Von Neumann replicator vehicle model

[HrvojeDjurdjevic]

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?

 

[tade]

do you have a link to Marletto's proof

 

[HrvojeDjurdjevic]

Here you are https://royalsocietypublishing.org/doi/10.1098/rsif.2014.1226#d3e2524

 

[tade]

Here you are https://royalsocietypublishing.org/doi/10.1098/rsif.2014.1226#d3e2524

thanks, and which part of it describes her proof that the second model is the only possible accurate way

 

[pbuk]

How sound and rigorous is her proof?

It seems tautological to me:
"we define a replicator as something that replicates, therefore in order for something to replicate itself it must contain a replicator".

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

Yes, unless I am wrong in believing it to be vacuously true.

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

I am not sure what you mean: the link you gave is to the publication in the Journal of the Royal Society following proofreading and refereeing.

I am not sure this has much to do with programming or computer science: it seems to relate to David Deutsch's "Constructor Theory" which seems to me to be a blend of quantum interpretation and other things I don't understand.

 

[berkeman]

Thread paused for Moderation...

 

[berkeman]

Thread is reopened provisionally. Let's be careful not to veer into the philosophical aspects of this work. Thanks.

 

[HrvojeDjurdjevic]

Yes, unless I am wrong in believing it to be vacuously true.

I do not know if it is vacuous, but it certainly is not very explanatory to prove that something is possible, something that we already know it exists, for more than 50 years. Basically, the discovery in molecular biology was a proof that Von Neumann's second model was realistic. However, that paper describes no other possible alternative, and it claims it is required for physical realization, and in the conclusion it states that this was proved.

I am not sure what you mean: the link you gave is to the publication in the Journal of the Royal Society following proofreading and refereeing.

I am sorry, I was not aware that I can find in such publications what were the criticial objections, and how they were responded. However, I still do not see where exactly...

it seems to relate to David Deutsch's "Constructor Theory" which seems to me to be a blend of quantum interpretation and other things I don't understand.

I do not understand either, that is why I am asking these questions. I am not sure what she actually proved, why, and how. To me, if replicator-vehicle is the only possible physical realization of self-reproducing automaton, that means that universal scanner is either impossible, or it is for some reason impossible to present it with a reference to an object it is part of, or whatever else is a case, which requires a replicator to be physically instantiated prior each process of self-reproduction. These of course were not Marletto's considerations when she wrote that paper, but we are not constrained only to analysis of her paper, in our discussion. Are we?

 

[HrvojeDjurdjevic]

And of course, I am not questioning if it is really so, that the replicator-vehicle is the only possible physical implementation of accurate self-reproducing automaton, I just ask if this was proved rigorously, in your opinion.

 

[HrvojeDjurdjevic]

Part of Von Neumann's genius is that I understand perfectly every sentence of his paper. For example, the consideration about how copier works: if it consumes the instance of replicator it was presented with during the process of copying, it has to produce two instances of the replicator in order to perform the task properly, otherwise, one is sufficient because, the input instance is preserved, ie, not consumed.
Part of Marletto's genius is that after reading her work, I understand only that what I understood before reading it. Rather obscure arguments and ideas hidden behind the mathematical formalism that I haven't learned so far. Which is of course not her fault, and I still hope I will one day.

 

[HrvojeDjurdjevic]

If I put aside the proof and focus on the result, what it actually tells us is this:

• universal scanner of objects is impossible
• universal copier of objects (apart from those objects which present descriptions of other objects) is impossible
• universal copier of descriptions of objects is possible and required for self-reproduction
• universal builder of objects is possible and required for self-reproduction
• controller of the last two automata is possible and required for self-reproduction

The logic is that if universal scanner of objects was possible, universal copier of objects would also be possible by composing universal scanner with universal builder, composition would be performed by a controller of these two automata, which also must be possible. But such copying would still be different from the way how the descriptions are copied, directly.
One can ask why are objects which present descriptions of other objects special, why are they exceptions that allow to be directly copied, and how was that proven? I may be missing some chapters of math and quantum physics to follow the exact logic of the proof, but intuition tells me that although descriptions of objects are as complex as objects they describe, the description of descriptions objects can be made simple: a linear chain of rigid elements.
This is simple, known in advance, does not require any scanning in order to determine its structure, just the content of that chain has to be copied, and that is why copying such objects is possible, regardless of its semantics and purpose (regardless of the fact that it contains descriptions of other objects).
Obvious analogy in computer science would be some rules that prevent direct copying of objects by using copiers of primitive types, because the object structure is not known in advance, but if objects are serialized in some standard way, packaged together with their description, then the deserializer does not need any additional information to deserialize the object, and such data can be copied using raw methods.

