Sur la pluralité des temps

 

[With apologies to Fontenelle, Entretiens sur la pluralité des mondes (1686). ]

A historian writes, that our modern sense of Time is no older than the industrialism of the United States;  though Time, to be sure, itself is rather older.

How does this fit in with the Bergsonian dichotomy of temps vesus durée (Essai sur les données immédiates de la conscience, 1889) ?

 

~

Note:

Newton himself, not concerned with psychology,  conflates the two:

Absolute, true, mathematical time, of itself and from its nature, without relation to anything exernal, flows equally; and its other name is duration.

-- Principia Mathematica

 

In histories of science, that passage may be cited in distinction to Einstein’s relativistic doctrines.  But one historian notes a caveat well prior to relativity:

 

Somehow Newton failed to see the circularity of this definition.  It has become clear since his day  that his concept of uniform (“equal”) flow of time  was redundant, since it is impossible to give any meaning to such an assertion of uniformity  unless the concept of time is already established.

-- Lloyd Taylor, Physics: the Pioneer Science (1941)

In the context of Relativity, self-standing Time  is abolished altogether:

 

“Raum für sich  und Zeit für sich  sollen völlig zu Schatten herabsinken, und nur noch eine Art Union der beiden soll Selbständigkeit bewahren.” (Minkowski, 1909)

(“Independent Space and Time  must sink into the shadowland”.)

 

~

Temps (the usual word for ‘time” in French) is a feature of physics;  durée (lit. ‘duration’), a feature of lived experience, of the mind.

The former experienced its own bifurcation into (absolute) Newtonian time, and (relative to the observer) Einsteinian or Relativistic time.  Though cognitively uncomfortable to the many, at the time of its introduction, after a bit of familiarity  it all fits comfortably into basic math and physics, the former being simply a limiting case of the latter.   (Similarly, the intelletual scandal of the discovery of Non-Euclidean Geometry  was eventually digested, with the Euclidean being a sort of limiting case of the Spherical and the Hyperbolic.)

So now (per our historian) we must wrestle with a new entity:  Taylorized time -- time cut into lengths by the stop-watch brandished by a steely-eyed time-and-motion man, seeking to squeeze the last ounce (excuse me -- millilitre) out of the workforce.

Since that has nothing to do with physics, it is no contribution to our understanding of temps, but is rather a new take on durée, varying historically and culturally.

~

Footnote:  I have always been a bit puzzled by Proust’s title A la recherche du temps perdu.   How shall we characterize his use of temps here?  One subtlety:  its implications and connotations evolve in the course of the novel.   A literal translation, In Search of Lost Time, sounds trivial, terrible.  Translator Scott-Moncrieff neatly skirted the problem with his resort to the Shakespearian Remembrance of Things Past.

~

For further pensées concerning Time, from both literature and from physics, try these:

=>  https://worldofdrjustice.blogspot.com/search/label/time

 

T-T-T-Time Monostichs

the ticking no-noise

of the night

-- Robert Penn Warren, All the King’s Men (1946)

 

a big grandfather clock  offered us

the slow ,      small,

in-di-vid-u-al   pellets   of

time .   .   .   .   .   .   .   .   .  

-- ibid

[A few pages later in the novel, that pithy abstract characterization  is fleshed out in its impact on the narrator’s consciousness:]

The grandfather’s clock, I suddenly realized, wasn’t getting any younger.  It would drop out a tick, and the tick would land inside my head  like a rock dropped in a well,

and the ripples would circle out and stop,

and the tick would sink down in the dark.

For a piece of time which was not long or short,

and might not even be time,

there wouldn’t be

an-y-thing…

Then the tock would drop  down the well,

and the ripples would circle out  and finish.

-- ibid

Zen Physics

A wristwatch worn

by a particle of light

would  not  tick     a-tall.

