Too Much of Nothing

[Note:  This title is an allusion to a Bob Dylan song.  Peter Paul and Mary did a wonderful cover of this, which achieved some airtime, some forty-odd years ago.  But I cannot find it on the Web.  The one older (B&W) video you do find   is not the album version, but a performance that is much more up-tempo, sunnier, and, well, shallower.  The haunting version that still echoes in my mind had strange harmonies and blue-notes, and funky harmonica.  As during the verse:

It’s ALL been done be-fo-ore,

It’s all  been  written  in  a bo-oo-k…

When there's too much of noth-innng

No-bod-y should loo-oo-ook!

The melody of the second line is just a monotone, but the way they rendered it, with tensely close harmony, so that the male and the female voice become indistinguishable -- another voice peels off from the crown and weaves its own magic -- more plaintive, more revival-like, than the versions available now. -- Unless, of course, the song has actually fermented in memory, grown richer over the years as I replayed it in my head, ripening and deepening like a fine red wine…

Anyone who can point me to this version  will earn my gratitude.]

~     ~

  

Gorgias presented his nihilist arguments in On Non-Existence; however, the original text is no longer extant.

-- Wikipedia, re the early Greek sophist

Etienne Gilson reports (La philosophie au Moyen Age, p. 196) re the work of one Frédégise (d. 834),

Epistola de nihilo et tenebris, où il soutient que le néant et les ténèbres  sont quelque chose, et non pas seulement l’absence de quelque chose.

So far, a trifling with words, but:

Il serait absurde de dire: nihil désigne une chose, si l’on admettait  en même temps  que nihil  signifie le néant.  Or, c’est précisément ce que nie Frédégise.  Le nihil auquel il pense  est celui dont Dieu a créé le monde, ex nihilo, c’est-à-dire  une sorte de matière commune et indifférenciée…

That final clause might strike us as a quibble, a bait-and-switch; but it is similar to the once-trending view of cosmogony known as Steady State (though here it was particles coming into being out of nothing, here and there on an ongoing basis);  the contemporary "Universe for Free" idea is a modern version.   Further, the affordances of later mathematics  would allow him to stick with his guns, without smuggling in any ontology via the back door.

*

Travaillant au noir,

le détective  se trouve aux prises

avec le Saint-Esprit

C’est quoi, le péché irrémissible ???

*

Thus consider the empty set -- something with which, once the New Math struck, every schoolchild has been familiar.   Concretely, it is nothing;  but abstractly, it is something, and this, by the same necessary motion of the mind, which considers Laurel and Hardy a pair, over and above the separate existence of Mr. Laurel and Mr. Hardy.  -- So far so vacuous, perhaps; but at least innocent of any theological special pleading.

Yet later mathematicians  contrived to construct the whole of the natural numbers -- and with that, the scaffolding of all that is  or (as it might be) may be -- out of this same empty-set.   One approach (Zermelo) identifies zero with the same; one, with the set containing the empty set;  two, with the set containing that.  Another approach (von Neumann), with more craft, took the empty set, and the set containing (nothing but) the empty set (quite a different thing altogether) -- well, the details are unimportant.  And lest you imagine that such an exercise were the idle fiddling of someone with too much time on their hands, know that John von Neumann was one of the hardest of hard heads; a pioneer of computer science; a mainstay of the Princeton intellectual-social scene; and possessed of clearances  of which you or I can only dream.

The empty set is thus Nothingnes, Reified.  So far -- despite von Neumann’s pulling all of set theory out of an empty hat -- you may be unimpressed.  After all, the use of this term can often be (as Quine likes to put it) “paraphrased away”:  e.g.  “A ∩ B = ∅” means neither more nor less than “A and B have no elements in common”.  But “experience has shown that the admission of ∅ as an actual object  enhances and simplifies the theory” (R. Goldblatt, Topoi , 2^nd edn. 1984).

~

For all its humble nothingness, Nothing has an awful lot of distinct names in mathematics.

The empty set itself is known also as the void set.  The set on which a function is zero is its zero set, and the complement of this is its cozero set.
The nullity of an operator is the dimension of its nullspace (or, in the case of a homomorphism of groups, the rank of its kernel).  More exotically:  the Nullstellensatz is a foundation of algebraic geometry.
In an algebraic structure, an element is termed nilpotent if it can be raised to a power to give zero.  This doesn’t mean that the element is ‘powerless’, as the etymology might suggest.  Thus, in the cyclic group of order p^2 (p a prime), p itself is nilpotent since its square is zero;  but it maps every other nonzero element to something nonzero.

