What I intend to suggest above is that the lifecycle/hypergraph
abstraction is a more expressive class of formal models within which one
can pose such problems, and we should be able to generate more
interesting answers by using it.
"""
There are many references above to investigate, and so far I have only begun to engage with some. I am preparing to read your preprint, and I have managed to track down a copy of Valiant's PAC. Two notable ideas Valiant raises are:
0. Membership to a complexity class as real: A machine is identified with the nature of its computation and not necessarily the fine details of its instantiation. For instance, fine details in the case of biology could be every aspect of its being in the world. I am reminded of the philosophical problems associated with identity tracing, as well as a certain empiricist perspective that days like today are in some sense more real than today. Valiant mentions that the universality of Turing's machine is the stable feature that ultimately matters, that a machine ought to be considered "the same" under perturbation of its parts so long as what it does computationally remains invariant.The slipperiness of notions like "remaining computationally invariant" and "perturbation of its parts" seem to be hotly debatable locales. In the spirit of Ackley's robust algorithms, perturbations of a quick-sort rapidly lead to nonviable algorithms, while bubble-sort can remain identifiable under significant perturbation. Additionally, as with genetics, there is the possibility of identifying perturbations (mutations) as an indispensable part of the organism. This kind of analysis does leave some questions open. Should we (by the thesis) consider a BPP-classed algorithm to be the same under perturbation when it becomes both determined and its expected time complexity remains invariant?
1. Scaffolding in protein expression networks: Here, Valiant suggests a protein level analogy to Nick's white smokers. Chaperone proteins, at the very least, are known to participate structurally in the process of error correction, namely correcting errors in folding. I am reminded of recent dives into other aspects of protein dynamics such as allosteric signaling. I can only imagine the computational liberties present for scaffolding when considering variation in PH (as narrow as it allows) or temperature. In these musings, I am reminded of the inhibitory (epiphenomenal?) role of the dictionary in the functioning of LZW data compression.
That Glen found your paper "positively pornographic" is high praise.
I hope to find the time to take the dive myself. In the meantime, I would love to hear more about your ideas concerning graphical models, as it is a place I have thought a bit about.
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