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Dear EricS,

 

It occurred to me that you, of all people, might have something to say about the question of how natural selection came about.  I assume it was “scaffolded” by some physical process or constraint in a manner analogous to the “scaffolding” of life by white smokers at the bottom of the sea.  Most accounts of evolution I have encountered start with the assumption of sufficient modularity for selection to go forward.  But given all the inevitable trait-entanglements in the developmental process, this assumption seems wildly gratuitous to me.  Any thoughts you might share with me (us) would be great appreciated.   I attach a decade-old outline of an essay I never wrote (because I wasn’t really comptent to do so) to explain the problem

 

Hope you are well and getting vaccinated soon.

Nick

 

Nick Thompson

[hidden email]

https://wordpress.clarku.edu/nthompson/

 


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David Eric Smith
Nick, hi,

I won’t be able to do anything like even a good-faith effort to reply to this thread.  The time it would cost me to compose something I wouldn’t either disagree with or regret having written will cost me more shame and punishment for delinquency than I can budget at the moment.

Your outline flags all good things.  I am not sure whether it provides a framework from which to make progress in a community that likes to fight (not FRIAM, the evolutionary silverbacks).

I do not claim, at all, to address an encompassing picture or propose a strategy that could be worked through to some satisfactory resolution.  I will claim that part of the problem is a bad problem in conceptual delineation in much (not all!) of the community, which the terminology canalizes and makes it hard to escape from.  For part of that I do have something I think is a corrective.  I don’t know if it will ever be accepted anywhere, so I put it on the BioRxiv here:

Don’t be concerned yet (or maybe ever) with what I build, but perhaps take it as a scaffold through which to see more clearly part of the existing problem, which I think is not too hard to correct.  

A good starting foil, which illustrates several of the points in your outline with its own internal contradictions, is this one by Lynch:
His whole thesis is that combinatorial factors aren’t heritable and so can’t be selected (the arch-form of which is Williams/Dawkins genic selection; the endlessly-nebulous form of which is the Units of Selection chautauqua that will never end; I guess Samir Okasha gives as good a version of it as can be found).  Yet Lynch ends by saying (somewhere near the bottom of the paper) “so you see, we are stuck with admitting that genotypes are the units of selection”, after just having said that the arrangement that makes a genotype different from a gene isn’t selectable.  

So I say go back a few steps and take a different tack.  Various parts of the following are all well handled by George Price, Warren Ewens, or Steve Frank, cited by me in the above:
1. Fisher says, distinguish the definition of fitness as a summary statistic, from the causal models of sources of fitness that you are trying to estimate from samples of that statistic.  Then fitness will never be a tautology.  
2. Fisher’s definition is apportionment of offspring to ancestors by type.  Immediately that summary statistic doesn’t exist for anything that doesn’t have a simple forward branching structure, so we have an unbridgeable conceptual inconsistency with Darwin’s differential reproductive success, which treated organisms (Steven Gould in SET argues very hard) and didn’t worry about how the mechanic of heredity would make that hard to quantify.
3. The only place the two don’t come into conflict are replicators, and voila! We have the corner into which the modern synthesis painted evolution, which led to excess emphasis on replicators and a lack of system to handle anything that isn’t a replicator.
4. Fisher of course mostly worked on diploid organisms, which are not replicators, but having introduced differential apportionment precisely to get out of the tautology “fit are the fit”, he said “well, if it doesn’t have one parent, do additive regressions”.  Shubik would go on an epic rant that if your definition of a process depends on which case you are trying to model, it was never a definition and you didn’t have either a theory or a formal system.  (What does “+” mean in this thing you call “addition"?  Well, depends on whether you are a republican or a democrat. etc.). All that is entirely right, and should be held to forever.  Lewontin would point out that regressions are not explanatorily or causally sufficient, since the thing you call fitness depends on idiosyncrasies of the sample of the population state.  So you call it a property assignable to genes, while ensuring that It never is, except in the cases for which you didn’t need it, and even those it mis-handles (in my paper; trivial but didactic example from an earlier paper of Ewens and Lessard, cited.)
5. So where are we now?  Population genetics has tried to do the best it can with this history, and aspires to the quite valid wish for a compact formal abstraction that will project out infinite detail but keep a usable computational system.  The way it does this — says I — is to call “evolution” a Polya’s Urn problem that hands _names_ of entities (genes or other “units of selection”) to The Rest of Nature, and nature hands back “fitnesses” for those names from a black box.  This separation is essential to their reduction, and it then dictates that fitness be the only channel for information flow.

6. So now I can say briefly what my claim is:
6a: Standard pop-gen is committed to separating gene counts from _what genes do_, the latter going into the black box of the genotype+environment -> phenotype -> fitness map.
6b. If you do that you have cut out infinitely many information channels that selection is actually using.
6c. Price recognized part of this, as later have Steve Frank, David Queller, and Ben Kerr and Peter Godfrey-Smith in varying ways.  Price kept with the idea he calls “corresponding sets” to define fitness, but didn’t make a draconian projection to replicators, because he recognized that definition could be applied at more than one stage in complicated lifecycles.  Frank, Queller, and Kerr have done other things, which I will let you find in the paper if you care; they are all good, and all stop short of an actual solution.

7. So I say, we can keep Fisher’s separation of summary statistics from causal model inference, but include a far richer set of information channels, by formalizing the idea of a lifecycle, and looking at the reproductive cycles within a collection of related possible realizations of the lifecycle, running regressions on those rather than on replication events.  This is no more radical than what we do in chemistry already, recognizing that a molecule is more than a bag of its atoms, even though the relations (bonds) get changed by reactions.  There are good tools for such modeling; it is still compact (though less so than the replicator abstraction), and in the sense of paradigm expressiveness and computational complexity, it is a qualitatively richer class.  
7a.  I would say that the way to say this is that we all throw out infinitely much of “what genes do”, or black-box it somewhere, but the lifecycle approach allows us to take in a category of things genes do, into the selection model itself, that the replicator abstraction requires us to exclude.
7b.  Really REALLY I do not mean I am introducing “other fitnesses”, or “generalized fitness” or any “modifier-fitness”.  Fitness is fitness; Price defined it well, it is a restrictive concept tied to either replicators or the modestly richer “corresponding sets”, and it omits infinitely much.  Don’t think about elephants.  What we want to do is recognize everything else in the universe that aren’t elephants.  There are infinitely many other summary statistics that are not fitness and that mean and cover different regularities.  We have machinery to use many of them; we should.
7c.  Another way to say this is that we start with an object semantics that is richer than the replicator and better able to capture features of the different character of biological objects and the transformations that relate them. 

