Frontiers of Pachydermy

Quantum theory takes this subjectivity  to a strange extreme:
 There is no elephant,

 only blind men.

-- George Johnson, Fire in the Mind (1995), p. 140

For more about our bulky friends the elephants, click here!

       Here come the Elephants

~

That epigram, pried from its context,  has a pleasingly Minimalist ring, rather like “Garfield minus Garfield”, though in our case  what is missing  is any elephant.

As for the sense in context:  The elephant represents a sought-for deterministic objective value for some quantized parameter (such as position, velocity, polarization).  The blind-men are the scientists or their measuring-instruments.  To their dismay, they discover that no such value exists:  the elephant is absent.

~

String theory, too, has (as in the parable of the blind-men) suffered from an overplus of versions, none canonical.  But now:

For the five string theories,
M-theory serves as  the unifying pachyderm.

Veracity, Verifiability, Vindication

[That is an ascending series.  Some things that are true, may yet be inaccessible to us -- temporarily, or forever;  a veracious person is someone who asserts only what he sincerely believes to be true (and -- for this quality to have any practical value -- has reasonable warrant for so believing, reasonable relative to the contemporaneous state of the art.)

Verifiable means that the assertion is ‘in the running’ for being experimentally (or proof-theoretically) confirmed, even though these happy results have not yet eventuated.

Vindicated means that the result has been supported, whether by (theory-supported) experiment, formal proof, or revelation.]

[Original post from 7 VI 2015]

A crisp, concise op-ed, in this morning’s NYTimes, “A Crisis at the Edge of Physics” by Adam Frank and Marcelo Gleiser (both professors of physics), states the case against (over-cantilevered or under-buttressed) speculation, not only for string theory (which has notoriously come in from a lot of pushback;  see Lee Smolin, The Trouble with Physics), but for supersymmetry generally.  The authors note that, as of even date, “no supersymmetric particles have been found” (perhaps they are hiding out in a back room, playing poker with the Higgs boson).  So far as that goes, not a problem;  plenty of propositions in math and science took centuries or even millennia to settle.  What disturbs the authors is that some champions of supersymmetry -- the jusqu’au-boutistes, we might call them -- may simply move the verificationist goalposts.

Some may choose to simply retune their models to predict supersymmetric particles at masses beyond the reach of the Large Hadron Collider’s power of detection -- and that of any foreseeable substitute.

Exactly the same concerns were voiced, a good decade earlier, by the mathematician-physicist Roger Penrose, in the section “Can a wrong theory be experimentally refuted?” (p. 1020 ff.), in The Road to Reality (2004), concerning “un-Popperian” practices in physics.

If that were only a problem for one avenue at the forward fringes of physics, that would not be a problem for most of us  as we bustle about our daily chores.  Yet the authors further suggest that certain well-traveled avenues  are actually cul-de-sacs:

The standard model, despite the glory of its vindication, is also a dead end.  It offers no path forward to unite its vision of nature’s tiny building-blocks with … gravity.

What really bothers the authors is something that goes well beyond physics:  “the specter of an evidence-independent science”.   And that specter has been haunting the West for some time, and increasingly reaches into the headlines, as witness the countermovements to the theses of natural selection or of global climate change.

Not being a physicist, I have no right to comment;  but, at the margins, this:

(1) The larger cultural worry, is the dissociation of the notion of Truth überhaupt  from that of Evidence and Argument. In that perspective, we would deplore the demand to dissociate theory from experiment.

(2)  Yet -- Do not forget  Einstein’s classic crack in 1919, anent the possible negative results of an experiment purporting to validate or refute General Relativity:  “Da könnt’ mir halt der liebe Gott leid tun.  Die Theorie stimmt doch.”  (Informal translation:  "I'm right.  Bite me.")

Die Theorie stimmt doch!

The consensus of scientific history (for right reasons or wrong)  has been to applaud  those cheeky remarks .

~

Einstein was speaking of his theory of gravitation.  But similarly for particle physics.

Compare, re Feynman and Gell-mann’s joint article “Theory of the Fermi Interaction” (written in 1957, and subsequently published in Physical Review):

The V - A theory was in disagreement with more than a half dozen experimental results on beta-decay,  but it was so beautiful  that the authors proposed it anyway, suggesting that all those results were wrong.

-- Harald Fritzsch, introduction to Murray Gell-Mann: Selected Papers (2010), p. 5

And:

The Standard Model … has been driven largely by certain powerful consistency requirements, hard to satisfy in such theories.  In order to appreciate something of the force behind these consistency requirements (which continue to drive the more modern speculative theories, such as string theory), we shall need to look at the structure of quantum field theory. … The theoretical requirements appear to be so tight  that it might seem almost incidental that these answers are actually in excellent agreement with experiment!

