Gödel’s Proof—Or Was it a Spoof?

When it comes to higher math, it’s a good policy to stay cheerful—and to resist the waves and waves of frustration that well up. Take one of the more prominent figures in that field, Kurt Gödel (1906-1978); he is famed for his incompleteness theorems. I managed to find a partial translation of his first paper (link). It was written when Gödel was but 25. He does the job—the job is to humble mathematicians forever—in just 15 pages (the paper is longer, but it begins and ends with the translator’s notes). It’s good to stay cheerful because with effort the essence will emerge—not from fully penetrating the actual originals, mind you, but because with the help of others one can get there. By essence I mean, enough to satisfy me that there is something worthwhile present here.

Gödel labored at a time when mathematicians were endeavoring to prove that various systems of mathematics were both complete and consistent. If they were neither—or one but not the other—the foundations of mathematics were in trouble. Those engaged in such labors were the really big names in twentieth century math: Abraham Fraenkel, Friedrich Frege, David Hilbert, Giuseppe Peano, Bertrand Russel, and Ernst Zermelo. What Gödel proved, and thus upset the apple cart was:

1. If the system is consistent, it cannot be complete.

2. The consistency of axioms cannot be proven within the system.

The reason for good cheer is that Gödel proved the liar’s paradox mathematically.  That paradox originates with Epimenides, an ancient Cretan philosopher-wit who asserted “All Cretans are liars.” If taken as a true statement, it is a lie; if as a lie, it contradicts itself. The modern way is to ponder the truth-value of  “This sentence is false.” Gödel substituted “not provable” for lie or falsity. He showed that such a statement can be formulated mathematically so that it is equally contradictory: if proved it is false, if disproved it is true.

Now completeness asserts that every proposition framed by a formal system can be proved. But consistency demands that the outcome of any process must result either in truth or falsehood, never both. Gödel therefore showed that mathematical systems are either one or the other: if they are consistent, they are incomplete, if they are complete, they are inconsistent. The consistent system must exclude the formula Gödel framed using the rules of the system and thus be incomplete. The complete system will include the Gödel number but, producing at least one paradoxical result, will be inconsistent.

But what Gödel actually proved, it seems to me, is that Man is not God—although we kind of knew that already. He himself was not only a true believer, he bought the traditional package with all of its frills and was dead certain that he would survive his own death. Good for you, Kurt Gödel. I bet you are still chuckling over your life’s achievements somewhere out there in the transcending ether.

F comes before M

My subject is the claim I’ve often seen that mathematics is the source of science and thus the father of modern technologies. A list then usually follows ending with radio, television, and of late the Internet. Just last night I read this paragraph in a distinguished book on Mathematics:

However, the Kantian explanation that we see in nature what our minds predetermine for us to see does not fully answer the question of why mathematics works. Developments since Kant’s time such as electromagnetic theory can hardly be endowments of the human mind or the mind’s organized sensation. Radio and television do not exist because the mind organized some sensation in accordance with some internal structure then enabled us to experience radio and television as consequences of the mind’s conception of how nature must behave.

                                                                                                                                            [Morris Kline, Mathematics, p. 342.]

Sure enough. But the thought here goes astray. It suggests that mathematics lies behind electromagnetism—and radio and television. No. Faraday discovered electromagnetism by experiment—before young Maxwell came around to translate it into elegant mathematical concepts. Thus F came before M. But it wasn’t Maxwell’s equations that led to radio but more unruly inventiveness by the likes of Edison, Tesla, Marconi, Morse, and the like; you look in vain for paeans to math in their histories. Television got itself going in 1884 when a twenty-three-year old German student named Paul Nipkow punched holes into a disk; he spun the disk above an illuminated picture and sliced, diced, and subdivided it into many tiny images that we now call rasters. That was the beginning.

No. Mathematics is the immensely helpful servant of science—and technology belongs to the inveterate tinkerers. Later, when inventions come to be commercialized and engineers get going in rationalizing the processes, each of them, of course, has had to master calculus and so forth and be handy with equations—although the results of the most useful of these are in the handbooks already.

My image is that of two horses harnessed to the same cart. One is strong and unruly, the other is elegant and spirited. The strong one does most of the pulling, but when it comes time to take photographs of the team, people take the picture from the side of the spirited, elegant horse. Oh, just look at it snort!

There is also a hierarchy here. Math belongs to the upper classes. Faraday came from a poor working class family and was self-educated (as an apprentice in a bookshop); he knew very little math; when he rose in stature and worked as an assistant to Sir Humphry Davy at the Royal Institute, people there did not consider him a gentleman. Maxwell came from the nobility, his father a lawyer and financially secure. The inventors like to grub about with matter, the mathematicians are more at home in the airy realms of concepts. Can we do without them? No. But let’s not forget where science really starts.

Finally, mathematics works because, when successful, it models reality. And reality works.

In the Furnace

A story in the New York Times reports on rifts appearing in the coalition opposing my favorite candidate, Vladimir Putin. Liberals look around at rallies and discover all kinds of people they don’t like, thus ardent nationalists and those who want a Russia for Russians, a designation that apparently excludes some ethnic minorities, among the non-Slavic migrant workers. Earlier stories report on violence—including a beheading—attributed to splinter nationalists.  The thought that came was: “We don’t live long enough to get wise, and by the time we do, we stumble about, and putting on socks is a labor.” A second thought was that until people emerge from the animal state, where tribalism is normal, they’re quite able to see “the other” as something to push away and even to kill—and feel righteous about it! The third thought? Hell and damnation. It keeps happening, over and over again. Nothing’s ever learned. The fourth was, Du calme! This realm, this earth, this life is a reverberatory furnace and not an end in itself. And by the time you realize that, you’re close to metal and about to be poured.

A Priceless “Free Speech” Moment

One way to sum it up is to say that today money may speak, but a hundred years ago bulls were well advised to wear pants. Puzzled? Read on.

