Eka-“Rubicon”

Apparently I never posted about the worthy but aborted TV IC series “Rubicon”.  But the new Showtime series “Homeland”, which piloted to rave reviews, has been compared to that effort.  It debuts tomorrow night;  just a heads-up.   I watched the pilot online;  it is quite good.

For background, here are some emails I sent to friends about the earlier series.

~~~~~~~~~~~~~~~~~~~~~~~~~

Here's an über-nerd response to the premier of "Rubicon" (about cryppies & über-IAs):

In the first shot, we see the central character -- a rumpled nerd -- come in to work and lay down the light reading he'd been doing at home.  The title is: "String Theory".

(A) At the most elementary level, for a general audience, this says:  "Theory, huh.  Guy's smart."
(B) At the next level, for those more clued-in, there is more of a shock:  the guy must be *really* smart.  For, string theory is notoriously the most mathematical part of physics -- the only Fields medal (math equivalent of the Nobel) ever awarded to a 'non-mathematician' was awarded to the physicist who powered string theory.
(C)  But at the next level -- the thing is ridiculous.  String theory, though hegemonic on campuses, has painted itself into a corner, and is provoking a reaction.  Notoriously, it has found *no* applications in the real world.  Hence, if you are an IA/cryppie nerd, you wouldn't go near it:  no-one but a virtually fulltime string-theorist understands string theory; as someone who (the show contends) must know everything about everything (including, crucially, Latin, in this episode) you certainly wouldn't waste your precious braincells on *that*.  (Contrast basic quantum mechanics, which has serious applications in quantum cryptography.)


There was an even more absurd moment when one of the supposed geniuses says, "Maybe it's a syllable-cipher" (re a set of...*four* objects).

BTW... despite the brainy sheen, judging by the tenor of the ads, the show is really aimed at audience (A).

~~~~~

Rubicon...
Okay, it's not exactly good, but I've got to watch something, and it just got a little bit better.
Bonus: The moderately intelligent show  elicits some quite intelligent commentary:

http://www.avclub.com/articles/the-truth-will-out,44856/

Also, Mystery-Science-Theater-style, commentary funnier than the show:

http://nymag.com/daily/entertainment/2010/09/rubicon_recap_whos_the_boss.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 J. v. Neumann, and I approved this message.)

~         ~

~

~~~~~~~~~~~~~~~

The Rise of Popcult

Not the spread, note: the rise -- in quality and aspirations.  As witness -- Rubicon.

Scene:  the mostly darkened offices of a key intelligence facility. It is late at night; alone, one dedicated analyst sits in a tiny office, monitoring a live feed  from half a world away.

Suddenly he startles -- leaps to his feat -- exits the room in alarm.  The viewers are confused:  Has he heard possible assassins breaking into the building?  It is unclear, as he gazelles up the stairways from floor to floor, shouting to see if anyone is there.   At last, from the back of a little library, a small voice pipes up.   It turns out that what our analyst desperately instantly needs is -- a linguist!  (Ever happen to you?)

“Do you speak Urdu?” he asks breathlessly. 
-- She looks at him quizzically.  “Doesn’t everyone?”  
-- Together they go to the little room.  Her mastery of Urdu is immensely attractive;  our analyst is smitten.

And in the course of their monitoring the feed (of a wedding in Pakistan), our analyst refers -- and of course the linguist understands -- to the “walima”.

Now, this is a standard Arabic word (maybe Urdu too), but not all that common;  I tried it flat-out on some colleagues and they were not sure.  It means ‘feast’ (here, a wedding feast).   And the writers of “Rubicon” felt they could casually toss such a word into the script.  (“Doesn’t everyone?”)

[Fn:  A horrible alternative is that, rather than this little-known word, the actor was butchering the pronunciation of a word common enough to have been borrowed into English:   ulema.  But this possibility we put far from our mind.]

