Milner-Zuckerberg Prizes for Mathematics

Peter Woit states: “At the Hollywood-style awards ceremony last night for $3 million string theory and biomedical research prizes, it was announced that Yuri Milner and Mark Zuckerberg will now start funding something similar in mathematics, called the Breakthrough Prize in Mathematics. … I’ve written extensively about the “Fundamental Physics Prize” and what I see as the worst problem with it (heavily rewarding and propping up a failed research program).  … The physics prize has turned out to be extremely narrowly targeted at one particular subfield of physics … the main argument for the prizes is that the money (and Academy Awards-style ceremonies) will help make them celebrities … I still think the whole concept is problematic. The US today is increasingly dominated by a grotesque winner-take-all culture that values wealth and celebrity above all else.”

Edward Witten’s misleading megaphone hype of M-theory led to his $3 million “Fundamental Physics Prize” from Yuri Milner. Yet the ad hoc 10/11 dimensional “theory” doesn’t lead to experimental tests of a useful sort.

I strongly disagree with everything Peter Woit states here (see footnote at end of this post for my take on his classic anti-capitalism politics), but especially his hypocrisy in speaking out against celebrity while also claiming to take a stand against the dictatorship of physics by one failed unification idea which has become a religious dogma among leading physicists, with objections being deemed heretical, resulting in excommunication. The dangers here need spelling out clearly:

(1) that if he acquires celebrity status as the “debunker of string theory” and gets his argument wrong, he’ll only make the problem worse for others (in other words, if he leads the anti-string lobby and fails to overturn string, he’ll be used as a straw man opponent by the string theorists);

(2) the only way to overturn a failed dogma theory historically has been to replace it with something better.  This is not Woit’s approach, which is to make criticisms without suggesting a better theory.  So, on this basis, Woit is making the problem worse and providing a straw man target;

(3) Woit reproduces the electroweak sector charges of the standard model (including chiral features, since right-handed spinors in his model have zero weak charge) by picking out a U(2) symmetry as a subset of SO(4) spacetime (on page 51 of http://arxiv.org/abs/hep-th/0206135, based on his 1988 paper “Supersymmetric quantum mechanics, spinors and the standard model”, Nuclear Physics, vol. B303, pp. 329-42), yet he does not try to strongly market this theory as an alternative by making it the focus of a book or popular article, instead writing weakly/humbly on page 51 of a long technical paper: “The above comments are exceedingly speculative and very far from what one needs to construct a consistent theory. They are just meant to indicate how the most basic geometry of spinors and Clifford algebras in low dimensions is rich enough to encompass the standard model and seems to be naturally reflected in the electro-weak symmetry properties of Standard Model particles.”

However it is clear that this fact – that progress in low dimensions is possible – leads Woit to his criticisms of string dogma.  In other words, Woit appears to me to be putting forward arguments against string which are weaker than they need to be, for a psychological reason (modesty).  Let’s make this fact crystal clear: Woit in 1988 discovered an alternative approach to developing a better understanding of electroweak symmetry, based on the mathematical representation of the U(2) symmetry in simple 4 dimensional Euclidean space.  This caused Woit to feel uneasy with Witten’s 1995 10/11 dimensional M-theory hype, despite the fact that Woit’s graduate work in computational (Wilson formulation) lattice QCD nuclear physics utilized Edward Witten’s earlier conjecture on the large N expansion (Witten’s 1979 paper: “Baryons in the 1/N expansion”, Nuclear Physics, vol. B160, pp. 57-115, a mathematical conjecture which seems to be based on thinking of the strong force using a hadronic string model).

Witten’s problem for physics today is his 1995 M-theory (conjecture) that 10 dimensional superstring is a brane surface on an 11 dimensional supergravity bulk. This speculation reinforces and hardens dogmas like SUSY, increasing the parameters of the Standard Model from 19 to at least 125 parameters in the minimally supersymmetric standard model.

The bottom line is, instead of presenting his strongest (objective) evidence against M-theory (his own research as a replacement direction for physics to go in), Woit instead raises a lot of relatively subjective arguments about the lack of “progress” in M-theory.  This is unsatisfactory, because “progress” is ill-defined in science: to someone digging in a hole, the deeper the hole gets, the more “progress” is being made.  To critics, it’s the opposite, and people in holes should stop digging.  Such arguments go nowhere, because if you are digging for gold and don’t know how deep the gold is (if it is there at all), it’s an arbitrary decision to quit.  Moreover, the more time and effort you “invest” (to critics: “waste”) in digging your hole, the less inclined you are to admit failure, lose face, etc.  Only when you get hungry and run out of supplies, are you likely to relent, and then you won’t admit failure. You’ll go to your grave dreaming of digging deeper in your hole.  The only way to defeat this, is for someone else to find the gold.  What drives some of us, is not the dream of seeing gold, but the desire to find the gold simply to discredit smug mathematical elitism.

