. .

Links . . (en Rechts, van alles wat ;-) . . Site map
Classic FM
Other online Radio Stations

. . The 'ECHO' project (on history of science): - Remember Claude Shannon (1916 - 2001).
Robert G.Gallager in Shannon at M.I.T : "He did not like to replow old ground, and was so creative that, if he started to think of something old, he would look at it in a different way and create something entirely novel." and: "... he always tended to work (or play) with many different types of problems at the same time." (info theory, genetics, cryptography, optimal investment portfolio, chess-playing machines, juggling robots, etc.)
Thomas M.Cover in "Shannon's contributions to Shannon Theory" (op.cit.): On the question of mathematical rigor, however, we should say that after fifty years it is clear that Shannon was correct in each of his assertions, and that his proofs - some of which might be considered outlines - could eventually be filled out along the lines of his arguments. It also must be said, given the breadth and scope of his theorems, that Shannon's intuition must have been anchored in a deep and natural theoretical understanding."
-- (NB: compare Fourier's spectral decomposition of periodic functions, which in 1807 was rejected by the French Academy of Sciences on grounds of insufficient rigor, but in 1821 published in a book by Fourier).
"Remembering Claude Shannon" (archive)

C.Shannon (on his information theory, 1948):
-- "It just happened that no_one else was familiar with both fields at the same time."

Feyman autobiography - "Surely you're joking, Mr. Feynman!"

On Semigroups as State-Machine closures, and Preserved State-partitions = Machine structure.

- My 8 papers on Arxiv (at front.math.ucdavis.edu)

Re: Question for Mathematics PhDs - NFB (sci.math Jan'99)

On Particle/Wave & Matter/Mind - Alternating Discrete/Continuous models in a hierarchy, and Memory!

"Sequential Dimension" of string-sets: Peano N={1}* vs. Cantor 2^N={0,1}*

Is mathematics a science? - Clarification of terms, by Arturo Magidin

Lightspeed : is independent of Frequency to within 6 x 10^(-21).

Caroline Thompson<\a> Homepage

Forgotten History - List of essential missers, by Caroline Thompson (2000)

Doppler interpretation of the Hubble Redshift : Halton Arp's objections.
See also Anomalous Quasar redshifts
The Redshift is quantized : in jumps of 8 km/s.

Etherwind and Lightspeed:
To claim, as Michelson-Morley did in the late 1800's, that there is no measurable ether wind by doing light-speed experiments on the Earth surface, and then conclude there is no ether medium for EM- waves -> is as rediculous and unfounded as to claim, on a quiet day, after sound-speed measurements in various directions with a null result, that there is no air for sound to propagate in!

[Summary 1] Ether as dissipative medium for EM-wave propoagation.

[Summary 2] Hubble redshift by Photon Decay (halflife 6 billion yrs)

From classical to modern ether-drift experiments : the narrow window for a preferred frame.

Dark Matter = Total Ether-mass? [ Galaxy density in Universe :: 1 pea / (mile)^3 ]

Observer in a moving lift Re: bending light in a gravity field.

Lunar Laser Ranging Experiments - (Webster Kehr) The Moon recedes 6 cm/year!
"It is easier to find a score of men wise enough to discover the truth than,
in the face of opposition, to find one intrepid enough to stand up for it." - A.A. Hodge

Re: Dayton Miller experiments repeated (re Michelson-Morley)

sciencedirect.com - my 12 papers on FSM (State Machines), Finite Semigroups, ...
. . . Arithmetic (Fermat, Waring, Goldbach, Log-arithmetic) and Logic (Boolean)
. . . [Preprint archive: free register - login and search for 'benschop']
de.arXiv.org - and 8 older versions (till dec 2001)

-- New book : -- "Associative Digital Network Theory" (preface.htm) :
. . . an Associative Algebra Approach to Logic, Arithmetic, State Machines.
- - See also : Digital_Network_Theory: Abstract at Wikipedia.org

"Additive structure of the Group of Units mod p^k ,
with Core and Carry concepts for extension to Integers"
- Direct proof of FLT,
published nov.2005 in AMUC - Acta Mathematica Univ. Bratislava

scimath (25 april 2006)

--- Sun, Moon and Star (;-)
History of the Redshift
- by B.Setterfield, D.Dzimano (dec-2003) : 'Quantized Redshift', definitely not Doppler.

Redshift FAQ - Setterfield

Everything is Expanding : Far-off and Close-by (Ray Tomes)

Quantity and Quality : Orthogonal - in a multi-dimensional world. (wsm-1933, 20apr04)

Time- and Frequency Domain views of Non-linearity (NFB 23-oct-2004)

Emergence of Quanta in a Causal Continuum - Tony Booth

The 'single-focus' syndrome danger (Mar.2000, NB)

Re: WSM Website and Wiki./ Etherons Discrete and Continuous models BOTH necessary.

Re: the Laws of Nature / 'facts' and context : it's all relative to agreed aim/context... - Reply

WSM-FotonTest - Testing for Foton-'particle' vs. Continuous_wave light.

Redshift by Wave dilation - Ingvar Astrand

Plasma Cosmology - based on currents in space (Alfvèn, Peratt: 1970's).. (full text)

- "The Iron Sun" Re: the Electric (Plasma) Universe.

The Big Bang never happened - book by Eric Lerner. - ( his homepage )

- Hubble telescope: Deep-space foto - with large variety of different galaxy-types --> No BigBang!

WSM-7736 Robert Dorsey
There have been experiments refining the Michelson-Morley experiment
by using helium instead of air in the test apperatus. The results
indicate an ether (quantum foam) flow. The following link is a 2002 paper
on that topic. - http://arxiv.org/PS_cache/physics/pdf/0207/0207010.pdf
The following link is to a 2004 paper, throwing stones at Einstein's
theories, that use the helium-mode interferometer experiments in its argument.
The following link is rather math intensive, but supports the idea
of a moving ether. http://arxiv.org/PS_cache/physics/pdf/0306/0306094.pdf
These papers may have their shortcomings, but at least they
demonstrate that the topic is open for discussion. -- RRD

The Electric Plasma Universe - by Mel Acheson (22jan02):
"Now the original question comes full circle. The problem is not that of supplying the energy to ionize neutral matter. The problem is that of dissipating the energy of already ionized matter. It's the act of neutralizing existing separations of charges that provides the prodigious energy driving and shaping the universe.
After seeing that the universe is already electrified, a calculation on the back of another envelope shows that gravity is too weak--by about 40 orders of magnitude! -- to account for the observed structure, movement, and dissipation of energy. It's the gravity universe that's impossible."

