The Half-Life of Facts by Samuel Arbesman

Author:Samuel Arbesman [Arbesman, Samuel]
Language: eng
Format: epub, mobi
ISBN: 9781101595299
Publisher: Penguin Group US
Published: 2013-09-15T16:00:00+00:00

. . .

THERE are all sorts of mathematical models for physical systems. Some try to actually mimic the complex mess we see around us, the most well-known of these being weather models. We don’t just want to understand how weather changes; we want to know how likely it is that it will rain tomorrow. So we input temperature details from throughout the country; wind speeds; barometric pressure values measured over time; and much more. These values are then put into complex equations and simulated in a powerful computer, allowing us to see what they all will be in the future, inside the computational world that has been created.

But these kinds of models, while very powerful, don’t allow us to say anything general about them. We can’t write down a simple equation for how the average air temperature of the entire country will affect rain, because the model is far too complex for that. To understand that sort of thing, or any other system for which we want to explain a certain phenomenon, we need to create much simpler models. These don’t make any claims for verisimilitude. Instead, they go to the other extreme and claim the following: We can make an extremely basic model that even with all the complexity of real life stripped away still has certain features of our complicated world. And if we can capture these features of our world, maybe we can understand why they occur. In our case, the question is whether a simple model can be made that exhibits phase transitions. This is exactly what Ising set out to do.

How does the Ising model work? Imagine we lay out a large deck of cards, in which each card is black on one side and white on the other, into a grid. When the cards are all on the same side—either black or white—the system is considered to be in one state, like a solid. Entirely uniform and understandable. However, if the cards are flipped randomly, and there are no regions of a single color, we have something much more irregular. We know such a system as a gas.

How does this system change? We choose a card and flip it. If we start with all the cards on their black sides, pretty soon we’ll start getting cards showing white, and soon enough we will have something that looks random and fits what I described as a gas.

As I’ve explained the system thus far, it seems like we’re just flipping cards at random. And a moment’s thought shows that flipping the cards at random will result in no overall change. If any part of a random grid of black and white cards is changed at random, the details of the picture will change: which specific cards are black and which are white. But if you zoom out, we still get the same overall picture: static.

But here’s where the model gets interesting. If, whenever we flip a card, we have the possibility of also flipping its neighboring cards to the same color, this little twist is enough to yield strikingly different behavior.

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