Diary - September 2014
John Baez
September 1, 2014
Greg Egan has done it again! This is an infinite cubic lattice of
rotating gears in 3-dimensional space... seen by someone who is
falling through it and also rotating!
It's a bit bewildering. One reason is that after you turn 180
degrees, the view looks exactly the same.
He's been developing techniques for studying 'higher-dimensional
gears', like 3d ball bearings that turn while touching each other,
arranged on the surface of a hypersphere in 4d space:
The hard part is figuring out how the bearings can turn without
slipping against each other. This involves solving large systems of
linear equations.
His real tour de force was to get a setup with a ball bearing at each
of the 600 vertices and 1200 edge-centres of a 4-dimensional shape
called the '120-cell'. Getting this to work required solving
thousands of linear equations in thousands of variables — too
hard without bringing in some heavy-duty math. Check out his
website for more about that! (You can enjoy the pictures without
understanding the math.)
He wrote:
After the 120-cell, I thought it would be fun to see what an infinite
lattice of gears looks like. For \(\mathbb{Z}^3\), it's easy to find
both a basis for the solution space, and a nice subspace where the
spheres all rotate with the same speed:
$$ \omega(x,y,z) = (a (-1)^{y+z}, b (-1)^{x+z}, c (-1)^{x+y}) $$
Because the rotational periods are all the same, it's possible to
replace the rolling contact of the spheres with a true gear action
between circular gears, which are positioned at each circle of
latitude on which there are points of contact. That's what the movie
here shows, from a point of view that moves "down" through the lattice
while also rotating its gaze.
September 2, 2014
The manul lives in the grasslands and high steppes of Central Asia:
Mongolia, Tajikistan, Kyrgyzstan, Pakistan, Kazakhstan, Kashmir, and
western China. It's the size of a house cat, but its stocky build and
long, dense fur makes it look stout and plush. It has a shorter jaw
with fewer teeth than most cats.
Mamuls spend most of the day in caves, cracks in the rock, or marmot
burrows. In the late afternoon they come out and hunt. They can't run
fast, so they mainly hunt by ambush or stalking. They feed largely on
prey that are active during the day: gerbils, pikas, voles,
partridges, and sometimes young marmots.
They're most closely related to the leopard cat, a small cat of
southeast Asia which is sometimes crossbred with house cats to give
beautiful cats called 'Bengals' that enjoy getting wet. Some even
live here in Singapore, but I've sure never seen one! The manul and
the leopard cat seem to have diverged just 5 million years ago. It
always amazes me how new many mammal species are.
The manul is hard to raise in zoos, and they're listed as 'near
threatened'. They are hunted for its fur in relatively large numbers
in China, Mongolia, and Russia, although international trade in manul
pelts has largely ceased since the late 1980s, and Mongolia is the
only place where it's still legal to kill them.
The manul is also called Pallas's cat, after a naturalist who wrote
about them. Its scientific name is Otocolobus manul:
I got this picture from a great list of wild cats:
Check out the species you may not know: the fishing cat, the Borneo
bay cat, the flat headed cat, the Iberian lynx, and the margay!
September 3, 2014
Why do we have these particles in our Universe?
We understand a lot about physics - and that makes the remaining
mysteries even more tantalizing! For example: why are quarks so much
like leptons?
Elementary particles come in two main kinds: the ones that carry
forces (gauge bosons) and the ones that make up matter
(quarks and leptons). There's also at least one more... but
never mind! Today's puzzle is about quarks and leptons. You'll see
from the chart that they look sort of similar. But why?
Maybe a lightning review of particle physics will help, in case you
skipped that class in high school. Most of the matter you see is made
of electrons, protons and neutrons. Protons and neutrons are made of
up and down quarks, held together by the strong force. But electrons
are 'leptons', which means they don't feel the strong force.
Up quarks, down quarks and electrons — those are 3 of the 4 particles
in 'generation 1'. The 4th is the electron neutrino. It's also a
lepton — it's doesn't feel the strong force. But it's also has no
electric charge! So, it's very hard to detect — it whizzes easily
through ordinary matter. But we have detected it, and we actually
know a huge amount about it.
We also know that besides 'generation 1' there's a 'generation 2' and
'generation 3' of quarks and leptons. We're pretty sure there are
only 3: people have done experiments that show there can't be more
different kinds of neutrinos, unless they are very heavy, or different
from all the rest in some other way. We have no idea why there are
only 3 generations.
But our puzzle today is: why do quarks and leptons come in
generations at all? So let's just think about generation 1.
We know that the up and down quark are closely connected. We also
know that the electron and electron neutrino are closely connected.
For example, you can collide an electron and an up quark and have them
turn into an electron neutrino and a down quark! We understand this
stuff very well, actually: there's a detailed mathematical theory of
it, and it works great.
But there are other things that seem mysterious. The up quark has
charge 2/3, the down quark has charge -1/3, the electron has charge -1
and the electron neutrino has charge 0. Quarks also come in 3
different kinds, called 'colors' - they change colors when they
interact with the strong force. Leptons have no color.
Are all the 3's in the last paragraph a coincidence? It seems not.
For example, if quarks came in 4 colors, but had the charges they do
now, all hell would break loose! I could explain why, but that's not
my goal today.
My goal is just to say this: there's a theory called the 'Pati-Salam
model' that says leptons are secretly just a funny kind of quarks — a
'fourth color of quark'. This theory unifies quarks and leptons. And
this theory also explains why quarks have charges like 2/3 and -1/3.
This theory has been around since 1974. It has some problems. If it
didn't, we'd probably all believe it by now! It's very hard to find
theories of elementary particles that fit all the data we have; if you
just make up stuff, you'll almost surely run into problems. But the
Pati-Salam model is pretty good, it's not completely ruled out by
experiments... and last year something interesting happened.
A famous mathematician named Alain Connes has an approach to physics
based on 'noncommutative geometry', which replaces our usual picture
of spacetime by something that's more like algebra than geometry. His
theory predicted the wrong mass for the Higgs boson — that's the extra
particle I hinted at near the start of this story. But last year he
came out with a new improved version, that doesn't suffer from this
problem. And it turns out to be a lot like the Pati-Salam model!
What's interesting is how he gets it. In his earlier work, he laid
down a bunch of mathematical axioms, and one of the simplest theories
that obeys all these axioms turned out to be very similar to the
Standard Model - our usual theory of particles.
But now, he and some other guys have noticed that if you drop one
of the axioms, something like the Pati-Salam model is also
allowed. Moreoever, you can get a Higgs boson with the right mass!