"The Wholeness of Nature" - Henri Bortoft (1996): Synthetic 'science'.
- - My comment (re 'undertanding' & memory)

Cantor's Theory: Mathematical creationism - sci.math (22nov04)

Question on Cantor-set & Kronecker - Bill Tait (U-Chicago)

Constructive Mathematics - by Alan Calder (Sci.American, 1979 p134-143) - Refs

Intro to Wavelets (IEEE)

Fermat Last Thm - "Breaking the Hensel Lift" mod p^(3k+1) for the Cubic roots of 1 mod p^k.

Cantor's uncountable infinity 2^N has 2 generators, vs. Peano's countable N: 1 generator.
Cantor's diagonal - in an infinite but countable size N x N binary matrix.

Fermat, Waring, Goldbach . . . Cantor, (in)finite FSM, Semigroups . . . General math/physics :
Fewago . . . Fermat, Cubic Roots . . . Waring PowerSum . . . Goldbach PrimeSum . . .

Carry <= Residue . . . Fermat's Marginal Note . . . Intro- FLT . . . Fermat = Anti-closure (+)

Selmer Local/Global . . . Additive Nr-theory . . . Semigroups, FLT . . . Philosophy

Fermat in Toulouse . . . Functions, Associative . . . Cubic Roots a^3=1 . . . Campaign

Cantor Diagonal . . . Integer State Machines . . . (in)finite . . . Controversy

Math-use Maslow . . . Ether, Redshift . . . I-Ching Basic 8 Hex . . . Quotes

Function composition & Arithmetic: Fermat, Waring, Goldbach via semigroup Z(.) mod m_k

Java/Birma 1942-'45 - Dagboek by JCB (Dutch, 310k pdf)

De Bataafse Mythe Rembrandt: 'De eed van Claudius Civilis' (Museum Stockholm)

Humor / Relegion
- "If God created us in his own image, we have more than reciprocated." — Voltaire (1694-1778).
- "Once there was a time when all people believed in God and the church ruled:
. . . This time is called the Dark Ages."
- "These are my opinions. If they were the Biblical truth, your bushes would be burning."
- "A cult is a religion with no political power." — Tom Wolfe.
- "A religion is a cult that succeded."
- "If Jesus knew what's going on in His name, He would turn in His grave."
- "Religion is to brain what tapeworm is to intestine."
- "A man without religion is like a fish without a bicycle."
- "Jesus died for somebody's sins, but not mine." — Patti Smith.

On the Structure of our Universe (Cosmology) - John Sankey
There are competing models of the universe (other than the Big Bang) : steady state models. In these views, the universe is eternal - a desirable philosophy for many (although that has nothing to do with science). Distant objects are red because light quanta gradually lose energy through postulated non-scattering interactions with the universe as they traverse it (tired light). Such lost energy would be turned into mass at a rate equivalent to only a hydrogen atom per cubic kilometre per year could produce a steady physical expansion thus a Doppler red shift similar to that we see. It is not, however, understood how a steady state universe could be gravitationally stable. (The 'cosmological constant' is a fudge factor, not an explanation. Besides, Einstein's version of it doesn't work.) Stars are in galaxies because gravitation is always attractive, therefore unstable, and will merge together into black holes once they dissipate their angular momentum relative to each other. Where does the radiation necessary for matter creation and space expansion come from once everything is sucked into black holes? Besides, the success of the quantum origin of the universe at predicting the distribution of elements long ago disheartened most supporters of steady state. About the only supporters of the pure steady-state universe left are those who propose that gravitational flatness is a necessary condition for existence of any universe. (Of course, they may just be right in that - measured densities keep inching towards that required for flatness.)
-- However, the real power of the Big Bang model is that it unites the two sciences that depend on big money : Astronomy and High-energy physics. Ever-larger particle accelerators, which pack more and more energy into a point, were not just self-generating data (more in, so more out), they were exploring 'the beginning of everything'. So were ever more powerful telescopes - seeing fainter meant seeing farther which in turn meant seeing nearer 'the beginning'. And so, astronomy and high-energy physics closed ranks - anyone who didn't support the standard model was out, from either field. The guiding principle of both fields became 'being right' rather than 'getting things right', in short, the 'big science' syndrome.

Theory in the Age of Digital Transformation : (by Henry Jenkins, MIT)
"What, then, is the work of theory in the age of digital transformation? Digital theory offers us explanations, interpretations, and predictions which enables us to manage the process of technological change and its impact upon our social, cultural, economic, political, and personal lives. Digital theory provides a point of intersection between the languages and practices of science and engineering on the one hand and the arts and humanities on the other. Digital theory embraces the utopian imagination not as a way of predicting the future but as a way of envisioning meaningful change and keeping alive the fluidity which digital media has introduced into many aspects of our social and personal lives. Digital theory identifies historical antecedents for contemporary media developments and at the same time, defamilarizes older media and opens them to re-examination. What is striking about the present moment is not simply that academic theorists have responded quickly to a changing media environment — itself a phenomenon virtually without precedents — but theory production has been embraced by the larger society. Theorists are interviewed as media celebrities in the pages of mass market magazines like Wired. Vernacular theory surfaces and is debated on almost every on-line discussion list and newsgroup as everyday citizens hope to better understand the nature of the transformations occurring around them. Theoretical arguments are forming the basis for the early court decisions which determine what model of regulation, intellectual property rights or anti-trust litigation is most appropriate for cyberspace. The impact of digital communications on all aspects of modern life has made the process of mediation remarkably visible and has created a new demand to answer questions which once would have seemed the arcane interest of media scholars."

table_of_physical_constants . . . Exact Particles .vs. Fuzzy Waves

. . . "If I don't see far, it's because Giants are standing on my shoulders." [Dave Rusin]

Yahoo group WSM - On naturals N and reals 2^N : numberline and Lattice.

Phi-wave Aether theory - C.H.Thompson (2004)

My interest in discrete math - Motivational discussion with Pertti Lounesto - sci.math dec'99

"Distant stars (spectra) blurr only in even-dimensional spaces". Pertti Lounesto.

Speed of sound - in various materials.

Limits to classic EM fields - Kirk McDonald (Princeton-U)

Wave structure of Matter - Gabriel LaFrenière.

