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

Die fröhliche Wissenschaft (lo gai saber)

I wish to make a serious argument about the relation of the cosmos, God, and the human purpose.

But I wish to do so in a certan lightsome mood.

-- James Schall, S.J., The Order of Things (2007), p. 60

Ein Universitätslehrer, der sein wenig anmutendes Spezialfach  reichlich mit Witzen zu würzen pflegt [to “sow it with jokes”].

-- Sigmund Freud, Der Witz und seine Beziehung zm Unbewussten (1905 ff)

These could serve as  motto for this site.

~

David Riesman (The Lonely Crowd, 1961)  laments the impairment of the American spirit of playfulness   at the hands of post-Puritan sobersides:  “It may be a long time before the damage done to play during the era depending on inner-direction  can be repaired.”

Richard Rorty writes (Philosophy and the Mirror of Nature, II.iv.1):

The spirit of playfulness which seemed about to enter philosophy around 1900  was, however, nipped in the bud.  Just as mathematics had inspired Plato to invent ‘philosophical thinking’, so serious-minded philosophers turned to mathematical logic  for rescue from the exuberant satire of their critics.  The paradigmatic figures in this attempt to recapture the mathematical spirit  were Husserl and Russell.

Here the via mathematica and the via jocosa are counterposed.   Whereas for us, they intertwine  like the rose and the briar.

Thus Gerald Holton, in a review (reprinted in The scientific imagination) of the work of Lewis Mumford:

I was … delighted with Mumford’s … acknowledgement that there is a subjective and qualitative side to the doing of science  which scientists hardly ever talk about, the “intellectual playfulness and aesthetic delight” in scientific work, which can be an enormously important component of scientific motivation.

“Playfulness” was one of the favorite words of the Romance philologist (and my former teacher) Yakov Malkiel -- though you would not have known it to look at that hard-working, ever-professorial man, twice over an exile.   This was evident, not only in his writing style (which, for better or worse, has influenced my own), but in his actual etymological practice.  Certain cruxes of etymology, which had resisted the usual attacks of sound-law philology, he would attempt to explain as the free creation of the human spirit: and indeed, such bodacious onomastic hippogriffs abso-blumin'-lutely do exist.  This, in contrast to the sobersides scholar who would attempt to lautgesetz back to some obscure figment of hypothetical Vulgar Latin, or else claim Celtic or Klingon substrate -- thus missing the joke.

E.g., 

On the subject of “Deviations from l’arbitraire du signe”:

There arises the possibility of elevating playfulness to the same kind of pedestal  as economy and clarity, particularly on the strength of linguistic developments where emotional coloration has been achieved  at the expense of economy, or clarity, or both.

-- Yakov Malkiel, “The Inflectional Paradigm”, in W. Lehmann & Y. Malkiel, Directions for Historical Linguistics (1968), p. 32

O mistress mine ....

It is key to the cognitive style of such thinkers as Richard Feynman;  and not accidentally, as retaining a streak of the child is helpful in leavening fact-impacted thinking.

Again Holton:

As Einstein himself once said, he succeeded  in good part  because he kept asking himself questions concerning space and time  which only children wonder about.

~

The original Provençal gai saber, which seems to lie at the center of a collection of near-equivalents (joyful wisdom, gai savoir), specifically  denoted the art of composing love-poetry in the then-contemporary style, that of the troubadours.  As that art has alas passed from the planet, felled by the effects of the Albigensian Crusade,  we use it (as did Nietzsche et alia) in a wider sense, denoting the desired confluence of homo sapiens and homo ludens.

*

Si cela vous parle,

savourez la série noire

en argot authentique d’Amérique :

http://www.linguasacrapublishing.com/justiceexcerptdivorce.html

*

We have a genuine philosophic eros.  Knowledge excites us.