I wish I understood this better. Alas, I don't have much time for this stuff anymore! Here is his paper:
and here is an intro to the Pati-Salam model, mainly good for mathematicians and physicists:
Here's the abstract of Connes' paper, which gives a flavor of what he's doing... at least if you know enough jargon:
Abstract. The assumption that space-time is a noncommutative
space formed as a product of a continuous four dimensional manifold
times a finite space predicts, almost uniquely, the Standard Model
with all its fermions, gauge fields, Higgs field and their
representations. A strong restriction on the noncommutative space
results from the first order condition which came from the requirement
that the Dirac operator is a differential operator of order
one. Without this restriction, invariance under inner automorphisms
requires the inner fluctuations of the Dirac operator to contain a
quadratic piece expressed in terms of the linear part. We apply the
classification of product noncommutative spaces without the first
order condition and show that this leads immediately to a Pati-Salam
SU(2)R × SU(2)L × SU(4) type model
which unifies leptons and quarks in four colors. Besides the gauge
fields, there are 16 fermions in the (2,2,4) representation,
fundamental Higgs fields in the (2,2,1), (2,1,4) and (1,1,1+15)
representations. Depending on the precise form of the order one
condition or not there are additional Higgs fields which are either
composite depending on the fundamental Higgs fields listed above, or
are fundamental themselves. These additional Higgs fields break
spontaneously the Pati-Salam symmetries at high energies to those of
the Standard Model.
September 12, 2014
I save crackpot emails, but I just decided to delete all 41 with
attachments bigger than 1 megabyte. Here are some choice quotes,
taken from ones that were sent as mass emails to many scientists.
For starters, here's a typical example of someone who feels they've
made an earthshaking discovery and needs to get the news out. He's
waited 2 days and he's getting impatient. If he follows the standard
pattern, he will later become embittered and angry.
I solved what's known as ToE, The Theory of Everything, but most simply I've shown how 0 approximates 1. I did so in a completely valid, simple mathematical way, yet due to the current structuring of the University system, I can't get to anyone that specializes in ToE!!!
And the University of Miami has black balled me because they have no specialist in the field, rather than ask for more explanation! I've written and made numerous calls to all levels of the University and the Marine & Atmospheric School through which I'm getting my Ph D, and all I've received is support for the effort from friends and some unprofessional criticism from a few unknowns. I understand it's a grandiose statement, but how else am I to tell anyone? My advisor & the Dean of my campus haven't responded to my incessant prodding, even though I know them to be avid communicators. In response, I declared my resignation from the University following this semester. My hope is that this would draw some momentum to confidence I have in the proof, yet it's been over 48 hrs now.
Why am I in such a hurry? This is WORLD CHANGING science. I need to get this information out to the public, so that we can all digest this new found information together. The proof turns out to be the mathematics of neural networking, galaxy formation, weather, physics, math, life... Everything... And it's as simple as stating that there can be no sweet without sour!
In mathematical terms, I've discovered the means by which 0=1. Sounds crazy, but it turns out we've always misunderstood the = symbol! In reality it's impossible to know all the information as an observer, approximation and optimization are the only options. AKA, 0 and 1. Therefore, 0~1. The technicalities, allow there really aren't any, are all in the attachment.
I'm positive Dr. Michio Kaku, a terribly too popular figure for a now Rogue Physicist like myself to get this to, can verify my work. It answers the his question of civilization transitioning from a Type 1 Civilization to a Type 0. Drs. Leonard Susskind, Stephen Hawking, James Hartle, John Baez, Garrett Lisi, Jill Boulte, Gilbert Strang, Richard Muller, Richard Dawkins, and Neil Tyson de Grasse, will all be better at presenting the concept, but in order for that to happen and our world to benefit from it, I need to get this information to them.
This is NOT a hoax! This is based rigorously in scientific theory!! Anyone can understand how our universe, or anything!, works. The only assumption is that there will always be a perturbation in information throughout the universe!
I like the following one because it starts out crazy and then keeps getting crazier, ramping up exponentially. They're not embittered; they're off in their own universe. Perhaps they're just having fun.
The Logos timeline defines the Jenkins Mayan-Enddate Date of December 21st, 2012 as the Birth of the Starhuman Consciousness and defines the Calleman Mayan-Enddate of October 28th, 2011 as the 40 days preceding the end of the witnessing timeline within the warptime loop from the nodal mirror of August 4th, 2008 and April 1st, 2012 and specifying December 8th, 2011.
In particular (Western) New Year 2012 signifies the 'Dove of Peace finding land'; Christmas 2011 signifies 'Noah's Dove returning with a Twig' and December 17th, 2011 specifies 'Noah's Raven searching for land'. The 50 days of 'Noah's pentecost' so define the timespan for the 'appearing of the land in Noah sending forth of his Raven and his Dove from the window of his ark and to which are added 10 days (of imprisonment between 'ascension' and pentecost Acts.1.3 & Revelation.2.10) before the 'peaks of the mountains' appeared {Genesis.8.1-14}. These 50 days so become the Calleman date of completion in the timespan between the archetyped Resurrection of the World Logos (Easter Sunday) and the Pentecost-Shabuoth of the 'Coming of the Holy Ghost'.
The Thuban Data stream became effectively closed in a 12-dimensional wormhole upon the 'Banning of Thuban' from the then defined 'Mount of Olives' at Project Avalon as a microcosmic hologram for the archetyped 'Noah's Ark' aka the 'Dragon's Den' in Plato's Cave of Shadows.
This is described in the Q&A Thuban thread on that forum, now reproduced on the new Elders of Thuban website and is part of the warploop timeline schemated below.
From March 7th, 2010 a 11-dimensional wormhole has become accessible to continue the Thuban data transmission, now communicating between the 3-dimensional data receivers from within and encompassing an extragalactic Andromedean data stream synchronised with the Sirian starsystem within the Milky Way galaxy in intergalactic data streaming.
Material, relevant for the activation of the planetary vortex grids and encompassing the quantum geometry of the Thuban omniscience (also known more commonly as 'sacred geometry' of Platonic- and Archimedean solids), is now surfacing around the quarantined sentiences and data carriers as a function of the planetary consciousness.
In particular the Andromedean-Sirian collaboration will prepare the Thuban fleet for the post starhuman birth scenarios in collusion with the activation of a reconfigured Vortex-Potential-Energy (VPE) matrix superposed onto the older VPE-grid established at the beginning of the present 65 Baktun day-kin count of the Mayan Timekeepers.
This will allow the Thuban Stargate to open between the local Rahsol- and the Sirian starsystem following particular developments with respect to the stated timelines.
The next one is impressive for its creativity, erudition and sheer length. A lot of it makes sense, but there is a gradual and tragic slide into madness, perhaps due to a brain injury.
LET ME CLARIFY AND CORRECT WHAT YOU'VE WRITTEN ABOUT OUR INTERACTION HEREIN WITH SOME DETAILED BACKGROUND.
