Tuesday, January 31, 2017

The Urysohn Metrization Theorem: a biochemical derivation


(I)  Various physicists, working with cesium-filled chambers and the like, have reported results that, at least as reported in the press, seem supraluminal.   Their technique is admirable; their results, at least as entertaining as that of the Euler disk; but they by no means dethrone the position of the speed of light in a vacuum, c, which still reigns at the center of physics.  Their surprising lab results may be compared with the paradoxical distinctions of group-velocity vs. phase velocity, in wave phenomena, or unphysical illusions such as in the thought-experiment of flipping a flashlight left to right-- millions of years later, on the arc of heaven as it were, an illumination mimics that trajectory with distances multiplied by a zillion, so that the 'signal' moves supraluminally, though nothing is actually moving left to right. A curiosity.  Einstein in heaven is not tearing his wild white hair.

(II) Various neuroscientists, sticking electrodes into hapless experimental subjects, detected electrical blips in the brain, as many as seven seconds before the fellow (responding to the prompting, “Coffee tea or milk?”) at last says, “Tea please.”

Neuroscientists -- an excitable lot -- froth over this.  “We feel we choose, but we don’t” enthuses one from the University College, London (whom I shall not name, so as not to defame; quotation from 1 Sept 2011 Nature).  Furthermore (adds one of his henchmen, in the same issue):

It’s possible that what are now correlations  could at some point become causal connections between brain mechanisms and behaviours.  If that were the case, then it would threaten free will, on any definition by any philosopher.

[“… any … any…” : sic; sic.]

The only reason such illation might have any color of probability, is that the neuroscientists (whose characters were formed in the laboratory, pithing frogs) regularly choose actions too trivial to reflect our real humanity.  In the case above -- I lied about the Stewardess Trilemma, really all the experiment was about was pushing some damned button, a button which moreover had no effect upon anything.  Boring beyond belief. No doubt the experimental subjects were in a coma throughout the experiment, or Dreaming of Babylon;  meanwhile the burblings of the subcortical tissues continued, much like the similar borborygmus of the bowels;  until eventually a finger twitched:  Ah what the heck, push now.
Not to knock it -- such results might even scale up.  Thus, to take the creature dear to the Churchlands, the sea-slug:  quite possibly its “choice” to slime-right or slime-left, at any given instant, owes its promptings largely to meteorological and other influences, with any accompanying mentation bearing but the faintest resemblance to the decision to enter the priesthood, or to see if cohomological algebra can yield insights into Yang-Mills theory.  But it doesn’t scale up to us -- at least, not to us at our best.  Prior, say, to coming up with the Urysohn Metrization conjecture, and then coming up with its proof, there was plenty of unconscious ruminating, and well more than seven seconds’ worth.  No mathematician denies it; all proclaim it.  (Poincaré stepping onto the bus.)   But that doesn’t mean that the truth of the Urysohn Metrization Theorem, or even the validity or coherence of our proofs thereof, are caused by, or bear any structural resemblance to, the sort of subcerebral singultus that so fascinates the guys in the lab.  While button-pushing may be close enough to a reflex action, that you could imagine it might just fall out of biochemistry, without invoking mind or will at all, that really doesn't work to explain such mental palaces as the UMT.

After all:  Free will, like the Cosmos itself, is a gift from our Maker, not just something we picked up at WalMart.  Hence  there is no a-priori reason why it should be intuitively understandable, or even analytically explicable (without millennia of hard work, and even then may lie beyond our poor powers), any more than is the Cosmos.

Sunday, January 29, 2017

Angst in January



The sun obscured through winter silver,
quite as you’d see it from Saturn, in all seasons:

distant;  impotent;   appalled.

