The n-Category Café

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New submission for Fri, 18 Jul 08:

[1] arXiv:0807.2665 [ps, pdf, other]
Title: Unifying Theories of Molecular, Community and Network Evolution
Authors: Carlos J. Melian, David Alonso, Diego P. Vazquez, James Regetz
Comments: Main 42 pages, Appendix 28 pages, 5 figures
Subjects: Populations and Evolution (q-bio.PE); Other (q-bio.OT)

The origin of diversification and coexistence of genes and species have been traditionally studied in isolated biological levels. Ecological and evolutionary views have focused on the mechanisms that enable or constrain species coexistence, genetic variation and the genetics of speciation, but a unified theory linking those approaches is still missing. Here we introduce evolutionary graphs in the context of neutral theories of molecular evolution and biodiversity to provide a framework that simultaneously addresses speciation rate and joint genetic and species diversities. To illuminate this question we also study two models of evolution on graphs with fitness differences, which provide insights on how genetic and ecological dynamics drive the speed of diversification. Neutral evolution generates the highest speed of speciation, species richness (i.e. five times and twice as many species as compared to genetic and ecological graphs, respectively) and genetic–species diversity (i.e., twice as many as genetic and ecological graphs, respectively). Thus the speed of speciation, the genetic–species diversity and coexistence can differ dramatically depending on whether genetic factors versus ecological factors drive the evolution of the system. By linking molecular, sexual and trophic behavior at ecological and evolutionary scales, interacting graphs can illuminate the origin and evolution of diversity and organismal coexistence.

Meaning cannot be based on dictionary definitions all the way down: at some point the circularity of definitions must be broken in some way, by grounding the meanings of certain words in sensorimotor categories learned from experience or shaped by evolution.

The Cyc project is attempting to give computers common sense, giving meaning to words in relation to other words. There are lots of terms and rules encoding a giant ontology. They sell systems that can, for instance, flag suspicious data–is Billy really 237 years old, or did you hit two keys at once? It knows that people have legs, and that if your right leg is in Kansas, your left leg is probably there, too.

Abstraction is just a data mining process on the ontology, hunting for analogies.

“We introduce the concept of a reachable set; a larger vocabulary whose meanings can be learned from a smaller vocabulary through definition alone, as long as the meanings of the smaller vocabulary are themselves already grounded. We provide simple algorithms to compute reachable sets for any given dictionary.”

SH: I’m interested in distinguishing pattern from randomness from examining output. What output fits a particular generating algorithm. Pi has such an algorithm and although its output passes randomness tests, Pi is not considered truly random by AIT definition. I don’t think there is a method to test to see if there are other algorithms which like Pi, pass all randomness tests, so when one sees a sequence of symbols, one can’t distinguish between if they belong to an finite pattern origin, or are infinitely random, or even just hugely large finite.

The symbols used can make well-defined words up to a point. The understanding of meaning is resolved from context which changes or is modified by other contexts. This has the effect of producing ever growing in complexity and size meanings of defined words so the dictionary grows.
That’s how a natural language dictionary works. A formal dictionary is only going to approximate the human function of reading and understanding so that dict. must also attenuate or compartmentalize.

To get to the point. A dictionary is a set of rules which demonstrate pattern.
John Case is an Emeritus COLT professor.
http://www.cis.udel.edu/~case/colt.html

He gives an example of a complicated sequence which has a generating rule used to form a detectable pattern. Then says,

“This rule can be written as a formal algorithm (or computer program). The problem of finding such rules gets harder as the sequences to generate get more complicated than the one above. Can the rule finding itself be done by some
computer program? Interestingly, it is
mathematically proven that there can be no computer program which can eventually find (synonym: learn) these (algorithmic) rules for all sequences which have such rules!”
My point is that if one attempts to capture meaning (find a rule which generates a meaningful pattern) that there is going to be a natural limitation imposed on the scope of its success, whether commonsense rules for CyC or a cycling self-referential dict. foundation.

I’m going to include a quote from David’s post because it seems to fit here, “a bag of words” and Polanyi.

“Meaning is gleaned without focal
awareness of the words conveying
it. To see the higher level once
must indwell in its lower parts,
as he puts it.” … On the other hand, Polanyi suggests the indwelling becomes more difficult the higher up a hierarchy you go.”
SH: I agree with this :-) and tried to use the word limitation above to express not being able to immerse and indwell. I think it matches the complicated algorithmic limitation that Case mentions
though maybe “complex” is a better word.
No holes in my bag of Scrabble letters.

An interesting project to get substantive about grounding for natural languages is Anna Wierzbicka’s Natural Semantic Metalanguage program; the idea is to find a core set of meanings that are rendered in the everyday vocabulary of all languages, to define all the others with. The current presentation is completely unmathematical (almost all the people doing it are math-phobes), but I think this could be changed by formalizing the syntax of the metalanguage.

Another random observation is that the assembly of meanings seems to involve some sort of linear logic (no Contraction or Weakening, i.e. the meaning of each word gets used once and once only), while reasoning itself doesn’t obey this restriction.

I suppose one might argue that several steps in your sequence involve taking a collection of weakly interacting homogeneous entities, and that is why mathematics continues to work adequately, where the organism as a combination of disparate tissues and organs is less mathematisable.

Even with very mathematisable entities there’s a tendency to use a narrative description. E.g., for stars:

After a star has formed, it generates energy at the hot, dense core region through the nuclear fusion of hydrogen atoms into helium. During this stage of the star’s lifetime, it is located along the main sequence at a position determined primarily by its mass, but also based upon its chemical composition and other factors. In general, the more massive the star the shorter its lifespan on the main sequence. After the hydrogen fuel at the core has been consumed, the star evolves away from the main sequence.

