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.

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.

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.

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.

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!

Chapter 3

Finished Chapter 3 of "A New Kind of Science". This is going to take more than one reading! I am enjoying the clarity of the presentation, though. Simple cellular automata give way to mobile ones and Turing Machines. I can see how he got so interested in the ideas. He must have liked graph paper when he was a kid, too. The generation of complexity from simple regularity fascinates. Let's hope I don't get too obsessed! When I read Mandelbrot's Fractals book I wanted to cover my walls with Julia sets and now I want to make wallpaper out of cellular automata patterns. I especially like the way he uses the binary system to number the rules for the automata. It makes me want to learn binary better. It would make it a lot easier to match patterns. That coding scheme in itself was quite a brainstorm. I'm beginning to think this fellow may be for real!

Spooky

OK, I'll admit it. It's a bit spooky. I just finished reading Chapter 2 of "A New Kind of Science". It lays out the complex, nay, random patterns that can be generated by simple rules operating on cellular automata. Why does it look so familiar? Something to do with generative grammar keeps popping up in my head. I like this book. It's stimulating, yet understandable to a lay lawyer such as I. I read Mandelbrot's book on fractals years ago, but couldn't keep up. So far, Wolfram hasn't lost me. He contains fractals and everything else, perhaps. Also, when I was a kid I used to love graph paper, doodling all the time. So maybe if I had done more of that, I would have discovered what Wolfram did.

Wolfram and infomercials

After reading the intro to "A New Kind of Science", I feel the way I do after reading the first part of a "get-rich-quick" ad or watching the intro to a multilevel marketing or real-estate infomercial.

"For years, I struggled, barely able to pay my rent or buy food for my dog. Then one day I stumbled on an amazing secret. That secret has changed my life"

Only, Wolfram says his secret will change not just your life but the way men think. It will not make you rich, just more wise than anyone else, and for only $44.95 plus shipping and handling. I can't wait for the secret to be revealed. I love the anticipation. The only problem is that in the dozens of get-rich-quick schemes I have fallen for over the years, after you found out the secret, you didn't get rich, quick or slowly.

The lesson of those scams, of course, was, "you are a greedy idiot". That was a lesson worth learning, but I hope Wolfram has a better lesson to teach.

Abiogenesis

Lots of activity over on Slashdot on the topic of the amount of oil left in the world. There were something like 600 posts to a story that Iceland is going to move its economy away from oil. Typical Icelandic iconoclasticism. Well, soon I'm sure they'll be sued for tapping too much of the earth's geothermal energy. Why, if they don't stop we'll all run out of steam!! No more steamboats or steam trains or hot steamy showers!! Stop the madness!!

Actually, though, most of the posts referred to the "refilling the oil fields" story in Newsday. I remember reading decades ago - probably in the mid '70s - about something called the Siljan Ring Hypothesis. The Siljan Ring is a granitic formation in central Sweden that is perhaps the oldest rock formation on Earth. Indications of hydrocarbons coming from wells drilled in that area cast doubt on the theory that oil came from biotic sources - dead dinosaurs and plants. The Siljan Ring is so old that it dates back to before there were animals or even plants. So oil didn't come from dinosaurs or even from plankton and algae in the ocean, but from methane left over from when the Earth was a ball of gas. That meant oil was essentially inexhaustible. The best thing about the theory was that it drove the typical environmentalist crazy. He would stop smoking his joint for a minute and get all wild-eyed. You could tell he was thinking, "Oh, no, what if that's true? The right-wing bastards will be able to drive their Cadillacs over the working classes forever! It can't be!!" Well, hey, guess what, here it is thirty years on. We've got plenty of petroleum, more being discovered every day. And the Siljan Ring Hypothesis, unlike the predictions of Paul Ehrlich and the Club of Rome, is alive and kicking.

Behavior is computation

I don't know what it means either, but I got it after reading the first chapter of Wolfram's book. The Principle of Computational Equivalence looks like the key idea I'm going to have to figure out. Wish me luck. Oh, and by the way, I did finish the NYT crostic. As usual, it fell apart after I spotted one longish repeated word. I'm starting to remember why I don't do crostics any more. Can't say I didn't enjoy it a little, though.