Thursday, January 26, 2017

The Ontology of Physics (updated)



The question at issue here is, What sort of entities are fundamental in physics?  E.g., in the late nineteenth century through early twentieth centuries,

whether atoms were real objects or only mnemonic devices for coding chemical regularities.
-- Abraham Pais, Subtle is the Lord (1982), p. 80

The idea of atoms in some sense  goes back to Ancient Greece; and today, they are taken for granted.  So it is surprising to laymen, how long opposition to a Realist take on atoms lasted among some philosophers and physicists (e.g. Ernst Mach).  An opposing view, from a leading German chemist:

Ostwald’s ‘Energetik’, according to which molecules and atoms are but mathematical fictions, and energy, in its many forms, the prime physical reality.
-- ibid, p. 83





Good bluff Rutherford, by contrast, had sucked atoms with his mother’s milk, and claimed that he “could see the little buggers as plainly as a spoon”.

Oddly, the debate on this seemingly practical laboratory matter,  had elements more characteristic of political or theological controversy, in which neither side has a prayer of of convincing the other by rational argument:

The most remarkable fact about the nineteenth century debates on atoms and molecules   is the large extent to which chemists and physicists spoke at cross purposes, when they did not actually ignore each other.
-- ibid, p. 80
~



Since that time, a host of new physical building-blocks have been proposed, and in some cases observed: from the unexpected and rather unwelcome muon (I.I. Rabi: “Who ordered that?”), to the massless chargeless neutrino (rather like Bishop Berkeley’s “ghosts of departed quantities”), through quarks, gluons, gravitons & gravitinos, selectrons & electrinos, axions, preons, virtual photons, phonons … such as might make even Rutherford gag.  But several of these are now widely accepted -- not as mere bookkeeping mechanisms, but as entities with further properties to be discovered;  so that the smart money has been on Realism, so far.

Ernest Rutherford,  swallowing an atom  but straining at a quark


Footnote:
We shouldn’t be too hard on old Ostwald  for backing the wrong horse in the Atoms Affair.   Dissident voices today would declare  as epiphenomenal not only atoms, but even the elementary particles of which those are admittedly merely bundles:  demoted to excitation-states of superstrings;  or emerging from the combinatorial-automaton structure of the world. 
Additionally, his Energetik has enjoyed a bit of a revival in some quarters:
  https://de.wikipedia.org/wiki/Energetik_(Philosophie)

More recently, information (or, solemnly, “The Information” -- Wheeler's "It from Bit") has emerged among some as a skeleton-key to everything else in the physical world.


Thus, at the bottom of everything, behind and beyond the Maya of the particle zoo, lies:

Thales:  Water.
Oswald:  Energy.
John Wheeler:  Information.


Stewardess:  Coffee tea or mi-ilk?
The Milesian:   Just water, thanks.


Or, a more recherché candidate, from philosopher Hilary Putnam:

Nothing has more physical significance than spectral measure.


(That might strike the layman as rather a … spectral candidate for the role of firmest substrate of all.)
~     ~     ~

The word “ontology” is not one you are likely to overhear at the bus-stop;  nor indeed does a physics-major typically run across it.   But the more we see physics as science (Wissenschaft) rather than a special kind of engineering (the “shut up and calculate” ethos of the years around WWII), the more we meet questions traditionally treated under that rubric -- and indeed, contemporaneously, even under that very name. 
As:

My own position is that the issue of ontology is crucial to quantum mechanics.
-- Roger Penrose,  The Road to Reality (2004), p. 785


Let us now return to the ontology of the consistent-histories approach.  The theory operates with entities called coarse-grained histories.  … The ontological status of the insertion of such a projector set  is still not fully clear. …  A history from a maximally refined set seems to me to provide a strong candidate for what might be regarded as ontologially ‘real’.
-- Penrose,  The Road to Reality (2004), p. 788

Present-day quantum mechanics has no credible ontology … The imporance of having an ontologically coherent quantum mechanics cannot be over-estimated.
-- Penrose,  The Road to Reality (2004), p. 860, 865


Re the notion of macroscopic quantum superposition being unproblematic:

This is taking a ‘pragmatic’ stance  that does not really address the ontological issues.
-- Roger Penrose,  The Road to Reality (2004), p. 812

And, full-bore:

Many contemporary thinkers seem to have supposed that, in discarding its mechanist ontology, physics had discarded its ontology:  matter had been dematerialized … The very progress of physics itself  seemed to them to call for the renunciation of mechanism and materialism  in favour of the de-ontologised view of science presented by Mach.
-- John Watkins, Science and Skepticism (1984), p. 138

