Pugnaciously vacuous definitions

At the beginning of his preface to the introductory exposition Philosophy of Logic (1970),  W.V.O. Quine quotes Tweedledee:

“Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t.  That’s logic.”

That was a bit of nineteenth century donnish waggery (though it does give rather the flavor of modal logics and possible-world semantics  in our own day).

Quine then drolly goes on:

If pressed to supplement Tweedledee’s ostensive definition of logic  with a discursive definition of the same subject, I would say that logic is the systematic study of the logical truths.

We pause for Homeric laughter.

Anyone schooled in the lore of Russell’s paradox and impredicative definitions, will recognize that the professor is having his fun.

He then has some more:

Pressed further, I would say that a sentence is logically true  if all sentences with its grammatical structure are true.  Pressed further still, I would say to read this book.

(Ah!  ‘Tis a plaint  we ourselves have often made:  Buy my books!)

[Note:  Contrast the  equally terse but quite unselfreferential definition of logic in

R. Goldblatt, Topoi , 2^nd edn. 1984:  “the study of the canons of deductive reasoning”.  Word for word, that’s very good.]

The jest is not without a subtle content, assuming as it tacitly does that there are such things as logical truths (a subject we see in a different light after Quine’s own extended attack on the analytic/synthetic distinction).   And it is quite in line with Quine’s celebrated existential bon mot:

    “To be is to be the value of a variable.”

To non-initiates, that will be mystifying;  to semi-initiates, cheeky; to familiar navigators of Quinespace, an ultra-compact allusion to his perennial concern with ontology in relation to quantification.

Put more pugnaciously:

Existence is -- what existential quantification expresses.

 -- W.V.O. Quine, “Existence and Quantification” 

[Further Quinefun  available here:
http://worldofdrjustice.blogspot.com/2015/01/quine-on-bunnies.html ]

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The celebrated Cambridge Philosopher of Bland, G. E. Moore, wrote in his Principia Ethica:

If I am asked, “What is good?”, my answer is:  Good is good;  and that is the end of the matter.

That is:  If you have to ask, I can’t tell you.  (Even so, that pseudo-definition is preferable to the nihilist/reductionist dismissal by the Eliminative Materialists.)

Indeed, I shall now venture a definition  quite in Moore’s spirit:

Truth is … what is true (and known to God as such), quite apart from human-knowability, let alone provability (whether by finitistic, intuitionistic, or classical means).

~

From a college textbook:

A measure space consists of a set X equipped with two fundamental objects:

(1) a σ-algebra M of “measurable” sets, which is a non-empty collection of subsets of X closed under complements and countable unions and intersections.

(2) A measure μ: M -> [0, ∞] with the following defining property …

-- Elias Stein & Rami Shakarchi, Real Analysis (2005), p. 263

The bolded terms are there defined; but the term measurable sets is not -- the clause that follows reminds us of the definition of a σ-algebra instead.  The authors acknowledge their sleight-of-hand (effectively remedied by material elsewhere in the book) by placing the offending word in quotation marks. -- Note that this typographic care exemplifies the semantic Akribie of math writers, which we have elsewhere praised.

Not all math authors are as onomastically aware as those.  As:

Old-fashioned text-books  tend to start off with mystifying definition of these terms:  Euclid’s own definition,  “A point is that which has no part”, is a good example.  After a perfunctory discussion of these, the author clears his throat, begins a new chapter, and gets going with some concrete examples:  the definitions are mercifully forgotten.

-- Stephen Toulmin, The Philosophy of Science (1953), p. 72

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To define -- literally, ‘delimit’ -- is by way of penning-in the definiendum with antecedently familiar landmarks.   To say that none such exist, is to refuse definition;  as in this classic hymn:

There is nothin' like a dame,
Nothin' -- in -  the -  world,
There is nothin' you can name
That is anything like a dame!

-- “South Pacific”

By this point  we have passed definitely from the realm of Oxbridge drollery to that of Joe on the Boat.  And here, indeed, we discover a whole subculture of definitional legerdemain, noticed in the delightful Dictionary of American Slang, by Wentworth & Flexner (1967).   In the Supplement we find this entry:

blivit   (n.)

   Anything unnecessary, confused, or annoying.  Lit. defined as “10 pounds of shit in a 5-pound bag.”  Orig. W.W. II Army use.  The word is seldom heard except when the speaker uses it in order to define it;  hence the word is actually a joke.

As a former harmless-drudge chez Merriam-Webster, I salute that as a gem of the lexicographic art.

