Thoughts 'n' Things

  Rudy Rucker, Infinity and the Mind, p. 38:

(**) Just as a rock is already in the Universe, whether or not someone is handling it,  an idea is already in the Mindscape, whether or not someone is thinking it.

This is itself a pleasant thought, recalling the ditty about God-in-the-quad; but in actual fact – I don’t think so.

(So you see—I am not an uncritical Platonist.  Platonic heaven must be so gerrymandered, as to exclude such things as cheese doodles and Sponge Bob Squarepants.)

The actual universe has (for example) -- whatever geometry it has:  regardless of whether there are rational creatures capable of understanding it, let alone deriving it.  Likewise the landscape of math.  But particular formulations of physics, and perhaps even of math – matrix mechanics v. wave mechanics, Cauchy analysis vs. non-standard analysis – do not exist in complete independence from their proponents.  They are, one might say, propositions, not objects.  The objects (or patterns, or whatever they are)  exist  even in the absence of  a person to spout propositions about them; but the propositions require a proposer.  – Nothing specially abstract here; the same thing is true of rocks.  This rock exists independently of any finite mind, but: “There lies a rock” and “Behold that rock!” and “What a rock that is!” must come out of some actual someone’s mind or mouth.

            The unbridledly idealistic view in (**) conjures up a skyscape of untethered thought-balloons.  It is pleasant to contemplate, in a comic-strip sort of way, but not to be taken too seriously.  For one thing, unlike the situation with mathematical truths, where anyone at any place or time might discover them, there is no way for a rational creature in another galaxy or dimension to reach out and grab one of those thought-balloons by the tail;  he is required to blow his own bubbles.  Whereas the structures of mathematics are like fixed landmarks, which one encounters again and again, from different approaches.  For instance:  Yang-Mills gauge theories, discovered by the physics expedition; and connections on fibre-bundles, discovered by the math team; and lo, they meet in the middle.  Likewise group-theory.  Different body-parts of this have been grabbed onto by matrix theory, algebra (symmetries of solutions to equations), geometry (the Erlangen program), particle physics (glad you could get here; meet Sophus Lie), and in time it becomes clear that it’s all part of the same elephant.  Whether they come from physics, or mathematics, or computer science, two such explorers may not realise that they have come upon the same mountain, till they have circled around it a bit and compared notes.  And this happens repeatedly.  We may summarize in an epigram:  The mindscape of mathematics is a multidimensional torus:  whatever direction you set off in, you eventually wind up back at Hilbert’s Hotel.

It turns out that Shing-Tung Yau likes this montane metaphor as well.  Cf. The Shape of Inner Space (2010), p. 103:

A mathematical proof is a bit like climbing a mountain.

And he nicely outlines the Yang-Mills case (p. 290):

The physicist Chen Ning Yang was similarly astonished to find that the Yang-Mills equations, which describe the forces between particles, are rooted in gauge theories in physics  that bear striking resemblances to ideas in bundle theory, which mathematicians began developing three decades earlier, as Yang put it, “without reference to the physical world”.  When he asked the geometer S. S. Chern how it was possible that “mathematicians dream up these concepts out of nowhere,” Chern protested, “No, no.  These concepts were not dreamed up.  They were natural and real.”

            Contrast the case with “thoughts”.  Supposititious entities of the mindscape, even some popular thought-balloon, tethered to a billion different heads, need never be rediscoverable by another explorer, nor acknowledged as real should he simply be grabbed by the lapel by one of the thinkers, and treated to an exposition of same.  For example, the notion held dear by countless generations of schoolboys around the globe, of the uniquely funny nature of flatulence, will never appear among the gravely ellipsoidal thought-balloons of the solons of Fdrmrphlandia; even “funny”, for them, is not well-defined, and not particularly worth defining.