 

[pbuk]

[*]universal builder of objects is ...required for self-reproduction

This is clearly not true: my cells (and therefore I) cannot synthesise amino acids yet they manage to reproduce (as have I).

I may be missing some chapters of math and quantum physics to follow the exact logic of the proof,

I don't see any maths or physics of any kind in Marletto's paper, just hand waving.

 

[HrvojeDjurdjevic]

Yes, thanks, obviously “universal” is a completely misplaced attribute here, and that is entirely my mistake.
They can build everything within the repertoire of the language for describing automata unambiguously, using the raw material prescribed by that language as building blocks in that process, nothing more. So, ribosomes can only build proteins using amino acids, nothing outside that scope. They rely on a supply of amino acids floating around them (because they cannot build them out of simpler raw material), just as enzymes which copy DNA (and only DNA, so they are not universal copiers either) rely on a supply of nucleotides.

 

[HrvojeDjurdjevic]

I don't see any maths or physics of any kind in Marletto's paper, just hand waving.

I wonder what did those who critically reviewed her paper see, what were their objections, and how she responded. I did not understand your response with respect to how can I access that info from the same page where the paper was published.

 

[HrvojeDjurdjevic]

I mean, do they publish only the polished paper, or can I see somehow the whole process of proofreading?
And it is not like I do not trust or appreciate your judgement, I would just like to have a second opinion from those whose academic assignment it was.

 

[pbuk]

I wonder what did those who critically reviewed her paper see, what were their objections, and how she responded. I did not understand your response with respect to how can I access that info from the same page where the paper was published.

That is not what I meant, sorry for any confusion. Details of the refereeing process are almost always private.

 

[HrvojeDjurdjevic]

OK, I think we can agree that we are here at the frontier of human knowledge, unlike majority of other threads in this particular forum. Would it be preposterous then to ask all science advisors resident at this forum, and finally Marletto herself to join us, and explain her contribution to human knowledge conveyed via that paper. Recently, I was accused by berkeman of degrading PF’s reputation by posting a link to my conversation with Google Bard about the same topic. Now, I would like to make up for that, by proposing an action that no other scientific forum offers to its members: I already wrote to Marletto, but she did not dignify that with a response, maybe she will, if someone else tries. And maybe this is not necessary, if there is already staff at this forum who can help, and write a version of her paper for dummies, but they did not notice the thread yet.

 

[HrvojeDjurdjevic]

By dummies I meant me, not you …

 

[HrvojeDjurdjevic]

I see forums such as this one as grassroots scientific projects, which however can be better connected with academic institutions, than an anonymous individual, who lacks academic credentials. Although I have an academic degree, I never submitted a paper in a scientific journal, and I do not think I am capable of it. After graduation, I immediately became an outsider of academic community, and now, when something interests me, I pretty much struggle to get answers. If this forum could serve that purpose, it would be a unique feature, which would highly increase its reputation. Usually, if more people ask the same question, it has more weight than any single one person, and the question is, what does that paper tell us about life, natural or artificial?

 

[berkeman]

Now, I would like to make up for that, by proposing an action that no other scientific forum offers to its members: I already wrote to Marletto, but she did not dignify that with a response, maybe she will, if someone else tries.

So you want us to spam her with e-mails to try to get her to join your PF conversation? Not going to happen.

I see forums such as this one as grassroots scientific projects, which however can be better connected with academic institutions, than an anonymous individual, who lacks academic credentials. Although I have an academic degree, I never submitted a paper in a scientific journal, and I do not think I am capable of it. After graduation, I immediately became an outsider of academic community, and now, when something interests me, I pretty much struggle to get answers. If this forum could serve that purpose, it would be a unique feature, which would highly increase its reputation. Usually, if more people ask the same question, it has more weight than any single one person, and the question is, what does that paper tell us about life, natural or artificial?

That is not PF's mission or purpose. Please re-read the PF rules (under INFO at the top of the page). This thread is on the verge of being closed again.

 

[HrvojeDjurdjevic]

berkeman, I do not expect from you anything constructive, unless you are forced to do it. There are other people at this forum who can judge that proposal.
As for the analogy, I think I just have to add one more sentence to complete it. Not only objects cannot be copied directly by using copiers of primitive types, but they cannot be serialized either, without knowing their description, in advance.
Hence, that would explain why both universal scanner and universal copier of objects are impossible. Not any kind of rigorous proof, or original for that matter (and I will inestigate both claims wherever circumstances allow me, I have a feeling it will not be here), but, still a worthy analogy.

 

[Frabjous]

You misunderstand actual scientific debate. It occurs via papers.

 

[HrvojeDjurdjevic]

I will try my best to write a good one.

 

[berkeman]

I will try my best to write a good one.

Great. We will await that publication (in a peer-reviewed journal); at that time we can reopen this thread. Thread is closed for now.