8. So from then one can do a few elementary things that nobody will care about, to convince the author that there is something to say in all this.  That and $5.50 will buy you a cup of coffee at Starbucks.  
8a. The Price Equation exists for lifecycles, and a variety of things that Fisher’s and Price’s form get wrong, in the sense of causal or explanatory insufficiency, are got correct by the lifecycle version.  It doesn’t mis-specify models without necessity, and doesn’t introduce population-state dependence where it isn’t needed.
8b.  The interpretation of Fisher’s covariance term as “causal”, which was wrong since the beginning and Warren Ewens correctly shows has always been wrong, becomes correct (at least for a much wider suite of phenomena) in the lifecycle model.
8c. If you formalize the model-inference problem in the theory of large deviations for trajectories (one should formalize everything in the theory of large deviations for trajectories if at all possible), you can extract the information channel associated with each lifecycle flow and regression coefficient, and in that way quantify _what_ information is coming in through the coordinated action of objects of different types at multiple stages in the lifecycle.  One also recovers all the usual stuff — least-squares criteria, additive projections if you want — in suitable small-error limits.


In all the above — apologies — I didn’t actually answer the theme of the thread, which is how developmental complexity relates to modularization either in the principle components of environment forcing, or in the statistics of heredity.  I fully think in D’arcy Thompson terms here, but I think the others on the list already do too, so there isn’t anything I can say that adds there.

I think the modularization question will turn out to be hard (sense of multi-faceted and rich, and branching into several principles that will become evident as we start to solve more cases of it), and will be related to the power of reinforcement acting on populations as a regularity-extractor.  I like what Leslie Valiant has to say in PAC, as a way of framing the issues, even though I know he is a punching bag for the geneticists because of various things they understand are important that he isn’t trying to understand deeply or deal with.  I don’t care that he had limitations; the question for me is whether there is a good insight there that could be developed further.

What I intend in the 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.

Anyway, long, sorry, but….

Eric



On Mar 25, 2021, at 6:52 AM, <[hidden email]> <[hidden email]> wrote:

Dear EricS,
 
It occurred to me that you, of all people, might have something to say about the question of how natural selection came about.  I assume it was “scaffolded” by some physical process or constraint in a manner analogous to the “scaffolding” of life by white smokers at the bottom of the sea.  Most accounts of evolution I have encountered start with the assumption of sufficient modularity for selection to go forward.  But given all the inevitable trait-entanglements in the developmental process, this assumption seems wildly gratuitous to me.  Any thoughts you might share with me (us) would be great appreciated.   I attach a decade-old outline of an essay I never wrote (because I wasn’t really comptent to do so) to explain the problem
 
Hope you are well and getting vaccinated soon. 
Nick 
 
Nick Thompson
 
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thompnickson2
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thompnickson2

Thank you EricS for this long and thoughtful answer.  I hope The Gang will spend a lot of Friday, mining it out.  What I, of course, appreciate the most is your acknowledging that The Problem is in fact A Problem.  That you give me some sources to read if I am ever to understand it better, is gravy … good thick dark gravy.

 

Nick

 

 

From: Friam <[hidden email]> On Behalf Of David Eric Smith
Sent: Wednesday, March 24, 2021 5:46 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Cc: David Eric Smith <[hidden email]>
Subject: Re: [FRIAM] (no subject)

 

Nick, hi,

 

I won’t be able to do anything like even a good-faith effort to reply to this thread.  The time it would cost me to compose something I wouldn’t either disagree with or regret having written will cost me more shame and punishment for delinquency than I can budget at the moment.

 

Your outline flags all good things.  I am not sure whether it provides a framework from which to make progress in a community that likes to fight (not FRIAM, the evolutionary silverbacks).

 

I do not claim, at all, to address an encompassing picture or propose a strategy that could be worked through to some satisfactory resolution.  I will claim that part of the problem is a bad problem in conceptual delineation in much (not all!) of the community, which the terminology canalizes and makes it hard to escape from.  For part of that I do have something I think is a corrective.  I don’t know if it will ever be accepted anywhere, so I put it on the BioRxiv here:

 

Don’t be concerned yet (or maybe ever) with what I build, but perhaps take it as a scaffold through which to see more clearly part of the existing problem, which I think is not too hard to correct.  

 

A good starting foil, which illustrates several of the points in your outline with its own internal contradictions, is this one by Lynch:

His whole thesis is that combinatorial factors aren’t heritable and so can’t be selected (the arch-form of which is Williams/Dawkins genic selection; the endlessly-nebulous form of which is the Units of Selection chautauqua that will never end; I guess Samir Okasha gives as good a version of it as can be found).  Yet Lynch ends by saying (somewhere near the bottom of the paper) “so you see, we are stuck with admitting that genotypes are the units of selection”, after just having said that the arrangement that makes a genotype different from a gene isn’t selectable.  

 

So I say go back a few steps and take a different tack.  Various parts of the following are all well handled by George Price, Warren Ewens, or Steve Frank, cited by me in the above:

1. Fisher says, distinguish the definition of fitness as a summary statistic, from the causal models of sources of fitness that you are trying to estimate from samples of that statistic.  Then fitness will never be a tautology.  

2. Fisher’s definition is apportionment of offspring to ancestors by type.  Immediately that summary statistic doesn’t exist for anything that doesn’t have a simple forward branching structure, so we have an unbridgeable conceptual inconsistency with Darwin’s differential reproductive success, which treated organisms (Steven Gould in SET argues very hard) and didn’t worry about how the mechanic of heredity would make that hard to quantify.

3. The only place the two don’t come into conflict are replicators, and voila! We have the corner into which the modern synthesis painted evolution, which led to excess emphasis on replicators and a lack of system to handle anything that isn’t a replicator.

