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Homepage2 on Astro-physics (redshift, foton-decay, ether): Truth depends on Axioms ::: Axiom = Self-evident = a matter of Opinion = Belief. . . . Ergo : Truth is Belief . . . (thus subjective, after all;-) On New Ideas in Science (and resistence to them), by Thomas Gold (1989). Paul Marmet: "...explanations which are compatible with Newtonian and semi-classical physics. We apply the principle of causality and avoid models requiring a probabilistic existence of matter and non-locality: with a stable (non-expanding) Universe, different from modern physics." Hubble redshift as non-Doppler effect: Photon decay ('tired light') in space by Inelastic collision of photons with Molecular Hydrogen. - Some of my papers on Arxiv (at front.math.ucdavis.edu) "Commonsense-in-Science Manifesto" ===================================== 1. . . A wave phenomenon requires a medium, So : . . . . a wave cannot propagate in vacuüm. 2 . . . . EM waves (light) propagate in space, So . . Space is not vacuüm (say 'ether' medium). 3. . . Perpetuüm mobile (lossfree) processes do not exist, So : . . . . . Wave propagation (light travel) is not lossless And if linear loss : redshift proportional to distance travelled. 4. . . Speed of wave propagation depends on medium density, And : . . . Density varies with Gravity field around heavy body. [!] So : . . . Interstellar space is filled with inhomogeneous medium, So . . . Lightspeed is not constant, and light bends around a star. Ref: - Redshift by Photon Decay 5. . . With matter (electron) as closed wave (closed photon) [*]: It makes sense that rotating matter (Earth) drags ether along. So: . . This adherence prevents ether-motion measured along Earth surface. (Michelson_Morley's null-result is no surprise, but their 'conclusion' (no ether) _is_ surprising, based on insufficient grounds: neglecting the alternative of ether-adherence to Earth) 6. [!] . . If ether density around heavy body decreases as 1/r And : . . . Gravity is defined as its gradient Then: . . . Gravity decreases as -1/(r^2) ---> Newton's gravity Law [!] 7. The constancy of lightspeed c holds for all frequencies with accuracy 10^{-21}. "The speed of light is independent of frequency within a factor of 6x10-21" (B.Schaefer) . . This points to the existence of a medium that determines speed c, since photons . . of widely different frequencies could in vacuüm travel at various speeds as . . determined at their generation, and maintain those various speeds forever. So: Einsteins axiom of constant speed c induces a medium for light propagation. [*] Is the electron a photon with toroidal topology? [*] by Martin van der Mark, J.G. Williamson (.pdf - 1997) 'All is EM field' - including elementary 'particles' ( donut structure of electron) Quasars, Big-Bang & Cosmological constant by dr. Paul Marmet From: IEEE Transactions on Plasma Science, V20, N6, pp958-964, 1992.

"Big Bang, Black Holes, and Common Sense" by David Pratt

Redshift History by R. Gray and J. Dunning-Davies (Hull Univ UK)

"A new non-Doppler Redshift" by dr. Paul Marmet.

On Fermat's marginal note, a suggestion N.F.Benschop (NMC-33, Apr.1998)

My father's diary on his Birma Railroad experience 1942-'45 (in Dutch).
Buy hardcover copy (Lulu.com) 75 pgs or Softcover.

Curiosity and Search . . . . . "An open mind is a joy forever "

. Inertia . . . . . . . . . . . . . . . . " Climbing Mount Prejudice "

. . Generalize . . . . . . . . "If a problem is too hard, generalize it "

. . . Simplify . . . . . " We have to fight uphill to rediscover the obvious "

. . . . Coincidence . . . . . . . . . " Life is fighting entropy "

My CV . . . Work . . . Play . . . ff . . finite fun . . (reflections in the finite)*

. . . . . . Intuition : . . Even if you don't see it, you still can smell it !

. . . . . . Bamboe . . . Chinese brush painting

Remembering Claude Shannon - - - (NB: 28-july-2002)

DigNetTh-bk - My new BOOK - preface.htm published by Springer Verlag (May 2009): Associative Digital Network Theory -- an Associative Algebra Approach to Logic, Arithmetic and State Machines See also Wikibooks.org . . and Wikipedia.org If stuck at Closure: use the Carry . . . Residue-and-Carry method to prove FLT and Goldbach Symmetric and Planar Logic Synthesis . . . Each boolean function BF_n for n<5 inputs is planar

Fermat, Waring, Goldbach -:- view Arithmetic as Function composition (semigroups) :
. . . Additive Number Theory : hard problems, solved via semigroups Z(.) mod m_k , and . . .

