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HrvojeDjurdjevic

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- TL;DR Summary
- Rigorous proof of the supremacy of the second Von Neumann's model of self-reproducing automaton

In his paper "Theory of self-reproducing automata", Von Neumann asserted that it is in principle possible to set up a self-reproducing automaton that consists of the following automata:

A scanner - given an object X returns a description of X

B builder - given a description of X returns a new copy of object X

C controller - initiates and coordinates self-reproduction

D byproduct - responsible for other tasks unrelated to self reproduction

Description is written in a formal language for describing automata unambiguously, used by a communication protocol between scanner and builder, practically always convertible to a single binary sequence, which he called a linear chain of rigid elements.

Builder utilizes raw material floating around the automaton.

Controller starts scanner and builder, each at the right time, presenting them with the right input, and handles their outputs.

To quote Von Neumann more precisely, he blended parts A, B and C into a single one that performs all their described tasks, that he called B, and he did not mention part D, in the context of that hypothetical and monolithic version of automaton, but it is still useful to specify all of the four, because it helps comparison and the analysis of possibility of physical (not via cellular automata) implementation of both models.

But it is easier, and for the ultimate purpose just as effective, Von Neumann said, to decompose a self-reproducing automaton into such parts (all of them are automata, except for E, which is a passive information medium):

A copier - given a description of object X returns a new copy of description of object X

B builder - given a description of X returns a new copy of object X

C controller - initiates and coordinates self-reproduction

D byproduct - responsible for other tasks unrelated to self reproduction

E replicator - description of (A+B+C+D)

Now, the obvious difference between the two models is that in the second case the description is not produced each time anew during self-reproduction process by scanning, it is just copied in that process and kept ready for the next instance of that process, being packaged together with the automata parts.

So, although intuition told him that this must be a simpler approach, better design, or whatever you wanna call it, Von Neumann did not formally and rigorously prove that this is the only possible model for accurate physical implementation, despite being math genius that he was, maybe he did not try at all, because he did not believe it is possible to logically prove it.

And yet, more than 50 years after Watson and Crick's discovery, armed with the knowledge of the fact that this is the only model implemented naturally at the molecular level known to us, Marletto in her "Constructor theory of life" managed to do exactly that, prove that the second model is the only possible way of accurate physical self-reproduction, taking into account a need for maintenance, plus some other considerations with respect to raw material, which both do not exist in case of implementation via cellular automata.

This is not the main result presented in her text, maybe it is not present at all if I misrepresented something, but I hope I did not.

Questions:

How sound and rigorous is her proof?

Would you be able to prove the same without looking at her proof?

Can you point to the relevant source that contains already performed and published proofreading of that text?

A scanner - given an object X returns a description of X

B builder - given a description of X returns a new copy of object X

C controller - initiates and coordinates self-reproduction

D byproduct - responsible for other tasks unrelated to self reproduction

Description is written in a formal language for describing automata unambiguously, used by a communication protocol between scanner and builder, practically always convertible to a single binary sequence, which he called a linear chain of rigid elements.

Builder utilizes raw material floating around the automaton.

Controller starts scanner and builder, each at the right time, presenting them with the right input, and handles their outputs.

To quote Von Neumann more precisely, he blended parts A, B and C into a single one that performs all their described tasks, that he called B, and he did not mention part D, in the context of that hypothetical and monolithic version of automaton, but it is still useful to specify all of the four, because it helps comparison and the analysis of possibility of physical (not via cellular automata) implementation of both models.

But it is easier, and for the ultimate purpose just as effective, Von Neumann said, to decompose a self-reproducing automaton into such parts (all of them are automata, except for E, which is a passive information medium):

A copier - given a description of object X returns a new copy of description of object X

B builder - given a description of X returns a new copy of object X

C controller - initiates and coordinates self-reproduction

D byproduct - responsible for other tasks unrelated to self reproduction

E replicator - description of (A+B+C+D)

Now, the obvious difference between the two models is that in the second case the description is not produced each time anew during self-reproduction process by scanning, it is just copied in that process and kept ready for the next instance of that process, being packaged together with the automata parts.

So, although intuition told him that this must be a simpler approach, better design, or whatever you wanna call it, Von Neumann did not formally and rigorously prove that this is the only possible model for accurate physical implementation, despite being math genius that he was, maybe he did not try at all, because he did not believe it is possible to logically prove it.

And yet, more than 50 years after Watson and Crick's discovery, armed with the knowledge of the fact that this is the only model implemented naturally at the molecular level known to us, Marletto in her "Constructor theory of life" managed to do exactly that, prove that the second model is the only possible way of accurate physical self-reproduction, taking into account a need for maintenance, plus some other considerations with respect to raw material, which both do not exist in case of implementation via cellular automata.

This is not the main result presented in her text, maybe it is not present at all if I misrepresented something, but I hope I did not.

Questions:

How sound and rigorous is her proof?

Would you be able to prove the same without looking at her proof?

Can you point to the relevant source that contains already performed and published proofreading of that text?

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