QuickBasic for animation of Wave Motion - Charles Peirce

Moon distance by Laser reflection - Apollo 11 (1969)

Pioneer_10 - shows decay of radiowaves (A. Stolmar)
. . . . - Photon halftime = 4.2 x 10^9 yrs

Redshift by Photon decay - Photon halftime = 6.5 x 10^9 yrs (M. Lewis)

"A photon has weight" - Williamson, van 't Hooft

- On the structure of our Universe : a balanced view (John Sankey)

Some 60 columns on Science - (Ira Pilgrim)

#13: Science and Belief . . Scientists are also Human. . (on the role of Inertia in Science)
"The fact is that while science has made a great deal of progress, human nature
hasn't changed. People often ignore facts that don't conform to their preconceptions.
Whether or not we want to admit it, scientists are people.
Years ago a small airplane made an emergency landing on a highway near Salt Lake City.
While the pilot waited for a car to come along to take him to where he could get help,
an automobile crashed into the airplane. When the driver of the car was asked if he
didn't see the airplane, he replied, "Yes, I saw it, but I didn't believe it."
I don't wonder why no one made Newton's observations (colors/prism) before him.
I suspect that someone might have, but he didn't believe it. And if he did believe it,
there was no one he could tell it to, nor could he get it published.

#19: Mystification
"The story of The Emperor's New Clothes tells how a group of tailors mystified
an emperor into believing that they had woven a suit of clothes that was so fine
that it couldn't be seen. A child, who had not yet been trained to accept
mystifications, points out that the emperor is naked. The story ends there.
-- The author doesn't tell you what happened to the child. Odds are that he
went to bed without supper and was forced to repeat over and over again
"The emperor knows all, and I know nothing". - That is the way of the world.
I could have tried to mystify you by saying it in Latin: Sic transit whatever.
If you didn't know the meaning of the word mystification, you know now.
There isn't a human being who hasn't been exposed to the process in school,
church, TV and every means of communication. Its purpose is to give one
person power over another through the (mis-)use of words.

Ron's place . . Biographies of interesting writers/scientists/philosophers/etc.

"Alternative Physics On Line" . . Critical notes by prof. U.Bartocci (U-Perugia.it)

SSE: Society for Scientific Exploration (Stanford-Univ, USA, 1982)
The primary goal of the international Society for Scientific Exploration (SSE)
is to provide a professional forum for presentations, criticism, and debate
concerning topics which are for various reasons ignored or studied inadequately
within mainstream science. A secondary goal is to promote improved understanding
of those factors that unnecessarily limit the scope of scientific inquiry, such as
sociological constraints, restrictive world views, hidden theoretical assumptions,
and the temptation to convert prevailing theory into prevailing dogma.

As science has developed, it has become increasingly compartmentalized.
This may make the operation of each discipline more efficient, but we run the risk
that the profession may not be responding to challenges that do not fit neatly
into the matrix of present-day science.
-- "Advances are made by answering questions.
-- Discoveries are made by questioning answers." ... Bernard Haisch :
. . . (Astrophysicist and past Editor of the Journal of Scientific Exploration)

Natural Philosophy Alliance (NPA)
. . A critical view on flawed assumptions in fundamental Physics (by professionals)

Red-shift of fotons: Lossy Light propagation in Ether, after all?
. . NB: Common Sense suggestion by an amateur;-)

Hubble Red Shift by Photon Decay: a sensible explanation - by Michael Lewis

Examples of Suppression in Science
"The Suppression of Inconvenient Facts in Physics" by Rochus Boerner, 2003.
. . . "Textbooks present science as a noble search for truth.
. . . However, for many scientists this is a cruel myth." [On unnatural inertia] :
- "In true science, theory always surrenders to the primacy of evidence.
If observations are made that, after careful verification and theoretical analysis,
are found to be inconsistent with a theory, than that theory has to go - no matter
how aesthetically pleasing it is, or how prestigious its supporters are, or how many
billions of dollars a certain industry has bet on it. But in current mainstream science,
the opposite occurs with disturbing regularity. Anomalous evidence is first ignored,
then ridiculed, and if that fails, its author attacked. Scientific conferences will not
admit it to be presented, scientific journals will refuse to publish it, and fellow
scientists know better than to express solidarity with an unorthodox colleague."
- R.G.Jahn - [On snug and inert 21st century science, due to vested interests] :
". . . Even more seriously, it is an establishment that persists in frenetically sweeping
legitimate genres of new anomalous phenomena under its intellectual carpet, thereby
denying its own well-documented heritage that anomalies are the most precious raw
material from which future science is formed."
- Nico B : It may well be that Europe, China and India, less industrialized than the US
- hence less liable to suffer from the above mentioned scientific inertia due to vested
interests - in the 21-st century recoup the initiative for a badly needed scientific élan.
- M.Psimopoulos, T.Theocharis : "How to test special relativity", Nature 319, p.269 (23jan86)
"... All sorts of experiments have already been conducted in space. But the few experiments
which might have truly tested the perhaps most fundamental and controversial hypotheses
in twentieth century physics- Einstein's postulates - have curiously not been done."
(NB: Only Extra-terrestrial measurements can test the Ether-Drag hypothesis;
. . . . the M/M experiment (1887): measuring light-speed along Earth surface is insufficient)
- Bryan G.Wallace : "The Farce of Physics"
Non-constant light speeds measured in planetary radar propagation tests (publication blocked).

OPTIS Satellite Based Optical Tests of Special and General Relativity (U-Düsseldorf.de)

Interview with Carver Mead (on his non-statistical 'Coherent Physics')
Q : "And so mathematical description was substituted for understanding?"
CM: "Absolutely. It's conceptual nonsense. You can calculate stuff with the theory, but
the words people put around it don't make any sense. That had the effect of driving the
more conceptually oriented students out of physics. We have ended up with more and more
mathematicians in the physics departments. Don't get me wrong, there's nothing wrong with
mathematics. It's the language we use to express the precise relations of physical law.
But there is an increasing tendency to mistake the language for the physics itself.
Once we lose the conceptual foundations, the whole thing becomes a shell game.
There are very few conceptual workers left in the field. Feynman was one of the last,
and he wasn't willing to take on the Copenhagen clan. Nobody was, until we come to
A.O.Barut, John Dowling, John Cramer, and a few others." [ . . . ]
Q : "What's the problem with point particles?"
CM: "Because they are assumed to occupy no space, so they must be accompanied
by infinite charge density, infinite mass density, infinite energy density. Then these
infinities get removed again by something called "renormalization." It's all completely
crazy. But our physics community has been hammering away at it for decades.
- - Einstein called it Ptolemaic epicycles all over again..."
Q : "Running through your work gives the idea that the deeper thing is probably simpler.
CM: "It always worked out that when I understood something, it turned out to be simple.
Take the connection between the quantum stuff and the electrodynamics in my book.
It took me thirty years to figure out, and in the end it was almost trivial. It's so simple
that any freshman could read it and understand it. But it was hard for me to get there
since all this historical junk was in the way." (NB: unlearning is harder than learning)
..."I think Einstein was a scientist in the truest sense in his response to the Copenhagen
interpretation. He said that none of us would be scientist if deep down you didn't believe
there is a set of regularities in the operation of physical law. That is a matter of faith.
It is not something anybody can prove, but none of us would be scientist if we didn't
have that faith." -- ( The 'strange' usefulness of Mathematics in Physics ;-)
Q : "Does biology have a problem analogous to the physics problem :
- - lots of people barking up trees, and few looking at the forest?"
CM: "Every scientific discipline does. Our establishment rewards that kind of behavior.
It's very, very hard to ask the deeper questions, because you won't get tenure that way."