 
In philosophy proper, ontology is fundamental, being prior to anything else.   In its application to or rather analogue within  physics, by contrast, it historically comes behindhand, as a setting in order of what-all several centuries of reflection and experiment have come up with:  We may think of it as a kind of cast of characters, not fully drawn-up until the play has been written:  in the course of writing it, you find out you need a ladies-maid, and so eventually she is placed upon the prefatory page of Dramatis personae, that typographically precedes the play itself -- and as a nice afterthought, you name her Lisette.  Similarly, particle physics did not begin by being defined, a priori, as (back among the Greeks) the Science of Atoms, or (later) as the Science of the Proton, the Neutron, and the Electron, or (later still-- the Barock Age) as the Menagerie-management of the Particle-zoo (with a fixed given roster of inmates), nor as the Curating of the Wiggling of Strings.  There is a thematic continuity throughout all these stages, but the staffage keeps changing.
As for the role of this Ontology, or Cast of Characters, it is not (despite the spectral example of traditional metaphysics per se) just something to admire from afar, like Mount Rushmore, but rather, as Goedel said pragmatically re which axioms we should adopt for math and logic, they should themselves possess generative potential -- by their fruits ye shall know them.  Thus, hard-headedly:

Kepler’s theoretical ontology, unlike Gilbert’s, was not organically related to his laws;  even if it could be squared with the latter, which seems doubtful, it failed to make any contribution to the testable content of his system.
-- John Watkins, Science and Skepticism (1984), p. 197

~     ~     ~     ~     ~

As remarked earlier, I may well go to my grave without ever grasping the concept of an observable, much less physical ontology in general.   Still, it is helpful towards organizing my thoughts, to have an online scribble-space, so that the matter is, so to speak, officially a topic, a project under way.   For now, this is just a whiteboard on which to stow some juicy quotes.  Your own juicy contributions are more than welcome.
For a more general surview of the ontology of the various sciences, click here.

~     ~     ~     ~     ~


Physics may be defined as the art of saying things about stuff (or stuff about things -- predications concerning entities, for the fastidious).  But what are these entities, whereof we predicate?  In the first place -- observables.

P.A.M. Dirac, The Principles of Quantum Mechanics (1930; 4th edn. 1958), p. 116:

From our assumption that the energy is an observable, there are sufficient stationary states for an arbitrary state to be dependent on them.

For a layman, this is bemusing.  The assumption that it’s an observable?   Can you observe it, or can’t you?  -- Evidently there is much more to qualifying as  “an observable” than merely being … observable.
(Compare Einstein, in one of his Zen moments: "It is the theory that decides what we can observe.")

P.A.M. Dirac, The Principles of Quantum Mechanics (4th edn. 1958), p. 458 (re certain eigenstates):

Science contains many examples of theoretical concepts which are limits of things met with in practice  and are useful for the precise formulation of laws of nature, although they are not realizable experimentally, and this is just one more of them.

Emphasis added.  “Limits” in the mathematical sense.
Note that “not realizable experimentally” does not constitute much of a disability.  What, after all, is?  “Carthage lost the Punic Wars”; “I love you”; “E8 is a 248-dimensional rotation-space”:  no, almost nothing is.


Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p.402:

Quantities such as position, energy, momentum, and the like, capable of measurement… will be called observables,  although it is not intended to imply that they are observable directly.

The caveat is troubling enough;  but now this:

In quantum mechanics, the state of a system is no longer defined by means of a number of variables having an immediate intuitive appeal … In fact, it is not defined in terms of observables at all;  it is simply a function in configuration space.


Carl Hempel, “Problems and Changes in the Empiricist Criterion of Meaning” (1950):
Green, soft, liquid, longer than  designate observable characteristics, while bivalent, radioactive, better electric conductor, and introvert do not.

This odd assertion, by a well-known philosopher of science, seems more psychological than scientific.  It is reminiscent of Locke’s distinction between simple and composite ideas.