Footnote:

Peter Woit attacks prizes for promoting capitalism with smug words: “The US today is increasingly dominated by a grotesque winner-take-all culture that values wealth and celebrity above all else.”

The problem is that this attitude ends up making prizes even more warped, because it introduces a political-type crusading aspect, rewarding high-profile scientists with failed grand unification theories but who are “worthy” in some other way. For instance, people either famous for making lots of money out of best-selling non-mathematical hype-style kids books “about mathematics”, or else famous for some kind of politically correct anti-capitalism or pro-environmentalism crusade (based on subjective or controversial interpretations of ambiguous data).

Apart from this purely “Matthew effect” corruption in prize ceremonies, there is also the egotism of those giving the prizes, which sometimes corrupts the selection of recipient: money is used to “buy” free publicity in the media, so you must give a prize to an already interesting or famous celebrity, to host an awards ceremony with media attendance. This is contrived “news” but it works.

Staged ad-style philanthropy is more praiseworthy than high-profile mega-rich celebrities begging those poorer to donate to good causes, while pretending to do this “free” (their payback is the relatively positive free “positioning” publicity they receive in the process of doing it, usually aided by public service awards). This is what Woit is missing in his analysis.

It’s not a choice of good versus bad options, but of bad versus very bad. It’s far better to take the lesser of two evils. Capitalism has its problems, but it works better than the USSR type socialist idealism, with its monolithic centralized control and its demotivating, restricting bureaucracy. Similarly, arbitrary prizes are vulnerable to corruption like capitalism, but probably work better than regimented consensus, which has its own set of groupthink problems.

Woit reproduces the electroweak sector charges of the standard model (including chiral features, since right-handed spinors in his model have zero weak charge) by picking out a U(2) symmetry as a subset of SO(4) 4-dimensional spacetime (on page 51 of http://arxiv.org/abs/hep-th/0206135 which is based on his 1988 paper “Supersymmetric quantum mechanics, spinors and the standard model”, Nuclear Physics, vol. B303, pp. 329-42), yet he does not try to strongly market this theory as an alternative by making it the focus of a book or popular article.

Although Woit “only” reproduced the electroweak charges and chiral features of the electroweak sector correctly in 1988, there has been some technical work since then dealing with the non-symmetry details of U(2) theory which Woit left untouched.  See, for example, the paper by Aranda, Carone and Lebed, U(2) Flavor Physics without U(2) Symmetry, http://arxiv.org/abs/hep-ph/9910392 which models the weak mixing angles (CKM matrix) and fermion mass relations.  So U(2) is not just a threadbare model of the electroweak sector charges and handedness.

Whether this specific example is totally correct or not, Woit’s conjecture that “The quantum field theory of the standard model may be understood purely in terms of the representation theory of the automorphism group of some geometric structure” (quoted from http://arxiv.org/pdf/hep-th/0206135.pdf, page 4) remains a promising avenue of investigation and should be rigorously pursued as an alternative to superstring.

Relevant technical trivia

Sophus Lie invented Lie symmetry group theory in 1874 and William Clifford invented Clifford algebras in 1876.  For the purposes of particle physics (but not necessarily math de la rigor mortis),  since Spin(n) is a double-cover of SO(n), they fit together and are therefore isomorphisms geometrically.  From the perspective of the number patterns involved, as utilized in particle physics, the following useful isomorphisms or equivalences hold:

Spin(2) = U(1) = SO(2)

Spin(3) = Sp(1) = SU(2) = SO(3)

Spin(4) = SU(2) × SU(2) = Sp(1) × Sp(1) = SO(4)

(It’s not always mathematically rigorous to treat an isomorphism as a strict equality, however useful it is in physics.  For example, E = mc²  if literally true would imply that 9 × 10¹⁶  Joules of energy has exactly the same price as 1 kilogram of manure.  If Einstein was literally asserting a simple equivalence, we could substitute or sell one for the other in that exact ratio.  Since nobody will buy 1 kilogram of manure for the same price as 9 × 10¹⁶  Joules  of energy, it’s obvious that the conversion equivalence is not always as simple as that.  Similarly, the equation 1 + 1 = 2 taken naively would suggest that two halves of a wedding cake are the same value as a whole  wedding cake.  It’s obviously not true.  If you chop 10 feet of rope into 10 separate 1 foot sections, you still have literally “10 feet of rope”, but may be of far less value to a sailor.  The point is, any equivalence in general may only have a limited range of exact validity, like an analogy between the similarities of different systems. Two halves of a car are less useful than one whole car.  This is so obvious that it is omitted from arithmetic, but this logical “reductionist problem” can cause problems in more abstract areas of science where things are not so obvious, and so you need to be far more careful.)

