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State transition in the turing machine are not modifiable, but one of the core advantages of the TM is that it's powerful enough to emulate state transition. So you can model the states of the new machine as data, add the transition mechanism as code, feed those to the TM and you have a new machine that can interpret input that was unrecognizable by the previous one. That's how programming languages works.

So yes, you can't modify the actual embodiment of the state transition if it does not offer you the capability to do so. But as long as it interprets data in a TM manner (input and output are colocated and the alphabet is the same), you can write code that will interpret data as code and manipulate code as data. Not by modifying the base substrate, but by adding a virtualization layer on top.

by Xirdus4 hours ago|

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That's less "code is data is a fact of computing" and more "if you ignore the part of code that's not data then all code is data".

by skydhash3 hours ago|

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At the base of it, the TM is an abstraction built with sets and relations. Just like most computers are merely signals flowing around a circuit that get generated from other physical phenomena and will be transformed to other physical phenomenas. You can't hack around physical laws, or ignore the axiomatical rules in mathematics. The code that is not data are those things.

Everything else is data.

by Xirdus3 hours ago|

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You are redefining both the term "code" and the term "data" in ways that I don't think most people would agree with - and more importantly, in ways that make it impossible to talk about von Neumann architecture.

by skydhash1 hours ago|

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Because code and data as well as the von Neumann architecture are derived things, not fundamental stuff. The Turing Machine and Lambda Calculus are pure invention thats are logically sound. Almost everything else is downstream of that.

By the time you get to programming language like C and LISP, and software like vim or firefox, everything is abstracted away and the only limits are self-imposed (or imposed by others that have done the work). They are not laws of nature.

So yes there’s a definition of code and data. But for the Turing machine, there’s only the tape and its content.