> say.  And as for dendrochronology going against your biblical date, I'm
> afraid I'd have to go with the tree rings.  Dendrochronology is one of, if
> not the most accurate chronometric dating method we have.  If you want to
> believe that the bible gives the "real" date that's fine, but I tend to
> believe more proven and trusted methods of dating.
> -ka
************
everyone benefiting from my work please email
my postmaster, my site will move unless those appreciative
send email to counter those trying to destroy it
************
A voice crying out and going unheard,
(40 years Oct 7) Nehemiah's (9:1) 50th JUBILEE of Tishri 24 
God's 1000 years has begun Sep 14 of 1996.
http://www.execpc.com/~elijah/Ezra1991CE.gif
Discover the world's true chronology thru the Bible at
          http://www.execpc.com/~elijah

AP, you are non-chivalrous to attact lady sweet like Darla.  Bad man like 
you writes evil.  You are always wrong!  I shall vanquish you with quick 
strokes of my Kevorkian-style.  Point-by-point, I've got logic that 
smushes your arguments like a wet toad under a car on a rainy night in 
South Dakota.  Read, and weep.
Archimedes Plutonium (Archimedes.Plutonium@dartmouth.edu) wrote:
: 
:    You have failed to see my point and my message. The point is, again,
: that if you seek to understand the world around you and you do so by
: only pen and paper on your laziness and talking with someone such as a
: math proof, that understanding can never be as important as another
: person who draws into his quest for understanding of the world by
: encompassing vast number and large part of his surroundings.
How dare you call Darla lazy?!?  I'll bet that she exercizes much more 
than you do!  And why this pen-and-paper phobia?  There's only ink in a 
pen, and it won't kill you, unless you eat it, and I'll bet that it 
tastes bad.  But maybe you like pen-ink, since you are so much a 
pea-addict. 
:   If your son spends 4 years at a school pushing pen and paper, no
: matter how cute and heavy. 
How dare you call Darla's adorable baby boy fat?!?  YOU'RE the fat one, 
I'll bet.  You never exercize, you tub-of-lard.  Get off of your fat ass 
and run a lap, macaroni-tummy.  I'll bet that lots of mathematicians 
could kick your celluliteeey derr-i-ere.  Especially ones who lift weights.
: You can say that mathematics, all of it is a phsyics
: warm-up experiment. 
Hah!  Like you ever do warm-ups.  Maybe you pick your nose for awhile 
before you type, and warm up your fingers that way.  And Darla will way 
whatever she wants about math, even if she says it is ever a rooty-tooty-
cauliflower.  And you won't do anything about it.
: Physicists are not so
: arrogant and have a better mind, for they tell you that a physics
: experiment can be falsified. 
Wrong!  Physics ain't falsifiable!  Guess again, screwy-dewey!
: But this is the case for
: mathematics also when you accept that a mathematics proof is merely a
: physics experiment that uses little physics equipment or apparatuses,
: usually only pen and paper.
What is your DEAL with the pen-and-paper dog-and-pony show?  Look, I've 
got lots of pens, in lots of wonderful colors, and I've got lots of 
paper, and I've got lots of paper that I've drawn pretty picktures on, 
and I've NEVER DRAWN AN ATOM!  They're too tiny to draw!  And why draw 
them, when they're already on the paper in the first place!  Like, DUH!
:   My advice to you is to open your mind. Recognize that there are
: people in the world who are thousands of times smarter than you and
: that when you read my posts, don't jump the gun and think that you are
: correct and I am wrong. 
No way!  Thousands of times?  Darla's pretty smart, ya know, and I'll bet 
that she wouldn't let you get anywhere near enough to put a ruler up to 
her head.  She'd karate-chop you and your weak Shaolin-style into little 
bits.  And what if Darla likes to keep her brain closed?  It's pretty 
cold out there, and a brain can get awfully chilly.  Your problem is that 
you've been opening your mind up too often, and you've gotten something 
nasty in it, like some pigeon droppings, or something.  I'll bet that 
your brain is foul, fetid, and rank.
I'll bet that you stink, too.  Go take a bath.
-- 

$$$ 666 $$$ 666 $$$ 666 $$$ 666 $$$ 666 $$$ 666 $$$ 666 $$$ 666 $$$ 666
		       hetherwi@math.wisc.edu
$$$ 666 $$$ 666 $$$ 666 $$$ 666 $$$ 666 $$$ 666 $$$ 666 $$$ 666 $$$ 666


Can someone tell of a site or source that will give me some
information on logic programming in the from of an introduction. It
maybe that this is the wrong group to ask this question so if it is
just tell me what the best group would be 
I also have to find out its relationship with logic and an example of
an application. I would be very grateful for any advice or help
Thanks in advance
+===============================================================+
| I'm as old as my tongue and a little bit older than my teeth  | 
| And I hope to keep both                                       | 
|              **************************                       |
|Roger Simms   *Definition of Maturity  *                       | 
|Sutton        *When you start worrying *                       |  
|England       *about Insurance         *                       |
|              **************************                       | 
+===============================================================+

Here is the problem: 
        Let K = {0, 1, ..., k - 1} (k > 1) be a set of k logic values.
Let Union and Intersection be two operators defined on K. Union is
defined as the bitwise OR operation between two elements represented in
binary numbers (having each log(k) bits, the base of the log is 2). Thus
for instance, for k = 8 we have, 1 Union 2 = 001 Union 010 = 011 = 3.
Intersection is defined as the bitwise AND operation between two
elements represented in binary numbers. Thus for instance, for k = 8 we
have, 5 Intersection 6 = 101 Intersection 110 = 100 = 4.
        Let k be a power of 2 (i.e. k = 2^r, with r > 0). Unary central
relations are the non-empty and proper subsets of K. A unary central
relation R is closed under Union and Intersection if x Union y and
x Intersection y are in R whenever x and y are in R. In other words:
(x in R and y in R) implies (x Union y is in R and x Inter y is in R).
        Now the problem statement: For k = 2^r, how many unary central
relations are closed under Union and Intersection ?
                                 ---
        I was not able to find a closed-form formula or even a recursive
formula.
        Using a computer program I find that, for k = 8 and k = 16,
there are 72 and 730 such unary central relations, respectively.
        There are eleven (11) unary central relations for k = 4:
        {0} {1} {2} {3} {01} {02} {03} {1,3} {2,3} {0,1,3} and {0,2,3}.
                        !!!GOOD LUCK!!!
With best regards.
A.N.