Further:

critical point: one where the derivative of the defining function is zero.

zero set: the set of all points mapped to zero by a function

singular (matrix): one whose derivative is zero

closed (differential form): one whose differential is zero

annihilator (of a subspace): the set of all functionals that map the subspace to zero

Cf. also the notion of a “set of measure zero”, which is not quite as zero-y as it sounds, since the ones we are interested in are generally infinite.

~

Etymological footnote.

In his memoirs, Souvenirs d’apprentissage (1991), André Weil, who has much larger accomplishments to his credit, takes a certain satisfaction in having introduced a new symbol for the empty set, which stuck:

Ø

He explains that he took this from the Norwegian alphabet, “et j’étais seul  dans Bourbaki  à le connaître”.

In his droll conspectus of mathematical history, David Berlinski, Infinite Ascent (2005) adds:

To the empty set is reserved the symbol Ø, the figure now in use in daily life to signify access denied -- a symbolic spillover, I suppose, from its original suggestion of a canceled eye.

Note:  A more profound comment  than might initially appear, given the Mediterranean context of the "Evil Eye" ...

 ~

In later Chomskyan linguistics, of the Government-and-Binding variety, "nothing" came to play a very large role indeed.  It came in different flavors -- trace and PRO -- and boasted the Empty Category Principle or ECP  as one of the pillars of the theory.

Yet such Nothings are as rich  as any Something:

So-called ‘empty’ categories  are not devoid of properties;  they are specified for syntactic features.  The term ‘empty’ refers [merely] to the fact that these categories are not associated with phonetic content.

-- Liliane Haegeman, Introduction to Government and Binding Theory (1991),  p. 288

Cf., indeed, Whorf’s celebrated treatment of the phrase/concept “empty gasoline cans”.

~

~  Posthumous Endorsement ~

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

this is what I would be reading: "

I Don't Do Divorce Cases

Murphy on the Mount.

(I am Benjamin Lee Whorf, and I approved this message.)

~         ~

~

Epigrams re le néant:

What we understand about God is not nothing; it may even be infinitely much;  but it is a set of measure zero in the larger space of what is true.

-- Dr J, Tischreden

A literary forerunner of the playful paradox “too much of nothing”:

We used to sing together -- in my case very tunelessly. I had inherited a plentiful lack of musical genius from my Mother, who had neither ear nor voice.

-- Edmund Gosse, Father and Son (1907)

Tiens !  Ceci vient à propos:

“The Power of Nothing”, by the aptly-named Michael Specter, in the current issue of The New Yorker.

*

Für psychologisch tiefgreifende Krimis,

in pikanter amerikanischer Mundart,

und christlich gesinnt,

klicken Sie bitte hier:

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

*

I am currently reading a book by Russell Standish, called Theory of Nothing -- basically a way of referring "by duality" to a Theory of Everything.
Rather wittier  is this epigram from a detractor of string theory (as it reaches its Landscape dead-end):  the theory has "gone from being a Theory of Everything, to a Theory of Anything."  I.e., where predictive value is lost, because Anything Goes.

[Update 21 Feb 2012]  And now this:
http://www.nytimes.com/2012/02/21/science/space/cosmologists-try-to-explain-a-universe-springing-from-nothing.html?src=me&ref=general

~

In his substantial general survey of modern philosophy, Roger Scruton is obliged to take notice of the existentialists and phenomenologists.   Appropriately, even delightfully, he places these in a chapter titled “The Devil”.

Heidegger … famously argued that there is something that is true of Nothing, namely that it ‘noths’ (Das Nichts nichtet.)

-- Roger Scruton, Modern Philosophy (1994), p. 458

(Heidegger fiddles with words  like an imbecile playing with his faeces.)

Then on to Sartre and L’Etre et le Néant  (a book I discovered in high school and seized eagerly, having heard that it was hip and rebellious and edgy and kewl -- and was baffled to find that it sux):

Nothingness, he tells us, lies ‘coiled in the heart of Being, like a worm’.  I can encounter Nothing at any juncture:  for example, when I look for someone in a café where I expect to meet him, and he is not there.  The world is suddenly colured by his absence;  and this negative fact has a peculiar reality   all of its own.

But however strange this experience, it is surely not an archetype of evil.  Entering Les Deux Magots to find that Sartre is not there  is one of life’s blessings.

