How Inevitable Is the Concept of Numbers?
Numbers are good tools, but some things are computationally reducible, and some not. Most interesting thing I've read recently. I had to read it three times to get the gist of it.
... we argued that even though at the most fundamental level numbers really aren’t involved, our sampling of what happens in the universe leads us to a description that does involve numbers. And in this case, the origin of the way we sample the universe has deep roots in the nature of our consciousness, and our fundamental way of experiencing the universe, with our particular sensory apparatus, place in the universe, etc.
What about the appearance of numbers in the history of science and engineering? Why are they so prevalent there? In a sense, like the situation with the universe, I don’t think it’s that the underlying systems we’re dealing with have any fundamental connection to numbers. Rather, I think it’s that we’ve chosen to “sample” aspects of these systems that we can somehow understand or control, and these often involve numbers.
In science—and particularly physical science—we have tended to concentrate on setting up situations and experiments where there’s computational reducibility and where it’s plausible that we can make predictions about what’s going to happen. And similarly in engineering, we tend to set up systems that are sufficiently computationally reducible that we can foresee what they’re going to do.
As I discussed above, working with numbers isn’t the only way to tap into computational reducibility, but it’s the most familiar way, and it’s got an immense weight of historical experience behind it.
But do we even expect that computational reducibility will be a continuing feature of science and engineering? If we want to make the fullest use of computation, it’s inevitable that we’ll have to bring in computational irreducibility. It’s a new kind of science, and it’s a new kind of engineering. And in both cases we can expect that the role of numbers will be at least much reduced...