-- Roger Penrose,  The Road to Reality (2004), p. 655-6

And more generally:

Polanyi delighted in drawing attention to cases where the scientific community ignored or waved aside or explained away  seeming counter-evidence to accepted theories.  He seems to have felt that a scientist would abrogate his personal responsibility for his beliefs  if he allowed them to be at the beck and call of experimental results.

-- John Watkins, Science and Skepticism (1984), p. 29

Nor must we wait until our own extravagant age of post-modernism and M-theory, to find ourselves confronted with an “All is Permitted” ethos in the realm of physics.

Karl Pearson, as a pioneer of statistical thinking in a wide range of fields, is in that respect  a representative of a hard-headed, just-the-facts-ma’am, shut-up-and-calculate approach to messy realities.  But when doing (what he thought of as) physics, his Romanticism, which early on was a major strain of his make-up, got the better of him.   In the years around 1890, he theorized about atoms in terms of the then-regnant ether theory:

He spoke  not of causation  but of analogy, indeed “analogies … of the vaguest description”, and in the context of this paper, his doubts about the human capacity to get at real objects or real causes  functioned as a license to invent … Since his ether model  so far  had strange, almost inconceivable properties, he discarded physical plausibility as a criterion of a good theory.

-- Theodore Porter, Karl Pearson (2004), p. 187

"You see it's all simply a matter of ether-squirts ..."

~

Working the equations of physics to their long-reaching logical conclusions, continually leads to apparent absurdities:  negative energies or frequencies, unobserved particles, particles moving backwards in time, a Hobson’s choice between acausality or indefinitely-proliferating alternate universes, and miscellaneous infinities.  Some physicists shudder at such;  others grin and say “Bring ‘em on.”  (Unfortunately, the latter are the ones favored in the popular media -- the phenomenon of Physics Porn.)  The problem is deciding when that is just the way Nature (inscrutably) actually works (in which case you have made a major discovery), and when it is merely absurd.  Will the Higgs boson turn out to have been more like the positron (born from the forehead of Dirac’s mathematics) and the pion (brain-born from Yukawa), eventually found in everyday space, or  instead  like the cute-sounding but still-missing photinos, squarks, and pentaquarks?

[Update July 2015]  Bzzt!  No sooner had I posted that, than experiments claim to have spotted one of the elusive critters:

http://www.nature.com/news/forsaken-pentaquark-particle-spotted-at-cern-1.17968

So here is the larger temptation -- the intellectual Occasion of Sin:

Beginning several decades ago, comparing the results of experimentally well-verified physics  with the predictions of the equations, scientists marveled at what was memorably dubbed “the unreasonable effectiveness of mathematics”, summed up by the epigram “the equations seem to give us more than we put into them;  they seem to be wiser than ourselves”.   But The Edge beckons when we start to conclude, that if our favorite equations predict something, then that something must be so (if only in the Multiverse) -- even if, to the guys in the lab, it doesn’t seem physically reasonable.

As Penrose puts it:

What is the physical justification in allowing oneself to be carried along by the elegance of some mathematical description  and then trying to regard that description as describing a ‘reality’?

-- Roger Penrose,  The Road to Reality (2004), p. 670

That question takes us back  to a very old debate -- as old as poetry :  What is the relation between Beauty and Truth?

In that essay, we concluded that, in a sense, ‘beauty’ (in a rather austere sense of crisp symmetric elegance, having more to do with the Parthenon than with a Miss America pageant or a Turnerian sunset) does characterize any deep theory in the mathematicized sciences -- but only in retrospect, after years and decades of its practitioners coming to appreciate its depth; the theory does not wear its beauty on its sleeve.

Thus, even in the case of the (relatively) well-behaved, now-long-familiar poster child of particle physics, QED:  Paul Dirac, the pioneer of QFT, wasn’t buying it.   In response to a 1936 experiment (by Shankland) which suggested (incorrectly, as it turns out) that energy need not be microscopically preserved,

Dirac immediately jumped at this opportunity to disown QED, claiming “because of its extreme complexity, most physicists will be glad to see the end of it."

-- Matthew Schwartz, Quantum Field Theory and the Standard Model (2014), p. 247

~

Taking physics on faith

Penrose again, concerning a couple of signature contributions by Richard Feynman -- probably the educated public’s favorite hip physicist since Einstein:

The path-integral approach is, it seems, almost wholly dependent upon a faith that the wildly divergent expressions that we are presented with (like the divergent series above) actually have a deeper ‘Platonic’ meaning  that we may not yet properly perceive.

-- Roger Penrose,  The Road to Reality (2004), p. 670

Theophysical note:  Here we see a reference to “faith”;  its truth-functional content may be roughly equivalent to “working assumption”, but since we are indeed dealing with such deep and ultimate matters of Platonism, the theological overtone is not actually out of place. 

