Minimalism vs. Nihilism

I’m currently reading an intermittently entertaining book by Jim Holt, with the simultaneously catchy and off-putting title  Why Does the World Exist?   (2012).    I actually gave my mother a copy for Christmas when it came out:  not having yet read it myself, but counting on that ever-companionable writer to make big ideas plain to the public, the notion being that she would read it, and then we would discuss it in our weekly phone-calls (we live on opposite seaboards:  she in a nursing-home on the west coast,  I in a sheltered workshop on the east).   Unfortunately, Alzheimer’s intervened, and we can no longer discuss anything substantive;  her days of wine and metaphysics are behind her.  Though, now, as I finally get around to reading it myself, it would seem that, in this particular case, she hasn’t missed much.  The problem is, his clear-headed addressal of that perennial topic of sophomore seminars -- Why is there Something, rather than Nothing? --  would have made an excellent laconic magazine-article, but Holt somehow wound up with a book contract for this ultimately (indeed, quickly) sterile subject, and has to pad things out.  So he takes various nugatory arguments by e.g. “metaphysical nihilists” more seriously than they warrant, and duly deflates them, but takes several pages doing so.

(Mr. Holt’s genteel approach to such gentlemen  is to humor them -- though, to his credit, ultimately to refute them.  Ours is rather to rip their throats out;  cf.  our diatribe contra Eliminative Materialism.)

The exercise calls to mind James Surowiecki’s canny column in this week’s New Yorker, “Punditonomics”, where he notes the (obvious) economic incentive to spew out short-shelflife twaddle if all you want is eyeballs.   A lot of that has been evoked by the disappearance of Malaysia Air Flight 370 (I actually work a few feet away from some Bureau integrees who are involved with that case, and poll them every so often.  BLUF:  UFOs are not involved.)   As Surowiecki reports,

The peak (or nadir) of the speculative frenzy  came when CNN anchor Don Lemon wondered aloud whether the plane might have been swallowed up by a mini black hole.

(Ceci renoue avec notre thème du néant.)  When a retired general who now shills as a CNN commentator, failed to cough out an equally (yet distinct!) OTT hypothesis, suggesting we wait and look at the facts,  the Host replied, revealingly,

“You know how cable news works, don’t you?  We got time to fill here!”

And thus, likewise, Mr Holt has some pages to fill, that were better left (in the spirit of Nothingness) elegantly blank.

On pp. 59-62, Holt gamely attempts a riff on nothingness as, “as Leibniz was the first to point out, the simplest of all possible realities,”  adding solicitiously, in case the reader has instinctually at this point  razzed in disgust, “Simplicity is greatly prized in science.”  (So, pipe down, you-all in the back row.)  In mathematics, by contrast, the technical term for this (the null group, or anything else) is:  trivial.

In the course of this, though, he does raise a somewhat interesting question:  “If our world turns out to have an infinite census of objects, why should it be, say, aleph-2 rather than aleph-29?  Only the Null World escapes this kind of arbitrariness.”  (The same observation applies to a finite ontology as well, of course.)  And the answer to that, we would suggest, as we have argued in a series of essays (Theologia Mathematica), is to take the invisible world seriously, quite on a par (as Gödel argued) with the visible (and  arguably  moreso).  Such infinities as exist, exist, and those that don’t, don’t, and there you have it.  (Of course, should there turn out to be some unexpected supremum like aleph-29, we will look for a principled understanding of that surprising fact.)   This line of thought has been applied more seriously to the problem of the cardinality of the continuum:  aleph-1 seems the only non-arbitrary value.

~

So what do you do when the puns on Nothingness run out?   If you’re a good author, like Jim Holt, you don’t simply repeat yourself, or inflate a chapter like a bicycle-tire:  You take the show on the road.   And so we are treated to a travelogue of several European and American capitals, meeting various Colorful Characters along the way.   It’s like a thematic tour, only instead of the theme being Chocolate or Wines,  it’s Big Ideas;  and instead of Mansions of the Rich and Famous,  it’s Cramped Apartments of the Brainy and Loquacious.

And thus we are whisked to Pittsburgh, where we make the acquaintance of the legendary Adolf Grünbaum, a Morris-Zapp-like personality, still robustly vigorous in advanced age.   And in addition to various choice philosophical obiter dicta, we are regaled with a memorable tale of the nighttime drive to the restaurant atop Mount Washington, the voluble crusty atheist at the wheel.  (B.L.U.F. : Never drive with the guy.)

[Afternote:   I have just begun reading the Collected Works of Adolf Grünbaum, the first volume of which  came out in 2013.  Evidently the wily old philosopher was delighted by the rather Zorba-the-Greek portrait he gets in Jim Holt’s book, for the dust jacket quotes Why Does the World Exist to the effect that “In the philosophical world, Grünbaum is a man of immense stature.  He is arguably the greatest living philosopher of science.”  On page one of the Introduction, the editor goes on to quote Holt at greater length along those lines.]

“…Mmmyess… Immmmense, that is quite the word ….”

Then before you know it -- like James Bond hopping from metropolis to metropolis -- we are in Paris, this time without the excuse of any actual philosopher to interview, the slender connective being the Café de Flore, where Sartre used to squat, and doodle about le néant (Why is there quelque-chose rather than rien du tout?, that is to say).   We never get any philosophy here, but the author does offer a vivid tableau of the nightlife of fashionable Eurotrash:

At a table in the back  I spotted Karl Lagerfeld, with his characteristic ponytail, dark glasses, and high white collar, in hushed conversation with one of his muses, who was wearing what looked like black lipstick.  Other than that, the place was pretty much empty: le Néant.

But then there was a noisy burst of activity.  A woman of a certain age … breezed through the front door, accompanied by a pair of what appeared to be Cuban gigolos  dressed in shell suits.  Giggling and grinding their teeth, this trio sat down with us  and began to jabber away.  The woman’s face was a sallow mask of leathery jollity, and she talked in a low croak  that put me in mind of Jeanne Moreau. … It seemed a good time to leave.

(Should you ask:  Why are there gigolos, rather than nothing -- the question is unanswerable.)

[Update 10 May 2014]  Jim Holt takes on Derek Parfit; wins by forfeit:
http://worldofdrjustice.blogspot.com/2014/05/have-theory-will-travel.html

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