4. Fisher of course mostly worked on diploid organisms, which are not replicators, but having introduced differential apportionment precisely to get out of the tautology “fit are the fit”, he said “well, if it doesn’t have one parent, do additive regressions”.  Shubik would go on an epic rant that if your definition of a process depends on which case you are trying to model, it was never a definition and you didn’t have either a theory or a formal system.  (What does “+” mean in this thing you call “addition"?  Well, depends on whether you are a republican or a democrat. etc.). All that is entirely right, and should be held to forever.  Lewontin would point out that regressions are not explanatorily or causally sufficient, since the thing you call fitness depends on idiosyncrasies of the sample of the population state.  So you call it a property assignable to genes, while ensuring that It never is, except in the cases for which you didn’t need it, and even those it mis-handles (in my paper; trivial but didactic example from an earlier paper of Ewens and Lessard, cited.)

5. So where are we now?  Population genetics has tried to do the best it can with this history, and aspires to the quite valid wish for a compact formal abstraction that will project out infinite detail but keep a usable computational system.  The way it does this — says I — is to call “evolution” a Polya’s Urn problem that hands _names_ of entities (genes or other “units of selection”) to The Rest of Nature, and nature hands back “fitnesses” for those names from a black box.  This separation is essential to their reduction, and it then dictates that fitness be the only channel for information flow.

 

6. So now I can say briefly what my claim is:

6a: Standard pop-gen is committed to separating gene counts from _what genes do_, the latter going into the black box of the genotype+environment -> phenotype -> fitness map.

6b. If you do that you have cut out infinitely many information channels that selection is actually using.

6c. Price recognized part of this, as later have Steve Frank, David Queller, and Ben Kerr and Peter Godfrey-Smith in varying ways.  Price kept with the idea he calls “corresponding sets” to define fitness, but didn’t make a draconian projection to replicators, because he recognized that definition could be applied at more than one stage in complicated lifecycles.  Frank, Queller, and Kerr have done other things, which I will let you find in the paper if you care; they are all good, and all stop short of an actual solution.

 

7. So I say, we can keep Fisher’s separation of summary statistics from causal model inference, but include a far richer set of information channels, by formalizing the idea of a lifecycle, and looking at the reproductive cycles within a collection of related possible realizations of the lifecycle, running regressions on those rather than on replication events.  This is no more radical than what we do in chemistry already, recognizing that a molecule is more than a bag of its atoms, even though the relations (bonds) get changed by reactions.  There are good tools for such modeling; it is still compact (though less so than the replicator abstraction), and in the sense of paradigm expressiveness and computational complexity, it is a qualitatively richer class.  

7a.  I would say that the way to say this is that we all throw out infinitely much of “what genes do”, or black-box it somewhere, but the lifecycle approach allows us to take in a category of things genes do, into the selection model itself, that the replicator abstraction requires us to exclude.

7b.  Really REALLY I do not mean I am introducing “other fitnesses”, or “generalized fitness” or any “modifier-fitness”.  Fitness is fitness; Price defined it well, it is a restrictive concept tied to either replicators or the modestly richer “corresponding sets”, and it omits infinitely much.  Don’t think about elephants.  What we want to do is recognize everything else in the universe that aren’t elephants.  There are infinitely many other summary statistics that are not fitness and that mean and cover different regularities.  We have machinery to use many of them; we should.

7c.  Another way to say this is that we start with an object semantics that is richer than the replicator and better able to capture features of the different character of biological objects and the transformations that relate them. 

 

8. So from then one can do a few elementary things that nobody will care about, to convince the author that there is something to say in all this.  That and $5.50 will buy you a cup of coffee at Starbucks.  

8a. The Price Equation exists for lifecycles, and a variety of things that Fisher’s and Price’s form get wrong, in the sense of causal or explanatory insufficiency, are got correct by the lifecycle version.  It doesn’t mis-specify models without necessity, and doesn’t introduce population-state dependence where it isn’t needed.

8b.  The interpretation of Fisher’s covariance term as “causal”, which was wrong since the beginning and Warren Ewens correctly shows has always been wrong, becomes correct (at least for a much wider suite of phenomena) in the lifecycle model.

8c. If you formalize the model-inference problem in the theory of large deviations for trajectories (one should formalize everything in the theory of large deviations for trajectories if at all possible), you can extract the information channel associated with each lifecycle flow and regression coefficient, and in that way quantify _what_ information is coming in through the coordinated action of objects of different types at multiple stages in the lifecycle.  One also recovers all the usual stuff — least-squares criteria, additive projections if you want — in suitable small-error limits.

 

 

In all the above — apologies — I didn’t actually answer the theme of the thread, which is how developmental complexity relates to modularization either in the principle components of environment forcing, or in the statistics of heredity.  I fully think in D’arcy Thompson terms here, but I think the others on the list already do too, so there isn’t anything I can say that adds there.

 

I think the modularization question will turn out to be hard (sense of multi-faceted and rich, and branching into several principles that will become evident as we start to solve more cases of it), and will be related to the power of reinforcement acting on populations as a regularity-extractor.  I like what Leslie Valiant has to say in PAC, as a way of framing the issues, even though I know he is a punching bag for the geneticists because of various things they understand are important that he isn’t trying to understand deeply or deal with.  I don’t care that he had limitations; the question for me is whether there is a good insight there that could be developed further.

 

What I intend in the 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.

 

Anyway, long, sorry, but….

 

Eric

 

 

 

On Mar 25, 2021, at 6:52 AM, <[hidden email]> <[hidden email]> wrote:

 

Dear EricS,

 

It occurred to me that you, of all people, might have something to say about the question of how natural selection came about.  I assume it was “scaffolded” by some physical process or constraint in a manner analogous to the “scaffolding” of life by white smokers at the bottom of the sea.  Most accounts of evolution I have encountered start with the assumption of sufficient modularity for selection to go forward.  But given all the inevitable trait-entanglements in the developmental process, this assumption seems wildly gratuitous to me.  Any thoughts you might share with me (us) would be great appreciated.   I attach a decade-old outline of an essay I never wrote (because I wasn’t really comptent to do so) to explain the problem

 

Hope you are well and getting vaccinated soon. 

Nick 

 

Nick Thompson

 

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gepr
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gepr
In reply to this post by David Eric Smith
That paper is positively pornographic! Well done.

If I understand what you're doing, which I most likely don't, the mechanized graphs are an excellent example of some rhetoric I'm currently trying to foist on some unwilling victims (re the "languages" within which we couch hypotheses, and how "language" choice sets a frame/paradigm).