~~~~~~~~

Sines of the Times

A note re the allusion to String Theory as a sort of fashion accessory in the TV show “Rubicon”, which pitches itself (and is publicised by others), as a brainy thriller for smart people (though it sadly falls short).

And now the current issue of The Economist features a fullpage fullcolor ad displaying a hip young fellow (who could almost be the Uberanalyst Will on AMC, with his ever-present messenger-bag) sporting (beneath a dark woollen sports coat)  a black T with the message:

            I  [icon] String theory

The roundish icon is in the syntactic place of the stylized heart that has come to represent the verb ‘love’ in slogans (sometimes retro-rendered as ‘heart’ in prose);  connoisseurs will recognize the illustration which appeared here and there in the more rarified press a while ago, being a simplified stab at depicting, or rather alluding to, the celebrated Lie group and polytope “E8”, a truly wiggy object found in (mathematical) nature, and which many string theorists identify as being found in physical nature as well, in that its Cartesian product with itself serves as -- well, I scarcely need to remind you all of this, but in the homely words of Wiki,

the gauge group of one of the two types of heterotic string and is one of two anomaly-free gauge groups that can be coupled to the N = 1 supergravity in 10 dimensions. E₈ is the U-duality group of supergravity on an eight-torus (in its split form).

But of course, you knew that.

So -- what is the ad for?  The TV show?   T-shirts?  Messenger bags?  Save-the-environment?  Ph.D. programs in geometrical physics?    --   None of the above.  But rather for a new sub-website run by the Financial Times  -- which, note, is not actually identified in the ad, save by its acronym FT (which for me has long connoted First Things, another serious publication, but not one for fashionable twentysomethings):

www.ft.com/smart

“Smart”.  Right.  Now, I’ve got no bone to pick with Smart, save as a slogan -- recalling “Bright”, the suggested euphemism for “Atheist”, aggressively pushed by the impossible Richard Dawkins.  And I was just about to pen one of my patented Cato-the-Elder O-tempora rants, when I thought -- wait.  Smart.  What if?  We could use some smart.  And, atremble with anticipation, I typed in the URL.

[…. time passes…]

And this is what you’ll find, on that "Smart" Site:

Exclusive this week:

Lucy Kellaway talks to Elle Macpherson  about bras and brands and being The Body.

O tempora, O garbage bag.

  

But the Baby Bear’s Porridge was Ju-u-ust Right…

Our Canadian Colleague comments, concerning a recent post (“Why is there Something rather than Nothing, Grandpa?”):

>> patterns not specifically tailored to the cerebral convolutions ... of ... the humble woodchuck.

>I think you are disagreeing here with most of the Christian theologians who have ever lived. Surely God created the universe just for us, so everything in it ought to make sense?

Now as it happens, I am at present reading a book that addresses this very issue -- but by a physicist, not a theologian (though he is a Christian):  Paul Davies, The Goldilocks Enigma:  Why Is the Universe  Just Right for Life? (2006).   The enigma in question refers to the program of the Anthropic Cosmological Principle.   This exists in various strengths, such as the Weak Anthropic Principle -- basically “We’re here because we’re here because we’re here because we’re here -- and if we weren’t, we wouldn’t be here to know it” -- and the Strong Anthropic Principle -- in short, that the universe was fine-tuned so as to bring forth -- Hi Mom! --  intelligent life -- with no doubt many variants in-between, such as the “Feeling off my feed but should soon be right as rain” Anthropic Principle.   Since book-length discussions of these are easily available, I won’t comment further.

*

The alert reader will have noticed, however, that so far I have sidestepped the challenge issuing from the hyperborean forests.

Before replying publically, I passed this note to my Spiritual Advisor, Dr. Massey:

Now in fact, I am unable to conceive that the universe was created "just for us" -- certainly not just for H. sapiens;  *possibly* for all rational species, of which there may be a great many.    This view is not heresy, I hope?