Similarly, my casual reference to “revelation” above, as denoting one of various routes to knowledge, was not flip.  Compare, from our hard-headed flinty-eyed philosopher of science:

If  we had a hot line to the Author of Nature, and if we had a clearly formulated IP [for which see below], an excellent question to put to him would be:  Is our IP true?  If he answered ‘Yes’, we could happily set a computer to work to print out all those h[ypothese]s that are singled out by our evidence  in conjunction with this authoritatively endorsed IP.
-- John Watkins, Science and Skepticism (1984), p. 93

And if that strikes anyone as credulous, note that most of us largely treat computers as oracles as well (e.g. in the proof of the Four-Color Theorem, or any of innumerable unsurveyable and possibly preposterous simulations).

Back to the sadder-but-wiser Penrose:

Even that archetypal renormalizable theory, QED, is not actually a finite theory, even after renormalization.  How can this be?  Renormalization refers to the removal of infinities from finite collections of Feynman graphs.  It does not tell us that the summation of all these resulting finite quantities is actually convergent. … In fact it is not finite, but has a ‘logarithmic divergence’.

-- Roger Penrose,  The Road to Reality (2004), p. 680

(Logarithmic divergence is comparatively mild, but it still gets where it's going -- an unphysical infinity -- in the end.)

As for the next step beyond QED (which is part of the Standard Model), QFT:

Strictly speaking, quantum field theory … is mathematically inconsistent.

-- Roger Penrose,  The Road to Reality (2004), p. 610

~

But let us set aside quantum mechanics, that known maze of paradox, along with its ever-more-speculative successors.  Surely matters stand better in the case of classical mechanics and electromagnetism, along with their tool-of-all-work, the venerable Lagrangian, which dates back to the eighteenth century. 

Yet even here, Penrose demurs:

In modern attempts at fundamental physics, when some suggested new theory is put forward, it is almost invariably given in the form of some Lagrangian functional. … However, I must confess my unease … The choice of Lagrangian is often not unique, and sometimes rather contrived … Even the Lagrangian for free Maxwell theory … has no obvious physical significance. … Moreover, the ‘Maxwell Lagrangian’ does not work as a Lagrangian unless it is expressed in terms of a potential, although the actual value of the potential, A, is not a directly observable quantity. … In most situations, the Lagrangian density does not itself seem to have clear physical meaning.

-- Roger Penrose,  The Road to Reality (2004), p. 491

Nor is Penrose a professional maverick or skeptic.   After all, the book we’ve been quoting from clocks in at over a thousand pages, and is subtitled “A Complete Guide to the Laws of the Universe”;  you wouldn’t do that if you thought physics was a crock.

~

Simply as an assertion, the Weyl curvature hypothesis  is perhaps more like a claim for ‘an act of God’  than a physical theory.

-- Roger Penrose,  The Road to Reality (2004), p. 769

Rule of Thumb:

Physics advances by dint of Physicists’ Encyclicals.

These are almost never arrived at purely deductively;  nor as the result of conclusive, slam-dunk experiment, leaving no leeway for doubt of validity nor variation in interpretation(**); yet neither do they come out of nowhere.

[**:   That classic 1919 experiment, about which Einstein was so dismissively cocksure, was not actually so probative as the newspapers made out.  Worse yet, that alltime- irreproachable über-icon of experimental virtuosity, the Michaelson-Morley experiment, traditionally cited as crucial for Special Relativity, did not really quite have the widely-advertised null result.  Lindsay and Margenau, in their history of physics, note this fact with some embarrassment, since so much of what they have to recount -- and which they do recount -- rests upon that pedestal;  they keep mentioning it with a proviso.  And at an even more elementary level in cosmology, the experimental results that led to the Red Shift principle: when Steven Weinberg painstakingly went over the actual original data, he pronounced himself baffled as to how Hubble ever extracted his famous monotonic relation from them.]

Schrödinger’s equation -- Feynman’s path-integrals -- the laws of thermodynamics:  inspired guesses, which awaited the mathematicians to tidy things up.

-- Not trying to debunk, here;  simply being historical.

(Feyerabend, too, was long  historical  in this sense, before he went over to the dark side.)

~

Donning our old lexicographer’s hat, let us look a bit more into the matter of vocabulary, the Wortfeld of terms for justification. 

Our negative result so far, entirely in line with Hume’s, is that, without an inductive principle, there can be no legitimate ascent from level-0  [i.e., things like “yellow patch, for me, here, now”] to level-1, or from level-1 to level-2, and that any inductive principle strong enough to “legitimise” the ascent  could not itself be legitimised.   If that is so, then it is obvious that there can be no legitimate ascent to still higher levels.