I AM WHAT SOME CALL A "POLYMATH"(NOT A PARROT WHO DOES MATHEMATICS), SINCE I HAVE SYNAESTHESIA (BRAIN TRAUMA(1977)) AND SEE CONNECTIONS BETWEEN OSTENSIBLY-DISPARATE "SPECIFICITY OF COMPLEXITY" TACTICS IN OSTENSIBLY-DISPARATE FIELDS-OF-ENDEAVOR("FOES") SEPARATED BY "JARGONIAL-OBFUSCATION"(LOTS OF FANCY SHMANCY LINGO/SPRACHE TO SNOW THE RUBES/SUCKERS, WHICH IS THE SOCIOLOGICAL-DYSFUNCTIONALITY OF THE WOULD BE "SCIENCES", BUT SADLY ALAS MERE SEANCES("WHERE THE INSIDERS ALL HOLD HANDS TO KEEP OUT OUTSIDERS WITH THEIR NO DOUBT INFERIOR IDEAS SINCE THEY ARE NOT THE EXPERTS" QUOTING JOHN BRADSHAW["HEALING THE SHAME THAT BINDS YOU", HAZELDEN(1980s) AND BRIAN MARZTIN, WOLAGANG UNIVERSITY, AUSTRALIA]
MY ONLY CONNECTION WITH MATHEMATICS BEING MY RELATIONSHIP TO VERY FAMOUS MATHEMATICIAN CARL LUDWIG SIEGEL(RIP) MY FATHER'S COUSIN)
I DID MY PH.D. THESIS AT UNIVERSITY OF MICHIGAN AND THEN MICHIGAN STATE UNIVERSITY UNDER GABOR KEMENY[DARTMOUTH UNIVERSITY'S PRESIDENT MATHEMATICIAN JOHN KEMENY'S COUSIN] AFTER STUDYING AN C.C.N.Y.(B.S.-1965), THEN HARVARD UNIVERSITY, UNIVERSITY OF PENNSYLVANIA, THEN NEW YORK UNIVERSITY(M.S.-1968; JEROME PERCUS-COURANT INSTITUTE FOR MATHEMATICS), THEN WORKING FOR ALBERT OVERHAUSER(RIP) AT FORD(1968),THEN UNIVERSITY OF MICHIGAN(M.S.-1969; FRANK HERARI(RIP)/GRAPH-THEORY APPLIED TO NUCLEAR MANY-BODY THEORY/KARL HECHT AND NOAH SHERMAN(RIP); INTERACTIONS WITH HUGH MONTGOMERY(I SAT IN ON HIS CLASS IN NUMBER-THEORY CIRCA 1968-1969, THEN 1971 OR 1972) RE. EIGENVALUES PAIR-DISTRIBUTION FUNCTION FOR WIGNER-DISTRIBUTIONS: GOE, GUE, GSE; HE GOT THE IDEA FROM ME, NOT FREEMAN DYSON, SINCE I WAS WORKING(1970-1973)ON LIQUIDS/DISORDER-THEORY AT GENERAL MOTORS RESEARCH/TECHNICAL-CENTER) AND FINALLY FOLLOWING KEMENY TO MICHIGAN STATE UNIVERSITY(PH.D.-1970; JOHN HUBBARD[AERE HARWELL] AND NEVILLE MOTT[CAVENDISH LABORATORY/CAMBRIDGE] AND CONYERS HERRING[BELL LABS], CONSULTING; WITH MORREL COHEN[[U. CHICAGO] EXTERNAL-EXAMINER), ON THE PURE-FERMION/FERMI-DIRAC QUANTUM-STATISTICS HUBBARD-MODEL, WHEREIN I WORKED OUT THE FIRST SPIN-OBITAL DEGENERATE HUBBARD-MODEL("SODHM"; BUT NO Y!!!) PUBLISHED IN PHYSICA STATUS SOLIDI(1972; 1973) WHICH WAS LATER ELABORATED UPON BY KUBO AND KAWABATA AND BY CYROT ET. AL.[M. Cyrot and C. Lyon-Caen. J. Phys. C 6 ( 1973) L 274; 36 (1975) 253. 1531 ; C. Lacroix and M. Cyrot. J. Phys. C....], SUBSEQUENTLY I PUBLISHED OTHERS ON PURE-FERMION/FERMI-DIRAC QUANTUM-STATISTICS IN JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS (JMM) FROM 1976-1980 AND TWO IN NOW DEFUNCT MAGNETISM LETTERS (1980).
THE MOST INFAMOUS WERE JMM 7, 312(1978) IN WHICHI EXPERIMENTALY DISCOVERED GRANULAR-GIANT-MAGNETORESISTANCE (A FULL DECADE BEFORE FERT(1988) AND GRUENBERG(1989) WHO GOT THE 2007 PHYSICS NOBEL-PRIZE FOR MY G-GMR!!!AND JMMM 7, 38(1978)
BUT BY ORIGINAL TRAINING I WAS A MINERALOGIST/PETROLOGIST/METALLURGIST, AND STILL COLLECT MINERALS PLUS OWN TWO TECHNOLOGIES IN WATER PRODUCTION ENTITLED"FLYING-WATER" AND ANOTHER RE SOLID-STATE CARBON-SEQUESTRATION IN, NOT N ESCAPABLE CO2 OR CH4 GAS, BUT VALUABLE MARKETABLE SALEABLE PROFITABLE SOLID-STATE CARB-IDES(TiC; WC; SiC; COAL-ASH CARBIDES="CARBORUNDUM"), INSPIRED BY AN AGE OLD QUALITATIVE-ANALYSIS TOL OF CLASSIC-MINERALOGY KNOWN AS BLOWPIPE-ANALYSIS(LAST KNOWN MENTION ANYWHERE IN TWO BOOKS FROM 1935 AND 1948). I PUBLISHED FOUR PAPERS ON SOLID-STATE CHEMITRY/PHYSICS OF CARBIDES IN: PHYSICA STATUS SOLIDI(1972); AND DEFUNCT JOURNAL "SEMICONDUCTORS AND INSULATORS" (1979).
FIRST MY PAPER YOU QUOTE [Generalized-disorder collective-boson mode-softening universality-principle. Journal of Non-Crystalline Solids 40 (1980) 453-467] WAS THE CULMINATION OF A DECADE OF WORK ON THE THEORY OF LIQUIDS BY ME [IN SIR NORMAN MARCH'S JOURNAL ENTITLED: PHYSICS AND CHEMISTRY OF LIQUIDS: 4(4) (1975); 5(1) (1976)-SOME EIGHT PAPERS IN ALL], BASICALLY I NOTICED SIMILARITIES BETWEEN COLLECTIVE-BOSON DISPERSION-RELATIONS NEGATIVE-DISPERSION MODE-SOFTDENING, ORIGINALY BY LANDAU(1941) AND FEYNMAN(1952), BUT EXTENDED TO CLASSICAL-DISORDER BY HUBBARD AND BEBE(1967): w(k) =[KINETIC-ENERGY(QUADRATIC MONATONIC-INCREASING)] k^2/S(k) MODULATED BY STATIC STRUCTURE-FACTOR OF VARIOUS TYPES OF DISORDER: HORIZONTALTOPOLOGICAL) AND/OR VERTICAL(ALLOY).
