COINCIDENCE AND COSMOS

[The following is from a letter sent to a friend, who had reported a troubling coincidence, some years ago.]

~

COINCIDENCE AND COSMOS

I don’t see those two coincidences – yours or mine – as particularly startling.  But neither my being unimpressed, nor your being impressed, should weigh particularly heavily in the epistemological balance-pan.  For mankind is notoriously incapable of estimating probabilities in most instances.

One of the side benefits of faith is supposed to be  that it tends to preserve us from superstitions that might otherwise get sucked in to the vacuum where faith should be. (Chesterton was fond of emphasizing, and dramatizing, this point.)  Actually I was never superstitiously inclined, even before baptism; but now there is a warrant to just wave these things off – things superficially much more suggestive.   For, I don’t believe that God communicates via such hole-in-corner monkey-tricks.

Such incidents, when they crop up, are undeniably intriguing.  The appeal seems to be  that they hint at a pattern on the other side of the carpet, which we see only wrong-side-on.  But then, as theists, we already know that; we don’t need the occasional odd chiming of chance, to tell us so.  What is worthy only of Las Vegas, should stay in Vegas.

*

One of the things  I’ve been doing with my new-found, fiber-furnished bandwidth, is watching free online episodes of a TV series, “Lost”.   The whole thing is predicated on Baader-Meinhof phenomena.   

The problem with that  as the basis for a multi-year series, is that it is all too easy to conjure up.  Just as magic tricks are yawners if performed on television, which can always resort to special effects, so spooky coincidences are startling only if they happen to you.   It’s a very lazy genre.   For comedy to work, it has to be funny; and even a decent car-chase demands artistry to stage.  But any footling apprentice can have a stranger say (after you meet him in an empty stadium in Australia, and then part company), “See you in another life”; and then a few minutes later, a world away on a mysterious island, in a bunker far below the earth, you run into the same guy, now wild-eyed and bearded, and stammer, “Y-y-y-you….!”   Still, “Lost” not a boring show.  The whole art consists in having an artfully selected Bridge-over-San-Luis-Rey set of castaways  -- the pert freckled girl, the doughty doctor whose stubble is never shorter nor longer than a four-day growth, the Black guy, the Fat guy, the this-and-that guy – and send them through a minuet of interactions, spiced by tingly synchronicities,  so that the coincidences become tonal, as in music.

Featuring prominently among the guiding coincidences of the show is a short sequence of small integers, arranged in order.  Fat Guy overhears a mental patient (whom the numbers have driven mad) muttering them over and over, and with them, wins the lottery!  Woo-ooo!  But then very bad things start happening to everyone he goes near!! Woo-oo-ooo!  And then they turn up engraved at the entrance to that bunker!  Woo-oo-ooo-oo-oooo!  The sequence, unremarkable upon inspection…

Actually, I must confess at this point, that I am loath to write the sequence down, though it is only the whim of a TV show.  It is not superstition exactly; more like, “Get thee behind me…”  For, although God does not communicate by such monkey-tricks, the Devil might…  Anyhow, it contains an old favorite “23”.   An otherwise highly intelligent (though atheist) friend of mine  was mesmerized by this number, whose spectral footprint seemed to be everywhere.  It turns out he is not alone in his obsession; an entire movie was made (unfortunately, not a good one), about the eerie qualities of this integer.

*

There is one place where startling coincidences really are intriguing; and it is as far from Old Pagan or New Age spookery as possible.  I mean:  math and science.  For, the same underlying structures keep popping up in a variety of guises; the wild kaleidoscope of the world  appears, upon analysis, to be dreamed up out of a few symmetries  and a few bits of colored glass.

