Elective Acolytes

 

Not many are called, and even fewer chosen.

Tales from the Vienna Circle Woods

 

Vienna, 1927:

After several more appointments with Schlick alone, Wittgenstein had been persuaded to get together with a select group from the Circle, though he had never once attended an official Circle gathering.

Waismann began, subconsciously, to imitate Wittgenstein’s speaking-patterns.  Schlick began to attribute  some original ideas of his own  to Wittgenstein, though they had been expressed before he had even read the Tractatus.  Wittgenstein must have approved of this submissive attitude:  by the fall of 1929  he was choosing to restrict his discussions to Schlick and Waismann alone, usually at Schlick’s home.

-- David Edmonds, The Murder of Professor Schlick (2020), p. 48-52

 

Though recalcitrant about joining, or even really following the lead of, the Wiener Kreis, Wittgenstein did attend their summer 1930 congress in Königsberg (the one-time hometown of Kant, who was the Circle’s Aunt Sally), which honored him with a presentation re “The Nature of Mathematics:  Wittgenstein’s Standpoint”.  Here he again encountered a couple who had known him as a teen:

Present too at Königsberg  were Professor Stanislaus Jolles and his wife, Adele.  They were the couple with whom Wittgenstein had stayed during his spell in Berlin, 1906-08.  Their relationship with their lodger had been affectionate;  Stanislaus felt protective and paternal toward “Little Wittgenstein”, as they called him.  But, as so often with Wittgenstein, there had been a rupture, and, typically again, it seems to have arisen from Wittgenstein’s perception that his hosts had fallen short of his exacting standards.

-- ibid, p. 97

It didn’t take much for the prickly master to cancel you (or, to use the term current among Berkeley lefty groupuscules during the 1970s before cancel acquired its later flavor among the Woke, to “break with” you).

If you did manage to remain in Wittgenstein’s good graces, it was a mixed blessing, for he tended to treat such scholars as acolytes or thuriféraires, rather than full colleagues.  Consider the case of Friedrich Waismann, mathematician and physicist, and a core member of the Kreis, who enjoyed the rare privilege of occasionally being closeted with Wittgenstein alone:

 

Waismann’s principal function was prompt and note-keeper.  One philosopher later described his relationship to Wittgenstein as one of “glove puppet to controlling hand.”  … There was something shocking about the degree to which he subordinated his interest to those of Wittgenstein, and the ingratitude with which his efforts were rewarded.
-- ibid, p. 101, 104

 

Bertrand Russell, a supremely well-established logico-philosophical panjandrum himself, could not be so scanted; yet “Bertrand Russell, according to Ayer, was now downgraded to being merely ‘a forerunner of the Christ (Wittgenstein)’.” (ibid, p. 109)

Russell himself was cordial to Wittgenstein, who had read Russell’s mathematical philosophizing, and who in 1911  showed up at Russell’s rooms in Cambridge, and soon formed a close relationship.   Russell had been a member of the Cambridge Apostles, cosily known to themselves as simply “the Society”;  and Wittgenstein received an invitation to join.  But once again, Wittgenstein held back from any circle whose multiplicity made them unwieldy to dominate as a whole.

In a letter of 1913, Russell wrote to a friend:

My friend Wittgenstein was elected to the Society, but thought it was a waste of time, so he imitated henry john roby and was cursed.

-- The Autobiography of Bertrand Russell (v. 1, 1951), p. 364

 

(The reference is to an earlier selectee, who disdained ever to attend the Apostle conventicles;  the miffed members promptly canceled him by decapitalizing his name for all eternity, and pronouncing a ritual malediction from time to time.)

 

~  ~  ~

 

In 1932, through the good offices of Gilbert Ryle, the Oxford philosopher A.J. Ayer  was introduced for the first time  to Wittgenstein at Cambridge.   Queried by the eminent Austrian  as to what was the most recent book he’d read (cocktail-party filler or ice-breaker, one would have thought),  Ayer replied, La Vida es Sueño, adding modestly that he hadn’t understood it very well.  That was actually owing merely to his shaky Spanish; but Wittgenstein apparently took it as trenchant skepticism, much along the lines of the logical empiricists protesting that they “didn’t understand” (i.e., considered as rubbish) a great many everyday non-scientific statements.  “From then on he treated me as a protégé.” (-- A.J. Ayer, Part of My Life (1977),  p. 120.)

Ryle appears later to have some regrets about those good-offices:

 

Ryle had met  and got along with  Schlick, but his encounters with Wittgenstein left him with serious reservations.  This was evidently a man who needed acolytes, not colleagues;  someone always on the brink of an explosion,  too quick to divide the world into the saved and the damned.

-- Nikhil Krishnan, A Terribly Serious Adventure:  Philosophy at Oxford  1900-1960, p. 54)

 

In the same memoir, the mild-mannered Ayer recounts the brusque reception that met Waismann, who had so long sedulously served Wittgenstein, when they later became colleagues at Cambridge University:

Waismann was Jewish, and when Vienna fell to the Germans  he fled with his family to England.   He went to Cambridge, which was willing to accept him, but Wittgenstein did not desire that what he regarded as a deceptive echo of his own thought  should be audible in the same university, and therefore announced that anyone who attended Waismann’s lectures  would not be allowed to come to his.