-- John Watkins, Science and Skepticism (1984), p. 105

In the following, we see a fine distinction drawn between justification and “vindication”.

The philosopher John Watkins imagines a principle, call it the Inductive Principle, which would answer Hume’s objections, to the satisfaction of inductivists.  What would then be the status of the IP?   He distinguishes several possible theses :  that it is “synthetic and true a-priori”, “synthetic and provable by a transcendental argument” (which latter turns out to be little more than “Well, it seems to work”), and:

*  IP is synthetic and empirically justified.

*  IP is synthetic, and, although it cannot be justified either a priori or a posteriori, it can be vindicated.

-- John Watkins, Science and Skepticism (1984), p. 93

The verb vindicate is slightly odd here;  usually it has moral overtones, of someone having been right against opposition or against the odds.   You verify someone’s age on his driver’s-license;  you validate a parking-stub; you vindicate a statesman’s course of conduct.

The term justification also has a richly complex ethico-theological usage in Christianity, quite opaque to an outsider.

~

More fine distinctions, this one semi-defined on the fly:

One’s degree of rational assent to a hypothesis should be controlled by its degree of confirmation (‘confirmation’ being understood in some quasi-verificationist or probabilist sense).

-- John Watkins, Science and Skepticism (1984), p. 118

Watkins then spins off into the world of proofs-and-refutations, abduction, and the like:

The sought-for relation between e[vidence] and h[ypothesis] is now inverted:  instead of an upward, quasi-verifying inference from e to h, we have a downward, explanatory derivation of e from h.

-- John Watkins, Science and Skepticism (1984), p. 119

Note those squirrely “quasi”s, by the way.  For all the wealth of the verificatory Wortfeld, no term seems quite to fit.

~

We have been focusing on physics;  but analytic philosophers have long discussed these matters in great depth.  A few representative teaser-quotes, giving some extra vocabulary, and the flavor of the debates:

The great contribution of [Quine’s “Two Dogmas of Empiricism”] was that it offered an essentially verificationist account of language  without committing the logical-positivist error of supposing that the verification of every sentence could be represented as the mere occurrence of sense-experiences. … Proof, which is verification by inference alone, thus becomes a limiting case, or a distinct species.

-- Michael Dummett, “What is a Theory of Meaning? (II)”, in: Evans & McDowell, eds., Truth and Meaning (1976), p. 111

… notorious problems about the connection between corroboration and verisimilitude …

-- Susan Haack, Evidence and Inquiry (1993), p. 105

Note here that, within the genus of positive instances, the term “confirming instance” is disastrously ambiguous  as between a supportive  and a nonsupportive species of positive instances.  By the same token, logical mischief has been wrought by the weasel word “verification”  and the equivocal verb “verify”.

-- “Is Falsifiability the Touchstone of Scientific Rationality”, in: Adolf Grünbaum, Collected Works, vol. I (2013), p. 15

[Update Dec 2015]  Physicists are beginning to get seriously perturbed by all this.

A Fight for the Soul of Science

https://www.quantamagazine.org/20151216-physicists-and-philosophers-debate-the-boundaries-of-science/

String theory is at the heart of a debate over the integrity of the scientific method itself.

http://www.nature.com/news/feuding-physicists-turn-to-philosophy-for-help-1.19076

[Update 19 Jan 2017] Philosophically on a more modest level than any of these "V's", is simple reproducibility of experiments --a minimum requirement for verifiability.  But there are problems even with that.  A new study of reproducibility released its results for the first five classic cancer-related experiments whose re-performance was attempted:  five experiments, five failures.   Background:

Cancer reproducibility project releases first results

The Reproducibility Project: Cancer Biology launched in 2013 as an ambitious effort to scrutinize key findings in 50 cancer papers published in Nature, Science, Cell and other high-impact journals. It aims to determine what fraction of influential cancer biology studies are probably sound — a pressing question for the field. In 2012, researchers at the biotechnology firm Amgen in Thousand Oaks, California, announced that they had failed to replicate 47 of 53 landmark cancer papers2. That was widely reported, but Amgen has not identified the studies involved.

Perhaps the clearest finding from the project is that many papers include too few details about their methods, says Errington. Replication teams spent many hours working with the original authors to chase down protocols and reagents, in many cases because they had been developed by students and postdocs who were no longer with the lab. Even so, the final reports include long lists of reasons why the replication studies might have turned out differently — from laboratory temperatures to tiny variations in how a drug was delivered.

http://www.nature.com/news/cancer-reproducibility-project-releases-first-results-1.21304?WT.ec_id=NATURE-20170119&spMailingID=53225513&spUserID=MjA1NjgwMjUyOAS2&spJobID=1083504884&spReportId=MTA4MzUwNDg4NAS2

String Theory for Trump Voters

A high-powered team of cybernetic linguisticians have run detailed studies and concluded that, from the standpoint of syntax,  Republican Presidential front-runner talks like a fourth-grader:

http://www.rawstory.com/2015/08/donald-trump-talks-like-a-4th-grader-linguistic-analysis/

That, as regards vocabulary and grammar, merely.  From the semantic-pragmatic standpoint, he speaks like a schoolyard bully.

