Part 999: My Fundamental Theorem of Biology

Are you a S J Gould fan? I think "a" will vary from time to time. Also there are probably different kinds of "a".

In between times a damping or stabilizing factor cuts in, causing a period of apparent regularity and also some aesthetics in forms.

Resha Caner said:

What I came up with as a "Fundamental Theorem of Biology" is P = (n^a)*f, where:

P = probability of viable organisms
n = number of nested levels
a = acceleration factor
f = lowest probability of self-assembly of a fundamental element

Initially all I focused on was the 'f' factor.

Given a set of fundamental elements, S, what are the probabilities of self-assembly? For example, suppose S = <P,Q,R,S,T>. Further, suppose we define rules of the form, If C then PQ, meaning that if condition C is met, P and Q assemble (join together). If the rules can be expressed mathematically, the probability of any statement (e.g. If C then PQ) can be calculated.

Given the probabilities of all these statements, a Markov transition matrix can be created. A Markov transition matrix is just an eigenvalue problem, which means that for simple cases, we can derive closed form equations for the probabilities of self-assembly.

If we assume a simple rule such as for any list of fundamental elements, there are equal probabilities of assembling with the element preceding and following it in the list, the equation that results is: f = 1 / (2^(n-2) + sum{i=2,n}(2^(i-2))). Several cases like this can be solved. However, they quickly become so complex as to make closed form solutions impractical and numerical solutions become necessary.

One means of numerical solution is TAM (Tile Assembly Method). If one programs rules for Markov chains as described above, it can be quickly demonstrated that TAM correctly approximates the closed form cases.

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I think this is in error and that you dont understand how evolution works.

"Viabale organisms" is not really a thing as evolution is always happening and all classfication is a bit arbitrary.

Resha Caner said:

Hi. Would you like some context for this thread?

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No.

Resha Caner said:

What I came up with as a "Fundamental Theorem of Biology" is P = (n^a)*f, where:

P = probability of viable organisms
n = number of nested levels
a = acceleration factor
f = lowest probability of self-assembly of a fundamental element

Click to expand...

What are your definitions of nested levels and acceleration factors?

Resha Caner said:

What I came up with as a "Fundamental Theorem of Biology" is P = (n^a)*f, where:

P = probability of viable organisms
n = number of nested levels
a = acceleration factor
f = lowest probability of self-assembly of a fundamental element

Click to expand...

You appear to be confusing abiogenesis and evolution. If the merger of the two in your formula is conscious and deliberate then the resultant simplification renders it pretty well meaningless. I need to know whether you were confused or conscious before commenting further.

Resha Caner said:

I am aware of the difference between abiogenesis and evolution.

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Formulation for "self assembly of a fundamental element" only relates to abiogenesis and thus is irrelevant to subsequent evolution. Alternatively, you are defining 'fundamental element' in such a way that it is not actually fundamental, but a derived element, with possibly novel functions.

You say that some of the definitions "would need some work". In the absence of that work all you seem to have is word salad, expressed as a pseudo -equation.

I'm not trying to be offensive (it comes naturally, with zero effort), but if you think you have something, you need to weigh in with a substantial effort, not these gossamer half-thoughts.

Resha Caner said:

What I came up with as a "Fundamental Theorem of Biology" is P = (n^a)*f, where:

P = probability of viable organisms
n = number of nested levels
a = acceleration factor
f = lowest probability of self-assembly of a fundamental element

Initially all I focused on was the 'f' factor.

Given a set of fundamental elements, S, what are the probabilities of self-assembly? For example, suppose S = <P,Q,R,S,T>. Further, suppose we define rules of the form, If C then PQ, meaning that if condition C is met, P and Q assemble (join together). If the rules can be expressed mathematically, the probability of any statement (e.g. If C then PQ) can be calculated.

Given the probabilities of all these statements, a Markov transition matrix can be created. A Markov transition matrix is just an eigenvalue problem, which means that for simple cases, we can derive closed form equations for the probabilities of self-assembly.

If we assume a simple rule such as for any list of fundamental elements, there are equal probabilities of assembling with the element preceding and following it in the list, the equation that results is: f = 1 / (2^(n-2) + sum{i=2,n}(2^(i-2))). Several cases like this can be solved. However, they quickly become so complex as to make closed form solutions impractical and numerical solutions become necessary.

One means of numerical solution is TAM (Tile Assembly Method). If one programs rules for Markov chains as described above, it can be quickly demonstrated that TAM correctly approximates the closed form cases.

Click to expand...