-- A.J. Ayer, Part of My Life (1977),  p. 132

 

Horresco referens, but such petty and revanchist behavior reminds me of Tr*mp.

~

 

The incomparable logician Kurt Gödel  played a notably honorable role in this Kreis of often quarrelsome prima donnas.   While faithfully attending their gatherings, he was content so remain modestly in the background, and be taken for a subaltern, while all the time excogitating, leading to work more important more lasting than anything any of the others in the Kreis would accomplish.   Again, let the portraitist tell it:

 

Although almost all Circle members became convinced that, drawing on Wittgenstein and Ramsey, they had solved the problems of mathematics -- that mathematical truths were a type of tautology -- Gödel had sat quietly at Circle meetings  without believing a word of this.  He was a mathematical Platonist.
-- David Edmonds, The Murder of Professor Schlick (2020), p. 148

 

Those affordances of the Circle, and of Wittgenstein in particular, were worse than useless: positively stultifying for the practice of mathematics.  [For our essays on the subject, consult

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

]

 

As for the excesses of acolytism, Gödel kept a level head:

 

While Schlick and Weismann revered Wittgenstein, Gödel was among several  bemused by the cult-like deference he inspired in his acolytes. … [And later, when Wittgenstein reigned at Cambridge:]  Many students became disciles -- who, like Waismann in Vienna, subconsciously came to mimic his mannerisms.

-- ibid, p. 149, 247

 

The socio-historian and polemicist Ernest Gellner  provides a glimpse of the Cambridge period of Wittgenstein’s ascendency.  There grew up

 

… the first set of ‘companions of the prophet’.  Initially, there was a small, carefully vetted, conventicle of devotees in Cambridge, in the years preceding the Second World War. … But the movement grew …

Maor premise:  all cultural cocoons, all forms of life, are valid and self-sufficient, and Wittgenstein has shown this to be the case.  Minor premise, never spelt out or discussed, but operationallly taken for granted:  only our cocoon is of any interest. … Entry to Wittgenstein’s seminar was restricted at the master’s whim, and the ideas circulated in privately-copied typescripts which Wittgenstein himself refused to have published.  This esotericism greatly enhanced the appeal of the ideas, which were treated as a major revelation by the adepts.

 

-- Ernest Gellner, Language and Solitude (posthum. 1998), pp. 160-165

 

(Parallels from the history of linguistics  during the Chomsky years, could be adduced…)

~  ~  ~

 

Let it not be supposed that the field of philosophy is at all atypical  among academic specialties, as regards such interpersonal rugosities.  Parallels from the history of linguistics  during the Chomsky years, could be adduced.  As, the mathematician Mark Kac, father of the linguist Michael Kac, remarks in his memoir:

 

Linguistics is a strange field, full of cliques and fiefdoms, each fiercely attached to its staked-out territory, and consumed with enmity toward the others.

-- Mark Kac, Enigmas of Chance (1985), p. 107

 

For an extended look at academic acolyte relations, pour yourself a brandy  and relax with these:

 

=> http://worldofdrjustice.blogspot.com/2013/02/chomsky-freud-and-problem-of-acolytes.html

and its appendix

=> https://worldofdrjustice.blogspot.com/2012/12/the-agony-and-acolyte_28.html

 

These include anecdotes about my fondly former Berkeley Doktorvater  in Rom. Phil.,  Professor Yakov Malkiel, including portraits of the (pro tem) Malkielitas, and one (canceled) Malkielito.  One will detect, in the telling, a Nabokovian tone;  which is only just, as the Malkiel family and the Nabokov clan  were BFFs in Berlin, back in the ‘30’s (while it lasted).

 

Thumbnails of mathematical terms

The following essay treats of the art of mathematical definition:

https://worldofdrjustice.blogspot.com/2014/01/what-is-mathematics-expanded.html

Here are some recent additions:

Ergodicity means, roughly, that … very long sample paths … end up resembling each other.

-- Nassim Taleb, Fooled by Randomness (2004), p. 59

Ergodicity, … that time will eliminate the annoying effects of randomness.

-- Nassim Taleb, Fooled by Randomness (2004), p. 144

Holonomy is a measure of how tangent vectors on a particular surface  get twisted up as you attempt to parallel-transport them on a loop.

-- Shing-Tung Yau, The Shape of Inner Space (2010), p. 129

The Lie Bracket of X and Y … informally … represents the net direction of motion if one first moves an infinitesimal amount in the X direction, then in the Y direction, then back in the XS direction and back in the Y direction, in that order.

-- Mark Ronan, “Lie Theory”, in Timothy Gowers, ed., The Princeton Companion to Mathematics (2008), p. 231

Logic

… [C. S.] Pierce’s last papers on logic, a subject which he defined rather surprisingly as ‘the stable establishment of beliefs’.

-- I. Grattan-Guinness, The Search for Mathematical Roots 1870 - 1940 (2000), p. 174

Logic is the infancy of mathematics, or conversely, mathematics is the maturity of logic.

-- Bertrand Russell, 1957, quoted in I. Grattan-Guinness, The Search for Mathematical Roots 1870 - 1940 (2000), p. 315

Spinors are analogues of tangent vectors.