To my immense relief, he thus replied:

No heresy there. Certainly, we must, by revelation, hold that only humans are created in the Imago Dei (I'm here, btw, using the nominative of the technical term, but after the preposition "in" in Latin, it would have been "in imagine Dei". I had originally typed just that, but thought better of it.)
In fact, a fairly straightforward reading of Genesis 1 would conclude that God did not create the universe for Man, but rather out of sheer goodness. Man was given an important caretaker role over that creation, but it wasn't made *for* him. Further, scripture attests a speaking animal in Numbers 22.

This keeps happening:  By a process of mediation and reasoning, I arrive at a conclusion that seems potentially alarming, only to discover that it is a doctrine tolerated or even advocated by the Holy Mother Church.

Even better, the learnèd doctor goes on:

In fact, a rereading of the delightful passage in Numbers 22 reveals that animals are experiencing the supernatural world on a level we humans are not. Balaam's ass, to be sure, cannot speak until the LORD "opened his mouth." But Balaam is not able to see the Angel of the LORD until God "opened his eyes."

Surely, after having his eyes opened, we do not conclude that Balaam is not really seeing the Angel. In the same way, we are not permitted to conclude that it is not really the donkey speaking. (In answer to some commentaries that say that God was merely speaking through the dumb animal.)

The Angel further points out that he would have spared the donkey and killed Balaam if they had come any closer.

So animals are, according to scripture, walking around and quite normally and naturally seeing what is invisible to us. And what do they see? They see a world filled with the servants and angels of God all around.

I have often noticed this phenomenon myself, particularly among the ducks.

*

A viewpoint somewhat more congenial to the thesis fathered above upon Christian theologians, may be found in Islam.  Although the Qur’an is overall strongly theocentric, in the matter of Adam  it is more anthropocentric than is the Torah.  For in Sura 2:31-33 we learn that God taught Adam the names of things, then stumped the angels and had Adam himself instruct the angels in the names;  and in verse 34, God orders the angels, “Bow down to Adam”:  which they did, but Iblis (Satan) refused, and thus became a kafir (unbeliever).

As for whether the cosmos itself was specifically made for mankind, 2:29 says only “It is He Who hath created for you all things that are on earth.”  This says nothing about other galaxies, let alone the cosmos as a whole, let alone Riemannian manifolds and E8.

E8: a Riposte (concluded)

Let us examine a bit more closely  Synge’s picture of physics as bricolage,  where theories have the intellectual status of just-so stories, and are really little more than pragmatic techniques, or tools -- Newtonian mechanics and relativistic mechanics each useful in its own sphere, like screwdrivers and spoons, but of little interest in their own right.   Now, this is not to knock the status of a toolkit -- my respect for competent carpenters and electricians borders on reverence -- but fundamental physics is not like that.

            Synge presents the Newtonian view as having not been replaced or refuted by relativity;  it rules as before in its own realm.  Newton’s good for some things, Einstein for others, and Wiccan no doubt for others still.   But this view assumes a confusion.  For it is not the case that Newtonism and relativity are independently valid in their own way but incompatible;  rather, Newtonism is the limiting case of relativity, in a way very familiar in mathematics;  its continued use in everyday life is simply a calculational convenience, a shortcut.   To continue the tool metaphore:  Einstein and Newton are not like screwdriver and pliers, but like a hammer, and an old shoe used as a hammer, good enough for the task at hand.

            Furthermore, it is a good thing, not a bad thing, when initially separate paths converge.  If you only know one way to climb a thing,  perhaps it is only a Potemkin mountain -- a paper-maché façade, hollow behind the north slope.   It is quite a relief -- and an ontological ratification -- to meet another mountaineering party that has scaled up the other side.

            The reader may be familiar with the story of how Schrödinger and Heisenberg separately found Rome by different roads.  Let George Gamow tell it, in Thirty Years that Shook Physics (1966), p. 3:

The simultaneous appearance of Schrödinger’s and Heisenberg’s papers  in two different German magazines … astonished the world of theoretical physics.  These two papers looked as different as they could be, but led to exactly the same results concerning atomic structure and spectra.