~

This, however, is by no means to criticize our (potential) next President.   (How foolish would that be, after all;  he’ll have the power to revoke our Junior Woodchuck Blogger License.)   Nay more, we have concluded that it is time to board that train before it leaves the station;  and accordingly, we are preparing a series of scholarly monographs, written at a fourth-grade level, for exactly this audience. 

The debut volume is called String Theory for Trump Voters, Simply Explained.   It responds to an express desideratum from the top.  “So what are these stupid little … stringy things, anyway?” the candidate mused in a recent broadcast.  “Sounds totally bogus!”

(A prerequisite for this opus  is the prequel, written at a third-grade level,  Quantum Field Theory is our Friend!)

Other titles in the series:

The Homoousian Controversy:  a Trumponomic perspective.

The Gospel according to The Donald.

In a junior-auxiliary line aimed at lower-information voters will be versions of the smash-hit “for Dummies” series, rewritten in Googolian “Simplified English”.   Offerings include:

“Computers for Dummies” for Imbeciles

“Intermediate Arabic for Dummies” for Deaf-mutes

and the unique, twice-distilled

“ ‘Algebraic K-Theory for Dummies’  for Morons”  for Trisomy-21.

Major credit cards accepted.

Eka-“Rubicon”

Apparently I never posted about the worthy but aborted TV IC series “Rubicon”.  But the new Showtime series “Homeland”, which piloted to rave reviews, has been compared to that effort.  It debuts tomorrow night;  just a heads-up.   I watched the pilot online;  it is quite good.

For background, here are some emails I sent to friends about the earlier series.

~~~~~~~~~~~~~~~~~~~~~~~~~

Here's an über-nerd response to the premier of "Rubicon" (about cryppies & über-IAs):

In the first shot, we see the central character -- a rumpled nerd -- come in to work and lay down the light reading he'd been doing at home.  The title is: "String Theory".

(A) At the most elementary level, for a general audience, this says:  "Theory, huh.  Guy's smart."
(B) At the next level, for those more clued-in, there is more of a shock:  the guy must be *really* smart.  For, string theory is notoriously the most mathematical part of physics -- the only Fields medal (math equivalent of the Nobel) ever awarded to a 'non-mathematician' was awarded to the physicist who powered string theory.
(C)  But at the next level -- the thing is ridiculous.  String theory, though hegemonic on campuses, has painted itself into a corner, and is provoking a reaction.  Notoriously, it has found *no* applications in the real world.  Hence, if you are an IA/cryppie nerd, you wouldn't go near it:  no-one but a virtually fulltime string-theorist understands string theory; as someone who (the show contends) must know everything about everything (including, crucially, Latin, in this episode) you certainly wouldn't waste your precious braincells on *that*.  (Contrast basic quantum mechanics, which has serious applications in quantum cryptography.)


There was an even more absurd moment when one of the supposed geniuses says, "Maybe it's a syllable-cipher" (re a set of...*four* objects).

BTW... despite the brainy sheen, judging by the tenor of the ads, the show is really aimed at audience (A).

~~~~~

Rubicon...
Okay, it's not exactly good, but I've got to watch something, and it just got a little bit better.
Bonus: The moderately intelligent show  elicits some quite intelligent commentary:

http://www.avclub.com/articles/the-truth-will-out,44856/

Also, Mystery-Science-Theater-style, commentary funnier than the show:

http://nymag.com/daily/entertainment/2010/09/rubicon_recap_whos_the_boss.html

~

~  Posthumous Endorsement ~

"If I were alive today, and in the mood for a mystery,

this is what I'd be reading: "

I Don't Do Divorce Cases

Murphy on the Mount.

(I am J. v. Neumann, and I approved this message.)