(-- after Brian Greene; slightly modified, to please the Muse)

Dr. Greene delivers himself of this epigram, in the course of explaining that we

 each of us, all of us,

 even Achilles and the tortoise,

move equally at the speed of light.

To be sure, in a Pickwickian sense (dividing our motion between space and time).

~

Clocks on Earth    tick

a tiny bit

s l o w l y

relative to those in interstellar space.

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

The Big Bang itself   is at the bottom

where all the worldlines  converge.

There is no time

before    that …

-- ibid, p. 81

Something to hum in the summer

Time-slices

Lemon ices.

Slices of time

with a wedge of lime.

[Those verses occurred to me  while reading a text on Special Relativity.

They do not constitute a substantive contribution to the subject,

but they were the best I could do at the … time.]

Twinned Eternities

In the poem portion of Nabokov's Pale Fire (1962), we read:

Outstare the stars. Infinite foretime and infinite aftertime.

The basic lexicon of Classical Arabic, as it happens (with its wealth of words), distinguishes these two, with a brief, monomorphemic word for each:

أبد  [abad] prospective eternity (with a terminus post quem but no end)

أزل [azal] retrospective eternity (with a terminus ante quem but no beginning)

Reflecting separately on these  raises interesting philosophical questions, e.g., regarding the indestructibility of the soul.  But as a merely intellectual matter, the picture will be clear to anyone who has got as far as geometry or calculus -- "half-infinite" directed intervals (such as the non-negative reals).

In Laughter in the Dark (English version 1938), Nabokov plays with the twinned hemi-eternities, in a passage full of satire:

“Haven’t I met your sister once?” queried Dorianna in her lovely bass voice.

“My sister is in Heaven,” answered Rex gravely.

“Oh, I’m sorry,” said Dorianna.

“Never was born,” he added.

Much is rustling beneath the sheen of this. First, Rex, po-faced, lays a logical snare for Dorianna, knowing that she would automatically assume that the now-absent soul is residing in the after-eternity (Arabic abad), which is all that most people ever think about, or even conceive to exist. An extra twist is provided by Dorianna’s automatic, flustered response at the unexpected reply – the conveyed sense is meant to be, “I’m sorry for your loss,” but simply stringing bits of syntax together yields, “I’m sorry that your sister is in Heaven.” (**) Rex then, indirectly pointing out the ambiguity in his initial statement, and implicitly rebuking Dorianna for failure to perceive ambiguity (again, in whatever sphere, most people don’t), reveals that this sororal Arlésienne is in fact at present domiciled in the ante-eternity (Arabic azal).

That passage, incidentally, rests as well on the paradox alluded to last time, that of the indestructibility of the soul. Intuitively, we think of a soul as the sort of thing (being brewed, after all, from the aethers of the Eternal One) that doesn’t simply wink out of existence. But by the same token, it shouldn’t be the sort of thing that simply winks in – in which case it must, as in the Platonic conception, be “stored up” somewhere (Rex specifies Paradise as the ‘green room’ or on-deck circle, though probably more from a faux-polite convenance than from any committed Platonism).

That observation does not exhaust the (depthless!) well of paradox subtending such insight. Follow it out, and you’ll encounter a retrospective version of the quantum-mechanical “many-worlds” scenario.

(**) P.G. Wodehouse plays on the same effect. In his world, earls are crotchety and idiosyncratic, and butlers are perforce imperturbable in the face of all.

            “Dash it, Beach, this egg is undercooked!”

            “Yes, sir.”

            “What – is the cook out sick again?”

            “Yes, sir.”

            “Well, I’ll be damned!”

            “Yes, sir.”

(Picture an infinitesimal lengthening of the glide initial: “Yyyes, sir.” The joke is, the double-meaning will be completely lost on the earl.)