I regret that I do not have the time to respond to this thread in detail. 
I have looked at Geoff Webb's article in
http://www.cs.washington.edu/research/jair/table-of-contents-vol4.html
and it seems to conflict with all my intuition built up as a practising 
statistician.
The subject of 'machine learning' is very closely connected with the 
fitting of statistical models to empirical data. What the ML people have 
contributed is a range of new algorithms and models but the fundamental 
questions remain unchanged. It is widely accepted in the statistical 
community that 'overfitting' of a data set [using a needlessly complex 
model] results in a fitted model closely tuned to that particular data 
set that has poor predictive power. This is not to say that there is not 
additional complexity to be discovered, just that the data set under 
consideration does not contain enough information about possible 
elaborations to the model to make it safe to fit them.
I recommend the book 
Model Selection   by H. Linhart and W. Zucchini
Wiley 1986   ISBN  0-471-83722-9
Murray Jorgensen
In article <32837820.7ACB@postoffice.worldnet.att.net>,
   kenneth paul collins  wrote:
>kenneth paul collins wrote:
>
>> From the view of WDB2T, Occam's Razor can be sharpened a bit. In
>> terms of WDB2T, the more-complex alternative simply does not fit
>> observations well, and it can be rejected solely on that basis.
>> And when one looks, one sees that this is the the same point that
>> I've been working to make with respect to the relative utility of
>> conventional Logic and this "new" WDB2T-optimization "Logic" I am
>> proposing.
>
>[For those who didn't read the "Decidability" thread, "WDB2T" is an 
>acronym for "What's Described By the 2nd law of Thermodynamics". 
>WDB2T refers to the Physical Reality that is described by 2nd Thermo, 
>not 2nd Thermo itself.]
>
>Yesterday, I came across a short, unsigned, report in the Nov 96 
>issue of _Discover_ magazine, p34, "Is Occam's Razor Rusty?". The 
>article reports on work done by Geoffrey Webb at Deakin University in 
>Geelong, Austrailia. In a series of experiments, Webb found that, 
>(quoting from the _Discover_ article) "for 12 of 13 problems analyzed 
>by the computer, the more complex decision-making process gave more 
>accurate results".
>
>The _Discover_ article quotes Webb: "'People are potentially missing 
>out on useful patterns because they're just looking for the simple 
>ones,' says Webb. 'Occam's razor influences and limits what science 
>can do with information." 
>
>The article ends without clarifying the point, but my interpretation 
>is that it's (Webb is) saying that Occam's razor =erroneously= 
>"influences and limits what science can do with information", and 
>since this contradicts the position that I've recently taken here in 
>sci.logic with respect to Occam's razor, I wish to explore this 
>matter further.
>
>This msg is an introduction to the new thread. I'll post further 
>discussion later today. ken collins
>_____________________________________________________
>People hate because they fear, and they fear because
>they do not understand, and they do not understand 
>because hating is less work than understanding.

In article <56afd6$10cu@pulp.ucs.ualberta.ca>,
   Bingham  wrote:
>The logical way to create a time machine is to accually cause one to
>create itself.  Simply look in you filing cabinet under the heading of
>Time machine.  There you will find all the plans you need to build a
>time machine.  Just make sure that when you have made it, go back in
>time five minutes before you looked into your filing cabinet and deposit
>the plans under a heading called Time machine.
I made one, after a design suggested by a Calvin and Hobbes newspaper cartoon. 
The problem is, no matter how long I sit in the box, it only goes forward in 
time. But it *is* remarkably reliable and accurate, and travels at a safe speed. 
It has never failed to take me forward, and the time when I emerge is *always* 
exactly what I had preset as the destination time. Plans available for a modest 
fee. :-)
Steve Bennett
[Moderator's note: Since it contains a bit of actual physics I have decided to 
accept this post, despite the fact that s.p.r. is an extremely serious newsgroup and
jokes have been known to cause confusion here.  Posters attempting followup
jokes are urged to remove s.p.r. from the Newsgroups line. - jb] 