~         ~

~

~~~~~~~~~~~~~~~

The Rise of Popcult

Not the spread, note: the rise -- in quality and aspirations.  As witness -- Rubicon.

Scene:  the mostly darkened offices of a key intelligence facility. It is late at night; alone, one dedicated analyst sits in a tiny office, monitoring a live feed  from half a world away.

Suddenly he startles -- leaps to his feat -- exits the room in alarm.  The viewers are confused:  Has he heard possible assassins breaking into the building?  It is unclear, as he gazelles up the stairways from floor to floor, shouting to see if anyone is there.   At last, from the back of a little library, a small voice pipes up.   It turns out that what our analyst desperately instantly needs is -- a linguist!  (Ever happen to you?)

“Do you speak Urdu?” he asks breathlessly. 
-- She looks at him quizzically.  “Doesn’t everyone?”  
-- Together they go to the little room.  Her mastery of Urdu is immensely attractive;  our analyst is smitten.

And in the course of their monitoring the feed (of a wedding in Pakistan), our analyst refers -- and of course the linguist understands -- to the “walima”.

Now, this is a standard Arabic word (maybe Urdu too), but not all that common;  I tried it flat-out on some colleagues and they were not sure.  It means ‘feast’ (here, a wedding feast).   And the writers of “Rubicon” felt they could casually toss such a word into the script.  (“Doesn’t everyone?”)

[Fn:  A horrible alternative is that, rather than this little-known word, the actor was butchering the pronunciation of a word common enough to have been borrowed into English:   ulema.  But this possibility we put far from our mind.]

~~~~~~~~

Sines of the Times

A note re the allusion to String Theory as a sort of fashion accessory in the TV show “Rubicon”, which pitches itself (and is publicised by others), as a brainy thriller for smart people (though it sadly falls short).

And now the current issue of The Economist features a fullpage fullcolor ad displaying a hip young fellow (who could almost be the Uberanalyst Will on AMC, with his ever-present messenger-bag) sporting (beneath a dark woollen sports coat)  a black T with the message:

            I  [icon] String theory

The roundish icon is in the syntactic place of the stylized heart that has come to represent the verb ‘love’ in slogans (sometimes retro-rendered as ‘heart’ in prose);  connoisseurs will recognize the illustration which appeared here and there in the more rarified press a while ago, being a simplified stab at depicting, or rather alluding to, the celebrated Lie group and polytope “E8”, a truly wiggy object found in (mathematical) nature, and which many string theorists identify as being found in physical nature as well, in that its Cartesian product with itself serves as -- well, I scarcely need to remind you all of this, but in the homely words of Wiki,

the gauge group of one of the two types of heterotic string and is one of two anomaly-free gauge groups that can be coupled to the N = 1 supergravity in 10 dimensions. E₈ is the U-duality group of supergravity on an eight-torus (in its split form).

But of course, you knew that.

So -- what is the ad for?  The TV show?   T-shirts?  Messenger bags?  Save-the-environment?  Ph.D. programs in geometrical physics?    --   None of the above.  But rather for a new sub-website run by the Financial Times  -- which, note, is not actually identified in the ad, save by its acronym FT (which for me has long connoted First Things, another serious publication, but not one for fashionable twentysomethings):

www.ft.com/smart

“Smart”.  Right.  Now, I’ve got no bone to pick with Smart, save as a slogan -- recalling “Bright”, the suggested euphemism for “Atheist”, aggressively pushed by the impossible Richard Dawkins.  And I was just about to pen one of my patented Cato-the-Elder O-tempora rants, when I thought -- wait.  Smart.  What if?  We could use some smart.  And, atremble with anticipation, I typed in the URL.

[…. time passes…]

And this is what you’ll find, on that "Smart" Site:

Exclusive this week:

Lucy Kellaway talks to Elle Macpherson  about bras and brands and being The Body.

O tempora, O garbage bag.

  

What Realism is Not

I just stumbled upon this;  and wondered, My gosh, might anyone imagine that, by Realism, I meant that?

Richard Rorty, Philosophy and the Mirror of Nature (1979), p. 334:

In just what sense were there physical features of reality  capable of being represented accurately only by differential equations, or tensors, before people thought of so representing them?

No mathematical physicist in his senses holds this delusion;  Rorty is tilting at a straw man.  The example of the discovery of the equivalence of wave mechanics vs. matrix mechanics, discussed previously, is well-known.   And one historian of physics opined that, if the seat of his pants told him anything, it was that the tensor formalism for General Relativity would eventually be replaced by something better.

Nor need two very different-looking approaches to the same thing  be mere historical contingencies, as was the case with wave mechanics vs. matrix mechanics, or the Chomskyan Extended Standard Theory vs. Generative Semantics (in Chomsky’s classic phrase, “notational variants”).  Rather, both views may be built into the very subject itself -- provably two sides of the same coin.  This is the vast and fascinating mathematical principle of Duality, which deserves an essay of its own.  In string theory, it is called Maldacena duality, and is a deep idea.

We could call the straw-man, overreaching philosophy “methodological Realism”, except that the phrase sounds too respectable, too much like an aspect  rather than an exaggeration  of  Realism.   Accordingly we shall dub it Tinkertoy Realism.

At all events -- to answer Professor Rorty's initial question:  planetary orbits existed prior to Kepler and Galileo,  and the electron prior to Millikan, in much the same sense that the nightingale antedates Keats.

