Desunt Cetera

I used to be convinced that mathematical objects are in some sense real. That numbers have an existence independent of humans knowledge of them. Recently, in a Wittgensteinian turn, I’ve come to the realization that the question “are numbers real” is a bad one.

The heart of the problem is that the question is ambiguous. Math is a set of models that attempt to describe phenomena we observe in reality. Those models are obviously invented. We didn’t discover them carved into a rock somewhere. The phenomena in the world they are describing are obviously discovered. So the answer to the (badly phrased) question is both. “Numbers” are a feature of a model humans invented to describe a physical phenomena. The physical phenomena that numbers model is something humans discovered in the world. The only way we have access to those things is through the intermediary that is our models. But this introduces a new problem.
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Logic, Mathematics, Metaphysics

You’ll have to forgive me, as the first part of this is reconstructed from memory, from a paper I read several months ago.

Lets do a little thought experiment.

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Mathematics, Musings

In one of those funny coincidences where it seems the popular mind is pregnant with an idea, an article was recently published to the programming section on reddit that mentions the busy beaver function. The article is titled “Who Can Name The Bigger Number?” and is essentially about trying to name very large integers.

The article is fairly long, but also quite interesting. The associated thread on reddit is also interesting, but is topped by a very similar discussion on the XKCD blog about naming large numbers.

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Logic, Mathematics