In article <327FD551.4A31@postoffice.worldnet.att.net>
kenneth paul collins  writes:
> Please, what are "p-adics"?
In article 
Dan Razvan Ghica  writes:
> It would be interesting if Archimedes Plutonium would steer his postings
> away from anti-mathematical-establishment conspiration-theory-esque
> rantings and tell us more about these mysterious p-adics, their fine
> properties and their potential impact on life from mathematics and physics
> to, say, accounting. 
In article 
Le Compte de Beaudrap  writes:
> 	Now why didn't I think of this? Arch, would it be possible to 
> please talk more about p-adics and less about how they will cause the 
> collapse of mathematics? Serious request, here: I don't mean to be snide 
> or sarcastic. Tell us about them.
  I do not have time for another p-adic dialogue now. My mind has to
stay concentrated on present ongoing agenda. However, I can repost my
entire first dialogue on p-adics. As I so often stated, the math
literature is a failure in the teaching of what p-adics are. There
should be a Schaum's type of basic outline of what they are so that
even a good High School student can learn them. The reason for this is
because noone ever realized the importance of Naturals = p-adics =
Infinite Integers. Until I came along in 1993, all math people thought
that p-adics were a mere exotica, an extension exotica of integers,
failing to realize and grasp that p-adics were the Naturals all along.
MAY 1993
-------------------------------------------------------------
	On 3May I argued with a Princeton U. Prof. J. H. Conway in the math
lounge around 1545 before he was going to give his lecture. Argue over
my proof of the countable Reals. 
	On 4May  I had the listing and was going to return to the Math lounge
at 15:30 hour and show Prof. Conway. My listing though will have a new
math concept, in fact, new numbers which I call infinite integers.  I
was sure that he would argue against them. What are the chances of
something new being accepted immediately? It took a long time for the
community of math majors to accept CantorÕs fake proof that the Reals
are uncountable.
------------------------------------------------------------
	PUBLISHED IN THE DARTMOUTH  11MAY1993
	Replying to Prof. J.H. Conway who argued against my proof published in
The Dartmouth  5Apr0053. Saying that I could not countably list the
Reals in the closed interval [.1,1], nor tell what Real in that
interval is matched with say the positive integer 500 or 501.
	Cantor's false proof for uncountable Reals is this:
where the digits b1 then c2 then d3 and so on endlessly are changed,
allegedly purporting to materialize a new Real not accounted for in the
original list. Thus one of the steps of the proof argument is a logical
contradiction-- both A and not A, specifically, an end to the
endlessness, yielding Cantor's false conclusion that the Reals in
[.1,1] are uncountable.
	This is my countable listing of the Reals in [.1,1] as follows:
1 «1  
10 «.10   
110 «.110   
120 «.120   
.            .
.            .
50 «.50   
.            .
.            .
	The matching of any Real in [.1,1] is the positive integer at which
the repeating of zeros starts. An underlined zero means endless
repetition of zeros. So I do not even need to use 500 I have plenty of
positive integers, nor do I need 2,3,4,5,6,7,8, and 9. Then 501 matches
with .5010 . What do I match .3 or (pi-3) which is .14159. . . in my
list. Again I drop the decimal point and this is new in mathematics. I
match .3 with the infinite positive integer 333. And for the irrational
number, the truncated pi of .14159. . . is matched with the infinite
positive integer 14159. . . . Applying the same scheme for truncated e
of (e-2).
	Infinite integers are new in mathematics, just as irrational numbers
were new when the Pythagoreans first discovered them. And they took a
very long time to get used to. Operations of add, subtract, multiply
and divide are easily enough worked-out. Multiplying 22  by the finite
integer 4 yields 88 . Adding, 6666 + 3333 = 9999 .
	Thus Cantor's alleged proof using Cantor diagonalization disappears,
for in the instant someone claims to manufacture a new Real, then it is
uniquely matched by its infinite positive integer. My matching above is
a mixture of both finite and infinite positive integers but I could
just as well use only infinite positive integers in my matchings. 
	Whenever a math professor balks about infinite positive integers, turn
the onus around, and ask him to immediately show you an aleph94 set.
Oops! What? He cannot show you that. Why of course not for alephs are
math fictions, funnier than science fiction because math fictions have
no partial truth value.  He can never give you a clear picture of the
transfinite number aleph94. Compare aleph94 with the picture of the
infinite integer 9494 or any other infinite integer. Mathmunchkin
professors would rather stare through the looking glass at Alice in
Wonderland than to embarrassingly admit that Cantor's proof was a fake
and that the Continuum Hypothesis (CH) was a complete chimera. So it is
not surprizing that many of the Fields Prizes were mistakes-- Cohen on
CH; Smale and Freedman (see my proof of the PoincarŽ Conjecture, The D
18Nov0051). Mistakes just as in the Nobel Physics Prize mistakes--1)
Glashow Weinberg Salam, since radioactivity is a quantum dual force to
electromagnetism; 2) Chandrasekhar, since gravitational collapse to the
size of the order of the Compton wavelength is a violation of the
uncertainty principle; 3) Bardeen Cooper Schrieffer in BCS
superconductivity, never before in the history of physics has so little
of an explanation been proffered and such a large prize given.  BCS
traders did a one-upsmanship on the bead traders for Manhattan.  Why so
many math prize mistakes? Because it is such a "small clubhouse
communityÓ, and worst yet it has no experimental evidence like in
physics to fall back on.  	
	Notice that in the last two years the Nobel Physics Prizes were
awarded in experimental physics.  The reason is that the committee is
well aware of the Plutonium Atom Totality-- PU theory. And they are
very nervous. Cautiously, the committee is steering on the safe side by
awarding only experimental physics.
	Infinite integers is for the future for I well realize that in this
present year 0053, the math community is retarded. The year 0000 is the
year of the nucleosynthesis and discovery of our Maker, a plutonium
atom. The old calendar is now scrapped as unscientific, as unscientific
as the measurement of length by the foot of some English King.
-------------------------------------------------------------
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium)
Subject: Re: Cantor Corrected, A proof that the Reals are Countable
Message-ID: 
Organization: Dartmouth College, Hanover, NH
References: 
Date: Mon, 16 Aug 1993 23:30:25 GMT
Lines: 23
        Infinite integers--that is the answer to uniquely matching
every Real in the interval (.1,1). Just drop the decimal point on the
Real in that interval you are looking at and that is an infinite
integer. There, all the Reals in that interval are matched uniquely by
an infinite integer. The alternative is to write Cantor's diagonal and
hope and pray that no student raises his/her hand and says "But in
order to manufacture that "supposed new Real " not in the original list
you had to STOP the endlessness of the positive finite integers. You
had to end endlessness which is a contradiction scooting unto a false
conclusion that the Reals are nondenumerable."
	Will present day teachers stay happy for long with the situation that
only in Cantor's proof is it acceptable to have a contradiction within
the body of the proof. But any other math proof a contradiction is
verboten. Did anyone of the quarrelsome sect to my original posting ask
themselves that perhaps they had best take another look at Cantor's
proof. That the proof may have cracks in it after all? Is the notion of
various different types of infinity intuitive? Not to me, for it just
means never ending. How can there be two different types of never
ending? What is the opposite two types of nothing? Ending endlessness
in the body of a proof is a contradiction. Cantor diagonal is great on
any finite set because it naturally stops and so there is no self
contradiction but creating a new number by halting the endless is a
logical contradiction.
-------------------------------------------------------------
Newsgroups: sci.math
Subject: Re: Cantor Corrected, A proof that the Reals are
Message-ID: <1993Aug20.014006.27459@husc14.harvard.edu>
From: kubo@germain.harvard.edu (Tal Kubo)
Date: 20 Aug 93 01:40:05 EDT
References: 
<25166s$92m@paperboy.osf.org>
 
Organization: Dept.  of Math, Harvard Univ.
Lines: 30
In article 
Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium) writes:
>In article <25166s$92m@paperboy.osf.org> karl@dme3.osf.org (Karl >Heuer) writes:
>
>> These are well-defined. It should be obvious how to add and 
>> subtract and multiply them; division is a little trickier.
>
>Karl I please need your help, you have shown the way. Please tell me >how to deal with division? It escapes me.
(1) Unless you add a "decimal point" to your system (but so that any   
      number has only a finite number of digits to the right of the 
      point), you can't divide by every "infinite integer". For
example, 
      you can't divide by 10. Even if you add the decimal point there  
      are some complications.
(2) The inverse of  (1-x),   is (formally) the infinite sum 1 + x + x^2
+ 
      x^3 + . . .   Try this with x=10 to see how to get 1/9 and -1/9. 
      Then try to generalize from there.
(3) The number system you are (re)inventing is called the "10-adic 
      integers". The version with decimal point, where you can also 
      divide by any nonzero number, is called "Q_2 x Q_5".
-------------------------------------------------------------
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium)
Subject: Re: 1 IS THE ONLY ODD PERFECT NUMBER PROOF
Message-ID: 
Organization: Dartmouth College, Hanover, NH
References: 
<2515i0$91c@paperboy.osf.org> 
Date: Fri, 20 Aug 1993 03:46:21 GMT
Lines: 7
       Dear Karl,
      You showed above how to make the ordinary finite integers a
special case of infinite integers (Re: Cantor Corrected). I do not know
if you review old files so I ask here. You mentioned in there "division
is a little trickier". Please Karl, I still do not see how to get
division. Please help. Thanks

>   The mathematics literature even up to this date, is horribly lacking
> in any elementary discussions of p-adics, what they are, how to
> multiply and divide with them. There strange characteristics. Why this
> lack? The answer is that noone but me ever thought they were anything
> more than a extension. I am the first to realize that they are the
> Naturals themselves, and that the Finite Integers were a field of
> ghosts, or angels that fit on the end of a needle.
> 
Jean Pierre Serre has a book called "A Course in Arithmetic" where he
speaks of many of the elementary properties of p-adic integers.  This book,
I think, is something of a standard in the subject.

Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium)
Subject: Re: FermatÕs Last Theorem
Message-ID: 
Organization: Dartmouth College, Hanover, NH
References: <2728f8$51j@news.u.washington.edu>
  
<278vgj$pi2@paperboy.osf.org> 
 
Date: Fri, 17 Sep 1993 03:19:22 GMT
Lines: 44
In article 
Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium)
>In article <278vgj$pi2@paperboy.osf.org> karl@dme3.osf.org (Karl 
>Heuer) writes:
>
>>Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium) writes:
>>>The eventual arithmetic proof of FLT, I am confident, will come 
>>>from the counting numbers; P-triples are possible only in exp2 
>>>because 2+2=2x2=4.
>>
>>I have my doubts as to the connection between that equation and 
>>FLT; however, you may be interested to know that other solutions 
>>are possible if you allow those left-infinite decimal strings that 
>>we discussed earlier. When k=4, there is a unique nonzero solution 
>>to N+N+N+N = N*N*N*N = M. Here is the answer, worked out to 60 
>>decimal places. You can check it by doing the arithmetic yourself, 
>>right to left.
>>
>>  N = . . .8217568575974462578891103859665245689398767183
>>            82655349981184
>>  M = . . .2870274303897850315564415438660982757595068735
>>            30621399924736
>>
>>Karl Heuer   karl@osf.org
>
>   Karl Heuer double bless you to the infinite Fields of Elysium. I >would not mind if you discovered the worldÕs first valid proof of >FLT, instead of me.
>   Karl can you do the same thing for exp3 and exp5, i.e., a unique >solution?
    Karl I think the proof would then go like this. Take any exp
greater than 2, then when there are rational solutions to FLT those are
turned into infinite integers by just deleting the decimal point. Near
the end of the proof would be something that only with finite integers
is a Ptriple possible because only 2+2=2x2=4.
    Then again I could be all wrong and there in fact exists a
counterexample to FLT provided that one considers infinite integers are
no different from finite integers. That is, finite integers are
infinite integers with just infinite repetition of zeroes to the left.
WOULD THAT NOT BE THE SUPREME IRONY SO FAR IN THE HISTORY OF MATH. That
there is a counterexample to FLT. The whole world will laugh
hysterically if Wiles gets approval and Ludwig Plutonium comes up with
the counterexample. Which choice would you pick--- a 1000 page math
community accepted (fake) proof, or a counterexample? So far my
confidence in the math community is that they would prefer the 1000
page ordeal.
-------------------------------------------------------------
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium)
Subject: Re: FermatÕs Last Theorem
Message-ID: 
Organization: Dartmouth College, Hanover, NH
References: <2728f8$51j@news.u.washington.edu>
  
<278vgj$pi2@paperboy.osf.org> 
Date: Fri, 17 Sep 1993 03:44:56 GMT
Lines: 9
In article <278vgj$pi2@paperboy.osf.org> karl@dme3.osf.org (Karl Heuer)
writes:
>
> N = . . .8217568575974462578891103859665245689398767183
>            82655349981184
> M = . . .2870274303897850315564415438660982757595068735
>            30621399924736
   LET US FIND A CROP OF COUNTEREXAMPLES TO FLT.
Ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha!
-------------------------------------------------------------
EMAIL
From: ÒTerry TaoÓ 
Date: Sat, 18 Sep 93 09:55:36 EDT
To: Ludwig.Plutonium@Dartmouth.EDU
Subject: Re: FermatÕs Last Theorem
Newsgroups: sci.math
In-Reply-To: 
References: <2728f8$51j@news.u.washington.edu>
  
