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Ever since Gödel we’ve had a pretty convincing proof that there is nothing that you can do in terms of reasoning that can’t be expressed using computation. And
by jameshart 5y ago
Ever since Gödel we’ve had a pretty convincing proof that there is nothing that you can do in terms of reasoning that can’t be expressed using computation. And since Turing we’ve got a framework that shows there’s nothing computable that you can’t compute using a universal computer.
So unless there’s something mystical beyond the realm of mathematics to ‘reasoning’ it can’t be a superset of computing.
If a finite amount of matter in a brain with a finite amount of energy can do it, then a universal computing machine with a finite amount of storage and a finite amount of time can do it.
- whatshisface 5y agoThere are actually a lot of well-defined things beyond the power of a Turing machine (for example a Turing machine plus a halting oracle that only works on Turing machines without a halting oracle) but in terms of finite amounts of electrons doing normal low-energy electronic stuff you are quite likely correct. Humanity may go beyond computability if as some papers have suggested quantum gravity requires solving uncomputable problems.
- selestify 5y agoEven if our brains reason based on quirks of quantum mechanics (seems unlikely given the scale at which neurons operate), what stops us from creating non-biological machines that interact with QM in the same way to produce artificial reasoning?
- whatshisface 5y agoI am not saying that anything more than a really big computer is necessary for reasoning, only that one day physics knowledge may reach beyond the Turing machine (quantum computing does not).
- jameshart 5y agoDo you believe human brains contain a halting oracle? Or the moral equivalent of one - something that enables our brains to accomplish some non computable reasoning task?
- whatshisface 5y agoNo, they probably don't.