OK, I let this sit for a while hoping it would develop a bit, but what we've seen so far is a bit thin.

Let's start with the formula for "P",

P = (n^a)*f

why does it take this form? How are the values assigned? and How is this connected to physical systems?

I also tend to agree with some of the other posters about this attempt and abiogenesis. Self-assembly would seem to apply to creating life from precursor chemicals, but doesn't seem to to apply to the development of one lifeform from another. I'm not saying there couldn't be formulae to describe such a scenario and evaluate its probability, but it probably isn't the same formula to describe abiogensis.

So it would be great to see how this formula comes into existence and then seeing it in action.

Resha Caner said:

Targeting a formulation meant to replicate evolution (abiogenesis, or any specific idea about biology) would be cheating (begging the question) and would miss the point of what I was doing. IOW, I disagree with your assessment.

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Your first sentence does not parse, so I am unable to understand why you disagree with my assessment. The fault appears to lie in the lack of clarity in your original exposition and now in your response. Perhaps you would try again.

Resha Caner said:

Hi. Would you like some context for this thread?

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We always thrive on context. Nature is big therefore the subject of nature is big.

Resha Caner said:

... but there are other possibilities.

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I would say there are a huge number of probabilities, in the midst of which the things you are specifying are also part. E.g varying conditions in the cosmos/on earth, some difficult to predict.

None of this explains "why" we have the minds, souls and spirits we have: but it helps us form a range of preliminary ideas for some of the hypotheses, where "inference" will be just as important as falsifiability. This sort of thing has on the wider scale always been very respectable and part of the life blood of the sciences.

Resha Caner said:

It would be easy to write a program where something evolves. It would be easy to write a program where nothing is created until an intelligent agent intervenes. Neither of those programs would mean anything. It begs the question to assume evolution or creation in the fundamentals. If the structure is to mean anything, it must be built from first principles that make no assumptions about the result.

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Why would you need to make assumptions about the result? We know the result - evolution. We know much of the detail of the mechanisms of evolution. I imagined what you were attempting to do was express those mechanisms as a formula. Why would you ignore what is already established through evidence and approach it via . . . well, I'm not sure what is was to be via.

Puzzled.

Resha Caner said:

Indeed, it seems I've done a poor job. ...

It would be easy to write a program where something evolves. It would be easy to write a program where nothing is created until an intelligent agent intervenes. Neither of those programs would mean anything. It begs the question to assume evolution or creation in the fundamentals. If the structure is to mean anything, it must be built from first principles that make no assumptions about the result. ...

Indeed. That is how I wanted to approach this - to show how it all developed. I didn't get a sense anyone had the patience to follow along, so I just plopped down a result. I'm not surprised it looks thin and meaningless.

But I'm at a loss how to proceed. I might suggest something like starting at the beginning and developing something together - something all participants can engage with - but ... meh ... I dunno. Sorry.

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Your equations would have to be well nigh infinitely more complex. I think science is built up by hints. For example, RNA and clay are crystalline. Popper proposes propensity fields - what I call happening places. One needs methodical realism in one's metaphysics, and one needs to (at least tentatively and provisionally) accept that the anthropic principle is not quite circular.

I like slow threads because I'm a slow thinker. Gould proposed relative "punctuations" in stable periods of mutations, when there were more mutations, often somewhat close-ish before or after major environmental changes. Cosmology sheds light.

Indeed some (sorry I forgot author names) think that a minute fraction of a split "second" after "the beginning" light happened, which may "explain" why it is so dominant in calculations in physics. I.e light seems to be a theme in the present "creation".

Science isn't a Wimbledon knockout.

The slapdash way science often gets conducted reminds me of the 1,000 piece jigsaw and when we had got to 200 pieces an irate Mother would want the lot swept off "the" table because she wanted to set tea and it was five to four.

We've got to have multi-theory hypotheses and multi-hypothesis theories, in every field, all the time. The table has got to be infinitely big.

Abduction from notions and induction has to constantly feed us ideas for consequent deduction. Speculative sciences are (sometimes unconsciously) usually 200 years ahead of the experimental and applications are usually 80 years behind that.

So, first principles will include light, the crystalline, the anthropic, and far more. Peirce and Husserl (whom I've only just started looking at) have ideas for hanging ideas on. According to M A K Halliday, Shannon and Wheeler were getting hints that matter, as matter, could be a special case of meaning.

Peirce liked equations, try him amongst others.

Indeed I was saying in another member's thread on eternal time (strangely lodged under "controversial" ) that spatial dimensions seem an intrusion while time seems an extrusion.