D. Ultimate Models for the Universe.
Yes, I'm not kidding, that's what Wolfram titled this section. He explained that he is looking for and is pretty certain he has found a "complete and precise representation" of physical reality. Or, at the least he's pointing the way there. He points out once again that because the universe might be more complex than we thought doesn't necessarily mean that the automaton that compiled it is all that complex. Heck, it could get ten or a hundred or a million times more complex and still it could be based on a very simple rule.
In some of his simplest, clearest language, Wolfram asks how we could ever find the rule for the universe, even if it is simple and how we would know it once we had found it. He provides simple clear answers. But his thoughts brought to my mind a Biblical quotation:
Seek and ye shall find; knock and it shall be opened unto ye.
There are no short cuts. You may have to do a lot of searching and there's no guarantee you'll find what you're looking for. Hey, that sounds like the universe I recognize, the one I live in every day.
In the notes to this section, which are almost as long as the section, Wolfram provides a potted history of models of the universe. It's excellent. Then at the end of the note he addresses the concept of whether the universe has a meaning. Since his model is based on an abstract mathematical logical system, not unlike the system from which the digits of pi are derived, W concludes that the universe has no more meaning than can be found in the sequence of digits after the decimal point in pi. A bit deflating, but I think he's got more deflating in store. Beat me!! At least I'm still the most important guy in MY universe!
Sunday, June 23, 2002
More links
To get away from Wolfram for a minute, I've seen several stories linking Timothy McVeigh, Terry Nichols and the Mideast terror web. The latest relates that the bomb - apparently set up by AlQaeda - that exploded outside the US consulate in Karachi was a diesel oil/fertilizer bomb like the one that half-destroyed the Federal Building in OK City. I know that's hardly proof, but combined with the fact that the missing OK City suspect's picture looks an awful lot like Jose Padilla/Muhajir and the fact that Terry Nichol's ex-wife's maiden name is Padilla and the discovery of messages between AlQaeda operatives just before April 19, 1995 talking about the destruction of American landmarks and specifically mentioning the Murrah Building - among others, to be sure - why you've got more than enough for a website, paperback and set of Congressional hearings.
By the way, the lack of American fatalities in the Karachi blast says good things about the lessons learned since Beirut and Oklahoma City. Unfortunately, Pakistani bystanders were not so lucky. If a 500-lb bomb can't even destroy a consulate, we've come a long way.
To get away from Wolfram for a minute, I've seen several stories linking Timothy McVeigh, Terry Nichols and the Mideast terror web. The latest relates that the bomb - apparently set up by AlQaeda - that exploded outside the US consulate in Karachi was a diesel oil/fertilizer bomb like the one that half-destroyed the Federal Building in OK City. I know that's hardly proof, but combined with the fact that the missing OK City suspect's picture looks an awful lot like Jose Padilla/Muhajir and the fact that Terry Nichol's ex-wife's maiden name is Padilla and the discovery of messages between AlQaeda operatives just before April 19, 1995 talking about the destruction of American landmarks and specifically mentioning the Murrah Building - among others, to be sure - why you've got more than enough for a website, paperback and set of Congressional hearings.
By the way, the lack of American fatalities in the Karachi blast says good things about the lessons learned since Beirut and Oklahoma City. Unfortunately, Pakistani bystanders were not so lucky. If a 500-lb bomb can't even destroy a consulate, we've come a long way.
Chapter 9 of Wolfram - This is the BIG one, folks!
One hundred and twelve pages that will change my view of the universe. At least that's what I was hoping. It does build from section to section, though, with a chutzpah that amazes. My only problem is that I'm not sure whether he's delivering the goods or not. I started college as a physics major, but ended up as a hippie political scientist and then went to law school. So I can spot an argument, but I can't compare Wolfram's conclusions about quantum mechanics or gravitational waves to the standard theory because I don't know it. Maybe that's an advantage in a way, though.
Section A - Reversibility
It seemed a little odd for W to address "reversibility" as the first point of a chapter telling how fundamental physics is explained by his theory. But he does a good job of it, pointing out how cellular automata can produce reversible results, that is, patterns in which it is possible to run the rule backwards as well as forwards. And in doing so, the patterns lose none of the randomness he says is necessary to explain how they can produce everything we see around us.