-- id.

~

There is a real sense in which “too much of nothing” applies to basic physics.

Most macroscopic objects behave in ways that do not tip us off to their quantum nature (save as what, for classical physics, was the paradox of the stability of atoms, was ultimately solved or at least frozen by the notion of quantization as applied to electron orbits).  But when we get rid of such objects -- when we attempt to get rid of everything, all matter whatever, and scrape down to the bare vacuum … the striven-for Nothing rebels, and that in the most violent way imaginable.  As a result of the Heisenberg Uncertainty Principle -- here, not as an epistemological limitation on ourselves, as (given its title) it is often taken to be, but as a literally creative faculty at the heart of Nature -- the classical featureless vacuum becomes instead the Quantum Foam:  a riot of virtual particles, and topologically  perhaps some nightmare analog of Alexander’s horned sphere.

One stroke of Alexander’s sword

will *not* undo this knot !

Update 25 III 2012]   And on that very topic… a book review in this morning’s NYTimes:  A Universe from Nothing, by Lawrence Krauss.  No new information or argument in this book, apparently;  it all comes down to what the meaning of Nothing is.

The book offers the sort of thing we have repeatedly polemicized against -- and with a “Nyaah nyahh I told you so” Afterword by Richard Dawkins, no less -- but as the reviewer, David Albert, does a fine job himself of polemicizing (“Let me put those niceties aside  and try to be quick, crude, and concrete” -- You go, guy, gloves off!) your correspondent can maintain his decorous Sunday Lenten silence, and merely link.

(The online site unaccountably buries the article, so this is something of a public service.)

http://www.nytimes.com/2012/03/25/books/review/a-universe-from-nothing-by-lawrence-m-krauss.html?_r=1&sq=&st=cse&%2334;david%20albert=&scp=1&%2334;%20krauss=&pagewanted=print

The subtitle of the book under review is “Why there is Something Rather than Nothing”.

Our own remarks on the matter  can be consulted  here:

http://worldofdrjustice.blogspot.com/2011/01/why-is-there-something-rather-than.html

[Update 7 April 2012]  Krauss provides a summary of his views here:

http://www.latimes.com/news/opinion/commentary/la-oe-krauss-cosmology-design-universe-20120401,0,4136597.story

Arts & Letters Daily provides a typically bone-headed teaser in its link to the article:

"Physics has undermined logic. Even nothingness is not what it seemed. The universe is devoid of meaning. That’s not such a bad thing."

*     *     *

~ Commercial break ~

Relief for beleaguered Nook lovers!

http://murphybros.blogspot.com/p/read-murphy-on-your-nook.html

We now return you to your regularly scheduled essay.

*     *     *

[Update  25 April 2012]  They’re at it  again…

ALDaily, shilling for nihilism, links to an interview with Krauss in the Atlantic , with this come-on:

More and more, physics is encroaching on philosophy. No surprise that philosophers feel threatened. They should, says Lawrence Krauss. Science progresses, and philosophy doesn’t.

As for the actual article … you can’t make this stuff up.  Their roving reporter just happened to hook up with the distinguished nihilist as he was coming from … a memorial service for professional atheist Christopher Hitchens.

If I were to write that, you’d think it was unfair satire.

[Update 10 June 2012] Jim Holt on l'affaire Krauss:

Physicists, Stop the Churlishness

A KERFUFFLE has broken out between philosophy and physics. It began earlier this spring when a philosopher (David Albert) gave a sharply negative review in this paper to a book by a physicist (Lawrence Krauss) that purported to solve, by purely scientific means, the mystery of the universe’s existence. The physicist responded to the review by calling the philosopher who wrote it “moronic” and arguing that philosophy, unlike physics, makes no progress and is rather boring, if not totally useless.

 [Update 30 September 2012]   Crashaw, “On Hope”:

Dear Hope! Earth’s dowry, and Heaven’s debt,

the entity of things that are not yet.

Subtlest, but surest being!  Thou by whom

our Nothing hath a definition.

(Note for scansion:  definition is here quinquesyllabic.  -- As is, indeed, the word quinquesyllabic itself.)

 ~

More on the vicissitudes of Nothing in mathematics.

In  the introduction to Timothy Gowers, ed., The Princeton Companion to Mathematics (2008), p. 14, we are presented with the following syllogism:

* Nothing is better than lifelong happiness.

