Friday, September 23, 2016

Zeno was not worrying about specifications or formal systems

Reader Alex Small writes:

"the fact that we can specify a process via an infinite list of statements does not mean that it is impossible for such a process to happen. There is an implicit assumption that the only physically feasible processes are those with finite specifications in some particular formal system."

But this is mistaking what the Greeks were worried about. There concern was not with specifications or formal systems. There concern was with the nature of space. And they were puzzling over whether space, in reality, was infinitely divisible, or was it somehow chunky, or atomic. And some among them noted that, if it is infinitely divisible, that seems to create some problems, such as it seemingly making it impossible for things to get moving.

The difference between worrying over this and worrying over specifications in formal systems might be clarified by my stating that I have no quarrel with the mathematical concept of the continuum at all. The fact that in a formal system, something might be specified as taking an infinite number of steps, and that we then treat those steps as if they were completed, leaves me as serenely unperturbed as the Buddha under the bodhi tree*. We can have a model of space as a continuum, and if it proves useful, well, for a model, that's all that counts.

The issue here is not about our specifications or any formal system: it is about reality.

* Remember his big hit, "Don't sit under the bodhi tree / with anyone else but me / anyone else but me"?

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"If your approach to mathematics is mechanical not mystical, you're not going to go anywhere." -- Nassim Nicholas Taleb