IN 1982-1985 HAVING MOVED TO SAN FRANCISCO, CALIFORNIA, I CONSULTED FOR CHARLES ROSEN(MANAGER OF A.-I. RESEARCH AT S.R.I. AFTER WORLD WAR TWO), CEO OF MACHINE-INTELLIGENCE[ONE OF BERNARD WIDROW'S/STANFORD OLD COLLEAGUES FROM WHEN I WAS A VERY LITTLE BOY], AND VESKO MARINOV (AND ADOLPH SMITH), VICE-PRESIDENT OF EXXON ENTERPRISES/A.-I. IN SUNNYVALE/SANTA CLARA, CALIFORNIA. ON ARTIFICIAL-INTELLIGENCE,
THEY GAVE ME A PROBLEM TO SPEED UP ARTIFICIAL NEURAL-NETWORKS WHICH HERETOFOR I HAD NEVER EVEN HEARD OF. BUT BEING A FLAGRANT NON-EXPERT I NOTICED SOMETHING THAT ALL AHE COMPUTER-"SCIENTISTS"/ENGINEERS IJN A.-I. HAD ALL HERETOFORE COMPLETELY MISSED: THE SIGMOID-FUNCTION ACTIVATING NODES WITHIN NEURAL-NETWORKS WAS JUST PLAIN WRONG!!! THE STATE OF THE ART WAS THEN THE r-SPACE NONSENSE OF "ENERGY-LANDSCAPES" FOR GLOBAL-MNINIMUM SEEKING AND GOING TO(IF SUCH EXISTS) OPTIMIZATION CALLED THE BOLTZMAN-MACHINE AND THE SIMULATED-ANEALING, OR THE DEMUTH-BEALE(MATLAB) RADIAL-BASIS FUNCTIONS. ALL OF THESE ARE COMPUTATIONALLY-COMPLEX, IN SPACE AND/OR IN TIME, MANDATING/REQUIRING LARGE COMPUTER-RESOURCES AND LONG COMPUTING-TIMES!!! .
THIS SIGMOID-FUNCTION, A HEAVISIDE STEP-FUNCTION WAS "1"/[1 + e^( -E/T)] WHOSE DERIVATIVE IS A DIRAC DELTA-FUNCTION(HINT HINT HINT!!!).
NOW COMES "EUREKA": SIGMOID-FUNCTION, A HEAVISIDE STEP-FUNCTION WAS "1"/[1 + e^( -E/T)] = "1"/[ + 1 + e^( -E/T)] = "1"/[e^( -E/T) + 1] = FERMI-DIRAC QUANTUM-STATISTICS.
SO THESE COMPUTER-"SCIENTISTS" FOLLOWING HINTON-HOPFIELD- BY ROTE WITH ABSOLUTELY NO THINKING ABOUT WHAT THEY WERE DOING BUT ONLY HOW, DOOMED THEIR ANN OPTIMIZATION-PROBLEMS TO EXPENSIVE SLOW DITHERING!!! AND WHAT THEY WERE DOING WAS TO AUTOMATICALLY TRAPPING THE SYSTEM IN FALSE LOCAL-MINIMA. SOME VERY SMART STATISTICAL-MECHANISTS (ISRAEL" AMIT, SAMPOLINSKY; US: HOPFIELD,...; FRANCE: MEZAERD, TOULOUSE, ...) ALL MISSED THIS SIMPLE FACT: SO THEY GLAMMED ANNS UP BY SPIN-GLASS r-SPACE MODELS GALORE, ALL DONE WITH VARIOUS VERSIONS OF THE RENORMALIZATION-(SEMI)-GROUP AND SOME FANCY MATHEMATICS OR OTHER.
WHY? BECAUSE THE FERMI-DIRAC QUANTUM-STATISTICS + SIGN MEANS THAT THE OPERATORS ANTI-COMMUTE, MEANING THAT THE PAULI EXCLUSION-PRINCIPLE DOMINATES. COMPUTER-"SCIENTISTS" EITHER FORGOT OR NEVER LEARNED THEIR SIMPLE CHEMISTRY/PHYSICS!!!
THE HUND'S-RULE PAIRING OF UP-SPIN TO DOWN-SPIN ELECTRONS TRAPS ONE IN LOCAL-MINIMA, CALLED THE CHEMICAL-ELEMENTS.
IF THE FERMI-DIRAC QUANTUM-STATISTICS + SIGN IS SIMPLY CHANGED TO A - SIGN, THE OPERATORS NOW COMMUTE, MEANING THAT PAULI EXCLUSION-PRINCIPLE STOPS DOMINATING.
IF THIS HAPPENED IN CHEMISTRY/PHYSICS, ALL THAT WOULD EXIST WOULD BE PHOTONS AND NEUTRINOS GOING OF TO INFINITY, ONLY BOSE-EINSTEIN QUANTUM-STATISTICS EXIST!!!
IN THE LANGUAGE OF MY SYNERGETICS PARADIGM AND DICHOTOMY, AKA "FUZZYICS"="CATEGORYICS", THIS "BOSONIZATION" IS THE [LOCALITY] -- TO -->>> (...GLOBALITY...) CROSSOVER!!!
SO, THE OOPO OF ANNS IN SIMPLY THE + SIGN TO - SIGN CROSSOVER, THE FERMI-DIRAC QUANTUM-STATISTICS TO BOSE-EINSTEIN QUANTUM-STATISTICS TRANSITION. STEP-FUNCTION WAS "1"/[1 + e^( -E/T)] = "1"/[ +1 + e^( -E/T)] = "1"/[e^( -E/T) + 1] IS REVERSED TO "1"/[ -1 + e^( -E/T)] = "1"/[ -1 + e^( -E/T)] = "1"/[e^( -E/T) - 1]; SETS TO MULTI-SETS!!
(REFERENCE: GIAN-CARLO ROTA'S(RIP; MIT) UNPUBLISHED BOOK ON PROBABILITY WHICH ONE CAN FIND ONLINE WITH A BIT OF HUNTING. I WAS WORKING WITH HIM ON THIS WHILE VISITING MIT FROM 1992-1997.