With the above isomorphism

SU(2) × SU(2) = SO(4)

where SO(4) is used to produce Woit’s U(2) electroweak particle charges, we can represent weak interactions by one SU(2) with massive bosons, and the other SU(2) as a hidden electrodynamics symmetry with massless bosons that reduces the Yang-Mills via a technical mutual magnetic self-inductance mechanism (which prevents the one-way motion of charged massless bosons, but not massive charged bosons; thus eliminating the charge transfer quadratic term in the Yang Mills equations and reducing them to Maxwell’s equations), to appear like the familiar Abelian U(1) Maxwell electrodynamics theory.

Backing this up SU(2) electrodynamics up further, the three Pauli matrices of SU(2) isospin are extremely similar in basic structure to the two gamma matrices of Dirac, with the third Pauli matrix being equivalent to Weyl’s chiral spinor:

SU (2) electrodynamics spinor. The sigma components in the second Dirac gamma matrix are themselves given by the SU(2) Pauli matrix, a fact which has helped to confuse the simplicity of this SU(2) electrodynamics symmetry. Dirac’s omission of chiral handedness from QED was later corrected by the addition of a chiral spinor by Weyl, yet the hype of Dirac’s work and the initial obscurity of Weyl’s (Pauli dismissed Weyl’s prediction of chiral effects until 1957 when the left handed nature of weak interactions was discovered experimentally) turned half-baked initial ideas into a dogma, which resists correction to this day.  The standard textbook approach to the standard model is that Dirac’s equation gives the lagrangian for massive fermions, and Weyl’s spinor only comes into play for “massless fermions” (formerly believed to be neutrinos).  But this is falsified by the empirical observation that neutrinos change flavor as they propagate and therefore have mass, despite engaging in weak left-handed interactions.  So it does appear that massive fermions can contradict Pauli’s ad hoc parity conservation law, thus Weyl’s handedness spinor applies to massive particles.   Electrodynamics is an SU(2) theory because of the fact you need 4 polarizations (not two as for onshell photons) for electromagnetic gauge bosons (offshell photons) to mediate attractive and repulsive forces in QED should make this clear, but is currently camouflaged by “proud statements” of the sort: “nobody understands quantum mechanics”, which are today used as an excuse to censor out progress.

The rationale for including Weyl’s chiral spinor in QED (not just in weak theory) goes back to Maxwell himself, who argued that the fixed direction of curl of the magnetic field circling around moving electrons (or a wire carrying a current) is evidence for a chiral handedness of spin: Maxwell had a spin angular momentum transfer  (spinning vortex or “gear box”) model for the mediation of magnetic forces through space.  Abstract gauge theory today needs to properly replace Faraday’s old field line theory, or Einstein’s curved space time theory, with a mechanism for force production by gauge boson exchange.  The Casimir force is an example: two conducting metal plates exclude pressure effects from the space between them by virtual photons of wavelengths that are longer than the distance between the plates.  Therefore, there is a deficit in the cut-off spectrum of wavelengths exerting pressure between the Casimir plates, compared with the full spectrum that is pushing them together from the surrounding space.  So the net effect is that they get pushed together.  Extending this, it’s easy to see that if electrodynamics is SU(2), the magnetic curl (self- inductance problem) for massless charged bosons only allows the exchange of charged-bosons to similar charged particles (thus causing them to repel); opposite charges can’t exchange charged-bosons because the geometry of the magnetic vectors of the exchanged bosons is such that they don’t cancel out but add together instead (so this exchange is impossible due to the uncancelled, infinite magnetic self-inductance of the charged bosons).  In summary, opposite charges repel, but similar charges don’t repel and are hence pushed together by a Casimir-type “attraction” mechanism.

