Tag Archives: Halting Problem

BB #64: Systems Bubble

For the last two weeks I’ve written a number of posts contrasting physical systems with numeric systems.

(The latter are, of course, also physical, but see many previous posts for details on significant differences. Essentially, the latter involve largely arbitrary maps between real world magnitude values and internal numeric representations of those values.)

I’ve focused on the nature of causality in those two kinds of systems, but part of the program is about clearly distinguishing the two in response to views that conflate them.

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Sideband #58: Halt! (or not)

Hamlet 2B or Not 2B

evaluate(2B || !2B)

Hamlet’s famous question, “To be or not to be?” is just one example of a question with a yes/no answer. It’s different from a question such as, “What’s your favorite color?” or, “How was your day?” What it boils down to is that the young Prince’s question requires only one bit to answer, and that bit is either yea or nay.

Computers can be very good at answering yes/no questions. We can write a computer program to compare two numbers and tell us — yea or nay — if the first one is bigger than the second one. Computers are also very good at calculations (they’re just big calculators, after all). For example, we can write a computer program that divides one number by another.

But there are questions computers can’t answer, and calculations they can’t make.

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