(posting from the Love Library at Univ of Nebraska, Lincoln)

 I am happy with the science thoughts that are coming to me
whilst on this trip. And me describe my most recent. I carry a
Rand McNally Compact Road Atlas on this trip for I am frequently
in a desire to see where I am going. And curious also. And the
capitals of the states are shown by stars. And so a trivia sort
of question popped into my mind as to which capitals are the
nearest to each other? And without looking I would have guessed
Rhode Island because it is the smallest state and so one of its
neighbors, perhaps Boston would be the closest of any two
capitals. So I was curious to find the answer and from the looks
it is Washington DC and Annapolis. But that is sort of cheating,
or, one can make a sort of "trick" question by not specifying
state capitols only but also include the capitol of the USA. But
that line of enquiry really does not interest me all that much.
I really do not care. But, this enquiry re-opened my old quest
of the 4 Color Mapping Problem.

  And so, right here, right now, I want to re-open that old math
problem. Many years ago I dropped posting about the 4-Color-Mapping
saying that it was really a 2-Color-Mapping.

  And that the 4-Color Mapping problem in mathematics was ill-
defined. This is the truth, that the 4-Color mapping is a very
ill-defined mathematical problem. Ask yourself this question,
can you have country boundaries without lines? Can you have a
boundary without lines? Can you have country-areas without lines
to demarkate the country from other adjacent countries? No. The
answer is no. You cannot have ‘points’ as the boundaries between
states or countries but that ‘lines’ are *necessary*.

  Because lines are necessary, therein is a proof that the 4-
Color-Mapping Problem is a fake math problem, a utterly ill-defined
and fake math problem. You cannot have adjacent countries or
states without lines demarkating those countries and states.
Hence, how many colors does it require to mapp all maps? The answer
is quite simple, it takes only 2. Black for the lines that are
boundaries and white for the area enclosed.

  The 4-Color-Mapping-Problem was a pseudo problem for it neglected
to realize that lines are essential requirement in the problem
and that these lines require a color also.

  I am glad in a way that I am returning to some mathematics proofs
but in another way I realize that mathematics is never as
important as any of the other sciences. Math is the least important
of the sciences and is the subject that one ought to concentrate
upon only when the important sciences such as physics, chemistry
biology geology, astronomy are taken care of.

http://www.newphys.se/elektromagnum/physics/LudwigPlutonium/
http://www.galstar.com/~ichudov/ppl/ap/index.html

An easy read
http://members.aol.com/randaminor
Regards,
john reed

Diane Maclagan has recently proved a result that she feels might be known,
and is trying to ask as many experts as possible if they have seen it.

Let N^d be the set of points in d dimensions whose coordinates are all
positive integers.  Define a partial order on N^d by setting

    (a_1, a_2, …, a_d)  <=  (b_1, b_2, …, b_d)

if a_i <= b_i for all i.  A "finite order ideal" of N^d is a finite
subset S of N^d with the property that if P is in S and P’ <= P then
P’ must also be in S.  Let J(N^d) be the set of all finite order ideals
of N^d, partially ordered by set inclusion.

Theorem.  J(N^d) has no infinite antichains.

"Antichain" just means no two elements are comparable (as opposed to
"compatible," the concept that is more commonly used in forcing).
Has anyone seen this before?  Is it a special case of a more general
theorem?  For more information, see Maclagan’s preprint at

   http://front.math.ucdavis.edu/math.CO/9909168

[Incidentally, I initially tried emailing this message to Bill Dubuque,
 whom I believe is very knowledgeable in this area, but the email I had
 for him bounced.  Does anyone know how to get in touch with him?]
—
Tim Chow       tchow-at-alum-dot-mit-dot-edu
Where a calculator like the ENIAC today is equipped with 18,000 vacuum tubes
and weighs 30 tons, computers in the future may have only 1,000 vacuum tubes
and perhaps weigh only 1 1/2 tons.   —Popular Mechanics, March 1949, p.258

It was ill-defined and not well thought out because it never
really addressed the main issue of boundaries. Boundaries require
lines and the entire problem is one of points, lines/curves
and areas. I am going to call curves as lines, but you can
think of the boundaries as lines in general.

If the 4-Color-Mapping Problem had consisted of just areas and
points with no lines involved then the history of its analysis
and attempts at proving it would now all be valid. But it’s
major issue is lines, and the 4-Color-Mapping Problem never
seriously faced the issue of the lines.

All boundaries are not points but lines. For instance a map of
the states of the USA, all of its boundaries are lines. If they
were points then the 4-Color Problem is a genuine problem, where
each point is either a point of one state or a point of the other
state. But the boundaries are not points but rather lines, and
the points of the boundary-lines do not belong to either state
that they separate.

  Thus, the 4-Color-Mapping Problem is really a 2-Color-Mapping
Problem and to be mathematically precise the Mapping Problem
degenerates into a 2-Color Mapping where 2 colors are necessary
and sufficient to Color all mapps. You need only two colors,
say, black and white. Black to color the boundary lines and white
to color all the states or countries.