~

It was the contention of “The Stokes Conjecture” (a chapter in my book, The Semantics of Form in Arabic)  that possession of such a neatly twinned pair of monomorphemes as azal and abad, as opposed to such roundabout (and nonce) phrasal confections as “infinite aftertime”, should track with a greater tendency of speakers of the language so outfitted, to be clear on the subject, for it to be cognitively relatively accessible, and thus to accrete around it  further developments both morphological (derivata) and semantic (metaphors).   Whether this be the case for Arabic letters and Islamic theology, I leave to my learnèd readers to make out.

~

The casual reference above, to the isomorphism of azal and abad, as constituents of infinite Time, to the half-rays  as subsets of the real line, conceals a textural disparity, in point of richness.   Not, as you might imagine, in favor of the human/experiential conception of Eternity, but the mathematical/intellectual science of the Real Line.

We really don’t know what to do with Eternity -- and literally, wouldn’t know what to do in it.    Like the silence of the infinite spatial reaches that so dismayed Pascal, we stand aghast at the prospect of doing anything “forever”, be it strumming harps or standing around on clouds swapping New Yorker captions.   The prospect of an infinite afterlife, for which we are supposed to yearn, is strictly baffling.

(Note that there is nothing heretical in that observation of human psychology;  notably, C.S. Lewis was converted to Christianity  before any sort of belief in or appreciation for  an infinite afterlife  was granted him.)
(For a mathematician's take on how the afterlife shall be spent, try this.
For an equine perspective,  this.)
(I riff upon the bafflement in the azal case, here.)

The Real Line, by contrast, is … infinitely diverting.   To begin with, even in a low-focus broad view (abstracting from the  so to speak  “quantum foam” of the infinitessimally inspected continuum), it harbors a great many other infinities within itself.  Thus, that infinite ray or half-line,  [0, ∞ ), is topologically equivalent to a mere half-open interval,  [0, 1):  in both cases, you can cover the space with a countably infinite sequence of disjoint intervals, no finite subset of which can do the job.  Thus, for the ray: [0,1), [1,2), [2,3) …. etc;  for the interval, [0, ½) [½,¾), [¾, 7/8) …

Further, the infinitude lies not only in thus stretching out forever, but in drilling down.   Any interval (even one that is closed, and thus compact) harbors infinitely many intervals as subsets;  and any such patch contains an uncountably infinite collection of points.  (We recall Dyson’s title, “Infinite in All Directions”, but with ‘directions’ differing qualitatively rather than simply like a compass needle.)

And those are just the appetizers.  The continuum is a regular zoo of exotic creatures -- the Cantor set, the Borel sets, projective sets, and a host of others studied in the discipline of “Descriptive Set Theory”.

~

As for those specifically twinned infinities, staring at each other from opposite sides of a mirror, they have a counterpart in modern physics, which takes reversibility of Charge, Parity, and Time (separately for some processes, in combination for others) as a kind of credo, like Liberté, Egalité, Fraternité.   Traditionally, time-reversed solutions were usually dismissed out of hand as unphysical;  other, more venturesome theorists, embraced them, telling fables of antiparticles as simply particles moving backwards in time, among other scenarios that chill the blood.

[ShoutOut:  Many thanks to Djinn ibn Sayârah  for help in formatting this for posting here.]

[Afternote]  My friend the Arabian theologian writes in :

Mark Twain wrote, regarding death:

“I do not fear death. I had been dead for billions and billions of years before I was born, and had not suffered the slightest inconvenience from it.”

That's kinda funny for as far as it goes, but no one who has experienced consciousness can be seriously flippant about it being snuffed out.

.

Slices of Time

Brian Greene monostich

(Not quite a monostich,

nor a haiku neither.

It is  what it is.)

Every moment is illuminated,

and every moment    remains illuminated.

Every moment  is.

-- Brian Greene, The Fabric of the Cosmos (2004), p. 141

https://en.wikipedia.org/wiki/Everything_Is_Illuminated

~

I have  on occasion  fulminated against “Physics porn” -- the tawdry down-dumbing of physics for a popular audience -- not so much a matter of (necessary) simplification, as of appealing to their baser, sensationalistic instincts.

