Quotable Words: The Mathematical Experience


Re-reading a classic by Philip J. Davis and Reuben Hersh that I first encountered in college. They are the perfect guides to math as a human endeavor, and its many touch points with non-STEM disciplines. Here they are quoting Herman Weyl about the uses of infinity…

 …purely mathematical inquiry in itself, according to the conviction of many great thinkers, by its special character, its certainty and stringency, lifts the human mind in to closer proximity with the divine than is attainable through any other medium. Mathematics is the science of the infinite, its goals the symbolic comprehension of the infinite with human, that is finite, means. It is the great achievement of the Greeks to have made the contrast between the finite and the infinite fruitful for the cognition of reality. Coming from the Orient, the religious intuition of the infinite, the άπειροv, takes hold of the Greek soul…

This tension between the finite and the infinite and its conciliation now become the driving motive of Greek investigation.

The Mathematical Experience (1981) p. 108

Advertisements

The Power of the Very, Very Small

Reading a delightful book by Simon Garfield (of Just My Type fame), In Miniature: How Small Things Illuminate the World. As in his other books, he’s droll, magically readable, and a companionable guide to the odd world of the tiny, which, as a Giacometti quote in the beginning points, out is more likely to give you a sense of the universe.

“The creation of small universes in which we may bury ourselves to the exclusion of all else will be at the core of this book.”

Simon Garfield

As a fan of the miniature, I offer three examples (which may or may not have caught his eye, I’m only a third of the way through).

The Thorn Rooms at the Phoenix Art Museum, the Art Institute of Chicago & other museums. Pictures don’t do these justice, of course, as they look like real rooms in reproduction, but when you are in front of them and their 1:12 model proportions, their domestic interiors come alive. They were created by Narcissa Niblack Thorne (1882-1966).

Then there is MVSEVM, at the National Museum of American Art,

which was commissioned for the renovation of that museum, and both honors and questions the idea of a museum.

Finally, there is Miniature Calendar, the meticulous obsession of artist Tatsuya Tanaka.

In Praise of News Print

The paper version of today’s New York Times came with a lovely insert, “The Daily Miracle,” a photo essay on the paper’s printing plant in College Point, Queens. The pictures are by Christopher Payne who has previously documented the making of a Steinway, as well as architectural and industrial topics, and has an eye for process monumental yet personal.

He captures the immense challenge of turning out a daily paper, one particularly resonant now that the materiality of the newspaper has given way to digital, pixels replacing ink, for many if not most. As somebody who makes a living pushing pixels, the physical newspaper seems ever more to to be a pinnacle of a certain kind human activity–of organization, craft, industry, know how, (and this isn’t just my growing up around them as the child of newspaper writers and journalism teachers. Luc Sante captures some of this in his graceful intro essay to the photographs,

The “new”New York Times bldg, c. 1888.

And then you can hold it in your hand, fold it, tear it, use it as a rain hat–a voluminous paper object with visual dazzle and hundreds of thousands of words representing the collected information of that moment: news, opinion, analysis, testimony, critique, charts, graphs, photos, displays. And it happens every day over and over again. Small wonder they call it “The Daily Miracle.”

Luc Sante

The photos aren’t online yet reasonably enough (although I’m betting they will be). So you will have to find a copy of Sunday’s paper. But there is a little info about the series here, https://www.nytimes.com/2019/03/24/reader-center/printing-plant-section-christopher-payne.html .

In the midst of getting sentimental about all things newsprint, I remembered the best printing joke, “What does the sign say in the NYTimes’ compositing room? All the news that fits, we print.”


Also worth noting: March 24 is Lawrence Ferlinghetti’s 100th birthday. He was a grand old man of beat poetry when I was a teenager, and that he is still around–as is his landmark North Beach store, City Lights Books–is enormously reassuring. Barry Mills has an essay worth reading up at Poetry Foundation. To Lawrence, in addition to wishing him the happiest of birthdays, I offer this quote from George Burns, another long-lived good guy, “If you live to be one hundred, you’ve got it made. Very few people die past that age.”

Remembering Mary Oliver

Provincetown poet Mary Oliver died yesterday at 83. Bryan Marquard has written a lovely obit in the Globe, and I’m sure more tributes will follow.

The Summer Day

Two of many of her poems that have stayed with me over the years.