A classic development of the pugnaciously uncooperative definition -- Lexicography with an Attitude -- is The Devil’s Dictionary, by Ambrose Bierce.  (Sample:  “fork: an instrument for putting pieces of dead animals into the mouth.”)  Similarly impish was Hobbes’ definition of paradox:  “an opinion not yet generally received”.

A Pugnaciously Vacuous definition of the meaning of life  can be viewed here:

http://worldofdrjustice.blogspot.com/2012/03/ask-dr-science.html

~

Quite other than such conscious humor, are cases like this:

Hamilton follows the Kantian notion of time closely in his “Essay on Algebra as the Science of Pure Time”.  Since the inner sense of time is more general than the outer sense of space, Hamilton concludes that algebra is a more general and fundamental branch of mathematics than geometry.

-- Thomas Hankins, Sir William Rowan Hamilton (1980), p. 268

As the discoverer of quaternions, Hamilton has as much right as anyone to deliver himself of after-dinner remarks (a genre of public speaking to which he was particularly devoted) about the nature of algebra;  but this one is horse-hockey.

 

(Psychohistorical note:  Hamilton was for a time utterly immersed in Kant;  this characterization of algebra as the “Science of Pure Time” stems from psycho-philosophical exuberance, rather than algebraical expertise. 

A curious tentative parallel might be made with Hamilton’s countryman G.K. Chesteron, who likewise was given to flights of literary exuberance;  both were in marital situations requiring a great deal of self-sacrifice,  which they met with infinite patience;  and both were given to a kind of idealism  which some might diagnose as compensatory.

Okay, beyond our pay-grade.  Yet as Silvan Schweber affirms in his perceptive review [Isis, 1982] of this exemplary socioscientific biography:  “Hankins has eschewed giving psychoanalytical interpretations, [but] to anyone interested in the psychodynamics of creativity, William Rowan Hamilton presents a fascinating case study.”)

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Another subcategory -- already bordered on by Hamilton’s epigram for the definition of algebra -- is formed by definitions which, while not vacuous, we might label Pugnaciously Perverse.   The poet Coleridge was (unfortunately) Hamilton’s philosophical mentor, even as regards what Science ought to be; and he defined that subject  thus:

“any chain of truths which are either absolutely certain, or necessarily true for the human mind, from the laws and constitution of the mind itself.  In neither case is our conviction derived, or capable of receiving any addition, from outward experience, or empirical data.”

-- Thomas Hankins, Sir William Rowan Hamilton (1980), p. 268

(That first sentence does oddly prefigure the sort of prose  churned out by the truckload by the epigones of Donald Davidson.  -- Note too the anticipation of Post-Modernism.)

~

Another non-cooperative move in the orismological game, is pooh-poohing the very definiendum -- denying that there is anything coherent to define.  One Christian writer (C.S. Lewis or Hilaire Belloc, I forget which) once said testily, that the notion of “the Renaissance” was a will-o’-the-wisp, used  by secular writers to mean “whatever I like that happened in the fifteenth and sixteenth centuries.”

~

Composing a truly vacuous definition  is harder than you’d think.

Thus, consider the Euclidean definition of a point (“that which has no part”) which our philosopher friend scoffed at;  and let us phrase it even more egregiously:

point:  a point-like figure

That actually has cognitive content.  It means:  To visualize what is meant when geometers refer to a punctum (as opposed to a linea, etc.), think of something like a pencil-point.  Do not think of something like a dance-floor, or the cosmos, or an elephant.

And:

set:  a set of elements

Here the definition is so far from vacuous that someone could reasonably object that it is actually false, since it excludes the null-set.   (In this ‘definition’, the stress, so to speak, is on “elements”; “set” could be replaced by “bunch” or “passle” or “bucketload”.)

For indeed:

There is no direct circularity  if we presuppose sets in our study of sets (or induction in our study of induction), since the first occurrence of the word is in the metalanguage, the second in the object language.

-- Michael Potter, Set Theory and its Philosophy (2004) , p. 9

In further defense of impredicativity:

Impredicative definitions are necessary for ordinary mathematics, as they are unproblematic if one adopts a realist attitude about the objects defined -- realist in just the sense that the objects exist in advance of the definitions, that they are picked out by the definitions, not created by them.  That imposes a substantial constraint on any acceptable philosophy of mathematics.

-- Shaughan Lavine, Understanding the Infinite (1994), p. 107

~

The grandfather of all tautological definitions is the one given by Yahweh in Exodus: 

~ ~ ~  I  Am   That  I  Am  ~ ~ ~

Yet at the same time, that is the best definition that could be given, since, in a common view of the Abrahamic religions, any limitative predication would be false.   (That view led in particular to the via negativa,  which insisted on the denial of all suggested predicates of the One.)

