[Equivalent rules = one Rulemaker?] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
Pages:1
Equivalent rules = one Rulemaker?
(Click here to view the original thread with full colors/images)
Posted by: Randall Carter Gray
I'm a disabled veteran with brain trauma exercising my brain as prescribed by my doctor, and I've chosen NKS to try to get my mind around. I've read parts of the NKS book, and it is surprisingly readable. So I have some pretty basic questions, but I like to think that there is truth and beauty in simplicity. As it is, I have no choice some days. But new medicines are life changing!
If all processes are governed by equivalent rules, i.e. computational equivalence, does that hypothetical support the idea of one Rulemaker; wouldn't multiple rulemakers, cooks, spoil the broth?
If complexity and randomness and determinism can come of basic rules, and if natural selection is not how increasingly complex forms advance, does this refute natural selection? Do the brutes always win? Isn't there allowance for the weaker ones, and doesn't this refute evolution? Dr. Wolfram seems to think that he has done away with natural selection as a governing principle ... am I reading this right?
I love to read the remarks and discussions. although I do get lost.
Thanks,
former intelligence specialist
Randall Gray
Posted by: Jason Cawley
No, there is no implication from equivalent rules to any underlying unity in details or "design". Universality is a mathematical fact or property of certain formal systems, and a large part of the point of NKS is that it is independent of the details of each underlying system. Once you have enough for universality, all its formal consequences are going to "kick in", regardless of any variety in the details of this system or that system.
An analogy would be the way we see bell curves all over in natural systems. Bell curves arise, purely formally, whenever you have independent randomness. It doesn't depend on the details, because it arises for a formal (mathematical) reason, whenever that requirement (independence) is met. So system A might have very different details from system B, but they both happen to share independence - you will see a similarity in statistics about each, without it implying that the details of A and the details of B have any common origin or similarity.
Mathematical truths like that have the characteristic, to philosophers, that they are true in all possible worlds. You can't make an inference from a purely formal fact, of that sort, to specific hypotheses about (a, or) the world's contents.
Now, to be careful about it, the principle of computational equivalence isn't a purely formal claim. It is an empirical claim about why we see similar forms of complexity in lots of diverse natural systems. But it is claiming that the origin of that empirical similarity, is a common formal cause. As a claim about where an empirical observation comes from, it is itself an empirical claim, and could be wrong as any empirical claim can be wrong.
I'd put it this way, in a conditional form. *If* all these diverse complicated systems are all over the threshold of universality, *then* it would follow as a purely mathematical fact, that they can all reach the same space of possible computations or behaviors, in a suitably large scale limit. And this would *explain* why we see the same sorts of complexity in all of them - precisely *without* positing any special similarity in their details. Just, they are all formally complicated enough to make it over the universality threshold. (Which plays the role played by statistical independence in my bell curve parallel).
I hope that helps with the first one.
As for the natural selection, NKS sees a more limited role for natural selection, within evolution, than some biologists have seen for it in the past. It isn't denying that natural selection occurs or is important. For some phenomena seen in biology, say, optimizing a wing shape for example, natural selection toward a functional "best" of some sort, is the likely correct explanation. But specifically for *complex* phenomena, NKS sees a different origin than natural selection.
The standard formula for Darwinian evolution recognizes a prior step, "descent with variation", before natural selection operates. The "with variation" part of that has always been understood to include random mutation, sexual mixing, some other processes like gene fixing by genetic drfit, and the like - all operating prior to selective pressure, and capable of causing genetic change even in the absence of any significant selective pressure this way or that. NKS expects a kind of algorithmic variety at that stage, to be more important as a cause of *complexity*, specifically, than some biologists have thought in the past.
Complexity isn't the only phenomena in life that needs explaining. And explaining it, isn't the only role natural selection plays in the usual picture of evolution. But many biologists have reached for explanations based on natural selection, when trying to explain e.g. why a leaf has exactly this shape, or an animal has exactly this pigmentation pattern, or overall shape, or shape of one of its parts. NKS suggests another cause for such things, in the prior "with variation" stage, independent of selection effects.
If with the right parameters, every possible leaf shape is seen somewhere - or the variety of shapes of seashells fill a whole range of growth parameters - or pigmentation patterns look like random samples of possible simple rules for laying down coloring in the process of growth - then no special selection in favor of this or that version of each process, would be required to get the complicated results we see. We'd see those forms of complexity simply because they are the typical results of certain kinds of simple programs. Of a kind we can see operating purely formally in computer experiments, or in other systems that aren't alive at all and haven't undergone millions of years of selective evolution.
If you can easily mistake a fracture or drainage pattern for a fern shape, say, why assume the fern shape had to arise by selective pressure, when it clearly isn't the source of the other two similar patterns?
This isn't any kind of argument against evolution. Evolution isn't natural selection, but a broader thing with many subprocesses going on within it. It is about shifting the role of natural selection with that process, seeing it as less necessary for certain forms of complexity especially - without doubting its presence and importance for other things.
Just as one might say, since genetic drift alone without selective pressure would cause X, X needn't be traced to natural selection specifically, one can say the same about a complex form that should result just from picking a simple program at random from an appropriate parameter space.
I hope that helps with the second question.
Forum Sponsored by Wolfram Research
© 2004-2008 Wolfram Research, Inc. | Powered by vBulletin 2.3.0 © 2000-2002 Jelsoft Enterprises, Ltd. |
Disclaimer
vB Easy Archive Final - Created by Xenon and modified/released by SkuZZy from the Job Openings