Who made the world?
Who made the swan, and the black bear?
Who made the grasshopper?
This grasshopper, I mean-
the one who has flung herself out of the grass,
the one who is eating sugar out of my hand,
who is moving her jaws back and forth instead of up and down-
who is gazing around with her enormous and complicated eyes.
Now she lifts her pale forearms and thoroughly washes her face.
Now she snaps her wings open, and floats away.
I don’t know exactly what a prayer is.
I do know how to pay attention, how to fall down
into the grass, how to kneel down in the grass,
how to be idle and blessed, how to stroll through the fields,
which is what I have been doing all day.
Tell me, what else should I have done?
Doesn’t everything die at last, and too soon?
Tell me, what is it you plan to do
with your one wild and precious life?

Poppies

The poppies send up their
orange flares; swaying
in the wind, their congregations
are a levitation

of bright dust, of thin
and lacy leaves.
There isn’t a place
in this world that doesn’t

sooner or later drown
in the indigos of darkness,
but now, for a while,
the roughage

shines like a miracle
as it floats above everything
with its yellow hair.
Of course nothing stops the cold,

black, curved blade
from hooking forward—
of course
loss is the great lesson.

But I also say this: that light
is an invitation
to happiness,
and that happiness,

when it’s done right,
is a kind of holiness,
palpable and redemptive.
Inside the bright fields,

touched by their rough and spongy gold,
I am washed and washed
in the river
of earthly delight—

and what are you going to do—
what can you do
about it—
deep, blue night?

One of my nature places, Mt. Auburn Cemetery last fall.

A Little Christmastide Smile

Storytelling goes well with the season (telling a ghost story was once a Christmas Eve tradition). The English satirist Saki (the pen name of H.H. Munro) does capture one response to the holiday.


They say (said Reginald) that there’s nothing sadder than victory except defeat. If you’ve ever stayed with dull people during what is alleged to be the festive season, you can probably revise that saying. I shall never forget putting in a Christmas at the Babwolds’. Mrs. Babwold is some relation of my father’s–a sort of to-be-left-till- called-for cousin–and that was considered sufficient reason for my having to accept her invitation at about the sixth time of asking; though why the sins of the father should be visited by the children–you won’t find any notepaper in that drawer; that’s where I keep old menus and first-night programs.

Mrs. Babwold wears a rather solemn personality, and has never been known to smile, even when saying disagreeable things to her friends or making out the Stores list. She takes her pleasures sadly. A state elephant at a Durbar gives one a very similar impression. Her husband gardens in all weathers. When a man goes out in the pouring rain to brush caterpillars off rose-trees, I generally imagine his life indoors leaves something to be desired; anyway, it must be very unsettling for the caterpillars.

Of course there were other people there. There was a Major Somebody who had shot things in Lapland, or somewhere of that sort; I forget what they were, but it wasn’t for want of reminding. We had them cold with every meal almost, and he was continually giving us details of what they measured from tip to tip, as though he thought we were going to make them warm under-things for the winter. I used to listen to him with a rapt attention that I thought rather suited me, and then one day I quite modestly gave the dimensions of an okapi I had shot in the Lincolnshire fens. The Major turned a beautiful Tyrian scarlet (I remember thinking at the time that I should like my bathroom hung in that color), and I think that at that moment he almost found it in his heart to dislike me. Mrs. Babwold put on a first-aid-to-the-injured expression, and asked him why he didn’t publish a book of his sporting reminiscences; it would be SO interesting. She didn’t remember till afterwards that he had given her two fat volumes on the subject, with his portrait and autograph as a frontispiece and an appendix on the habits of the Arctic mussel.

It was in the evening that we cast aside the cares and distractions of the day and really lived. Cards were thought to be too frivolous and empty a way of passing the time, so most of them played what they called a book game. You went out into the hall–to get an inspiration, I suppose–then you came in again with a muffler tied round your neck and looked silly, and the others were supposed to guess that you were “Wee MacGreegor.” I held out against the inanity as long as I decently could, but at last, in a lapse of good-nature, I consented to masquerade as a book, only I warned them that it would take some time to carry out. They waited for the best part of forty minutes, while I went and played wineglass skittles with the page-boy in the pantry; you play it with a champagne cork, you know, and the one who knocks down the most glasses without breaking them wins. I won, with four unbroken out of seven; I think William suffered from over- anxiousness. They were rather mad in the drawing-room at my not having come back, and they weren’t a bit pacified when I told them afterwards that I was “At the end of the passage.”

“I never did like Kipling,” was Mrs. Babwold’s comment, when the situation dawned upon her. “I couldn’t see anything clever in Earthworms out of Tuscany–or is that by Darwin?”

