CS + Math

In most?domains, a million is a large number. In EDA, a hundred billion is normal, and predictions are for trillion-transistor chips by 2030. If you design a trillion-transistor chip in 1000 days (about 2? years), that's a billion transistors a day, over a thousand per second. That takes a lot of computer science and mathematics, or CS+math.

The Mathematical Ideal

If you studied physics in school, you will have encountered things like frictionless pullies, inelastic wires, and incompressible fluids. Objects that are perfectly black. Of course, in the real world, there are no frictionless pullies. No paint absorbs absolutely all light (although?Vantablack?is pretty close).

It's not just physics either: economics has the idea of a perfectly competitive market, where?all companies sell identical products, companies are able to enter or exit without barriers, and buyers have perfect information.

Of course, one reaction to all these non-existent ideal concepts is to say that we can't do physics or economics because it's a waste of time to work with things that cannot exist. But most of the time, the world is "linear," and the values we derive from working with these idealized objects are very close to the real-world values when pulleys have friction, and black bodies reflect a little light. For the perfectly competitive market, perhaps the closest we get to that is the DRAM market in semiconductors.

It doesn't always work like this, though. Sometimes the world is not linear but chaotic. You may have heard the story about Edward Lorentz. He created a primitive weather model, but it ran really slowly on the computers of the time (1961). He takes up the story:

At one point I decided to repeat some of the computations in order to examine what was happening in greater detail. I stopped the computer, typed in a line of numbers that it had printed out a while earlier, and set it running again. I went down the hall for a cup of coffee and returned after about an hour, during which time the computer had simulated about two months of weather. The numbers being printed were nothing like the old ones. I immediately suspected a weak vacuum tube or some other computer trouble, which was not uncommon, but before calling for service I decided to see just where the mistake had occurred, knowing that this could speed up the servicing process. Instead of a sudden break, I found that the new values at first repeated the old ones, but soon afterward differed by one and then several units in the last decimal place, and then began to differ in the next to the last place and then in the place before that. In fact, the differences more or less steadily doubled in size every four days or so, until all resemblance with the original output disappeared somewhere in the second month. This was enough to tell me what had happened: the numbers that I had typed in were not the exact original numbers, but were the rounded-off values that had appeared in the original printout. The initial round-off errors were the culprits; they were steadily amplifying until they dominated the solution.

This was the first known example of what has become known as the "butterfly effect", where a butterfly flapping its wings in Paris can affect a tornado in Nebraska.

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