- #36
matt grime
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You weren't suppposed to understand them, hell, I don't really understand them. And these are on small part of one small part of... of mathematics.
To refer to the genome as being self-aware is a very strong statement with far-reaching implications. The issue will be presented in a forthcoming publication [60]. I briefly describe here the main points needed for this presentation. Our logic and mathematics are based on the notion of a set composed of elements. Implicitly, the set is closed and static, the elements have a fixed identity (it does not change due to the fact that they are part of the set) and they either do not have internal structure or, if they do, it is not relevant to the definition of the set. The set is defined by an external observer, i.e., it is not a result of self-assembly of the elements under a common goal. The elements, being passive and of no structure, do not have any information about the set. The definition of sets leads to logical paradoxes (Russel-type, like the famous barber paradox) when we try to include a notion of self-reference. Russel and others have devoted much effort to construct formal axiomatic systems free of inherent logical paradoxes. Gödel's theorem [62,63] proved that they all have to be "incomplete", including the Principa Mathematica of Russell and Whitehead. It is important to emphasize that Gödel's theorem applies to closed systems which are also fixed in time. I propose that one has to take an entirely different approach and not start with the notion of sets of elements. I believe that here is exactly where the reductionist approach fails. We cannot reach self-awareness starting from passive elements, no matter how intricate their assembly. I propose to replace elements by agents, that possesses internal structure, purpose and some level of self-interest, and whose identity is not fixed. The notion of a set is replaced by a cell, which refers to a collection of agents with a common goal and mutual dependence. It also implies that the system of agents is open, i.e., it exchanges energy and information with the environment. I argue that, in order for a cell of agents to be self-aware, it must have an advanced language, i.e., a language which permits self-reference to sentences and to its grammar. The language also enables the individual agents to have information about the entire system.
Intuitively, phi says "I have the property psi."
selfAdjoint said:You missed the word "intuitively" by which the author is signalling you that he's going to lie for pedagogical purposes. Just like ascribing will-power to genes when talking about adaptation. It ain't so, McGee.
The statements are self-referent; their inner nature is determined by a refenerence to itself. They don't have awareness, but a great interrelated congeries of them might generate a kind of awareness as an "emergent" property.
phoenixthoth said:If a law is untenable then it won't last long, no matter who wants it too. If it works well as a part of physical reality, it could stick around for a while to come.
selfAdjoint said:But I have an an awareness that isn't just self reference in the wff sense. Where did that come from? Not from the wffs! Apparently it's emergent; and yes, with all emergent properties, since they cannot be tracked back to the elements, there arise difficulties of bounding. How many grains of sand does it take to make a pile, if a pile can slump, but a grain can't?
phoenixthoth said:What's your opinion: does the following statement demonstrate on some level self awareness:
This statement consists of letters and spaces and punctuation.
?
selfAdjoint said:I do not find the statement to be self-aware. In this case I think it is because the self-reference is STATIC. The statement does not transform in any way because of the reference. Whereas the kind of self-reference generated by Goedel numbering, where an arithmetic statement, in expressing its arithmetic value, turns out to also be making a statement about its own provability, that is much closer to awareness, but I don't think Goedel would have thought so. Certainly Wittgenstein who disdained all work with wffs as cheap tricks, wouldn't have.
I guess my minimum and not claimed to be sufficient for awareness would be something you could call background-free dynamic recursion. Whatever that means!
Let us go back to the LEGO metaphor. It would be easy to build a computable LEGO universe following Kampis's instructions. For the set of all LEGO structures is countable, and may therefore be mapped into the set of binary sequences, in a one-to-one manner. And each binary sequence may be represented as a Turingmachine program, i.e. as a map from binary sequences to binary sequences. Therefore, using Turing machines, each LEGO structure could be interpreted as a function acting on other LEGO structures. The only problem with this arrangement is that it does not satisfy clause (c) of the definition of component-system. Not every LEGO structure is realizable by our dynamics. Only some computable subset of LEGO structures is realizable.
But now -- and here is where my thinking differs from Kampis's -- suppose one adds a random element to one's Turing machine. Suppose each component of the Turing machine is susceptible to errors! Then, in fact, every possible LEGO structure becomes realizable! Structures may have negligibly small probability, but never zero probability! This is an example of a component-system which is computable by a stochastic Turing machine.
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That's too bad.selfAdjoint said:Phoen, I tried to link to it and got this
Never saw that one before.