Chapter 7 - Mechanisms in programs and nature - Stephen Wolfram
This chapter lays out the interesting bits about cellular automata as compared to all the other mechanisms one could use to understand the working of natural processes. You get quite a bit more on randomness. Wolfram clarifies that randomness in natural processes has always been seen to come from the environment or from imprecision in mechanisms. He gives an example of a beam of light spread by parabolic mirrors and then reflected off several flat mirrors. No matter how carefully you polish the mirrors, some imperfections will remain to distort the patterning of the beam’s reflections, whether after 10 or 100 or 1000 reflections. Or, the beam itself could be imperfect because of atmospheric particles or fluctuation in the light source. The randomness one sees in cellular automata, however, Wolfram says is an entirely different kind of randomness, one inherent in the process that would remain even if an apparatus could be made fault-free. This, he suggests, is the sort of randomness that Nature uses. Maybe next chapter I’ll find out a little more about how Nature uses randomness.
This chapter goes on to address continuity and discreteness in natural and cellular patterns and several other patterns. As it’s sixty-plus pages long, I’ll have to have another look at it to do it justice. It is, however, keeping my interest.
Wednesday, June 05, 2002
World Cup
Break from Wolfram today to take in the US-Portugal World Cup game at 5 AM. Just barely got up in time for the kickoff. It was just stunning to see the boys stuff in three goals with no response from the Portegees! Amazing, unreal, even the own goal deflection from Landon Donovan's cross. It was like they could do no wrong. Figo did not seem to be that much of a factor. Beasley and Donovan seemed to be able to attack at will. Then before half time Portugal scored and the US pulled its head into its shell and hung on for dear life in the second half. That was much less entertaining. Jeff Agoos's own goal was an "uh-oh" moment that seemed to foreshadow a collapse, but the cave-in never materialized. Portugal just didn't seem to be on their game. The US players seemed as active and motivated at the end of the game as at the beginning. Great effort, guys! On to the final rounds!! One gets dreams of an overall US victory to set the cheese-eating surrender monkeys on their heels, but I still realize intellectually that's vanishingly unlikely. If I had to bet right now, I'd say Germany v. Brazil in the final and Deutschland comes out uber alles. They were great in their shellacking of the Saud family team which at the moment controls part of Arabia. I got cable just for the World Cup and it seems to have been worth it. Looking forward to more tired but happy mornings.
Break from Wolfram today to take in the US-Portugal World Cup game at 5 AM. Just barely got up in time for the kickoff. It was just stunning to see the boys stuff in three goals with no response from the Portegees! Amazing, unreal, even the own goal deflection from Landon Donovan's cross. It was like they could do no wrong. Figo did not seem to be that much of a factor. Beasley and Donovan seemed to be able to attack at will. Then before half time Portugal scored and the US pulled its head into its shell and hung on for dear life in the second half. That was much less entertaining. Jeff Agoos's own goal was an "uh-oh" moment that seemed to foreshadow a collapse, but the cave-in never materialized. Portugal just didn't seem to be on their game. The US players seemed as active and motivated at the end of the game as at the beginning. Great effort, guys! On to the final rounds!! One gets dreams of an overall US victory to set the cheese-eating surrender monkeys on their heels, but I still realize intellectually that's vanishingly unlikely. If I had to bet right now, I'd say Germany v. Brazil in the final and Deutschland comes out uber alles. They were great in their shellacking of the Saud family team which at the moment controls part of Arabia. I got cable just for the World Cup and it seems to have been worth it. Looking forward to more tired but happy mornings.
Tuesday, June 04, 2002
Chapter 6 - Starting from Random
More and more about cellular automata in all their manifestations. Instead of starting with one black cell and filling up sheets of graph paper, this chapter investigates the variations that happen when the top line of the automaton contains a varied array of black and white squares. The big surprise? The results aren't all that different from "simple" automata. They tend to cluster in four types. In the course of the investigation, the concept of randomness itself comes in for a thorough grilling. I've come to trust Wolfram's elucidations as not just clear but interesting and innovative. One example: A certain simple cellular automaton produces a pattern which gives a line of random white and black squares if you run your finger right down the middle of it. As far as can be determined, this sequence is purely random, unpredictable. And yet if you run the pattern again from scratch, it produces the same pattern, still internally random. But if you know the pattern, how can you say it's random? This reminds me of the stage in a puzzle where you don't think you'll ever get it, but something inside you tells you that if you just keep on going,the solution will come clear. I'm looking forward to it. The next chapter promises some application of all this theorizing to real-world events.