More on ‘Memento’

[A follow-up to this post]


 The fact that one can colorably argue for so many alternative endings, suggests that, as with String Theory purporting to explain Everything or maybe nothing, or like the search for an all-too-ubiquitous “John G”, the problem has too many open parameters:  we seek in vain to escape from these excessive degrees of freedom.

            The classic detective tale illustrating the possibilities of multiple interpretation -- of false bottoms beneath falser ones -- is G. K. Chesterton’s “The Honor of Israel Gow”, one of the Father Brown stories.  What makes that story -- splendid in its technical construction -- something more than an epistemological curiosity, is Chesterton’s never-wavering moral seriousness.  (You can read that story here.)

*

            Director Nolan tried another intricate box-within-boxes puzzler (in this case, dreams within dreams) in “Inception” (2010).   That he was unable, despite a much larger budget, top actors, good cinematography, and many more years of experience, to match the tautly-wound intensity of “Memento”, highlights that earlier achievement.   The dedication, the moral motive force, and sense of personal urgency, that propel “Memento”, are lacking in the later work, and leave it a mere puzzle-box.

            And yet, with passage of time, and no replies to the pointed plot-questions, I now suspect that “Memento”, for all its intensity, and for all our digging, adds up to less than it promises.   We might exclaim, with Swann:  “Dire que j’ai gâché des semaines de ma vie, pour un film qui n’était pas mon genre!”

*

            Our son said:  “Since you liked ‘Memento’, try ‘Shutter Island’.”   And indeed, there are striking parallels, most notably in the look-and-feel of the central character -- a hunted, haunted figure, ostensibly engaged in detective work.  And that far-fetched possible interpretation of ‘Memento’ I mentioned earlier, whereby it parallels the second, revised ending of ‘The Cabinet of Dr. Caligari’ -- the bad guy is actually a psychiatrist who has been attempting to help the protagonist, who turns out to be a killer -- is realized here.

["Shutter Island" just received a very bad review:
http://latimesblogs.latimes.com/lanow/2011/01/meat-thermometer-stabber-sentenced-to-more-than-40-years-in-prison.html  ]

E8: a Riposte (concluded)

Let us examine a bit more closely  Synge’s picture of physics as bricolage,  where theories have the intellectual status of just-so stories, and are really little more than pragmatic techniques, or tools -- Newtonian mechanics and relativistic mechanics each useful in its own sphere, like screwdrivers and spoons, but of little interest in their own right.   Now, this is not to knock the status of a toolkit -- my respect for competent carpenters and electricians borders on reverence -- but fundamental physics is not like that.

            Synge presents the Newtonian view as having not been replaced or refuted by relativity;  it rules as before in its own realm.  Newton’s good for some things, Einstein for others, and Wiccan no doubt for others still.   But this view assumes a confusion.  For it is not the case that Newtonism and relativity are independently valid in their own way but incompatible;  rather, Newtonism is the limiting case of relativity, in a way very familiar in mathematics;  its continued use in everyday life is simply a calculational convenience, a shortcut.   To continue the tool metaphore:  Einstein and Newton are not like screwdriver and pliers, but like a hammer, and an old shoe used as a hammer, good enough for the task at hand.

            Furthermore, it is a good thing, not a bad thing, when initially separate paths converge.  If you only know one way to climb a thing,  perhaps it is only a Potemkin mountain -- a paper-maché façade, hollow behind the north slope.   It is quite a relief -- and an ontological ratification -- to meet another mountaineering party that has scaled up the other side.

            The reader may be familiar with the story of how Schrödinger and Heisenberg separately found Rome by different roads.  Let George Gamow tell it, in Thirty Years that Shook Physics (1966), p. 3:

The simultaneous appearance of Schrödinger’s and Heisenberg’s papers  in two different German magazines … astonished the world of theoretical physics.  These two papers looked as different as they could be, but led to exactly the same results concerning atomic structure and spectra.

We are, in hindsight, not overly surprised by this, since by now we most of us accept that there is something there at the quantum level, something real, something other than subjective, to be described.   It is describable by two quite different mathematical approaches, much as our peak may be scaled by walking up the north face  or rappelling up the southern cliffs.    Nor is such ‘duplication of effort’ a waste of time, for  in this instance, not only the factual success, but even the approaches themselves retained their usefulness -- for determining energy levels, Schrödinger’s wave mechanics was calculationally more convenient; and Heisenberg’s matrix methods had the edge when it came to calculated the intensities of the radiated frequencies.   Or, alternately, P.A.M. Dirac, The Principles of Quantum Mechanics (4^th edn. 1958), p. viii:

Quantum mechanics … is known under one or other of the two names ‘Wave Mechanics’ and ‘Matrix Mechanics’, according to which physical things receive the emphasis in the treatment, the states of a system or its dynamical variables.