But they're academics. And I am not. So I'd like to confirm that you've submitted it somewhere, regardless of your expectations of acceptance? I don't need to know where. If so, I'll feel more confident in encouraging them to read it.


On March 24, 2021 4:46:23 PM PDT, David Eric Smith <[hidden email]> wrote:
>I will claim that part of the problem is a bad problem in conceptual
>delineation in much (not all!) of the community, which the terminology
>canalizes and makes it hard to escape from.  For part of that I do have
>something I think is a corrective.  I don’t know if it will ever be
>accepted anywhere, so I put it on the BioRxiv here:
>https://www.biorxiv.org/content/10.1101/2021.02.09.430402v1.abstract
><https://www.biorxiv.org/content/10.1101/2021.02.09.430402v1.abstract>
>
>
--
glen ⛧

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uǝʃƃ ⊥ glen
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David Eric Smith
Hi Glen,

Thank you, and yes, I did submit it somewhere.  There are a couple of different evolution journals where this kind of subject is published.  They all have length limits — 140 characters or something like that — which this thing exceeds.  I don’t even remember which of them I sent to, because their formats turn out to be quite similar.  Mostly I was trying to get it before the eyes of a couple of people whom I hope the editor will ask as reviewers, who I think will immediately understand what the move is, because it is so close to where they have already come, and that they will agree that it is a kind of natural completion of what Price and also they were trying to do.  After that the editor will reject it, but I can ask for advice on whether there is anyplace it could be published, without violating the conditions of review.  

I am horrible at timeliness on reviews, and during COVID, everyone else has become uncommonly bad as well.  So it could be years before I hear anything.  I have another paper that is now out for about 30 months to a Springer journal; this one has only been out maybe 8 or 10 months.

Many thanks,

Eric


> On Mar 25, 2021, at 8:02 PM, ⛧ glen <[hidden email]> wrote:
>
> That paper is positively pornographic! Well done.
>
> If I understand what you're doing, which I most likely don't, the mechanized graphs are an excellent example of some rhetoric I'm currently trying to foist on some unwilling victims (re the "languages" within which we couch hypotheses, and how "language" choice sets a frame/paradigm).
>
> But they're academics. And I am not. So I'd like to confirm that you've submitted it somewhere, regardless of your expectations of acceptance? I don't need to know where. If so, I'll feel more confident in encouraging them to read it.
>
>
> On March 24, 2021 4:46:23 PM PDT, David Eric Smith <[hidden email]> wrote:
>> I will claim that part of the problem is a bad problem in conceptual
>> delineation in much (not all!) of the community, which the terminology
>> canalizes and makes it hard to escape from.  For part of that I do have
>> something I think is a corrective.  I don’t know if it will ever be
>> accepted anywhere, so I put it on the BioRxiv here:
>> https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwww.biorxiv.org%2fcontent%2f10.1101%2f2021.02.09.430402v1.abstract&c=E,1,BJI4v-sKlAKG9TTqIjaeaWW0r---JGH7j68TIOfK62NVQsDk3M1v4LKlGLHYHYl0IGS6JpyKBEFpWW760HkvNqZI01T4whPz2owBEjJEDEpvH3wrgQ,,&typo=1
>> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwww.biorxiv.org%2fcontent%2f10.1101%2f2021.02.09.430402v1.abstract&c=E,1,PiNnB4Mea11E3NbOf1J9kiBNwaJm_D356Z9AK-rtlkWlamy0uIN4X23SortvEWwhFmu1adf-m6N63uM8CxTaVIkw5JBVfpjNgjmV75TSNav8oe1eXG9LRLs,&typo=1>
>>
>>
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jon zingale
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"""
I like what Leslie Valiant has to say in PAC, as a way of framing the issues, even though I know he is a punching bag for the geneticists because of various things they understand as important that he isn’t trying to understand deeply or deal with. I don’t care that he had limitations; the question for me is whether there is a good insight that could be developed further.

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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David Eric Smith
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Jon, hi and thank you,

So, I am not going to be knowledgeable or sophisticated enough to have a conversation with you as an equal on computational complexity classes and algorithms.  I can tell you what I was hoping to take from Valiant, on the assumption that it is compatible with the current best understanding of complexity classification of problems.  If I say things that, through lack of technical understanding, stand for qualitatively wrong assertions, please correct if you are willing to.

I guess there are topics here that could be discussed partly disconnected, and then I have to recall why I brought them up together.  I’ll start with the disconnected.

On Apr 27, 2021, at 1:46 PM, jon zingale <[hidden email]> wrote:

"""
I like what Leslie Valiant has to say in PAC, as a way of framing the issues, even though I know he is a punching bag for the geneticists because of various things they understand as important that he isn’t trying to understand deeply or deal with. I don’t care that he had limitations; the question for me is whether there is a good insight that could be developed further.

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?

For definiteness, I will have in mind some problem class with constant structural description and a scaling variable, such as 3-sat, that is NP.  I understand that classification to mean that, over all ordinary discrete-step solution algorithms with some bound on their parallelism in relation to the system size, no algorithm will certainly find a solution to an arbitrary instance with a time cost in a smaller class than exhaustive elaboration — meaning exponential in the problem size (even if the exponent is smaller than exhaustive elaboration).  Compare that then to some other problem class that is simpler, P or some sufficiently low order polynomial, or whatever.

What I hear Valiant trying to get at with his “learnable” functions is an assertion about how reinforcement learning can either produce a solution or contradiction itself to an arbitrary instance, or somehow be mapped to or select an algorithm that can do that.  I understand his claim to be that, if the problem class is of sufficiently low complexity, reinforcement can obtain solutions almost-surely within some time bound, but if the problem is NP, reinforcement cannot (directly, or by way of selecting some implementation of an algorithm), produce solutions.  I am not sure I know “precisely" what the claim is.  Of course it could not produce a solution in less than exponential time cost, by the stipulation that the problem is NP.  So to be saying that the problem is not “learnable”, I assume Valiant is asserting that reinforcement could not arrive at a solution almost-surely, at all.  

I’m not sure, even if the above is okay to say, it makes claims about how any given algorithm will hold up under perturbation of its steps or rules.  I have assumed these complexity classes are frontiers that cannot be surpassed.  But any given instantiation of any given solution, if disassembled and re-arranged, presumably yields another function that is simply of a different kind, which could be far behind the frontier.  So in your comment I seem to see two topics: about the limiting performance over all solutions, and about robustness characteristics of any particular solution, relevant (?) in different contexts?