We are, in hindsight, not overly surprised by this, since by now we most of us accept that there is something there at the quantum level, something real, something other than subjective, to be described.   It is describable by two quite different mathematical approaches, much as our peak may be scaled by walking up the north face  or rappelling up the southern cliffs.    Nor is such ‘duplication of effort’ a waste of time, for  in this instance, not only the factual success, but even the approaches themselves retained their usefulness -- for determining energy levels, Schrödinger’s wave mechanics was calculationally more convenient; and Heisenberg’s matrix methods had the edge when it came to calculated the intensities of the radiated frequencies.   Or, alternately, P.A.M. Dirac, The Principles of Quantum Mechanics (4^th edn. 1958), p. viii:

Quantum mechanics … is known under one or other of the two names ‘Wave Mechanics’ and ‘Matrix Mechanics’, according to which physical things receive the emphasis in the treatment, the states of a system or its dynamical variables.

And (p. 115):

The Schrödinger form is the more useful one for practical problems, as it provides the simpler equations. … Heisenberg’s form for the equations of motion  is of value in providing an immediate analogy with classical mechanics.

Or again (R. F. Streater & A. S. Wightman, PCT, Spin & Statistics, and All That (1964), p. 4):

Throughout this book, states will be described in the Heisenberg picture of quantum mechanics.  The Schrödinger picture is much less convenient for the description of a relativistic theory, because it treats the time coordinate on a very different footing from the space coordinates.

And:

P.A.M. Dirac, The Principles of Quantum Mechanics (4^th edn. 1958), p. 311:

The Schrödinger picture is unsuited for dealing with quantum electrodynamics, because the vacuum fluctuations play such a dominant role in it. … They get bypassed when one uses the Heisenberg picture, and one is then able to concentrate on qualities that are of physical importance.

Dr. Matrix

Dr. Wave

Approaching an abstract but genuine reality from two different theoretical complexes  has its counterpart in different experiments, or different means of calculation, strengthen each other when they arrive at the same result.   Thus Einstein, in his annus mirabilis of 1905, when not inventing Relativity, found it worth his while  to “develop theoretically  three independent methods for finding Avogadro’s number.” (Abraham Pais, Subtle is the Lord (1982), p. 55.)   It was worth his while because, independently of our endeavors, this number is indeed there.

Summarizing:  For epistemology, the fact that two or more radically different approaches each manages to describe the phenomenon of interest, reassures us that we really do have our arms around this thing.   The lesson goes over, I would submit, in cases where what is being described is nothing so tangible as an atom (which Rutherford reportedly saw in front of his face as plainly as a spoon), but rather a four-manifold, or a simple Lie group.

~ ~ ~

Afterword.

I recently happened across the following curious passage:

The algebras G_2, […] E_8  are called exceptional.  In 1945, Chevalley remarked  that the existence of these algebras  is a brutal act of Providence  which we must accept blindly.  Perhaps this should be revised today  to assert that the source of these algebras  is the wisdom of the Deity  in allowing the Cayley numbers to exist.

-- Irving Kaplansky, “Lie Algebras”; in: T. L. Saaty, ed.  Lectures on Modern Mathematics, vol. I (1963), p. 126

~ ~ ~

There’s one further type of brane in M-theory  that is really surprising.  This brane is the edge of spacetime. … The photons at the edge of spacetime participate in supersymmetric E₈ gauge theory.

-- Steven Gubser, The Little Book of String Theory (2010), p. 95

E8: a Riposte (continued)

[A continuation of this.]

