Posted on 09/04/2002 11:23:46 AM PDT by betty boop
Stephen Wolfram on Natural Selection
Excerpts from A New Kind of Science, ©2002, Stephen Wolfram, LLC
The basic notion that organisms tend to evolve to achieve a maximum fitness has certainly in the past been very useful in providing a general framework for understanding the historical progression of species, and in yielding specific explanations for various fairly simple properties of particular species.
But in present-day thinking about biology the notion has tended to be taken to an extreme, so that especially among those not in daily contact with detailed data on biological systems it has come to be assumed that essentially every feature of every organism can be explained on the basis of it somehow maximizing the fitness of the organism.
It is certainly recognized that some aspects of current organisms are in effect holdovers from earlier stages in biological evolution. And there is also increasing awareness that the actual process of growth and development within an individual organism can make it easier or more difficult for particular kinds of structures to occur.
But beyond this there is a surprisingly universal conviction that any significant property that one sees in any organism must be there because it in essence serves a purpose in maximizing the fitness of the organism.
Often it is at first quite unclear what this purpose might be, but at least in fairly simple cases, some kind of hypothesis can usually be constructed. And having settled on a supposed purpose it often seems quite marvelous how ingenious biology has been in finding a solution that achieves that purpose….
But it is my strong suspicion that such purposes in fact have very little to do with the real reasons that these particular features exist. For instead…what I believe is that these features actually arise in essence just because they are easy to produce with fairly simple programs. And indeed as one looks at more and more complex features of biological organisms ¯ notably texture and pigmentation patterns ¯ it becomes increasingly difficult to find any credible purpose at all that would be served by the details of what one sees.
In the past, the idea of optimization for some sophisticated purpose seemed to be the only conceivable explanation for the level of complexity that is seen in many biological systems. But with the discovery…that it takes only a simple program to produce behavior of great complexity [for example, Wolfram’s Rule 110 cellular automaton ¯ a very simple program with two-color, nearest neighbor rules], a quite different ¯ and ultimately much more predictive ¯ kind of explanation immediately becomes possible.
In the course of biological evolution random mutations will in effect cause a whole sequence of programs to be tried…. Some programs will presumably lead to organisms that are more successful than others, and natural selection will cause these programs eventually to dominate. But in most cases I strongly suspect that it is comparatively coarse features that tend to determine the success of an organism ¯ not all the details of any complex behavior that may occur….
On the basis of traditional biological thinking one would tend to assume that whatever complexity one saw must in the end be carefully crafted to satisfy some elaborate set of constraints. But what I believe instead is that the vast majority of the complexity we see in biological systems actually has its origin in the purely abstract fact that among randomly chosen programs many give rise to complex behavior….
So how can one tell if this is really the case?
One circumstantial piece of evidence is that one already sees considerable complexity even in very early fossil organisms. Over the course of the past billion or so years, more and more organs and other devices have appeared. But the most obvious outward signs of complexity, manifest for example in textures and other morphological features, seem to have already been present even from very early times.
And indeed there is every indication that the level of complexity of individual parts of organisms has not changed much in at least several hundred million years. So this suggests that somehow the complexity we see must arise from some straightforward and general mechanism ¯ and not, for example, from a mechanism that relies on elaborate refinement through a long process of biological evolution….
…[W]hile natural selection is often touted as a force of almost arbitrary power, I have increasingly come to believe that in fact its power is remarkably limited. And indeed, what I suspect is that in the end natural selection can only operate in a meaningful way on systems or parts of systems whose behavior is in some sense quite simple.
If a particular part of an organism always grows, say, in a simple straight line, then it is fairly easy to imagine that natural selection could succeed in picking out the optimal length for any given environment. But what if an organism can grow in a more complex way…? My strong suspicion is that in such a case natural selection will normally be able to achieve very little.
There are several reasons for this, all somewhat related.
First, with more complex behavior, there are typically a huge number of possible variations, and in a realistic population of organisms it becomes infeasible for any significant fraction of these variations to be explored.
Second, complex behavior inevitably involves many elaborate details, and since different ones of these details may happen to be the deciding factors in the fates of individual organisms, it becomes very difficult for natural selection to act in a consistent and definitive way.
Third, whenever the overall behavior of a system is more complex than its underlying program, almost any mutation in the program will lead to a whole collection of detailed changes in the behavior, so that natural selection has no opportunity to pick out changes which are beneficial from those which are not.
