[bjornsing]

Yes, on the abstract computation side of the link register machines are much more intuitive.

But on the physical side of the link they are much less intuitive IMHO: it’s much less clear that “this is just a machine that I could build in my garage”.

[tsimionescu]

The Turing machine is definitely not some machine that you could build in your garage. None of the mechanisms are specified or even specifiable. The important part, to Turing ateast, is that it perfectly matches what a human does while computing a number, and that there are no magical steps like 'thinking'. Read symbol, change internal state, write other symbol down, rinse and repeat.

All of the details of how a symbol is read, recognized, how it alters the internal state, how the next symbol is chosen, or even how many symbols you actually need are not mentioned and even considered irrelevant. Turing wasn't building one of these, he was proving that this model captures all known computation, and that even so it is undecidable whether this machine would ever stop for any arbitrary computation.

[bjornsing]

No “the Turing Machine” isn’t a machine you can build in your garage. It’s an abstraction.

But any individual Turing machine is. Building a simple one is not very hard, and you can imagine supplying it with more and more tape as it needs it.

It’s thus the only model of computation that I can fully imagine “working”. And that to me is the beauty of Turing’s contribution.

[skissane]

The “physical side” was probably more important when Turing first came up with the idea, and people struggled to conceive of computers because none had yet been built. Nowadays it is arguably less necessary because they are an essential part of everyday life, and most people learn some programming before learning theoretical computer science.