-- James Schall, S.J., The Order of Things (2007), p. 22

Da nun  in meine Darstellung  mancherlei einfließen wird, was strengen Richtern  unwissenschaftlich erscheinen muß,  so möchte ich dieses  einigermaßen  durch das Zugeständnis entwaffnen, daß dem Ganzen  die Überschrift  Allotria gebühre …

-- Hugo Schuchardt, “Der Individualismus in der Sprachforschung”, in Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 422

~

The fact that language is used for communication  is no more intrinsic to it  than its use to tell jokes …

-- Norbert Hornstein, Logic as Grammar (1984), p. 119

So far, however, from exalting the raconteur’s art, that passage stems from a practitioner of the singularly humorless Chomskyan Government-and-Binding school;  and means, not to enrich our notion of language with that of humor, but to squeeze it dry  even of semantics.

Cf. Karl Jaberg, Spiel und Scherz in der Sprache (1930).

Math Porn

As we remarked earlier (Mathsex) the intersection of mathematics and literal pornography is a set of measure zero.   (A perhaps/perhaps-not  related fact, is that mathematicians themselves are entirely sexless.   They certainly do not reproduce biologically;  in fact, they do not even reproduce academically, most great mathematicians having been lousy lecturers -- and I mean really, really bad.  Instead, each individual mathematician-to-be  receives an Annunciation -- from which archangel, I alas do not know, never having received one, despite fervent prayers.)

Even “porn” in the journalistic sense, not of actual pornography, but of tawdry crowd-pleasing shallow presentations of deep subjects, seldom if ever is to be found in the same bar-booth with Mathematics.  (For a list of subjects that do so lend themselves to marketplace exploitation, consult our definitive document:  Funporn.)

Yet it is now our sad duty to report, that we have, for the very first time in our young life (young with respect to the afterlife, that is;  w.r.t. any of you-all whippersnappers, ancient), encountered an actual specimen of “math porn” (although in a very limited sense, as we shall see):  Popular Lectures on Mathematical Logic (sic, sic, sic), published in English in 1981, by the philosopher-logician Hao Wang.

There is a long tradition of lectures to the general educated public on scientific topics, by men preëminent in their field.  These were often later collected and published as volumes, sometimes with “Popular Lectures” in the title, by such true luminaries as Mach, Kelvin, Helmholtz (these in physics, though, note;  not mathematics).  The heyday for this activity was the late nineteenth century.   Their success presupposed a pool of educated laymen keenly interested in learning more about the intellectual forefronts of the day.

In America, the tradition survives sparingly, in university towns.   While our family lived in Princeton, I used to attend evening lectures at the IAS, held in their largest lecture hall.  Occasionally the audience was overflowing -- standing, or sitting on window-ledges.

Wang’s book likewise originated in public lectures -- though not perhaps to the general public, since they were given at the Chinese Academy of Science  (in 1977; translated  and published in English  four years later).   But by no stretch of semantics do they qualify as “Popular Lectures”, nor even as “Introductory Lectures for Logic Majors”.   (Of course, Wang himself may not be responsible for the English title of his book;  it may have been cooked up by some hunchbaked, drooling drone in the marketing department.)   Already on the eighth page of the introductory lecture, we read this (typical) passage:

Around 1960, Hanf numbers appeared, and Scott proved that measurable cardinals yield nonconstructable sets.  Results often mentioned as being impressive  are Morley’s theorem on categoricity in power, and applications to algebraic problems by Ax and Kochen.

Solovay soon proved the consistency without dependent choice  of the proposition that every set of reals is Lebesgue measurable.  (He has to assume that there are inaccessible cardinals;  it remains an open problem whether this stronger assumption can be avoided.

(There is no definition of any of these terms, like “inaccessible cardinals”, in early pages.  You’re supposed to already know this stuff.)   Now, for a non-specialist, it will be hard to judge just where that passage stands in the spectrum of difficulty;  but as a thumbnail comparison:  at Harvard, I took introductory logic in the philosophy department, and then straight logic in the math department, and we never got anywhere near these topics.

Lest  for some reason  Wang might have shoved all the hard stuff into the very first lecture, so as to clear the auditorium of lightweights, and become more pedagogical later on, I opened the book at random, happening upon this:

Exercise 2.  Find a direct proof of Corollary 1.3 without appeal to Lemma 1.1

You do not pose such homework in a “popular lecture”.  The book’s title amounts to false advertising  -- publishing-fraud.

