Archive for April, 2012

A deep coincidence

Tuesday, April 10th, 2012

Next Sunday many people are going to be writing about the sinking of the Titanic.

I thought it would be nice if at least one person celebrated a somewhat more hopeful moment: Today is the 100th anniversary of that great ship’s maiden voyage out of Southampton on her way across the Atlantic.

This is also an occasion to note the following numerological oddity: The ship sank in the year ’12, on 4/15 (on Sunday, when we commemorate the anniversary of that great tragedy, it will of course also be the year ’12, on 4/15).

And where now lies the wreck of the RMS Titanic? Down under the sea, at a depth of exactly 12,415 feet.

Mere coincidence?

Sketching Abraham Lincoln

Monday, April 9th, 2012

The other day, while lecturing to a class, I wanted to use some well known historical figure within a thought experiment. So in about five seconds I drew something like the following on the blackboard, and then I continued: “Imagine if Abraham Lincoln…”

But then I paused for a moment, looked at the picture, and said “It’s funny. if I just took away the hat, it would be Jesus.”

The class laughed, but the thought stayed with me. How little do you need to draw in order to invoke any given famous person? Perhaps we can rate iconic public figures on a scale — the simpler the drawing required, the more iconic the figure.

What would be the equivalent visual sketch for Elvis or Marilyn, Groucho or Woody, Garland or Sinatra, Nixon or Thatcher, Chaplin or Hitchcock, Lennon or McCartney, Freud or Einstein, Hitler or Gandhi?

In some cases we might get it down to very little indeed, such as John Lennon as a pair of glasses. Perhaps we could apply some sort of information theoretic analysis, in the spirit of Claude Shannon, to rate our historical icons.

I wonder who would come out on top.

iPad as 8-track

Sunday, April 8th, 2012

We now know for sure that sometime in the near future Google will be coming out with a consumer-wearable heads-up augmented reality display. And simple logic tells us that its major rivals are hard at work on similar competing platforms.

Which means that soon there will be no reason at all for whatever cyber-information you are looking at to require a display screen. Any convenient wall, table, pants leg, your friend’s shirt, or the spaces in between can show the info you need. In the scheme of things, we are rather close now to an eccescopic world.

Which means that the iPad and its many imitators may soon be as out of date as an old 8-track tape player. For all of the current excitement around these tablet devices, they may shortly come to be seen as one of those transitional technologies that seems, in retrospect, oddly quaint.

A secret chart

Saturday, April 7th, 2012

Leonard Cohen once said “please understand, I never had a secret chart to get me to the heart of this or any other matter.” I suspect the man was being disingenuous. If anybody has a secret chart, Leonard Cohen does.

Today I went back through about the last year or so of my blog, and I realized that I have been compiling my own secret chart. Behind every post — — and every sequence of posts — there is a deeper story, one that is not explicitly revealed on the page. I suppose this is the case for all writers.

In my own case, I can recognize the stretches of time when I was feeling joy or excitement, restlessness or despair. Some posts are painful to read now because they bring me back to a moment in my life when I was dealing with something quite difficult, and others are a delight to read because they take me back to a time when things were flowing, and everything felt deeply right.

In some ways a blog and a journal are precisely opposite forms. In a blog you say only what you are prepared to be heard by the entire world. In a journal you pour out everything that you wish to be heard by your own heart.

Yet in both cases, there is a chart, drawn by your words, tracing out the changing contours of your inner life. There is, most definitely, a chart.

Floating displays are the new robot

Friday, April 6th, 2012

In certain vintage SciFi, the key signifier that you were in a cool futuristic world was the presence of robots. “Metropolis” had its robot Maria, “Forbidden Planet” had Robby the Robot, “Star Wars” had R2D2 and C3PO, and “Lost in Space” had an endearing Class M-3 Model B9, General Utility Non-Theorizing Environmental Control Robot.

But it seems we have moved on, and robots are sooo yesterday’s tomorrow.

Now your future requires a flat rectangular display that floats in midair, as recently seen in “Iron Man”, “Eureka”, “District 9”, “The Hunger Games” and a host of cheesy commercials by everyone from Apple Computer to Microsoft to Corning Glass.

Why these displays need to be rectangular is anybody’s guess. It is one of the eternal mysteries, like the question of why that magical object for instant gratification you are holding in your hand needs to be so artfully rounded (I meant your SmartPhone. Please get your mind out of the gutter).

The change makes sense. In 20th century America, the robot was a signifier of an essentially industrial economy — the “impossible object” that represented the technological aspirations of such an economy.

The magical rectangular display floating in the air is the corresponding impossible object to signify the technical aspirations of an information-based economy.

Once we have moved on, in another twenty years or so, to a nano/neuro-based economy, I wonder what we will choose as our new impossible object.

First impressions

Thursday, April 5th, 2012

In response to yesterday’s post, Dagmar said: “A beautiful body doesn’t attract me, only a beautiful mind does.” I think she was referring to the clichĂ© that first impressions are about appearance.

But I don’t think that is true. There are a lot of objectively beautiful people out there, but for the most part we don’t find them compelling. There is actually something off-putting for many people about seeing a vacant soul within a beautiful shell.

The great movie actors capture us not because of their looks — although they generally (though not always) look quite presentable — but because we are drawn in by something about their movement, the way they speak, their facial expression, a light in their eyes.

Then, having seen them perform, we associate the way they look with beauty, and so we come to view their appearance as the epitome of attractiveness.

I think this is also true in our personal lives. We are each far more intelligent than our conscious minds and our cultural limitations generally permit us to be. This intelligence allows us to acquire a vast amount of information about another person’s essential being in the very first moments that we meet them. But we have neither the language nor the skills even to understand that we have acquired that information, let alone to fully process it.

