stevestory
Posts: 13407
Joined: Oct. 2005
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kairosfocus January 22, 2018 at 1:50 pm
DiEb,
definitionitis is an old complaint and too often a disease of the hyperskeptic that makes a mountain out of a mole-hill.
In the context, we have dealt with configuration spaces, which can be regarded as phase spaces in which momentum issues are not material.
In such spaces, we can see complexity through combinatorial explosion, e.g. for text strings. Since such strings can be used to describe a 3-d entity or a process etc, discussion on strings is WLOG.
Now, certain clusters of configs in the space of possibilities w [for omega the traditional symbol in stat thermo-d] may be observably and identifiably distinct e.g. by providing some structurally based function, such as the correctly assembled parts of a 6500 c3 fishing reel, my favourite case. Thus we have a cluster of states that are functional in some way and a vastly larger number of clumped or scattered states that will not function in any relevant way.
Of course the issue that relevant systems are self replicating is trotted out. the problem is we are looking at a cell-scale von Neuman kinematic self replicator, which is a further example of functionally specific complex orgtanisation and associated information that needs to be explained before it is allowed to drive all sorts of conclusions.
Yes, OOL must be solved first.
We then can ask ourselves, how do we get to such a cluster or island of function, a case e from a zone E within w.
If by blind chance and/or mechanical necessity, any reasonable assignment of probabilities of accessing cases c for a complex case such that c is in E, will be rapidly negligibly different from zero.
Exponential explosion of possibilities as n bits have 2^n possible configs. More complex cases can be reduced to bits.
This of course runs into challenges of numerically or algebraically defining probabilities and defining functional targets.
There is an answer: search challenge.
Long since put here at UD and elsewhere.
Once the space w is for at least 500 – 1,000 bits, we are looking at 3.27*10^150 – 1.07*10^301 possibilities.
The atomic resources and atomic interaction rates for the 10^57 atoms of the sol system for the low end and the 10^80 for the observed cosmos at the high end, are such that the fraction of selected possibilities c from w is negligibly different from 0.
So, it is maximally implausible to reach any reasonably isolated island of function in the space by blind search.
Plausibility fail, backed up by utter want of empirical observation.
And, search then is implied as sampling of subsets in config spaces relevant to our studies.
Here, as default, blindly by chance and mechanical necessity.
Try AA sequence space and codon space that targets it. We could try random bit strings for AUTOCAD, hoping to come up with a design for a reel, or we can try random ASCII text to get text from the corpus of literature in English or the like.
All these cases give the same result, for rather obvious reasons.
Likewise, we can then say oh we have some circumstance that searches are very effective as natural selection is held to be. Of course that is within islands of function, when we need to find the islands as the first problem, not incremental hill climbing within the island.
In any case as searches are effectively subsets, they come from the power set of the space and so are exponentially harder, space of size w has power set of size 2^w. Search for golden search is far worse than direct search per whatever atomic level interactions occur in sol system or observed cosmos.
Such cases of functionally specific complex organisation and associated information have just one well known causal source: intelligently directed configuration.
But the whole point is, after years and years you and others of like ilk still want to sweep that inconvenient fact off the board and so repeatedly rhetorically pretend we have not provided a serious answer.
It has been there, for decades.
KF
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DiEb January 22, 2018 at 2:31 pm
KF, you obviously have no idea how modern mathematics work. |
I can haz numbars?
  
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