Eugen Merzbacher, Quantum Mechanics (1961, 2nd edn. 1970), p. 153:
Following Dirac, we call observable any Hermitian operator which possesses a complete set of eigenfunctions.

This might sound opaque to some, but for a math guy it’s the clearest statement yet, by far.  Of course, what it amounts to physically, intuitively, is something else…


Gerald Holton, The scientific imagination (1978), p. 202:

The idea of making quantitative indicators of anything at all  fascinates some persons, and repels others as dangerous or absurd.  This difference is caused largely by thematically incompatible -- and therefore often unresolvable -- personal views concerning the ability of quantifiables to lead to … the deepest reality.

Note the silly dichotomy -- as though failing to lead to "the deepest reality" (a deeply suspect term) meant that they couldn't be "indicators of anything at all".

~


I had some fun above, playing with a rumpled old word like stuff, shoving it before the microphone of science.  Here a gifted popularizer  makes similar play  with pronouns:

[In its] Einsteinian reframing … is spacetime a something?
-- Brian Greene, The Fabric of the Cosmos (2004), p. 39

In that historical context, the question concerned the ontological status of (the novelty) ‘spacetime’, as opposed to the traditional notions of the independent entities, space, and time.
(More recently, spacetime has been demoted in some theories -- not returning to a Cartesian product of space and time, but being derived as an epiphenomenon of more fundamental items.  Thus, twistor theory, among others.)

If there is no aether to provide the standard of rest, what is the what  with respect to which this speed is to be interpreted?
-- Brian Greene, The Fabric of the Cosmos (2004), p. 45

If an individual electron is also a wave, what is it that is waving?
-- Brian Greene, The Fabric of the Cosmos (2004), p. 88

(Here the wordplay inheres not in the pronoun what, but in the verb.  He could more conventionally have written, “What is the medium for the wave?”, but the startling verbal formulation ‘makes it strange’, confronting us with something more fundamental.)
~
Stephen Hawking, A Brief History of Time (1988; 2nd edn. 1996) p. 75:

The fact that confinement prevents one from observing an isolated quark or gluon  might seem to make the whole notion of quarks and gluons as particles   somewhat metaphysical.  However, there is another property of the strong nuclear force, called asymptotic freedom.  The concept of these entities  was already well-defined, or not, as the case may be:  certainly well-defined as bookkeeping conventions, if nothing more.   Asymptotic freedom -- “at high energies, the strong force becomes much weaker, and the quarks and gluons behave almost like free particles” -- simply adds a further mode of observing their effects:  and in this case, their effects when they are relatively ineffectual -- quarks on holiday.

Failure to be observable in isolation certainly doesn't make a thing "metaphysical" (in the colloquial bad sense intended here).  You cannot observe a "brother" in isolation:  dissect him down to his last tissues, nothing will reveal his brotherhood but the historical context.  Nor, perhaps, can you observe Coulomb attraction in a single isolated particle -- it takes two to tangle.  (I might be wrong on this -- the photon cloud and all that.  But how does the cloud tell you whether you've got an attraction or a repulsion?)


Steven Weinberg, Dreams of a Final Theory (1992),  p. 181:

The positivist concentration on observables like particle positions and momenta  has stood in the way of a “realist” interpretation of quantum mechanics, in which the wave function is the representation of physical reality.


Wiki, "Quantum field theory" (excellent article, btw):

In quantum field theory, unlike in quantum mechanics, position is not an observable.

From the point of view of quantum field theory, particles are identical if and only if they are excitations of the same underlying quantum field.  Thus, the question ‘Why are all electrons identical?” arises from mistakenly regarding individual electrons as fundamental objects, when in fact it is only the electron field that is fundamental.


The global phase of the wave function  is arbitrary, and does not represent something physical.

Wiki, "Implicate and explicate order" (of interest only to those who are already devotees of guru-physicist David Bohm):

 Bohm’s paradigm is inherently antithetical to reductionism … and can be regarded as a form of ontological holism.


Wiki, “Introduction to Gauge Theory”:

The electric field and the magnetic field are observable, while the more fundamental electromagnetic potentials V and A  are not.