Fourth, if random mutations can only, say, increase or decrease a length, then even if one mutation goes in the wrong direction, it is easy for another mutation to recover by going in the opposite direction. But if there are in effect many possible directions, it becomes much more difficult to recover from missteps, and to exhibit any form of systematic convergence.
And finally…for anything beyond the very simplest forms of behavior, iterative random searches rapidly tend to get stuck, and make at best excruciatingly slow progress towards any kind of global optimum….
It has often been claimed that natural selection is what makes systems in biology able to exhibit so much more complexity than systems that we explicitly construct in engineering. But my strong suspicion is that in fact the main effect of natural selection is almost exactly the opposite: it tends to make biological systems avoid complexity, and to be more like systems in engineering.
When one does engineering, one normally operates under the constraint that the systems one builds must behave in a way that is readily predictable and understandable. And in order to achieve this one typically limits oneself to constructing systems out of fairly small numbers of components whose behavior and interactions are somehow simple.
But systems in nature need not in general operate under the constraint that their behavior should be predictable and understandable. And what this means is that in a sense they can use any number of components of any kind ¯ with the result…that the behavior they produce can often be highly complex.
However, if natural selection is to be successful at systematically molding the properties of a system then once again there are limitations on the kinds of components that the system can have. And indeed, it seems that what is needed are components that behave in simple and somewhat independent ways ¯ much as in traditional engineering.
At some level it is not surprising that there should be an analogy between engineering and natural selection. For both cases can be viewed as trying to create systems that will achieve or optimize some goal….
…[I]n the end, therefore, what I conclude is that many of the most obvious features of complexity in biological organisms arise in a sense not because of natural selection, but rather in spite of it.
Good grief, apochromat! You're suggesting that thinking machines would be a vast improvement over human beings; for we are, among other things, certainly not "fault tolerant." :^)
Wolfram thinks we may be able to make machines that emulate human thinking. But he suggests that machines would have to experience the world as humans do, right down to biological details, in order to really think as humans do.
Yep -- all that "background processing" going on. It's simply amazing when you think of it. The unconscious mind is highly underrated these days.
Speaking of art, objective reality and Penrose - here's another interesting page from the Sir Roger Penrose Society science and fun cannot be separated.
It's not so much a matter of a desire to believe weird things as reconciling weird facts with a modern scientific paradigm. We don't have anything like all the answers and some of our "answers" may be wrong ones.
You quickly undermine anything useful or truthful if you allow non-material or supernatural explanations. For then, anything we perceive as material could, in fact, be supernatural. Anything we perceive as truthful, could, in fact, be an unfathomable supernatural.
Seems to happen a lot these days, Alamo-Girl. Which sets me to ruminating:
Wolfram writes, “Given any rules it is always possible to develop a form of description in which these rules will be considered simple. But what is interesting to ask is whether the underlying rules of the universe will seem simple -- with respect to forms of description that we as humans currently use.”
What a tantalizing remark! That second sentence seemingly can be read in various ways. One, there appears to be an ontological question, a reference to certain properties of human consciousness that may be modifiable under an evolutionary process in which natural selection has at least some role to play. Two suggests an epistemological question: The statement seems to be a reference to the methods we choose to make descriptions of the world. Three, there seems to be an allusion to what's essentially a cosmological question.
The Ontological Question: Here’s where I come down with a bit of a case of cognitive dissonance in reading Wolfram. Some of his statements about the nature of human thinking seem contradictory to me. For example, his Principle of Computational Equivalence basically holds that there's nothing so very special about human thinking at all. Indeed, the computational processes going on in a rock (at the particle level at least) may be every bit as complex as the kinds of processing going on in the human brain. If computational equivalence exists between the two, then it seems that if human intelligence is able to evolve, then rock intelligence must also be able to evolve. Wolfram doesn't push this parallelism. But he tells us he suspects that virtually all kinds of systems, at least here on earth, that are not obviously simple are fundamentally computationally equivalent. He frequently makes the point that human intelligence -- and human beings themselves -- really aren't all that special at the end of the day.
