Sunday, August 21, 2011

Minimalism in Physics

Truth is ever to be found in simplicity,
and not in the multiplicity and confusion of things.
-- Isaac Newton

In using the term “minimalism” in evaluating styles of physics, I am importing  into the philosophy of science  a term mostly associated with the arts.  The move may or may not be fruitful.  But here is a well-known parallel move, from Gerald “Mr. Themata” Holton, in The scientific imagination (1978), p. 7:
I have proposed … thematic analysis (a term familiar from somewhat related uses in anthropology, art criticism, musicology, and other fields).  ]

The whole enterprise of physics, from ancient times to today, is itself  in one sense  Minimalist, in that it seeks to sweep aside the riot of epiphenomena, and to discover underlying laws, from which that riot derives.  It does not so much banish the fullness of reality, as bracket it:  we hope later to derive much of it back, in an explanatory manner.  (Note:  Not quite the same thing as Reductionism.)

To some extent, all rational inquiry ‘minimizes’ -- idealizes, works with toy models, etc.   Some more than others -- economics notoriously so, tossing out so much bathwater that sometimes the baby goes missing.   Others roll up the sleeves of their labcoats and go in elbow-deep to the mess of reality, little bothering with economy or philosophy.   Chemists, in particular, seem perfectly content to potter about in labs, to discover stuff, invent stuff, patent stuff.  They literally multiply entities, in that they invent chemicals that weren’t there before.   Whether they thereby multiply them beyond necessity (mustard gas, thalidomide,  napalm, LSD) is a matter of individual taste.  But certainly the ethos is anything but austere.
And likewise, for the most part -- biology, geology, astronomy, engineering, what have you. 
But modern physics  raises parsimony to a central tenet, almost the prime purpose of the whole enterprise as currently understood.  This development being by now taken for granted among those of the guild, it may not be apparent how odd this really is.

The goal for some time has been the “Theory of Everything”.  This certainly sounds like a Maximalist program:  but really it is not.   For the knights who pursue this grail do not actually intend to explain any of the things that real people care about   and that motivated the enterprise of physics in the first place:  why the sky is blue, why snowflakes are the way they are, why clouds are shaped that way, what lightning is all about, why airplanes can fly…  (Purported explanations of these things exist, but the ones I’ve heard seem all fallacious.)   Instead, they want to wrap their arms around a passel of abstractions, so complex as to leave the plain man -- nay, any but the professional physicist -- behind many decades ago, and show that, at a still deeper level, they are all but facets of One Big Thing.  (Hedgehog physics, we might dub this.)  This is Minimalist, and ferociously so.

It may be objected:  All that is nothing but plain reductionism, which is simply to say:  Science.  No call to drag in an arts-related term like “Minimalism”.  -- But I believe there is an aesthetic dimension -- seldom mentioned in journal articles, though over-emphasized in popular writing -- which lies outside the bare logical necessities.  As,
“There shouldn’t be laws of physics,” Strominger maintains. “There should be just one law, and it ought to be the nicest law around.”
(Quoted in Shing-Tung Yau, The Shape of Inner Space (2010), p.  14.)

Gerald Holten, characterizing the attitude of Einstein (The scientific imagination, p. 281):

At stake was nothing less than finding the most economical, simple, formal principles, the barest bones of nature’s frame, cleansed of everything that is ad hoc and redundant.
In his own personal life, the legendary simplicity of the man was an integral part of this reaching for the barest minimum on which the world rests.


Central to the program is the “unification” of the various fundamental forces -- meaning, showing them to be symmetry-broken castoffs of an original single Force.    An analogy in evolutionary biology is explaining various related species  as having descended under various environmental pressures  from a common progenitor.   Only -- in physics, the enterprise is far more audacious than this analogy would suggest, if all you are thinking of are the breeds of dog, or the various canine species, or even the various land-mammals.   The forces are so fundamentally different in their phenomenology, that the task is more like tracing the common descent of the penguin, the echinoderm, and the paramecium.   Or even the mastodon, the gnat-swarm (considered as a sort of collective entity), and the sand-dune.   A tall order.

The reason so hubristic a program could come into existence despite the odds, is that it had an early success:  Maxwell’s unification of electricity and magnetism, back in the nineteenth century, truly a monument of the human intellect.  Now, later analysis has suggested that this success was something of a lucky fluke:  in the four macroscopic dimensions in which we reside, electricity and magnetism are both expressed by a vector.  You can not only analogize these, the one to the other, but calculate with them in the ordinary way -- say, forming their cross-product to get the Poynting vector.  In higher dimensions, electricity would be a vector and magnetism would be a tensor, and they would not play so nicely together.

The next success along these lines was far spookier:  the unification of electromagnetism with the “weak force”, into an unassuming-sounding entity called electroweak.   Now, this is far more bizarre than it seems. Electricity and magnetism were always rather like Batman and Robin, typically showing up together in the lab.  Whereas the weak “force” seems, to my untutored mind, like a force in some Pickwickian sense, like the  “force” of a metaphor in a poem.  A thing more different than electrostatic attraction or repulsion  can scarcely be imagined:  it deals neither in repulsion nor attraction, but rather in a handful of obscure and scarcely explicable processes such as beta decay.   Even to have conceived the project of their unification  was an act of extraordinary intellectual audacity;  the eventual success is, well, beyond any but specialist comprehension.