~

In this ontological context, it is far from clear how the phrase ‘more like’ is to be applied.  Comparison of historical theories gives no sense that their ontologies are approaching a limit:  in some fundamental ways, Einstein’s general relativity resembles Aristotle’s physics more than Newton’s.
-- Thomas Kuhn, in I. Lakatos & A. Musgrave, eds., Criticism and the Growth of Knowledge (1970), p. 265


Cf. too Dirac’s remarks (1951) that the aether concept was ripe for resuscitation.


[Update 8 May 2012] And now this:
The philosophical status of the wavefunction — the entity that determines the probability of different outcomes of measurements on quantum-mechanical particles — would seem to be an unlikely subject for emotional debate. Yet online discussion of a paper claiming to show mathematically that the wavefunction is real has ranged from ardently star-struck to downright vitriolic since the article was first released as a preprint in November 2011.
The paper, thought by some to be one of the most important in quantum foundations in decades, was finally published last week in Nature Physics
They say that the mathematics leaves no doubt that the wavefunction is not just a statistical tool, but rather, a real, objective state of a quantum system.

I told you so...


Physicists reify space-time. They elevate it from a four-dimensional diagram used to record their experience into the kind of “real essence” that Bohr warned us not to seek.
-- David Mermin (March 2014), at:


~

Not the same as the question of the building-blocks (ontological bricks) of physics, but related to it, is that of the Boundaries of Disciplines:  between physics and neighboring fields (chemistry, mathematics, …) and within physics itself (mechanics, astronomy, electromagnetism, condensed-matter, nucleonics, quantum theory, …).   In one sense, the question is idle -- you are working on whatever project you are working on, with methods appropriate thereto, however outsiders might classify them.  But it also has practical consequences, e.g. in the writing of textbooks.  As:

The traditional teaching of thermodynamics and statistical mechanics  as distinct subjects,  has often left students with their knowledge  compartmentalized, and has left them ill-prepared to accept newer ideas such as spin temperature or negative temperature  as legitimate and natural.
-- F. Reif, Fundamentals of statistical and thermal physics (1965), p. viii

That, from the textbook we used in stat mech at Harvard -- in the physics department, though previously I had only met notions of enthalpy, temperature, free energy, and entropy, in a chemistry course.

Similarly, Lindsay & Margenau remark, in their historical overview Foundations of Physics (1936), that they are moving away from treating optics and electrodynamics as distinct disciplines, “the former being, since Mawell’s time, really a branch of the latter.”


~

God’s-truth vs Hocus-pocus:

It is tempting to dismiss these quantum waves  as mathematical contrivances … but in the laboratory these “probability waves” can be manipulated with mirrors …
-- George Johnson,  A Shortcut Through Time (2003), p. 38

.

Tuesday, January 24, 2017

Help for Hebrew-learners


It is to be counted among the beauties -- nay, the graces -- of Classical Arabic,
as indeed still practiced by the more observant in our own day,
that, before reading-forth Scripture
(or indeed  any text  indited in that language 
wherein the Koran was revealed),
you utter the word  -- just this! -- :

Bismillah.”

Which, being Englished, is as much as to say:  In nomine Dei.
(Let us pause as we contemplate the majesty of al-ism -- ha-Shem.)

~

And now  this winter evening,  reading poetry by candle-light,
and savoring a bit of brandy
(forbidden to the devotees of al-Rasûl,  
but mercifully permitted to those of Moses,
or of the Nazarene Carpenter)
I happened upon these passages,
from the pen of Charles Reznikoff (1894 - 1976;  born in America
of emigrant Ashkenazi parents):

How dificult for me is Hebrew:
even the Hebrew for mother, for bread, for sun
is foreign. How far have I been exiled, Zion.

I have learnt the Hebrew blessing before eating bread;
is there no blessing before reading Hebrew?

~

Time was, one time,  back in the day,
that I fared forth at lunchtime  in the company of damsels:
a lovely Jordanian muslimah, whose name in Arabic means ‘gentle rain’,
and a stern German, a Swabian Christian
(brought along quasi as chaperone)
at a time when I myself,  all pagan and unbaptised,
was quietly Christianizing:
and requested that the Muslimah  should say grace before our meal.