It’s 1907 and the leading tobacco company in the United States, American Tobacco, signs a contract with a stage-coach line. We’re talking about the horse-drawn variety. The company wants to use the sides of the stage-coach to advertise one of its most popular brands, “Bull” Durham. The ads are made and affixed, the first stage-coach heads out. A huge public outcry follows. Why? Well, the bull’s testicles are so prominently featured in the ad that people daren’t even look!! The City of New York, always a guardian of public morality, arrests the stage coach driver. The coach is rapidly shunted out of sight. Then as now (some things never change), the affair bursts into litigation, and that, in turn, eventually reaches the Supreme Court no less. It is now 1911. And the Supremes uphold the city’s action, approve of the ban. What!? you cry. Hadn’t those benighted judges heard of free speech yet? No doubt they had. It’s just that they clean forgot it—staring at those humongous testicles.

A Higgs Gem

Fans of physics are undoubtedly aware of the fact that recently the folks at the Large Hadron Collider in Geneva undertook tests to detect the Higgs boson. It’s called “the God particle,” named that by Leon M. Lederman, a Nobel laureate in physics, because of its great importance for understanding matter—although he says, in jest, that he called it that because his publishers refused to let him call his book The Goddamned Particle instead—and that because the problem is so difficult and expensive to solve. The Higgs boson is thought to give matter its mass.

Now there is no subject more obscure than quantum physics—not because it really is but because the practitioners of this art are unwilling to discuss it in plain English. I sometimes think that they might refuse because, once spelled out, ordinary people might not be quite so impressed. But occasionally one finds some accessible explanations. I did, and I’d like to share it. Call it a Higgs pentahedron, something of a gem. Back in 1993 William Waldegrave, science minister in the United Kingdom, challenged physics to give a one-page answer to this question: “What is the Higgs boson, and why do we want to find it?” The journal Physics published five winning entries, and these are accessible here.

The answers, taken together, give a very good understanding, particularly David Miller’s—but that one is really further illuminated by reading the others. Such clarity is extremely rare—like real gems.

What I got out of it is that in physics there are fields, and one of them is the Higgs field. Now to understand “field,” think of a lake. That’s the field. But when energy in some way disturbs that lake, why then there are waves. Call each wave a “particle.” As there are no lakes without waves, there are no fields without particles, and the Higgs field has its own, the Higgs boson. It’s not really, like, a thing—just like the photon isn’t either. The photon is the wave in the lake called electromagnetism. You’re in the picture, I think. It is also quite evident that such mysterious lakes and particles arise from mathematical models built to make sense of observations—thus in the subatomic realm from photographs taken of “particle” collisions at such places as the Large Hadron Collider.

Putting the Right Quote in His Mouth

I came across a delightful quote today reading Current Book No. 1. The quote was attributed to George Santayana (1863-1952). It said: “There is no God and Mary is His Mother.” Tell you the truth, that didn’t sound like Santayana to me; but then my memories of that gentle philosopher go too many years back. This one has wit, to be sure, but there is also bite. So on returning home from Jeffrey’s Honda, where, believe it or not such delights visit me at right regular intervals while waiting, I turned to Bartlett’s—and amazed actually to find the quote attributed to Santayana. But the attribution, while assigned to the philosopher, was actually to the poet Robert Lowell (1917-1977), and specifically to a poem in Lowell’s Life Studies titled “For George Santayana.” So the search didn’t end there. Finally I found the poem and herewith reproduce its first stanza:

In the heydays of ‘forty-five,

bus-loads of souvenir-deranged

G.I.’s and officer-professors of philosophy

came crashing through your cell, 

puzzled to find you still alive,

free-thinking Catholic infidel,

stray spirit, who’d found 

the Church too good to be believed.

Later I used to dawdle

past Circus and Mithraic Temple

to Santo Stefano grown paper-thin

like you from waiting. . . .

There at the monastery hospital,

you wished those geese-girl sisters wouldn’t bother

their heads and yours by praying for your soul:

“There is no God and Mary is His Mother.”

Now I’ve been a writer, a poet—and also an editor. So I have sympathies for the editor of Bartlett’s who decided to stick this one in—and under Santayana. Irresistible. Particularly to certain Catholics of the damaged sort like me…

The Mouth of the Mice

The future also throws its shadow, itself a worthy subject—but not today’s. What I mean to indicate, however, is that we’re planning a trip down to the Florida Keys, and in preparation for that I’ve been looking at maps. In that process I noticed that the Keys, if extended northward, actually begin well above the Bay of Biscayne in a detached chain of islands of which Miami Beach is a part. A satellite view of that (clicking on image will enlarge it, Esc returns):

This sort of meditation brings memories, in this case of earlier trips to Florida. Then up floated a name: Boca Raton. That place is way higher than Miami, and looking at it one sees no bays of any sort. This got me curious. I learned that the original name had been Boca Ratones—and that raton is a mouse, not a rat, in Spanish; the word for rat is rata, pl. ratas. Next I learned that the original location of that name was actually associated with the much more southerly Bay of Biscayne. Well. That bay is a pretty good-sized boca, meaning mouth. So. The Mouth of the Mice.

The marvels of modern life. With Google’s satellite mapping images, I started to look for the teeth of those mice. My assumption was that that gracefully curving thin line of islands that form the Florida Keys and then run in parallel with Florida’s land mass might at one time have been more prominent at the outer edge of that bay. The next two pictures show the map itself and then a closeup of a portion immediately south of Key Biscayne. Here they are:

 

Quite visible in the center of the second picture, faintly brown, are rock formations lying close to the surface of the ocean—and the black channels mark the places where water had once carved paths for itself as it flowed into the sea. Was that rock lying higher in the old, old days when Boca Ratones had been named? I expect so. Or were sea-levels lower? To answer that question I’d have to undergo serious study—rather than meditating idly on an  upcoming trip into places quite wondrously different than the eastern edge Michigan where once the Penobscot people roamed.

