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).

 

Difficulty is Hard

[Note:  Rather in the spirit of those of our essays which we have labeled “faux-naïf”, the title of this one might be called “pseudo-stupid”.  

Compare a formulation we likewise favor, “Infinity is big.”   That epigram is double-edged.  First, it mimics the naïve astonishment that the novice feels, not only upon being introduced to the idea of infinity, but even large-but-finite things like a googolplex.  (As a child, I marveled over that one, much as I marveled over the brontosaurus, and for the same reasons.)  But beyond that, it alludes to the fact that infinity is much bigger than you can imagine when you first meet it as “1,2,3, …. keep going forever”.  And this, in two qualitatively different ways:  

 (a)  The whole “Hilbert’s hotel” Marx-Brothers-stateroom routines you can play with countable infinity (well described by Rudy Rucker in Infinity and the Mind).   

(b) That countable infinity, for all its capaciousness, is merely the smallest infinity; beyond it lies the uncountable infinity which denumerates the real numbers.   That one you can still kind of get a handle on;  but then in turn, infinitely many much larger infinities  rise beyond.

Too, the epigram is tricky to turn around into ‘Finitude is small’.  For, although anything finite is immeasurably smaller than infinity -- infinitessimally so -- so too is any given finite quantity, not immeasurably small to be sure (the ratio can be measured exactly, and differs for different quatities, unlike the case when comparing it with infinity), still unimaginably small (in psychologically evident sense which could be more rigorously defined) with respect to some other finite quantity, which therefore is unimaginably larger than it is.  (Think Graham's Number, or some iterated Ackermann function thereof.) There is, indeed, a lot of elbow room in the land of the finite.  To get a handle on it at all, you stop talking about individual quantities altogether, and instead investigate rates of growth of various kinds of function.  Some have been discovered which increase with a dizzying rapidity, next to which the proverbial “exponential growth” is like watching paint dry.

The concept of “difficulty” is not nearly so dizzying as that;  still, here as well there are at least two levels.  (1)  That felt by the ordinary layman, “Gee, this stuff is hard.”  (2)  A sharper and deeper sensation felt by many of those who have devoted a lifetime of study and practice to math and the sciences:  “Some of this stuff is difficult in ways I never even knew existed."

And, rounding out the paradox hidden in the apparent tautology,  the apparent converse is false:  for ease does not come easy, but only with much practice, and a certain gift.]

In the post linked to immediately below, we examined essayistically  the peculiar difficulty of mathematics -- not merely the well-known fact that a majority of schoolchildren find that algebra hurts their head, but that everyone, all the way to the top of the professional pinnacle, eventually butts up against something that baffles them, and weighs on their brain:

            De Stultitiâ

In the following, we surveyed less drastic analogues of the phenomenon, in such fields as linguistics and physics:

           

            On Scope and Difficulty

In the following series of essays, we examined the (difficult) question of intellectual depth, comparing and contrasting that with the (mostly psychological, not particularly deep) notion of difficulty:

           On Depth

Now (in the spirit of that last essay-series), we pass  to views internal to the field;  and this in two perspectives:

(1) Psychological:  simply a scattering of quotations, illustrative of the groans and misereres, of those who have attempted to scale this cognitive Olympus.

(2)  Mathematical:  Hints at ways in which certain areas or aspects of mathematics can be qualitatively “difficult”, quite apart from any intellectual limitations of its practictioners.

~

Psychological

Otto Hahn, My Life (1968), p. 90: "I remember Professor Rubens once asking me: `How do you manage to distinguish between all these names and remember all their chemical properties into the bargain?  It's all so frightfully complicated!'"

Imre Lakotos' catty footnote in Lakotos & Musgrave, eds., Criticism and the Growth of Knowledge (1970), p. 114: "Neurath's [1935] shows that he never grasped Popper's simple argument."

Ronald Clark, Einstein: the Life and Times (1971), p. 333: Wolfgang Pauli, quite sure of his own brilliance, nonetheless wrote to a friend in the 1920's: "Physics is very muddled again at the moment; it is much too hard for me anyway, and I wish I were a movie comedian or something like that  and had never heard anything about physics."

Freeman Dyson, Disturbing the Universe (1979), p. 54: at Cornell, "Hans [Bethe] was using the old cookbook quantum mechanics that Dick [Feynman] couldn't understand.  Dick was using his own private quantum mechanics that nobody else could understand."

Mark Kac, Enigmas of Chance (1985), p. 112: "I had a look at some of Wiener's work on Brownian motion  but found it extremely difficult to follow."

& p. 115:  Kac contributed to the invariance principle, which is "now textbook stuff".  Yet "a recent book on the subject  is outside my comprehension."  [Note that this does not mean, "contains much material that was new to me", but rather:  "Even after working my way through the book, I cannot understand it.  God willing the next generation will be able to."]

Richard Rhodes, reviewing Abraham Pais' biography of Niels Bohr in NYTimes Book Review, 26 I 92: "It's sometimes heavy going, and I was reminded along the way of Luis Alvarez telling me that when he read Mr. Pais's biography of Einstein  he'd skipped the hard parts.  If a Nobel laureate could skip the hard parts, so can we all."

John Langlands, in his first of a series of IAS lectures (fall 99), said he'd wanted to be a physicist, but physics was "too difficult", so he had to settle for being a humble mathematics professor at the Institute for Advanced Studies.

Gigerenzer et al, The Empire of Chance (1989), p. 97: Ronald Fischer's writings are "not always transparent  to even the most hermeneutic reader".