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.

The concept of scaffolding seems to be extremely fertile, and is closer in a recognizable way to the _very small_ thing I was trying to do within that paper.  I happen to be re-activated on scaffolding for various other reasons that I won’t digress on here.  The connection would be that, to understand the questions about memory and selection that genetics wants to ask, you would need to judiciously include aspects of “what genes do” — together with each other — into your abstraction for what a system’s states and transition rules are.  That was what the hypergraph formulation was meant to support.

I will mention, however, that the anecdotes of response to COVID vaccines have me thinking that, in a different life, I could have greatly enjoyed researching sex differences in immune response.  Immune response in people is such an exceeding tangle of components, accreted over deep time, with very complex interplays, and many of them set fo a quantitative trade-off between sensitivity and aggressiveness of protection, against noise-suppression and avoidance of self-harm.  How the regulation of that system should somehow be co-tangled with the other complex regulations of sex difference — how much comes from components on the sex-determining chromosomes, versus how much is systemically modulated by long pathways that are only sex-linked very indirectly — would be a perfect challenge to “complexity” science.  I have thought, anecdotally, of women’s immune responses as being, modestly but significantly, more sensitive and better regulated than men's, but the spectrum of responses turns out to be a quagmire.  See
(e.g. p.39).
Yet this seems to trade off against increased incidence of some common autoimmune diseases such as lupus and MS, in women.  How does one understand the vast complexity of selective forces and developmental commitments that result in these simple blunt statistics?

But back to your question.  I agree.  The fact that we _have_ chromosomes, and _have_ ontogenetic and developmental regulatory sequences; that there even are categorical functions that identify “genes” within which variation creates “alleles”, is the ultimate scaffolding.  Because I have to deal with RNA-World Origin of Lifers all the time, to whom everything is just a point-set of 1-off atoms of function carried on short RNA segments, I am sensitive to the enormous gulf between the model they put forth for the world, and what life became by the time it became “genomic” per se.  To very material-literalist minds, there is no question here: molecules just get longer and the number of things linked by covalent bonds increases.  There isn’t really even a word for the defined sequence of gene interactions in unicells — “development” as a technical term is meant to refer to the regulatory sequences governing multicellularity.  But to me, the emergence of defined “roles” in a choreographed cell-building “program” is _the_ interesting thing to understand about the integration of fragmentary functional molecules.  Multicellular development is then just an elaboration on that theme after various other architectural transitions (the stuff Chris Kempes does so well with Tori Hoelher and others).  

This, I think, is where I connect back to Valiant.  My intuition is that the “bag of genes / bag of functions” paradigm of the RNA-Worlders becomes something that selection can no longer impose any sense on, already at fairly small bags.  If Leslie is right, then compared to the set of all possible bags and all function composition combinations they could hold, the set of things selection can ever impose sense on becomes vanishingly small as the bags get large, as small as P < NP.  Merely-linked gene fragments in a macromolecule might be the bags, or cells might be.  If that intuition is valid, then the only things selection could ever rescue from chaos become those that get canalized into these ur-developmental “programs”, with defined roles for genes, and merely allelic variation within each role.  I would like to find a formal way to frame that assertion as a question and then solve it.

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.

I don’t think I said this in the early email to Nick and then Glen, but the place where I see my interest taking a coherent form is a bit to the side of the small and particular thing in this paper.

There is a broad class of phenomena that can be abstracted in what I have taken to calling “3-level systems”, by which I mean the following:

1. Level 1 are “rules” in the way the rule-based systems people use the term.  They could be reaction _mechanisms_ in graph-grammar chemistry, or site-rewrite rules in Walter Fontana’s site-graph abstractions for systems bio.  The rules have an algebra of dependencies, and category theory seems to be a good language for talking about how these can be embedded in contexts in a structure-preserving way.  Vincent Danos, Walter Fontana, and that whole crowd, and recently Nicolas Behr, as well as the MOD group are my go-to experts on this.

2. Level 2 are the “generators” of stochastic processes in a conventional sense.  They consist of contexts for the rules, and of transformations.  In a sense, they are “generated by” the rules (but they will “generate” a stochastic process in the level below them).  So reaction mechanisms from level 1, represented as graph-fragment rewrites, can act on a few starting molecules to produce an expanding set of actual, whole molecules, and the reactions that interconvert them.  Or for site graphs, rules, acting on any state of some protein type, can produce all the possible configurations.  The natural representation for these systems (at least for chemistry) is the hypergraph.  There is still an algebra of operation of reactions, but it is simpler than the algebra of rules, and mostly about counting.

3. Level 3 is then the state space, in which states are things like counts of all the possible species.  So the state space is just a lattice.  The “generator” from Level 2 is the generator of stochastic processes over this state space, and it is where probability distributions live.

I like these systems because a finite collection at any level can generate an indefinitely or infinitely large collection in the level below it.  So finitely many reaction mechanisms can generate an infinitely large hypergraph (the formose network or the HCN polymerization network).  Likewise, even a finite hypergraph can govern probability flows for indefinitely many particles, which is where mass-action chemistry and the classical world come from.

To return to your specific question: my interest is less in graphical models, as a class, than in the relation of these three levels of mathematical objects and how compactly encoded order at one level can govern cryptic but essential order in the level below it.  (Related to what makes a problem solvable, so back to the beginning.)  The hypergraph, at level 2, is interesting in its own right just because it is a generator of powerful and complex processes, and can be used to describe lots of stuff both expressively and yet analyzably.


If I could be doing this for a living, I would be.

Btw., Andres Ortiz-Munoz at SFI is a maven of the rule-based world.  Artemy Kolchinsky is a maven of non-equilibrium stochastics.  I keep hoping the two of them will notice something really original to do together.

All best,

Eric




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jon zingale
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jon zingale
EricS,

Thank you for the kind and thoughtful response. Your 'three levels'
project is interesting to me and reminds me (even if only tangentially)
of an analysis I worked on regarding food webs, n-species Lotka-Volterra,
and ABMs. I wanted to clarify for myself what each level of analysis
offered or bracketed relative to one another. There:

1. Food webs were analyzed as weighted graphs with the obvious Markov
chain interpretation[ρ]. Each edge effectively summarizing the complex
predator-prey interactions found at level 2, but without the plethora
of ODEs to solve.