T. Van Flandern, J.P.Vigier : Experimental Repeal of the Speed Limit for Gravitational,
Electrodynamic, and Quantum Field Interactions, Foundations of Physics, 32 (2002) p.1031-68

Metaphysics / Natural Philosophy - On the Wave Structure of Matter

Pertti Lounesto on far-star spectra : NOT blurred in odd dimensional space!

Is the electron a photon with toroidal topology? - by M. van der Mark, and J. Williamson
Donut structure of electron
Abstract : symposium talk (TU Eindhoven, 2001)

Michelson/Morley : measuring in a medium moving along with the Earth proves nothing about 'Ether'.

Remember history ... re Hubble Red-shift: 20 yrs after Einstein's RTh

Einstein on Ether, he called it 'ponderable matter' (lecture 5 May 1920, Leiden Univ;-)

Caroline Thompson physics site : Common sense is less common than you think,
. . . but C.H.Thompson has it! - Comments

Re: Steady-state Universe : Matter converted into wave energy in some places and back again in others."

Don't rock the Boat : Can you blame them? After all, one cannot be careful enough about one's reputation...

Large precession of Mercury's orbit near the Sun : due to ether density modulation near a heavy body?

Red-shift by photon friction in 'ether' :
. . . Frequency dependent energy loss: lower (red) freq's travel further (less damping)

(Re: Occam's Razor in Math & Physics): Common Sense ... seems less common than you'd think...

Re: a minimal 'particle' (electron) being an ether_tornado? : _Why_ (if indeed) are all electrons the same?

"Threshold" as the difference between quantity & quality. - Re: the difference between particle and wave.

What is the lifetime of an electron? : The energy loss could re-appear as low freq. 'background radiation'.

Test this hypothesis of ether-drag : the Mercury orbit precession .. using established orbit CAD

Dark Matter/energy by vanderL :
-- "Why do you insist on discussing the concept of God, it has nothing
to do with science, and the idea of God is not falsifiable (the hallmark of
a scientific model). You cannot disprove the existence of such an entity,
so you cannot approach it scientifically. Look at electric-cosmos , and if
needed just keep on reading, it explains how science should work and then
it explains how stars function when viewed in electrical terms, especially the
more exotic variable stars suddenly seem a lot less exotic. I think it is worth
a very careful look.
-- I hope we can discuss the topic of dark energy/ dark matter a little further.
I agree with you that the Big Bang theory is just that, a theory. Concepts like
inflation, neutron stars/neutronium, black holes, dark matter and dark energy
are all theoretical constructs, invented to keep the BB theory alive.
-- It should be the other way around, first we gather data, then we make a model
and then we test and adjust the model. If too many adjustments are needed the
theory is probably wrong and we need a new theory. I don't see this happening at all.
-- When looking at the Big Bang, it keeps limping on, because people believe that
it MUST be true, just like religion, in disregard of overwhelming evidence against it.
In my opinion an Electric/Plasma model would fit the data better, but everyone
should make up its own mind. And don't let other people tell you what to believe."

Re: "The Einstein Hoax" (sci.math 14jan2000):
- On lossy light propagation, and from the outside looking-in...
Theory-edge (6sep98) : - FLT(case1) and the 'triplet' structure of units in semigroup Z(.) mod p^k

Re: Problem with Cantor's diagonal argument (re finite case) - Cantor & Binary matrix row permutations

Re: Why the attack on Cantor's Theory? - A simple string generation difference Peano N vs. Cantor 2^N

Re: Does the set of all sets exist? - Sets, power sets & Cantor's binary representation.

An interesting discussion - on FLT / Wiles' proof / Psychology / Science & Math.

ilja-schmelzer : General Lorentz Ether Theory.

A New Non-Doppler Redshift . . by Paul Marmet, Herzberg
. . Institute of Astrophysics, National Research Council, Ottawa, Canada

Possible Cause of Red-shift? - String Theory Discussion Forum

All about the MM experiment - Forgotten history of Michelson-Morley experiment 1887 (J.R.Redbourne)

List of articles on Cosmic 'ether' (aether)

"Dayton Miller and the Ether-Drift" : Critical historical remarks.

Re: Do you actually need an ether model?
. . Only if you don't allow perpetuum-mobile (lossless foton travel is un-natural)

--> We would do best to remember our history!

(-->) Indeed, and in fact Hubble - in his 1931 paper with Humason - warned in a footnote
that his 'Doppler' view of the Redshift was just an assumption, for the time being,
and that it could well be caused by a 'tired light' (or a 'foton-decay') process,
proportional to traveled distance (versus proportional to speed). He admitted the
properties of intergalactic space were just not known at that time (or are they now?
- e.g. can a parellax measurement of the DISTANCE to far stars with redshifted spectrum
be done with any sufficient accuracy ?-)

By the way, congratulations on the charming farmer/mouse story. I actually thought his
neighbour's name was Zweistein, who showed that there is no 'air' for sound to
propagate in, after accurate sound-propagation speed measurements in three
orthogonal directions, while in a riding closed train compartment without windows
(which of course he did not know at the time;-)
see http://home.iae.nl/users/benschop/ether.htm

For a math approach, via Maxwell E/M eqns *with* damping coefficient in a dissipative
medium (you may call it 'aether' or 'ether' or 'cosmic soup' if you like)
see Mike Lewis on Foton Decay (hypothesis;-) at http://members.chello.nl/~n.benschop

He derives a foton half-time of 1/(h.c^2) sec, which is about 6.5 billion years
(nasty idea: does an electron or proton have a finite lifetime ? Yakh . . . )
Of course, if one - as a real scientist - disavows any 'perpetuum mobile' ,
then one equally strongly despises the idea of a foton (cq. light) travelling
for bilions of years *without* any loss of energy (detect some irony ?-)

Oh well, as many a farmer will agree, it is all human psychology man !!
Since when do vested intersts NOT have an enormous inertia ?! [ Human Inertia ]

PS: The Redshift is a VERY weak effect, and was detected some 20 years AFTER Einstein's
great theory..... Even E himself gave 'space' some specific deformation properties
(but do keep calling it Vacuum, please... since it is PURE : dissipation is
for farmers and engineers, not for real scientists ;-)

Re: What is a Crackpot? - On dissident / alternative 'common sense' model of the Cosmos.