Brian Greene does not practice that. The books of his that I have read (The Elegant Universe, The Fabric of the Cosmos) -- with titles like the Parthenon, elegant but restrained -- are worthy examples of haute vulgarisation.   The matters he treats of  are difficult to explain, even to fellow-physicists (if they work in a different lab, and thus subscribe to a different groupthink); he does a laudable job of trying.  Moreover, the fellow writes really, really well -- at times even poetically (witness the above).

Nor is the cited haikustich  poetry merely.  The idea behind it, appears in the next paragraph  in plain prose:

Einstein said that the problem of The Now  worried him seriously.  He explained that the experience of the Now  means something special for man, something essentially different from the past and the future, but that this important difference  does not  and cannot occur within physics.

Albert Einstein,  worrying about The Now

That is not to suggest that the Now at all resembles a mathematical instant, as in the calculus and thus in classical physics.  Each perceived ‘moment’ of consciousness presumably corresponds to an integral over some interval.   The ‘density’ being integrated need have no determinate evaluation at a single point of the continuum, any more than does the Dirac delta.  The psychological present is more of a Nowabouts.

The same point, with a different metaphor:

The practically cognized present is no knife-edge, but a saddle-back, with a certain breadth of its own  on which we sit perched.

-- William James, The Principles of Psychology (1890), vol. I, p. 609

The present is simply the past’s ever-moving outer edge.

-- Hendrik Hertzberg in The New Yorker, 18 Dec 2006, p. 33

~

That the “now”, as such, has no special status in physics, is unsurprising, since it is relative to each observer.  That simultaneity (implicitly dependent thereon:  “Both A and B are happening now”) turns out to be untenable, was a shock introduced by Einstein; eventually you sort of learn to live with it.   The real scandal is that physics is likewise agnostic as to any distinction in principle between the future and the past.   And that thesis is cognitively and theologically abhorrent.

Feynman among others calmly accepted solutions to equations, whereby certain particles ran backwards in time.  At its grandest, as a prominent mathmatician-cosmologist writes, “the time-reverse of the universe  is just as much a solution of the dynamical equations” as the one we thought we lived in (Roger Penrose,  The Road to Reality (2004), p. 729).

For humans, the unidirectionality of time’s arrow  is as fundamental as the privileged status of the Now.  America’s premier 19^th-century psychologist, on remembering:

However the associationist may represent the present ideas as throning and arranging themselves, still, the spiritualist insists, he has in the end to admit that something, be it brain, be it ‘ideas’, be it ‘association’, knows past time as past, and fills it out with this or that event.

-- William James, The Principles of Psychology (1890), vol. I, p. 2

eppur’ si muove …

~

James crops up in the first paragraph of a New York Times op-ed concerning durée (subjective time) from 10 May 2015, by Gregory Hickok, a professor of cognitive science:

In 1890, the American psychologist William James  famously likened our conscious experience to the flow of a stream … the stream … of consciousness.

The professor then puts his predecessor in his place:

Recent research has shown that the ‘stream’ of consciousness  is, in fact, an illusion.  We actually perceive the world in rhythmic pulses rather than as continuous flow.

The cognitive scientist then climbs down a bit from the claim that this insight is “recent” -- “Some of the first hints of this new understanding came as early as the 1920s, when physiologists discovered brain waves.”

One suspects, however, that James would not slap his forehead upon being apprized of this newly-minted insight, since he cites “the Humian doctrine that our thought is composed of separate independent parts, and is not a sensibly continuous stream”.  (Hume wrote in the eighteenth century.)

Pugnaciously vacuous definitions

At the beginning of his preface to the introductory exposition Philosophy of Logic (1970),  W.V.O. Quine quotes Tweedledee:

“Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t.  That’s logic.”

That was a bit of nineteenth century donnish waggery (though it does give rather the flavor of modal logics and possible-world semantics  in our own day).