The Comedy

Here a note triggered by a post on Laudator today (“Did Adam Laugh Before the Fall?”)—and its chain of references. In my youth, long before I’d ever read it, or knew anything about the history of the title, I used to take great comfort in The Divine Comedy—and even more later when, in my college days, I became mad about theater and took a minor in Drama. This comfort may have come from my mother, but in any case it delighted me to think that at the Highest there was Laughter. Later I learned that my delight hadn’t been intended, actually. The work was originally La commedia di Dante Alighieri; someone else added the Divina and took the author out of the title. To modernize the sound of that, if I wrote something today and meant what Dante had meant by his title, I would call the work The story of Arsen Darnay. Commedia meant, self-deprecatingly, common or low art, popular, for the people, written in the ordinary language, not in Latin. Furthermore, it ended happily—whereas the “serious” stuff never did. That post today also made me wonder: Did Genghis Khan ever Laugh? Did Stalin? Did Hitler? Did Homer? Just kidding…

Elections, Elections

They’re everywhere, everywhere. Even we are now actively committed. The superpac ads are exploding all around us, we’re attending every spellbinding debate, we’re hitting the streets canvassing for our candidate, It (our candidate is unusual in being an It) is, we think, the only candidate worthy of political effort. And It only wants to raise our taxes (which tells you how we vote around here) by a staggering 0.7 mills per annum—or as much of that at maximum that It will need over the next eight years to balance Its budget. Yes, we say! Yes, to that.

Industrialized Alkaloids

What do caffeine, cocaine, nicotine,  and morphine have in common? They all come from plants in which they form a relatively small part of plant tissues. The psychoactive effects of ingesting these molecules have caused humanity to harvest them long before anything like civilization dawned. The first three help us manage stress by acting simultaneously as stimulants and as relaxants; the last, along with codeine, alleviates pain. All belong to the chemical family of alkaloids; thus the molecules feature ring-formations in which nitrogen is dominant but linked to other elements.

Recently Brigitte and I were talking about nicotine, and the subject of people in the Andes chewing coca leaves came up. Didn’t that help those living in high altitudes where oxygen is thin? That got me to thinking about the sometimes disastrous consequences of human ingenuity. These plants were used in pre-industrial times—indeed as some are still used today, like coca leaves still are, like coffee still is—in a form that does very little harm. Egyptian doctors used to tell their patients to eat poppy seeds to lessen pain. I recall my mother telling us that Hungarian peasant women used to tie poppy seeds in a bit of cloth and give it their babies to lick in order to keep them quiet; these were ordinary poppies, not the opium variety, but all poppies contain the drug. The American Indians chewed tobacco or smoked it in ritual settings—but that smoke was far too harsh for inhalation. The strongest of these drugs, morphine, was the first to be industrialized as smoked opium—and thus it began to harm its addicts. Extracted and purified cocaine is also a wildly addictive drug—but it requires highly developed industrial processing to extract it in concentrated form. And in the case of tobacco, its transformation into cigarettes is the chief reason why lung cancer ranks so high as a killer. Cigarettes are mild, the inhalation of the smoke is easy—and the nicotine reaches the brain almost instantaneous and thus releases hormones and neurotransmitters in such magnitudes that the effects are very rapid and highly desirable.  

In some areas, a lot of knowledge is a dangerous thing; chew on a leaf and ponder this while the coffee brews. A lot of knowledge mixed with a highly commercialized culture—now that becomes really dangerous.

Not a Lot of Popularizers

1975 The Tao of Physics

1979 The Dance of the Wu Li Masters

1984 The Looking Glass Universe

1984 In Search of Schrödinger’s Cat

1988 The Symbiotic Universe

1988 A Brief History of Time

1989 Coming of Age in the Milky Way

The 1970s and 1980s produced a rash of popular books on physics. In 1994 came Michio Kaku’s Hyperspace, another book I bought along the way, but the curious thing is that string theory does not lend itself to popularization quite so much—either that or the hot air has cooled in this balloon: we don’t have a string of books on string theory; it is too evidently a theory based on pure mathematics. When one of those twin brothers goes off on a decades-long trip to outer space at speeds close to the speed of light—and returns to find the other twin an old man while he is still full of testosterone—why that’s a worthy plot. Trips into Hilbert space, a mathematical dimension, just don’t have the same sort of impact.

The less accessible a subject, the less it will be known to the public—and the more so, if it is deemed important, will it be wrapped in awe. Mathematics wins that prize hands down. I’ve been reading Morris Kline’s book, Mathematics: The Loss of Certainty, a Christmas gift from Brigitte—she who knows what I need. It is not an attempt at popularization, to be sure, but the closest thing we’re likely to get. It was published in 1980 by Oxford University Press and tells the (I’m not kidding) nail-bitingly suspenseful story of the history of math. As Brigitte will testify, I’ve read many, many books of which, at first, I’ve understood at most, say, twenty percent of the content. I have some of the characteristics of the junk yard dog. This book is one of them. It is my conviction that anything made by humans is accessible—if only one makes the effort to penetrate the subject. Eventually, as John von Neumann said of math, you get used to it. And after years, one fine day, we find out that it’s true. The grand old patterns of human nature appear quite clearly again, and what felt like impenetrable fog becomes the same-old. The mild reward is that, at that point, you can eventually feel the problems the great but largely unknown names (who’s ever heard of Kronecker, Borel, Lebesgue , and Baire, for instance) actually felt as real. In my own case, alas, once I’ve penetrated the actual pattern of the thing, I tend to lose interest. I’m interested in the shape of things. For me it’s all about orientation. I appreciate the work of popularizers, and almost-popularizers like Morris Kline, because they let me get there faster.