~

The infraction perpetrated by the Wang book is minor -- a scattershot gallimaufry of sketches-for-an-idea-for-an-article on unrelated subjects, mislabeled as a popular introduction to a single subject -- and may well be laid at the door of the publisher rather than the author.    But now we must notice something more serious:  actual pandering to the public’s ignoble propensities, in the matter of math.  The book is titled The Math Instinct:  Why You’re a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs), by Keith Devlin.

It has been well remarked, “As a rule, perjury in subtitles should be forgiven”.  This formulation was by Tony Rothman of Princeton, writing in American Scientist (March 2007), reviewing a biography by Siobhan Roberts, of the solid geometer Coxeter, King of Infinite Space, bone-headedly subtitled The Man Who Saved Geometry.  (It didn’t need saving, and he didn’t do it.)   But in the “Why You’re a Mathematical Genius” case, it is not just something tacked on by the publisher, it goes to the heart of the book:  “Devlin tries to make the subject less intimidating by demonstrating that math is all around us.”   That formulation is already cognitively-impaired;  “math” is all around us only in the sense that relativistic quantum mechanics is all around us.  Stuff is all around us, and a very few people (not you, not me) are able to make sense of some of it, somewhat (though less than is popularly assumed) by deploying a mathematical armamentarium:  neither Nature’s intricate hidden design, nor the occasional successes of experts, make you a mathematical “genius”.   And actually, few would be fooled by such transparent flattery (though it is of a left-handed sort, since the reader’s putative “genius” is, with the next breath, set at the level of lobsters);  one wonders why the publishers thought the public would be suckered-in by such fluff, rather than nauseated.   The answer no doubt is that such an approach is in tune with the general trend in America to “celebrate” one another’s narcissism.   That frame of mind does not make for keen exposition; as the reviewer in American Scientist remarks (Nov 2005, p. 572),

Devlin seems uncertain what his readers will need to have explained.  He reminds us that bats are mammals, but doesn’t define Ohm’s Law.

The case is the sadder since Devlin himself knows better.  He once wrote a very good semi-popular survey (only “semi-“, since equations do appear), Mathematics:  The New Golden Age (1999).   In this case, the rather grand subtitle is actually warranted: for while the great age of math as a handmaiden to physics is behind us, in the past half-century or so  it has effloresced to an astonishing extent as a multiply-connected enterprise in its own right -- with just enough new practical uses in cyptography and (if this one prove more than a dream) string theory, to keep it anchored.

~

It is now our happy privilege, likewise to report, that the other book occupying us this weekend, is precisely the opposite to the sugar-coating of the Wang packaging:  The title austere, uninviting;  the content as propaedeutic and intuitive as it is possible to be.  We refer, with reverence, to a book likewise originating in (semi-) public lectures (at UCLA, in the early 1980s):  Richard Feynman’s QED, published by Princeton in 1985.

The title might inspire a spurious sensation of familiarity:  quod erat demonstrandum, in which case it might fit a set of lectures on high school geometry.  But no, the acronym denotes something much more fearsome, something …. (but send the children to bed, before you scroll down)

…

…  nothing less than …

(horresco referens)

…

 =>  QUANTUM ELECTRO-DYNAMICS.

For years (decades, actually) I avoided this slender volume, though it stood on my shelves, owing to the misapprehension that, based on its titled subject-matter (which presupposed basic quantum mechanics) it must be significantly more difficult than the Big Red books, aimed at physics-major freshmen, on which I was weaned.  Yet not so.  Feynman, a master of exposition, offers the most intuitive account possible, of a highly non-intuitive subject.   Intuitive, yet not dumbed-down:  it takes a genius to tackle that.

But nota bene:   He never endeavors to coax you into thinking something is easier than it is, nor to flatter you that you have understood something when you have not -- both being common expository strategies of popularizers of science in this Age of Self-Esteem.

Rhetorically -- engagingly -- Feynman adopts the opposite strategy, hinting at what you are up against, though not bullying.  In the opening of the introductory lecture, he makes the quite accurate though socially/intellectually scandalous observation that

Everybody who comes to a scientific lecture  knows they are not going to understand it, but maybe the lecturer has a nice, colored tie to look at.