Was There a Big Bang? . . I Honestly Don't Know . . (2002, 3rd ed.) by Richard Carrier

Hubble Red Shift by Photon Decay: a sensible explanation - by Michael Lewis

- Universal Kinetic Energy Field . . by Dan K. McCoin
- UniKEF: Ether links

Tribute to Jean-Pierre Vigier and the Causal Model of Quantum Mechanics
. . . Book review: on electron = 'particle' guided by its corresp. wave (in 'ether' medium). Vigier writes: . . . "In my opinion the most important development to be expected in the near future concerning the foundations of quantum physics is a revival, in modern covariant form, of the ether concept of the founding fathers of the theory of light . . . [I]t now appears that the vacuum is a real physical medium which presents some surprising properties". (p 272)

Red Shift and Distances. . . by Mike and Sue Lawrence. . . Chapter 10 : Tired Light

- History of Einstein's Relativity- vs. Lorentz' Aether- Theory

> - "The Einstein Hoax" - by H.E.Retic (1997)
> If you have read the material at above Website, and have an objective
> criticism, you will receive a courteous reply. And, if your criticism
> cannot be refuted, your input will either be incorporated to correct
> the text or, if the criticism is of sufficient import, the text will
> be withdrawn. So far, the material has received two types of response.
> One type (60%) is extremely favorable, the other type (I presume from
> the "idiot savant" community) is insulting but has yet to provide an
> objective criticism on any point. One thing can be stated with
> certainty, the World is entitled to a higher quality of workmanship
> from those to whom it has granted World Class status.
> E-mail:- retic@viconet.com

NB:  I'll have a closer look.

As an interested "crank" (someone who's not averse to thinking for
himself, despite the dangers of it in an established thinking frame;-)
have look at http://www.iae.nl/users/benschop/ether.htm :

"Red-shift of fotons: Lossy Light propagtion in Ether, after all?"

Which might just attain a slightly more established gloss if indeed
the Maxwell equations could be extended to include a loss term...
See  http://members.chello.nl/~n.benschop   (by Michael Lewis)

Does'nt every process in Nature dissipate -- a "perpetuum mobile"
being rather utopean. *Why* should light propagation through
billions of lightyears be any different ?-)
Ciao, Nico Benschop.             | AHA: One is Always Halfway Anyway
http://www.iae.nl/users/benschop | Institute of Advanced Engineering

zyx.org/BIGBANG - A balanced critique on 'religious zeal' in present-day science.

prof. Allen Rothwarf (1935 - 1998) incl.: "An Aether model of the Universe".

. . Some life wisdom one-liners . . by Andy Rooney.

. . Pictures of the Evoluon (Philips, Eindhoven, NL) . . homepage Kees Stravers

. . Pictures of Geldrop (N-Brabant, NL) . . About Geldrop - (Dutch, with foto's)

electron-photon.pdf - Is the electron a photon with toroidal topology?
. . Martin van der Mark, John Williamson (.pdf, 270k, 25 pgs)

"The Ring of Hyperintegers" . . (Patrick Reany) - On p-adics and 'infinite residues', Clifford Algebra, &c.

Controversy : - Tradition vs. modern, continuous vs. discrete, &c

Filosofy : - Intuition and imagination in Math.

On tough arithmetic problems - Why they are so hard, and what to do about it.

Right function notation x(fg) vs. g(f(x)) - Attributed (anecdotal) to AntiZeus , Athens, 450 BC

There are too many B.A.D. mathematicians
- by Melvin Henriksen (The Mathematical Intelligencer, V.15 - 1993)
[... BAD = Bigoted and Destructive ... Math-journal editors ] "They have little difficulty concluding that if they see no application of an area to what interests them, it should be pushed out of the "important" general journals. This is not as easily done with journals published by the A.M.S., but when it is, the mechanism used is to take control of the editorial board and/or the position of managing editor while making sure that no member is a specialist in an "inferior" field. Whereas the journal is still advertised as one that publishes articles in all areas of mathematics, anyone who submits a paper in certain areas is told that no member of the editorial board has the expertise to evaluate it, or that the paper is "unduly technical" and should be submitted to a specialized journal. Since these boards are almost always self-perpetuating, once a field is deemed unfit for the journal, it stays that way.

" Something Rotten at the Core of Science? " . . by David F. Horrobin
The Supreme Court questioned the authority of peer review.

Many scientists and lawyers are unhappy about the admission by the top legal
authority in the United States that peer review might in some circumstances
be flawed [1]. David Goodstein, writing in the Guide to the Federal Rules of
Evidence - one of whose functions is to interpret the judgement in the case of
Daubert - states that "Peer review is one of the sacred pillars of the scientific
edifice" [2]. In public, at least, almost all scientists would agree.
Those who disagree are almost always dismissed in pejorative terms such as
"maverick," "failure," and "driven by bitterness."

Peer review is central to the organization of modern science. The peer-review
process for submitted manuscripts is a crucial determinant of what sees the light
of day in a particular journal. Fortunately, it is less effective in blocking
publication completely; there are so many journals that most even modestly competent
studies will be published provided that the authors are determined enough.
The publication might not be in a prestigious journal, but at least it will get
into print. However, peer review is also the process that controls access to funding,
and here the situation becomes much more serious. There might often be only two or
three realistic sources of funding for a project, and the networks of reviewers for
these sources are often interacting and interlocking. Failure to pass the peer-review
process might well mean that a project is never funded. Science bases its presumed
authority in the world on the reliability and objectivity of the evidence that is
produced. If the pronouncements of science are to be greeted with public confidence
- and there is plenty of evidence to suggest that such confidence is low and eroding
- it should be able to demonstrate that peer review, "one of the sacred pillars of
the scientific edifice," is a process that has been validated objectively as a
reliable process for putting a stamp of approval on work that has been done.
Peer review should also have been validated as a reliable method for making
appropriate choices as to what work should be done. Yet when one looks for that
evidence it is simply not there.