Synge waits until well into his second volume (J. L. Synge, Relativity:  The General Theory (1960), p.  104) to really let rip against Realism; and since he was himself very much a mathematical physicist, rather than an empirical experimenter, his testimony must be respected as coming from within the tent.  He distinguishes “Natural Observations” (NO) from “Mathematical Observations”, and opines:

Between NO and MO  there is a sharp and decisive break.  Only the simplest MO (counting) can be regarded as being NO also … Generally MO involve infinity (irrational numbers, differential calculus, and so on) and so lie outside physics and outside nature.

This is exactly the position of Kronecker (“Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk”).

He then delivers himself of a curious passage, which Irrationalists would seize on with glee (fortunately none of them are reading this):

The peculiar fascination of theoretical physics  lies in the art of forcing meaningful truth out of the meaningless equation NO = MO, which is a symbolic form of the assertion that natural phenomena obey exact mathematical laws.  The true inequality NO =/= MO should not be spoken above a whisper, because it is extremely dangerous.   If believed, it would sever mathematics from physics, and reduce both to sterility through lack of mutual fecundation.  It is whispered here only as an apology to those readers who expect to see the mathematics of relativity [which he presents in great detail] tied to the physics of relativity  by a strong chain of clear thought.  It cannot be done.

These ring like the Night Thoughts of a relativistic physicist, on the eve of taking his own life.

            Despite his conspiritorial tone in that passage, Synge was by no means alone in his reservations. Here is another anti-Realist view from the world of physics:

A. D’Abro, The Rise of the New Physics (1939), vol. II, p. 728:

A hyperspace is obviously a mathematical fiction; and waves that can be represented only in a fictitious space  must themselves be unreal.

Now here indeed is a statement that has been overtaken by events.  In the view of string theory, this hyperspace, far from a mathematical fiction, is a physical fact, the one we live in;  indeed, we must beware lest those compactified but very real extra dimensions someday unfurl in our faces.  --  The point here being, not to make any point whatsoever about cosmic geometry, let alone to proclaim the truth of string theory:  but simply to counsel against that “obviously”, when dismissing the Realist picture.

[concluded here]

E8: a riposte

[a continuation of this]

Writes J. L. Synge,  in Relativity:  The Special Theory (2^nd edn. 1965), p.  163:

According to this hypothesis [viz. that of a unique mathematical structure for nature], the mathematical formulae of physics are discovered  not invented,  the Lorentz transformation, for example, being as much a part of physical reality as a table or a chair.

Hear, hear! The Realist raises his glass with a sigh, basking in the warm glow of these purling words.  -- But suddenly, the author surprises us with a basin of ice-water in the face:

But this hypothesis of a unique mathematical structure for nature  is actually very naïve.  It is the product of the eighteenth century, a period when mathematics was understood much less than it is today, and it is unacceptable to any physicist who has thought about mathematics, or any mathematician who has thought about physics. [Oh, snap!] When understood properly (i.e. as mathematicians understand them) these concepts exist in the human mind and not in nature;  it is a meaningless waste of time to debate whether the ratio of two measured lengths is rational or irrational, or whether matter is continuous or discontinuous, because the concepts of irrationality and continuity belong to a world of the intellect, a world of mathematics, and not to the real world in which phenomena occur and are measured by pieces of apparatus.

(… slow burn…)

And again, p. 207:

Is matter really discrete or continuous? … That question must be regarded as quite meaningless.  For ‘continuous’ is a mathematical word, not a physical word, and has only a very vague bearing on nature;  we must not try to attach physical meanings to mathematical concepts which involve infinite processes.

[…]  The above remarks merely underline the philosophical attitude [quoted above].  It is a theme that bears repetitition.

( Somehow in these last bits, I detect the tones of Dolores Umbridge…)

And p. 308:

We use  now this mathematical representation, now that,  seeking those representations which are convenient to work with  and which yield at least some correct physical predictions.