* But a cheese sandwich is better than nothing.

* Therefore, a cheese sandwich is better than lifelong happiness.

Nobody buys that;  but it’s hard to put your finger on where the reasoning goes off the rails.   The author rewords the first proposition as

For all x, lifelong happiness is at least as good as x.

Here the seeming noun nothing was covertly a quantifier.   Whereas  “the second sentence cannot be rewritten in these terms  because the word nothing is not playing the role of a quantifier.  Its nearest mathematical equivalent is something like the empty set.”

~

In a single review from March 25, 2001, the New York Times Book Review treats together  the following three titles:

THE BOOK OF NOTHING

Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

By John D. Barrow

ZERO

The Biography of a Dangerous Idea

By Charles Seife

THE NOTHING THAT IS

A Natural History of Zero

By Robert Kaplan

Der Fall Rorty (Explication de texte)

 Richard Rorty, Philosophy and the Mirror of Nature, p. 19:

If we try to clarify the orthodox notion of ‘the divine’, we seem to have either a merely negative conception, or else one explicated in terms of the notions of ‘infinity’ and ‘immateriality’. Since reference to infinity explains the obscure by the more obscure, we are left with immateriality.

            Rorty seems to have solved the Packing Problem:  This is ten pounds of bullsh*t in a five-pound bag.

            The first clause first, though it is the least exceptionable.  It neither says nor presupposes anything false; the bias is merely rhetorical.  We “try to clarify” (evidently doomed in our efforts, so obscure is the clarificandum) – as though clarification were not likewise a necessity for everything from rocks to snowflakes to the Continuum Hypothesis.  Bishop Berkeley tried, and failed, to clarify Newton’s fluxions; Cauchy succeeded.  Next!  -- And then those little tweezers, the squotes:  I use them myself, so I know what they’re used for.  Preferably not to denigrate divinity before we’ve even begun (“…of ‘the divine’ ….”).   

            The “merely negative conception” does point to a real current in theology (both Christian and Islamic), but a current so rich, that the “merely”, while essentially an emotion-word, almost rises to the status of a lie.  For the “negative conception”, the  via negativa, (discussed elsewhere in this series;  just click on the label) is nothing like nihilism, nothing like negativism, nothing even like skepticism.  It is a stance arrived at after a long – centuries-long – attempt to characterize, in positive terms, what is… well, it turns out, very difficult to characterize, at least in terms of the predicates we inherited from our hunter-gatherer and pastoral past.  We might compare it to the history of our contemplation of the Continuum Hypothesis.  In the early days, red-blooded mathematicians naturally set out on their stallions to prove it (positively) true; or, failing that, to prove it (positively) false.  The current position (after much intermediate agony)  is:  It is true in some models; false in others; and independent of the axioms as usually deployed in set theory.  This whole “independent of the axioms – neither true nor false, exactly, but not nonsense either” is a rich notion, almost too rich to digest,  which required millennia to arrive at.  It is indeed a kind of (unanticipated) negative result; but not “merely negative”.  And since the problem of God is a superset of the problem of the Continuum Hypothesis, we cannot well expect a simple etch-a-sketch portrait of the guy (as it were, posing along the boardwalk at Ocean City).  (Indeed, if you follow me closely, my adducing the C.H. for comparison, so far from being some typical theistical opportunistical move, if anything undermines our naïve conception of the Creator; at least, its initial effect on myself was sickening, as bad as the Beagle on Captain FitzGerald.  And there will be no post-initial effect for quite some time, until – God grant it – I gain greater insight into the thing.)

He goes on:  ”or else one explicated in terms of the notions of ‘infinity’ and ‘immateriality’.”

(Note again the sneer quotes, offered in lieu of argument by this ‘philosopher’.)

Being passably ignorant of theological history, I cannot say whether these two epithets, among the many that might be hazarded as regards the Godhead, are the two statistically most prominent ones, but let us suppose they are.  No theologian, and no widow lighting a candle, ever imagined that these were the crux of the thing.  The integers are infinite and immaterial; so is the Infinite Penguin; we worship neither.  How about “Creator”, “Redeemer” and “the ground of our morality”, yo?

  “Since reference to infinity explains the obscure by the more obscure…”    Good… Lord.  I wish it were so.   If the nature of the divine were actually clearer than the nature of infinity – I wouldn’t need to write this essay, it could be left to the kindergarten teacher, while the rest of us dance table-top, champagne in hand.   Infinity – by which I shall here always mean, the very teensiest flavor of same, aleph-nought – has been very well studied by now.  It is virtually suitable for the nursery.