<278vgj$pi2@paperboy.osf.org> 
 
Organization: Princeton University
Cc:
In article  you write:
>In article  
>Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium)
>
>>In article <278vgj$pi2@paperboy.osf.org> karl@dme3.osf.org (Karl 
>>Heuer) writes:
>>
>>>Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium) writes:
>>>>The eventual arithmetic proof of FLT, I am confident, will come 
>>>>from the counting numbers; P-triples are possible only in exp2 
>>>>because 2+2=2x2=4.
>>>
>>>I have my doubts as to the connection between that equation and 
>>>FLT; however, you may be interested to know that other solutions 
>>>are possible if you allow those left-infinite decimal strings that 
>>>we discussed earlier. When k=4, there is a unique nonzero solution 
>>>to N+N+N+N = N*N*N*N = M. Here is the answer, worked out to 60 
>>>decimal places. You can check it by doing the arithmetic yourself, 
>>>right to left.
>>>
>>>  N = . . .8217568575974462578891103859665245689398767183
>>>            82655349981184
>>>  M = . . .2870274303897850315564415438660982757595068735
>>>            30621399924736
>>>
>>>Karl Heuer   karl@osf.org
>>
>>   Karl Heuer double bless you to the infinite Fields of Elysium. I 
>>would not mind if you discovered the worldÕs first valid proof of 
>>FLT, instead of me.
>>   Karl can you do the same thing for exp3 and exp5, i.e., a unique 
>>solution?
No.
Theorem. The equation N+N+N=N*N*N has no solution in 10-adics, apart
from N=0.
Proof: consider the powers of 2 and 5 in N. Suppose 2 divides N a times
and 5 divides N b times. The lhs of the above equation has 2^a 5^b as
its factors of 2 and 5 (which are by the way the only primes in
10-adics), and the rhs has 2^3a 5^3b as its factors, hence a and b must
be 0.
But then, if neither 2 or 5 divides N, then N must be invertible,
unless N=0. Thus, dividing by N, we get N*N = 3. But comparing the
final digits of both sides, we see that this is impossible.
Similarly: The equation N+N+N+N+N=N*N*N*N*N has no solution in
10-adics, apart from N=0.
Proof. Suppose 2^a5^b are the prime factors of N, again. Then the lhs
has prime factors of 2^a 5^(b+1) and the rhs has prime factors of 2^5a
5^5b. But these can never match, hence there is no solution (unless
N=0; 0 is the only number that has non-unique prime factorization).
The fact that  N+N+N=N*N*N has no solutions in 10-adics, whereas there
ARE solutions of FLT in 10-adics for n=3 (see for example the post by
William Schneeberger), shows that there is no proof that ÒFLT is true
for n=3 => N+N+N=N*N*N for some non-zero NÓ unless you use a property
of the integers that the 10-adic integers do not have.
>
>    Karl I think the proof would then go like this. Take any exp 
>greater than 2, then when there are rational solutions to FLT those 
>are turned into infinite integers by just deleting the decimal point.
An important point here: the operation of turning rational numbers into
infinite integers by deleting the decimal point does NOT preserve
addition or multiplication. For example, in rationals
.33333...   x  .33333....  =  .11111....
whereas
....33333  x  ....33333  =  .....88889
and
.5555....  +  .4444...   = 1
whereas
....5555    +  ....4444    = ....9999
Thus, a rational solution of FLT does not automatically lead to a
10-adic solution of FLT.
>Near the end of the proof would be something that only with finite 
>integers is a Ptriple possible because only 2+2=2x2=4.
I would very much like to see a proof of this statement: if you can
prove this, then you have proved FLT. Then again, see an above point
that you would need to use a property of the integers that is not
shared by the 10-adic integers.
>   Then again I could be all wrong and there in fact exists a 
>counterexample to FLT provided that one considers infinite integers 
>are no different from finite integers.
What you mean here is that there exists a counterexample to FLT in
infinite integers. It is not quite correct to say that Òinfinite
integers are no different from finite integersÓ. Every finite integer
is a 10-adic integer, but not conversely. What is true is that
multiplication and addition are the same operation for both of them.
However, finite integers have several properties that 10-adic integers
do not have, for example, they are all finite. Another is that
induction works for finite integers, but not for 10-adic integers. 
(otherwise, you could prove that all 10-adic integers were finite by
induction).
>   That is, finite integers are infinite integers with just infinite 
>repetition of zeroes to the left. WOULD THAT NOT BE THE SUPREME 
>IRONY SO FAR IN THE HISTORY OF MATH. That there is a 
>counterexample to FLT.
The commonly accepted wording of FLT ends Ò... where a, b, c, n are
(finite) integersÓ (with the finite added for emphasis). If you remove
this last phrase, then the FLT that most mathematicians think of would
then have to be called ÒFLT for integersÓ. It is true that FLT is false
for p-adics, matrices, quaternions, and a lot of other number systems.
In this sense, there are counter examples to the general FLT. But there
is no counter example to FLT (integers): this was proved by Wiles.
>   The whole world will laugh hysterically if Wiles gets approval 
>and Ludwig Plutonium comes up with the counterexample. Which 
>choice would you pick--- a 1000 page math community accepted 
>(fake) proof, or a counterexample? So far my confidence in the math 
>community is that they would prefer the 1000 page ordeal.
There seems to be a point you keep missing. If you change the
definitions of terms (like integer, real, etc), then theorems change as
well. Thus,
ÒFLT for normal integersÓ (Wiles)
is a different theorem than
ÒFLT is not true for 10-adic integersÓ (proved by many people)
and both results (admittedly one is very long, the other very short),
are good mathematics and knowing one does not automatically get you the
other result. So there is no real irony, except that theorems that hold
for one number system need not hold for all number systems.
Of course, you may dispute that the commonly accepted definition of
ÒintegerÓ SHOULD be the commonly accepted definition. But even if you
replace the concept of integer, the ÒoldÓ concept of integer is still a
valid one, so you canÕt just blithely say (for example) Òwell, if I
redefine integers to be 10-adic, so the reals are now equal cardinality
to the integers, then there is no infinite set with smaller cardinality
than the reals anymoreÓ, because the ÒoldÓ notion of integer still
exists.
Terry
-------------------------------------------------------------
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium)
Subject: Re: Fermat's Last Theorem
Message-ID: 
Organization: Dartmouth College, Hanover, NH
References: 
<278vgj$pi2@paperboy.osf.org>  
<27glo6$elj@paperboy.osf.org> 
Date: Mon, 20 Sep 1993 15:39:46 GMT
Lines: 15
In article <27glo6$elj@paperboy.osf.org> karl@dme3.osf.org (Karl Heuer)
writes:
>In article  >Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium) writes:
>>does this above monster 4N=N^4 repeat in a block like Rational >>numbers repeat
>
>No, it doesn't.
   Karl is this new number which you discovered (if you do not have a
name for it as yet, I suggest HeuerPu Numbers, but that is up to you)
analytic irrational or transcendental? Given that concepts of
transcendental can be translated to P-adic.
   Also, please tell me if there is a mirror reflection in the Reals of
HeuerPu Numbers. Is there a Real number between 0 and 1 which has
HeuerPu properties?
-------------------------------------------------------------
EMAIL
Date: Tue, 21 Sep 93 00:01:54 EDT
From: ÒKin ChungÓ 
To: Ludwig.Plutonium@Dartmouth.EDU
Subject: INFINITE INTEGERS
In-Reply-To: 
Organization: Princeton University
Cc:
Before you embrace the so-called Òinfinite integersÓ too closely,
consider this straightforward sum:
....9999999999999999999999999999999999999999999999999
+....0000000000000000000000000000000000000000000000001
___________________________________________
  ....000000000000000000000000000000000000000000000000
Using your identification of the (finite) integers with a subset of the
infinite integers, this shows that (-1) = ...9999. Do you see what IÕm
trying to get at?
-------------------------------------------------------------
From: karl@dme3.osf.org (Karl Heuer)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 21 Sep 1993 20:59:42 GMT
Organization: Open Software Foundation
Lines: 25
Message-ID: <27npvu$blc@paperboy.osf.org>
References: 
<27glo6$elj@paperboy.osf.org>  
In article 
Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium) writes:
>(if you do not have a name for it as yet, I suggest HeuerPu Numbers, 
>but that is up to you)
I've been calling N^k=k*N the "LP equation". I don't think its
solutions need names of their own, but "LP numbers" will do for now.
>   Karl is this new number which you discovered analytic irrational or transcendental? Given that concepts of transcendental can be translated to P-adic.
It's easy to prove that it's irrational, because the rationals have the
same properties in the 10-adic numbers that they do in the reals. Since
it's a zero of the polynomial x^k-k*x, it's a (non-Real) irrational
algebraic number.
>Also, please tell me if there is a mirror reflection in the Reals
The LP equation has real solutions for all k; e.g. sqrt(3) for k=3. 
(As someone else already noted, these solutions will have magnitude
>1.)
There are similarities to the Reals, but it's not just a renaming. 1/3
exists as a (repeating) 10-adic integer, but it's not . . .3333; it's .
. .66667 instead. (Multiply it out: . . .66667 * 3 = . . .00001 no
matter how many places you carry it to.) Also, x^2 = 3 has a solution
in the Reals but not in the 10-adics; while x^2 = -31 has a solution in
the 10-adics but not in the Reals.
-------------------------------------------------------------
From: karl@dme3.osf.org (Karl Heuer)
Newsgroups: sci.math
Subject: Re: P-ADIC NUMBERS: RENAMED AS INFINITE INTEGERS
Date: 21 Sep 1993 21:14:12 GMT
Organization: Open Software Foundation
Lines: 12
Message-ID: <27nqr4$bpe@paperboy.osf.org>
References:  
In article 
Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium) writes:
>   Let us rename the math subject "P-adic Numbers" to that of 
>"Infinite Integers."
I'd rather keep the existing terminology. There are several consistent
models of arithmetic that include objects that look "infinite" in some
sense: the Hyperintegers/Hyperreals, the Surintegers/Surreals, the
compact number line, the Riemann sphere, the transfinite ordinals, the
transfinite cardinals, etc.
The only thing that's "infinite" about the p-adic numbers is their
representation as a digit string, and that's analogous to the infinite
number of digits in a non-terminating Real.
-------------------------------------------------------------
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium)
Subject: Re: P-ADIC NUMBERS: RENAMED AS INFINITE INTEGERS
Message-ID:  
Organization: Dartmouth College, Hanover, NH
References:  
<27nqr4$bpe@paperboy.osf.org>
Date: Thu, 23 Sep 1993 16:34:43 GMT
Lines: 17
In article <27nqr4$bpe@paperboy.osf.org>
karl@dme3.osf.org (Karl Heuer)
>I'd rather keep the existing terminology. There are several >consistent models of arithmetic that include objects that look >"infinite" in some sense: the Hyperintegers/Hyperreals, the >Surintegers/Surreals, the compact number line, the Riemann >sphe,
the transfinite ordinals, the transfinite cardinals, etc.
>
>The only thing that's "infinite" about the p-adic numbers is their 
>representation as a digit string, and that's analogous to the infinite 
>number of digits in a non-terminating Real.
   How about TRANSFINITE INTEGERS? Any objections?
   I am trying to give a good name to these infinite strings for
another assault on CantorÕs claim that there are more than one type of
infinity.
-------------------------------------------------------------
From: "Terry Tao" 
Subject: Re: Wiles proof of FLT
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Sun, 26 Sep 93 17:10:49 EDT
In-Reply-To: <5509284@blitzen.Dartmouth.EDU>; from "Ludwig Plutonium"
at Sep 26, 93 5:07 pm
>
> Terry tell me if all P-adic numbers have inverses. Can you prove it
>
If P is prime, then all numbers which are not multiples of P have
inverses. (in other words, all numbers whose last digit is not 0.)
If P is not prime, then all numbers which are coprime to P have
inverses, i.e. the last digit of that number is coprime to P.
To prove it, it is sufficient to show that you can invert the last N
digits, for each N. This is a standard exercise in modular arithmetic.
Terry
p.s. I would still like to hear your comment on my proof that there
must be a counter-example to FLT. Do you think my proof is flawed?
-------------------------------------------------------------
EMAIL
From: ÒTerry TaoÓ 
Date: Tue, 28 Sep 93 20:34:10 EDT
To: Ludwig.Plutonium@Dartmouth.EDU
Subject: Re: FermatÕs Last Theorem
Newsgroups: sci.math
In-Reply-To: 
References: <2728f8$51j@news.u.washington.edu>
  
