Did Logic and Math always belong to the Machines?
I was reading Hamming’s Art Of Doing Science And Engineering today, specifically the chapter where he asks the question whether tmachines can think. He gives a few examples, of theorem proving systems from the 90s, and other areas where a machine can supposedly ‘think.’
Assuming, computation is a fundamental property of the universe, and that these proofs can indeed be mechanically derived: could it be the case that all this while it has been humans who have been trying to emulate a ‘idealized’ machine when trying to do mathematics and proofs?
This claim is more well-founded perhaps when we think of arithmetic, we know the results of a long multiplication are “out there somewhere” and that we could technically compute it in my minds, but it is primarily a machine’s work to perform the arithmetic reliably and quickly.
Perhaps proofs are the same way. When a machine comes up with a proof, it is in the nature of the machine to compute them reliably and correctly; and we humans have been the imitators.
If we assume that we do indeed live in such a world: then where does the human belong in the whole loop?
As more things got automated, humans asked more and more questions (assuming benevolence) to
- Understand the universe better.
- Improve the quality of their lifes
So, perhaps we will continue to do the same, just because a few proofs are being written by machines, does not imply everything is”solved.” We have further interesting things to get to, update our understanding, and then ask deeper questions.
The second part, the quality-of-life part, is more ‘engineering’ work than science or discovery, and I think will continue on for a long time, because here the requirements lie more in human-intent which will always continue to evolve.