            If I have hesitated to push the infinity-of-the-integers business too far (their infinity, as opposed to their Necessity), it is not because it is too obscure:  it is rather too simple, too almost shallow.  I can tell you a lot more about little-omega (that least, most modest infinity, with the ordinal type of the natural numbers) than I can about, say, something really difficult, like a duck.

            As for “immateriality”, that’s… immaterial.  Is He immaterial, or nonmaterial, or intangible, or  ethereal, or abstract, or funereal  -- wholly or partly so? Some say He once walked through Jerusalem, leaving footprints in the sand.  That is intriguing, if true (trust Rorty to latch on rather to the boring possibility); but as for immateriality, that is no part of our interest in, or devotion to, Him.  Smurfs are immaterial for the matter of that, and I don’t go to Smurfs on Sunday.  In fact, given a choice (say, by a dating service) between a Material entity and an Immaterial, I’d go with the Material every time.  It might tickle our idle curiosity to find out, whether He is – or rather, for that is nonsense, to what extent and in which ways He is ` ` ` immaterial ‘ ‘ ‘ (and here it is the philospher’s use, not the possible pis-aller use by the theologian, that I am punctuationally excoriating), -- how like a ghost, like the air, like the integers, like the non-algebraic numbers, like the angels, like aleph-one, like our late great-grandfather, like a poem once spoken but never written down, how like a prayer we would have uttered, but that the Reaper came too soon …. You’d need a lot of terminological tidying-up for the question to even make sense, and it isn’t worth doing.  Those who believe they have had some actual experience of God, have a number of tart things – be they true be they false things, but – a number of sharp and hard things, to say, about these experiences, which in no way resemble the mumblings of a sociophobic agnostic concerning the silences of a fog-enveloped all-encompassing blancmange. To ignore all this and focus on “immaterial”, is like never bothering to learn Relativity, yet loudly wondering (peevishly) about just what was Einstein’s favorite flavor of ice cream. (My understanding, incidentally, is that he preferred minkowskian, with sprinkles.)

            Nothing hangs on this red-herring of the “immaterial”.  Most folks who have had (as they imagine; again, righly or wrongly) any immediate experience of God, tend to emphasize the personal.   My own conception of the Creator is actually more immaterial than most, because I’m emphasizing the actual nature of the Creation, than which the Creator is logically-necessarily more complex: a Creation which has – I mean just plain in terms of Measure Theory -- far more of the mathematical (call that abstract or immaterial or whatever you like) than it does of rocks, or turds, or mxlnthnkxs. (These last are certain purely material items of Universe #138; they greatly outnumber our atoms, but there are far fewer of them than there are  integers.)  Were I someday actually to run into the chap, and were He to appear in the quite tangible aspect of Mr. Natural seated beneath a tree, I should, to be sure, feel mildly surprised, but philosophically neither cheated nor refuted.

(Key to that last paradox:

 While we dub the Lord the “Necessary Being”, that description, like that of “Father” or “Creator” or the “Lord of Hosts”,  does not exhaust Him.  It is impossible to conceive of Him as being nothing but the Necessary.  For in that case He  really would be just a giant math book. Hence the boring quality of the ontological argument (whether valid or not). We can conceivably deduce certain things about God along those lines, but nothing of His concreteness.)

*

Rorty adds, later down the page:

If it makes any sense to speak of the existence of universals, it would seem that they must exist immaterially.

First:  It does indeed make sense to talk of universals, if it makes sense at all  to talk about integers, or modus ponens, or “all men are mortal”, or “the most wonderful mom there ever could be”   -- this “existence of” pre-modifier is something of a rogue.  It makes sense to talk of Hamlet, unicorns, democracy, love, and prime numbers; what is added by this “existence of”?  “Please pass the existence-of  salt.”  No, nonsense.

Next: These universals may “exist”, if you like, `immaterially’, or in any other fashion – I wouldn’t insist on the point, nothing hangs on this. For all I care, they exist in a pickle-jar; none of their properties (in universe after universe) are affected thereby.  As it happens, I personally tend to see Hilbert space as rather more concrete and well-defined, and mountains as rather more abstract and ill-defined, than has hitherto been customary. Likewise, Schubert’s piano sonata in B flat is – abstract /ideal/ immaterial/ call-it-what-you-may, it is still acoustically-ontologically tangible, and each recording or performance thereof is quite concrete.