The second lecture, raising this observation to the status of a meme, opens thus:

This is the second in a series of lectures about quantum electrodynamics, and since it’s clear that none of you were here last time (because I told everyone that they weren’t going to understand anything), I’ll briefly summarize the first lecture.

The next begins:

This is the third of four lectures on a rather difficult subject -- the theory of quantum electrodynamics -- and since there are obviously more people here tonight than there were before, some of you haven’t heard the other two lectures  and will find this lecture almost incomprehensible.  Those of you who have heard the other two lectures  will also find this lecture incomprehensible,  but you know that that’s all right:  as I explained in the first lecture, the way we have to describe Nature  is generally incomprehensible to us.

This stance, though fey in a way, is yet preferable to that of the Theory-of-Everything charlatans who babble on about Beauty, implying that they can share their vision by mere dermatological osmosis.   There was one such on NPR’s science show last week  -- a string theorist yet, which is to say:  a specialist in a fashionable but drastically unintuitive math-packed would-be-physical theory, which, additionally, may well be actually wrong as a description of the real world -- or, worse, “not even wrong”.  But the interviewer kowtowed and pandered, and the interviewee luxuriated in his 15 famous minutes, as in a warm bubble-bath, complete with rubber duck.

A far more prominent string-theorist, Frank Wilchek, of the IAS, has a similar piece in a recent issue of Nature / Physics (Nature, by the way, seems to be in some ways following Scientific American down the path of corruption), calling on us all to “celebrate Beauty”.  -- By all means, say I, let us do so, and preferably in the altogether;  but don’t go calling it physics.

~

[Update & after-reflection]  The title (and thesis) of Devlin’s book are misconceived in a rather subtler and more substantial way than the undraped pandering of the subtitle:  The Math Instinct.     Because, in fact, there isn’t any.

I satirized the thesis that there is one -- honed, like the other instincts, by Natural Selection -- here:

The Urysohn Metrization Theorem:

an Adaptationist Account

However, the Ultradarwinians were not our real quarry in that sotie, but rather the mathematical Nominalists.

Devlin’s title echoes that of an earlier and much better work of scientific popularization, Steven Pinker’s The Language Instinct.   Here, the title is no mere gimmick from the marketing department:  the author is well aware that, properly understood (something that itself is no easy task), the positing of a language instinct constitutes a highly contentful, counterintuitive, scientifically testable, and in some quarters bitterly controversial hypothesis.   It is one that Chomsky and those in his intellectual wake  have been investigating with great ingenuity, for over half a century now.   They have made a telling case (though one that has become more difficult to understand as the theory itself advanced, rather the way Galilean mechanics are more intuitively accessible than Quantum Field Theory), one which need not here be passed in review.

With mathematics, matters lie quite otherwise. …

[To be continued, if reader interest warrants.  In the meantime, consult our counterthrenody to the thesis of universal mathematical genius:   Oligophrenia Mathematica.  ]

[Update Oct 2013]  Continued here.

More physics porn (further updated)

Contemporary atheists point to cosmological findings of the Big Bang Theory era, to argue that no Creator is logically necessary.   Earlier writers, compassing the same end of assailing theism or even deism, likewise adverted to Big Bang Theory, but put an opposite spin on it.  A philosopher, reviewing Filosofskie Problemy Sovremennoi Fisiki (Moscow, 1957), by  Marxist author Ernst Kolman:

He appears to reject outright the docrine of a cosmological commencement, on the grounds that such theories inevitable lead to the invocation of non-material causes  and hence to religion.  Do they?  How pleased some of our theologians would be if this were so.

-- Ernest Gellner, Contemporary Thought and Politics (1978), p. 138

(Note:  Gellner is not here by any means espousing deism, but merely critiquing one instance of Physics Porn.)