Of course these games are very educational, but, personally, I prefer bridge.

On Christmas evening we were supposed to be specially festive in the Old English fashion. The hall was horribly drafty, but it seemed to be the proper place to revel in, and it was decorated with Japanese fans and Chinese lanterns, which gave it a very Old English effect. A young lady with a confidential voice favored us with a long recitation about a little girl who died or did something equally hackneyed, and then the Major gave us a graphic account of a struggle he had with a wounded bear. I privately wished that the bears would win sometimes on these occasions; at least they wouldn’t go vaporing about it afterwards. Before we had time to recover our spirits, we were indulged with some thought-reading by a young man whom one knew instinctively had a good mother and an indifferent tailor–the sort of young man who talks unflaggingly through the thickest soup, and smooths his hair dubiously as though he thought it might hit back. The thought-reading was rather a success; he announced that the hostess was thinking about poetry, and she admitted that her mind was dwelling on one of Austin’s odes. Which was near enough. I fancy she had been really wondering whether a scrag-end of mutton and some cold plum-pudding would do for the kitchen dinner next day. As a crowning dissipation, they all sat down to play progressive halma, with milk-chocolate for prizes. I’ve been carefully brought up, and I don’t like to play games of skill for milk-chocolate, so I invented a headache and retired from the scene. I had been preceded a few minutes earlier by Miss Langshan-Smith, a rather formidable lady, who always got up at some uncomfortable hour in the morning, and gave you the impression that she had been in communication with most of the European Governments before breakfast. There was a paper pinned on her door with a signed request that she might be called particularly early on the morrow. Such an opportunity does not come twice in a lifetime. I covered up everything except the signature with another notice, to the effect that before these words should meet the eye she would have ended a misspent life, was sorry for the trouble she was giving, and would like a military funeral. A few minutes later I violently exploded an air- filled paper bag on the landing, and gave a stage moan that could have been heard in the cellars. Then I pursued my original intention and went to bed. The noise those people made in forcing open the good lady’s door was positively indecorous; she resisted gallantly, but I believe they searched her for bullets for about a quarter of an hour, as if she had been an historic battlefield.

I hate traveling on Boxing Day, but one must occasionally do things that one dislikes.

The Christmas Music You Need Right Now!

Three bits of music to make your holiday bright.

1. A cover of “Santa Claus is Coming to Town” that makes you very curious about what he will do when he gets there. It will be fun I bet, if he plays guitar like this!

2. The Bach Double Violin Concerto swings (not a Christmas piece per se, but Bach always seems to go with the holidays). His musical also takes so well to jazz: makes you wonder about the space time continuum.

 

3. Finally, the hymn “While Shepherds Watched Their Flock by Night”–as set by Daniel Read, a Colonial American composer. It’s performed by a professional choir, but in a vernacular shape note style (of which more at a later date). 

Merry Christmas!

Talking Heads: Maggie Smith + Alan Bennett

Seeing that Alan Bennett had a new play out and another touring sent me back to his mid-80s monologues, Talking Heads, which were originally written for the BBC and later performed as stage pieces (including at DC’s Studio Theater). Wonderful examples of giving an actor a deck of narrative cards and letting them turn them over one by one over the course of 40 or so minutes. The result reveals an arc that neither the audience nor the performer quite expected, often a quietly devastating report on the compromises and indignities of everyday life, and yet droll and funny.

The performances were also great–Bennett himself in one–and most memorably Maggie Smith as a vicar’s life in an Anglican parish in  A Bed Among the Lentils. It’s long, but worth watching the whole thing.

Callas + Tebaldi = Caballé

News came down last week that the great Spanish soprano Monserrat Caballé has died. There’s a nicely done obit in the New York Times  with some wonderful excerpts of her singing (check out the pianissimi in the Granados bit from YouTube).

And she is the focus of the beginning of the Gramophone Podcast .   It’s from there that the Callas + Tebaldi equation comes. James Jolly of Gramohphone reports that this was the Times’ headline on Caballe’s history making debut in New York City in 1965, substituting for Marilyn Horne in a performance of Donizetti’s Lucretia Borgia at Carnegie Hall. I will have to look up the clipping to confirm, but the general idea seemed to be that Caballé combined the beautiful sound of Renata Tebaldi, the Italian soprano beloved for her creamy middle register and warmth in Puccini and Verdi, as well as the dramatic fire of Maria Callas, whose roles ranged further than Tebaldi’s, particularly to the orate bel canto operas which she helped revive, and Caballé went on to triumph in. (In truth Callas could make beautiful sounds and Tebaldi had dramatic power to spare in the right roles, but the analogy still rings true.)