Here too it is possible to go astray, seeing significance where there is none.The great Eddington was much taken with the fact, that the Fine Structure Constant of physics (a dimensionless number, of course, otherwise its numerical value would be arbitrary) is very very close to 1/137 (or whatever the figure was).  Odd he should have noticed, this, actually; did he carry around reciprocals of all the integers in his head?  Anyhow, he hypothesized that the FSC was exactly 1/137; and busied himself attempting to explain the discrepancy as measured.  Well, it turned out to be mere gematria.  The FSC is not the reciprocal of an integer, and there’s an end to it.

The smaller the integer, the more it is likely to play a role in disparate structures essentially by happenstance.  Two is the king of them all – duality, binarism – and thus is indeed a very significant number, but rather in the way that water is a significant compound – you don’t get goosebumps when you discover another example.   Much more troubling are huge numbers, such as the ratio of the strength of the Coulomb force to that of gravity – how do you construct a cosmos out of such ill-matched yoke-mates?   Or, to take a recent example from mathematics, consider such apparently unrelated fields as the study of j-functions, and that of finite simple groups.  The first nontrivial factor in one of the series of the former is 196,884; the smallest number of dimensions in which the largest of the latter can operate, is 196,883.   A connection, or close but no cigar? 

~

Foot-note (tail-note, butt-note) anent the Dark Prince.

Two of my favorite Christian authors, G.K. Chesterton and C.S. Lewis,  offer antithetical depictions of the Devil.  Chesterton’s is more romantic and medieval:

Roses are redder  when you believe in the Devil.

Lewis’s, by contrast, in the Silent Planet trilogy, in Screwtape, and in The Great Divorce, depicts what we might call the Trivial Devil (though no less dangerous for all that).  There is no romance to him; there is, we may say, Nothing to Recommend Him.  He is no Satanic Majesty, but more like a Satanic Misery,  a Satanic Minionism -- a Mere Mechanism.  And as a mechanism, he is given to chitter-chattery repe(titi)tition.

An example of what we could term a “diabolical” coincidence, in this Lewisian sense,  occurs in “The Matrix”, when a black cat (Satan in miniature, as it might be) passes, right to left, outside the doorway, and then, right after that, or sort of seguing into it, a -- a black cat passes, right to left, outside the doorway.   Neo remarks on the coincidence, merely curious, but his more seasoned team-mates are instantly more knowing and alarmed, for they recognize a revealing glitch in the diabolical master-program that runs the Matrix.   The faults and behaviors of the dark lords who run the place, are eminently mechanical, since they are, in fact, machines.

Minimalism in Physics (updated)

Truth is ever to be found in simplicity,

and not in the multiplicity and confusion of things.

-- Isaac Newton

[Note: 
In using the term “minimalism” in evaluating styles of physics, I am importing  into the philosophy of science  a term mostly associated with the arts.  The move may or may not be fruitful.  But here is a well-known parallel move, from Gerald “Mr. Themata” Holton, in The scientific imagination (1978), p. 7:

I have proposed … thematic analysis (a term familiar from somewhat related uses in anthropology, art criticism, musicology, and other fields).  ]

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

To some extent, all rational inquiry ‘minimizes’ -- idealizes, works with toy models, etc.   Some more than others -- economics notoriously so, tossing out so much bathwater that sometimes the baby goes missing.   Others roll up the sleeves of their labcoats and go in elbow-deep to the mess of reality, little bothering with economy or philosophy.   Chemists, in particular, seem perfectly content to potter about in labs, to discover stuff, invent stuff, patent stuff.  They literally multiply entities, in that they invent chemicals that weren’t there before.   Whether they thereby multiply them beyond necessity (mustard gas, thalidomide,  napalm, LSD) is a matter of individual taste.  But certainly the ethos is anything but austere.

And likewise, for the most part -- biology, geology, astronomy, engineering, what have you. 

But modern physics  raises parsimony to a central tenet, almost the prime purpose of the whole enterprise as currently understood.  This development being by now taken for granted among those of the guild, it may not be apparent how odd this really is.