2. N-species Lotka-Volterra, while being a jumble of equations, offered
dynamics. Here, one could get insight into how the static edge values
of level 1 were in fact fluctuating values in n-dimensional phase
space. But still, one is working with an aggregate model where species
is summarized wholly by population count.

3. ABMs, in theory, ought to be the whole story of individuals located
in space and time. There the agents (a lynx, say) 'decides' what to eat
based, perhaps, on what is most readily available. But as everyone on
the list knows, analysis at such a fine-grained scale is simply a mess.

I never did get as far with the analysis as I would have liked, and I
never got the chance to share my findings, so yeah, thanks for the
tangential opportunity, here and now, to say just this much.

1'. "site-rewrite rules in Walter Fontana’s site-graph abstractions"

Fleshing out some of your references, I found this Fontana paper[σ].
As you suggest, the style is fairly straightforward category theory.
Site-graphs and their morphisms form a well-defined category and a
number of universal constructions (push-outs, pullbacks, cospans,...)
are used to analyze the algebra and to establish its logic.

2'. "There is still an algebra of operation of reactions, but it is
simpler than the algebra of rules, and mostly about counting."

I am not entirely sure that I follow the distinction. Am I far off in
seeing an analogy here to the differences found between my one and two
above? I would love to have a facility with stochastic techniques like
these, but I most likely will need to remain a spectator for the rest
of my days. Occasionally, I meet LANL folk that can talk Feller and
Fokker with ease, and I am always jealous. It would be great to even
have a better understanding of where Lie groups (something I can at
least think about) meet the stochastic world.

3'. "So the state space is just a lattice. The “generator” from Level 2
is the generator of stochastic processes over this state space, and it
is where probability distributions live."

Please write more on this. By 'just a lattice' do you mean integer-valued
on account of the counts being so? Is the state space used to some
extent, like a modulii/classifying space, for characterizing the
species of reactions? I feel the fuzziest on how this level and the
2nd relate.

I am thankful to have had drinks with Artemy on a number of occasions,
though I am embarrassed to have never asked him to blow my mind, as he
could so easily have done.

I am working, slowly, through Valiant's discussion of evolvability
problems regarding monotone disjunction and parity. I will hopefully
have more to say soon. One thing that stands out for me is the idea
that Lamarck could be so right, but about the wrong thing, a concept
in search of a problem. While Lamarckism wasn't right for Darwin, it
was fine for perceptrons.

"""
If that intuition is valid, then the only things Selection could ever
rescue from chaos become those that get canalized into these ur-
developmental “programs”, with defined roles for genes, and merely
allelic variation within each role. I would like to find a formal way to
frame that assertion as a question and then solve it.
"""

Yes, that would be very exciting.

Cheers,
Jon

ps. I wrote Nick and Frank about a dream a day or two before your
post, where I found myself sitting with a figure that kept morphing
between Chris Kempes and Marcus. The figure was attempting to explain
a Turing complete ball game to me. I appreciate the synchronicity.

[ρ] Here, I mostly followed Levine's approach to computing trophic level.
  https://www.sciencedirect.com/science/article/abs/pii/002251938090288X

[σ] https://arxiv.org/pdf/1901.00592.pdf



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thompnickson2
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thompnickson2

Jon,

 

Mostly your comments were out of my league. 

 

However, one probably irrelevant fragment caught my eye.

 

While Lamarckism wasn't right for Darwin… .

 

Darwin always was a Lamarckian and became ever more so with every passing edition of the Origin. My favorite question in Biology orals was, “Who was the most famous Lamarckian?” 

 

I think you could say, with out contradiction

 

While Lamarckism isn’t right for most contemporary  Darwinians… .

 

 

… but evern that is becoming less true. 

 

I think you are talking about Weismann and Weismann’s Barrier?  Lamarckism was definitely not right for Weisman.

 

Nick Thompson

[hidden email]

https://wordpress.clarku.edu/nthompson/

 

-----Original Message-----
From: Friam <[hidden email]> On Behalf Of jon zingale
Sent: Wednesday, May 5, 2021 10:45 AM
To: [hidden email]
Subject: Re: [FRIAM] (no subject)

 

EricS,

 

Thank you for the kind and thoughtful response. Your 'three levels'

project is interesting to me and reminds me (even if only tangentially) of an analysis I worked on regarding food webs, n-species Lotka-Volterra, and ABMs. I wanted to clarify for myself what each level of analysis offered or bracketed relative to one another. There:

 

1. Food webs were analyzed as weighted graphs with the obvious Markov chain interpretation[ρ]. Each edge effectively summarizing the complex predator-prey interactions found at level 2, but without the plethora of ODEs to solve.

 

2. N-species Lotka-Volterra, while being a jumble of equations, offered dynamics. Here, one could get insight into how the static edge values of level 1 were in fact fluctuating values in n-dimensional phase space. But still, one is working with an aggregate model where species is summarized wholly by population count.

 

3. ABMs, in theory, ought to be the whole story of individuals located in space and time. There the agents (a lynx, say) 'decides' what to eat based, perhaps, on what is most readily available. But as everyone on the list knows, analysis at such a fine-grained scale is simply a mess.

 

I never did get as far with the analysis as I would have liked, and I never got the chance to share my findings, so yeah, thanks for the tangential opportunity, here and now, to say just this much.

 

1'. "site-rewrite rules in Walter Fontana’s site-graph abstractions"

 

Fleshing out some of your references, I found this Fontana paper[σ].

As you suggest, the style is fairly straightforward category theory.

Site-graphs and their morphisms form a well-defined category and a number of universal constructions (push-outs, pullbacks, cospans,...) are used to analyze the algebra and to establish its logic.

 

2'. "There is still an algebra of operation of reactions, but it is simpler than the algebra of rules, and mostly about counting."

 

I am not entirely sure that I follow the distinction. Am I far off in seeing an analogy here to the differences found between my one and two above? I would love to have a facility with stochastic techniques like these, but I most likely will need to remain a spectator for the rest of my days. Occasionally, I meet LANL folk that can talk Feller and Fokker with ease, and I am always jealous. It would be great to even have a better understanding of where Lie groups (something I can at least think about) meet the stochastic world.