Sometimes it does take decades to get anywhere at all. It’s been a long time since I’ve first started looking into physics—a subject entirely inaccessible until one has managed at least a certain level of comfort with mathematics, which, these days, is physics. Until then a vast complex field that throws huge shadows over everything, from practical life to cosmology, has the aspect of watching an elaborate thirteenth century Japanese drama unfold, told entirely in Japanese, and all you get is the emotional toning of the harsh shouts of the samurai engaged in its battles.

Proving God in the Lab

It startled me a little the other day to discover that Dr. Robert J. Spitzer, a priest, was giving lectures on the Anthropic principle on EWTN, the Catholic Television channel. The Anthropic principle dates to 1973 and was first offered by physicist Brandon Carter. It suggests that the universe is fine-tuned in detail to make life possible.

Behind this principle are two assumptions. One is that the universe began, thus that a big bang took place. The other is that the starting conditions, the basic laws, might have been different. Three of these are gravity, the strong force (holding atomic nuclei together), and the electromagnetic; that last holds electrons in place around atoms and makes molecules possible. Very small changes any in these values would have produced a universe in which life would not have been possible. To take just one, gravity, if gravity were greater stars would have burned out more rapidly—no time for evolution. If weaker, no suns would have formed, no light would have nurtured life on planets; indeed planets wouldn’t have formed either. The principle is much more elaborate, but this much will suffice. The principle is named anthropic, thus related to man, because without finely-tuned laws, no humans would have come about.

The theory is not, of course, accepted in mainstream science; every discussion of it is bristlingly defensive. Modern science doesn’t hold with any kind of “tuning” at all; tuning implies a NoNo, namely that somebody is out there, behind the cosmos. At the same time, the principle at least implicitly views “life” as arising from matter; otherwise no tuning would be necessary. Alongside the big bang theory, which appears also to point at a “scientific” description of creation, the Anthropic principle is a favorite of those who would ground faith on the presumably more respectable foundations of science than on human intuition.

I’ve always found the Anthropic principle dubious for simple reasons. We don’t know what life is. We also haven’t the faintest notion about the basics of matter and have no proven theory of gravity (one of the tuned characteristic); all we have is descriptions of it. In one sense reality is an enormous Rorschach inkblot which permits any kind of projection whatsoever.

This prompted me in the beginning (of this blog, that is) to write a spoof on “the new saints” (link). One of the co-discoverers of the big bang was Georges Lemaître, a Belgian priest and physicist. I’ve always shared his very sensible approach to the subject. When he got word that Pope Pius XII was about to address the subject in a favorable manner, Lemaître hastened to the Vatican to put in a good word with Papal advisers. The big bang is just a scientific theory. And the fate of these is often to be overturned in time. The story of that intervention is told in this article (link). Lemaître’s own words, quoted in that article, are appropriate:

As far as I can see, such a theory remains entirely outside any metaphysical or religious question. It leaves the materialist free to deny any transcendental Being… For the believer, it removes any attempt at familiarity with God… It is consonant with Isaiah speaking of the hidden God, hidden even in the beginning of the universe.

That’s the right approach.

Definitions and their Consequences

The A.D.A.M. Medical Encyclopedia defines autism, in part, as follows:

Autism is a developmental disorder that appears in the first 3 years of life, and affects the brain’s normal development of social and communication skills. Autism is a physical condition linked to abnormal biology and chemistry in the brain.

This is a general definition, not the clinical one. That one is found in the Diagnostic and Statistical Manual of Mental Disorders (DSM). Today the New York Times reports that the fifth edition of DSM may redefine the condition. Both the current text and the proposed change are accessible here, courtesy of the American Psychiatric Association. The link takes you to the proposed change; the old one is under the tab labeled DSM-IV. The change appears to be a tightening of the definition—and thereby hangs a controversy.

Under tighter rules fewer people will be diagnosed—and therefore qualify for various financial programs in support of autistic individuals. The new definition will no doubt continue to serve in the identification of genuine cases of children who really have this condition.

But there is another aspect to this story. Autism, a relatively newly recognized condition, has seen explosive growth, which may or may not be real. What do I mean by that? Here is a condition that manifests poorly developed social and communications skills; but its underlying physical causes are unknown. Thus it is similar to ADHD (attention deficit hyperactivity disorder), another very prevalent condition. Government funded support programs have developed for both. But where the condition is difficult to diagnose by physical tests and the behaviors may be caused by something other than physical conditions—and where program are present—the tendency of physicians is to diagnose a fundable condition and then to breathe a sigh of relief.

I call this a newly recognized condition. Indeed. My 1967 Webster’s Collegiate defines autism as “absorption in fantasy as escape from reality.” I find myself quite autistic, under this definition—to the benefit of mystery novel writers.

Let me wrap up this topic with a footnote. That A.D.A.M. in the medical encyclopedia stands for Animated Dissection of Anatomy for Medicine.

On the same NYT front page today the second lead story reports on sharply rising attacks by the new Afghanistani army on NATO forces. Here we have a definitional problem of another sort. Those whom we cajole or coerce to serve in an army we have created as the country’s occupying power are defined as allies. But the definition doesn’t seem to fit—because the alliance isn’t altogether voluntary.

Austen Before Kodak

In the National Portrait Gallery in London hangs what appears to be an unfinished portrait of Jane Austen executed in pencil and in watercolors. It is the work of her sister, Cassandra. Anyone wishing to see pictures of this writer need but to go to Google Images and type in “Jane Austen” to see lots. Cassandra’s portrait, of which I reproduce a cropping from a BBC documentary shown on Austenonly (link), apparently served as the starting point for many other portraits produced much later, each as it were “improving” on the original. The picture may not have been entirely successful—the reason, perhaps, why Cassandra only colored the face. The National Portrait Gallery (here) cites a niece of Jane’s as follows: “There is a look which I recognize as hers, though the resemblance is not strong, yet as it represents a pleasing countenance it is so far a truth.” The picture dates to 1810, thus more than a decade before photography began as the daguerreotype. I’ve been thinking about Austen again because I’m reading P.D. James’ most recent novel, Death Comes to Pemberly. And today I learn that Eastman Kodak has declared bankruptcy. The days of old-fashioned photography on film are drawing to a close. So I thought I’d mark the day.