<278vgj$pi2@paperboy.osf.org> 

Organization: Princeton University
Several observations.
(1). In my mind, the reason why 2 is exceptional in FLT is not because
2x2 = 2+2, but rather because 2 is even. If n is odd, then FLT can be
rewritten in the much more beautiful
u^n + v^n + w^n is never 0 unless uvw is 0 (where u,v,w are integers).
(2). P-adic counter-examples to FLT have been known for some time -
almost at the same time that they were discovered. P-adics are like
real numbers, in a sense: who's interested in a real number
counter-example to FLT?
(3). Wiles uses special properties of the finite integers that the
infinte integers do not have, one of which is that there are infinitely
many primes in the finite integers.
(4) Your statement "Wiles's proof contradicts the Fourier theorem" is
indirect non-existence - after all, that's what you said when I used
the same principle to show that FLT must be false for finite integers.
(5) FLT is true for finite integers, false for p-adic integers. Each
finite integer is a p-adic integer, but the set of finite integers is
only a SUBSET of the set of p-adic integers. They are different things,
and you have two different FLTs for two different number systems. FLT
is assumed to be over the finite integers unless otherwise specified,
so your statement that ÒAll proofs of FLT are fakeÓ is wrongly deduced.
However, you have made a true deduction in saying that no proof of FLT
can rely purely on algebraic manipulation, because of the p-adic
counter example. It must use a property that the finite integers have
but the infinite integers do not, for example
(a) induction;
(b) infinitude of primes;
(c) no zero divisors (WillÕs two numbers, a and b, multiply to 0)
etc.
Terry
-------------------------------------------------------------
EMAIL
From: ÒTerry TaoÓ 
Subject: Re: Fermat's Last Theorem
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Tue, 28 Sep 93 22:22:46 EDT
In-Reply-To: <5569918@blitzen.Dartmouth.EDU>; from "Ludwig Plutonium"
at Sep 28, 93 10:18 pm
>
>--- You wrote:
>However, you have made a true deduction in saying that no proof of >FLT can rely purely on algebraic manipulation, because of the p-adic >counter example. It must use a property that the finite integers >have but the infinite integers do not, for
example
>--- end of quoted material ---
>Thanks that is important I needed that.
>
>Terry tell me if there is a Real analog of that number Karl produced. >Karl says it is greater than 1. Can you pinpoint it better.
>
the cube root of 4.
Terry
-------------------------------------------------------------
EMAIL
From: ÒWilliam SchneebergerÓ  
Subject: Re: your counterexample posting
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Wed, 29 Sep 93 12:10:41 EDT
In-Reply-To: <5581074@blitzen.Dartmouth.EDU>; from ÒLudwig PlutoniumÓ
at Sep 29, 93 11:39 am
Sorry, I don't have a copy. But here's the deal:
We solve a == 0 (mod 5)
 a == 0 (mod 25)
 a == 0 (mod 125)
     .
     .
     .
and
 a == 1 (mod 2)
 a == 1 (mod 4)
 a == 1 (mod 8)
by the Chinese Remainder Theorem. Similarly we solve
 b == 0 (mod 5)
 b == 0 (mod 25)
 b == 0 (mod 125)
 b == 0 (mod 625)
     .
     .
     .
and
 b == 1 (mod 2)
 b == 1 (mod 4)
 b == 1 (mod 8)
     .
     .
     .
Now one can prove that a*a=a, b*b=b, a*b=0, a+b=1. This leads
immediately to the fact that, for all (finite natural numbers) n,
a^n + b^n = c^n where c == 1.
There are, however, much more interesting solutions to FLT in these
numbers. The above solution may well be considered trivial as abc == 0.
For the p-adic numbers (infinite integers in a prime base p) the above
solution does not exist. But I know that there do exist solutions for n
relatively prime to p(p-1).
Will
-------------------------------------------------------------
EMAIL
From: ÒTerry TaoÓ 
Subject: Re: Schneebergers post
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Wed, 29 Sep 93 14:45:31 EDT
In-Reply-To: <5581425@blitzen.Dartmouth.EDU>; from "Ludwig Plutonium"
at Sep 29, 93 11:55 am
>
>Hi Terry. I lost Schneebergers post of counterexamples. Would you >have a copy? Please relay
>
I haven't got that post either, but here's how you can compute them:
The idempotents of the 10-adics are the solutions of a^2 = a. Thus
their first digit must be 6 or 5 (by considering the problem modulo 10)
- the idempotents 0 and 1 being discounted. Let us, say, consider the
one with last digit 5: they sum up to 1 anyway.
You can compute successive digits iteratively. If the next digit is a,
i.e. the last two digits are 10a+5, then the last two digits of the
square is 25, so a must be 2.
Similarly, if we let the next digit be b, so the last three digits are
100b + 25, then the last three digits of the square is 625, hence b =
6. And so on.
Terry
-------------------------------------------------------------
EMAIL
From: ÒTerry TaoÓ 
Subject: Re: Schneebergers post
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Wed, 29 Sep 93 15:02:53 EDT
In-Reply-To: <5581425@blitzen.Dartmouth.EDU>; from "Ludwig Plutonium"
at Sep 29, 93 11:55 am
Actually, all you need to do is take 5 and keep squaring it. The powers
of 5 will converge in the 10-adic topology to one of Will's numbers.
(recall: whereas the metric in say the reals, is |x-y| for the distance
between x and y, the metric between two p-adics x and y is 1/p^n, where
n is the highest number of times that p divides x-y.)
Terry
-------------------------------------------------------------
EMAIL
From: ÒWilliam SchneebergerÓ  
Subject: Re: your counterexample posting
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Wed, 29 Sep 93 15:21:43 EDT
In-Reply-To: <5581838@blitzen.Dartmouth.EDU>; from ÒLudwig PlutoniumÓ
at Sep 29, 93 12:15 pm
So, I guess, some solutions for exponent 3 are
              a == 1
              b == 10
              c == . . .52979382777667001
              a == 1
              b == 20
              c == . . .4437336001
              a == 1
              b == 30
              c == . . .4919009001
In fact for any finite n, a == 1, b a multiple of 10, we can solve the
equation of FLT.
But, look, all IÕve shown here is that in the 10-adic numbers there is
a solution to the equation. I have _not_ contradicted the statement of
FLT which says that there is no solution among the usual finite
integers. This is more of a problem.
Later.
-------------------------------------------------------------
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium)
Subject: Re: Wiles's proof of FLT
Message-ID: 
Organization: Dartmouth College, Hanover, NH
References: <27st80$asv@clipper.clipper.ingr.com>