-- Shing-Tung Yau, The Shape of Inner Space (2010), p. 131

Betrachtungen eines Unphilosophischen (quater)

I don’t like purely philosophical works.  I think a little philosophy should be added to life and art, by way of seasoning;  but to make it one’s specialty  seems to me  as strange as eating nothing but horseradish.

-- Boris Pasternak, Doctor Zhivago (1957) (ch. XIII.16; Lara speaking)

Nicht vom Wetter spricht sie, nicht vom Schneider,

höchstens von den Grundproblemen  beider.

-- Christian Morgenstern

[I wrote the following around twenty years ago, before I was baptised.  Just stumbled on it while cleaning up some files. 

Since that time, I’ve read a fair amount of philosophy, often with pleasure, and dabbled in composing some.  But the treatment here of the cognitive problem does not need revision or retraction.]

I must conclude, reluctantly, that I am of a  not very philosophical cast of mind.  Intellectual, yes; thoughtful, I hope so; but philosophical, in the sense of spontaneously grappling with the questions that engage those denominated philosophers, alas not.

Had I never read a line of academic philosophy, I could contentedly have walked for seven decades down the lanes of life, kicking at stones and appreciating the trees, without once wondering, let alone worrying, whether a name denotes a universal, or rather a concept, rather than (snicker snicker) a thing. Left to my own devices, I would likely never have asked whether Being even had a nature. let alone what the bugger might be.

Such questions as these have never troubled my sleep; and it is only with the greatest difficulty than I can induce them to trouble my waking hours.  Yet we read, in the letters of our betters:

"What distinguishes a man from a word?  There is a distinction, doubtless."

--C.S. Pierce, "Some Consequences of Four Incapacities".

This I no more ponder than whether a hawk may be discerned from a handsaw -- indeed, it rather recalls the grotesque title of the neurologist Oliver Sacks, The Man Who Mistook His Wife for a Hat.  Yet Peirce concludes, alarmingly, that "The word or sign which man uses  is the man himself."  Should we be troubled by this?

Doing philosophy – well, I seldom do.  But when reading philosophy – something never undertaken save after a sound night's sleep, in the company of pots of strong coffee – I have often had the horrible experience of carefully lucidly processing each phrase of a sentence as it comes along, then finding, when I reach the sentence end, that the meanings of the initial phrases have evaporated:  as were intelligence but a porthole on a passing landscape, seizing each piece clearly as it looms into view, but at the expense of losing the last.  (That was rather a long sentence itself; let us pause.)

            (Pause.)

            Herewith a specific instance, taken from a little work in paperback (Arthur Danto, What Philosophy Is) known for being a relatively clear and non-technical introduction for the layman:

            "It is demonstrable that, for any system of sentences – any theory, say – which satisfies exceedingly weak and undemanding formal criteria, just this alleged desideratum can be achieved."

            This is not a long sentence; and for the first two-thirds of it, it actually calls up to me very visual ideas.  "Any system of sentences – any theory, say": I picture these sentences as speech-balloons, dangling from a mobile, with little hand-icons pointing at other sentences which they imply or from which they derive.  "Which satisfies exceedingly weak and undemanding formal criteria":  here our hypothetical theory is embodied as a sort of Doctor Watson, waving his hand with bluff good humor, in dismissal of the trifling demands made upon him: "No trouble at all, sir!"  And as for that initial "It is demonstrable that", well, we all know that "It is demonstrable that P" means (for the plain man) just that "P", and moreover gives you license to swallow P without troubling yourself to prove it or make it plausible, or even to understand it very deeply:  just one of those solid facts that people our Watsonian society, which the tradespeople have somehow seen to.

            Then comes "just this alleged desideratum".  Alas: this sends you haring back to the previous paragraph, or previous page.  And the "alleged" is troubling:  do we desire this (whatever it is), or do we not?  This centrifugal tension makes subtly more difficult the task of going back and finding the antecedent for "this".  It's not like "she": hmm, hmm, complicated, this, -- aha, Natasha Nikolayevna.

            Now:  one fact about philosophy, which makes the subject hard to follow, is rather to its credit.  Namely:  we never know what might be called into question.  So we can't just sit back and nod  as bits of received opinion are spooned into our open mouths.

            In many non-philosophical areas of life, we can count on so much that is unchallengeable, that their arguments are like sermons in a lazy church.  We can doze; we can idly watch the fly buzzing across the stained-glass windows; and miss nothing that is essential, for we have already all that is essential, the rest is embroidery.  As, in the radical Sixties, syllogism went rather like this.

Granted:
     (1) Amerikkka is a honkey-assed imperialist pig
     (2) The righteous Vietnamese people are righteous, popular, and Vietnamese.

From this it follows:
     (3) Blah de blah de blah de blah (rahht ohwn!) 

Everyone goes home satisfied.

What does it mean, to be "unphilosophical"?  It cannot spring simply from stupidity – which is a general term; too much counter-evidence in collateral fields.  Nor ignorance – not after having sat at the feet of the philosophical:  for, failure to absorb their wise lessons would have to be due either to stupidity (already ruled out of court) or "unphilosophicality" : quite possibly present, but this is the quality to be explained.  (I recall a case from some years ago, in which some Brazilian peasants, or Indians, were brought to trial for having killed quite a number of people: and were acquitted, on the grounds of "invincible ignorance".  A charming verdict; egomet etiam, nolo contendere; but again, this is the explicandum, not the explicans.)