"Additive structure of the Group of Units mod p^k ,
with Core and Carry concepts for extension to Integers"
- - - Triplet structure, and direct FLT proof (16 pgs), published Nov.2005 in:
AMUC - Acta Mathematica Univ. Bratislava

Péano- and Cantor- sets and their generation: sequential dimension

Child's arithmetic ( = exponential ;-( . . . Stable economic growth of 3 % per year,
. . . then *(1.03)^n yields economy *10 ... *100 ... *1000 after n = 78 ... 156 ... 234 years !

NB: . . . One Generation = 26 yrs ==> Your grandchildren live 10 x dense than you . . .

Humor / Relegion
"If God created us in his own image, we have more than reciprocated." — Voltaire (1694-1778).

and at : de.arXiv.org (old versions: before dec-2001) Redshift by Photon Decay by M.Lewis

Among others :
- Finite Semigroups of Constant Rank, and the five Basic State Machine types.
- On Log-arithmetic, Fermat's Small Theorem, and the powers of 3 (mod 2^k).
- Extending Fermat's Small Thm to r^{p-1} mod p^3, for divisors r | p +/- 1.

My cup-a-soup :

[-4] Internal State of Computer Science (ICS73.pdf)
. . . . . . . My original motivation for Digital Network Theory <=> Finite Semigroups
[-3] Re: unify all branches in math - and some math history (sci.math 19feb02)
[-2] Re: Problem with Cantor's diagonal argument
. . . Cantor's Diagonals generate powerset 2^N by permutations of w x w table rows (sci.math 15feb02)
[-1] Fermat's Anti-Closure n^p (+) as Generator (.htm) . . . . . . . . . . . . news:sci.math - 28nov98
[0] Function composition of symmetries -n, 1/n for FLT (.htm) . . . . . . . . . . . . sci.math - apr98
[1] Triplets and Symmetries of Arithmetic mod p^k (.pdf) . . . Semigroups and Arithmetic (Fermat Last Theorem FLT)
[2] On the structure of Constant-Rank State Machines (.pdf) . . Sgrps and Sequential Logic Synthesis
[3] Fermat and the Cubic roots of 1 mod p^k (.html) . . . . . . . .Breaking the Hensel lift . (1 page clue)
[4] On the triplet structure of arithmetic mod p^k,....
[5] On Fermats' marginal note: a suggestion (.pdf) . . . Cubic roots: a^3=1 mod p^k (marg-abs.htm)
. . . . Quotes E.T.Bell (.htm) : . . . . . . . . . . . . On abstraction, specialisation and divergence.
[6] On powersums representing residues mod p^k(.pdf) . . . . " Waring-for-residues " (nw-abstr.htm)
. . . . . -------- Each residue mod p^k is the sum of at most four p-th power residues --------
[7] Arithmetic with squarefree modulus, its lattice of groups,
. . . a primesieve, and Goldbach's conjecture(.pdf) . . . Goldbach proof (old version 2002):
[8] -- Fermat, Waring, Goldbach -- (.htm) . . . . . . . . . . . . . . . . . . via Semigroups Z(.) mod m_k
[9] One more crank (.htm) sci.math - may98 . . . . . . . Hasse-Minkowski thm and Selmer's group
[10] How diagonal is Cantor's diagonal ? (.htm) . . . A Bootstrap process generating the reals.
. . . . . . . . . . . sci.math 5jun98 . . 6jun98
[11] Semigroups and FLT (.htm) . . Z(.,+) mod m . . . . . . Function composition linking (+) and (^)
[12] New Math (base p) applied to FLT (.htm) . . . . . . . . (Fermat?) computing a^3=1 mod 7^2.
[13] Re: Orthogonality (.htm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sci.math - 3nov98
[14] Re: Primitive roots of Unity (.htm) . . . . . . . . . . . . . . . . . . . . . . . . sci.math - 3nov98
[15] -- Stumbling over Aladin's lamp .. sci.math 13nov98 . . . . . . . . . . sci.math 10nov98
[15'] A simple direct FLT proof after all ? (despite the Hensel lift) . . . . sci.math - 1aug00
[16] Fermat's anti-closure n^p(+) as generator / BOOA constructor . . . sci.math - 4dec98
[17] Re: Finite versus Infinite (a matter of taste) . . . . . . . . . . . . . . . . . . sci.math - 16feb99
[18] Re: Why the attack on Cantor's Theory? . . from Cardinals to Types . . . sci.math 27feb99
[19] Easter primes do not exist: 2^p != 2 mod p^3 (prime p) sci.math 12apr98, and :
[19b] Divisors r of p-1 (resp. p+1) have distinct r^{p-1} mod p^3 . . Carry-extend Fermat's Small Thm. (.pdf)
[20] The role of prejudice in the exact sciences . . . a non-discussion on nmbrthry.list (14mar99)
[21] My +/- 3*2* Binary Multiplier . . . . US patent 59.23.888 (13 july 1999):
. . . 3 is semi-primitive root of 1 mod 2^k, Log-arithmetic (dual base 2,3) .. Intro(.dvi) , (.pdf)
[22] Sequential dimension of finite and infinite closures: N vs 2^N . . . sci.math 7oct99
[23] ISM : Integer State Machines . . . . . . M(Z,A) state set Z, inputs A={+1, -1,swap(2)}
[24] Discovering the Triplets in Z(.) mod p^k . . (a+1)b=(b+1)c=(c+1)a = -1, abc = 1 (mod p^k)
[25] On FSM-decomposition and Semigroups (= sequential closure): part I . . . . . part II
[26] On Reals (as un-real concept) : . . One can specify only countably many reals anyway!