I’ve always liked this picture and have viewed all others as somehow failing. The clue to that is the phrase I quote above: “a look which I recognize as hers.” Even Cassandra may have rendered her sister as prettier, perhaps, than she was, but she did manage to capture “a look.” Someday perhaps fairly soon all photos will be held exclusively on minute surfaces of doped silicon accessible only by means of machines and electricity. And when electric power fails or flags at last, those picture will be altogether lost unless someone bothered to print out copies and saved them in an album. And then back to the drawing board… 

St. John’s College

The college has two campuses located in Annapolis, MD and in Santa Fe, NM. Few things are rooted so deeply in time, but this college grew out of King William’s School in Maryland founded in the colonial year 1696. The school’s curriculum is grounded in the great books and is unified, meaning that all students take the same courses and all courses are required—no majors, minors and all of that machinery. Paradoxically, this very elite program was the consequence of failure—the curriculum adopted in 1937 when the college, organized along conventional lines, was facing a desperate financial crisis. The “new program” miraculously saved it. To get a feel for what such a program means, here is a link to the reading list divided by year.

Long observation teaches that virtually any conceivable good (or evil) will have its place somewhere on this plane of existence. A place like St. John’s is a little unbelievable—and two campuses yet. We learned of the existence of this school in a curious way, through a letter that one of Brigitte’s swim-exercise friends shared with her, a letter written by the friend’s grandniece. The letter-writer, a young woman in her sophomore year, casually describes some of her studies—along with lots of other things. The contents of the letter and its stunningly good English almost shocked. A forgery? A little joke? No. For real. Both of us observed a minute of reverent silence after having read it—not quite trusting our eyes, as it were.

To Be a Tree

It may well be, if we but knew it, that this dark realm is here to shape

Countless avenues for spirits to help them make their Great Escape.  

Who is to say that grasses, trees, that animals and plants are waste,   

That only humans hold the keys and will be raised, allowed to taste, 

Experience the real salvation? We can’t. We only ever

Know other beings’ emanation, signs, and sights. Endeavor

Although we might to get a view from the inside, we fail, we can’t,

Although a smile, the other’s sighs, sometimes produce the small, scant

Hint that our life is also in  their eyes. On walks betimes I feel

That trees and I communicate, indeed that rustling leaves conceal

The meanings they articulate to one another too. There is no waste.

The dog has feelings, thoughts, and dreams. Matter, spirit are so interlaced

In dogs we can’t make out the seams where in them souls from bodies part.

The inwardness of flowers, in trees the deep emotions in their hearts?

That knowledge isn’t ours. Is there a gulf here? Or just degrees?

Sometimes for an hour’s spell on walks I ponder such odd mysteries.

Youth, Illusion

We watched The Prime of Miss Jean Brodie again after a lapse of four decades. Miss Brodie is a fictitious, charismatic teacher in Scotland brim-full of romantic notions, the religion of true art, and an admiration of the emerging men-on-horseback of her time, Mussolini and Franco. The first time and now again my Mother’s romantic admiration of all things Italian (when I was still a child) came back powerfully as I watched Miss Brodie. Today—what with the passage of those decades—the realization came that the world always looks quite different in youth. Hope always springs eternal, and when the rosy fingers of some great new dawn seem to be coloring the edges of the sky, young hearts enlarge. So it had been with my then still very young Mother—before the grim tales of the various collective horrors actually unfolded. At my age one knows too much. Nothing any longer deceives or tempts—no Arab Spring, no Tea Party, no Occupy Movement. A while back now we had an occasion to see some of Leni Riefenstahl’s films; she was both Hitler’s best propagandist and unquestionably one of the greatest film talents of the last century—alas she got it both wrong, her subject and the time. But it is worth while sometimes to imagine seeing those movements, Mussolini’s, Hitler’s, as the people of their countries saw them early on. Then, as now, I am sure, those over 70 remained unimpressed, indeed quite dubious. It takes a lot of years before this wondrous, green or snow-glittery lovely world reveals its true face as the valley of the shadow of death. Is that man suffering depression? Naw. Quite cheerful; not what it sounds like. But one just knows. If in doubt, give it time.

Let’s Hear it for the Minus

Negative numbers deserve respect such as they rarely ever get.

In Math they have been dubbed absurd, an adjective that really hurt

When the nasty appellation saw its earliest application

In quite ancient, hoary times. Too long have nasty crimes

Like that stained Abstraction. Our times now call for action!

Let us rise now and defend numbers we can’t apprehend

Wearing those humbling minus signs they’re forced to show in lines

Doing subtraction which adds or division which just pads

Positive numbers’ sums. Let’s join and clear those slums

Below the Zero’s sway. Arise from Berkley to Bombay.

Negatives have a true domain in which they ought to reign

Supreme rather than merely be used when needed—cavalierly.

Wine, Loaf, Thou—and Math

Omar Khayyám (1048–1131), known to most by means of Edward FitzGerald’s translation (using a loose meaning for that word) of the Rubaiyyat, was also and perhaps predominantly a mathematician and a philosopher of the school of Avicenna. As I noted earlier (here), I am now reading a wonderful book on mathematics—one of whose early themes is Euclid’s fifth postulate about parallel lines. Khayyám played in that game too, and it delighted me to discover the page of a Persian manuscript of his reproduced by Wikipedia (link). Looks odd that, doesn’t it. FitzGerald was a wonderful poet but apparently challenged in finding original material. His Rubaiyyat is a kind of free, rearranged, and often reinterpreted rewrite. Robert Graves offered a more authentic version, but got shouted down. Meanwhile I note that people of a certain stripe—those who, like Khayyám, believed in the priority of intuition in knowledge—nonetheless often spend huge chunks of their time on mathematics, and the higher the individuals’ rank and fame, the more likely that turns out to be. Avicenna (Ibn Sina), whose thought Khayyám followed, was of that persuasion too.