 

3'. "So the state space is just a lattice. The “generator” from Level 2 is the generator of stochastic processes over this state space, and it is where probability distributions live."

 

Please write more on this. By 'just a lattice' do you mean integer-valued on account of the counts being so? Is the state space used to some extent, like a modulii/classifying space, for characterizing the species of reactions? I feel the fuzziest on how this level and the 2nd relate.

 

I am thankful to have had drinks with Artemy on a number of occasions, though I am embarrassed to have never asked him to blow my mind, as he could so easily have done.

 

I am working, slowly, through Valiant's discussion of evolvability problems regarding monotone disjunction and parity. I will hopefully have more to say soon. One thing that stands out for me is the idea that Lamarck could be so right, but about the wrong thing, a concept in search of a problem. While Lamarckism wasn't right for Darwin, it was fine for perceptrons.

 

"""

If that intuition is valid, then the only things Selection could ever rescue from chaos become those that get canalized into these ur- developmental “programs”, with defined roles for genes, and merely allelic variation within each role. I would like to find a formal way to frame that assertion as a question and then solve it.

"""

 

Yes, that would be very exciting.

 

Cheers,

Jon

 

ps. I wrote Nick and Frank about a dream a day or two before your post, where I found myself sitting with a figure that kept morphing between Chris Kempes and Marcus. The figure was attempting to explain a Turing complete ball game to me. I appreciate the synchronicity.

 

[ρ] Here, I mostly followed Levine's approach to computing trophic level.

  https://www.sciencedirect.com/science/article/abs/pii/002251938090288X

 

[σ] https://arxiv.org/pdf/1901.00592.pdf

 

 

 

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jon zingale
You're right ;) That is also one of my favorite facts about Darwin.



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thompnickson2
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thompnickson2
In reply to this post by thompnickson2

Oh, and …. this problem …

If that intuition is valid, then the only things Selection could ever rescue from chaos become those that get canalized into these ur- developmental “programs”, with defined roles for genes, and merely allelic variation within each role. I would like to find a formal way to frame that assertion as a question and then solve it.

… is the one that keeps me awake at night.

 

Let me put it another way: When the waiter rolls up the dessert cart, you are so dazzled by choice between the crème caramel, the tiramisu and the chocolate mousse cake, that you never stop to wonder how the cart got created.   

 

Nick

 

 

 

From: [hidden email] <[hidden email]>
Sent: Wednesday, May 5, 2021 2:01 PM
To: 'The Friday Morning Applied Complexity Coffee Group' <[hidden email]>
Subject: RE: [FRIAM] (no subject)

 

Jon,

 

Mostly your comments were out of my league. 

 

However, one probably irrelevant fragment caught my eye.

 

While Lamarckism wasn't right for Darwin… .

 

Darwin always was a Lamarckian and became ever more so with every passing edition of the Origin. My favorite question in Biology orals was, “Who was the most famous Lamarckian?” 

 

I think you could say, with out contradiction

 

While Lamarckism isn’t right for most contemporary  Darwinians… .

 

 

… but evern that is becoming less true. 

 

I think you are talking about Weismann and Weismann’s Barrier?  Lamarckism was definitely not right for Weisman.

 

Nick Thompson

[hidden email]

https://wordpress.clarku.edu/nthompson/

 

-----Original Message-----
From: Friam <[hidden email]> On Behalf Of jon zingale
Sent: Wednesday, May 5, 2021 10:45 AM
To: [hidden email]
Subject: Re: [FRIAM] (no subject)

 

EricS,

 

Thank you for the kind and thoughtful response. Your 'three levels'

project is interesting to me and reminds me (even if only tangentially) of an analysis I worked on regarding food webs, n-species Lotka-Volterra, and ABMs. I wanted to clarify for myself what each level of analysis offered or bracketed relative to one another. There:

 

1. Food webs were analyzed as weighted graphs with the obvious Markov chain interpretation[ρ]. Each edge effectively summarizing the complex predator-prey interactions found at level 2, but without the plethora of ODEs to solve.

 

2. N-species Lotka-Volterra, while being a jumble of equations, offered dynamics. Here, one could get insight into how the static edge values of level 1 were in fact fluctuating values in n-dimensional phase space. But still, one is working with an aggregate model where species is summarized wholly by population count.

 

3. ABMs, in theory, ought to be the whole story of individuals located in space and time. There the agents (a lynx, say) 'decides' what to eat based, perhaps, on what is most readily available. But as everyone on the list knows, analysis at such a fine-grained scale is simply a mess.

 

I never did get as far with the analysis as I would have liked, and I never got the chance to share my findings, so yeah, thanks for the tangential opportunity, here and now, to say just this much.

 

1'. "site-rewrite rules in Walter Fontana’s site-graph abstractions"

 

Fleshing out some of your references, I found this Fontana paper[σ].

As you suggest, the style is fairly straightforward category theory.

Site-graphs and their morphisms form a well-defined category and a number of universal constructions (push-outs, pullbacks, cospans,...) are used to analyze the algebra and to establish its logic.

 

2'. "There is still an algebra of operation of reactions, but it is simpler than the algebra of rules, and mostly about counting."

 

I am not entirely sure that I follow the distinction. Am I far off in seeing an analogy here to the differences found between my one and two above? I would love to have a facility with stochastic techniques like these, but I most likely will need to remain a spectator for the rest of my days. Occasionally, I meet LANL folk that can talk Feller and Fokker with ease, and I am always jealous. It would be great to even have a better understanding of where Lie groups (something I can at least think about) meet the stochastic world.

 

3'. "So the state space is just a lattice. The “generator” from Level 2 is the generator of stochastic processes over this state space, and it is where probability distributions live."

 

Please write more on this. By 'just a lattice' do you mean integer-valued on account of the counts being so? Is the state space used to some extent, like a modulii/classifying space, for characterizing the species of reactions? I feel the fuzziest on how this level and the 2nd relate.

 

I am thankful to have had drinks with Artemy on a number of occasions, though I am embarrassed to have never asked him to blow my mind, as he could so easily have done.

 

I am working, slowly, through Valiant's discussion of evolvability problems regarding monotone disjunction and parity. I will hopefully have more to say soon. One thing that stands out for me is the idea that Lamarck could be so right, but about the wrong thing, a concept in search of a problem. While Lamarckism wasn't right for Darwin, it was fine for perceptrons.