Quine then drolly goes on:

If pressed to supplement Tweedledee’s ostensive definition of logic  with a discursive definition of the same subject, I would say that logic is the systematic study of the logical truths.

We pause for Homeric laughter.

Anyone schooled in the lore of Russell’s paradox and impredicative definitions, will recognize that the professor is having his fun.

He then has some more:

Pressed further, I would say that a sentence is logically true  if all sentences with its grammatical structure are true.  Pressed further still, I would say to read this book.

(Ah!  ‘Tis a plaint  we ourselves have often made:  Buy my books!)

[Note:  Contrast the  equally terse but quite unselfreferential definition of logic in

R. Goldblatt, Topoi , 2^nd edn. 1984:  “the study of the canons of deductive reasoning”.  Word for word, that’s very good.]

The jest is not without a subtle content, assuming as it tacitly does that there are such things as logical truths (a subject we see in a different light after Quine’s own extended attack on the analytic/synthetic distinction).   And it is quite in line with Quine’s celebrated existential bon mot:

    “To be is to be the value of a variable.”

To non-initiates, that will be mystifying;  to semi-initiates, cheeky; to familiar navigators of Quinespace, an ultra-compact allusion to his perennial concern with ontology in relation to quantification.

Put more pugnaciously:

Existence is -- what existential quantification expresses.

 -- W.V.O. Quine, “Existence and Quantification” 

[Further Quinefun  available here:
http://worldofdrjustice.blogspot.com/2015/01/quine-on-bunnies.html ]

~

The celebrated Cambridge Philosopher of Bland, G. E. Moore, wrote in his Principia Ethica:

If I am asked, “What is good?”, my answer is:  Good is good;  and that is the end of the matter.

That is:  If you have to ask, I can’t tell you.  (Even so, that pseudo-definition is preferable to the nihilist/reductionist dismissal by the Eliminative Materialists.)

Indeed, I shall now venture a definition  quite in Moore’s spirit:

Truth is … what is true (and known to God as such), quite apart from human-knowability, let alone provability (whether by finitistic, intuitionistic, or classical means).

~

From a college textbook:

A measure space consists of a set X equipped with two fundamental objects:

(1) a σ-algebra M of “measurable” sets, which is a non-empty collection of subsets of X closed under complements and countable unions and intersections.

(2) A measure μ: M -> [0, ∞] with the following defining property …

-- Elias Stein & Rami Shakarchi, Real Analysis (2005), p. 263

The bolded terms are there defined; but the term measurable sets is not -- the clause that follows reminds us of the definition of a σ-algebra instead.  The authors acknowledge their sleight-of-hand (effectively remedied by material elsewhere in the book) by placing the offending word in quotation marks. -- Note that this typographic care exemplifies the semantic Akribie of math writers, which we have elsewhere praised.

Not all math authors are as onomastically aware as those.  As:

Old-fashioned text-books  tend to start off with mystifying definition of these terms:  Euclid’s own definition,  “A point is that which has no part”, is a good example.  After a perfunctory discussion of these, the author clears his throat, begins a new chapter, and gets going with some concrete examples:  the definitions are mercifully forgotten.

-- Stephen Toulmin, The Philosophy of Science (1953), p. 72

~

To define -- literally, ‘delimit’ -- is by way of penning-in the definiendum with antecedently familiar landmarks.   To say that none such exist, is to refuse definition;  as in this classic hymn:

There is nothin' like a dame,
Nothin' -- in -  the -  world,
There is nothin' you can name
That is anything like a dame!

-- “South Pacific”

By this point  we have passed definitely from the realm of Oxbridge drollery to that of Joe on the Boat.  And here, indeed, we discover a whole subculture of definitional legerdemain, noticed in the delightful Dictionary of American Slang, by Wentworth & Flexner (1967).   In the Supplement we find this entry:

blivit   (n.)