B- Irreversibility and the Second Law
Once again, I wish I knew more about the Second Law of Thermodynamics. I'm sure it's more complicated than: "Everything's falling apart and there's nothing anyone can do about it." But Wolfram's message here seems to be "it ain't necessarily so". His automata patterns show that the king's horses and men can occasionally produce something that looks like Humpty Dumpty out of all that eggshell and protoplasm. I guess that means I have to say "the yolk's not necessarily always on them". King's anything - especially "men" - are non-PC these days, but W apparently doesn't care. He's been holed up with his automata since before there was any such thing as PC. Some patterns show a different kind of order emerging from randomized chaos from that order which existed before the chaos was generated. With many "mights" and "perhaps", W also points out the structures that occur, some of them separated by what look like "membranes". Curiouser and curiouser. The treatise on reversibility in the first section of the chapter makes more sense now.
C - Conserved Quantities and Continuum Phenomena
Hmm. Some cellular automata exhibit conservation of the number of squares of any one color. Wolfram compares this to the law of conservation of matter and energy - and momentum. Every so often I flash on how bold and confident Wolfram is about his comparisons. I almost want to see him fall flat on his face. But somehow he makes it all seem reasonable, almost inevitable.
A new word (for me): Ergodicity. Google found me a note about it, in, of all things, a game theory context:
In particular, his models show ergodicity. Basically, this means that if you have a large number of such systems, and at any one time p percent of them are in a given state, then every single one
of them will spend about p percent of its time in that state. (Technically, there's a distribution over the states such that the state-space average of any well-behaved function equals its
time-average starting from almost any state, if you take the latter over a long enough interval.) Ergodicity is a very strong property, and one of the stronger predictions his models make; it goes
away if the agents are not perverse, or can remember unlimited stretches of the past, in which case each population will lock in to a single convention forever. It is also liable to be hard to test
empirically, because it can take a considerable time to converge on the ergodic distribution, and in the meanwhile the game people are playing is apt to have changed.
Now that that's clear, I think I'll actually post this. More on the way about Wolfram's Chapter 9. A lot more.
One hundred and twelve pages that will change my view of the universe. At least that's what I was hoping. It does build from section to section, though, with a chutzpah that amazes. My only problem is that I'm not sure whether he's delivering the goods or not. I started college as a physics major, but ended up as a hippie political scientist and then went to law school. So I can spot an argument, but I can't compare Wolfram's conclusions about quantum mechanics or gravitational waves to the standard theory because I don't know it. Maybe that's an advantage in a way, though.
Section A - Reversibility
It seemed a little odd for W to address "reversibility" as the first point of a chapter telling how fundamental physics is explained by his theory. But he does a good job of it, pointing out how cellular automata can produce reversible results, that is, patterns in which it is possible to run the rule backwards as well as forwards. And in doing so, the patterns lose none of the randomness he says is necessary to explain how they can produce everything we see around us.
B- Irreversibility and the Second Law
Once again, I wish I knew more about the Second Law of Thermodynamics. I'm sure it's more complicated than: "Everything's falling apart and there's nothing anyone can do about it." But Wolfram's message here seems to be "it ain't necessarily so". His automata patterns show that the king's horses and men can occasionally produce something that looks like Humpty Dumpty out of all that eggshell and protoplasm. I guess that means I have to say "the yolk's not necessarily always on them". King's anything - especially "men" - are non-PC these days, but W apparently doesn't care. He's been holed up with his automata since before there was any such thing as PC. Some patterns show a different kind of order emerging from randomized chaos from that order which existed before the chaos was generated. With many "mights" and "perhaps", W also points out the structures that occur, some of them separated by what look like "membranes". Curiouser and curiouser. The treatise on reversibility in the first section of the chapter makes more sense now.
C - Conserved Quantities and Continuum Phenomena
Hmm. Some cellular automata exhibit conservation of the number of squares of any one color. Wolfram compares this to the law of conservation of matter and energy - and momentum. Every so often I flash on how bold and confident Wolfram is about his comparisons. I almost want to see him fall flat on his face. But somehow he makes it all seem reasonable, almost inevitable.
A new word (for me): Ergodicity. Google found me a note about it, in, of all things, a game theory context:
In particular, his models show ergodicity. Basically, this means that if you have a large number of such systems, and at any one time p percent of them are in a given state, then every single one
of them will spend about p percent of its time in that state. (Technically, there's a distribution over the states such that the state-space average of any well-behaved function equals its
time-average starting from almost any state, if you take the latter over a long enough interval.) Ergodicity is a very strong property, and one of the stronger predictions his models make; it goes
away if the agents are not perverse, or can remember unlimited stretches of the past, in which case each population will lock in to a single convention forever. It is also liable to be hard to test
empirically, because it can take a considerable time to converge on the ergodic distribution, and in the meanwhile the game people are playing is apt to have changed.
Now that that's clear, I think I'll actually post this. More on the way about Wolfram's Chapter 9. A lot more.
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