And (p. 115):

The Schrödinger form is the more useful one for practical problems, as it provides the simpler equations. … Heisenberg’s form for the equations of motion  is of value in providing an immediate analogy with classical mechanics.

Or again (R. F. Streater & A. S. Wightman, PCT, Spin & Statistics, and All That (1964), p. 4):

Throughout this book, states will be described in the Heisenberg picture of quantum mechanics.  The Schrödinger picture is much less convenient for the description of a relativistic theory, because it treats the time coordinate on a very different footing from the space coordinates.

And:

P.A.M. Dirac, The Principles of Quantum Mechanics (4^th edn. 1958), p. 311:

The Schrödinger picture is unsuited for dealing with quantum electrodynamics, because the vacuum fluctuations play such a dominant role in it. … They get bypassed when one uses the Heisenberg picture, and one is then able to concentrate on qualities that are of physical importance.

Dr. Matrix

Dr. Wave

Approaching an abstract but genuine reality from two different theoretical complexes  has its counterpart in different experiments, or different means of calculation, strengthen each other when they arrive at the same result.   Thus Einstein, in his annus mirabilis of 1905, when not inventing Relativity, found it worth his while  to “develop theoretically  three independent methods for finding Avogadro’s number.” (Abraham Pais, Subtle is the Lord (1982), p. 55.)   It was worth his while because, independently of our endeavors, this number is indeed there.

Summarizing:  For epistemology, the fact that two or more radically different approaches each manages to describe the phenomenon of interest, reassures us that we really do have our arms around this thing.   The lesson goes over, I would submit, in cases where what is being described is nothing so tangible as an atom (which Rutherford reportedly saw in front of his face as plainly as a spoon), but rather a four-manifold, or a simple Lie group.

~ ~ ~

Afterword.

I recently happened across the following curious passage:

The algebras G_2, […] E_8  are called exceptional.  In 1945, Chevalley remarked  that the existence of these algebras  is a brutal act of Providence  which we must accept blindly.  Perhaps this should be revised today  to assert that the source of these algebras  is the wisdom of the Deity  in allowing the Cayley numbers to exist.

-- Irving Kaplansky, “Lie Algebras”; in: T. L. Saaty, ed.  Lectures on Modern Mathematics, vol. I (1963), p. 126

~ ~ ~

There’s one further type of brane in M-theory  that is really surprising.  This brane is the edge of spacetime. … The photons at the edge of spacetime participate in supersymmetric E₈ gauge theory.

-- Steven Gubser, The Little Book of String Theory (2010), p. 95

E8: a Riposte (continued)

[A continuation of this.]

Synge waits until well into his second volume (J. L. Synge, Relativity:  The General Theory (1960), p.  104) to really let rip against Realism; and since he was himself very much a mathematical physicist, rather than an empirical experimenter, his testimony must be respected as coming from within the tent.  He distinguishes “Natural Observations” (NO) from “Mathematical Observations”, and opines:

Between NO and MO  there is a sharp and decisive break.  Only the simplest MO (counting) can be regarded as being NO also … Generally MO involve infinity (irrational numbers, differential calculus, and so on) and so lie outside physics and outside nature.

This is exactly the position of Kronecker (“Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk”).

He then delivers himself of a curious passage, which Irrationalists would seize on with glee (fortunately none of them are reading this):

The peculiar fascination of theoretical physics  lies in the art of forcing meaningful truth out of the meaningless equation NO = MO, which is a symbolic form of the assertion that natural phenomena obey exact mathematical laws.  The true inequality NO =/= MO should not be spoken above a whisper, because it is extremely dangerous.   If believed, it would sever mathematics from physics, and reduce both to sterility through lack of mutual fecundation.  It is whispered here only as an apology to those readers who expect to see the mathematics of relativity [which he presents in great detail] tied to the physics of relativity  by a strong chain of clear thought.  It cannot be done.

These ring like the Night Thoughts of a relativistic physicist, on the eve of taking his own life.

            Despite his conspiritorial tone in that passage, Synge was by no means alone in his reservations. Here is another anti-Realist view from the world of physics:

A. D’Abro, The Rise of the New Physics (1939), vol. II, p. 728:

A hyperspace is obviously a mathematical fiction; and waves that can be represented only in a fictitious space  must themselves be unreal.

Now here indeed is a statement that has been overtaken by events.  In the view of string theory, this hyperspace, far from a mathematical fiction, is a physical fact, the one we live in;  indeed, we must beware lest those compactified but very real extra dimensions someday unfurl in our faces.  --  The point here being, not to make any point whatsoever about cosmic geometry, let alone to proclaim the truth of string theory:  but simply to counsel against that “obviously”, when dismissing the Realist picture.

[concluded here]