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Another style of coyness with definition  is illustrated in the following, immediately after the authors have introduced Maxwell’s Equations  for E and H in free space:

At first we do not attempt to give physical meaning to these symbols.  We merely say:  let us assume that there exist physical quantities represented by symbols having the indicated properties, and see what these equations say about the quantities.  From the last two equations [to the effect that E and H -- whatever they might be -- have divergence zero], it is clear that E and H are solenoidal …

-- Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p. 303

After a few pages of discussion, the authors summarize:

In a very real sense, therefore, these equations may be said to constitute a definition of E and H.

-- Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p. 306

Thus, back where we began.  The dangled definition in intuitive terms, is ultimately withheld:   No dessert until you finish your broccoli;  then -- Your broccoli was your dessert.

They subsequently reinforce the apophatic stance:

Physical meaning of E and H:  … The only real importance of the quantities is involved in the fact that they satisfy the field equations. … It seems most logical to go the whole way and treat E and H as defined by the field equations in all cases.  The commoner definitions can then be looked upon as mere picturizations. -- Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p. 311

E & H:  They Are That They Are.

~

Lakatos offers his translation of an epigram from Poincaré:

    Mathematics is the art of giving the same name to different things.

Now, that is not vacuous (i.e., vacuously true, or anyhow only infinitessimally informative), since it is egregiously false;  but it is a witticism, not a blooper, since we all know that Poincaré was perhaps the leading mathematician of his time -- he has some cards up his sleeve, which he will slip out when it suits him.

For a series of essays on the art of definition, with especial reference to math,
try these:
http://worldofdrjustice.blogspot.com/search/label/definition

Debunking the Matrix (further exfoliated)

Some it-from-bit proponents  stretch this logic still further.  They look on the universe as a giant computer simulation.  Among those who have taken this view  are Ed Fredkin and Stephen Wolfram, both of whom hypothesize that the universe is a “cellular automaton” … Perhaps the most radical cosmos-as-computer advocate is the American physicist Frank Tipler … It involves no actual computer:  his cosmos is all software, no hardware.

-- Jim Holt, Why does the World Exist? (2012), p. 190

This Sunday morning’s New York Times   brings an unexpected double-scoop of intellectual fare (a reminder of why I still subscribe,  despite the spreading stain of the Narcisso-Traffickers  that started in the “Style” section and has infected almost everything else):  not one, but two  lucid reviews  of recent philosophy-porn   masquerading as physics porn (indeed, it is only that beelzebubian visage behind the cosmographical mask, that merits the attention of the non-physicist), by that excellent defender of clear thought, Dr. Edward Frenkel, whom we have previously had occasion to praise.  To have two reviews, by a single reviewer on a single day, is unusual;  one is in the Book section, one in the Week-in-Review.

The first piece, “Is the Universe a Simulation”, is less a review  than a reverie, using a classic old novel of Bulgakov as a (fairly random) launch-point.  Along the way, he restates the thesis that philosophically-minded mathematicians largely embrace, that of Platonism:   Were the Lord to launch another universe somewhen, it might not evolve dinosaurs or Twitter, but Fermat’s Last (or, Wiles’ first) Theorem  will still be true.   Properly mulled-over, a lot may follow from this;  consult our series of essays on the implications of mathematical Realism, begun here:  

            Theologia Mathematica

Frenkel then manfully addresses  the extremely tiresome thesis, that the whole cosmos might be a hoax -- just one gigantic computer-simulation by some pimpled hacker living off in his mother’s basement somewhere beyond Neptune, or whatever-the-hell.   Similar ideas were discussed as far back as Plato (“Plato’s Cave”);   the “Matrix” scenario of current popular mythology  is simply a digital update, without really adding depth or plausibility to what is essentially a theological (specifically:  diabolical) idea.    Abandoning the caution of Plato, for whom the notion was just an allegory, “the Oxford philosopher Nick Bostrum” (Frenkel reports) “has argued that we are more likely to be in such a simulation than not."    (My own hunch:  Bostrum himself is nothing but a fragment of malware, invented to provide a much-needed rhyme for "nostrum"; but the rest of us are real.)