            One possible partial explanation is that, apparently, despite gross this that and the other thing, I do actually, more or less, in some sense, believe in God.  This may even be largely unconscious, but it does determine things.  As:  Good heavens!  Here He went and made Eden for our grandsires to saunter in, and angels to attend our fallen birth – and you're worried about the existence of tables??!??!*  Get a life, man!  Get an afterlife!

[*On page 100 of Danto's booklet, we have an image of the philosophically inclined scientist  swallowing an atom  but straining at a table.]

It is a stylistic characteristic of the philosophic genre, that its reported combatants are generally abstract and shadowy, unnamed figures.  Not Gould vs Dawkins, or Quine vs Chomsky, but: the Realist; the Representationalist; the Phenomenalist, each with his separate agenda; curiously dispassionate partisans, like players in a masque. 

            In one sense, this should make for clarity.  As, I may know a whole bunch about Chomsky, or Chesterton, or Orwell, but it is different from the bunch of things known by disputant P., and different still from the sub-bunch of things that have caught P's attention in the present case.  Hence, when P. says: "….(Orwell)….", a million bells go off in my head, which may obscure his message.  Whereas, when the don refers to the Realist, there is no clanging, nothing to refer to but the Realist's résumé.

            And yet and yet… It is with this as with the medieval allegories, where ((Danger)) orates to ((Faithful)) anent ((Beauty)), and the eyes turn to glass.  These creatures have no form – no warts – no tits – it is difficult to attend, hard to become engaged.

            This lack of philosophical engagement has few consequences for the practical matters of life, such as renewing a driver's license.  Still, it bothers me.  For, philosophy is reputedly fundamental – indeed, is so virtually by definition.  Smart people are presumably interested in problems of ontology, while stupid people are interested in football scores.  [A surprisingly large number of smart people are interested in baseball.  This cannot, then, be an intellectual failing; but it may be a perversion.  The question remains open.]

*     *     *

~ Commercial break ~

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

We now return you to your regularly scheduled essay.

*     *     *

Yet I am troubled by questions of epistemology, for the good and simple reason that certain people whom I know  (those notorious Other Minds, in whose complete integrity I believe implicitly) seem to know (or say that they know) what I don't know; nor know I  how (or whether) they do know it.

As:

CEO (cigar clenched in right mouth-corner, speaking laconically out of the left):  Nyaahh… Dis noo magneddic-stawritch standid, it'll nevah catch on, da mahhkit'll riject it.

Me (thinks): How the F*** does he know that?!?!?

~

On a good day, then, and with a good book, I can – granted, not do, but at least – read philosophy, and engage with it:  an EKG would reveal busy little blips and bumps, I'm not just flatlining with the book open, the mental equivalent of an all-day sucker.  And admittedly, most of the enjoyment comes from the crackling style (as with Quine) or the apt examples (Strawson, Geach), rather than from any genuine penetration into the delicious mysteries of what it means, what it really means, to say that x equals (wait for it) x.  So the author of the book need not feel that his labor is wasted:  here is John Q. Public with his engine turning over and that author's very book in his hands (those hands which might equally as well have held a breast, or a beer).  And yet – the book once laid upon the night-table, all its arguments and all its concerns  go out like a light.

            It is not so with, say, poetry.  To read poetry before retiring is as dangerous as drinking espresso for a nightcap: I toss and turn, the lingering rhythms like a hot blanket, which cannot be cast off till I drag myself out of bed, snatch a bathrobe, and WRITE - WRITE - INDITE!  Whereas philosophical propositions  spark no further fever.  I lay down the volume, fall into a dreamless sleep, and perhaps the next day have some vague lingering recollection – "Yes, that 'x' thing, it was equal to, let me see, was it 'y'? -- no!  'x', that's it!  x = x.  My, the things one learns."  Or:  “Is it true, that snow is white?  Mmmm..mmyes!”

            Perhaps a policy of not asking overmany fundamental questions too often, is not so much intellectual laziness, as the better part of epistemological valor.  For, truly to nail down the simplest everyday phenomenon, is largely beyond the reach of science.
(Physics is really good at addressing problems that it invented itself, like muons;  not so much when it comes to snowflakes, or lightning, or wind.)

            In addition, when you go to the scientist, thou sluggard, you find him not exactly bent over the philosophy-of-science books either.   And this, not only among those sooty alley-dwellers the chemists, with their practical pots, but even those austere, unstained – theoretical physicists, nay, mathematicians.  Mathematics does not need metamathematics to go about its business, whether devising formulae that will predict the stresses of actual bridges, or proving theorems about ideal manifolds in n-space.  (We may define pure mathematics as the subject in which Bertrand Russell does not know what he is talking about, though what he says is none the less true.)

~     ~     ~

~  Posthumous Endorsement ~

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

this is what I'd be reading: "

I Don't Do Divorce Cases

Murphy on the Mount.

(Ich bin Thomas Mann, and I approved this message.)

~        

Other  tragic examples:

Valéry était atteint  de cécité philosophique.

-- Etienne Gilson, Linguistique et philosophie (1969), p. 234

Freud himself  confessed to an insensitivity to philosophy -- or at any rate, to academic philosophizing -- after reading a book a colleague had recommended:

“You cannot imagine how alien all those philosophical convolutions  seem to me.   The only feeling of satisfaction they give me  is that I take no part in this pitiable waste of intellectual powers.  Philosophers no doubt believe that  in such studies  they are contributing to the development of human thought;  but every time, there is a psychological  or even a psychopathological problem  behind them.”

