"I don't write about AI"--I find myself saying this to friends and colleagues with some frequency. And yet the topic is difficult to avoid these days. Below are some notes on one of the fundamental problems in AI: Is is possible for a discrete machine to model continuous phenomena? Instead of trying to solve the problem--indeed I suspect it is unsolvable--computer scientists might simply stipulate it as an axiom. Every discipline rests on a series of fiat decisions. Why not AI as well?
One of the first things I teach in my undergraduate course on "Creative Coding" is the concept of data type, and, more specifically, the distinction between two primitive types, integer and float.
The integers are, of course, the arithmetical counting numbers; they are whole values and advance by discrete steps: 4, 5, 6, 7... Whereas floats (short for floating-point numbers) represent values with a decimal or fractional component, for example 0.1 or 3.141592.
Informally I instruct my students to think of integers as "digital" numbers and floats as "analog" numbers. Of course that's not technically true, since both integers and floats are discrete, finite values; and indeed both are themselves represented by integers (confirming the truism that all digital computers are, in fact, digital). But it's true in spirit. Integers are chunky and monadic, like digital units. While floats are quasi-continuous and fine-grained, like analog magnitudes. Continue reading