Frenkel then brings something new to the table by bringing our attention to a recent paper, “Constraints on the Universe as a Numerical Simulation”, written by a couple of physicists.   These authors, after some introductory mumbo-jumbo, making a logic-free leap from their own experience fiddling around with our primitive Earth-computers (not even a quantum computer;  more like a Model T), put forward that, if this cosmos really is nothing but a simulation, on some extra-cosmic calculational entity  (which,  in all likelihood,  would bear no resemblance whatever, either in hardware or software, to their idea of a computer -- as, in that hypothesized world, there is no reason to posit a mirrored existence of figments of the simulation -- no silicon, no electrons -- and the entity itself need not be digital, since there exist other types of computation) then such & such anomalies would no doubt appear (the exact nature of these being extracted directly from the podex), and that, training our telescopes aloft, these might detected in, umm,  cosmic rays.    (We pause to give the reader time to gasp at the iridescence of this idea.)  For the ancient Chinese, doubtless a similar insight:  ultimate Reality might resemble a giant abacus.

Note 1 :  This notion, that some tiny anomaly, some ‘wrinkle-in-time’ sort of thing, could tip us off to the amazing fact  that the whole of history, mind, and reality  is all just one big fake, is apparently not new.  Russell Standish (Theory of Nothing, p. 83) cites David Deutsch, John Barrow, and Daniel Dennett  as having each put forward some variation on the basic idea.   Novelistically, the fancy is perhaps congenial, to any who enjoy Sherlock Holmes, who figures out the whole mystery on the basis of some anomaly in a bit of cigar-ash.   But given that the cosmos (of which we glimpse barely a smidgen) is one big patchwork of mysteries and anomalies, a few of which are more or less described (in ever-changing terms) by this or that discipline of science,  one should not expect any such gotcha.   (How about the sudden arrival on our consciousness of “dark” energy and matter, outweighing the homegrown kind several times over?  Is that a roundoff-error?  A software glitch?)

Note 2 :  If leprechauns exist, these too might be somehow reflected in the Microwave Background Radiation.  

[Update 27 February 2014]  The keen-sighted philosopher-linguist Roger Lass  suggests a much simpler experiment that should settle this question  once and for all:

If we had spectacles of the right shade of green, we could see leprechauns.

-- Roger Lass, On explaining language change (1980), p. 86

 

Meta-note:  For those mesmerized by any invocation of the MBR, cf. Steven Weinberg’s account of going back to the original measurements behind Hubble’s announcement of the redshift law:  Weinberg could scarcely perceive any pattern in the data, and reckoned this another instance (as with Galileo) of an intuitive perception of what must be true, being tricked-out as an experimental result.

*     *     *

~ Commercial break ~

For a mini-movie of our own, try this:

The Penitent and the Impenitent Thief

We now return you to your regularly scheduled essay.

*     *     *

Frenkel then closes on a wholesome note, once again evoking the possibility of a timeless Platonic realm for the truths of mathematics.    Actually I fail to detect any nexus between that idea and the It’s-all-an-illusion trope, other than that both were first propounded by Plato.

~

Conceivably  what put Frenkel in mind of the (logically unrelated) Platonic-math idea in the context of the World-as-Maya meme, is cross-flavoring from the other item he reviewed today,  Our Mathematical Universe, by Max Tegmark.  Here he sinks his teeth into something more substantial than that brain-afflatus by the Oxford philosopher:  a recent, full-length (and lengthy) book, from a respected traditional publisher, written by a tenured professor at one of the leading universities of the exact sciences, M.I.T.    And the formidable mathematician Edward Frenkel does the reading public a great service, by suggesting (though he puts it nicely) that the speculative portion of the book is hogwash.

The keynote for this graceful review, the concetto (‘conceit’ in the Elizabethan sense) that provides the satiric theme, takes off from an incautious admission from Tegmark, who (giving hostages to Fortune) describes his two selves -- the mainstream physicist versus the Wild Ideas Guy -- as Dr. Jekyll and Mr. Hyde.  The former wrote the pretty much run-of-the-mill sounding survey of modern physics for the Tired Business Man (a much-practiced and apparently profitable genre);  the latter pushes the farrr-out (though possibly vacuous or untestable) theses,

(1)  That all the world is not, as you might have thought, a stage, or a panorama, whereon the romance and tragedy of our lives plays out, but (basically) one great big scrawl on some (humanly meaningless) mathematical blackboard; 

and

(2)  That our own universe is just one feuillet in a great flaky pastry of parallel worlds.  (The universe, not as blanc-mange, as with the monists, but as baclava.)

[Note:  I am paraphrasing.  Tegmark himself puts the matter less colorfully.]

These two ungainly theses  are not, I suspect, actually logically related, pace their perpetrator.   Tegmark suggests that (1) implies (2), in that, as the reviewer summarizes, “he believes that any mathematical structure  spawns its own universe, and that all of these universes exist in parallel and on an equal footing.”   Actually (2) has been championed on two other, quite different grounds, neither purely  mathematical:  on the ground of physics (the Landscape idea), or of biology (the cosmology-cum-Darwinism of Lee Smolin).
(You could also argue that (2) is implied by, or at least in the spirit of, the ancient and later medieval Principle of Plenitude.)