Professor Edsger Wybe Dijkstra (1930-2002), The strengths of the academic enterprise, EWD 1175, University of Texas, 9 February 1994:

“In the wake of the Cultural Revolution and now of the recession I observe a mounting pressure to co-operate and to promote ‘teamwork’.  For its anti-individualistic streak, such a drive is of course highly suspect; some people may not be so sensitive to it, but having seen the Hitlerjugend in action suffices for the rest of your life to be very wary of ‘team spirit’.  Very.  I have even read one text that argued that university scientists should co-operate more in order to become more competitive….. Bureaucracies are in favour of teamwork because a few groups are easier to control than a large number of rugged individuals.  Granting agencies are in favour of supporting large established organizations rather than individual researchers, because the support of the latter, though much cheaper, is felt to be more risky; it also requires more thinking per dollar funding.  Teamwork is also promoted because it is supposed to be more efficient, though in general this hope is not justified. … the co-operation seems more to force the researchers to broaden their outlook than to increase the efficiency of the research. … everybody complains about the amount of red tape … Why should a vigorous, flourishing department seek co-operation when it is doing just fine all by itself? It is the weak departments that are more tempted to seek each other’s support and to believe that there is might in numbers.  But such co-operation is of course based on the theory that, when you tie two stones together, the combination will float.”

Update (17 December 2013):

Woit deemed famous for criticizing Zuckerberg prize

As predictable, Woit is now deemed, by Business Insider, a “famous math professor” for his pretty much worthless criticism of Zuckerberg.  All Woit is doing in the”criticism” is a disfavor to physics, by effectively preventing himself from being considered a possible recipient of such prizes, and thereby preventing his own theory from being funded with the sort of money required for its media hype to the extent needed for it replace string theory as a major research direction!

Update (3 Jan 2014): To his credit, Peter Woit has made a stance against the cringeworthy self-imposed money-making-aimed-self-censorship by fashion-dominated journals: “The policy of Physics Today to charge $30 to look at an article seems to have no point other than to ensure that no one does it.”

Real “freedom” of the press (internet) for everyone, or  “intellectual communism” – as contrasted to the anti-“intellectual communism” of pro-Marxist “financial communism” of anti-capitalist people in the BBC/Guardian/left wing who are paid subsidies or USSR style taxation funding for issuing biased “information” or propaganda (analogous to opinions of the Witten M-theory variety, dressed up as facts) – is the number one “problem” for “journalism” in the internet age.  How do journals and journalists retain their elitism when anybody is now free to circumvent their groupthink censorship?  The whole idea of “freedom of the press” is a complete lie: see the 3 January 2014 released secret UK National Archives file PREM 19/1394 which 22 May 1984 report by Sir James Goldsmith for the Defense Strategy Forum of the National Strategy Information Center, Soviet Active Measures versus the Free Press: A European Perspective, stating:

“Then comes the outer layer consisting of those who follow fashion and seek easy praise. Responsible journalists can also be disinformed by these campaigns. When a journalist works on an article, he refers to the press cuttings file which covers the subject about which he is writing. Information … will be used over and over again. So, once the press cuttings files have been polluted by propaganda, the false information will be repeated quite innocently and as it is repeated will gather further credibility and momentum. … Here are some thoughts … We need … better journalism. The better informed the public, the better equipped it is … The trouble with today’s intellectual environment is that few dare discuss the problem. … It is taboo. … It is a genuine problem which needs free and open discussion. … in a free country the best remedy is wide publication of the true facts. … journalists should investigate and publish. But they face a problem. There is a tradition of forbidden areas. Dog must not eat dog. Not only is it unpopular to expose a colleague or a journal, bit it is also difficult to find papers who would publish your material. Investigation should not be concentrated on the unpopular. It takes no courage to be fashionable, to express conventional wisdom and comfortably to join the pack in attacking the same wounded stag. Courage resides in saying the truth that does not please and which can make you a pariah in the eyes of your peers. This precisely is the duty of the press and one of the great justifications for the freedom of the press.”