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

It may be objected:  All that is nothing but plain reductionism, which is simply to say:  Science.  No call to drag in an arts-related term like “Minimalism”.  -- But I believe there is an aesthetic dimension -- seldom mentioned in journal articles, though over-emphasized in popular writing -- which lies outside the bare logical necessities.  As,

“There shouldn’t be laws of physics,” Strominger maintains. “There should be just one law, and it ought to be the nicest law around.”

(Quoted in Shing-Tung Yau, The Shape of Inner Space (2010), p.  14.)

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

At stake was nothing less than finding the most economical, simple, formal principles, the barest bones of nature’s frame, cleansed of everything that is ad hoc and redundant.

In his own personal life, the legendary simplicity of the man was an integral part of this reaching for the barest minimum on which the world rests.

*

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

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

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

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

*

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

Templeton-Prize winner Paul Davies,  in The Goldilocks Enigma (2006), p. 264, takes rather understated notice of this:

The disadvantage of the multiverse theory is that it invokes an overabundance of entities, most of which could never be observed, even in principle.  This profligacy strikes many people as an extravagant way to explain bio-friendliness.

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

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

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

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

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

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

It was hardly an idea calculated to appeal to a man with a taste for desert landscapes  … There are more than 10^500 versions of string theory  lounging indolently about.

-- David Berlinski,  The Deniable Darwin (2009), p. 532-3

*

It will sometimes not be obvious, which proposals are Minimalist in spirit.  Thus, imagine some wretched Nominalist, who balks at the infinite, and proposes that the numbers needed for physics  are finite -- specifically, the field of integers mod a prime p (necessarily quite large, to accord with observation).   Finite’s gotta be simpler, more minimal, than infinite, right?  Roger Penrose retorts (The Road to Reality (2004), p. 359):

A physical theory which depends fundamentally upon some absurdly enormous prime number  would be a far more complicated (and improbable) theory than one that is able to depend upon a simple notion of infinity.

More precisely:   The problem is not essentially that the number is so large, but rather, with infinitely many primes to choose from, the choice would seem arbitrary:  in much the same way that the omniscient computer in  The Hitchhiker’s Guide to the Galaxy reveals, quite disappointingly, that the Meaning of Life is … “26”.

*

Differing from a theory-wide programatic theoretical minimalism, is a kind of personal cognitive-epistemological economy, described by Gerald Holton, The scientific imagination (1978), p. 158:

Fermi ordered the overwhelming and vast amount of knowledge  into a set of very few principles and ‘cases’, which allowed him to understand almost any new problem as an example of one of about seven primitive or primary physical situations.  Fermi would return throughout his career  to a listing or digest of the chief ideas in physics, which he had made when he first organized the field for himself as a young student.

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

*

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

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

-- Etienne Gilson, Linguistique et philosophie (1969), p.  163

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

Bonus quote:

Willem de Sitter found an exact solution to Einstein’s field equation … having no matter at all. … Why should we be interested in such a universe?  Because the real universe is of rather low density …

-- J. Richard Gott, The Cosmic Web (2016), p. 16

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Apophthegms of Physics

Hertz: “Maxwell’s theory is Maxwell’s system of equations.”
By itself, this is a witty, eminently quotable, and meaningless comment.

-- Abraham Pais, Subtle is the Lord (1982), p. 119

~

There may be such a thing as habitual luck.  It is like hidden parameters in physics.

-- Stanislaw Ulam, Adventures of a Mathematician (1976), p. 119

Or as Yogi Berra once put it:  That is too much of a coincidence to be coincidental.

The Trinity (triune unity -- re-renewed)

[In observance of Maundy Thursday,  a re-post  from yesteryear.]