This new composite entity, this hippogriff, the electroweak, was subsequently unified with the “strong force”, yielding the hyperweak of today’s Standard Model.   The next -- and long elusive -- step, is the unification of that with gravity.   Now, to your average toddler, the natural analogy would be rather between electrostatic and gravitation attraction -- both, in their simple nonrelativistic forms, central forces obeying an inverse-square law    But your average toddler, like your average Nobel-Prize-winner-in-anything-but-Physics, would be mistaken.   And so the torch has passed to an ever-more-esoteric brotherhood, in particular  the magi of String Theory:  pale, spectral beings, who neither eat nor defecate, and whose results -- well, they do not as yet have anything so vulgar as actual verifiable physical results, mind you, but they do have theories, and conference papers, incomprehensible to all but the magi.  That does not mean they are on the wrong track;  perhaps they, and they alone, are on the right track, in which case, the more fools we.


A startling development in some corners of recent physics  is an actual ‘Maximalism’ -- basically, the catastrophic breakdown of any parsimonious project, yet not taken as a reductio ad absurdum of reductionism itself, but rather embraced, by amor fati (a fancy name for making the best of a bad bargain).   No longer can one really -- nor does one aspire to -- explain anything, since everything that might exist, does exist, and the (now uninteresting) facts of the matter in our own neck of the woods  can be chalked up to Selection Effect.  (We satirized this Rabelaisian Fay ce que voudras  here).   

Templeton-Prize winner Paul Davies,  in The Goldilocks Enigma (2006), p. 264, takes rather understated notice of this:
The disadvantage of the multiverse theory is that it invokes an overabundance of entities, most of which could never be observed, even in principle.  This profligacy strikes many people as an extravagant way to explain bio-friendliness.

Likewise, though for different reasons, the earlier Many-Worlds school (or cabal) of quantum theory,  in which entities -- again, entire universes in this case -- are multiplied, not simply beyond necessity, but beyond common decency.

The ethos of all this is atheistic -- a-anything, really.  It is perhaps no accident that Hugh Everett, an early pioneer of many-worlds, was (in Wiki’s words) “a committed atheist".  Or that the thélémisme of the distinguished hexagonal/pentagonal humanist  was taken up with gusto  by the diabolist Aleister Crowley, the stench of whose cinders may occasionally bother your nostrils, whenever a high wind blows up from Hell.

[Update 27 III 12]  Freeman Dyson in the current NYRB, reviewing a book by Margaret Wertheim about eccentric amateurs:

String cosmology is different. String cosmology is a part of theoretical physics that has become detached from experiments. String cosmologists are free to imagine universes and multiverses, guided by intuition and aesthetic judgment alone. Their creations must be logically consistent and mathematically elegant, but they are otherwise unconstrained. That is why Wertheim found the official string cosmology conference disconcertingly similar to the unofficial Natural Philosophy conference. The insiders and the outsiders seem to be following the same rules. Both groups are telling stories of imagined worlds, and neither has an assured way of deciding who is right. If the title Physics on the Fringe fits the natural philosophers, the same title also fits the string cosmologists.

[Note:  Dyson -- a notably fair man -- has long been a fixture of the Institute for Advanced Studies in Princeton; and the IAS, in recent years,  has been premier in string theory.  So Dyson's assessment here  is by no means that of an envious outsider.]

On the extra profusion of different string theories, a mathematician remarks dryly,

It was hardly an idea calculated to appeal to a man with a taste for desert landscapes  … There are more than 10^500 versions of string theory  lounging indolently about.
-- David Berlinski,  The Deniable Darwin (2009), p. 532-3

It will sometimes not be obvious, which proposals are Minimalist in spirit.  Thus, imagine some wretched Nominalist, who balks at the infinite, and proposes that the numbers needed for physics  are finite -- specifically, the field of integers mod a prime p (necessarily quite large, to accord with observation).   Finite’s gotta be simpler, more minimal, than infinite, right?  Roger Penrose retorts (The Road to Reality (2004), p. 359):
A physical theory which depends fundamentally upon some absurdly enormous prime number  would be a far more complicated (and improbable) theory than one that is able to depend upon a simple notion of infinity.
More precisely:   The problem is not essentially that the number is so large, but rather, with infinitely many primes to choose from, the choice would seem arbitrary:  in much the same way that the omniscient computer in  The Hitchhiker’s Guide to the Galaxy reveals, quite disappointingly, that the Meaning of Life is … “26”.


Differing from a theory-wide programatic theoretical minimalism, is a kind of personal cognitive-epistemological economy, described by Gerald Holton, The scientific imagination (1978), p. 158:
Fermi ordered the overwhelming and vast amount of knowledge  into a set of very few principles and ‘cases’, which allowed him to understand almost any new problem as an example of one of about seven primitive or primary physical situations.  Fermi would return throughout his career  to a listing or digest of the chief ideas in physics, which he had made when he first organized the field for himself as a young student.

Our own thoughts about such Leading Ideas in other areas, may be surveyed here.


A curious philosophico-cosmogonic anticipation of the TOE vs. Landscape divide  goes back several hundred years:

Leibniz … assure que la perfection de Dieu ne lui permettait pas de procéder d’autre manière que de la meilleure … mais Thomas d’Aquin sait que, créant du fini, un Dieu infini pouvait librement créer un nombre illimité d’univers différents, tous bons  et chacun commençant de manière différente.
-- Etienne Gilson, Linguistique et philosophie (1969), p.  163

And indeed, though Leibniz coinvented the calculus, we must say that, here, from a mathematical standpoint, it is Saint Thomas who is closer to the target.


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