Even a Little Learning…

Even a little learning teaches that human nature is always in trouble. Drinking deeper confirms it. A good example comes in today’s post on Laudator Temporis Acti (link); it is delightfully titled—but it could’ve been titled “So What Else Has Changed.”

Some stray thoughts that rose, reading that. Note the language. Rose. Not progressed. In our times, though ever more hesitantly, we believe in progress. That belief contradicts what plainly lies in front of us. Progress is either personal, creative or it’s just as vanishing as everything else. Ocean waves don’t progress, they just rise and fall; tides ebb or flow.

Those with little learning, like me, don’t know where the Pierian spring is located. Irritated, I looked it up. Turns out that a portion of Greek Thessaly was called Pieria (link). In that region is Mount Pierus. The Greeks though that the Muses lived there. Being a mount it had at least one spring.

The phrases comes from Alexander Pope poem, An Essay on Criticism. Scholars have traced it back to Petronius’ Satyricon. Here is the verse in J.M. Mitchell’s translation.

I LOSE MY WAY

But whether he’s nursed ‘neath the fortress grim of the armed Tritonian maid,

Or a Spartan settlement nurtured him, or the home where the Sirens played;

His boyhood’s years he must give to song, and quaff the Maeonian spring

With a generous heart; he must hurry along, just giving his steeds their fling,

With Socrates’ pupils, and unafraid, he must learn from Demosthenes

To wield the orator’s giant blade; and — when he has learned all these —

Then let the poets of Roman race throng round, and, their old Greek dress

But lately shed, in native grace, lend him their own loveliness.

Let the page have done with the dusty Court, let Fortune go her own way;

Let the theme be banquets and fields hard fought, told bravely in warrior lay;

Let Cicero’s thunders try thy soul; be these thy strengthening.

So in full flood high thoughts shall swell from the true Pierian spring.

Kaleidoscopy

Kaleidoscopes produce their beautiful images by causing bits of colored glass to move about in a restricted field. The source of their movement is gravity as the device is turned. The pleasing images are caused when two or more mirrors multiply a single image and create a symmetrical composite. Now what interests me here is that the bits of colored glass (or whatever else is used) never change—except their locations relative to each other. The only energy entering the system is the turning of the device; that invokes the pull of gravity. Yet the image appears to be perpetually new. But what we’re really looking at is something rather static.

The kaleidoscope, for me, serves as a wonderful analog to politics. Here the pieces are “interests” of every conceivable kind—economic, ideological, religious, philosophical, social. They arise from unchanging human characteristics; only such characteristics—never anything creative or original—ever become visible within collectives. The gravity is self-assertion. The mirrors are the media. The kaleidoscope of politics is, to be sure, many-fold more complex. The pieces are capable of changing color, size, and shape, but the moving force behind them remains the same. Each election is yet another turn of the device—but afterwards, although the image changes, nothing else ever does.

Those poor little pieces of glass. I bet, deep down, strange yearnings make them long for the ocean beach. They would, if they could, escape and return to nature, once more moved, when moved at all, by the surging surf. And at vast intervals in glass-bead time they would see, say, the brief visit of a gull and the even more rare descent of an exploring beak.

One Jewel in the Crown

Entering my library last evening, I encountered a small round table prominently positioned in the entry passage. On it lay some six stacks of stark, white Xeroxed pages. They spelled out the grim facts of our local system’s financial woes. The Grosse Pointe communities in Michigan are unambiguously wealthy, but our library is suffering. Property values have plummeted and with it property taxes; our library gets 91 percent of its revenues from that source. County and state aide to libraries have shrunk 26 percent since 2007. We are now facing a 45 percent cutback on collection purchases and a 50 percent cut in administrative services—never mind all the rest. This leaflet, to be sure, is intended to drum up support for a millage rate increase. The library won’t close anytime soon. But it brought back a recurring thought: libraries are certainly at least one jewel in the crown of higher culture. I watch their health closely as an indicator, only too aware that the higher ranges of human experience depend on helpful institutions, and those, in turn, on a certain order and degree of wealth.

In the small circles of those concerned with books, the words of Ammianus Marcellinus, a sardonic fourth century Roman historian of Greek origin, echo. A gruff rhetorical phrase in his writings, describing his environment, was “libraries closed like tombs.” The time referred to was 380 AD. Now, to be sure, it was just a throw-away remark more intended to convey a flavor than the results of an exhausting census; we hear such comments quite often in our day as well. Careful scholars like George W. Houston (writing in the Library Quarterly in 1988) point out that Ammianus did not mean public libraries; they survived in the West at least until 455 AD. But you get my drift; the death of the Roman Empire did spell the death of such public institutions.

I got to wondering about those Roman public libraries. They existed, sure enough, but had a different character than our lending libraries. Books, meaning scrolls, could be taken out and read—not at tables but in surrounding gardens, standing in the shade or walking about; under the eaves in the shade, as it were. Public readings were a common feature at these places so that even those of the great majority who could not read could gather and hear books read aloud. Books, literature, learning, the intellectual, the spiritual life belong in some ways to the immaterial dimension so that their structures are really relationships between people of like interests. But in this realm we can’t partake of any kind of community without physical underpinnings. These require stalwart votes to pass that temporary millage increase. Failing that, here in Grosse Pointe, one of the jewels in the crown of the Detroit metro area, we will lose one of our three library branches and face 30 percent cutbacks in hours and in staff.