More and more about cellular automata in all their manifestations. Instead of starting with one black cell and filling up sheets of graph paper, this chapter investigates the variations that happen when the top line of the automaton contains a varied array of black and white squares. The big surprise? The results aren't all that different from "simple" automata. They tend to cluster in four types. In the course of the investigation, the concept of randomness itself comes in for a thorough grilling. I've come to trust Wolfram's elucidations as not just clear but interesting and innovative. One example: A certain simple cellular automaton produces a pattern which gives a line of random white and black squares if you run your finger right down the middle of it. As far as can be determined, this sequence is purely random, unpredictable. And yet if you run the pattern again from scratch, it produces the same pattern, still internally random. But if you know the pattern, how can you say it's random? This reminds me of the stage in a puzzle where you don't think you'll ever get it, but something inside you tells you that if you just keep on going,the solution will come clear. I'm looking forward to it. The next chapter promises some application of all this theorizing to real-world events.
Sunday, June 02, 2002
Chapter 5 - Two Dimensions and beyond
This chapter of " A New Kind of Science" makes one point - if you look at higher dimensions to find greater or more common complexity, you're not going to find it. It's got neato illustrations and clear if somewhat lengthy expositions of why expanding the basic scheme of cellular automata from flat graph paper to wire grids does not produce any greater insights into how Reality produces the complexity we see all around us. Ha! And we all thought in college that "higher math" would get us closer to absolute truth! Give it up! At least I haven't been overwhelmed yet by the avalanche of incomprehensible equations I've been fearing. I'm getting in the back of my mind the feeling that the reaon it took life so long to emerge from the primordial ocean of chemical soup was that the gods were sitting around waiting for the mechanism to happen on the one or two combinations out of millions that would allow complexity to happen. Just think of all the graph paper and chicken wire they must have gone through. The same process must also have gone on within the gas clouds before the birth of the galaxy, solar system and Earth herself. Ah, I love speculating about the author's conclusions! It would be a waste of $44.95 plus shipping if I couldn't be proven fantabulously mistaken at least once.
This chapter of " A New Kind of Science" makes one point - if you look at higher dimensions to find greater or more common complexity, you're not going to find it. It's got neato illustrations and clear if somewhat lengthy expositions of why expanding the basic scheme of cellular automata from flat graph paper to wire grids does not produce any greater insights into how Reality produces the complexity we see all around us. Ha! And we all thought in college that "higher math" would get us closer to absolute truth! Give it up! At least I haven't been overwhelmed yet by the avalanche of incomprehensible equations I've been fearing. I'm getting in the back of my mind the feeling that the reaon it took life so long to emerge from the primordial ocean of chemical soup was that the gods were sitting around waiting for the mechanism to happen on the one or two combinations out of millions that would allow complexity to happen. Just think of all the graph paper and chicken wire they must have gone through. The same process must also have gone on within the gas clouds before the birth of the galaxy, solar system and Earth herself. Ah, I love speculating about the author's conclusions! It would be a waste of $44.95 plus shipping if I couldn't be proven fantabulously mistaken at least once.
Numbers
Finished Chapter 4 "Systems based on Numbers" of Stephen Wolfram's "A New Kind of Science" before falling asleep for twelve hours or so. After failing differential equations three times in college I never thought I would want to have much to do with numbers again, or especially equations. This chapter was pretty painless, though, and clearly enough makes the author's point that systems based on numbers aren't different in kind from cellular automata that you can draw on graph paper without using any numbers. The distinctions between/among rational and irrational numbers are clearer to me now and the lesson that complexity resides everywhere under the surface if we just look hard enough has been hammered into my brain with the result that I will now be looking for it everywhere. On to dimensionality!
Finished Chapter 4 "Systems based on Numbers" of Stephen Wolfram's "A New Kind of Science" before falling asleep for twelve hours or so. After failing differential equations three times in college I never thought I would want to have much to do with numbers again, or especially equations. This chapter was pretty painless, though, and clearly enough makes the author's point that systems based on numbers aren't different in kind from cellular automata that you can draw on graph paper without using any numbers. The distinctions between/among rational and irrational numbers are clearer to me now and the lesson that complexity resides everywhere under the surface if we just look hard enough has been hammered into my brain with the result that I will now be looking for it everywhere. On to dimensionality!
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