Expecting something elaborate, along the lines of
words I had heard
at the table-grace  of comfortably Protestant-raised relatives,
(“Bless this food to our use,
 and us to thy service … “)

instead she said,  just this:

Bismillah.”

(Such polyvalent brevity 
is actually not characteristic of Arabic,
which seems to have a distinct blessing for every occasion,
along with an appropriate rejoinder.

As, to someone who has just had a haircut:

“Na`îman !”

:

“Allah yin`im `aleek !”  )

~

E’en so!  May not the Hebrew words
that bless the bread,  thus bless the text?

O ye of Zion and of Judah,
of all the Diaspora,
  !

Sunday, January 22, 2017

A simple recipe


Re Einstein’s relativity theory of 1905:

The new theory is based  in its entirety  on two postulates:
 1.  The laws of physics take the same form in all inertial frames.
 2. In any given inertial frame, the velocity of light is the same  whether the light be emitted by a body at rest  or by a body in uniform motion.
-- Abraham Pais, Subtle is the Lord (1982), p. 141

A simple recipe -- but which requires some care in the baking !


[For our own essay at minimalist postulationism, try:  

The Complex Conjugate of Joyce Kilmer





They might exist -- but I don’t know ‘em:
dendrites,  pithy as a poem.



Monday, January 16, 2017

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

Sunday, January 15, 2017

"Great Question"


Two flatulent practices relating to the posing of questions  have characterized political discourse in recent years, to the disbenefit of the polity.

(1)  Particularly associated with Donald Rumsfeld, though the maneuver antedates him, is posing ‘questions’ to oneself and immediately answering them.  Thus, let P and Q be propositions:  instead of saying simply

P.  Not-Q

the rhetorician draws it out into a monologue masquerading as a dialogue:

Is P true?  Sure it is!  Is Q true?   Absolutely not!

The advantages to the speaker are:

(a)  He gets to choose the ‘questions’, irrespective of whether anyone is interested in them or whether anyone would phrase the question in that manner.   As a result, they are invariably softball ‘questions’.
(b)  He gets to dwell in a bubble of his own voice.  Reporters, voters, maiden aunts, all fade into a kind of Meinongian subsistence;  and the Dialectic collapses to a trivial instantiation in the palaver of a single man.

Disadvantages to the audience include:

(c)  There is usually a substantive concern whether some proposition P be true, or what to do about it, or the like.   Yet by this slight-of-tongue, the bloviator poses instead some verbally related but substantively etiolated variant P-prime, and addresses that instead, thereby providing no real information or analysis, but leaving the impression that he has addressed P.
(d)  You have to listen to twice as much verbiage as for a straightforward “P” -- ten pounds of rhetoric in a five-pound bag.  And in time it gets freaking annoying.


(2)   In politically pre-sanitized settings like “town-halls” and related social Spectacles, an array of voters, carefully selected to represent each of the pressure groups to be pandered to, is permitted to pose a simple-minded, vaguely worded question, thus pushing a given button on the candidate’s library of prerecorded on-message speechlets.   But in a new development, the politician moves to snuggle-up to said Potemkin voter, with an enthusastic

   “Great question !!”

before launching in to her canned response.

The practice, repeated ad nauseam  (cf. SNL’s parody of Hillary Clinton’s use of this and similar maneuvers, in their satire of the Presidential ‘debates’), is distressing  even apart from its smarminess.    For the sort of low-info voter who most needs to be buttered-up and flattered, is least in position to actually pose a “great question”, or even a probing or pointed one.    Nor will, say, a scientist giving carefully-prepared, expert testimony on a complex subject  be patronized from the Congressional panel with a “Great question!”   The domains of “Great question!” and great questions, are virtually mutually exclusive.

~

And now, by an unhallowed congressus of these two tricks -- by Beelzebub out of Medusa -- comes the Great Rhetorical Question.  One came up this morning on NPR.


A Republican senator was touting Trump’s intention to
(i)  Increase spending (e.g. on infrastructure and defense)
and
(ii) Decrease taxes,
while
(iii) Holding down the deficit.