 The history of the 4-Color-Mapping Problem from Cayley on down
has been a mathematical schizophrenic ill-defined problem. So
ill-defined that only an alleged (yet insane) computer proof
has been offered for the 4-Color-Mapping Problem

  I offer a 2-Color-Mapping, and this offer of mine of several
years past is a *counterexample* that the 4-Color Mapping
Problem is a fake. Give me any configuration of countries
and I can color it with only 2 colors, black for the boundary
lines and white for the countries.

  This post is a proof that the 2-Color-Mapping Problem is true
and that the 4-Color-Mapping Problem is a fake and ill-defined
mess.

file under 4-Color-Mapping in
http://www.newphys.se/elektromagnum/physics/LudwigPlutonium/

Does anyone have any suggestions for books relating to Zeno’s paradox and
the cinematographic view of reality.  Also quantum spacetime.

Thanks
HLW

    1st CALL FOR PAPERS — CSL 2000

                Annual Conference of the
   European Association for Computer Science Logic

 Fischbachau/Munich, Germany, August 21-26, 2000

CSL is the annual conference of the European Association for
Computer Science Logic (EACSL). The conference is intended for
computer scientists whose research activities involve logic, as
well as for logicians working on issues significant for computer
science. Suggested, but not exclusive, topics of interest are:

* automated deduction and interactive theorem proving
* categorical logic and topological semantics
* constructive mathematics and type theory
* domain theory
* equational logic and term rewriting
* finite model theory, database theory
* higher order logic
* lambda and combinatory calculi
* logical aspects of computational complexity
* logical foundations of programming paradigms
* logic programming, constraints
* linear logic
* modal and temporal logics
* model checking
* program extraction
* program logics and semantics
* program specification, transformation and verification

INVITED SPEAKERS

Miklos Ajtai (Almaden), Paul Beame (Washington),
Andreas Blass (Ann Arbor), Egon B"orger (Pisa),
Yuri Gurevich (Seattle), Bruno Poizat (Lyon),
Wolfram Schulte (Seattle), Saharon Shelah (Jerusalem),
Colin Stirling (Edinburgh).

PROGRAM COMMITTEE

Edmund Clarke (Pittsburgh), Peter Clote (M"unchen),
Kevin Compton (Ann Arbor), Erich Gr"adel (Aachen),
Gerhard J"ager (Bern), Klaus Keimel (Darmstadt),
Jan Willem Klop (Amsterdam), Jan Krajicek (Praha),
Daniel Leivant (Bloomington), Tobias Nipkow (M"unchen),
Helmut Schwichtenberg (M"unchen), Moshe Vardi (Houston).

PAPER SUBMISSIONS

Submitted papers must describe work not previously
published. They must not be submitted concurrently to a journal
or to another conference. Papers authored or coauthored by
members of the Program Committee are not allowed.  Submissions
must not exceed 15 pages (in the usual format for Springer
LNCS), including title page, figures and references. The title
page must contain: title and authors; physical and e-mail
addresses; telephone and (if available) fax number for each
author; identification of corresponding author, if not the first
author; an abstract of no more than 200 words; a list of
keywords.

Submissions must arrive by January 31, 2000. Notifications of
acceptance will be sent by April 17, 2000, and final versions
are due May 19, 2000. Authors are invited to send manuscripts by
electronic mail, as uuencoded gzipped or attached postscript
files and an ASCII file containing the abstract and the address
of the corresponding author:

* see the conference home page for instructions
 http://www.tcs.informatik.uni-muenchen.de/csl2000/
* or send a message with subject "submission information" to
 csl2000-…@tcs.informatik.uni-muenchen.de

Concerning further questions about the submission procedure
please contact

 Helmut Schwichtenberg
 schwi…@rz.mathematik.uni-muenchen.de
 Phone +49 89 2394 4413
 Fax   +49 89  280 5248
or
 Peter Clote
 cl…@tcs.informatik.uni-muenchen.de
 Phone +49 89 2178 2241
 Fax   +49 89 2178 2238

PUBLICATION

Papers accepted by the Program Committee must be presented at
the conference and will appear in a proceedings volume, to be
published by Springer Verlag in the "Lecture Notes in Computer
Science" series.  Final versions of accepted papers will be due
by May 19, 2000.  The format for camera-ready manuscripts will
be that of Springer LNCS; instructions can be found in the LNCS
home page at:
 http://www.springer.de/comp/lncs/index.html

IMPORTANT DATES

Paper submissions      January 31, 2000
Notifications of acceptance     April 17, 2000
Final version due                   May 19, 2000
CSL 2000 conference      August 21-26, 2000

ADDITIONAL INFORMATION

CSL 2000 home page:
    http://www.tcs.informatik.uni-muenchen.de/csl2000/
CSL 2000 local organization:
    csl2000-…@tcs.informatik.uni-muenchen.de