The Jekyll/Hyde bifurcation  can actually be detected in the very title of the book under review, which reads in full:

OUR MATHEMATICAL UNIVERSE

My Quest for the Ultimate Nature of Reality

The principal title is unexceptionable:  the universe can certainly be described as “mathematical”, and has been so, with respectable success, at great length.   There are other adjectives one could likewise apply to the thing, but “mathematical” is by now a no-brainer.   The enterprise has indeed been successful in unanticipated ways and to a degree that surprises its own practitioners:  the theme of the “Unreasonable Effectiveness of Mathematics”.

[Note:  That is indeed a phenomenon worth pondering.  But to conclude from the way that mathematics keeps saving the bacon of physicists, to the exclusively ‘mathematical’ character of the universe, is no more convincing than the traditional philosophical epigram, to the effect that the reason our minds can comprehend the universe (well, some of it, somewhat) is because The Universe Itself Is Mind-Like.

Actually more sophisticated than either of these monicities, is the following dual view, put forward by the great early-nineteenth-century mathematician and physicist,  Hamilton (of quaternions and Hamiltonian fame):

There are, or may be imagined, two dynamical sciences:  one subjective, a priori, metaphysical, deducible from meditation on our ideas of Power, Space, Time;  the other objective, a posteriori, physical, discoverable by observation and generalization of facts or phenomena:  that these two sciences are distinct in kind, but intimately and wonderfully connected, in consequence of the ultimate union of the subjective and objective in God.

(quoted in Thomas Hankins, Sir William Rowan Hamilton (1980), p. 175  ]

The subtitle, by contrast, is pure Philosophy Porn, of a sort typically peddled by physicists.   (For a classic polemic from a couple of generations ago, see Susan Stebbing’s Philosophy and the Physicists (1937).)  You should be wary of any book purporting to be hard science (as opposed to the memoirs or musings of a hard-scientist) which contains in its title any of the following words:

My

Quest

Ultimate

Nature-of-Reality

Tegmark’s subtitle manages to pack all of these into a single confined space (rather like quarks).

~

Anyhow, in a nutshell, Tegmark’s gambit is to resolve the puzzle of the Unreasonable Effectiveness of Mathematics  by a kind of homeopathic-medical reason:  you see, math fits the cosmic body (cures the disease) because, in its questy “ultimate nature”, it is the cosmic body, or rather vice versa, if you please.  Any sophomore passing around the joint at a late-night bull-session, would be stunned by such an insight.   For us, it’s more like a koan or a tautology (well and good).  But he wields this trope/tautology  to arrive at something  in some ways  equally tautological (namely, as far as it goes, which isn’t far), though its spiritual implications (if taken too seriously) are odious:  Namely, that a person is (nothing but) “a pattern in space-time”.

(Recently I struggled through an initially catchy but ultimate dreary book with a similar message, by a semi-Tegmarkian, Russell Standish, called the Theory of Nothing.  More anon.)

No doubt aware of the danger that his scheme threatened to dissolve into vapidity, Tegmark attempts to restore it to the coveted status of an Empirical Hypothesis (we have learned, with Chomsky, to become very reverent when we hear this phrase).  Frenkel quotes him: “One of the key testable predictions of the Mathematical Universe Hypothesis  is that physics research will uncover further mathematical regularities in nature.”   With this ludicrous lapalissade, Tegmark becomes the Thomas Friedman of Mathematical Physics.   Frenkel remarks, more gently, though with satirical quotation-marks,  and with what, for anyone conversant with the philosophy of science, has bite:

This “prediction” is as far from the scientific method  as the purported universes are from one another.

~

Tegmark’s scheme amounts to a kind of Eliminative Immaterialism, quite different in ethos from the Materialist variety found among those influenced by the more nihilistic currents of neuroscience (and against which we have polemicized here), but compassing the same end  of removing, from our view of life, everything that makes it worth living.   Professor Frenkel is a gentlemanly writer, but does permit himself this much by way of sarcastic retort:

    What accounts for consciousness, for example?  “I think that consciousness is the way information feels when being processed in certain complex ways,” Tegmark says.

     I tried to process this information, but didn’t feel much.

Why -- by what uncanny coincidence -- do the curviculous abstrudelings of the Eliminativist mind or mouth (or other orifice), of whichever (im)materialist stripe -- so resemble a spiraling pile of sirreverence?  Perhaps because, in their innermost reality, they are a pile of sirreverence.