Even the Sky

Everybody’s voting in New Hampshire tonight, including the Michigan sky. But the light breeze high up had already erased the name of the candidate by the time we saw the Sky, its X.

Quick Update of McLuhan

The tedium is the message.

Language and Meaning

Language is the carrier of meaning. A source of useful contemplation for me of late has been the possibility of communication by meanings alone, dispensing with the carrier. Not that that’s possible in this dimension, but it may be possible in the Beyond. The thought here is that the carrier actually influences that which it carries. There is Marshall McLuhan’s famous aphorism, The medium is the message. Supposing that we are awaiting the Dalai Lama. Here is this ornate pillared building and the crowd is on wide steps leading up to it, a wide boulevard below. And here comes the Dalai Lama—on a bicycle. The bicycle is his carrier. But suppose the Dalai Lama arrives in a long, sleek limousine. Three or four people stumble out first, not least the chauffeur, wearing a uniform. Finally the Lama himself clad in Tibetan robes. Yet another image. The Lama comes by helicopter—and the furious wind of his descent make people raise their hands to fend off the blast of air. The carrier modifies the meaning. — Abrupt shift. — For me the words “original sin” carry a very potent meaning. In many ways it is one of the most useful meanings for understanding at least human reality. But the words that carry it also carry extra baggage that causes many people to reject their meaning. We would agree on a whole lot more things if meanings came to us naked.

Libraries Don’t Vanish

Several hours of Internet outage this morning stopped my habit-world dead in its tracks. My mornings are spent on the web, and the outage made me feel as if someone big had sat down on my chest. It took me a few aimless circles around obstructions down in this basement before vague memories returned. Ah, yes. Back in the Long Ago. I used to write on paper with a pen under a bright light. And all else equal I might have read a book. I had worked in the Long Ago. Back then the telephone facilitated communications, but the work proceeded on paper. The institutional support was the publishing industry and libraries. Libraries sometimes closed, but they did not disappear. Nor did the books of publishers when they went out of business. The books remained on shelves. Answers were difficult to get, to be sure, and it took longer to get them.

Back when the world began, thus in Tirschenreuth immediately after World War II, we had no libraries; indeed it took two or three years before even a tiny bookstore opened. At first we had no newspapers either. Later on, living in Staufenberg to the west, the nearest so-called library was in Gernsbach three kilometers away, and we paid a small fee there for every borrowed book. Indeed, when I come to think of it, that was the only library I ever visited in Germany. In Kansas City, after our arrival here, weekly trips to the downtown library became a sacred ritual.

I went upstairs to commune with Brigitte. Libraries. In Europe. She is some years my senior and remembers more about those times. The war had no sooner ended, she relates, than the occupying powers caused all libraries to close. Bang. You can hear doors slamming and the locks clanging shut. Why? Well, libraries were ordered to sanitize their contents—to remove all traces of history-rewritten produced by the Nazi powers. In her school library in Weissenfels, whole shelves were actually covered with signs forbidding even touching books. A small set of shelves were open to the students—while ideological cleaning proceeded. The city’s main library, a grand structure, stood dead and mute for years. Call it a library outage. But the physical structure still remained.

Everything has a silver lining. Last time this happened I went half crazy talking to recorded voices at AT&T and resetting two computers at regular intervals for the better part of a day. But it turned out that the Internet returned miraculously all on its own. Did so again today. I wrote on paper. I read a book. A novel experience in the morning. Brought back memories of another time. Not all bad, the Long Ago. I seemed to have a lot more time this morning.

Dust Bunnies

An addendum to the last post. Having to do some basement cleaning today, a thought occurred. If Maxwell, Lorentz, Einstein, and countless other physicists had expended their energies and equations on how dust bunnies form—and applied the resulting insights to the improvement of brooms—they might have benefitted me, today, a whole lot more than by thinking deeply about spacetime.

Has a Crack Appeared?

I came across an interesting and recent development in physics dating to 2009. The Scientific American reported on the matter on November 24, 2009 (link); New Scientist had an article on it dated August 9, 2010; that article is not online, but a summary of it is presented by The Daily Galaxy (March 24, 2011, link).

The discoverer in question is a physicist working at the University of California, Berkeley named Peter Horava or Petr Hoyava or, most likely, Petr Hoava. (That box stands for an r with a caron on top of it; the ASCII code is not recognized by Blogger.) Horava is also, according to Wikipedia, a member of the theory group at Lawrence Berkeley National Laboratory. Horava’s discovery, working with an allotrope (read “form of”) carbon known as graphene, is that the behavior of this carbon at near absolute zero temperatures suggests that Einstein’s spacetime may not be real at all, that gravity acts differently in different temperatures, that the warping of space and time by mass may be illusory. What we see is caused by gravitation which does not act uniformly everywhere. This view appears to confirm  the claims of quantum physics that gravity is due to an exchange of particles, like electromagnetism, in this case the graviton, not due to the deformation of spacetime.

Now this discovery is beginning to make waves for a reason. It promises, finally, a unified theory of gravitation which will make the results observed by general relativity and quantum physics agree with each other—but, to be sure, at some expense to General Relativity’s claim to universal applicability. Well.

And there is more. As might be expected, views of black holes, the big bang, dark matter, dark energy, and the expansion of the universe all appear in very different light. For this reason, rather than summarily dismissed, Horava’s suggestions and modified equations are getting a lot of attention from quantum physicists.

I note this here because spacetime is my favorite bête noire. Yet it is so fundamental to general relativity that any crack that separates those two words means a revolution in physics. Unfortunately I cannot hope personally to check the results however much I’d like to. It would require me to master Maxwell’s equations presented in his On Physical Lines of Force (link), the Lorenz transformations that “correct” or “complete” them, and—for that matter—the evolution of concepts as rendered in the language of mathematics all the way from the days of aether to the present. I haven’t got the right stuff. But I have a very keen intuition!

