I took advantage of an opportunity to see Wolfram talk about his new (2006) book "A New Science," in hopes his explanation would be easier than reading the book, or would stimulate me to read it.
It was a fascinating, and a bit chilling, talk. You feel you are on the
verge of some great, earthshaking insight -- if only you were just a bit smarter!
Here are my notes on his appearance.
Steven Wolfram's presentation to the Software Development Forum, California, 13 February 2003, with regard to his newly published book A New Science.
(He has a slight British accent for some reason; I believe he is American.)
*He began experimenting with automata - rows of 8 bits, each row is one of the 256 possible variations on 8 bits on or off. Take one "rule" and build row upon row, one above the other, creating a frieze-like pattern, and the idea is the see what kind of pattern each rule can create. Is the pattern simple? Complex? Highly complex? Random? Repeating? According to what pattern? Provably nonrepeating?
*He spoke of cycling through the variants as "miles." Around Mile 30, there was some regularity but surprisingly complicated patterns - not really regular. Analysis techniques showed some examples of "perfectly random sections" in the pattern being built up.
*In looking at his sample pictures, I saw a rug-like design that appeared to have regularity chunks, or patterns, embedded within a random overall image. Either randomness scattered through the pattern, or chunks of patterns embedded in the randomness. I think, personally, there's something important about that fact. Sort of like when you see short chains of patterns in the otherwise random rolls of a die.
By Mile 110 he had reached patterns so complex that you could not mathematically predict the future form of the pattern -- you could only tell what was going to happen on the next row by running the program. Can't *predict* what it will do from first principles. Can't get ahead of the system -- can't anticipate, can't take a shortcut and meet the pattern up ahead. This is inherent in the nature of the complexity he's talking about here--it can't be overcome no matter what kind of computing device you use to try to get ahead of the pattern--a Turing machine, parallel computers, anything -- there are no shortcuts, and any alternative calculation you use takes at least as long to reach the same point as the main system takes to reach the same point.
This turns out to be a critical insight. He said it addresses in some ways the "problem" of "free will"--although reality may be an expression of a pattern, the future steps in the pattern can't be predicted on first principles.
*Early tries: Simple rule for primes, produced nothing interesting. Something involving the digits of pi - simple rule to generate, but nothing interesting resulted (it either makes a simple repeating pattern, or settles down to a simple repeating pattern after a while). His 8-bit pattern system, though, ended up generating patterns that did not repeat, or that repeated according to no obvious outside rule--it would repeat for a while and seem to settle down, then abruptly take off in some wild direction.
*Nature, he says, seems to have a secret to making complex things -- because nature is not constrained, it can try anything, or try everything, including things that aren't predictable as to results.
Mollusk Shell Patterns, for example -- The row of shell pattern is generated by cells growing along the edge of the mollusk--including pigment cells that seem to reproduce the kind of automata pattern he was playing with! (He showed examples and it's really remarkable.) But does it at random -- a random choice of which simple program to use. Just as Steven tried with his variants, so too with the mollusks. Which makes sense--that's what you would expect, yes? In a random Darwinian nature? I ask?
Same is true in leaf shapes, snowflakes.
*But doesn't automata already assume too much e.g. the grid that underlies it?
Wolfram guesses that space, at a low enough level, is discreet, not continuous. But what is its structure? A network. Joke: The network is the universe. A network of points connected to each other.
Time -- the universal clock by which the universe gets its evolving patterns "updated" in synchronicity? No. He thinks time is an illusion.
Causal invariance? Means only one thread oat a time no matter what order the universe updates = Yes.
Relativistic invariance is derivable from this notion. (Whatever that means.)
So -- a formula that creates the universe?
*He shows a cube-like drawing that updates and seems to grow and get complicated quickly. Is this the Big Bang?
(It sent chills down my spine to think on it.)
*Rule of computational equivalence:
1. There is an upper limit to computational sophistications.
2. Any program that passes a certain threshold--below which it was generating simple regular patterns--quickly jumps up to the sophistication limit. (There aren't medium sophisticated, medium-high sophisticated, and high sophisticated, for example. The world is almost binary: Simple; complex.)
3. Implication: These maximally sophisticated systems are by definition Universal Computers.
(*My Q as I looked at his sample pictures: Why do we humans find these highly complex displays so beautiful?)
4. Can't build a computer more sophisticate than this limit! Therefore can't build a computer more sophisticated than nature. Therefore can't build computation that predicts the universe ahead of time. There Are No Shortcuts!
Thus: Computational Irreducibility!
The only way to figure out where the Universe will be 10,000 Steps from now -- is to do the preceding 9,999 Steps, in order. Can't shortcut it.
*The "Problem" of Free will: Though arising out of underlying rules, sufficiently complex to be inherently unpredictable, so as a practical matter, human decision making is free of the constraints of the rules even though it is following the rules. (Paradoxical.)
*Is the math we use only math? A Are these maths or systems based on other axiomatic systems? He says there are 100,000 possible axiom systems, of which we have only studied a dozen!
*The progress of science has been progress in discovering things that aren't special--ordinariness! For example, that the Earth is not the center of the universe, that our Solar System is nothing special, that human evolution is of one wit the evolution of other creatures. Now: Nothing special about computations that create the complex world around us!
*Complex physical processes do NOT imply intelligent!
*Universe made of simple rules, but to see where the rule will lead, you must live, you must let the rule run, and see where it leads.
*Application of these insights? New raw materials for making machines, for doing new things in science, for creating new models. Discover the primitives with which you build the universe.
Will play out over the course of the coming decades.
*Why did he use 8 states (binary)? Because 3 connections works to produce this level of complexity. Four connections would produce more states, but would not produce levels of complexity that are orders of magnitude more cool and complex. Once you pass the minimum, in other words--once you hit 3--you've got all you need to produce everything! Having more buys you nothing!
If we were able to test possible universes, there's probably a way to tell why we have this universe rather than any other.
Q&A
*He's a skeptic about quantum computing. Too much idealization in the measurements. It idealizes away much of the computational process. (?)
*For various reasons, there is no magic formula or ingredient that leads to complex behavior. There is no predictable aspect to complexity -- it is truly irreducible. You have to run the rule to see its effects or where it will end up.
*Chaos -- perturbation based on initial conditions for highly sensitive formulas. A prediction of his approach is that if you run the system, it produces a random result--as with Rule 30, for example--but if you run it a second time you will get the same random pattern. (Definition of pseudo random, yes?)
*He published his book rather than submit his theories to the learned journals because the peer-review process is cliquish and complicated. Paradigm shifts are messy -- best prediction of outcome for a fundamental shift is the amount of anger that greets it.
Some areas of science have become very polemical (as with evolutionary theory) and he does not want to get involved in polemics about his theory. By spreading it around (through his book), he supports those who want to build on it, rather than those who want to engage in entertaining mudslinging….