There is also about all three–and many singers before and since–that x factor of vocal charisma, a sound that seems to saying something personal to you and always catches your attention.  Caballé has it and is one that set a template for a life time of loving opera for me. Perhaps something to attribute at least in part to first encountering her singing as a 13 year old (during my age inappropriate introduction to opera). Everything about her sound, the distinctive vocal color, the the odd glottal stop sound you could hear in her pronunciation, and most of all the ability to spin out soft high notes that that seemed like she was breathing for you. Soft enveloping sound is not what comes to mind first in opera, but those moments are many and she excelled in them.

So in love with her voice was I that I did what any teen does. Played her records over and over and made anybody I could listen to her. My go to introduction “Signore Ascolta” from  Turandot which ends with with one of those magical high notes. Here it is from a concert.

And here is something I’ve always loved, and should be in the dictionary under “soft high singing: perfection,” “Dupuis le jour” from Louise. (Not sure of the source: maybe from a gala performance for Rudolph Bing.)

 

It seems like the music you hear as a teen sets a template for what “music is” and for me at least Caballé’s sound will always be a big part of what “opera is.”  I’m grateful for that.

Let Slip the Dogs of War

Computer security guru Bruce Schneider’s “Cryptogram” for September has a frightening look into cyberwar of the future, courtesy of an excerpt from a Center for Strategic and International Studies report.

The U.S. secretary of defense had wondered this past week when the other shoe would drop. Finally, it had, though the U.S. military would be unable to respond effectively for a while.

The scope and detail of the attack, not to mention its sheer audacity, had earned the grudging respect of the secretary. Years of worry about a possible Chinese “Assassin’s Mace” — a silver bullet super-weapon capable of disabling key parts of the American military — turned out to be focused on the wrong thing.

The cyber attacks varied. Sailors stationed at the 7th Fleet’ s homeport in Japan awoke one day to find their financial accounts, and those of their dependents, empty. Checking, savings, retirement funds: simply gone. The Marines based on Okinawa were under virtual siege by the populace, whose simmering resentment at their presence had boiled over after a YouTube video posted under the account of a Marine stationed there had gone viral. The video featured a dozen Marines drunkenly gang-raping two teenaged Okinawan girls. The video was vivid, the girls’ cries heart-wrenching the cheers of Marines sickening And all of it fake. The National Security Agency’s initial analysis of the video had uncovered digital fingerprints showing that it was a computer-assisted lie, and could prove that the Marine’s account under which it had been posted was hacked. But the damage had been done.

There was the commanding officer of Edwards Air Force Base whose Internet browser history had been posted on the squadron’s Facebook page. His command turned on him as a pervert; his weak protestations that he had not visited most of the posted links could not counter his admission that he had, in fact, trafficked some of them. Lies mixed with the truth. Soldiers at Fort Sill were at each other’s throats thanks to a series of text messages that allegedly unearthed an adultery ring on base.

The variations elsewhere were endless. Marines suddenly owed hundreds of thousands of dollars on credit lines they had never opened; sailors received death threats on their Twitter feeds; spouses and female service members had private pictures of themselves plastered across the Internet; older service members received notifications about cancerous conditions discovered in their latest physical.

Leadership was not exempt. Under the hashtag # PACOMMUSTGO a dozen women allegedly described harassment by the commander of Pacific command. Editorial writers demanded that, under the administration’s “zero tolerance” policy, he step aside while Congress held hearings.

There was not an American service member or dependent whose life had not been digitally turned upside down. In response, the secretary had declared “an operational pause,” directing units to stand down until things were sorted out.

Then, China had made its move, flooding the South China Sea with its conventional forces, enforcing a sea and air identification zone there, and blockading Taiwan. But the secretary could only respond weakly with a few air patrols and diversions of ships already at sea. Word was coming in through back channels that the Taiwanese government, suddenly stripped of its most ardent defender, was already considering capitulation.

What is particularly frightening about this scenario is that it hardly seems to require whiz-bang technology, just social engineering to exploit ordinary human issues, albeit on a massive scale. Think for a moment if a chaos-sowing counterpunch came, and effectively destroyed the ability of world to process electronic payments, keep the lights on, have a functioning transport system, if only for a day or two. Let’s hope the scenario remains the domain of science fiction.