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Are the Androids Dreaming Yet?

The best analogy I can find to illustrate iterative knowledge discovery is the 1970s family game ‘Battleship’. The game consists of two 10 by 10 grids that you plug your ships into. All the ships are linear shapes of a few squares in length. The players cannot see each other’s ships and must guess where they are. A very simple way to do this would be to ask your opponent whether they have a ship on the top left square and continue systematically across the board, square by square, until you reach the bottom right hand corner. This would eventually find every ship. If every ship were a piece of knowledge we could discover all the knowledge in the world by simply stepping through the board one cell at a time, but it would take a long time.

A better way to play Battleship is to pick a square at random. If you get a hit, explore linearly around the hit. This will efficiently find the rest of the ship. The same might be true for knowledge. We could take random shots, get lucky and move linearly to flesh out our knowledge. Once we had exhausted an area we could take a step away at random and again hope for another hit. This process is exactly the way some people imagine the frontier of knowledge expands.

But, it is wrong.

The monkey moon shot story explains…

“I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a monkey on the moon and returning him safely to Earth.”

President Monkey

The monkey nation is asked to mount a moon shot. After a little time a monkey is asked to report on progress.

“I can report,” says the monkey, “I have climbed a particularly tall tree on the tallest hill on my island and have made over seven hundred meters progress towards the moon, although this is only 0.0001% of the way there, this has been quick so I believe we are well on the way.”

You see of course the problem. Progress in many problems is nonlinear. Moving a bit of the way towards the goal does not provide any actual progress: That is the problem with knowledge. It is not linear in structure. You need to take leaps to discover new knowledge. You can not simply look around in the general area. Such leaps are mathematically huge. The chance of making a successful one by pure chance is virtually zero.

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