 ~

Richard Feynman, a highly engaging guy and no spoilsport, yet disliked the tawdry “three quarks for Mr Mark” sort of foolishness that the public laps up like frumenty.  In QED (1985), he wrote (p. 136):

The quarks have an additional type of polarization that is not related to geometry.  The idiot physicists, unable to come up with any wonderful Greek words anymore, call this type of polarization by the unfortunate name of “color”, which has nothing to do with color in the normal sense.

And (p. 145)

The “flavor” of this quark is called c, and I haven’t got the guts to tell you what c stands for, but you may have read it in the newspaper.  The names are getting worse and worse!

("Charm".)

And all this was prior to the horrors of .... "The God Particle" ...

~ We here reprint a post from August 2011. ~

"What is that streaking 'cross the evening sky?"

"It's a bird!"  "It's Balloon Boy!"   "It's the HI-I-IGGS  BOSON !!!"

In an earlier post, I commented on the debased public presentation of physics, comparable to the way in which Natural History is reduced to giant colored plastic dinosaurs (with or without Adam&Eve in the diorama, according to taste).

Do  note:  the epithet "porn" is hurled, not at the content, but at the presentation.  As Edward Wilson lamented (in Consilience, p. 268),  concerning Americans' attitude towards science:

They don’t understand it, they prefer science fiction, they take fantasy and pseudoscience like stimulants to jolt their cerebral pleasure centers.

Even more trenchantly, Richard Dawkins, in his essay “Drawing Room of Dukes”:

‘Science Weeks’ and ‘Science Fortnights’ betray an anxiety among scientists  to be loved.  Funny hats and larky voices  proclaim that science is fun, fun, fun.

(Having myself tried to scale its cliffs, I can rather attest, that it is hard, hard, hard -- and gets unbelievably harder as you near the summits.)

Our remarks here are thus in the spirit of  Dawkins,  who wrote “I am attacking only the kind of populist whoring that defiles the wonder of science.”   By no means are the barbs aimed at science, nor at haute vulgarisation.

*     *     *

~ Commercial break ~

http://www.youtube.com/watch?v=4TWpcZGE_q4

We now return you to your regularly scheduled essay.

*     *     *

~     ~     ~

The other day, a most useful site, aldaily.com, which links to articles of especial interest from around the globe (though only in English), saw fit to link to this one, in the Irish Times:

         'God particle' may be discovered soon

No, don’t bother to click -- spare your forefinger.   The brief wisp of an article announces, not any actual development, but a hope or anticipation of a possible eventual development, namely the ‘discovery’ (something of a misnomer; see below) of the freaking Higgs boson.  (Somehow I can never resist calling it that.  Might as well re-dub it the FHB.)  Such an anticipation has been in the news for many, many years, and has grown mold.

For those (chiefly children and Pacific Islanders) who have not yet heard of the marvelous (though possibly non-existent, anyhow completely unobserved) FHB,  the article explains:

It has been called the “God particle” or the “stuff that makes stuff stuff” as, without it, there is a mystery as to how objects get their mass.

Don’t misunderstand -- it will be very nice if they do ‘discover’ the Higgs boson, since particle physics is rather a mess, and needs all the help it can get.  It would be like filling in a gap in the periodic chart of the elements.   But how would it be more than that?  True, there is a mystery as to how objects get their mass.  But at that level, there is a mystery, how Time got its start, or Why is there something rather than nothing.   At this level, such questions are fundamentally unanswerable:  we have hit rock bottom, our spade is turned.  

Still, there is much that can usefully be done.   Thus, Newton did not discover the fact of gravitational attraction, let alone explain how it came to be -- as he well knew.   What he did was posit a precise formula -- the inverse-square law -- which, when you do the math (and he had to invent much of the math) turns out to fit precisely the observed orbits of the planets, as well as the behavior of falling apples.   This was a formal tour de force, and was of immediate philosophical significance as well, as uniting the supralunary and sublunary spheres, traditionally thought to obey quite different laws.  Nay further, as Arthur Koestler puts it epigrammatically  in The Act of Creation (1964):

This equally applies to the discoveries of the artist who makes us see familiar objects … in a strange new revealing light … Newton’s apple and Cézanne’s apple  are discoveries more closely related than they seem.

Now, there are two basic ways in which some new constuct, like the FHB, might be desirable. 