But one is left wondering whether Wolfram really believes this. (How would he explain himself if he did?) For the basic paradigm of the new kind of science he’s doing is a model of systemic, dynamic, apparently random evolution according to simple rules. In any case, he appears to make hypothetical allowance for a superior type of intelligence that is not computationally equivalent to us -- for among other things hypothetically it may have far greater powers of pattern recognition than we do. I refer to Extraterrestrial Intelligence (see more below). So if pattern recognition is part of what’s needed to identify computational sophistication -- intelligence -- then it seems likely we humans do better at this than rocks. What would be the meaning of biological evolution, if humans and rocks were fundamentally computationally equivalent, anyway? (But then maybe I'm just “mixing my metaphors” here….)
The Epistemological Question. What is the best way to proceed, if we really want to understand the laws of the universe? The approach of mathematics? Physics? Engineering? Or simply by observing (and modelling) the evolution of systems in nature, taking our cues from diligent study of their behavior, including that of cellular automata of many different types? Of course, there are limits to this; for we are invariably, inevitably ourselves parts of the systems we want to observe: We never see what is from outside, which presumably is the only way we could see it “whole.” Our contingent position introduces all kinds of problems of uncertainty, incompleteness, undecidability.
Historically, mathematics has been regarded as the most dependable and fruitful approach to making elegant descriptions of the universe -- for its detachment and universality, its reliance on formal proofs, etc. So mathematics has been heavily integrated into the natural sciences. But in the end, methods premised on mathematics have some drawbacks to Wolfram’s way of thinking. For he writes:
“It is not surprising that there should be issues in science to which mathematics is relevant, since until about a century ago the whole purpose of mathematics was at some level thought of being to provide abstract idealizations of aspects of physical reality (with the consequence that concepts like dimensions above 3 and transfinite numbers were not readily accepted as meaningful even in mathematics)…. At times the role of mathematics in science has been used in philosophy as an indicator of the ultimate power of human thinking. In the mid-1900s, especially among physicists, there was occasionally some surprise expressed about the effectiveness of mathematics in the natural sciences. One explanation advanced by Albert Einstein was that the only physical laws we can recognize are ones that are easy to express in our system of mathematics.”
Thus we are dealing with the world in a manner that may be fundamentally constrained by the nature of the tools we use to explore and describe it, and/or limitations in the way human beings process information coming from the outside world (i.e., via sense perception and its mediation by a hierarchy of physical structures in our bodies and brains), not to mention our finite and contingent position within the universe.
The Cosmological Question. “So is it in the end sensible to think of the universe as a single structure in spacetime whose form is determined by a set of constraints? Should we really imagine that the complete spacetime history of the universe somehow always exists, and that as time progresses, we are merely exploring different parts of it, or should we instead think that the universe --more like systems such as cellular automata -- explicitly evolves in time, so that at each moment a new state of the universe is in effect created, and the old one lost?
“Models based on traditional mathematics equations -- in which space and time appear just as abstract symbolic variables -- have never had to make much distinction between these two views. But in trying to understand the ultimate underlying mechanisms of the universe, I believe that one must inevitably distinguish between these views.”
Arguably, the traditional approach of science, with its reliance on purpose-built tools for the achievement of results, probably works best for the first view. But I just don’t believe the universe is like that. I think Wolfram’s observation is correct: In a certain sense, what you get out of systems of traditional mathematics and science is pretty much what you put into them in the first place. That’s why he thinks we humans could benefit by trying some other way….
O you can “chalk me up” as warm to view two -- with qualification: I don’t believe the “old” state is ever “lost.”
But now we’re moving out of cosmogony, and into the dreaded waters of theology which Wolfram has taken such pains to avoid in his book -- as is entirely commendable for a work of its kind, conducted firmly within the rationalist tradition. But he doesn’t entirely succeed in that regard, IMHO.
But that’s an issue for another time; except merely to note that the “evidence” we have for ET is just about as good and certain as the “evidence” we have for God. (Again, IMHO, FWIW.)
Here are some of the reasons Wolfram cites for why hard evidence of ET life may have eluded us so far:
“If extraterrestrials exist at all an obvious question -- notably asked by Enrico Fermi in the 1940s -- is why we have not encountered them. For there seems no fundamental reason that even spacecraft could not colonize our entire galaxy within just a few million years.
“Explanations suggested for apparent absence include:
“-Extraterrestrials are visiting, but we do not detect them [except perchance we may have detected ET artifacts -- i.e., crop circles, which many people have suggested are ET navigational aids];
“-Extraterrestrials have visited, but not in recorded history;
“-Extraterrestrials choose to exist in other dimensions;
“-Interstellar travel is somehow infeasible;
“-Colonization is somehow ecologically limited;
“-Physical travel is not worth it; only signals are ever sent.
