My own book may be crap, but I am certain, when such an imbalance in profitability as the one I have just described emerges, between photojournalism and selfies, that it is all over. This is not a critical judgment. I am not saying that the photos of Pol Pot are good and the selfies are bad. I am saying that the one reveals a subject and the other reveals an algorithm, and that when everything in our society is driven and sustained in existence by the latter, it is all over.
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.
How do we know what’s the right direction [for computers to take]?
Ultimately it comes down to taste. It comes down to trying to expose yourself to the best things that humans have done, and then trying to bring those things in to what you’re doing.
Picasso had a saying: “Good artists copy, great artists steal.” And we (at Apple) have always been shameless about stealing great ideas. And I think part of what made Macintosh great was that the people working on it were musicians and poets and artists and zoologists and historians who also happened to have been the best computer scientists in the world. But if it hasn’t been for computer science, these people would all be doing amazing things in life in other fields. And they brought with them — we all brought to this effort — a very liberal arts air, a very liberal arts attitude, that we wanted to pull in the best we saw in these other fields into ours.