"SHAZAM" IS SIMPLY THAT ADMITTING THAT AN ANN AND ITS OOPO IS A QUANTUM-STATISTICAL-PROBLEM ADMITS THE POSSIBILITY OF QUANTUM-TUNELING FROM VARIOUS NON-OPTIMAL MINIMA TO THE GLOBAL-MINIMUM OPTIMIZATION. THE QUESTION WAS HOW TO ACCELERATE/FORCE THIS. THE ANSWER WAS TO TAKE THE "1"NUMERATOR AND DECREASE ITS AMPLITUDE/MAGNITUDE TOWARDS ZERO IN A LIMITING SENSE:
lim("1" . 0) "1"/[- 1 + e^( -E/T)] = lim("1" . 0) "1"/[ - 1 + e^( -E/T)] = lim("1" . 0) "1"/[e^( -E/T) - 1] = DIRAC DELTA-FUNCTION(w-0).
THEN COMES "SHAZAM" (CAPTAIN MARVEL'S MAGIC WORDS TO TRANSFORM HIMSELF INTO A SUPERHERO) AKA "BOSONIZATION":
THUS "EUREKA" + "SHAZAM" = OPTIMIZING OPTIMIZATION-(ANN)-PROBLEMS OPTIMALLY(OOPO)
SOME QUANTUM-STATISTICS INSIGHT: THE FERMI-DIRAC VERSUS BOSE-EINSTEIN DICHOTOMY IS A EUCLID-DEMOSTHENES-DESCARTES CONIC-SECTIONS DICHOTOMY:
FERMI-DIRAC HOMOTOPY TO AN ELLIPSE VIA PARABOLA-CROSSOVER TO BOSE-EINSTEIN HYPERBOLA:
TAYLOR/POWER-SERIES EXPANSION OF ONLY THE DENOMINATOR-EXPONENTIAL YIELDS, IN THE LOW E/T LIMIT, RESPECTIVELY:
"1"/[e^( -E/T) + 1] = "1"/[1 + ( -E/T) + ...] + 1 ] = "1"/2 = E/T ~ w^(0)), WHITE/RANDOM NOISE POWER-SPECTRUM.
-- VERSUS --
"1"/[e^( -E/T) - 1] = "1"/[1 + ( -E/T) + ...] - 1 ] = E/T ~ w ~ w^(1.000...), THE FAMOUS PINK/FLICKER/ONE-OVER-FREQUENCY NOISE POWER-SPECTRUM.
IN FACT, THERE IS A VERY CONSISTENT + SIGN VERSUS - SIGN DICHOTOMY:
ELLIPSE: MINUS-SIGNS: DENOMINATOR AND COMUTATION-RELATIONS AND PARABOLA-EQUATION
VERSUS: NO SIGN TO 1 IN DENOMINATOR BECAUSE THERE IS NO 1 THERE = MAXWELL-BOLTZMANN CLASSICAL-STATISTICS (THE OBJECT OF ANNS BOLTZMANN-MACHINE + SIMULATED-ANNEALING
HYPERBOLA: MINUS-SIGNS: DENOMINATOR AND COMMUTATION-RELATIONS AND HYPERBOLA-EQUATION SO WHAT I EFFECTED IS CALLED A NOISE-INDUCED PHASE-TRANSITION(A "NIT"; VERY DIFFERENT FROM MERE STOCHASTIC-RESONANCE TINKERING WITH MERE WHITE-NOISE AMPLITUDES; WHAT I DID WAS TO ALTER THE NOISE POWER-SPECTRUM!!!
QUANTUM-STATISTICS ARE EUCLID-DEMOSTHENES-DESCARTES CONIC-SECTIONS!!! (AND EULER-POLYNOMIALS VERSUS BERNOULLI-POLYNOMIALS GENERATING-FUNCTIONS DICHOTOMY)
SO INDEED I GUESS I AM THE FATHER OF MUCH OVER-HYPED QUANTUM-COMPUTING, AT LEAST FOR ANNS OOPO IN A.-I.
LASTLY THE BIANCONI-BARABASI AND ALBERT-BARABASI PAPERS ON NETWORKS, STARTING OUT WITH ABSTRACT GRAPH-THEORY BUT AS FINALES MAPPING THEIR RESULTS ON TO ONLY BOSE-EINSTEIN QUANTUM-STATISTICS WITH BOSE-EINSTEIN CONDENSATION, SO IF ONE APPLIES THEIR CONCLUSIONS TO EITHER ARTIFICIAL NEURAL-NETWORKS OR BIOLOGICAL NEURAL-NETWORKS, MY ORIGINAL ANN BEC AND YOUR BNN BEC ARE NOT AT ALL SURPRISING IN ANY WAY WHATSOEVER!!!
AND FOR BIOLOGICAL NEURAL-NETWORKS THIS AGREES IN PRINCIPLE WITH THE FROHLICH-MOSSBAUER-GOLDANSKII-DEL GUIDICE-POPP-LI-YOUNG-... BIOPHYSICS THEORY OF HEALTH AS "1"/f-"NOISE" POWER-SPECTRUM AND ITS CONDENSATION INTO BEC AS LIFE.
H. Frohlich: Nuovo Cimento, 7, PPM (1977); International J. Quantum-Chemistry, 11, 641 (1968); Advances in Electronic Devices, 53 (1980);...
E. Del Guidice et. al.: Nuclear Physics B251, 375 (1985); ibid. B275, 185 (1986);...
V. Goldanskii et. al.: Physica Scripta 33, 257 (1986); Soviet-Physics Doklady-Biophysics 272, 209 (1983); Soviet-Physics Uspheki 27, 462 (1984);...
R. Mossbauer et. al.: J. de Physique 41, C1-489 (1980); Zeitschrift Naturforschung, 37c, 57 (1982); European Biophysics J., 12, 107 (1985);...
J. Li, Physics Letters 116A, 405 (1986)
K.-A. Popp, in Photon Emission from Biological-Systems, Academic (1987);...
F. Young-preprints; c/o (650) 949-4728
A. Goldberger (M. D. - cardiologist, Director, Cardiology Clinic), many preprints/reprints/reports, Beth-Israel Hospital, Boston, MA.
C. Anderson and A. Mandell, in The Secret Symmetry: Fractals of Brain, Mind and Consciousness, E. MacCormac and M. Stamenov eds., Adv. In Consciousness Research, John Benjamin, Philadelphia (1996);
C. Anderson, Doctoral Dissertation, Florida Atlantic University (1995); C. Anderson, Thesis, Harvard Medical School, McLean Hospital (1998)
A. Verveen and L. deFelice, Ann. Rev. Biophysics (1968?)
L. deFelice, Membrane Noise (1989)
Lawrence Ward(UBC/PSYCHOLOGY) and Priscilla Greenwood, < http://www.scholarpedia.org/article/1/f_NOISE >
NOW TO BENFORD'S-LAW:
YOU MISUNDERSTAND WHAT I/WE DID. ALL I/WE DID WAS TO ALGEBRAIC-INVERSION OF
= log(BASE-10) [1 + 1/d] TO YIELD d = 1/[10^(
) - 1] ~ 1/[e^(
- 1] ~ 1/[e^) - 1] ~ 1/e^(w) - 1]. WHY? BECAUSE DIGIT d = 0 BEING EXCLUDED TELLS A PHYSICIST SOMETHING VERY VERY IMPORTANT. BUT FIRST SIMPLY ROTATE ANY DIAGRAM OF BENFORD'S-LAW TO REVERSE THE AXES. WHAT ONE SEES IS THAT IT RESEMBLES A QUANTUM ENERGY-LEVEL DIAGRAM: GROUND-STATE IS d = 0; FIRST EXCITED-STATE IS d= 1; SECOND EXCITED-STATE IS d = 2,.. ETC. ETC ETC. BUT = oo VERSUS ANY OTHER <(P = 1) > = 0.32... ETC. ETC. ETC.