–
Dr. Thorsten Altenkirch                 phone : (+49 89) 2178-2209
Theoretical Computer Science            fax   : (+49 89) 2178-2238
LMU, Munich, Germany                    Oettingenstr 67, D105
http://www.tcs.informatik.uni-muenchen.de/~alti
—
    _              _
 __| |___   ___ __(_)  __ _ _ _  _ _  ___ _  _ _ _  __ ___  Das
/ _` / -_)_(_-</ _| |_/ _` | ‘ \| ‘ \/ _ \ || | ‘ \/ _/ -_) Moderatoren
\__,_\___(_)__/\__|_(_)__,_|_||_|_||_\___/\_,_|_||_\__\___| Team

Beiträge für de.sci.announce bitte an de-sci-annou…@de.uu.net senden.
Gewünschte Headerzeilen (Followup-To, Newsgroups etc.) bitte in den Header
oder am Anfang des Textes einfügen.

I am finishing up the membership roster for the Association for
Symbolic Logic, for publication in the December issue of The Bulletin
of Symbolic Logic.  So if you have moved in the past year, I hope you
sent a change of address to the ASL office in Illinois.  If not, that
office is a…@math.uiuc.edu; better send cc to me.

If the URL for your home page is not on my directory of websites of ASL
members (www.math.ucla.edu/~hbe/aslweb.html), you are invited to send
me that also.

If you are not even a member of ASL, then you didn’t need to read
this.  But if you did read this far, you can rectify the situation by
joining.  See www.math.ucla.edu/~hbe/join-asl.html.

–Herb Enderton
  h…@math.ucla.edu

 A solution to the paradoxes has two sides:  the philosophical and the
technical.  The paradoxes are, first and foremost, a philosophical
problem. Strictly speaking, a solution is simply to pinpoint the exact
step where the reasoning that leads to contradiction is fallacious.
But clearly, an oracular declaration is hardly likely to be
satisfying.  Some kind of explanation must also be forthcoming.  This
makes the enterprise very difficult, because explanations are not
logical animals like proofs, but instead refer to psychology.  If some
blah-blah doesn’t convince you, well then to you it is not an
explanation; if it does, then it is.    
 A technical solution is an axiomatization which avoids Russell’s
paradox.  If one can pinpoint where the paradox reasoning is
fallacious, then one show know how one can avoid it.  Evidently, the
philosophical solution must motivate and justify the technical.  
 A comprehensive solution links Russell’s paradox to the Liar, and
proves correct our intuitive belief that they share a common lineage.
The philosophical solution for the Liar is thus related to the
technical solution for Russell’s paradox.
 One final word.  So many solutions have been provided that it is
hardly likely that one can say anything original on the subject.  The
best one can hope for, is to say it more loudly.

In physics we have this magnificent splitting up of realms of
parameters such as particle to wave to aether. Or of momentum to
position to charge.

And it is curious that mathematicians from Euclid to myself never
thought that mathematics may be split up into realms such that it is
inappropriate and silly to try to saddle the momentum with position and
gain 100% certainty. Or to saddle wave with particle or vice versa and
again achieve 100% certainty.

Surely, it is thought that mathematicians are smart and keen folk and
that seeing something such as duality and triality, that math would
also have duality and triality. But no, mathematicians are of a
mindcast that there subject is absolute certainty in all details.

Curious, because mathematicians in the 19th and 20th century saddled
infinity with finiteness. They believed that Natural Numbers were all
species of finiteness. And applying this finiteness to infinity, these
mathematicians of Cantor and beyond strapped and saddled infinity so
much with finite numbers that they could sally-forth and announce to
the world that infinity comes in various types. That you can have one
order of endlessness and yet another order of endlessness.

  To the common person on the street when told that endlessness has
various types of endlessness, he often is sceptical and right he should
be, for everything that does not come to an end is the same. There is
only one type of endlessness.

  So, how was the world of mathematics deluded by transfinite
infinities? And the answer is really quite easy in retrospect.  When
you make a edict, or an absolute commandment that finite exists and
then measure everything against this finite then you come up with
illusions and delusions.

  If you say that a number can be 100% finite with no markings of
infinity on it, then you get into trouble. The physicists resolved
their problems of duality in the 20th century, but the mathematicians
with their rift over finite and infinity, whether the number 24 is
really the Infinite Integer …000024 are just beginning to see how
silly and fake most of their work was.

  It was natural flow of events that Newtonian Mechanics would come
before the deeper truth of Quantum Mechanics. And it was a natural flow
of events that mathematicians would think that "finiteness" can exist
without infinity and that this finiteness can be applied to the
"infinite" to uncover truths about the infinite. It was natural for the
history to believe Natural Numbers = Finite Integers, until a more
wiser age when it was realized that all numbers have a component of
infinity. The 20th century had a revolution in physics where Newtonian
Mechanics was overthrown. Mathematics must still await her revolution
to overthrow her fakery of Natural Numbers = Finite Integers.

hello. I am a total neophyte in the realm of logic. I was introduced to logic
in a math survey course in community college. I would like to find a resource
for truth tables on the internet, and the search engines have let me down. can
anyone help me with this? thanks in advance
russell