Subject:  Re: This unintelligible Newsgroup....   (sci.math - 22 Apr 2002)
   From:  Nico Benschop 
    Org:  Digital Research : Finite Associative Networks
Kevin Buhr wrote:
> "Math Enthusiast"  writes:
> >
> > If I may ask, what is the grade/degree of education of the
> > majority of people in this group?
> [..good advice..]
> There are plenty of texts, though, that *will* teach you the basics
> of these fields, and many of them will be accessible to someone
> without a calculus background. Set theory and abstract algebra are
> endlessly fascinating, and many undergraduate texts won't assume
> anything more than high-school math.  Undergraduate point-set
> topology doesn't really require calculus either (and some texts
> won't even assume you know what a set is), though it's helpful to
> have some calculus, linear algebra, and analysis as a source of
> concrete examples for all the abstract concepts.
> [...] -- Kevin Buhr 

And also:
   not just *what* you know, but *how to apply* it is important!
And next to studying the basic stuff, try to read the history of
how and why it came about: read the original papers, like George
Boole "The Laws of Thought" (1854) where you see his motivation
(as son of a preacher, interested to check the God-existence 'proofs'
of Spinoza and Clarke - his model of the Aristotelean logic they used
is a simple form of arithmetic ('idempotent' : x^2 = x --> x=0 or x=1)
which much later became the basis of set theory, as fundament of math.
His book is available from Dover publications, which publish many
original books in science & math.

Or (I'm doing research in synthesis of logic circuits & State Machines)
read Claude Shannon's original paper (AIEE 1938) as MSc student in MIT,
where he proposes to use Boole's (binary) algebra, then 90 years old
(!), to model the behaviour of combinational logic (relay-) circuits.
A marvelous book, qua motivation & insight (for math up to 1945;-)
is E.T.Bell: "The Development of Mathematics".

In general, go to the source, study the history of _how and why_,
prefer multi-focus over narrow single-focus (although that takes
more time, yet worth it;-) and you'll be much better motivated
to contribute and work constructively. Success.
The clue is 'zelf-denkzaamheid' (think for yourself)
       and give your intuition a chance:
"It is a miracle that curiosity survived formal education"- A.Einstein

-- NB - http://home.iae.nl/users/benschop/search.htm

Discussions . . (on newsgroup sci.math 2001 / 2002) :

28oct99 - Re: Solving FLT - By reviving the carries (multiple of modulus p^k) beyond mod p^k.

21aug00 - Re: I am disappointed in God - NB --> P.Lounesto: Groups (symmetries) are not All - take Semigroups!

12jan99 - Re: JSH: What I do. - On FLT via residues mod p^2 (odd prime p), and the EDS property.

6.oct99 - Re: Does the set of all sets exist? - A generative view of infinite sets: Peano's N (1 gen), Cantor's 2^N (2 gen)

17'nov02 - Re: Maximal commuting families of functions - Commuting functions : context = commut've semigroups.

17nov02 - Re: Dijkstra's Quotes Considered Harmful - Not if you know the context: 'structured programming'.

3jun99 - Re: what is intuition? - On "intuition" as a form of analogy, or 'isomorphism with experience'.

6nov02 - Re: Cantor and Goldbach - Cantors 'uncountable |B*| for |B|>1 has little to do with Goldbach

21sep02 - Re: What is so special about Fermat, save the well-known facts, surely. - Anti-closure of x^p(+), etc.

27may98 - Re: Tired light. - "All we know gets 'tired'." --> Why are photons the only exception? (re Occams razor)

26may98 - Tired light - sci.physics thread of 75 items on: Can a photon lose energy (by Planck E = h.nu --> freq. nu decreases)

6sep02 - Re: Einstein's worldwide fame 83 years - Red shift by Photon decay (by Michael Lewis: Guest on my homepg chello.nl)

15"aug02 - Re: Kill file for ng? - Stout fellow! Full marks to you. - For our Dutch readers: "Stoute jongen!";-)

15'aug02 - Re: Kill file for ng? - Some critics focus on the smallest imperfections, ignoring everything else.

15aug02 - Re: Is that all there is? - Maslow's hammer theory: why math is so useful...

13'aug02 - Re: Is that all there is? - Teleology: the future pulls, vs. more common: the past pushes (deterministic)

13aug02 - Re: Is that all there is? - Behavioural modes (as at birth): Greed + Ignorance (about the consequences)

2aug02 - Re: Could the Goldbach conjecture be undecidable? Decidable -> [T or F], Undec'le -> [~T and ~F] : irrelevant

1'aug02 - Re: The best 20th Cent. mathematician (vote here) - v.Neumann: 'wide-band' math approach, + critique (E.T.Bell)

1aug02 - Re: The best 20th Cent. mathematician (vote here) - Bourbaki's - and French - first ;-)

31'july02 - Re: Is there anything left yet to prove - The main problem is: formulating the right/important questions...

31july02 - Re: JSH Science, math and fashion - don't you expect trouble with that cripple English language ?

30july02 - Re: Euclid's axioms, where did they come? - Fed-up to remember all thms, he decided to take a generative view...

30'july02 - Re: base 10 - A weak reason for hex-code: pi/4 = 1 - 2 x \sum 1/(16n^2 -1), for n=1..inf

29"july02 - Re: base 10 - First base 60 (Sumerians) then base 12, and now base ten, and base 2 (CS)

29'july02 - : Re: Could the Goldbach conjecture be undecidable? - No, there is no counterexample (proof at arXiv)

29july02 - Re: The best 20th Cent. mathematician (vote here) - "NB is a work of fiction! " - Nota Bene: N. Bourbaki (math) --> Reals = Fiction ! indeed

27july02 - Re: The best 20th Cent. mathematician (vote here) - Claude Shannon (Boolean Alg. for Digital Ccts, + Info-theory)

26july02 - Re: When mathematics and belief collide - 'Sawtooth' evolutionary Law: Extremes increase, and then collapse (etc)

18'july02 - Re: Natural Numbers are flipped-over Reals - Each integer is finite =/= 10-adic residue (mod 10^n, n-->oo)

18july02 - Re: JSH: What a waste. - Object Oriented Programming & OO-Math (and Louis de Funes' soup;-)

16july02 - Re: Coolest thing in math? - Krishna's advice to Arjuna (qua motivation & result).

3dec98 - Re: -- Fermat's anti-closure n^p(+) as generator - BOOA constructor : Balanced Object-Oriented Algebra

11'jul02 - Re: Memorization comes before understanding - Quotes Feynman: 't should be simple to explain...

11july02 - Re: What was FLT? - On Fermat's marginal note: did he have a proof? Or just a (partial) clue...

10july02 - Re: Memorization comes before understanding - 'memory'=filterbank. "The Wholeness of Nature" (Henri Bortoft)

4july02 - Re: Question about Cantor's diagonal proof - Uncountable nr. of strings |A*| over alphabet A iff |A|>1

3july02 - Re: Representation theory - of groups (and other associative algebra's, like semigroups by matrices;-)

2'july02 - Re: logical reasoning for "proof by contradiction" - Boolean truth table: A --> B == ~B --> ~A

2july02 - Re: Question about normality and number bases - Erdos/Graham conj. 1980: 2^n base 3 has digit 2, except n=2, 8.