In a paper on modelling in Hadron physics, Stephan Hartmann writes

Working in various physics departments for a couple of years, I had the chance to attend several PhD examinations. Usually, after the candidate derived a wanted result formally on the blackboard, one of the members of the committee would stand up and ask: “But what does it mean? How can we understand that x is so large, that y does not contribute, or that z happens at all?” Students who are not able to tell a “handwaving” story in this situation are not considered to be good physicists.

Judging from my experience, this situation is not only typical for the more phenomenological branches of physics (such as nuclear physics) but also for the highly abstract segments of mathematical physics (such as conformal field theory), though the expected story may be quite different.

In this paper, I want to show that stories of this kind are not only important when it comes to finding out if some examination candidate “really understands” what he calculated. Telling a plausible story is also an often used strategy to legitimate a proposed model.

If I am right about this, empirical adequacy and logical consistency are not the only criteria of model-acceptance. A model may also be provisionally entertained (to use a now popular term) when the story that goes with it is a good one. But what criteria do we have to assess the quality of a story? How do scientists use the method of storytelling to convince their fellow scientists of the goodness of their model? Is the story equally important for all models or do some models need a stronger story than others? These are some of the questions that I address in my paper. In doing so, I draw on material from a case-study in hadron physics.

He concludes

We will now make more precise what a story is. A story is a narrative told around the formalism of the model. It is neither a deductive consequence of the model nor of the underlying theory. It is, however, inspired by the underlying theory (if there is one). This is because the story takes advantage of the vocabulary of the theory (such as ‘gluon’) and refers to some of its features (such as its complicated vacuum structure). Using more general terms, the story fits the model in a larger framework (a ‘world picture’) in a non-deductive way. A story is, therefore, an integral part of a model; it complements the formalism. To put it in a slogan: a model is an (interpreted) formalism + a story.

I think this chimes well with Polanyi’s point that all forms of knowing rely on unformalisable components. In fact, he claimed all forms of knowledge rely on what is tacit, or inarticulable. We might say that stories can take us further in the effort to articulate as much as possible than formalisms alone.

Kurzweil has several bad habits, such as treating processes which occurred over millions of years as pointlike events (the Cambrian explosion did not happen in a day, and neither did the invention of stone tools). In addition, ever since The Age of Spiritual Machines he’s been brushing off the “proximity of the familiar” — often, the timeline will be more crowded as you approach the present, not necessarily because things happen faster, but because we have more data. Start with a Poisson process in which each event leaves a “fossil”, add in a constant probability per unit time for a given fossil to decay, and your fossil record will show exponentially increasing waiting times between surviving fossils as you go back into the past. Uniformitarianism plus an imperfect fossil record gives the illusion of accelerating change.

A distinction frequently made in the philosophical literature is between ontological and epistemological emergence, i.e., whether it’s just a question of our not being able to predict how the whole operates from knowledge of the parts, but that there are actually new, irreducible properties, which may be captured by laws for that level.

There’s a metaphysical posture in between Platonist Realist and Antiplatonist (which comes in various flavors), regarding your comment: “So there’s no real sense in which “the nation” exists. Clearly the “state” exists, in that there is objectively a government of the US, and there’s a country that exists in that some people have legal citizenship.”

That is, the Nation and the State exist, as does Roman Law (and its derived Scottish Law) or Napoleonic Law (and its derivative in Louisiana) or English Law (and its offshoot American Law as Baseball and Cricket are offshoots of Rounders), or the Black Queen in Chess. They exist as mental constructs.

Persistent, consistent mental constructs, shared by many people, as part of the “stuff” of law or Chess. They obey consistently with respect to operators (amendment, appeal procedure, tournament Chess rules) which tranbsform Structures and have conserved Properties.

Mathematics, in this sense, “is carried in the heads of people” – but that does not deny them ontological or epistemological standing, nor make them mere games played on paper and blackboards for an elite to use to obtain power and money and prestige and sex, nor in any way prevent Emergence.

As to what “Emergence” means now, that is hotly debated at, for example, the International Conference on Complex Systems, every year (or every other year as it were). It nearly leads to fistfights.

“We have to read musically, testing the precision and rhythm of a sentence, listening for the almost inaudible rustle of historical association clinging to the hems of modern words, attending to patterns, repetitions, echoes, deciding why one metaphor is successful and another is not, judging how the perfect placement of the right verb or adjective seals a sentence with mathematical finality.”

[How Fiction Works, James Wood, Farrar, Strauss and Giroux, 2008, 288 pp.]

Such Lovely Lies, Gideon Lewis-Kraus reviews “How Fiction Works” by James Wood.

“Wood’s new book, ‘How Fiction Works,’ is his most sustained attempt to describe, in 123 numbered sections, how this instruction proceeds. His initial focus is on ‘free indirect style,’ whereby the narrator moves the story along through a character’s voice such that ‘we see things through the character’s eyes and language but also through the author’s eyes and language. We inhabit omniscience and partiality at once.’ This is the essence of fiction-making: We readers know that an author has invented this character, but we also feel as though the character exists somewhere outside and beyond the author’s invention. We are divided between what we know to be fake and what we nevertheless momentarily postulate as real. Good characters promise us that their invented freedom has meaning, and we react to them accordingly. (Wood, in this way, pretends to write about books while writing about life.)”

“When we reach a word that ‘belongs’ not to the character but to the narrator, ‘we are reminded that an author allowed us to merge with his character, that the author’s magniloquent style is the envelope within which this generous contract is carried.’ This contract’s chief clause is that a novel is something you can at any moment put down. It is thus obliged to offer generous terms. As the burden of the novelist is to give her readers reason to keep reading, the burden of the untethered critic (as opposed to the academic one, whose authority is institutionally granted) is to offer enough gratuitous pleasure and intelligence that he is taken seriously….”