-- quoted in Ernest Jones, Freud: The Last Phase (1957), p. 140.

(Assignment:  How do these observations apply to the case of Wittgenstein?  Discuss)

Latest update:  
"Even when I have moved away from observation,  I have carefully avoided any contact with philosophy proper.  This avoidance  has been greatly facilitated  by my constitutional incapacity."
--  quoted in Ernest Jones, Freud: The Last Phase (1957), p.335

The Penguin Paradox

If you’ve ever read an introduction to linguistic or analytical philosophy, you will have met the concept of the “semantical paradoxes”, such as Grelling’s.   These involve the limits of language -- although, not in the usual way whereby there is so much you wish to impart but you can’t put it into words :  rather the opposite.  Language, unbridled, can take us places we should never go, and needs to be regimented -- to have limits set upon it, like a wayward teen.  (Russell to language:  “You - are - so - grounded !!”)

One of the variant colors or flavors  is:  What is the largest number not nameable in fewer than twenty-two syllables?   (There is a variant that replaces fewer with less, and thus can say “twenty-one”;  but grammatical decorum forbids.)

So you think about it, and come up with some number with a lot of nines in it, and proudly present your answer.  Then the presenter grins and says:  Ah, but I just named it with that very phrase, and it took me one syllable less to do it!

Actually, I can top that.

So, for fifty points:

=> What is the largest number nameable by an English monosyllable??? <=

(Thinks …   thinks …)

(Hmmmmmmm ……….)

And the answer is:

Bob.

“Bob” is my name for a certain very, very big number.  He’s huge.  And Bob is the largest because there are only finitely many English monosyllables, which were dealt out to a bunch of us, and I waited till everyone else had christened his number first.  Bob is defined as the sum of all those numbers.

(Same strategy Lyndon Johnson used in wrangling his election to the Senate.)

Since I discovered this paradox, parable, or whatever it is,  I get to name it.  I call it The Penguin Paradox, because I like penguins.

“Bob”s official mascot

.

Alexander Grothendieck

From the graceful pen of Edward Frenkel  comes this appreciation of the prodigious mathematician Alexander Grothendieck:

http://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-grothendieck-a-mathematical-visionary.html

Frenkel’s summary of Grothendieck’s approach  is phrased in distinctly Platonistic terms:

Grothendieck’s genius was to recognize that there is a “being” hiding behind a given algebraic equation (or a system of equations) called a scheme. The spaces of solutions are mere projections, or shadows of this scheme.

That formulation goes beyond the basic assumptions of mathematical Realism, adding a quasi-personalistic, quasi-spiritual metaphorical dimension.   We might epigrammatize the matter thus:  bare-bones Realism (embraced by most mathematicians as a lower bound) is to the view attributed to Grothendieck, somewhat as deism is to theism.

Frenkel concretely illustrates this (neo-)Platonistic / Plotinean stance of  seeing the relatively concrete and familiar, as but a pale and lesser projection of some higher, transcendent, but paradoxically more solid Reality (which dwells in Platonic heaven, sipping some higher-dimensional nectar), in his justly celebrated book for the layman:

Imagine a world in which natural numbers are replaced by vector spaces;  that is, instead of number 1  we have a line, instead of number 2  we have a plane… Addition of numbers is replaced by the direct sum of vector spaces,  multiplication by their tensor product.  The number 3 is a mere shadow of the 3-dimensional space, reflecting only one attribute of this space, its dimensionality.

-- Edward Frenkel, Love & Math (2013), p. 155

That insight is superficially reminiscent of Bertrand Russell’s definition of, say, the integer three as being not basic, but the rather the (infinite) set of all triads { {Moe, Larry, and Curley}; {Huey, Dewey, and Louie}; {the Andrews Sisters}; ..}  Russell’s move always struck me as, at best, an obscurum per obscurius (or even a clarum per obscurius);  at worst, a parlour-trick.    Frenkel’s suggestion likely goes much deeper -- indeed, to a depth I am in no position to assess.

Finally, without the structural richness of Frenkel’s proposal, but perhaps more accessibly, this from a pair of noted philosophers-of-science:

The abstract objects of thought  such as “numbers” [or] “perfectly straight lines” .. are real parts of nature, even though they do not exist as particular things, but as the relations or transformations of such particulars.

Morris Cohen & Ernest Nagel,  An Introduction to Logic and Scientific Method (1934), p. 372

~

Frenkel reminds us that Grothendieck, dramatically and notoriously, Threw It All Away, resigning his institute and seceding from the mathematical world, upon learning of its defense funding.   Frenkel points indeed to the possibility that even a subject so “gloriously useless” (as it was seen back in G.H. Hardy’s day) as number theory, can have crucial cryptographic applications which, in turn, invite subversion by the intelligence community.   He states, indeed, that such subversion did take place, at the hands of a three-letter Agency too numinous to name, in the case of Elliptic Curve Cryptography.  Yet ironically, that very field was pioneered by a theoretician politically of the far left, Neal Koblitz.  (I knew him slightly when we were both math majors and antiwar activists at Harvard, and recall him fondly here.)