I spend a fair amount of time in the company of Muslims these days;  indeed, at present, by an accident of the seating-chart, I probably spend more time in close propinquity with Muslims, than with Christians, Hindus, Jainists, Jews, and Zoroastrians combined.   (Lotta LDS, though.  Plus all that could change with the next re-org, as my next podmates might be Zoroastrians.)   [Update March 2017:  And now, in fact, our branch chief is a Zoroastrian.] There is an effort of good-will on both sides;  my Sunni neighbor points eagerly to passages in the Koran, where good things are promised to ‘believers’ (mu’miniin) rather than specifically ‘Muslims’ (muslimiin).  A kind-hearted man, he hopes to be with me in Paradise, and not to gaze down on me roasting in Hell.  (`Uqbaalak, ya shaykh.)

Now, we Christians know implicitly, that the doctrine of the Trinity is no polytheism:

that Father, Son, and Holy Ghost, are not at all like Apollo, Zeus, and Hera, say, but more like le père Dupont, at once father, and Frenchman, and fireman.   But to explain this to our Muslim friends, is difficult.   I often have to fall back on saying:  the Trinity is a Christian mystery; it may be true or false (in some transcendental sense of those categories), but it is no descendent, direct or indirect, of the sort of pagan polytheism which stuffed the Kaaba with idols, and peopled the trees with dryads, and Olympus with squabbling gods.  For us as for you, God Himself -- Allah -- Yahweh -- e’en He -- is indeed One.

Yet this unity by no means necessitates or logically entails, that there could be no parts at variance within the Godhead, even to dissension.  (Of course, their absence might be a truth of the Church, and thus beyond dispute;  I am speaking here only of logic, the only subject in which I have been ordained.)  How indeed could we ever know otherwise (save by some enigmatic Revelation)?  After all:  We are made in His image, and we ourselves are a bundle of contradictions;  and He contains us, as a proper part.  (Additionally, that Eloi, eloi passage would seem to point in that direction.)

~

C. S. Lewis saw rightly when he compared the notion of the Trinity (purely as regards its intellectual coherence, rather than anything theological) with the ‘separate’ faces of a cube -- which latter is, however, nothing more nor less than the sum of all of them.  (Indeed, if you were to go with a sort of ‘projective cube’, with antipodal faces identified, our new Cube (topologically a three-torus) would even consist of exactly three parts.)

The historian of physics D’Abro offers a similar parable, along the lines of Abbot’s Flatland (A. D’Abro, The Rise of the New Physics (1939), vol. II, p. 653), his quarry being however, not the Trinity, but the (in some ways similar) “wave-particle duality”:  or, as we might term it, the wave-particle identity.  He imagines our various perceptions of something we believe to be one entity, but which sometimes seems a triangle, and at others, a circle:  eventually we realize that it is a cone, seen now this way, now that.  And, regarding the separateness/unity of electricity and magnetism:

The theory of relativity brought about the fusion of the two aspects, no longer by utilizing the background of 3-dimensional space, but by introducing the more refined background of 4-dimensional space-time.   The underlying entity, the partial aspects of which are electric and magnetic, were found to be the 4-dimensional electromagnetic tensor  situated in space-time.

-- A. D’Abro, The Rise of the New Physics (1939), vol. II, p. 653

The Trinity, we may confide, whatever in its unknowable essence it may be, is at the very least as complex as a  tensor.

~

Pascal (Pensées, 1670 [posthum]), has a very odd passage, asserting the alienating nature of God’s complexity -- or perhaps not -plexity, but monolithicness :

S’il y a un Dieu, il est infiniment incompréhensible, puisque, n’ayant ni partie ni bornes, il n’a nul rapport à nous.  Nous sommes donc incapables de connaître  ni ce qu’il est, ni s’il est.

Ni s'il est ! -- A useful first step towards an antidote  might be to drop that assertion about God's lacking any parts.

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Non-Acronym of the day: “Jason”

The saga of Jason and the Argonauts  has spun off some delightful dubbings.  One, the “Argo” escapade, we discussed here.   Another was the secret elite group of physicists called Jason.  

An intrepid historian of science  ran down the true etymology, after an initial (indeed, “initials”) red-herring:

I asked my husband’s physicist-colleagues  “What’s Jason?” and collected the following:  Jason is an acronym fof July-August-September-October-November, the months this group of academic physicists   met secretly to solve the problems  the Defense Department couldn’t.