~

Frenkel may be  in a sense  overqualified for grappling with the mathematical niceties of Tegmark’s thesis (1), taking them more seriously than they deserve.   He scores a point against the scheme  in a brief passage that will probably whiz by most readers,  implicitly alluding to the foundational debate of recent decades, concerning the role of set theory versus category theory versus topos theory et alia, and concludes that Tegmark fails the “What is Mathematics?” test, concluding

Mathematical structures constitute but a small island of modern mathematics.  Why would someone who believes that math is at the core of reality  try to reduce all of reality to just this island?

I doubt  however  that this observation  strikes more than a glancing blow at the ontological heart of Tegmark’s argument.  Tegmark probably doesn’t want to reduce the cosmos specifically to set theory or fibre-bundles or anything else, but rather to water the thesis to such vagueness that it stands immune from refutation.

Compare J. M. Keynes’ Treatise on Probability (1921), with its dismissal of certain mathematical window-dressing which loses the reader in the details, all the while resting on epistemological fallacies.  

Indeed, for the possible mathematical “handwaving” of Tegmark,  cf. the computational sleight-of-hand in the scholarly paper Frenkel treats of in his other review, that of “Constraints on … Simulation”.  (Again, I have abbreviated the title  in line with the Chomskyan linguistic aesthetic.)  I have made fun of the Hype Around the Higgs, but really that quest is quite well defined (though it has run into experimental difficulties) compared with the suggested search for (unspecified) anomalies in the running of the Entity wherein we are a simulation  on the assumption that they will be analogous to the quirks of their own no doubt buggy software.   Since the nature of the hypothesized computational device which is running the universe as a sort of screen-saver  is utterly unknown (to begin with, it needn’t be digital), that cannot constitute a serious hypothesis in terms of computer science.   And the suggestion that we might trot off and try to salt the tail of a cosmic ray so as to settle a fundamental ontological and theological question, was probably made in jest.   One imagines the scenario:   “Look!  That proton just zagged when it should have zigged -- ergo everything is just one big illusion and  life is meaningless! “  (Such a sally might serve our cocky sophomore to lure a co-ed temporarily into his bed, but would not attract the kind of woman one needs to marry.)

~

Historical Footnote:

This computer-simulation/Matrix meme  is just the latest, technology-inspired variation on a very old topos (using that term now in its literary  rather than the mathematical sense):  that Things Are Not As They Seem.   But note that the latter overarching idea, comes in two radically different flavors.

The one is that the universe as we experience it  in reality makes less sense than it seems (in any morally or humanly recognizable terms);  the other, that it makes more.    The former is  found among pagans and atheists; the latter begins with Plato, and culminates in Christianity.

Among polytheists, there is the notion of Maya -- an all-encompassing "illusion (or more accurately a "delusion")”, as Wiki puts it -- for Hindus.   The pagan Greeks held that there was another order of reality behind the one we can see, peopled by gods and sylphs and whatnot, but so far from giving meaning to our lives here below, Olympian society (and that of the satyrs and what have you) was no improvement on our mortals petty folly here-below;  almost the contrary.   In King Lear’s formulation:  

            “As flies to wanton boys are we to th' gods.

            They kill us for their sport.”

Utterly otherwise is the Christian picture.    Here too, things are not as they seem; but with this difference:  the deeper meaning is not (if anything) worse, as among animists, for whom ill-intentioned demons  lurk behind every mutter;   nor is it alien in kind to what happens here, as in the bleakest views of the atheistic mechanists,  for whom there is nothing but l’homme machine,  or of contemporary reductionists, who intuit nothing but Hermitian operators with no agenda beyond themselves.   Rather, it supplements ourselves, rounds us out, without abolishing us.  (In Hegelian terms, we are thus aufgehoben -- sublated -- in the fuller reality.)   True, for Plato in his famous cave, we are but shadows -- but, crucially, shadows cast by something, something real and round -- rounder and realer than our temporary shadow selves, as an object is  to the shadows cast.   For behind that trio of ill-laid crooked sticks, there thrones an abstract Triangle in the Platonic realm (where, whatever the varying lengths of its legs, the sum of its internal angles  in radians  is eternally, or rather extratemporally, pi;  behind and above this loaf’s cost in drachmae, the fullness of the Natural Numbers  in their calm infinitude;   and behind and beyond and above ourselves ….  Ah, we must wait for Christianity to get a glimpse of that!