Now, probably Rucker meant to restrict the realm of “ideas” to just some of them.  Not, “Wouldn’t it be fun to dip Suzy’s pigtail into the inkwell!”, but things like “The square of the hypotenuse is equal to the sum of the squares on the other two sides.”  Fine; but careful, here.  The Pythagorean theorem has  as its basis  a fact about Euclidean geometry, in every possible world; just as Fermat’s Last Theorem expresses (in a possibly somewhat contingent and imperfect way) a fact about the natural numbers.   But a fact is not the same thing as an idea.  As a matter of fact, there is a coffee stain on this shirt; but “the idea of this coffee-stained shirt” is no strut or girder of God’s architectonics.  An idea concerning a fact of mathematics, in a finite mind,  may bear – must bear -- but an imperfect relation to the fact itself (‘fact’ here used broadly: it may refer to a wildly transfinite complexus of relations, some of them perhaps perceptible only to angels).   Most people’s ideas of mathematical truths bear as much relation to the truths themselves  as does a crayon scribble to the Sistine Chapel  which it might (based merely upon memory of a fleeting ill-lit glimpse) attempt to depict.  To posit that all truths of mathematics exist as Ideas in God’s mind, is logically allowable, but really adds nothing, and is in any case unknowable. To identify these truths with the neuronal states of the pitiful meat-wads sloshing around in our half-cracked crania, is to add nothing at all, but is rather to detract.

[Appendix]  Karl Kraus apparently entertained a notion of independent or pre-existent thoughts.  He speaks of someone being

von der Präformiertheit der Gedanken  überzeugt, und davon daß der schöpferische Mensch  nur ein erwähltes Gefäß ist; und davon, daß die Gedanken und die Gedichte da waren  vor den Dichtern und Denkern.

-- “Heine und die Folgen”, reprinted in J. Franzen, The Kraus Project, p. 88

The whole ‘meme’ idea (itself a meme) is similar -- not that the various Chiclet-thoughtlets were truly Platonically pre-existing, but that, once hatched, they lead a promiscuous existence, wandering into people’s minds  like pollen into our air-passages.

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Footnotes from the 19^th century:

Dedekind … allowed his philosophy of mind  much reign, with a ‘proof’ that “there are infinite systems”;  for he gave  as evidence “the totality S of all things, which may be objects of my thought”, since  as well as any of its elements s,  it contained also “the thought s’ that can be the object of my thought …This ‘proof’ did not gain a good reception.”

-- Grattan-Guinness, The Search for Mathematical Roots 1870 - 1940 (2000), p. 105

For Frege,

In contrast to subjective ‘ideas’ (Vorstellungen), ‘thought’ was intended in an objective sense, rather like state of affairs, sharable among thinkers  and indeed independent of anyone thinking then.

-- I. Grattan-Guinness, The Search for Mathematical Roots 1870 - 1940 (2000), p. 190

Esse est percipi (redivivus ter)

“To be is to be perceived” -- Bishop Berkeley
[corresponding to the Latin   esse est percipi, pronounced ESS-ay est pare-KIP-ee.  Percipi is the passive infinitive, a delightful category, which does not exist in any of the other languages with which I am conversant.]

“We call a real dynamical variable whose eigenstates form a complete set   an observable.”  -- Paul Dirac

“To be  is to be the value of a variable.”  --  W.V.O. Quine

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~  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.

(I am Bishop Berkeley, and I approved this message.)

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Three radically different takes on  being and seeing.

(Cf. "Seeing is believing" -- vs. Berkeley:  Being seen  is being.)

The first and most famous of the epigrams above  applies to the ontology of basic objects, such as coffee-cups -- about which no plain man has any doubts whatsoever.   (Quine's quip  will, however, frequently detain us further;  e.g. here.)

A related but different question  concerns things which, unlike a coffee-cup or its relativistic mass, you cannot directly perceive -- though someone else might.

Scott Soames, Philosophical Analysis in the Twentieth Century (2003), vol. I, p. 17, re the views of G.E. Moore:

For things presented in space, but not things to be met with in space, to exist is to be perceived.  That is, afterimages .. and pains  can only exist when they are perceived or experienced.

Or, classically,  “Beauty is in the eye of the beholder”.

A psychological vice ontological version of Bekeley’s epigram, is the vernacular “Out of sight, out of mind.”  (Cf. French, "Si tu te tais, ni vu ni connu.")  Or, as Fielding wittily put it in Tom Jones,

De non apparentibus, et non existentibus,

eadem est ratio. -- In English, ‘When a woman is not seen to blush, she doth not blush at all.’ 

(Lawfolk interpret this Latin tag more prosaically:  “What is not juridically presented cannot be judicially decided.”   Spoilsports.)