-- Ann Finkbeiner, The Jasons (2006), p.  xii

That suggestion quickly dissolves  in the universal solvent of Common Sense:

These stories I didn’t believe.  An acronym for months sounded silly.  [But more tellingly:] Academics couldn’t meet that long during the school year because they had institutional responsibilities.

-- id.

Another false-lead was the assertion that Jason was named after one of the members’ family dog.   Not.  The true story she tells on pages 39-40:  the wife of one of the members chose it, after the Greek myth -- most appropriate for a group that was going after the scientific equivalent of Golden Fleece.

The author adds some linguistic details:

“Jason is both a collective and a proper noun:  if you belong to Jason, you are a Jason.” (p. xiv)

Jason is usually capitalized [completely],  JASON, as though it were an acronym.  I have no idea why -- maybe because, written like a name [with only the first letter a capital], it might be taken to be a personal name.  I shall not capitalize it.

(p. xxviii)

Another reason it was initially written all-caps is that DoD and the IC often so style cover-terms.

~

The choice of Jason as a group name  is typical of the playfulness of physicists.  When DoD does the dubbing, the result is likely to be humdrum. As,

The task force was called the Defense Communications Planning Group, or DCPG, a name chosen for its meaninglessness.  (p. 77)

When a secret project does get a lexical designation, this may be chosen precisely to throw off anyone to whom the term might get leaked.  Thus, the Manhattan Project:  so named because it had nothing to do with Manhatten, and indeed was centered at locations far from any city.  One of the things they worked on (my Dad did, for one) was called “Tube-alloy”, a nicely misleading alias for uranium (which is an element, not an alloy).

Lawrence Livermore monostich

a glowing yellow tent   against a black sky

and a laser shining   straight up to God

[Source: Ann Finkbeiner, The Jasons (2006), p. 166]

Narcissism versus Arrogance (and Hubris)

Back to the correlation to narcissism, of various scientific disciplines.  (This is the continuation of an essay begun here.)

It is beyond contest, that (say) chemists and civil engineers have a reputation for very low doses of Drama, compared with (say) physicists.   But what are the traits that gave physicists such a rep?

It is seldom really narcissism, for that is a matter of individual, personal psychology.  If there is self-regard, that among physicists is more that of the guild -- a corporative trait, which might strike outsiders as arrogant. 

Ann Finkbeiner, in her fine history of the elite advisory group known as the Jasons (who were overwhelmingly physicists), gives an anecdote from an oceanographer (p. 138), recalling an uncharacteristic foray into oceanography by the Jasons:

I did resent this “the ocean is a wonderful summer playground for smart physicists who can do it in their spare time”.  You may know this thing called physics arrogance.  It’s real.

Indeed, Finkbeiner reveals (p. xvii) that at one point “I wanted to call this book The Arrogance of Physicists.”

Now, arrogance can co-exist with narcissism, and flavor it;   but they by no means need be co-present.  Thus, the eponym, Narcissus himself, was not arrogant in the least:  he was dreamily, solipsistically folded-in on himself.

Consider the humble confession of quantum wizard Wolfgang Pauli in 1925:

At the moment, physics is again terribly confused.  In any case, it is difficult for me, and I wish I had been a movie comedian or something of the sort, and had never heard of physics.

Yet many anecdotes are told about Pauli’s arrogance -- within physics : e.g. “What Professor Einstein says” (he concedes) “is not so stupid”.  Or the damning phrase “Not even wrong” (recently the title of a book attacking the very integrity of String Theory).   Or consider this joke (quoted by Ann Finkelbein in The Jasons, 2006):

A physicist gets to heaven  and God asks him if there’s anything he’d like to know, and the physicist says, “Yes, please.  Why is the Fine Structure Constant 1/137?”  God gives him the explanation, and the physicist says, “No, that’s wrong.”