[ A parallel:   For a highly entertaining, though painful, account of Simon Norton,  once Conway’s collaborator, but who likewise Threw It All Away, see the book by Alex Masters, The Genius in my Basement  (2011) ]

I never met Grothendieck, nor so much as approached the foothills of his cloud-surmounting summits;  but my introduction to mathematics did come via one of Grothendieck’s students, Robin Hartshorne, here portrayed:

http://worldofdrjustice.blogspot.com/2011/12/adventures-in-algebraic-geometry.html

We touch upon Grothendieck tangentially in several essays;  here they are:

worldofdrjustice.blogspot.com/search/label/Alexander%20Grothendieck

[Another parallel:  Grothendieck’s abrupt withdrawal from mathematics, and his sometimes surly subsequent comments on its practicioners, recalls that more recent self-reclusion of the Russian topologist Grigori Perelman, who quit his institute in 2005, with the remark that “I have been disappointed in mathematics and I want to try something else.”   Now, to anyone who grasps the subject, disappointment with mathematics is almost inconceivable -- it’s like being disappointed with the Universe, or with penguins, or with life itself.   Other statements he has made suggest that his quarrel is not with math per se  but with certain mathematicians.

For a poignant glimpse of the daily routine of this semi-recluse, try this:

http://www.lepoint.fr/monde/le-genie-qui-s-est-retire-du-monde-30-09-2010-1246189_24.php  ]

~

In other cryptographic news … This week’s New Yorker has a review by Anthony Lane of “The Imitation Game”, which takes us back to the WWII code-breakers at Bletchley Park, with mathematician Alan Turing at the center.   With his welcome skeptical eye, Lane punctures the movie’s superstar approach to the material:

No word is breathed, for instance, of the Polish cryptographers who did much of the heavy lifting on the project  before Turing came on the scene.  As for the cracking of codes, it is shrunk to single, Oh-my-God epiphany, triggered by a comment in a pub.

That last motif is strikingly reminiscent of the trumped-up Eureka moment ascribed to Gauss in the movie “Die Vermessung der Welt” (which we reviewed here), whose insights into differential geometry were supposedly engendered -- in a flash, on the spot -- by a buxom mädchen handing him an apple from the knowledge-tree.

Another warning-sign:   The role of Turing’s  Comely Female Sidekick (de rigueur in Hollywood these days) is played by Keira Knightley, an overactress whose pornographic approach to proximity to great men of science, in the movie “A Dangerous Method”, we earlier had occasion to denounce.

~

[Late-evening update]  And now, fellow devotees of that supreme queen of the noösphere, math -- now that we have all stuffed our tummies with turkey, and are sprawled upon the couch:  as we are probably not just now engaged in settling the Hodge Conjecture (and making but scant progress if we are), let us rather refresh the neurons with a bit of mathematical merriment:

How Now, Round Cow

~

Sotie : 

le mathématicien  et la conspiration Riemann

Борис Березовский

~

[Update, 30 November 2014]  Further thoughts.

(1) Integers as shadows

That epigram, that petite phrase,  “The number 3 is a mere shadow of the 3-dimensional space”, continues to intrigue.  Further thoughts on the subject here:

From Finitude to Infinity

The point being that Frenkel/Grothendieck are here proceeding in the less-familiar opposite direction.

(2) “Goodbye to All That”

The catchphrase “I Threw it All Away” is from Bob Dylan.   An earlier more familiar expression is “Goodbye to All That”, the title of a memoir by the poet Robert Graves.

To fascinate a public beyond the circle of connoisseurs, a mathematician (or physicist, or chess-player) needs to sport some quirk, some handle onto which the layman can hang his attention.  That is massively true of Turing, first because of his role in the thrillingly clandestine -- and militarily crucial -- cryptographic factory at Bletchley park;  and more recently -- and less relevantly, from any mathematical standpoint -- by reason of his personal predilections (held in common with such extra-scientific figures as Ἀντίνοος and the Baron de Charlus) which at present have reached an apogee of public celebrity.   On a more modest scale (no blockbuster biographies, no movies) the careers of Emmy Noether or Ada Lovelace come to mind.

For anyone not a member of the identity-groups in question, such chance affiliations are mathematically and philosophically boring.   But not so a figure like Groethendieck, who reached intellectual levels that most of the rest of us can only pant and sigh for -- then threw it all away, in a contemptuous gesture.   For that is a challenge to all of us, whatever our private identities;  it calls into question the very value of the ‘it’ for which we so painfully and vainly strive.

A well-known example from chess:  Bobby Fischer, who withdrew from the sport at the top of his game.

Or, in the sixteenth century, the pioneering anatomist Vesalius, who, having published the book that settled his fame forever, and still a young man, left the field and became a simple physician to a valetudinarian Emperor.

A grey-area variant of this motif is found in the case of Simon Norton.   True, he voluntarily withdrew from the field;  but in view of his later pointless eccentricities, we cannot avoid the suspicion by then he had largely Lost It.

That variant motif forms the spine of Rebecca Goldstein’s fascinating mathematico-philosophical novel,  The Mind-Body Problem.

And while Goldstein manages to craft a good read out of the tragedy, in the typical case of gradually fading powers, it is just sad.  Thus Lagrange, and other victims of Oligophrenia mathematica tardiva,  chronicled in the appendix to this essay:

De Stultitiâ

 

Other examples of burnout:  

Newton had a nervous breakdown a few years after publishing his Principia, and never did real science again.