__ L S D : Less simplistic directions [*.html] : . . . a wider view - beyond Logic and Arithmetic :

[a] . Cubic roots of 1 . . . . . . . . . . . . . . . . . Triplets /3/ and Symmetry /2/ of FLT mod p^k roots
[b] . Residue and Carry . . . . . . . . . . . . . . . . . for Closure and Generation ( confirm and explore)
[c] . A day with Fermat in Toulouse . . . . . . Did he find the cubic root solution of FLT mod 7^2 ?
[d] . I-Ching (symbol 59 and text) . . . . . . The Solution . (of a stuck-at situation: whip-up water)
[e] . Bibliotheca Philosophica Hermetica (Amsterdam)
. . . " Newton wrote more on alchemy than on any other subject" (we lost something? Why vs. How)
[f] . I-Ching : 8 basic icons , Yi-Jing info . . Chinese philosophy: Balanced Change, Cyclic Time
[g] . On Dynamic Balance and Bootstrap . . . On a balanced psychology (Maslow and Spangler)
[h] . Weighing Cantor's Evidence . . . . . . . . . . . . . . . On math, EE-practice and real infinity
[i] . Red-shift of fotons by decay: Ether after all? . . . . . . . . . . On lossy light propagation.
[j] . Strange dominance of math in world model . . . . . . . . . Maslow's "hammer and nails"
[k] . Re: Pi is no piece of Pie . . . . . . . . . . . . . Finite atomism vs Infinite partition (sci.math)
[l] . On controversies . . . . . . . . Finite/Infinite, Discrete/Continuous, Tradition_/Modern_units
[m] . Something Rotten . . . . at the Core of Science? (Trends in Pharmacological Sciences)
[n] . On Digital physics (Fredkin) . . . and Cellular automata (Steven Wolfram)
[o] Bush' Mission to Mars (TIME 23feb04): " Sending humans to Mars sounds
. . . fantastic, like something to strive for. But the problem is that the mission will
. . . just give us another world to mess up. Untill we have a complete change of
. . . attitude and behaviour, let's stay away from other planets!" (L.Fourie, S-Africa)
---- "Why should we spend vast amounts of money to reach Mars when the chance is very
---- high that the mission does not provide anything to improve our lot here on Earth?
---- Why not allocate those billions for "home improvement"? How about curing cancer,
---- aids and other diseases; cleaning our water, air and soil; feeding hungry nations.
---- [NB: Or making the Sahara fertile. A few hundred billion dollars/euros can go a long way!-]
---- Why confront the hazards of outer space when we should be fighting homelessness,
---- poverty and unemployment on Earth? (C.Brunish, Oregan, USA)

[V] . Campaign : for the Cubic roots of Unity, breaking Hensel's lift (re: FLT), and
to promote finite transformation Semigroups and functions for Logic, Arithmetic, FSM's [2].
--- If you like this direct approach [3] to FLT (case_1): tell a friend (or even me ;-)
--- And if you do not like it : please tell me why;
. . . certainly if you can disprove the EDS argument [3] for the cubic root solution.

. . . To view/print *.dvi files (PC/Windows): download latex2e/MiKTeX