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Comment by meroes | Hacker News Reader

Isn’t this just taking a common sense concept and adapting it to the concepts and language of Turing machines and also topology?

While yes it shows these are good tools, capable of confirming/proving these intuitions and showing exactly how these specific systems achieve that, is there ever any concern we are making too many redundant concepts? That may lead to confusion and obfuscate the search for novel ideas, which I think won’t always happen through said tools. It’s not like these kind of intuitions were on shaky grounds or could be disproven.

I wonder if anyone shares these opinions?

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> While yes it shows these are good tools, capable of confirming/proving these intuitions and showing exactly how these specific systems achieve that, is there ever any concern we are making too many redundant concepts? That may lead to confusion and obfuscate the search for novel ideas, which I think won’t always happen through said tools.

On the contrary, coming up with good general abstractions reduces the number of concepts you have to keep in your head and makes it much more possible to search for novel ideas. Imagine trying to figure out whether a given computing device was different to other computing devices without having the general concept of a Church-Turing computer - you wouldn't even get started.

Math is all about taking a notion from life that you might consider “common sense” and using it to solve a problem. You have to prove it works carefully though.

This is Turing’s works where he is translating the idea of a human “computer” into a mathematical machine.

What is common sense about it?

> is there ever any concern we are making too many redundant concepts

I need to read the contextual work, but I think it's actually the opposite here. Turing is a mathematician and is transferring a "foreign" notion into common mathematical concepts. It is a recasting of the concept so that it can be used. It isn't done just to do it.

These results help when you want to think about compression algorithms for example.

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