It is this knowledge — derived not from some voodoo magic, but from the full functioning of our own brains — that can cause us to be instantly attracted to another person. It is not their physical appearance that attracts us. Yet we will persist in believing that it is, because the truth seems preposterous.

Smashing walls

Wednesday, April 4th, 2012

You, being human, have a barrier around you, a kind of semi-permeable membrane. Most of the time the people you meet stay firmly outside this membrane. You talk with them, perhaps work together, share a joke or two, but there is a point beyond which they cannot go.

They have a barrier around them as well which, it is understood, you cannot trespass. Occasionally you will get glimpses of the terrain that lies beyond, but if you are smart you know to keep those insights to yourself.

These walls are firmly established, carefully tended to. We keep them in good repair. On occasion we bring out the plaster and paintbrush to patch up a spot here, cover over a stain there. As we work we usually ignore that wrecking ball sitting in the corner.

The wrecking ball of course is sexual passion — those romantic connections that can spark in a moment, thereby keeping the world populated. You never know when that old machinery will fire up and get to work on some spontaneous wall smashing. It’s exhilarating work, that smashing down of walls, all explosions and flying debris.

Afterward, when things have run their course, you might be left with nothing but a big gaping hole in your wall, one that perhaps provides an unsightly view to your inner world, of some unfortunate pile of dirty laundry suddenly in plain sight.

At which point you grab your spatula and your paintbrushes, and you patiently get to work fixing up the wall.

Secretly hoping, of course, that one day something else will come along and smash into it.

Upon hearing from a friend in Hawaii

Tuesday, April 3rd, 2012

A friend just sent me an email all the way from Hawaii.

As I was reading her message, I was perfectly aware that it is, in fact, a lovely day here in New York. Spring has sprung, and the weather is becoming downright reasonable. The gods, it seems, having forgiven us our trespasses, have at last relented from their long vernal temper tantrum.

Yet my memories of Hawaii — of Kawaii, of Maui, of lush trees and glistening blue ocean, of long mountain hikes and finding shells by the cool breeze off the shore — remind me that even a beautiful sunny day in Manhattan is not, how shall I say, a day at the beach.

There is a certain kind of peace and calm that is simply not what we are about, here on our teeming shore.

And I think about my friend, happily observing the waves or reading some escapist novel from her shaded chaise by the beach, and I am delighted for her.

The infinite revolution

Monday, April 2nd, 2012

Tucked away inside yesterday’s blog was one of the most important innovations in the entire history of mathematics — the ability to deal with infinitely small things. This innovation was independently developed by Newton and Leibniz in the mid-seventeenth century — the former working in England, the latter in Germany.

Infinity is a slippery thing, and naive questions like “What’s the value of one divided by zero” can just result in nonsense. What both Newton and Leibniz realized is that you can sneak up on infinity — by starting with two finite things, and then sending them both off to infinity together.

And that’s exactly what yesterday’s discussion about e was doing: A naive statement like “Something infinitely close to one raised to an infinitely big power” — would produce no sensible answer. So instead we put a throttle on both parts of this statement, by sending several finite things off to infinity and watching where the result heads off to.

It’s a little like sending a rocket ship into space. You can’t see the rocket ship after it has left the solar system, but if you know enough about its launch trajectory, you can predict where it will be in the sky even after it has become too small to see.

In the case of yesterday’s discussion, (1 + 1/n) gets closer and closer to 1, as n gets bigger. Meanwhile we are raising to a progressively higher power. The result (1 + 1/n)n indeed converges to a single number — e = 271828… — as n becomes ever larger, and our little rocket ship disappears into the night sky.

So many aspects of our modern life — the fruits of research into physics, biology, chemistry, electronics, economics, manufacturing, computers, vehicle design, and much more — depend on this astonishing innovation from over three hundred years ago. It really is a kind of infinite revolution.

Getting your grandmother’s interest

Sunday, April 1st, 2012

A colleague of mine once asked me if I knew of any way to give a simple intuition for the value of e, the base of the natural logarithms. He was teaching a class to non-technical students, and he said he had no problem giving them an intuition for the value of π. After all, π is just the ratio between circumference and diameter: How far it takes to travel around a circle (or around the rim of a glass of beer) divided by how far it takes to travel across the same circle (or the same glass of beer).

“I wish,” he said, “there were some way to explain the value of e that was so simple my grandmother could understand it.”

As it happens, I saw my friend Josh the next day, and posed the question to him. “So you want your grandmother to understand the value of e? No problem,” Josh said. “Here’s a way that’s guaranteed to work.”

“One thing grandmothers understand is saving their money in the bank,” he continued. “You tell your grandmother `Look Grandma, suppose you put a dollar into a bank at 100% interest. At the end of a year you will have two dollars.'”

Grandmothers, he assured me, understand this kind of thing.

Now suppose there’s another bank down the block that also gives 100% interest, but which compounds every six months. If you invest your dollar there, then at the end of six months you have $1.50, and at the end of a year you have 3/2 as much again, or $2.25. Chopping the year into two pieces definitely makes for a better investment.

Further down the block is another bank that offers to compound once a month, chopping the year into 12 pieces, giving you an even higher return. A fourth bank compounds every day, chopping the year into 365 little pieces, and the returns just keep getting better.

Finally, you come to a bank that compounds continually. At every moment it’s giving you (1 + 1/n) of your money, where the year is chopped into n vanishingly small pieces. That bank gives you the best value for your money. In fact, at the end of the year, your one U.S. dollar has turned into two dollars and 71.828183… cents, or e.

A formal definition of e is actually the limit of (1 + 1/n)n as n goes to infinity. And that’s what you just explained to your grandmother.