   Anything unnecessary, confused, or annoying.  Lit. defined as “10 pounds of shit in a 5-pound bag.”  Orig. W.W. II Army use.  The word is seldom heard except when the speaker uses it in order to define it;  hence the word is actually a joke.

As a former harmless-drudge chez Merriam-Webster, I salute that as a gem of the lexicographic art.

A classic development of the pugnaciously uncooperative definition -- Lexicography with an Attitude -- is The Devil’s Dictionary, by Ambrose Bierce.  (Sample:  “fork: an instrument for putting pieces of dead animals into the mouth.”)  Similarly impish was Hobbes’ definition of paradox:  “an opinion not yet generally received”.

A Pugnaciously Vacuous definition of the meaning of life  can be viewed here:

http://worldofdrjustice.blogspot.com/2012/03/ask-dr-science.html

~

Quite other than such conscious humor, are cases like this:

Hamilton follows the Kantian notion of time closely in his “Essay on Algebra as the Science of Pure Time”.  Since the inner sense of time is more general than the outer sense of space, Hamilton concludes that algebra is a more general and fundamental branch of mathematics than geometry.

-- Thomas Hankins, Sir William Rowan Hamilton (1980), p. 268

As the discoverer of quaternions, Hamilton has as much right as anyone to deliver himself of after-dinner remarks (a genre of public speaking to which he was particularly devoted) about the nature of algebra;  but this one is horse-hockey.

 

(Psychohistorical note:  Hamilton was for a time utterly immersed in Kant;  this characterization of algebra as the “Science of Pure Time” stems from psycho-philosophical exuberance, rather than algebraical expertise. 

A curious tentative parallel might be made with Hamilton’s countryman G.K. Chesteron, who likewise was given to flights of literary exuberance;  both were in marital situations requiring a great deal of self-sacrifice,  which they met with infinite patience;  and both were given to a kind of idealism  which some might diagnose as compensatory.

Okay, beyond our pay-grade.  Yet as Silvan Schweber affirms in his perceptive review [Isis, 1982] of this exemplary socioscientific biography:  “Hankins has eschewed giving psychoanalytical interpretations, [but] to anyone interested in the psychodynamics of creativity, William Rowan Hamilton presents a fascinating case study.”)

~

Another subcategory -- already bordered on by Hamilton’s epigram for the definition of algebra -- is formed by definitions which, while not vacuous, we might label Pugnaciously Perverse.   The poet Coleridge was (unfortunately) Hamilton’s philosophical mentor, even as regards what Science ought to be; and he defined that subject  thus:

“any chain of truths which are either absolutely certain, or necessarily true for the human mind, from the laws and constitution of the mind itself.  In neither case is our conviction derived, or capable of receiving any addition, from outward experience, or empirical data.”

-- Thomas Hankins, Sir William Rowan Hamilton (1980), p. 268

(That first sentence does oddly prefigure the sort of prose  churned out by the truckload by the epigones of Donald Davidson.  -- Note too the anticipation of Post-Modernism.)

~

Another non-cooperative move in the orismological game, is pooh-poohing the very definiendum -- denying that there is anything coherent to define.  One Christian writer (C.S. Lewis or Hilaire Belloc, I forget which) once said testily, that the notion of “the Renaissance” was a will-o’-the-wisp, used  by secular writers to mean “whatever I like that happened in the fifteenth and sixteenth centuries.”

~

Composing a truly vacuous definition  is harder than you’d think.

Thus, consider the Euclidean definition of a point (“that which has no part”) which our philosopher friend scoffed at;  and let us phrase it even more egregiously:

point:  a point-like figure

That actually has cognitive content.  It means:  To visualize what is meant when geometers refer to a punctum (as opposed to a linea, etc.), think of something like a pencil-point.  Do not think of something like a dance-floor, or the cosmos, or an elephant.

And:

set:  a set of elements

Here the definition is so far from vacuous that someone could reasonably object that it is actually false, since it excludes the null-set.   (In this ‘definition’, the stress, so to speak, is on “elements”; “set” could be replaced by “bunch” or “passle” or “bucketload”.)