Now, this nation has been down that road many times before, both in speechifying and in practice;  so apart from the apparent logical incompatibility among those three desiderata, there is a track-record here, for anyone who cares to examine it.   That, however, is beyond the capacity of most pop journalists practicing today, as well as the attention-span of the average voter.    The substitute for critical inquiry, is a mere statement of undifferentiated unwillingness to be convinced -- the lazy-man’s lo-cal substitute for genuine skepticism (anatomized here).   In this case, the reporter’s Clarence-Darrow move was simply to ask, again, how (i)-(iii) might cohere.   But the politician was ready for it:


“Yes -- How can we address the problem of doing the things that need to be done, while holding the line on the deficit, without addressing the question of Entitlements? -- Great question!”

That may or may not be a Great Question, but the reporter had not posed it;  the rhetorician was congratulating himself.   And in so doing, bait-and-switched the subject from the incompatibility of (i)-(iii) to the problem of those pesky Entitlements.  A perfectly legitimate subject of debate, but here snuck-in via a side door.


~

The considerations above  recall to mind  what, for Europeans, must be the original Potemkin-“question” scam:  to wit, the Socratic dialogue.


The scenario has been solemnly sanctified,  countless times  over many years decades centuries.  The method has been dignified with the title  maieutic (etymologically relating to widwifery), whereby the savant or solon, by adroit interrogation, draws forth from the naïve listener (like a tapeworm from the bowel) innate knowledge  such that all might marvel that he hath.

As a build-up, this is terrific, only… You actually read the texts, and what you see is Socrates holding forth, more or less commendably, and harvesting the plaudits of uncomprehending minions or yes-men.



Thus, a demonstration of the Urysohn Metrization Theorem, via the Socratic method.

Socrates:  Let us, therefore, consider any topological space whatsoever, so that it have a countable basis.  You agree?

Minion: Sho’ nuff, boss!


Socrates: And may we not further stipulate, that said space be regular?  -- Surely that is not too much to ask!

Minion: True dat, Socrates!!

Socrates:  Whence it follows that, our space being regular, for any point thereof, we may define a continuous function  positive at that point, but vanishing outside of a neighborhood of that point. -- You agree?

Minion: Word up dawg, Socrates !!!!

Socrates: Whereupon we may plainly see, that by defining an infinite series of functions from said space, to …

(Socrates drones on;  the minion dozes, but his snores are taken as assent.)

Socrates: Whereupon we may plainly see, that our original space may be smoothly embedded into the countably-infinite Cartesian-product of the cube, which we earlier (you do recall this, don’t you, minion?) proved to be metrizable.  This metric is inherited by our embedded space in the subspace topology, thus proving the theorem.

Minion:  U da man, Socrates !!!

Socrates (beaming upon the evidently innate insight of his pupil):  Great answer !!!

Note:   We have it on good authority from the memoirs of Oxford dons, that any tutor who attempts to apply the Socratic “method” to draw wisdom out of the maws of wool-gathering undergraduates, comes up empty.

Ostracean Epigram



“If you’ve never had a religious experience, it’s folly to believe in God.
 You might as well believe in the excellence of oysters,
 when you can’t eat them without being sick.”


(Quotation from Aldous Huxley’s novel of 1928, Point Counter Point, p. 13.)

Friday, January 13, 2017

Michener monostichs


Re the onslaught of the Tatars in the thirteenth century against eastern Europe:

In a clatter of lances   and a swirl of dust,
they were off to the far adventure.

The result was:

Cities, because of their walls, escaped
these horsemen;  no village did.

As for the heroic but outmatched defenders:

They were Christian  in the great good sense of this word.


(Citations from the historical novel by James Michener, Poland (1983).   Connoisseurs of history might detect a parallel in present events.)

Sunday, January 8, 2017

Is Trump a Trumpist?