“Explanations for apparent lack of radio signals include:
“-Broadcasting is avoided for fear of conquest;
“-There are active efforts to prevent us being contaminated;
“-Extraterrestrials have no interest in communicating;
“-Radio is the wrong medium;
“-There are signals, but we do not understand them.”
Anyhoot, as they say, “absence of evidence is not necessarily evidence of absence.” :^)
* * * * * *
Wolfram, IMHO, is a feast! Sorry this is so long -- but you have the most striking insights and observations, and I have more questions than answers. A-G, thank you so much for writing, and for reading through this long piece.
I printed out yesterday and hope to dig into today. =)
I recognize the humor in that remark. "Fault-tolerance" is a concept that I consider inextricably bound to practical AI and to real intelligence, and it's very easy to overlook examples of it in everyday life. Voting is inherently fault-tolerant, for example, because the winner doesn't need every voter's vote. Anticipating and avoiding problems is also fault tolerance, as is healing. Society actually demands that individuals have some tolerance to internal and external faults.
I believe that an in-depth analysis of fault tolerance could shed light on some of the most interesting philosophical and legal questions.
But he is not a moveable feast. I wish he had split it into two volumes.
I read some of his discussion on numbers last night. He represents numbers as cellular automata. One of the series he looks at is f(n) = 2*f(n-1) (i.e., 1, 2, 4, 8, etc.). It has a very simple, clean representation as a CA.
I wonder why we chose the number system that we did. For example, two is twice one, but three is only 50% more than 2. Why not make the percentage difference between the numbers a constant? The decreasing percentage increase helps to account for Benford's (Zipf's) Law.
If we look at five sticks, it's easy to see that adding a stick will obtain the next number. But if we look at a pile of sand, we don't know what the next number is without more information. Was the pile created a cup at a time, or a bucket at a time? Using a constant percentage between numbers, we don't need more information, we just add x% more sand. The constant percentage approach is Markovian (depends only on the step before it). The brain likes Markov processes; it strives to create Markovian hierarchies.
I think the brain had evolutionary pressure to keep a high level of cerebral interconnection when dealing with numbers. The astonishing computational capabilities, and symbolic limitations, of the autistic savant provides clues as to why this is so. It's interesting that autism and asperger's cases are skyrocketing.
Fascinating, apochromat. This sounds analogous to what Wolfram says about the practical effect of randomness in systems. I don't have the book with me where I am, so I have to speak from recollection. He suggests that randomness has a critical function in systems, of smoothing over or averaging out "shocks" to the system, mitigating threats to it over time. That is, randomness acts as a kind of cushion, dissipating "bad" effects that would otherwise spread and propagate in a manner threatening to the system's good order over time. How close does this come to the idea of fault tolerance as you understand it?
I take your point about how such a thing could shed light on important philosophical and legal -- and I would add political -- questions.
Perhaps that is so, apochromat. It's certainly worth checking out. Certainly, quantum uncertainty has been so perplexing, it's said that some physicists are happy to stay "agnostic" about its causes -- just so long as the quantum equations keep working. Plus all these new critturs -- quarks and leptons et al. -- keep popping up, often quite unexpectedly. Perhaps these are part of the "randomness principle" -- fault tolerance(?) -- needed to stabilize space-time systems globally???
Sounds perfectly reasonable to me, apochromat. Indeed, I don't know how a person who is a bona fide searcher after the truth of reality could proceed in any other manner. The quest is everything: For that which is sought in all probability can never be fully possessed.
Ouch! If that's true, Nebullis, then it seems to me Wolfram's book will end up being only about Wolfram, and not about what he alleges it's about. And time will tell the matter, in due course.
This awesome universe we live in seems a tad stingy about revealing its "secrets." It seems an attitude of humility on the searcher's part would be the wise course. But here I go again, "anthropomorphizing" the universe.... Just take it all with a grain of salt.
All I can say is I haven't seen him display arrogance. But I think I've seen displays of humility. FWIW. Anyhoot, I like the book: It has opened doors for me. On the other hand, I'm the sort of person who needs to have my doors opened for me; for I have no formal training in the fields he touches upon. But speaking as a generalist, I have found him extraordinary helpful.
If you have the time and interest, maybe you should just "unfilch" the book and form your own impressions of it.
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