Date: Wed, 29 Sep 1993 16:24:55 GMT
Lines: 15
In article 
Ludwig.Plutonium@dartmouth.edu  (Ludwig Plutonium) writes:
>FLT was outstanding because there is no proof of FLT in the general >case. The general theorem of FLT has no proof because transfinite >integers are just as real as finite integers. All attempts at a proof >of the general equation of FLT are doomed to
failure. 
   PROOF OF FLT. The general form of FLT where a^n+b^n=c^n are such
that the four numbers a,b,c,n could be transfinite integers as well as
finite integers. Hence a proof in the general case is impossible. The
counterexamples in the P-adics is the proof. Anything else would have
to restrict the four numbers a,b,c,n to finite number cases and show
that in those restrictions there are no P-triples. QED

Please forgive this "clerical" post which is in this 
news group because I'm in the midst of a discussion that 
is very-important to me.
My email has been out all day, and is still not working. 
I can send via web pages, but cannot send from my own 
mail server, and cannot receive anything.
Newsgroups are still OK. ken collins
_____________________________________________________
People hate because they fear, and they fear because
they do not understand, and they do not understand 
because hating is less work than understanding.

In article <56dgil$fcs@netserv.waikato.ac.nz>,
   maj@waikato.ac.nz (Murray Jorgensen) wrote:
>I regret that I do not have the time to respond to this thread in detail. 
> . . .
Apologies, but I forgot to point out that I added the newsgroups
sci.stat.math  and  comp.ai.neural-nets
to a thread which started in sci.logic.
Murray Jorgensen,  Department of Statistics,  U of Waikato, Hamilton, NZ
-----[+64-7-838-4773]---------------------------[maj@waikato.ac.nz]-----
Doubt everything or believe everything: these are two equally convenient
strategies. With either we dispense with the need to think.
                                                       - Henri Poincare'

> Archimedes Plutonium (Archimedes.Plutonium@dartmouth.edu) wrote:
> : 
The redoubtable AP comments---
> :    You have failed to see my point and my message.
Well, *sigh* what I actually failed to see were the several email messages
warning me (too late) not to ever answer one of your posts.  Now I
understand why.
I saw your point and your message---I happen to disagree, which, last time
I checked, was my right and was not a green light for condescension and
derision from you.  
It is unfortunate that instead of using proper logical argument to attempt
to prove your "points,"  you chose to descend to a personal attack on me.
To quote Dr. Foakes-Jackson (1855-1941) of Cambridge ..."It's no use
trying to be clever, we are *all* clever here.  Just try to be kind."
Darla
---who hereby thanks her brave champions, both public and private.

In article 
David Kastrup  writes:
> Ludwig, I like to call you Ludwig still, do you mind? I am
> divorced now because I would lecture my wife in bed instead
> of doing the physics she wanted. I have the scherr habit of 
> lecturing even though I don't understand what I am lecturing
> about! I have been a pedantic lecturing fool all of my life,
> and it is an uncontrollable habit of mine.
In article <1993Dec4.013650.12700@Princeton.EDU>
wiles@rugola.Princeton.EDU (Andrew Wiles)  writes:
>> Not quite.  Mathematics does not care one hoot about reality or
>> applicability, it cares about consistency.
In article    (Gerd
Faltings@Max-Planck-Institut.Bonn) Gerd Faltings writes:
>>> I can develop a number system in which 1+1=0 and work with it and
>>> derive theorems about it quite fine as long as I keep consistent.  It
>>> does not matter for this that one sheep plus one sheep does not make
>>> no sheep.  Sheep are not good for modulo 2 arithmetic.  But if I look
>>> carefully, almost every mathematic system *can* be applied in some
>>> ways: calculation modulo 2 is quite well-suited to finding out whether
>>> the light is on depending on how many people happened to throw the
>>> switch.
In article <1993Dec4.013650.12700@Princeton.EDU>
wiles@rugola.Princeton.EDU (Andrew Wiles)  writes:
>> That's the difference: in physics, different world models are sort of
>> "winner takes all" oriented (although no winner is up to now none,
>> only quite a lot of non-winners been thrown out of the race).
>> I am a winner.
In article    (Gerd
Faltings@Max-Planck-Institut.Bonn) Gerd Faltings writes:
>>> In mathematics, Newtonian mechanics and relativistic mechanics could
>>> coexist quite nicely: different axiomatic systems do not need to obey
>>> the same laws as long as they obey their respective axioms.
>>>
>>> That one of them applies better to modern reality does not make it
>>> mathematically illegitimate, only physically.  It just happens that
>>> *relative* speed counts in the universe, not absolute.
>>> 
 John.Coates@University.of.Cambridge 
(John Coates) writes :
>>>> Depends on what you mean by "wrong".  In mathematics you are allowed
>>>> to do crazy things (like allowing a fake proof to get published and
>>>> ignoring any opposition) and see where that would take you, as long as you
>>>> carefully watch that you are not mixing up your "real-world"
>>>> expectations with actual consequences of the changed systems.
In article    (Gerd
Faltings@Max-Planck-Institut.Bonn) Gerd Faltings writes:
>>> Not at all, the link is one-way.  It might, however, make more
>>> physicists interested in a branch of mathematics (p-adics) which they
>>> otherwise would rather choose to ignore.
> 
> But all this is one-way: being able to apply real numbers or p-adic
> ones or whatever does not influence the validity of the use of natural
> numbers, but at most the interest taken in them.
> 
> -- 
> David Kastrup                                       Phone: +49-234-700-5570
> Email: dak@neuroinformatik.ruhr-uni-bochum.de         Fax: +49-234-709-4209
> Institut fuer Neuroinformatik, Universitaetsstr. 150, 44780 Bochum, Germany
  I changed my mind, Gerd, mind telling Witten tomorrow when you
telephone him that I now think the first case of where the p-adics are
found essential in physics and where the Finite Integers are inadequate
is  ' harmonic oscillators ' such as springs and even the Coulomb force
law. I first thought that the Quantum Hall Effect of its bizarre math
numbers will be the first essential need for p-adics but now I think it
is harmonic oscillation. The p-adics in fact are numbers of harmonic
oscillation.
  What does it feel like Gerd, to have the physicist show you the
correct mathematics of Naturals = p-adics = Infinite Integers and you
were playing with the silly fiction of Naturals = Finite Integers.
Please ask Witten for he knows physics. Need to find out where in
physics the p-adics are essential and simultaneously where the Finite
Integers are inadequate to do the job.