For indeed:

There is no direct circularity  if we presuppose sets in our study of sets (or induction in our study of induction), since the first occurrence of the word is in the metalanguage, the second in the object language.

-- Michael Potter, Set Theory and its Philosophy (2004) , p. 9

In further defense of impredicativity:

Impredicative definitions are necessary for ordinary mathematics, as they are unproblematic if one adopts a realist attitude about the objects defined -- realist in just the sense that the objects exist in advance of the definitions, that they are picked out by the definitions, not created by them.  That imposes a substantial constraint on any acceptable philosophy of mathematics.

-- Shaughan Lavine, Understanding the Infinite (1994), p. 107

~

The grandfather of all tautological definitions is the one given by Yahweh in Exodus: 

~ ~ ~  I  Am   That  I  Am  ~ ~ ~

Yet at the same time, that is the best definition that could be given, since, in a common view of the Abrahamic religions, any limitative predication would be false.   (That view led in particular to the via negativa,  which insisted on the denial of all suggested predicates of the One.)

~

Another style of coyness with definition  is illustrated in the following, immediately after the authors have introduced Maxwell’s Equations  for E and H in free space:

At first we do not attempt to give physical meaning to these symbols.  We merely say:  let us assume that there exist physical quantities represented by symbols having the indicated properties, and see what these equations say about the quantities.  From the last two equations [to the effect that E and H -- whatever they might be -- have divergence zero], it is clear that E and H are solenoidal …

-- Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p. 303

After a few pages of discussion, the authors summarize:

In a very real sense, therefore, these equations may be said to constitute a definition of E and H.

-- Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p. 306

Thus, back where we began.  The dangled definition in intuitive terms, is ultimately withheld:   No dessert until you finish your broccoli;  then -- Your broccoli was your dessert.

They subsequently reinforce the apophatic stance:

Physical meaning of E and H:  … The only real importance of the quantities is involved in the fact that they satisfy the field equations. … It seems most logical to go the whole way and treat E and H as defined by the field equations in all cases.  The commoner definitions can then be looked upon as mere picturizations. -- Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p. 311

E & H:  They Are That They Are.

~

Lakatos offers his translation of an epigram from Poincaré:

    Mathematics is the art of giving the same name to different things.

Now, that is not vacuous (i.e., vacuously true, or anyhow only infinitessimally informative), since it is egregiously false;  but it is a witticism, not a blooper, since we all know that Poincaré was perhaps the leading mathematician of his time -- he has some cards up his sleeve, which he will slip out when it suits him.

For a series of essays on the art of definition, with especial reference to math,
try these:
http://worldofdrjustice.blogspot.com/search/label/definition

Hour Wars (fusée horaire)

Time was, if an Anglo-American sought a safe unflustering topic to discuss in the drawing room, topic of choice was the weather.    But now, in the midst of global climate change and its strenuous deniers, so bland and traditional a greeting as “Hot enough for you?” is liable to provoke a fistfight.

Alright -- Into the lumber-room of forbidden subjects it goes, lying anyhow among the jumble of race, class, religion, economics, sex, and all the other no-nos.   So, what remains as a sufficiently anodyne conversation opener?

How about, “What time is it?” ? -- Well, so far  that sally leads to no bloodshed on the Yankee side of the Atlantic:  But do not try it in Spain.  That nation is now heatedly debating bringing its time-zone into line with geographical reality.   Sounds straightforward enough.    But -- How did it ever get out of sync in the first place?  Turns out it was nakedly political;  you can hear the strange tale here:

   http://www.medi1.com/player/player.php?i=5631230

In summary:  The dictator Franco, back in his heyday, changed his country’s highterto realistic and conformable timezone  to be one hour later -- so as to share the timezone of the fascist dictatorships, Germany and Italy, to the east!   And to this day, no-one has undone it.