Math Note

The book under consideration is Morris Kline’s Mathematics: The Loss of Certainty. Wonderful book—and a nice companion to one I’d recently read on Hellenistic Science (link on this blog). For as long back as I am able to remember, I’ve always thought of mathematics as a language—natural, perhaps, for someone like me who had to master three languages beyond my mother tongue before I was sixteen—and someone who got deeply into computers more or less by playing around with their insides. This work tells me that math was long and traditionally viewed as something else—the code deeply embedded in Nature and revealing the secrets of God’s design. The loss of certainty, therefore, is a modern phenomenon, another great disillusionment—but one I had been spared. Math viewed as language explains more. It suggests that math has two aspects: its rules of application, thus its grammar, and the meaning assigned to perfectly legal equations and functions—which may be quite defective.

‘Twas brillig, and the slithy toves

Did gyre and gimble in the wabe:

All mimsy were the borogoves,

And the mome raths outgrabe.

     Lewis Carroll, Jabberwocky

Nothing wrong with the grammar here. Now when it comes to reality, some of the most familiar aspects of which quite escape genuine physical grasp—such as the workings of gravity—giving explanations for them using the pristine grammar of math but meaningless concepts is good fun for toves and the mome.

Old Gifts and New

Today the new brings the old. Quite some time ago my brother, Baldy, discovered that a book had been published about Tirschenreuth, the Bavarian town. It’s a modest place of around 9,000 inhabitants, but one of our important family locations. We lived there as a family as World War II came to an end. Multiple posts here hark back to that place. I’ve intended to mention that book here for a long time, but the means of showing it were lacking. Now a new gift, called the HP Photosmart 5510, provides the means. It is a printer, scanner, copier, and photo printer all rolled into one. Until now I’ve had to photograph books or their contents. Now I have a new tool. Herewith three images produced using Photosmart, beginning with the book itself.

The title of the book is Long Ago in Tirschenreuth. That word, Damals, does not have an actual English equivalent. A forced translation of it is There Once, that “once” not further amplified, but the word’s essence is remembrance. The author is Eberhard Polland, a writer, the publisher is Bücherhaus Rode, Maximilianplatz 38, 95643 Tirschenreuth, Germany. The book appeared in 2010.

An image of the market square (Maximilianplatz formally, but everybody called it Marktplatz) is a kind of signature for this town if the photo includes the town’s church, named Mariä Himmelfahrt (Mary’s Ascension).

The region is blessed with high quality clay deposits, and one of the oldest industries in the region, although not in Tirschenreuth itself any more, is porcelain. One of the producers of the finest high quality porcelain is Falkenpozellan GmbH located not far away in Bärnau on the Czech border. Well, Tirschenreuth was the first, and the factory was right in town—damals. The old ad reproduced in this book of remembrance says on top: “A nurturing place for German quality work.”

My Photosmart is another and this time an American instance of quality workmanship. It speaks to my computer by wireless means; we’ve tried its prowess printing photographs, and, by golly, they look just like the photographs of old, brilliant colors, stiff little pieces of shiny paper. This gift came to me from a virtual person, ECDI, the acronym of our company name. We live in a mysterious world where invisible persons give valuable, tangible gifts. Thank you, ECDI; thank you, Baldy, for that book.

Ordinariate of the Chair of St. Peter

Precisely two years ago I wrote a post (link) on an Apostolic Constitution, Anglicorum Coetibus (Groups of Anglicans). Today comes a story in the New York Times telling us of the first implementation of that constitution. An Episcopal group has been joined in communion with the Catholic Church. Its former bishop, Jeffrey N. Steenson, has been named the Ordinary of the Chair of St. Peter headquartered in Houston. My post explains what an “ordinary” means; by this appointment Steenson becomes a member of the United States Conference of Bishops, indeed the first married priest ever (three children).

Soon after my original posting I noticed that that post began gathering a steady readership. At first I thought the title caused this traffic (When the Ordinary is Extraordinary); then I began to wonder; but the stats don’t really tell you anything. My post had noted an event that had taken place on November 4, 2009 and we had read about in the pages of the The American Conservative. The odd coincidence of today’s story on that subject, first broached January 2, 2010 here, appearing in the paper on January 2, 2012, makes me think: Meaningful coincidence. So here it is, recorded.

Recalling Eliade

Full turns of Time’s big wheel always cause me to recall Mircea Eliade (1907-1986). He was one of the chaotic but inspired thinkers who influenced people like me, thus people who rashly jettisoned tradition, religion in youth. People like me needed guides who seemed to have embraced the modern but then had come to doubt it. Another such was Carl G. Jung. I was exposed to such brilliant modern interpreters of the traditional as Etienne Gilson, but stuff like that flowed over me and left no trace. Traditionalists did not engage the world I thought I knew. Brought up in, but rejecting, a tradition in which the liturgical year played a major guiding influence, I had to read a book like Eliade’s Cosmos and History: The Myth of the Eternal Return before I intuitively understood the genuine meaning underneath such structures as the liturgical year. To think of myth as actual, real, here and now—that’s something of a leap. But exactly the same process fashioned my approach to mathematics. I was taught it in the traditional way—which assumes that I’ll be a good boy and simply cram the information, learn the rituals, and accept all that without intuitive assent. I didn’t. I put math right next to religion as something to be despised—useful in minor ways but beneath the dignity of genuine engagement. Until later—when I tackled the subject on my own.  Odd this. But there always will be people of my sort who don’t take well to regimentation—those for whom, in fact, regimentation is a signal that something must be viewed as dead. Education can’t be mechanized—not the real thing. But teaching anything at all effectively is extremely expensive in time and money. But when it’s done right, at least we get something for the effort and resource expended.