27'jun02 - Symmetry in binary code : Reals on [0,1] .vs. naturals N > 0

27jun02 - Cantor & 'vanishing evidence' = Suspect finite intuition (one of w= Omega reals missing)

26"jun02 - Int'l Conf. "Galileo Back in Italy - II" - Bologna, May 1999 (contra 'Big-Bang hypothesis')

26'jun02 - Re: groups.yahoo / useyourbrain/message/34 - Big-Bang doubts: a new movement (refs)

26jun02 - Re: Interesting review of A New Kind of Science - Chaos Theory .vs. Digital Network Th = FSM's = (Finite) Semigroups

24jun02 - Re: Do most mathematians denounce ANKOS? - Matrices : Linear Algebra / Semigroups : Cell Automata : Associative Alg : Function Compos'n

22jun02 - Re: Interesting review of A New Kind of Science - Reviews S.Wolfram new book (1200 pgs) on cellular automata vs. physics.

19jun02 - Re: Kadanoff on A New Kind of Science - Cell Automata = FSM network = Associative Algebra = Semigroups

18jun02 - Re: Binary Maths.. . . . n = 2^k -1 and n^2 both have k ones (in binary code).

2apr02 - Re: Semigroups of order n - FSM synthesis : my motivation for studying finite semigroups.

1'mar99 - Re: Why the attack on Cantor ? - The 'set' of Reals : Potential vs. Completed infinity

1mar99 - Re: Why the attack on Cantor's Theory? - Set theory is since Boole (1854), not Cantor (1880+).

27feb99 - Re: Why the attack on Cantor's Theory? - Cantor's uncountable reals are just the strings over any binary alphabet.

6mar99 - Re: Why the attack on Cantor's Theory? - Applied math & physics vs. pure math: a matter of taste.

5jun02 - Re: What is an "algorithm"? - Only countably many of the uncountable reals can be specified !

3june02 - Re: The Economist reviews Wolfram - Cellular automata --> Why not semigroups (assoc func netw)?

11jun02 - Re: Einstein's worldwide fame 83 years - Hubble-satellite telescope looks deep space: full mix old/new!

30may02 - Re: Einstein's worldwide fame 83 years - Ref to Steve Rado's work.

29'may02 - Re: Einstein's worldwide fame 83 years - 3 more points to consider . . .

29may02 - Re: Einstein's worldwide fame 83 years - 5 points in favor of Light & photon dissipation (redshift)
- Dissipative light propagation (in 'ether') + photon decay.

28'may02 - Re: Collatz Multiple Choice Placement Exam - Binary pattern 3(2^k -1) = 3(1s1) = 10s01, s = 1_string

28may02 - Re: Z x Z_n - Endo(S) of semigroup S = A* as its 'generalized symmetries' = 'structure'.

7may02 - Re: some people actually think math is more important than engineering - Discrete Math and EE (FSM Synth)

6may02 - Re: are the Natural Numbers finite-integers or are they p-adics - Residues vs. Naturals; Doubt on Wiles' FLT proof by L-series

3may02 - Re: Moral Superiority & illlusions - Re WW2, scientists, weapons research and human behaviour

2'may02 - Re: Goldbach's Conjecture proved; p-adic proof thereof - Some history: non-discussion on NMBRTHRY list.

2may02 - Re: Goldbach's Conjecture proved; p-adic proof thereof - Nonsense: p-adics =/= naturals.

1'may02 - Re: more NFB garbage - Pertti Lounesto ignores "revival the carry" (complementary to residues)

1may02 - Re: more NFB garbage - Says Robin Chapman ;-)

29apr02 - Re: Can a^p + b^p == c^p mod p^k (odd prime p, 0< a,b,c< p) - Start at FST* (core mod p^2) to prove FLT: carries make the difference.

24'apr02 - Re: How sure are theorems? (In reference to Pertti Lounesto) - On friend and foe, in sci.math

23!apr02 - The Hypotenuse Fairy - ASCII art fairy.

23"apr02 - Re: Case against mathematicians: Astronomy analogy - Big-Bang, Redshift & Lossy light propagation ('ether')

23'apr02 - Re: Meaning of eigenvalues/vectors? - Own frequencies of a dynamic system

23apr02 - Can a^p + b^p =/= c^p mod p^4 (odd prime p, 0< a,b,c< p)? - Basis of FLT (case-1): carries make the difference

22'apr02 - Re: This unintelligible Newsgroup.... - What education do sci.math-ers have ?

22apr02 - Re: How sure are theorems? - Pertti Lounesto: never sure, one can only falsify.

17apr02 - Re: Millionaire Mathematics - Natural Binary (Cantor) table: permuting rows yields diagonals all subsets of N.

16apr02 - Re: Millionaire Mathematics - Continuum Hypothesis, and exponential growthrate of a set.

15'apr02 - Re: Fermat 's Last Theorem" - Can (x+y)^p = x^p + y^p (mod p^2) extend to integers X=x, Y=y mod p^2 ?

15apr02 - Re: Millionaire Mathematics - Anything that grows exponentially (like 2^n) is uncountable (for n-->inf)

09'apr02 - Re: sci.math a teaching tool? - On 0.999... = 1.0 and '...' as 'limit' concept.

09apr02 - Why did Boole's property-calculus become set-theory? - Especially infinite sets require a generative specification!

08"apr02 - Re: How to see the complex roots of a cubic polynomial - Not what you know, but its use counts.

08'apr02 - Re: Is zero an even integer? - 'Morons' on sci.math, and nitpickers : Mainline .vs. Detail

08apr02 - Re: Mysticism of 666 - Linear .vs. Quadratic approach to life.

02apr02 - Re: Semigroups of order n - some personal motivations and history.

01apr02 - Re: Semigroups of order n - NB: 'Chinese' carry thm - the complement of "Chinese remainder thm"

28mar02 - Re: Question on Godel's incompleteness theorem - Continuum Hypothesis: on string sets A* and B* (|A|=1, |B|=2)

27mar02 - Re: Origins of transfinite numbers - Old Greek and Indian "Quint Essence" (the 5 QE Basic elements of seq.logic)

25mar02 - Re: Who will get the Fields medal in August ? (which Chinese?-) . . . the remaining Chinese Carry Thm.

14mar02 - Re: Fermat's Last Theorem - NB: mod p^{3k+1} - Breaking the Hensel lift by quadratic analysis (over mod p^k)

13mar02' - Re: Value Of A Sci.Math Post Proportional To Replies? - Natural law: Quantity x Quality = Constant.

