北京麻雀 (Sparrows of Beijing)

北 Beijing 2008 - 5

5

A Compilation of Nash and Newberry

- John Nash

He was scribbling and scrolling and doodling and drawing, and all things that one needs to know to not be doing business as usual. He was supposed to be doing something usual and instead was doing something unusual, so as not to be distracted by other things that should not be even mentioned. But in the back of his mind was something more important. In fact, far more important than Go – it being Japanese players who popularized the game of doing nothing more than placing dots on a grid. What he was thinking about betting on the turn of the cards - “poker.”

Turn of phrase - when every single equation could be surmounted with ease. In fact, he would do so in the flash of an eye just because he could. He would do so just to prove to his roommate that he could. Even though no one else could see that roommate. He knew he existed if no one else could.

Turning the cards in his mind and working out the best way of a three-clear game – he had heard once from some German professor that three was the magic number. But instead of walking through individual cards, he was walking through cards in general, and working out at which point the cards favored not to bet, as opposed to when they should. This line, he then realized, was the equilibrium line – not just for poker, but any gain that could be played. Well, any game that was finite, the infinite games were another story. Not that he would not solve it eventually, but it was a different order of problems to solve. Again, not that he would not solve it in some later paper.

Equations then are written out, somewhat haphazardly. It was beauty in the mind if not on the first paper – but someone would clean it up, that is what people who devoted their lives to putting markings on the paper did, after all. But he was not interested in the lexicon of paper and ink, particularly, though he would have to master this. A knew that there was origami, which was tempting his Vitra passer, and he would have to sit down and master it.

Here, sitting in the library, he would not call it the “Nash Equilibrium”—not because he was not sure it would be called that, but because he would leave it to others to label. He was sure they would, so why bother to explain to them? He copied out the words again because he realized that even he did not understand. And this would not do; it was a short paper, and therefore, it had to be precise.

So, he copied the first pages over again, making clear details that had been foggy. He did not even look at what he had done; he stuffed it in an envelope and sealed the finely mottled back stickup on the envelope. He then hesitated and finally realized that he did not know how many stamps it would take.

This was an annoyance, but perhaps it was best to do so now rather than later.

Thus, he stood up, looking both ways - because you never know who is watching. He settled his feet and strutted out into the vast inside of his mind, thinking of all the games – even ones he did not know the rules. It was a light from a shadow unseen.

- Sterling Newberry

It was a laboratory, more specifically a commercial laboratory. Every bit of wood, steel, and machinery was accounted for. Everything had a purpose. And in this particular case, it was something that once upon a time had been declared impossible. In 1913 the preeminent thought of the day was that if one captured X-rays and used it in the same way that light was used – it would take a mile to cross the X-ray in the same way. Of course, the obvious reasoning was that this would be impossible, and therefore no X-ray microscope could ever be imagined to exist at all.

But many years later, someone came up with the idea of grazing the X-rays against a filter. Think of it as just a kiss on the X-ray lens, instead of blazing the way that light would be diffracted. This was not good enough to be marketed, but it did show pictures. And so, there was a hunt for the right material that would do a better job and thus be the first commercial X-ray microscope.

Down here with neon white light shining on faded white walls, with gray steel bookshelves to refer to notes, one man tried the same thing as the others. He toiled away at this, first taking electrons and absorbing them to get X-rays. Then after it hit a block of tungsten, it was then focused into the grazing chamber. It was in the late afternoon that one of the technicians grabbed him on the cuff. And begin talking in, for a technician, a mindless babbling of words. It would take me about 10 pages to describe what he said and the interruptions that Newberry put to him. And he was taciturn and listened for more than he spoke.

What was happening was this: the technician did not believe that the light was really being absorbed by the detectors. Newberry rolled his eyes because he knew that at least 10 times all the technicians had been trained to believe that while they could not see it, there was indeed light passing through this, just X-ray light. Which was far far far too short for human eyes to see. So, what happened with the technician is he grabbed his badge – which had a filter for x-rays – and took a screen, with many captures of light – and stuck the two of them in the way of the light source.

But what happened next surprised the technician. Yes, he saw the screen—but he saw a different screen, and it was not the same as what he had popped in. Sterling Newberry knew that the second image was very, very small and was, in fact, the mounting screen for the image—enlarged.

It was enlarged by enough to see the screen, whereas, in reality, it was thousands to an inch. But here it was. About a millimeter, which was several times its real size. It was then that an idea struck him, though it would take some doing to adjust and expose the X-ray light.

What the idea was was this: do not take the X-ray light, instead take the shadow, and enlarge this shadow until it is visible. So, one step was to take electrons and convert them into two X-rays. The next step was to take the X-rays and shine them through what you want to look at, then far away but photographic film for X-rays to capture the light.

What he and no one else would understand, is that the theory of Nash and the experimental of Newberry were the same thing. Because in the game one player puts up money, but it does not mean that it is at risk until someone else puts up money to bet against it. This is the same way that an X-ray does not do anything until there is a picture to capture its light. It does no good for it to pass through the specimen, except if there is a photographic plate to capture. Just as it does no good for a man to wager money unless someone else calls his raise.

It was a light visible and yet unseen until someone developed the picture.