This post is a recap of where I last left my Meloncolia I project, my last word being this paper where I derived the following information relationship:
I(p) = I(1/N) + I(q) + I(b)
1.0
....and where:
I( ) represents the information function --log( ),
p is the absolute probability of an outcome. The implication is that p is extremely small as it represents a tiny minority of favourable cases among the huge space of platonic possibility. In the context of Meloncolia I the cases of relevance and interest is the class of organic configurations. Clearly within the context of all that is possible this class of organised complexity is very small. Thus it follows from the definition of information that I(p) is very high.
b is the conditional probability of the outcome under scrutiny. This probability is within the bonds of practical realization - that is, it must be high enough to mean that the outcome has a realistic chance of occurrence. e.g. life exists so we expect it that its conditional probability is within the realms of practicability given the age and size of the universe. It follows then that the information embodied in b is relatively low.
q is the probability of the physical constraints which constitute the conditions that make b a conditional probability.
The above three probabilities were the concern of William Dembski's "conservation of information" thesis. If for the moment we forget the first term on the right hand side of equation 1.0 it is easy to see why it is so termed. In order to get I(b) sufficiently small for its corresponding outcome to be realistic, the absolute information embodied in I(p) must be soaked up in the conditions needed to make the outcome associated with b realistic. That is, the absolute improbability of p can only be expressed as the product of the improbabilities of q and b - which in information terms means the corresponding information values are summed. An example of the kind of precise physical set up embodying the information implicit in q needed to give evolution a realistic chance is the spongeam.
The I(1/N) term
However, I have added a third term on the right-hand side of equation 1.0. This term, I(1/N), is the information created by activity or searching. In the most elementary model N represents a simple sequential searching of the possible cases in the huge volumes of platonic space. Under these circumstances it is clear that because I is a logarithmic function, I(1/N) grows extremely slowly with N, so slowly in fact that we can understand why this term is easily missed from 1.0. A conservation law of sorts, nevertheless, still holds in as much three terms sum to a constant, but the existence of I(1/N) makes for a dynamic equation where information shifts from one term to another, rather than having a situation that is in stasis. However, the existence of the term I(1/N) may be liminal and difficult to perceive, for whenever we do algorithmic searches conventional computational activity is creating information only very slowly given the processing technology of our current machines.
***
I would submit that equation 1.0 gives us hints about the nature of intelligent activity and this becomes clearer once we include the activity term in the information conservation equation. Without this dynamic term the equation we are left with pertains to a static system that does nothing, leaving the question of where does the information come from? dangling. This prompts dualistic attempts to fill the gap with a mysterious thing called "intelligence" which is eminent to physical systems and all but beyond further scientific scrutiny: It's no surprise, therefore, that IDist Robert Marks should believe intelligence to be a different genus to physical activity (or "natural processes" - sic) rather than seeing that activity as bound up with Intelligence. Further, it is of no surprise that some de facto IDists see the nature of intelligence as beyond their terms of reference. In short, the philosophical problems with their explanatory filter has brought their inquiry to an end. It is not that adding the dynamic term I(1/N) to equation 1.0 answers all the questions, far from it, but we are effectively zooming in on the subject of intelligence itself and resolving it into parts which may help take the inquiry beyond de facto ID's God Intelligence-of-the-Gaps.
Computations and also, I would maintain, human mental activity produces envelopes of tentative experimental possibility. These envelopes or "halos" are scrutinized for the fulfillment of high level objectives thus making the process of intelligence teleological. If a configuration is discovered that fits these general objectives the envelops generated by the trial process are discarded. In such trial systems the information is, as it were, back-loaded into general and sometimes very fuzzy teleological goals rather than front-loaded into the very tight and precise constraints signified by I(q) in equation 1.0. Because there may be many configurations that fit the general goals selection of a particular outcome could be probabilistic. (See here for more details)
Equation 1.0 may also give us a clue about the nature of learning. Huge activity is needed to create the information required to fulfill teleological goals. When that information is found it may be stored away and used to update the I(q) term which then acts to constrain future searches. In the activity of human thinking learning no doubt considerably reduces the search space.
Computations and also, I would maintain, human mental activity produces envelopes of tentative experimental possibility. These envelopes or "halos" are scrutinized for the fulfillment of high level objectives thus making the process of intelligence teleological. If a configuration is discovered that fits these general objectives the envelops generated by the trial process are discarded. In such trial systems the information is, as it were, back-loaded into general and sometimes very fuzzy teleological goals rather than front-loaded into the very tight and precise constraints signified by I(q) in equation 1.0. Because there may be many configurations that fit the general goals selection of a particular outcome could be probabilistic. (See here for more details)
Equation 1.0 may also give us a clue about the nature of learning. Huge activity is needed to create the information required to fulfill teleological goals. When that information is found it may be stored away and used to update the I(q) term which then acts to constrain future searches. In the activity of human thinking learning no doubt considerably reduces the search space.
Disclaimer: The above is certainly not being proposed with any claim to scientific authority. The above is more about speculative world view synthesis as I attempt to make an epistemic trade off between proposing embracing high level theoretical speculation against empirical rigor. It is more an avenue of speculation which is not going to be everyone's cup of tea; see the epistemic note below which was my response to a Facebook entry on epistemology.
Appendix: An Epistemic Note:
It was requested that I make a comment on the following facebook entry:
Quine would agree with me that there is no difference in type comparing religion and science.They are both science and just differ in degree.There are just varying degrees of scientific goodness. Religion is in fact just bad science.There may be a god but it is much less likely to be found or understood by bad science. Quine said:
"For my part I do, qua lay physicist, believe in physical objects and not in Homer’s gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing, the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conceptions only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience."
My reply, below, is that whilst I agree that there is a general category of epistemology that runs from standard science through world view synthesis to religion, we need to factor in epistemic tractability which varies with the object of study. Objects such as springs and precipitates are very different in terms of epistemic tractability to say "evolutionary history"; accordingly standards of "proof" vary.
Timothy V Reeves I believe there is an epistemic continuum from elementary spring extending and test tube precipitating science, through economics, sociology, history, evolutionary psychology to outright world view synthesis which includes what we think ultimate reality to be. (The latter includes religion). The epistemic common factor here is one of a contentious but hopefully constructive dialogue between experience and our theoretical narratives which attempt to make sense of our experience. So I’m inclined to agree with the view that elementary science is on the same epistemic continuum that religion is on.
But… and it’s a really big but….But that continuum is not necessarily a continuum of “good and bad” science/rationality, but one of epistemic tractability. For example the objects that social scientists and historians deal with are far less epistemically tractable than, say, springs and chemicals in as much as those objects are far more complex and erratic in their presentation. Hence someone can practice bad science with a very tractable ontology and yet another person can do good history with the far less epistemically tractable objects of history. In short it would certainly be wrong to judge historians by the standards of the “physical sciences” when the ontologies dealt with are very different in complexity, accessibility and presentation.
One has to factor in the nature of the ontology one is dealing when discussing this subject. In “Against Method” Feyeraband is good on the subject of how hard epistemic method is to pin down to anything definite even within the so-called “physical sciences”
As for “physical objects” – Quine really needs to reflect on what this means – it’s a loaded term that makes little sense given that the concept of “physical objects” presumes a huge mountain of epistemic and theoretical refection even before they can be defined and understood with anything less than a vaguely felt understanding.
Timothy V Reeves ..and one of those non-physical objects with all the potential for generating controversy is the question of very complex nature of science itself. In the philosophy of science we attempt to turn the tools of observation and theoretical narrative onto themselves, thus giving us a "science of science", the quintessential reflexive endeavour!