Ironic note:   Any such explanation from God  would in fact have been wrong -- since (as we now know) the value of the Fine Structure Constant, though close to 1/137, is not exactly that, and thus is not a ration of (small) integers at all:  it’s just one of those boring physical parameters that drone on and on, and could just as well have been somewhat different.  The conjecture that it might actually be a pure integer ratio  caused a certain amount of numerological excitement back in the day, but that turned out to be a false alarm.

~

We have frequently written about the related but distinct notions of depth  versus difficulty (in math and science).   This comparison/contrast of narcissism versus arrogance (the former being key to our American culture, the latter to our politics) may likewise prove fruitful.

Stepping out a further circle of semantic nuance, we find hubris.  Like narcissism and arrogance, this can be an individual characteristic, as it was among the Greeks who named the concept.   But it can also characterize the goals and self-conception of an entire discipline. And beginning at least in the twentieth century, if not earlier, physics could well be described as hubristic.

[TBC]

Metrization, Mensuration, Measurement

We earlier treated the matter of a metric on a topological space, in a series of essays beginning here:

The Urysohn Metrization Theorem:  for real this time

Now, as lagniappe, we offer a pair of Metrization Epigrams, which the budding mathematician, stuck for an opener with that leotard-clad vision at the espresso bar, can use for a pick-up line:

 A discrete space is like the autistic atomism of the Tractatus, or Leibnizian monads.

An indiscrete space is (as one writer charmingly put it), “really quite crowded:  each point is an accumulation point of every other set.”  (One pictures the Jellyby children in Bleak House, ever tripping over one another’s legs.)

(Believe me, chicks go wild over such things.  Or at least, if you are like most gangly Adam's-apple-challenged graduate-students in math, it’s your last best shot.)

~

It is by no means only topological spaces that one might wish to subject to a metric: all kinds of things, really:    Which species lie how close to which others (and different metrics -- phenotypic, cladistic, etc. -- yield different results);  which languages are neighbors in linguistic space (again there is a phenotypic/cladistic distinction:  descent vs. Sprachbund); which people have a natural affinity with which other (seating-plans at dinner-parties; blind dates; etc.)  And more generally, what is the curvature tensor of the noösphere?

As (from a philosopher of science):

One sometimes wants to say that a theory has much more testable content than some other statement:  for instance, the Newtonian theory has much more testable content than ‘The moon orbits the earth’.  But our apparatus, as it stands, does not entitle us to say this.  We have no metric for testable content.

--John Watkins, Science and Skepticism (1984), p.  185

Compare Keynes’ critique of relative subjective probabilities.

Here a noted philologian on the notion as applied to languages:

Was nun die Sache selbst anlangt, so meine ich  daß immer Sprache und Sprache, mögen sie auch noch so weit auseinander liegen, in wissenschaftlichem Sinn  enger zusammengehören  als Sprache und Literature, seien es auch die  desselben Volkes.

-- Hugo Schuchardt, “Über die Lautgesetze”  (1885), in Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 85

And here, indeed, he polemicizes against the nominalist treatment or ‘indiscrete toplogy” of diachronic linguistics:

Ist es denn nun nicht an sich ganz gleichgültig, ob rom. andare von adnare oder addare oder ambulare oder einem keltischen Verbalstamm herkommt;  ob in diesem Dialecte  l zu r  und in jenem  r zu l  wird usw.?   Welchen Sinn haben alle die Tausende etymologischer und morphologischer Korrespondenzen, die Tausende von Lautgesetzen, solange sie isoliert bleiben, solange sie nicht in höhere Ordnungen aufgelöst werden?

-- Hugo Schuchardt, “Über die Lautgesetze”  (1885), in Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 84

~

This metaphor of ‘metrization’, outside the exact sciences, is very loose, as it is not strictly needed -- for taxonomic purposes, a more approximate neighborhood-system will suffice (a “Uniformity”) so to speak -- and still less is to be obtained.