 

"""

If that intuition is valid, then the only things Selection could ever rescue from chaos become those that get canalized into these ur- developmental “programs”, with defined roles for genes, and merely allelic variation within each role. I would like to find a formal way to frame that assertion as a question and then solve it.

"""

 

Yes, that would be very exciting.

 

Cheers,

Jon

 

ps. I wrote Nick and Frank about a dream a day or two before your post, where I found myself sitting with a figure that kept morphing between Chris Kempes and Marcus. The figure was attempting to explain a Turing complete ball game to me. I appreciate the synchronicity.

 

[ρ] Here, I mostly followed Levine's approach to computing trophic level.

  https://www.sciencedirect.com/science/article/abs/pii/002251938090288X

 

[σ] https://arxiv.org/pdf/1901.00592.pdf

 

 

 

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David Eric Smith
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Re: FW: (no subject)

David Eric Smith
The more, that the cart is a system-level outcome of compatibility of interfaces among what are just more desserts, all the way down, though of several different kinds….

On May 6, 2021, at 5:29 AM, <[hidden email]> <[hidden email]> wrote:

Oh, and …. this problem … 
If that intuition is valid, then the only things Selection could ever rescue from chaos become those that get canalized into these ur- developmental “programs”, with defined roles for genes, and merely allelic variation within each role. I would like to find a formal way to frame that assertion as a question and then solve it.
… is the one that keeps me awake at night. 
 
Let me put it another way: When the waiter rolls up the dessert cart, you are so dazzled by choice between the crème caramel, the tiramisu and the chocolate mousse cake, that you never stop to wonder how the cart got created.   
 
Nick 
 
 
 
From: [hidden email] <[hidden email]> 
Sent: Wednesday, May 5, 2021 2:01 PM
To: 'The Friday Morning Applied Complexity Coffee Group' <[hidden email]>
Subject: RE: [FRIAM] (no subject)
 
Jon,
 
Mostly your comments were out of my league.  
 
However, one probably irrelevant fragment caught my eye.
 
While Lamarckism wasn't right for Darwin… .
 
Darwin always was a Lamarckian and became ever more so with every passing edition of the Origin. My favorite question in Biology orals was, “Who was the most famous Lamarckian?”  
 
I think you could say, with out contradiction
 
While Lamarckism isn’t right for most contemporary  Darwinians… .
 
 
… but evern that is becoming less true.  
 
I think you are talking about Weismann and Weismann’s Barrier?  Lamarckism was definitely not right for Weisman. 
 
Nick Thompson
 
-----Original Message-----
From: Friam <[hidden email]> On Behalf Of jon zingale
Sent: Wednesday, May 5, 2021 10:45 AM
To: [hidden email]
Subject: Re: [FRIAM] (no subject)
 
EricS,
 
Thank you for the kind and thoughtful response. Your 'three levels'
project is interesting to me and reminds me (even if only tangentially) of an analysis I worked on regarding food webs, n-species Lotka-Volterra, and ABMs. I wanted to clarify for myself what each level of analysis offered or bracketed relative to one another. There:
 
1. Food webs were analyzed as weighted graphs with the obvious Markov chain interpretation[ρ]. Each edge effectively summarizing the complex predator-prey interactions found at level 2, but without the plethora of ODEs to solve.
 
2. N-species Lotka-Volterra, while being a jumble of equations, offered dynamics. Here, one could get insight into how the static edge values of level 1 were in fact fluctuating values in n-dimensional phase space. But still, one is working with an aggregate model where species is summarized wholly by population count.
 
3. ABMs, in theory, ought to be the whole story of individuals located in space and time. There the agents (a lynx, say) 'decides' what to eat based, perhaps, on what is most readily available. But as everyone on the list knows, analysis at such a fine-grained scale is simply a mess.
 
I never did get as far with the analysis as I would have liked, and I never got the chance to share my findings, so yeah, thanks for the tangential opportunity, here and now, to say just this much.
 
1'. "site-rewrite rules in Walter Fontana’s site-graph abstractions"
 
Fleshing out some of your references, I found this Fontana paper[σ].
As you suggest, the style is fairly straightforward category theory.
Site-graphs and their morphisms form a well-defined category and a number of universal constructions (push-outs, pullbacks, cospans,...) are used to analyze the algebra and to establish its logic.
 
2'. "There is still an algebra of operation of reactions, but it is simpler than the algebra of rules, and mostly about counting."
 
I am not entirely sure that I follow the distinction. Am I far off in seeing an analogy here to the differences found between my one and two above? I would love to have a facility with stochastic techniques like these, but I most likely will need to remain a spectator for the rest of my days. Occasionally, I meet LANL folk that can talk Feller and Fokker with ease, and I am always jealous. It would be great to even have a better understanding of where Lie groups (something I can at least think about) meet the stochastic world.
 
3'. "So the state space is just a lattice. The “generator” from Level 2 is the generator of stochastic processes over this state space, and it is where probability distributions live."
 
Please write more on this. By 'just a lattice' do you mean integer-valued on account of the counts being so? Is the state space used to some extent, like a modulii/classifying space, for characterizing the species of reactions? I feel the fuzziest on how this level and the 2nd relate.
 
I am thankful to have had drinks with Artemy on a number of occasions, though I am embarrassed to have never asked him to blow my mind, as he could so easily have done.
 
I am working, slowly, through Valiant's discussion of evolvability problems regarding monotone disjunction and parity. I will hopefully have more to say soon. One thing that stands out for me is the idea that Lamarck could be so right, but about the wrong thing, a concept in search of a problem. While Lamarckism wasn't right for Darwin, it was fine for perceptrons.
 
"""
If that intuition is valid, then the only things Selection could ever rescue from chaos become those that get canalized into these ur- developmental “programs”, with defined roles for genes, and merely allelic variation within each role. I would like to find a formal way to frame that assertion as a question and then solve it.
"""
 
Yes, that would be very exciting.
 
Cheers,
Jon
 
ps. I wrote Nick and Frank about a dream a day or two before your post, where I found myself sitting with a figure that kept morphing between Chris Kempes and Marcus. The figure was attempting to explain a Turing complete ball game to me. I appreciate the synchronicity.
 
[ρ] Here, I mostly followed Levine's approach to computing trophic level.
 
 
 
 
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