And here I mean not merely the vision of the simple, who imagine that one day the curtain will rise,  and from there on  nothing but lollipops and sugar-plums (though even that vision is preferable to the leaden landscape of Hades or of Sheol).   Nay rather, even for the best and most skeptical among us -- “a sense that life has a plot” (Frederick Buechner, The Sacred Journey ,1982), or C.S. Lewis’s metaphor of reality as of kind of intricate Persian carpet,  which now we see only from the underside (a tangle of thread-ends, only hinting at the greater order verso):  whereas then, we shall see the pattern plain.

~

The general idea (2)  has three interrelated variants:  the Landscape;  the Multiverse; and the Many-worlds view of metaphysics.  This last is an offspring of Bohmian quantum-mechanics out of modal logic, and is favored today by many philosophers.

As for the Landscape, its status as a sheer dead-end to explanatory physics, has been well pointed out by physicists, and we need not add to that.   But this complexus of ideas yields moral implications as well, whose effects, again, are largely deleterious.  Back to Standish:

The appeal of euthanasia is to end suffering.  But how could it do that if the suffering person has first-person immortality?  The euthanased person may no longer be in your world, in your life, but would nevertheless be experiencing continued suffering in another universe, if not greater suffering  beause of your actions.  This  for me  is a powerful argument against euthanasia.

-- Russell Standish, Theory of Nothing (2006; 2^nd edn. 2011), p. 150

Actually it is an argument -- not powerful, but sophomoric to the point of imbecility -- against doing anything at all, ever.  Why pay this parking-ticket, or return this library book, when in another universe  ‘twill remain unpaid, unreturned?

Through equally twisted reasoning, he pretends to arrive, not at nihilism, but -- well, who knows, it is intended as an olive branch:

Quantum immortality is thus a very good incentive to behave altruistically, a grounding for the golden rule of Christianity.

-- Russell Standish, Theory of Nothing (2006; 2^nd edn. 2011), p. 150

The “golden rule” is not specifically Christian, but no matter:   No thanks;  you can keep your olive branch.  It does not even rise to the level of a poisoned chalice:  more like a stale Twinkie.

~

The theses that our cosmos is either (1)  just a sort of computer-game, or (2) just a randomly-constituted sliver in a randomized stack of non-communicating random slivers,   are two of the most noxious ideas of our time, and Edward Frenkel has done a service by cocking an informed and skeptical eyebrow at both of them.   But there is a third burning issue of our day, that of the Zombie Apocalypse, which he has left unaddressed.  For that, we must turn to Professor Noam Chomsky.

Chomsky on the Zombie Apocalypse

(Note that that is a monostich, all by itself.)

[Update May 2016]  While performing routine janitorial services on this blog, I discovered that this crucial contribution by the renowned Professor Chomsky, has been suppressed from the Internet!

As of even date, what you get, when you click, is this:

http://www.dailykos.com/story/2014/02/16/1278055/-Noam-Chomsky-Breaks-Down-the-Zombie-Apocalypse?detail=hide

This story has been removed.

This story has been unpublished and you do not have permission to view it.

At least they admit it!   In the future, you’ll see nothing, or else clicking the link will introduce a virus, to your hard disk  or your brain.

For connoisseurs, this whole shifty business  bears the unmistakeable digital fingerprints of …

            The Riemann Conspiracy !!

This is not a glimpse of hidden Reality.  Rather, it is a *simulation* of such a glimpse, whose Being is restricted to the silver screen.

~

Weiteres zum Thema:

For more on the limits of simulation, try this:

            In vitro/ In vivo

 For more on Maya, the multiverse, and the Landscape, this:

            “Why is there Something rather than Nothing, Grandpa?”

The topic of “narcisso-trafficking” is largely foreign to this post, referring not to anything discussed here, but to the infected areas surrounding the remaining atolls of the main NYT news section and the (partly corrupted) Book Review.   However, readers have enjoyed the coinage, so here is a link to some essays on the subject.

~

Noch Weiteres zum Thema:

Just a musing note on the possible nature of the hypothetical Entity with which the ‘simulation’ (i.e., the actual universe -- the real world) takes place.   The more you strip away unwarranted hidden assumptions about what the thing might be like (Sequential? -- Not necessarily;  Digital? -- Not necessarily;  Silicon-based? -- Not necessarily;  Physically embodied at all? -- Not necessarily;  etc.) the more we are left with a recedingly distant conjectural Whatnot, of unknown character, and of baffling vastness, which, for humility and simpliticy, we might as well call (to coin a phrase) “the Mind of God.”   And a Christian will have no special objection to that metaphorical depiction -- though with one proviso:  that the puppets or rather “avatars” in this all-encompassing Simulation (if you enjoy that rather insipid metaphor) are divinely/’cybernetically’ provided with Free Will.    That is the redoubt which the eliminativists and mechanists are ever intent to storm, and that is what the Historical Church would defend, if need be  by the sword.