As, a pair of British linguists comments:

One recent attempt by French researchers  has given us the term dialectometry, which describes a formula for indexing the dialect ‘distance’ of any two speakers in a survey.  So far, the utility of the index has not been demonstrated.

--J.K. Chambers & Peter Trudgill, Dialectology (1980), p. 112

This, in the synchronic arena, is reminiscent of the glottochronology of Morris Swadesh, who attempted a sort of carbon-dating of linguistic evolution, based on an assumed universal rate of lexical decay, in the absence of direct evidence.

[Update 17 January 2016]  Another cautionary tale about the fetishization of metrics:

Two of our most vital industries, health care and education, have become increasingly subjected to metrics and measurements. Of course, we need to hold professionals accountable. But the focus on numbers has gone too far. We’re hitting the targets, but missing the point.

http://www.nytimes.com/2016/01/17/opinion/sunday/how-measurement-fails-doctors-and-teachers.html?ref=international

Philologisches:

Whether, in that opening paragraph, the author wrote “metrics and measurements” intending to refer to two distinct though related concepts, or whether it was just an idle bit of synonymic accumulation like “bequeath and bestow” for those who might be unfamiliar with the somewhat technical word metric, is there unclear.  But it does raise a linguistic point.

The word metric, and its close kin meter, metrical, metrization, derive from Greek.

Mensuration and commensurable  go back to Latin mensura.

Measure comes ultimately from that Latin word as well, but via the phonetics of medieval French.

The same Indo-European root  is said to lie at the base of all of them.

English, an etymological patchwork, has some tendency to layer its vocabulary by origin, Greek roots being reserved for the most technical, followed by Latin,  with the Saxon vocabulary as jack of all work.  In this, it contrasts with German:  to Graeco-English oxygen, hydrogen, nitrogen  correspond homely-sounding Germanic compounds Sauerstoff (‘sour-stuff’), Wasserstoff, Stickstoff.   And Freud’s German originals for the English ego and id, were nothing but nominalizations of the ordinary pronouns, das Ich & das Es.

Roughly such tiering is at work in our Wortfeld of ‘measure’. 

Measure sounds reasonably English (though partly just because it chimes with pleasure and leisure, which are likewise French words in disguise), and is in everyday use for all purposes (though it also has technical specializations, as in mathematical measure theory).

Latinate mensuration (little used) is scarcely more than a stuffy synonym for ‘measuring’;  commensurate has everyday though businesslike uses (“a salary commensurate with the job responsibilities”); while commensurable is mostly technical, whether in its mathematical sense, or its more recent philosophic sense (“commensurable discourses”).

Metric is kind of a green-eyeshade/clipboard sort of word at best.  It becomes fully technical in mathematical uses like metric space and semi-metric,  finally soaring off into the intellectual empyrean with metrizable.

~

Still wearing our lexicographer’s hat, here is an attestation for a word with which I had previously been unfamiliar, used by a philosopher of science.  After a rather confusing Gedankenexperiment judging the verifiability of a physical geometric hypothesis, involving all sorts of skulduggery with measuring rods, and “tampering with the semantic anchorage of the word congruent”  (that’ll get you two weeks in the clinky  without the option), and in which Albert Einstein (from beyond the grave) plays a role like that of Fantomas, battling the equally post-mortem shade of Pierre Duhem,  our professor writes:

The required resort to the introduction of a spatial dependence of the thermal coefficients  might well not be open to Einstein.  Hence, in order to retain Euclideanism, it would then be necessary to remetrize the space.  ….  Einstein’s geometric articulation of that thesis  does not leave room for saving it by resorting to a remetrization in the sense of making the length of the rod vary with position or orientation  even after it has been corrected for idiosyncratic distortions.  But why saddle the Duhemian thesis as such  with a restriction peculiar to Einstein’s particular version of it?  And thus why not allow Duhem to save his thesis by countenancing those alterations in the congruence definition which are remetrizations?