One, like Newton’s Universal Gravitation, it might be illuminating, in that it would formally unite gravity with something else, which is the goal of the Theory of Everything.   But in that case, it would seem, the intellectual work has already been done:  someone has calculated that, given a particle of such&such particulars, it would be a key that would fit both locks.   And that might constitute a conceptual tour de force, only -- the actual ‘discovery’ of the particle is philosophically an anticlimax:  it would not be really a discovery, the way penicillin or X-rays or the Cosmic Microwave Background -- previously unsuspected -- were discovered.   It would simply mean that the already-posited and largely-understood particle  was finally physically spotted -- the way the positron was spotted, after Dirac had predicted its characteristics with math.

 [Update 23 April 2012]  Thus indeed now Steven Weinberg:

"The discovery of the Higgs boson would be a gratifying verification of present theory, but it will not point the way to a more comprehensive future theory. We can hope, as was the case with the Bevatron, that the most exciting thing to be discovered at the LHC will be something quite unexpected. Whatever it is, it’s hard to see how it could take us all the way to a final theory, including gravitation."

http://www.nybooks.com/articles/archives/2012/may/10/crisis-big-science/?pagination=false&printpage=true

Unfortunately, this happy scenario may not be the case.  Rather, we may be faced with Case Two:  the particle is needed, not because, like the calculus and the working out of the consequences of the inverse square laws, it is a key that opens many doors;  but only because, for purely formal reasons, without it, you’re screwed.  Such is the picture as presented in Wikipedia:

The existence of the particle is postulated as a means of resolving inconsistencies in current theoretical physics …

In other words, the Standard Theory is sweating beneath the auditor’s eyeshaded gaze,  “We seem to have uncovered certain inconsistencies in your physicofinancial statements…”, and the hope is that adding yet one more creature to the Particle Zoo  will stave off the day of reckoning for a time.

Okay, so:  a non-story, at many levels.   Why, then, did a well-informed site like aldaily choose to link to it, rather than to any of a number of substantive scientific articles for a lay audience?  (For examples, see any issue of the excellent American Scientist.)   The answer is obvious:  the tawdry misinvocation of the Deity in that misbegotten amelus of a nickname, “the God particle”, which manages to degrade comprehension of both science and religion at one go.

[update 19 IV 11:]  aldaily has now promoted that piece of tripe to its coveted "nota bene" section.

[update 21 IV 11:]  Ah, just what we needed:  toss in the much-battered metaphor of the Holy Grail (now decapitalized and pluralized):

http://www.financialexpress.com/news/physics-and-the-search-for-the-holy-grails/779476/0

[update 26 IV 11:] As we anticipated.... "Nevvah mi-ind..."

And so the media once again climbs down from its puffed-up non-event.  But meanwhile they have sold some more newspapers, and John Q. Citizen can feel that he has kept "up-to-date" with Science.

[update 28 IV 11]  As an antidote to all this, see the current New Yorker for some excellent physics reportage.  The subject -- quantum computation and Many Worlds -- is difficult to approach without falling into mystification or gee-whiz, but reporter Rivka Galchen manages nicely.

[update 14 VIII 11]

More digs at Higgs

The FHB is beginning seriously to get on my tits.   Now this:

To More, the usual concept of empty space was meaningless because space is always filled with divine spirit.  To us, the usual concept of empty space  may be similarly elusive, since the empty space we’re privy to  may always be filled with an ocean of Higgs field.

 -- Brian Greene, The Fabric of the Cosmos (2004), p. 270

Ergo, a new Paternoster, for the Physics-Porn crowd:

            Our Particle, who art in Aether,

            Shallow be thy name …

[update 24 VIII 11]

The alarming possibility just occurred to me, that this post might be misconstrued as dissing physics popularization  as a genre, as a whole.  Not at all !  There are several quite excellent books.  Heading the list would be the brief and very readable title by Richard Feynman, The Character of Physical Law (1965).

~

~  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.

(My name is Dick Feynman, and I approved this message.)

~         ~

~

[update 18 IX 11]

Cf. now also this.

[update 24 IX 11]

And this.