Russell seems to have fried many of his math neurons in the course of writing his Principia (memo to prodigies:  Don’t try to write a Tenth Symphony, and don’t write a book called Principia).   He did much interesting philosophical work after that, but mostly with other areas of his capacious brain.

Somewhat in the spirit of the Stith-Thompson index of folkloric motifs, to I Threw It All Away (TaleType #1729a), we add:

* Taken all away (#1729b):    Persecution took them out of the game, at the height of their powers: Galois (permanently) and, for those who considered that he was hounded to death, Turing.  Temporarily: André Weil and Neil Koblitz (during their imprisonment -- though both managed to use their ‘time inside’ more profitably mathematically  than most of us do with all the free time in the world).

* Would throw it all away, if had to do it over again (#1729c):

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."

Schrödinger, to Niels Bohr:

“If all this damned quantum jumping were really here to stay, then I should be sorry I ever got involved with quantum physics.”

[quoted in: -- Roger Penrose,  The Road to Reality (2004), p. 516]

More such anecdotes here:

http://worldofdrjustice.blogspot.com/2012/06/on-truth-and-beauty-golden-oldies.html

* Should throw it all away, if that’s how they feel (#1729d):  String theorists who have wound up at the dead-end of the Landscape picture.  (“The reductionist voyage that has taken physics so far  has come to an end.  Since that is what they believe, I can’t understand why they don’t take up something else -- macramé, for example.”  More here.)

It depends upon what the meaning of “will” will be

This morning offered an extraordinarily bone-headed article in the Washington Post, whose title on the Web site (I no longer subscribe to the print edition, out of concern for that newspaper’s misuse of innocent trees),  

“How President Obama will be impeached”

http://www.washingtonpost.com/blogs/post-partisan/wp/2014/06/18/how-president-obama-will-be-impeached/

Now, that is no more than we had come to expect from the hapless WaPo (if the fellow truly possesses a crystal ball with that resolving power, he should put his abilities to better use, such as divining the next winning ticket for the lottery, or making millions betting big on the ongoing World Cup contest, which has seen a lot of unpredicted upsets this time around).    We would not have bothered to click on the link, but for curiosity, simply to see whether the scribbler in question was an official  marquee op-ed-er like Charles Krauthammer, filling one of the designated billets for Right-wing Nutcase (so that the Post can continue to claim to be Fair and Balanced), or simply a junior-varsity blogger permitted to invoke the Post.  (Turns out it’s more like the latter, though with a seat on the Board.  Indeed, forcing myself to read to the end of the article, I tentatively conclude that he is probably neither right-wing nor a nutcase;  merely, analytically underequipped.)

Once you read the actual article, however, you see that it does not actually speak of what will happen, but what “possibly” will happen -- what might happen.   That sets a much lower bar.  Thus, I couldn’t tell you who will win the upcoming contest between the Warriors and the Scouts, but I can confidently tell you who might win:  the Warriors.  Or, possibly, the Scouts.  (Fair and Balanced is our (are our?) middle name.)

On a charitable reading of the case, then, our blameless columnist, studiously hewing to Popperian and Baconian principles of evidence and argument, has been betrayed once again that cursed tribe of headline-writers  -- the Web ones if anything worse than the print -- who try to turn a non-story into an apparent story, with click-bait in the link.  (We ourselves are occasionally tempted -- by the cloven-hoofed Bad Angel on our left shoulder -- to stoop to such tactics.  I briefly considered titling this piece   

XXX TAYLOR SWIFT NUDE PIXXX

TEEN QUEEN BARES ALL

to drive traffic to the site, but then the ivory-winged Good Angel on my right shoulder whispered:  But It Would Be Wrong.**)

(** We remain, however, in back-channel negotiations with the Bad Angel, to see if we might somehow nonetheless turn this tempting opportunity to account.)

Thus, if all you are talking about is how the President “could” be impeached (note: impeached, not convicted), there is no story there, for the answer is obvious.  All you need to do to impeach, in the strict sense of that word, is to round up fifty-one percent of clowns and loonies in the House, something that you can accomplish simply by whistling, or by leaving a plate of Cheez-Whip out on the bench.  Then, Bingo!, you’ve got yet another effect-free pointless Congressional “resolution”, like repealing the law of gravity or whatever.  The “Base” then goes off and has a chortling-fit (while stuffing their jowls with corn-dogs), while the rest of the world goes about its business.  “Les chiens aboient, la caravane passe.”  That is Democracy at work;  I expect you learned all about it in Civics class.

Unfortunately, the actual blogger before us (as against his ideal counterpart in Platonic heaven), writes (rather self-importantly -- “I warned Democrats”, tut-tut, hem-hem):

Writing about Rep. Eric Cantor’s  (R-Va.) stunning primary defeat last week, I warned Democrats that the House majority leader’s loss was as much a wake-up call for them as it was for the GOP. Well, now I want to warn them about a very real possibility: President Obama will be impeached if the Democrats lose control of the U.S. Senate.