PRUEVA 01

"Mark C. Chu-Carroll"  wrote:
>It's pretty damned pathetic when you can't even answer the most trivial
>of questions about your discoveries. You claim to have found a complete
>fossil skull embedded in a rock sample in which all of the material has
>been significantly compressed. And yet, you claim that it's still hollow.
>You've *got* to be able to explain that, or else your entire theory can be
>completely dismissed without further consideration.
>But instead of even making an attempt to intelligently defend your claims,
>you just ignore the question.
>So *who* was it who's afraid of the truth?
Marc:
I've told you once, I've told you twice and I'll tell
you once again:
My answer to ``Who's afraid of the truth?"
Why, obviously, just about everyone in the scientific
establishment whose job it is to seek honest answers
to the time-honored question of man's initial emergence
on The Good Earth.
After all, anyone involved in this pursuit -- particularly, physical
anthropologists, with all their ``schooling'' -- is more than well
aware that not a shred of evidence links man to the cat-size,
monkey-like insectivore of 60-65 million years ago, from whom the
scientific establishment has unceasingly claimed we evolved.
Yet, primarily because of vested interests, these physical
anthropologists and others fail to speak out and challenge a theory
that has more holes than a gold prospector's pan.
To add insult to injury, anytime someone comes along with proof that
man may well have existed eons before Mr. Insectivore, these
``scientists"  play Mr. Ostrich and hide their head in the sand.
They're doing it now with the human skull embedded in the boulder, an
incredible specimen that offers the evidence -- incredible as it may
be -- that man INDEED was around while coal was being formed.
As for your other question, Marc: How do I explain why the skull
protruding from the boulder is hollow (since there's a hollow sound
when it is tapped)...
I really can't give you a definitive answer. I can only guess that it
was embedded in mud that had slowly hardened and, in time, more
hardening took place.
Undoubtedly, there are other possible explanations. And based
on the boulder's size and shape, one would have to be that
the entire skeleton is inside, in a seated position, and the boulder
had been molded around the corpse, in some sort of burial ceremony.
Or, if that's too farfetched, perhaps the skull was removed and placed
in this precise position -- the skull visible -- and the boulder
shaped around it, the way we put photographs of loved ones in frames.
This theory cannot be dismissed out of hand because, even patholgists
would have to agree, the cause of death undoubtedly was due to a
fractured skull.

Alioune Ngom wrote:
> 
> Here is the problem:
> 
>         Let K = {0, 1, ..., k - 1} (k > 1) be a set of k logic values.
> Let Union and Intersection be two operators defined on K. Union is
> defined as the bitwise OR operation between two elements represented in
> binary numbers (having each log(k) bits, the base of the log is 2). 
> Intersection is defined as the bitwise AND operation between two
> elements represented in binary numbers. 
>       Let k be a power of 2 (i.e. k = 2^r, with r > 0). Unary central
> relations are the non-empty and proper subsets of K. A unary central
> relation R is closed under Union and Intersection if x Union y and
> x Intersection y are in R whenever x and y are in R. In other words:
> (x in R and y in R) implies (x Union y is in R and x Inter y is in R).
> 
>         Now the problem statement: For k = 2^r, how many unary central
> relations are closed under Union and Intersection ?
>                                  ---
> 
>    I was not able to find a closed-form formula or even a recursive
> formula.
> 
Nice problem, indeed. I've no solution yet, but a more general 
formulation:
"How many "sub-lattices", closed under + and *, 
 can be obtained from a Boolean lattice over r elements?"
For instance, the same problem arises if you consider 
a set of r elements and the lattice of all its susbsets, 
with standard set Union and Intersection.
Just a partial hint for a recursive formula: 
with r elements you can at least include all the
cases obtained for 1 <= s < r, thus retaining
only s out of r elements (=bit positions in your formulation), and
these elements can be chosen in comb(r s)=r!/((r-s)!s!) different ways.
The other (r-s) elements have fixed values.
E.g. In your example r=2. With s=1 (k=2), we have, in binary notation:
{0}{1}{0,1}, which can be extended to yield:
{0} -> {00}{01}{10} (these are trivial cases)
{1} -> {10}{11}{01}  
{0,1} -> {00,10},{01,11},{00,01},{10,11}
(it seems that principle of inclusion-exclusion should be used here
to avoid counting twice or more a same configuration) 
Let me know if you find a solution!
Paolo
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Paolo Ciaccia    
DEIS - CSITE-CNR         
University of Bologna - ITALY 
mailto:ciaccia@cs.unibo.it
http://www.cs.unibo.it/~ciaccia

Archimedes Plutonium (Archimedes.Plutonium@dartmouth.edu) wrote:
:   My advice to you is to open your mind. Recognize that there are
: people in the world who are thousands of times smarter than you and
: that when you read my posts, don't jump the gun and think that you are
: correct and I am wrong. Say to yourself, I am reading AP and I can
: learn something new today.
Who is this guy, is he just a tad self important or is it just me?
Rob -2nd year UG chemist. University of Warwick
Tanstaafl

In sci.math RobC  wrote:
: Archimedes Plutonium (Archimedes.Plutonium@dartmouth.edu) wrote:
: :   My advice to you is to open your mind. Recognize that there are
: : people in the world who are thousands of times smarter than you and
: : that when you read my posts, don't jump the gun and think that you are
: : correct and I am wrong. Say to yourself, I am reading AP and I can
: : learn something new today.
: Who is this guy, is he just a tad self important or is it just me?
: Rob -2nd year UG chemist. University of Warwick
: Tanstaafl
That's just AP. He's our (sci.anything) pet lunatic. Just ignore him.
Dave.

> To quote Dr. Foakes-Jackson (1855-1941) of Cambridge ..."It's no use
> trying to be clever, we are *all* clever here.  Just try to be kind."
> 
> Darla
> ---who hereby thanks her brave champions, both public and private.
Hooray for you Darla. You know now, that you are damned to the river
Styx or something like that now, don't you? Archie Pootonium is quite a
(dishwasher) character. He hates anyone who disagrees with his
"theories", which are obviously idiotic, and have been proven so. They
carry no weight or importance here.
However, A.P. is quite intelligent. If you get him to coverse on a
worthwhile subject, he can be quite interesting and resourceful.
As far as his attacks upon you, forget them.
Mike
P.S. 
Welcome to the club