John Conway, 17 XI 1999: "I studied Quantum Mechanics with Dirac. Quantum Mechanics is hard to understand, even when you can answer the questions on the exams.  And I couldn't answer the questions on the exams anymore."  [Yet another mathematical genius who found physics "too hard".]

David Berlinski, The Advent of the Algorithm (2000), p. 157: "Gödel lectured on his own results … the mathematicians (and philosophers) at Princeton for the most part could not and did not understand a word of what he said…"  [Note:  Here, nevertheless, the audience was mathematically the most sophisticated in the world.]

I.M.Yaglom, Felix Klein and Sophus Lie (1988), p. 54:

“Lobschevsky’s colleagues  failed to understand his work.  Since they did not want to write negative reviews, they simply ‘lost’ the text.”

I.M.Yaglom, Felix Klein and Sophus Lie (1988), p. 55:

“This symbolic language, using a minimum of words, made it very difficult for Bolyai’s contemporaries to read his great work.”

I.M.Yaglom, Felix Klein and Sophus Lie (1988), p. 57:

“His review was extremely negative.  Bunyakovsky failed to understand Lobachevsky’s ideas.”

I.M.Yaglom, Felix Klein and Sophus Lie (1988), p. 61:

“The audience listened attentively to Riemann’s lecture “Ueber die Hypothesen, welche der Geometrie zu Grunde liegen”, but did not understand it.”

I.M.Yaglom, Felix Klein and Sophus Lie (1988), p. 78:

“Readers were unprepared for Grassmann’s approach and for his idiosyncratic style… Grassmann’s first book was ignored by mathematicians.”

I.M.Yaglom, Felix Klein and Sophus Lie (1988), p. 148:

The letter that Gaulois wrote on the eve of his death was published, “but, obviously, the item was not understood by anyone at the time  and was ignored.”

I.M.Yaglom, Felix Klein and Sophus Lie (1988), p. 153:

“Typically, the officers who proposed the problem  refused at first to consider Monge’s solution, being certain that his mathematical training was insufficient for solving it.”

I.M.Yaglom, Felix Klein and Sophus Lie (1988), p. 177:

“Further explanations proving the mathematical validity of all of Klein’s constructions  were not convincing: he who does not wish to see, will not see.”

Hamilton's intellectual biographer calls that mathematician's  Lectures on Quaternions "hundreds  of all but impenetrable pages".

~

Mathematical

First, certain subfields within mathematics are considered inherently substantially more difficult than others, at least for new entrants:

A Vertex Operator Algebra is an infinite-dimensional, Z₊-graded vector space with infinitely many products.  It is not an easy definition, and there are no easy examples.

-- Terry Gannon, in Timothy Gowers, ed., The Princeton Companion to Mathematics (2008), p. 539

In reference to a certain operation on elliptic curves:

This construction can be regarded as the very beginning of Hodge theory, a powerful branch of algebraic geometry  with a reputation for extreme difficulty.

-- Jordan Ellenberg, in Timothy Gowers, ed., The Princeton Companion to Mathematics (2008), p. 191
[As for garden-variety algebraic-geometry, that is formidable enough:
http://worldofdrjustice.blogspot.com/2011/12/adventures-in-algebraic-geometry.html ]

Second, certain familiar problems, now considered elementary, turn out to be very difficult to solve in real generality and with proper rigor.    Thus, one of the first problems you meet in freshman physics is that of the Vibrating String.  Later, after mastering calculus and advanced calculus, you move on to Real Analysis -- and meet the thing again. Browsing through the standard textbok of F. Riesz & B. Sz.-Nagy, Leçons d’analyse fonctionelle [translated as Functional Analysis, 1955], I was surprised to find, well towards the end of the book, a chapter “Applications to the Vibrating String Problem”.

Similarly, one author remarks that only in recent times have certain classic problems in physics been settled rigorously, using the full arsenal of topology -- but that topologists are given scant credit, since the physicists imagined they had settled these matters long ago (though their proofs were fallacious).

Or cf. Charles Fefferman, who, in his article on the Navier-Stokes equation, places front and center  its status as a surprisingly tough nut to crack:

The Euler and Navier-Stokes equations describe the motion of an idealized fluid.  They are important in science and engineering, yet they are very poorly understood.  They present a major challenge to mathematics. … Although the Euler equation is 250 years old, and the Navier-Stokes equation well over 100 years old, there is no consensus as to whether Navier-Stokes or Euler solutions exist for all time, or whether instead they “break down” at a finite time. 

in Timothy Gowers, ed., The Princeton Companion to Mathematics (2008), p. 193-4

All this is of more than academic interest, since Navier-Stokes rules hydrodynamics which governs the oceans and the atmosphere, and hence determines whether we shall all go blithely on or whether shall one day disappear in a polar vortex or the like.  (As I write [7 January 2014], the temperature has been hovering around zero Fahrenheit, but with a high of 72 forecast for Saturday -- four days from now.  It feels as though we may have entered a region of unstable vorticity.)

(Thus spooked, I read on, and on p. 196 encountered this:

In the Euler equation … solutions can behave very strangely.  A two-dimensional fluid that is initially at rest, and subject to no outside forces, can suddenly start moving …

For the past few days, I’ve been reading a novel by Stephen King, and passages like that cause the hairs on the back of the neck to bristle like quills upon the proverbial porpentine.)

~

For more from this pen, try this:
http://www.linguasacrapublishing.com/justice.html