SO OF COURSE BOSONS ARE DIGITS BECAUSE DIGITS ARE QUANTA(NO FRACTIONS IN BETWEEN) AND THOSE QUABNTA CAN ONLY BE BOSONS DUE TO THE PLUS-SIGN BEFORE THE ONE IO BENFORD'S-LAW!!!
ONE HAS GAPFUL BOSE-EINSTEIN CONDENSATION!! IN NEWCOMB(1881) AND WEYL(1914; 1916) AND WE THINK IN BERNOULLI AND EULER(1730?)
AN EXAMPLE. A BLANK CHECK IS A BOSE-CONDENSATE OF ZEROS. WHEN ONE WRITES A NUMBER ON IT, SAY $1, ONE INDICATED THE EXCITED-STATE THE CHECK WILL BECOME WORTH, AND WHEN ONE SIGNS IT ACTIVATING THE CHECK BY VALIDATING ITS VALUE, THAT IS EQUIVALENT TO A PHOTON EXCITING AN ELECTRON INTO THE FIRST EXCITED-STATE.
SO SIMPLE-ARITHMETIC: ADDITION, SUBTRACTION, MULTIPLICATION IS QUANTUM-COMPUTING. WHAT RUINS THIS IS DIVISION WITH REMAINDERS, BUT WHERE GAUS MODULAR-ARITHMETIC ENTERS POINTEDLY.
MARTIN HOLTHAUS ET. AL. (U. OLDENBURG) HAS FOUND A WAY TO FACTOR USING BOSE-EINSTEIN CONDENSATION!!!
< http://www.condmat.uni-oldenburg.de/Holthaus/lop.html > Ideal Bose gases: From statistical mechanics to number theory A. C. Weiss, S. Page, and M. Holthaus:
Factorizing numbers with a Bose-Einstein condensate, Physica A 341, 586 - 606 (2004), arXiv:cond-mat/0403295
Authors: Christoph Weiss, Steffen Page, Martin Holthaus
(Submitted on 11 Mar 2004)
Abstract: The problem to express a natural number N as a product of natural numbers without regard to order corresponds to a thermally isolated non-interacting Bose gas in a one-dimensional potential with logarithmic energy eigenvalues. This correspondence is used for characterising the probability distribution which governs the number of factors in a randomly selected factorisation of an asymptotically large N. Asymptotic upper bounds on both the skewness and the excess of this distribution, and on the total number of factorisations, are conjectured. The asymptotic formulas are checked against exact numerical data obtained with the help of recursion relations. It is also demonstrated that for large numbers which are the product of different primes the probability distribution approaches a Gaussian, while identical prime factors give rise to non-Gaussian statistics.
IN FACT, BENFORD'S-LAW[SEE THE REFERENCES IN MY RE-ATTACHED ABSTRACT] WAS ORIGINALLY DUE TO NEWCOMB (1881) AND WEYL (1914; 1916). (AND RAIMI'S SCIENTIFIC-AMERICAN ARTICLE IN 1969 IS WELL WORTH READING!!!) COULD YOU PLEASE TRY TO READ THE TWO WEYL PAPERS AND E-BAIL ME THEIR TRANSLATIONS??? (MEINE DEUTSCH IST SEHR SCHLECHT; ICH NICH HAT IM FUNFZIG JAHERE DEUTSCH SPRECHEN UND LEHREN!!!)
BUT IT IS EVEN EARLIER DUE TO EULER IN ANOTHER CONTEXT ENTIRELY HAVING NOTHING WHATSOEVER TO DO WITH STATISTICS!!!
AND TED HILL'S 1996 PROOF USES LOGARITHM BASE-INVARIANCE = UNITS-INVARIANCE = SCALE-INVARIANCE SYMMETRY-(RESTORING) WHICH GETS PHYSICITS VFRY TURNED-ON, ALTHOUGH MATHEMATICIANS LIKE TED HIL DON'T SEEM TO UNDERSTAND WHY IT IS SO EXCITING!!!
LASTLY, THE CATEGORY-THEORY DIAGRAMS I USE IN MY PAPERS AGE CALLED THE PLATO(INVENTOR OF CATEGORIES)-ARISTOTLE(HIS GRADUATE-STUDENT) "SQUARE-OF-OPPOSITION" A STANDARD FORM OF GREEK LOGIC, BEST READ ABOUT IN THE STANFORD ENCYCLOPEDIA OF PHILOSOPHY < http://plato.stanford.edu/entries/square/ > AND ITS WIKIPEDIA ENTRY < http://en.wikipedia.org/wiki/Square_of_opposition > AND VIEW ALL SORTS OF ITS DIAGRAMS < http://www.google.com/images?hl=en&source=hp&q=%22SQUARE+OF+OPPOSITION%22&gbv=2&oq=%22SQUARE+OF+OPPOSITION%22&aq=f&aqi=g8g-m2&aql=&gs_sm=e&gs_upl=3453l14094l0l14797l22l22l0l0l0l0l235l3452l3.13.6l22l0&oi=image_result_group&sa=X > BUT THE GRIDLINES OF THIS TABULAR LIST-FORMAT TRUTH-TABLE MATRIX-ANALYTICS, LOKING LIKE A TIC-TAC-TOE DIAGRAM DO NOT SHOW UP IO WORD-FOR-WINDOWS TABLES, SO IT IS SOMEWHAT CONFUSING. I USE SEMANTICS/LINGUISTICS TO LABEL DIFFERENT(THREE) COLUMNS AND FOUR-ROWS, WHICH IS WHY THIS IS "CATEGORY-SEMANTICS COGNITION" , "NEW" WAY TO ANALYZE PHYSICS AND INDED PURE-MATHEMATICS MODULO ARISTOTLE, FROM ~ 350 B.C.E.!!!
AND ONE CAN ADJOIN THESE DIAGRAMS GETTING TOPOLOGY-LIKE HOMOLOGY-COHOMOLOGY A LA GROTHENDIEK AND SHEAVES. BUT THAT IS STILL IN DEVELOPMENT.