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A noted intuitionist philosopher, anent “the celebrated [loathsome, leprotic -- ed.] thesis that mathematical statements do not relate to an objective mathematical reality  existing independently of us”, writes that, on such a view, to be is to be conceived:

Unlike material objects,  mathematical objects are, on this thesis, creations of the human mind.  They are objects of thought, not merely in the sense that they can be thought about, but in the sense that their being is to be thought of [or rather, thought into existence -- ed.];  for them, esse est concipi.

-- Michael Dummett,  “ The Philosophical Basis of Intuitionistic Logic”, in: Truth and other enigmas (1978), p.  228

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The above is really just a placeholder post, reminding me to someday address the deeper problem of observables.   This may never happen.  To begin with, even in the simplest quantum-mechanical case, an observable is an operator on Hilbert space, so you have to wrap your mind around that.  With some luck and some study, that might be doable.  But just now I encountered the following dismaying sentence:

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

I may well have retired to my hamster farm, before ever figuring such things out.

In the meantime, some further thoughts about ontology  here.

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Bonus quote:

  How do you know you’re having fun  if there’s no one watching you have it?

  --Douglas Adams, The Restaurant at the end of the Universe (1980).

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Visitors to the site have enquired about the pronunciation of the classic Latin phrase “esse est percipi”.   About this (although I used to be editor of pronunciation at Merriam-Webster, back in the day) I have so far had nothing to say.  Embarrassed, I messaged my colleague and comrade Dr. Keith Massey (officially out of comms, but reachable in the bush), as follows:

More than once, someone has searched the blog via
   pronounce esse est percipi
-- alas in vain.  In my head, I have always pronounced this pear-KIP-ee, but, given that the vowel is short, the Latin would be more like PEAR-kip-ee, no?
Or rather, the Vulgar Latin, since Latin itself, being quantitative, lacked phonemic lexical stress.  Correct so far?
A second question is how philosophers in various countries pronounce it -- anglicized, frenchified, etc.

Swifter than lightning, our colleague replied:

In classical Latin the C is always pronounced as a K. But we don't know when the thing started to change before E and I. I suspect it was already being realized regionally as something else in the Late Imperial period. And speakers of Latin dialects took to pronouncing their classical Latin as if it were their living register. And so, in France,  percipi was pronounced “persipee”. In Italy perchipee, and in Spanish pershipee (attested still in Ladino) and later, in Iberia as perthipee, and, yet later in the New World, as persipee.

Accent in Latin is a hotly debated topic. I personally follow the view that the classical accent is unknowable and therefore all we have to work from is the living dialects and the rules of Ecclesiastical Latin. And so, penultimate except in a few cases. Accent falls in the syllable before -ibus. But I'd say perCIPee.

As for Anglo-Latin, this is an exciting topic. There's some evidence that a Romance language survived in the Isles for a several centuries after the withdrawal of forces in 380. It apparently, from inscriptional evidence, turned long E into a long I, fecit --> feecit. The way we pronounce phrases like Habeas Corpus may actually be representative of the pronounciation of Anglo-Romance, rather than a later scholastic recasting.

Those further interested in this topic can consult the essay by Thomas Pyles, “The Pronunciation of Latin in English:  A Lexicographical Dilemma”, reprinted in his Selected essays on English usage (1979).  Executive summary:  The history is so tangled, it is now an unresolvable mess.

In his “Tempest in Teapot: Reform in Latin Pronunciation”, reprinted in the same volume, Pyles quotes an amusing epigram that alludes to what became of Latin in Spain, where original v and b merged into a bilabial fricative:

~ Felix natio, ubi vivere est bibere ~

[Variant: "o felix iberia, ubi vivere est bibere"]

For further adventures in pronunciation, click here. 

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Distinguishing discontinuous state-reduction (which he dubs R) from linear evolution as per the Schrödinger equation -- i.e., the “collapse of the wave-function” upon “observation”, a mathematician remarks:

I do not mean to imply that the experimenter deliberately sets up a ‘measurement’ to achieve this.  … Nature herself is continually enacting R-process effects,  without any deliberate intentions on the part of an experimenter or any intervention by a ‘conscious observer’.

-- Roger Penrose,  The Road to Reality (2004), p. 593

Thus achieving the esse of percipi  ‘naturally’ (vacuously).

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