            Now, we quite agree that it doesn’t make sense to say whether a numerical physical measurement is rational or irrational.   And certainly, in physics, infinities are tricky.   The continuum may indeed not be what the doctor ordered for the texture of spacetime.  And we agree that it may be convenient to employ this or that formalism for this or that particular problem.  (We shall develop this point further in our discussion of the wave picture vs. the matrix methods in quantum mechanics:  but shall draw a very different moral from that of Professor Synge.)   And yet we hold to our Realist position:  which has, moreover, practical consequences, and is not simply a matter of private preference in ontology.

            The Realist claim is that mathematical objects are as real as physical objects.  That is not to claim that any given mathematical object -- be it the continuum, E8, or Klein bottles -- is actually instantiated in this particular physical cosmos, let alone that it applies everywhere and across the board.   Thus, take the continuum.  Our own spacetime may well be granular, not continuous;  the cosmos might be finite, both in diameter and duration.  It might even be downright cellular, as in Stephen Wolfram’s view.

http://en.wikipedia.org/wiki/A_New_Kind_of_Science

Furthermore, the continuum itself is among the most mysterious of mathematical objects;  it is, after all, the eponym of the spectacularly counterintuitive status of the Continuum Hypothesis.  It sticks in the craw even of some mathematicians (though not the ones we prefer to share a beer with), let alone physicists or shopkeepers.

            However.  Considered purely as an object of group theory, E8 has calculable values along certain dimensions of assessment  (algebraic properties): Let us call the dimensions of assessment  "alpha, beta, gamma" … , and the values we calculate  "alpha-0, beta-0", etc.  Thus, for E8 (reading the values out of Wiki), alpha might be “What is its dimension?”, and alpha-0 turns out to be 248;  beta might be “What is its rank?”, and the answer “8”;  “What is its center?” -- “Trivial”; “What is the order of its Weyl group?” -- “696729600” (but you already knew that) …

            Now:  Suppose that spacetime does turn out to have six extra compactified dimensions, and that heterotic string theory is indeed the gospel truth.  Now, those in a position to know, inform us that  in that case  there are only two possible choices for the gauge group of our world.    Recall that earlier gauge groups we’ve met were things like the rotation of a wheel, things whose reality is familiar even prior to their employment as gauge groups:  but now we must choose between  SO(32) and E8 X E8.   The choice must be made on the basis of certain physical predictions.   Assessment-dimension lambda, for instance, might turn out to be physically measurable (specifying, say, the spin of a graviton, or the mass of a magnetic monopole, or what have you);  lo and behold, lambda-0 in E8 X E8 turns out to correspond what we have measured, whereas the different value that falls out of SO(32) does not;  and so forth for some other assessments.

            All right then:  The Realist thesis in this case says simply that adoption of E8 -- which is, in this view, pre-existent, and independent of physics just as it is independent of politics -- is a package deal.   Not every fact and feature about E8 will be physically interpretable, let alone measurable;  but for any that is -- say, omega -- the value as measured experimentally must turn out to be omega-0.   If it doesn’t, we have a problem.  E8 being pre-existent, and not invented by ourselves for our own convenience, it cannot be toyed and tinkered with, selecting some features and rejecting others in a Procrustean attempt to match experiments.   And Synge’s picture of using Newton or Einstein, merely as the mood moves us, as though one were an Allen wrench and the other a pair of pliers, won’t do at all.   If the mathematical structures we seem dimly to glimpse behind the veil of the world  were analogous, not to mountains, but to man-made tools, then we could always kludge one up for the occasion.   Then physics would be the theoretical equivalent of toenail clippers and pinking shears.