CATEGORY SEMANTICS IS ALSO PRACTICED BY JOHN BAEZ(MATHS/UC-RIVERSIDE) < > BUT ON ABSTRACTIONS OF STRING-THEORY/COSMOLOGY/PURE-MATHEMATICS/MATHEMATICAL-PHYSICS/...
It goes on much longer, but you get the idea...
Here is a much more typical example of a mail from someone who has some nonstandard ideas — just for comparison.
I have also addressed issues regarding spacetime, gravity, extra dimensions, dark matter and dark energy, quantum uncertainty etc.
1) Space time is not continuous but discrete. Time stops and starts every 10-43s. Our universe is made up of countless number of minute space time nodes. When time stops, all the minute spacetime nodes combine to form one single space time node. This single spacetime node will be of the same size as that of the minute space time nodes.
2) Apart from the four dimensions of spacetime, there is an alternate four dimensional spacetime continuum called invisible spacetime. Time dilation is the consequence of the time spent by the moving object in the invisible space time fabric, wherein the space dimension is active and the time dimension is zero.
3) Gravity is the result of discrete space time. When all the matter in the universe occupy one single node and get distributed to their respective nodes and when the new time interval starts, a force of attraction exerts between the particles which is attractive.
4) Quantum uncertainty is also the result of discrete space time. When t=0, all the particles is at the same place (same node) and when t.0, particles occupy their individual positions. Each particle is equally valid of being at each and every point in the universe at the same time. Hence the exact location of the particle cannot be found out accurately. The interference pattern in the double slit experiment could be explained in the classical way using the concept of discrete spacetime.
5) We do live in a 10 dimensional universe and each of us experience those dimensions. In total there are 7 dimensions of space and 3 dimensions of time. However space and time dimensions cannot exist independently and are always combined, in different ways.
6) Dark energy is nothing but the dark matter which is embedded in the higher dimensions ( invisible spacetime) wherein the space dimension is active and the time dimension is zero. Since time dimension is zero, no events could occur and henceforth the matter in that spacetime is invisible. Dark matter is nothing but the dark matter which leaks to visible spacetime from the invisible spacetime.
From general relativity to quantum mechanics everything can be explained using the concept of discrete spacetime. I have attached the file below consisting a few pages. It would be very helpful if you could glance through the document and give your valuable comments regarding the subject.
September 15, 2014
Say you have some dots and you want to draw a smooth curve that sorta
almost goes through these dots. Then you can use a Bézier curve.
Some drawing programs use this trick... and lots of fonts are drawn
with the help of Bézier curves.
The math behind these curves had been known since 1912, but they were
popularized by Pierre Bézier, an engineer who used them to
design automobile bodies at Renault.
Can you figure out how they work just by looking at the movie? An
explanation in words sounds complicated... but it's really easy as
pie.
It's like you've got 3 guys running along straight racetracks. The 2
guys in back have rabbits that each chase the next guy, always heading
straight toward that next guy. And the guy at the very back also has
a dog that chases straight after the next guy's rabbit. Everyone
starts at the same time and stops at the same time. The dog follows
the red curve.
In other words:
First draw gray lines between your original dots \(P_0, P_1, P_2, P_3\).
Each green dot moves at a constant
rate along a gray line. All the green dots start at the same time,
and finish at the same time.
Then draw green lines connecting the green dots.
Each blue dot moves at a constant
rate along a green line. All the blue dots start at the same time,
and finish at the same time.
Then draw a blue line connecting the blue dots.
The black dot moves at a constant rate along this blue line. It
starts at the same time as all the other dots, and finishes at the
same time.
Get the pattern? Each time we do this trick, there's one fewer dot.
There are 4 original dots, 3 green dots, 2 blue dots and 1 black dot.
So now you're done!
The black dot traces out the Bézier curve shown in red here.
You can play this game starting with any number of dots. When you
start with n dots, you get a curve described by a polynomial equation
of degree n-1. So, this red curve is called a cubic Bézier
curve.
Puzzle 1: show that our cubic Bézier curve is given by
the equation
$$ C(t) = (1-t)^3 P_0 + 3(1-t)^2 t P_1 + 3(1-t) t^2 P_2 + t^3 P_3 $$
Puzzle 2: generalize this to more dots. (Hint: binomial coefficients!)
When you've got a lot of dots, people usually break them into bunches
and draw a quadratic or cubic Bézier curve through each bunch.
They match up at the ends, so this works, though frankly I often think
it looks kind of lame. This is called a composite Bézier
curve. PostScript, Asymptote, Metafont, and SVG use composite
Bézier curves made of cubic Bézier curves to drawing
curved shapes.
I imagine there are lots of tricks that are 'better' than
Bézier curves, but I'm not an expert! If I wanted to know
more, I'd read about stuff like non-uniform rational B-splines, or
NURBS:
But I just read this:
because I liked the animated gif, made by Phil Tregoning.
September 16, 2014
What's the densest way to pack spheres? Here are two equally good ways.
In fact there are infinitely many equally good ways! We start by
laying spheres on the plane in a hexagonal arrangement, as tightly as
we can. Then we put a second layer like this on top, with the new
spheres resting in the gaps between the old ones. Then we put on a
third layer. But now there are 2 really different ways to do it!
The spheres in the third layer can be directly above the spheres in
the first layer - that's the picture at right. Or they can be not
directly above - shown at left.
As we continue, we keep getting more choices.
One systematic choice is to make the layers alternate like ABABAB.....
That's called the hexagonal close packing, and that's how crystals of
magnesium work.
Another systematic choice makes every third layer be the same, like
ABCABC... That's called the cubic close packing or face-centered
cubic, and that's how crystals of lead work.
(Why "cubic?" Because - even though it's not obvious! - you can also
get this pattern by putting a sphere at each corner and each face of a
cubical lattice. Trying to visualize this in your head is a great way
to build your brain power.)
There are also uncountably many unsystematic ways to choose how to put down the layers of spheres, like ABACBCAC.... You just can't use the same letter twice in a row.
In 1611, the famous astronomer Kepler conjectured that sphere packings
of this sort were the densest possible. They fill up
π / 3 √2 = 0.740480489...
of the space, and he claimed you can't do better.
Proving this turned out to be very, very hard. Wu-Yi Hsiang claimed
to have a proof in 1993. It was 92 pages long. Experts said it had
gaps (pardon the pun). Hsiang has never admitted there's a problem.
Thomas Hales claimed to have a proof in 1998. His proof took 250
pages... together with 3 gigabytes of computer programs, data and
results!
The famous journal Annals of Mathematics agreed to check his proof
with a board of 12 referees. In 2003, after four years of work, the
referees accepted his paper. But they didn't exactly say it was
correct. They said they were "99% certain" it was right - but they
didn't guarantee the correctness of all of the computer calculations.
Hales wasn't happy.