The usual defense of a “free press” is totally wrong: it was mass press in Britain in the 1930s which rubbished, ridiculed and censored Churchill’s warnings about Hitler and the Nazis, instead playing the song of appeasement and “collaboration” for pacifist utopia and Nobel Peace Prizes all round for pacifists like Sir Norman Angell.  The mass media is professional, which means it’s profession (money-making) relies on being fashionable: money corrupts the professional journal or journalist (who won’t sell papers or TV time to be paid if unpopular) just as it corrupts the professional politician (who won’t get elected and paid unless he is popular enough to get votes), or the professional scientist (who won’t get paid unless he gets sponsorship).  Real freedom of equality for speech on facts or a “communism of thought”, is opposed by precisely the bigots who are professional liars, the “Marxist communists” who want not a communism or freedom and equality of ideas but a communism of money.  They want to censor people on any reason other than fact (because they have no fact to defend themselves with).  “Marxist communists” want to dictate opinions but never to listen to facts.  They are professional (money making) quacks.  God knows how long they will continue to be lauded.  What’s wrong is allowing a freedom of speech on unsubstantiated opinion, but permitting fashionable bigots to censor facts that contradict their popular opinions.  There are many ways to sort this problem out.  Bullets.  Vitriol.  A censorship of opinion to clear a breathing space for an airing of facts.  A discrimination between opinion and facts based on objective evidence.  These methods traditionally “don’t work” because they don’t maintain hegemony, in other words they’re like the Ancient Greek style method of democracy (daily referendums on issues, not a choice between two near-clone parties once every four years) which was considered too “volatile” or “insecure” by the founders of dictatorship or “modern democracy”.  (Daily referendums are perfectly possible logistically and technologically, with the same systems as the secure databases that allow millions of people to safely access online bank accounts daily.)  If you look at how modern “democracy” works, with people forced to start campaigns and effectively fight propaganda wars for years against status quo for every tiny revision to nonsensical groupthink-error laws, it’s very similar to dictatorship.  Its’ whole aim is to hinder change as much as possible, not to aid or objectively facilitate it!  No wonder why people get tired of political propaganda.  Politics, like string theory, attracts the Stalinist mind-set.

Sir Basil Henry Liddell Hart, Why Don’t We Learn from History?, PEN Books, 1944; revised edition, Allen and Unwin, 1972:

“If a man reads or hears a criticism of anything in which he has an interest, watch whether his first question is as to its fairness and truth. If he reacts to any such criticism with strong emotion; if he bases his complaint on the ground that it is not in ‘good taste,’ or that it will have a bad effect – in short, if he shows concern with any question except ‘is it true?’ he thereby reveals that his own attitude is unscientific. Likewise if in his turn he judges an idea not on its merits but with reference to the author of it; if he criticizes it as ‘heresy’; if he argues that authority must be right because it is authority; if he takes a particular criticism as a general depreciation; if he confuses opinion with facts; if he claims that any expression of opinion is ‘unquestionable’; if he declares that something will ‘never’ come about, or it is ‘certain’ that any view is right. The path of truth is paved with critical doubt, and lighted by the spirit of objective enquiry… We learn from history that in every age and every clime the majority of people have resented what seems in retrospect to have been purely matter of fact … We learn too that nothing has aided the persistence of falsehood, and the evils resulting from it, more than the unwillingness of good people to admit the truth … Always the tendency continues to be shocked by natural comment, and to hold certain things too ‘sacred’ to think about. I can conceive no finer ideal of a man’s life than to face life with clear eyes instead of stumbling through it like a blind man, an imbecile, or a drunkard – which, in a thinking sense, is the common preference. How rarely does one meet anyone whose first reaction to anything is to ask: ‘is it true?’ Yet, unless that is a man’s natural reaction, it shows that truth is not uppermost in his mind, and unless it is, true progress is unlikely.”  (Emphasis added.)

BBC and Guardian newspaper and others who read their copy unfailingly manage to swallow the liars propaganda (hook, line and sinker), thus taking the wrong side because  journalists and their readers always find fiction more appealing and saleable (££££$$$$££££$$$$, money) than facts!  Thus, they prefer utopian hopeful fantasies to tough reality. They are ideologues who want to believe in contrived propaganda that reinforces their ideals:

“… fashionable trends of thought and ideas are carefully separated from those which are not fashionable … what is not fashionable will hardly ever find its way into periodicals or books or be heard in colleges.  Legally your researchers are free, but they are conditioned by the fashion of the day.  There is no open violence such as in the East; however, a selection dictated by fashion and the need to match mass standards frequently prevent independent-minded people from giving their contribution to public life. There is a dangerous tendency to form a herd, shutting off successful development. I have received letters in America from highly intelligent persons, maybe a teacher in a faraway small college who could do much for the renewal and salvation of his country, but his country cannot hear him because the media are not interested in him. This gives birth to strong mass prejudices, blindness, which is most dangerous in our dynamic era.”

– Aleksandr Solzhenitsyn’s 1978 Harvard address (section discussing the dictatorship by fashion in the Western media).