-- “The Falsifiability of Theories”, in: Adolf Grünbaum, Collected Works, vol. I (2013), p. 72-3

As indicated, I couldn’t really follow the dialectical taffy-pull in that conterfactual-strewn discussion, but simply cite the passage as though on one of those “citation slips” we used to rely on at Merriam-Webster.

~

I just now happened upon a passage which we quoted earlier in another context (here):  a use, by a mathematician (or if you prefer, a logician) of the in-itself-not-expressly-mathematical term measurement,  not in a technical mathematical sense such as measure zero or measure theory,  but sliding mathwards towards concepts very far from any plain man’s conception of “measurement” (as: wholly non-numerical, non-quantitative   fundamental group):

Mathematics is, as it has always been, largely the science of measurement.  But “measurement” must here be understood as referring to more than the meter stick.  The genus of a topological figure  measures one of its aspects;  objects of genus zero  are in a sense simpler than those of higher genus. 

There are many dimensions of measurement ….:  characteristic, transcendence degree, cardinality, fundamental group … Occasionally we are so successful in the science of measurement  that we can completely characterize an object … by giving, as it were, its latitude and longitude:  its measurements in the relevant dimensions.

-- Herbert Enderton, “Elements of Recursion Theory”, in:  Jon Barwise, ed. Handbook of Mathematical Logic (1977), p. 554

I originally cited that as a not-especially-successful attempt (in its first sentence) at a one-line characterization of What Mathematics Is.    Measurement, in the usual sense, is common to a great many studious activities, from chemistry to engineering to dressmaking.   He only manages, in what follows, to make that characterization  more or less work, by moving the goalposts  and re-defining measurement in his own Pickwickian sense.
 

~

A philosophically alert historian of physics  calls attention to a linguistico-philosophical subtlety in the word measurement as it is used in quantum theory:

In all cases, an observation is accompanied by a measurement.  The converse is not true, however, for we may quite well perform a measurement and yet fail to observe the result.  [ndlr:  That much is true but trifling, but then he goes on to make his point.]  Now in considering the disturbance generated by an observation, we must make clear that the disturbance is caused by the physical measurement, and not by the cognitive act whereby the result of the measurement is comprehended by the percipient. … The observation is rendered possible by the collision of the photon with the particle, and hence it is this collision which constitutes the measurement.

-- A. D’Abro, The Rise of the New Physics (1939), vol. II, p. 667

Here he is not making an actio/actum distinction in the term measurement (though one exists; for the actum, “Her measurements are 36, 28, 36”), for we are still dealing with actio here:  but he is at pains to remove the connotation of a (human) action -- a human act, which one foggy school of thought has deemed central and essential  to all of quantum physics.  Observation, D’Abro is saying, is a human action;  measurement is whatever triggers the collapse of the wave-function.

~

This whole question of measurement  is, for the man meditating over brandy, frankly pretty annoying.    We want to know the scheme of things -- if equations be at the base of it, well and good, the more general the better.  (As:  Hamiltonian dynamics;  Set Theory; Topology.)  Beholding Saint Peter’s or the Taj Mahal, we wish to savor the whole, and perhaps to penetrate to the aesthetic and formal ideas behind them;  but we do not wish to know the length or this or that member in centimenters, nor how much the materials cost, etc. Such matters are distinctly hypo-ouranian.

In latterday musings upon quantum theory, measurement has been lifted to a role rather like that of (in earlier days) action, or conservation of energy -- or rather, like that of the Demiurge, bringing entities (or the values of their parameters) into existence.  Yet in practice, they don’t always even tell you much about what you are trying to measure.

Measurements on the force of attraction between two electric charges  will not  in general  verify Coulomb’s law.  We observe that the force depends  in some peculiar way  upon the position of external charges, which suggests to us that the measured effects  are not entirely due to the system in question, namely, the two test charges.

-- Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p. 524

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