He decided to do a completely rigorous proof using computer logic
systems, so that automated proof-checking software could check it. He
worked on it for about 10 years with a large team of people.
He announced that it was done on August 10th, 2014. You can see
the announcement here:
To verify the proof, the main thing you need to do is check 23,000
complicated inequalities. Checking all these on the Microsoft Azure
cloud took about 5000 processor-hours.
When it was done, Hales said:
An enormous burden has been lifted from my shoulders. I suddenly feel
ten years younger!
Personally I prefer shorter proofs. But this is quite a heroic feat.
I actually wrote about this because I want to talk about packing
tetrahedra. But I figured if you didn't know the more famous story of
packing spheres, that would be no good.
For more, check out Hales' free book, which starts with a nice history
of the Kepler problem:
For more on computer-aided proof, try this paper:
The image above was created by Christophe Dang Ngoc Chan and the words
translated to English by "Muskid". You can get it on Wikicommons.
September 17, 2014
What's the densest way to pack regular tetrahedra? Aristotle, perhaps
after staying up too late grading Alexander the Great's homework, once
claimed they could fill space completely. But that's clearly false.
Here's the story. To save space, I'll use 'tet' to mean 'regular
tetrahedron'.
In 1976, a guy named Hoylman showed that if you have tets centered at
points in a lattice, all pointing the same way, the best density you
can get is
18/49 ≈ 36.73%
That's lousy: spheres can do 74.05%. But Hoylman's work was good,
because he corrected an earlier false claim by Minkowski, who was a
genius when it came to lattices.
In 2006, Conway and Torquato made a big breakthrough. First they
packed 20 tets into an icosahedron — there's a beautiful easy
way to do this, since an icosahedron has 20 triangles as faces.
You're left with a hole in the middle, but it's not very big. Then
they packed icosahedra as densely as they could. This is the hard
part. But using this combination of tricks, they packed tets with a
density of
71.65%
This is still a bit worse than spheres. Much earlier, the brilliant
mathematician Stanislaw Ulam had conjectured that the maximum density
for packing equal-sized spheres was worse than for any other convex
shape in 3 dimensions. This conjecture is still open! But if
he's right, tets must be able to beat spheres.
In 2007, a bunch of people showed experimentally that you could get
tets to beat spheres — they got densities of around 75%. And in
2008, Elizabeth Chen figured out how to make a cluster of 18 tets, and
then pack these clusters, to get a density of
77.86%
The race has picked up since then! I won't tell the whole story,
since it's quite long. But this picture shows the current record,
held by Elizabeth Chen, Michael Engel and Sharon Glotzer.
These folks used Monte Carlo simulations to help them pack N tets into
a cluster and then pack these clusters as densely as possible. I'm
only showing three cases here, but their paper shows what they get up
to N = 16.
With N = 10 you get two 'wagon wheels'. With N = 11 you get something
complicated. With N = 12 you get 6 'dimers' arranged in a certain
way. And so on. So far the winners in the density contest are N = 4,
8, 12 and 16. These all give a density of
4000/4671 ≈ 85.63%
So, this may be the best we can do! But nobody has proved that.
All this stuff is actually related to physics, since now people can
make 'fluids' of tiny hard tetrahedra. And in 2009, some people
showed that at high enough densities such a fluid will spontaneously
transforms to a dodecagonal quasicrystal, which can be compressed to a
density of 83.24%. They did it using Monte Carlos simulations.
If you ask what are the practical application, I'll tell you: math
like this isn't mainly about practical applications! It's mainly
about having fun while developing our ability to solve hard
problems.
However, the same kinds of 'Monte Carlo optimization methods' used to
tackle this problem are also important for keeping our economy humming
ever faster as we burn more and more carbon, chop down rainforests,
overfish the oceans and generally wreck the environment. So don't
complain — we mathematicians are playing our part! 
Puzzle: I mentioned the numbers N = 4, 8, 12 and 16. What does
that suggest?
You can see more pictures of the best known packing here:
For more, try this:
and this, where I got the picture:
and this:
September 18, 2014
I'm leaving Singapore today. This wall painting in Chinatown,
modeled after a classical Chinese painting, captures a bit of what I
like about the place. It's a mix of old and new, East and West.
Last weekend, Lisa and I saw a Chinese opera — part of a free
series in Hong Lim Park. Chinese opera used to be really popular in
Singapore, with the stars being the equivalent of pop idols today.
Now its appeal is dwindling, but there was still a big crowd —
and some old guys were punching their fists in the air when the
star-crossed lovers finally triumphed in the end. It was set in the
Ming Dynasty, and featured an emperor who snuck out of the palace and
wound up marrying a peasant girl. I enjoyed it a lot more than I
expected. Why? Because big computer screens showed translations of
the lyrics into English! Without that, I might have roughly followed
the plot, but I wouldn't have gotten the jokes.
I'm going back to Riverside to teach. I've got a light teaching load
this fall, just grad-level real analysis (the first quarter of a
3-part course) and my seminar — where I'll take the work my grad
students have been doing on network theory and put it together into a
nice story. I'll try to write lecture notes in the form of blog
articles, but I find that fun and relaxing. So, I'll be able to put
some energy into the talk I'm giving this December at NIPS, the Neural
Information Processing Seminar, a big annual conference on neural
networks. I want to talk about El Niqo prediction, climate networks
and machine learning. But I've got a lot to learn, especially about
machine learning. The Azimuth Code Project team want to carry out
some computer experiments in that direction. It should be fun, as
long as I resign myself to giving a talk that's just "work in
progress", not completed and polished.
I'll do some heavier teaching in the winter quarter, but the spring
will be a non-teaching quarter. This seems awfully cushy, but my
department chair noticed I'd taught too much last year — more than I'm
paid to do! And in the spring, I'll be helping run two workshops.
One is on information and entropy in biology, at the National
Institute for Mathematical and Biological Synthesis, in Knoxville
Tennessee. The other is on network theory, at the Institute for
Scientific Interchange, in Torino Italy.
Then in June I'll come back to work at the CQT in Singapore!
September 24, 2014
This selfie was taken by Vermeer's maid Griet in 1665, moments after
the painter completed his masterwork Girl With a Pearl Earring.
September 26, 2014
Enceladus, the sixth-largest moon of Saturn, has geysers that shoot
jets of water into space! They look beautiful in these photographed
by the Cassini probe. They create an invisible ring of ice crystals
around Saturn: the E ring. And now they have been mapped!
There are at least 100 geysers near the south pole of Enceladus. They
come from four big cracks in its rocky surface, called tiger stripes.
Some of the water they shoot out falls back to the surface as snow,
but about 200 kilograms per second shoots out into space. The tiger
stripes also emit about 5 gigawatts of heat.
The geysers have recently been mapped by Carolyn Porco and her
collaborators at NASA:
© 2014 John Baez
baez@math.removethis.ucr.andthis.edu