That paragraph is quantificationally confused -- actually, probably deliberately so (of that, more anon) --  in a way probably not apparent to most readers unfamiliar with the tradition of Frege and Russell, so allow me to unpack it.  It commingles, as a syntactico-semantic mess, several distinct propositions:

(A) There is a very real possibility that the Dems may lose control of the Senate.

[DBJ:  Uncontroversially true.   “Very real possibility” is more than a mere “possibility” -- a weak condition, that, which would apply to the potential for a Martian takeover of both houses -- but is less than a “preponderant probability”; hence, uncontroversially true.]

(B)  A Republican majority in the Senate could  [or:  likely would;  or:  definitely will] tilt the psycho-political playing-field in a way that makes it more likely that a gaggle of excitable simpletons in the Lower Body may bestir themselves to move a vote to impeach.

[Hypotheses respectively quite plausible; plausible; possible though unlikely.]

(C)  The resulting likelihood that the House vote to impeach, now becomes a certainty, 100%.

[False.]

In the next paragraph, our scribe actually attempts such distinctions among probabilistic niceties -- not very expertly, certainly nothing to attract a nod from Bayes or Kolmogoroff, but still, commendable:

Yeah, yeah, I read Aaron Blake’s astute piece in The Post on the impeachment process. He says “probably not” to the question of whether the House could impeach Obama. But “probably” is not “definitely.” And with the way the impeachment talk has gone, “probably not” could become “absolutely” if the Senate flips to the Republicans.

Then, however, comes another bait-and-switch (and this is one of the two reasons that I speculated the quantificational conflation of A+B+C above, may have been deliberate).  The writer observes, quite correctly, that “To officially remove a president from office, two-thirds of the Senate must vote to convict him on those articles of impeachment” (nods of recognition from all of you who paid attention in Civics Class, provided such a thing still exists and hasn’t been replaced by YouTubing class or whatever  these days), but then skates back out upon thin empirical ice:

A Republican-controlled Senate could lead to Obama becoming the third president impeached and the first ever to be removed from office.

I don’t make this prediction lightly.

But “Republican-controlled” simply means “51 Republicans”, not “sixty-six and two-thirds Republicans”.    (Actually, to round up enough votes to convict, the Republican Party per se would not need to have even 51 votes in the Senate, provided they could reach the magic figure of 2/3 by forming a coalition with such potential newcomer Senatorial caucuses as the Teapatriot Party, the Segregationist Party, the Montipythonic Very Silly Party, and so forth, thus reducing the rump of Adults to impotence.)   And nobody is predicting that latter outcome in the next elections.  Yet that is precisely the eventuality that must be assumed for his column to make any sense, since, as he himself reports at length:

Last August at a town hall meeting, Rep. Blake Farenthold (R-Tex.) cited the Senate as a reason for not pursuing impeachment. “If we were to impeach the president tomorrow, you could probably get the votes in the House of Representatives to do it,” he said in response to a constituent upset about “the fraudulent birth certificate of Barack Obama” and who wanted him punished. “But it would go to the Senate and he wouldn’t be convicted.”

and so forth for several similar depressing examples.  In other words, the principle here illustrated is

(P) It would be pointless to impeach unless there is some reasonable possibility of securing a conviction in the Senate.

[Strictly speaking, Principle P is not an alethically assessable proposition -- assessable in the dimension of (even relative) truth or falsity -- but springs rather from a different World of Discourse, that of political calculations and expediency.   Sometimes a doomed effort is, politically, exactly the right thing to do, in the playbook of Machiavelli rather than Aristotle;  rather like a pawn sacrifice.  But few parties to the argument here dispute (P) in that sense, so we may ignore that logical nicety.]

The problem comes with the column’s implied proposition Q:

(Q)  If the next elections produce a (bare) Republican majority in the Senate, then there is a reasonable possibility of securing a conviction in the Senate;  ergo, argument (P) against impeachment disappears.

And that is highly unlikely, since it would require a minimum of sixteen Adults (whether Republican or Democrat) to vote with the loonies.  (Mere abstention would not suffice.)

~

Afternote:

The second reason alluded to above (“more anon”) for suspecting that some of the journalistic smoke-and-mirrors here might be deliberate, calculated simply to maximize the number of click-throughs rather than reader understanding, is the queasily vague way in which the word impeach is used, both in the article itself, and in general loose public discourse;  in particular, several officials are quoted using the problematic phrase successfully impeach,  which so far as I know lacks legal definition as a phrase (along the lines of corporate personhood, statutory rape, etc.), and thus is ambiguous between the senses ‘succeed in impeaching (sensu stricto)’ (which is alethically equivalent to "impeach" simpliciter) and ‘impeach, followed by successful prosecution in the Senate’.   In the course of discourse, the semantics of “successfully impeach” doubtless segues vaguely back and forth between these two quite distinct meanings.

Post-Afternote:

Having toyed with the quantificational apparatus so painstakingly illumined by Quine et alia, our columnist then breaks boldly into the territory of what we assume to be an attempt at Brouwer-style Intuitionist alethics (and I quote):

 ~ Obama is not on the ballot in November,

but Obama is on the ballot in November. ~

Also sprach the Zen master.

Meta-Post-Afternote:

Our attorneys have reached a compromise agreement with the journalistic Bad Angel.   We hereby post the following illustration (for educational purposes only),

Tch tch.  Very bad.

while firmly condemning it.

(But, now that we have your complete attention:
  Buy my books !!!)