The current issue of The New Yorker  features a superb essay by Kelefa Sanneh, concerning the POTUS-to-be (currently just the PEOTUS, though acting more like an emperor).  There are too many fine passages for us to cite just one or two -- best to go read the whole article on their website.   Nor is there any point in my indulging in political commentary of our own:  I am not a credentialed politico, our Junior Woodchuck Blogger’s License©  being restricted to topics of Theologia mathematica, penguins, and pataphysical incunabula (qq.v.).   Yet I shall venture two remarks, the first in the capacity of someone who has subscribed to that magazine for over half a century by now (and once, as a teen, spent a week at the New York Public Library reading back-issues beginning with 1925);  the other qua philologist.

(1) The New Yorker began as a magazine of gentle humor and amused observation.  Over the decades, it has grown more serious, more spare, and focusing more on nonfiction.   Even The Talk of the Town, the opening section, and long the precinct of the badaud and the flâneur,  now typically opens with a political piece (as it does this week, though Sanneh’s offering  quite puts it in the shade).   Yet in the course of his discussion, Sanneh observes, in passing, one of the oldest characteristic tics of the Talk of the Town style:  the small, telling detail that, without trespassing at all upon snark, nor overtly satirizing the person in question, does present the reader with an opportunity of drawing his own conclusions.  Describing a conclave at the Heritage Foundation:

Every seat in the auditorium was taken, one of them by Edwin Meese, Attorney General under President Reagan, who was in the front row, and whose phone was almost certainly the source of a pleasant symphonic ringtone that briefly intruded upon the proceedings.

(2)  Towards the end of the discussion, the author asks:  “Is Trump a Trumpist?”  The sense of that deliberately paradoxical formulation is that the kaleidoscopic sequence of Mr. Trump’s obiter dicta  may not cohere into any firm worldview (some observers called him “a powerful but inconstant champion of his namesake philosophy).  But the form of the formulation  harks back to a tradition of similar epigrams, whose ancestry we traced in an earlier note,  reprinted for convenience  here.

~     ~     ~

Theodor Reik, a Viennese collegue of Freud for thirty years, recounts:

Freud once smilingly said to me:  Moi, je ne suis pas un Freudiste.”
(Why did he say it in French?  It is perhaps a variation of a French quotation that is unknown to me.)
Theodor Reik, Listening with the Third Ear (1948), final chapter

A clue lies in the morphology.  The usual adjective in French is not Freudiste, but freudien.   Freud was quite clearly alluding to an analogous quote -- again in French, yet again  from a native speaker of German:  Karl Marx, who, towards the end of his life, famously stated “Je ne suis pas un marxiste.”
In both cases, these major thinkers were rejecting the excesses of their acolytes.

Naturally the philologer  cannot stop here.  Why the devil would Marx have said the thing in French?   Clearly he must be echoing yet another quotation, one which eventually must be set in a purely francophone context.

With a bit of research and some help from Google, we were able to determine the source:  Napoleon, in exile on Elba, is reported to have said (shaking his head),
            “Je ne suis pas  bonapartiste.”
Here the semantics is rather different:  He has not retrospectively rejecting those who followed him in his prime, but recognizing how far he himself has fallen.

Surprisingly, the trail does not end there.    Although this is the earliest recording such French quotation, it exactly echoes an earlier quotation from King Alfred (Ælfrēd se Grēata),

            “Ech nam Ælfrēdsmann.”

And there the trail goes faint:  yet it winds down through the dark ages, all the way back to Athens, where Plato was once heard to state:

            “Ego ouk eimi Platonistes.”

(We could go further, but suspect that our readers have been neglecting their Hittite.)



Monobear teddystich




The happy bear   is all secure,   snuggling in the darkness

Friday, January 6, 2017

Eilenberg and Steenrod Walk Into a Bar


[Note:  The following, extremely funny joke,  requires   as a prerequisite  a sound knowledge of Category Theory.    For readers who lack this qualification, the punchline will appear blank.]

Set-Up: Eilenberg and Steenrod   walk into a bar;  one of them has had a few already, the other is dressed as a Scotsman. 
The bartender, looking from the one to the other with some concern, says,

“Why the long face?”

Punchline:  Steenrod glances at Eilenberg and wisecracks back,  

                                ?                          !! ”