[continued here]

E8

(Chastened by the stern but just admonishments of our Canadian colleague, regarding the tinsel and pinchbeck allure of Web celebrity based merely upon citizens’ obsessions with CUTE HEDGEHOGS and PLAYFUL PENGUINS,

http://pyesetz.livejournal.com/

we return now to the straight and narrow of Cantorian realism, leaving aside all reference to our animal friends, not excluding the lowly hedgehog (who knows but One Big Thing) or the HUMBLE WOODCHUCK.   You will find no mention of the HUMBLE WOODCHUCK in anything that follows;  and he that were so foolish as to search on the string

!! => “humble woodchuck” <= !!

in hopes of googling-up this essay, would surely search in vain.)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

E8

Before we proceed further, so that we have some acquaintances in common, let us consider our new friend,  E8.  This way, when I have occasion to refer to him again in future, we shall all give a knowing nod.

http://en.wikipedia.org/wiki/E%E2%82%88

Now, E8 is, frankly, not such a big deal:  it’s just a single, exceptional simple Lie group (albeit not an exceptionally simple one), even if it does turn out to be the symmetry group of string theory, and thus of all the world.  For actually, all our major experiences of life – our loves, our sorrows, our proofs of the Riemann Hypothesis --  are carried out  quite independently of string theory (be that worthy enterprise  well-founded or no).  No need to get all misty and mystical about it, though journalists and publishers love to do so because it moves more newsprint and books.  (The “God Particle”, egad; it’s just a frigging Higgs boson.)  You could with as much reason wax mushtical over the mere numbers zero and one – the Nihil and the Ens, if you wish – who heroically alone shoulder all the burden of binary description, which encompasses so much.

            Nevertheless, in its own small way, E8 does have a certain fascination for us, the fascination of a small thing, perfected past admiration, as by a master craftsman, with all eternity wherein to work, and whose very existence seems a paradox, like a spinning top.  After all, word of this fait divers from the normally cleidoic mathematical world  did manage to make it into the print editions of both Le Monde and the New York Times,

http://www.nytimes.com/2007/03/20/science/20math.html?ref=science

thus elbowing out whatever might otherwise have occupied those column inches, be it an account of an auto accident, or a lost cat.  And this, despite the utter incapacity of the journalists to give us the least idea of what has been actually discovered.  It is as though they had sent a correspondent to cover a major speech, and then reported, “We could not make out a word he said.”  As the Times reporter put it (beneath the swooning headline  “The Scientific Promise of Perfect Symmetry”):

Eighteen mathematicians spent four years and 77 hours of supercomputer computation to describe this structure, with the results unveiled Monday at a talk at the Massachusetts Institute of Technology.

But it still is not easy to describe the description, at least not in words.

“It’s pretty abstract,” conceded Jeffrey D. Adams …

“You can’t really picture it,” Brian Conrey, executive director of the American Institute of Mathematics, said of E8--

and then offered his own endearingly goofy stab at a depiction: “It’s some sort of curvy, torus type of thing.”  (A torus, for those who are not aware of this, is a donut with a college education.)

Most previous symmetries have been simple enough in themselves -- like, translation (that is, just boogying along in a straight line), which is as simple as it gets -- but startling in physical consequences.  Thus:  symmetry in translation along the time axis -- and  voilà , Conservation of Energy!  Rotational symmetry -- conservation of angular momentum!  Likewise, to say that “the gauge symmetry of the electro-magnetic field is U(1)” is again to invoke the familiar wagon-wheel.  Even the PCT intricacies (Parity, Charge, Time) are based simply on the shuffling of easily visualisable bivalences (left vs. right, positive vs. negative, sooner vs. later);  the implications of these for physics, however, are beyond the reach of most of us.  With E8 we arrive at a symmetry group that is itself well-nigh incomprehensible -- certainly not surveyable without very extensive practice and training.  As for its ultimate physical implications -- anybody’s guess.   But whatever its ultimate fate in physics, the fact is, E8 is already there, in just the same way that the symmetry of a rotating wheel is there, and would still be there even if our cosmos happened not to contain anything physical that actually rotates.  We discovered E8;  we didn’t invent it.

[Update 4 Jan 2011:  The above provoked a playful and entertaining meditation by our Canadian Colleague:
http://pyesetz.livejournal.com/103055.html
Enjoy.]

[continued here]