~

For an alternate take on it all, try this:
http://murphybros.blogspot.com/2010/12/murphys-theory-of-cosmology.html

~

~  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 James Monroe, by jingo, and I approved this message.)

~         ~

~

[Update 17 May 2014]  An op-ed this morning, by the excellent columnist Joel Achenbach, refines the point:

It was the science story of the year: Astrophysicists held a news conference at Harvard on March 17 announcing that their South Pole telescope had found evidence of gravity waves from the dawn of time.

Cosmology doesn’t get any bigger than this. The discovery was hailed as confirmation of a mind-boggling addendum to the big-bang theory, something called “cosmic inflation” that describes the universe beginning not in a stately expansion but with a brief, exponentially rapid, inflationary spasm.

Science is a demanding and unforgiving business, and great discoveries are greeted not with parades and champagne but rather with questions, doubts and demands for more data. So it is that, in recent days, scientists in the astrophysics community have been vocalizing their concern that the South Pole experiment, known as BICEP2, may have detected only the signature of dust in our own galaxy.

These doubters say, in effect, that rather than seeing the aftershock of the birth of the universe the scientists may have seen only some schmutz in the foreground, as if they needed to clean their eyeglasses.

http://www.washingtonpost.com/national/health-science/big-bang-backlash-bicep2-discovery-of-gravity-waves-questioned-by-cosmologists/2014/05/16/e575b2fc-db07-11e3-bda1-9b46b2066796_story.html

A claim of having proved Inflation, only to meet (it may be) the most humiliating possible Deflation.

Achenbach relevantly quotes Sagan: “extraordinary claims demand extraordinary evidence”.   And yet more:  Cosmology does get any bigger than that, when it pretends to have settled fundamental philosophical/theological/existential questions (which “tensor B-modes”, however tasty to the cognoscenti, are not, being purely physics-internal).  A fortiori, claims to have motivated, or even proved, the (I repeat: diabolical) thesis that all the world is worse than dirt on the lens -- good honest dirt, after all, at least is of the earth -- that it is a mere Simulation -- a farce, kluged-up  not even by an (in)decent Devil, but merely some pimpled Programmer -- all morality, all emotion, all human values  of less moment than the bumf with which said Programmer wipes his arse -- such a philosophical program requires rather more than a conjecture that some … future experiment might detect a wanton ripple in this or that, which should occasion the conjecture's proponents to exclaim, “That’s it!”, and to toast the event with some warm champagne, left over from some previous pseudo-sighting of the Higgs boson.

Read the full article, which is of great sociological interest  beyond its relevance for physics.  And some of the readers’ comments as well;  as:

The usual argument for inflation is that scalar perturbations cannot produce B-modes in the polarization of the cosmic microwave background radiation (CMB), and that the only possibility to generate them is through tensor perturbations (gravitational waves). Vector perturbations (local rotational modes) are not really considered. 

But if a local privileged space direction exists due to space-time geometry, local rotation around this direction can be present in the early Universe and generate CMB B-modes.

For a more upbeat presentation of the BICEP2 results:

“This is a totally new, independent piece of cosmological evidence that the inflationary picture fits together,” says theoretical physicist Alan Guth of the Massachusetts Institute of Technology (MIT) in Cambridge, who proposed the idea of inflation in 1980. He adds that the study is “definitely” worthy of a Nobel prize.

http://www.nature.com/news/telescope-captures-view-of-gravitational-waves-1.14876

[Update 19 June 2014]

Now, after weeks of wrangling, discussion and debate with peer reviewers and other astrophysicists, the group, which goes by the name Bicep, has published its paper in the journal Physical Review Letters. The authors, led by John Kovac of the Harvard-Smithsonian Center for Astrophysics, write that they stand by their discovery — but they also now acknowledge that it is possible that interstellar dust might have produced much or even all of their signal.

“The basic takeaway has not changed; we have high confidence in our results,” Dr. Kovac said in a phone call.

http://www.nytimes.com/2014/06/20/science/space/scientists-debate-gravity-wave-detection-claim.html?hp&action=click&pgtype=Homepage&version=HpSum&module=second-column-region&region=top-news&WT.nav=top-news

To acknowledge that mere dust, rather than gravity waves, “might have produced … all of their signal” [emphasis added], yet to maintain that the takeaway has not changed, is paradoxical on the face of it.  On croit rêver.