Yesterday I talked about the cubes {1, 8, 27, 64, 125, ...} and how their first differences {7, 19, 37, 61, ...} might at first seem to lack an obvious pattern, but taking the second differences {12, 18, 24, ...} takes you down to the simply related level. Taking the third differences {6, 6, ...} brings us to the perfectly stable level, where chaos dissolves into order.

But this (as I noted) is a handpicked example. Perhaps the "messy real world" lacks the beauty of these abstract mathematical objects? Perhaps it would be more appropriate to talk about neuroscience or gene expression networks?

Abstract math, being constructed solely in imagination, arises from simple foundations - a small set of initial axioms - and is a closed system; conditions that might seem unnaturally conducive to neatness.

Which is to say: In pure math, you don't have to worry about a tiger leaping out of the bushes and eating Pascal's Triangle.

So is the real world uglier than mathematics?

Strange that people ask this. I mean, the question might have been sensible two and a half millennia ago...

Back when the Greek philosophers were debating what this "real world" thingy might be made of, there were many positions. Heraclitus said, "All is fire." Thales said, "All is water." Pythagoras said, "All is number."

Score: Heraclitus 0 Thales 0 Pythagoras 1

Beneath the complex forms and shapes of the surface world, there is a simple level, an exact and stable level, whose laws we name "physics". This discovery, the Great Surprise, has already taken place at our point in human history - but it does not do to forget that it was surprising. Once upon a time, people went in search of underlying beauty, with no guarantee of finding it; and once upon a time, they found it; and now it is a known thing, and taken for granted.

Then why can't we predict the location of every tiger in the bushes as easily as we predict the sixth cube?

I count three sources of uncertainty even within worlds of pure math - two obvious sources, and one not so obvious.

The first source of uncertainty is that even a creature of pure math, living embedded in a world of pure math, may not know the math. Humans walked the Earth long before Galileo/Newton/Einstein discov...

Artem Sinyakov

Artem Sinyakov

Artem Sinyakov

Artem Sinyakov