13mar02 - Re: Distribution of primes among values of polynomials - There's someting quadratic about the primes ...

12mar02 - Re: Inverse Goldbach Conjecture - counterexample - on each Truth having its context : Math (mod axioms) [2]

11mar02 - Re: JSH: Well, it's my stage. - A bit of history can't do harm (Fermat: residues mod p, Gauss, carry)

08mar02' - Re: Countability - countable set N, and uncountable sets (B_i)* with |B_i|= i>1 : 2^Z , Z! , Z^Z .

08mar02 - Re: No infinite lists: a proof - well, not quite . . . it all depends.

07mar02' - NB: 'for all n' versus 'independent of n' - Sets vs. Properties

07mar02 - Re: Discrete, continuous. It's all the same - Nearly but almost ;-) On countable vs. uncountable.

04mar02 - Re: JSH: FLT Proof is still a test. - How can Wiles' L-series residue method yield integer FLT result?

"NB: "Furthermore, regarding one of its corollaries: the truth of the FLT conjecture on the sum
of to integer p-th powers (prime p>2) not being a p-th power (Frey's impetus of 1985 for Wiles
to start digging in): I *do* have a lingering doubt, or rather a methodical question, regarding the
*residue_method* ('local') of proof that Wiles used, to derive a result such as FLT which holds
for *integers* ('global'), at least as I understand it from a simple description by Simon Singh
in his book 'Enigma...'
. . I voiced this concern as a question here in this NG several times: my problem is equivalent
to the argument used for the impossibility of deriving a global result (on integers, such as the
FLT inequality) from a local method, viz. using only residues (re: Hensel's expansion lemma,
in his p-adics number theory)

01mar02 - Re: Thanks - NB: Endo tower over Z_m(+) - On hiearchy (+) --> (.) --> (^) --> ?? (mod m)

22feb02 - Re: Goldbach's conjecture - Why is it so hard to prove ? [2]: and agreed symbolism.

21feb02 - Re: Hey, what about base 1? - Cantor binary k x k table: Row permut's link powerset 2^k to sym.group S_k

19feb02 - Re: unify all branches in math - and some math history. . .

15'feb02 - Re: Problem with Cantor's diagonal argument (finite case) - Cantor Diagonal generates powerset 2^k by permutations

15feb02 - - Re: Problem with Cantor's diagonal argument (re finite case) A* = all strings over A : Uncountable iff |A| > 1.

14feb02 - Re: Problem with Cantor's diagonal argument - Cantor: 'uncountable' for engineers, not reals but just strings...

13feb02 - Re: [NFB] Benschopwatch - Primitve roots of 1 mod p^k, divisors r | (p +/-1), and idempotents e^2==e mod p+/-1

09feb02 - Re: No Elementary proof of FLT in sight - Maybe via FST extension, and cubic roots of unity(mod p^k)

08feb02' - Re: A polynomial considered." - After Wiles' proof ('95), is an elementary direct proof of FLT still interesting?

08feb02 - Re: On Mathematics and commonsense - . . . and the infinite (not really difficult to imagine;-)

06feb02" - Re: Mathematics is made for the adventurous - Realist vs. Escapist, Common-sense vs. no-sense

06feb02' - Re: Against angels and the Fregean-Cantorian Theory of Number - Why Peano's countable N ~ 2N : both have ONE generator (+1)* ~ (+2)*

06feb02 - Re: Element is its own multiplicative inverse? - Euler: if a problem is *really* hard, generalize it! (to keep it simple)

31jan02 - Re: What is isomorphism? - Iso-morph = same-form: thus same structure, indepent of various representations.

29jan02' - Re: Question on FLT - In: a^p+b^p=c^p (FLT) take exponent p as base for residue cond'n (mod p^k)?

29jan02 - Re: cranks vs. psychotics - Crank vs. 'expert' in a new field? (good intuition on what's missing) [2]

28jan02' - Re: Infinite integres? - Symmetry xxxxxx1.1xxxxxx (One is Always Halfway Anyway: AHA) p-adics vs. reals [0,1)

28jan02 - Re: Looking for a wildcard. Prefer direct proof FLT_inequality over Wiles' "route over the North pole".

25jan02 - Re: Definition of a group - On reversible processes, and associativity nec. for 'iteration'.

23jan02 - Re: What Ben Schopman does get about Number Theory -
. . . . . . . . . . On FLT and Clifford Algebra of : x^n+y^n=(xe1+ye2)^n being inf. dimensional for n>2.

22jan02 - Re: What Benschopman does get about Number Theory : a^p + b^p =/= (p^k-1)^p mod p^{mk+1} for m=3.

21jan02 - Re: What I dont get about Number Theory - Number representation in base p useful for p-th powers, and FLT.

18jan02 - Re: maths as empiric activity - On nitpicking ;-) . . .

17jan02' - Fermat, Waring, Goldbach - Solve hard additive arithmetic problems via semigroups Z(.) mod m_k, and the 'carry'.

17jan02 == Symmetry is nice , but not without a pinch of Asymmetry! (on dissipation)

14nov01 - Re: On Hawking's method of thinking - On intuition in maths

07oct01 - Reasons to keep an open mind - An open mind is a joy forever. . [2] . . 01oct01

01oct01 - Re: Why mathematicians had to be liars - The Hensel lift *can* be broken, for an FLT mod p^k equivalence.

26sep01 - Re: Should we get rid of infinity and recursion? - On Boole's "Laws of Thought" (1854), and Spinoza

18sep01 - Re: The thirst for Challenge - Fermat (1640), and the Cubic roots of 1 mod p^k

14sep01 - Re: At my signal - Give them h.L! - On breaking the Hensel lift : in special case a^3 == 1 mod p^k

10sep01 - Re: why do you like math? - 'Proof' is based on transitive closure.... of axioms: no 'news'
Re Robin Chapman....
'Proof' is based on transitive closure

21jan01 == Re: miles, yards, feet, acres - Tradition vs. Modern & efficient.

19may00 == Re: Dear Nico B. (Not Benschop) & 5 BSM - 'BOOA constructor' : Balanced Object Oriented Algebra

08oct99 == Re: Naturals N={1}* vs unNaturals 2^N={0,1}* (Peano/Cantor) - On Cantor's diagonal :
. . . . . . . . (non-arithmetic) strings in A* = uncountable iff |A|>1

13nov98 - Re: What's so special about 10^11 ? - Special meaning #42 (I-Ching): "Balanced Growth" = Essence of Life

06nov98 == Re: Primitive Root Question - and Fermat's Small Theorem n^p == n mod p (prime p, all n)

(c) N.F.Benschop (Amspade Research) dec'01