And yet further a bit (Rorty goes on):

“…the immaterial – the mystery beyond the bounds of sense…”

Now this is a nice phrase, suggesting in particular  the existence of something beyond the confines of the lavatory, where nominalists spend so much time; so we receive it with respect.  Still, conscience oblige, we are compelled to observe, that the “bounds of sense” are a purely relative, species-bound, even individual- and moment-bound notion. A pickle-jar exists beyond the bounds of the blind bat, that doesn’t make it a mystery.  Hilbert space exists beyond the bounds of certain uninstructed individuals; whose bad?  The Blorks of the planet Fnoid can neither see nor touch a stationary object, but they can move it, and then sense it, using their solutions to the equations of motion, and this more accurately than with the eyes.   Cantor and Gödel had a sense for the infinite that compares favorably with many an ear for music or nose for wine. 

            And as for “mystery”, a term often used as a sort of hand-waving dismissal: many things, both physical and immaterial, are mysterious until you study them; others, unmysterious until you study them.  Rocks are much more mysterious after the discovery of atoms (my my, mostly empty space. And yet so solid).  Fractions, which every kindergartner now takes for granted, spooked the Egyptians, who for some reason expressed them, not in the simple form of today, but as an elaborately calculated sum of reciprocals.  Algebraic numbers, imaginary numbers, lose their mystery in a single intellectual wedding-night.  Transcendental numbers like e and pi, retain – or rather have gained, in mystery, but in a specific sort of mystery in each case: indeed, we have a solid handle at the hither end of it.  It is a mystery we never would have discovered, let alone elucidated, had we adhered to a Rortyan agnostic-proctological underview.

*

Edward O. Wilson, Consilience (1998), p. 190, re Rorty’s replacement of epistemology with hermeneutics:

Discourse among scholars, in short, can proceed without worrying about consilience.  About rigor too, it would seem.  Although this concession is welcomed by postmodernist scholars, it is a premature surrender that would drain much of the power and joy from scholarly inquiry.

Wilson counsels eschewing such a replacement, “except at cocktail time” -- a wise proviso, since indeed, prattling on about hermeneutics is much more likely than epistemological discourse  to get you laid.

 

Theologia Mathematica: I (ctd)

[a continuation of this]

            To return to the thought:  It might not have been the case that all the (roughly, macroscopic) wobbles and writhings of the natural world  should coalesce into an austere mechanical description of quite general validity, but it turns out that (to a broad extent) they do.  Nor that the insane exceptions at the quantum level (mostly microscopic, but probably much beyond this  as we learn more and more) should line up in a wholly, almost unimaginably different  but still orderly system: but they do, though in a way not even dimly anticipated before our own era.  So now:  do noëtic events (the “supranatural”) likewise cohere into some larger system?  (We don’t strictly know, and intuitions have broken both ways:  the existentialists glumly nursing their absinthe, and Christians ecstatically tasting of the Communion wine.)  And if so, does this system in any respect resemble what previous thinkers and theologians have imagined?  Nescio; but I’ll say this:  If it does, it does so (I imagine) by grace and revelation, not by any logical necessity  arguing simply from the world as we find it.  I’m pretty certain (in the practical sense that I have laid a wager with Providence, and am on the line for standing a round of beers, win or lose) that it does cohere;  but I am not so certain, not so certain at all, that the coherence has a description  even in principle comprehensible to ourselves – beyond some almost infantile inkling, like that of a baby, still unseeing, scenting the milk of the breast.

            This negative possibility  --  apophatic theology, the “via negativa” -- is familiar from theologians – Jewish, Christian, NeoPlatonist, and Muslim alike  -- holding the view that God is beyond all predicates – neither hot is He, nor cold, neither long nor short, bearded nor beardless …
-- Bohr's "complementarity" is a sort of dual to this:  Both wave and particle are they; both causal (psi-functions) and acausal (classical-positivistic, as chastened by quantum mechanics).

~

Sidenote on the “via negativa”:

Besonders characteristisch für die “negative Theologie” der spekulativen Mystik  is die Unzahl der Bildungen mit Vorsilben, die den Inhalt des Grundverbums  ins Gegenteil verkehren … entsinken, entwerden …

-- Fritz Tschirch, Geschichte der deutschen Sprache (1969, 2^nd edn. 1975), vol. II, p. 83

[more here]