Wolfram

I received Stephen Wolfram's new book, "A New Kind of Science" yesterday. Despite being warned by another blogger that it may be "all hype", I was intrigued and hopeful. I will report my impressions. The introduction certainly sets up some large goals, nothing less than to revolutionize hard science, social science, even art and philosophy. An odd feature - Wolfram lays out the number of keystrokes he used in the twenty years since he conceived the idea for the book (billions) and the distance he drove his mouse, which came to about a hundred miles. How did he ever figure that last one out? And how does that make his product better? Some bloggers with bloggorhea (new word?!) probably exercised their metatarsals to a similar extent. Maybe the central question for me is: Does this "New Science" create opportunities for composing a new kind of word puzzle? I'll keep you posted.

Vultus est index animi

So, tell me, why is the above unexceptionable yet curiously cautionary sentiment posted on the message board of a gas station in downtown Tallahassee, Florida, yep, right there at the intersection of Tennessee and Monroe? And on the reverse was "Carpe diem", for which you can at least make the argument that it's familiar. Someone educated is reduced to being a cashier at a gas station, I would guess. Is this a cry for help or a manifesto of identification with the laboring masses? Who can say? Perhaps he now and then even pumps gas, joining a long line of penniless intellectuals. In the Paris of Abelard, poor but industrious students might have lowered themselves to feeding horses, one supposes, muttering Latinisms. It was a surprise, possibly as much of a surprise as seeing that Cox and Rathvon are now composing the crostic in the Sunday Times Magazine. They could have been doing it for years, since I haven't looked at crostics for, probably, fifteen years. But this one was hard! I haven't finished it yet, since it isn't in a NYT Magazine I personally possess. I have to sneak around these days to feed my puzzle jones. sic transit, gloria!

Here's a copy of a letter I sent to Pejmanpundit and to Jane Galt on Live from the WTC about the Second Amendment:

ear Pejman,

Great article in FoxNews. I thought you might be interested in my powers-based argument below. Why don't people argue from basic principles any more, or have I just not been looking in the right places?

About the wording of the Second Amendment: The possible
dependency of the second clause "the right of the people to keep and bear arms shall not be infringed" on the existence or necessity of a "well-regulated militia" seems irrelevant to what, if any, powers the Amendment is reserving to the Federal government. That's of
course
one of the major stumbling blocks for interpretation. The Bill
of
Rights does not create or even define rights. It, like the rest
of
the Constitution, only defines the legitimate powers of the
Federal
government. The Amendment makes it clear that the right to keep
and
bear arms resides with the people, and that no state or Federal
government has the power to infringe that right. The definition
of what "keep and bear arms" means should depend on the original
Constitution, not the Second Amendment. Otherwise, why would this
amendment have been added?

The Second Amendment grants no powers whatever to the Federal
government, especially and particularly not the power to infringe
the
people's right to keep and bear arms. The Ninth and Tenth
Amendments
nail that down. The only reason for the addition of this
amendment
can have been to clarify that the Federal government did not have
this power. The Founding Fathers must have feared that some other
section of the Constitution might have been interpreted to give
this
power to the Federal government.

It is absurd, therefore, to say that the amendment's restriction
of
the Federal government's power to control individual keeping and
bearing of arms was conditional on the need for a militia. The
Federal government had and has no such power, or at least
certainly not from the Second Amendment. The contention that it
does, and that with the withering away of the need for a militia
the
inherent power springs into existence full-grown, reflects the
mistaken view that the Federal government has every conceivable
power
unless the Bill of rights tells us it doesn't have that power.
It's
just the other way around. In order to give the Federal
government
the power to infringe the people's right to keep and bear arms,
the
Second Amendment would have to be repealed by another amendment
which
specifically gives the Federal government that power. That ain't
gonna happen.

Robert Speirs
Tallahassee, Florida

PS You might be interested to know that in a speech to the
Constitutional Convention on June 8, 1789, James Madison suggested
the Second Amendment, among others, but in this speech the
"militia"
clause came after the "shall not infringe" clause. Here's the
URL:

http://odur.let.rug.nl/~usa/P/jm4/speeches/amend.htm

It's my personal opinion that the "militia" clause was thrown in
as
one possible justification for not meddling with the right of each
individual to keep arms. That makes it at most an explanation,
not
a condition. RS

It is the new millennium and I can't wait for the next big thing

How do I know it's a new era? At Wal-mart this morning I bought "Cheese Spam"! It's my two favorite things in one can! Not only that, but as all we spamophiles know, the opening of the can involves now only the pulling of a ring. That's too bad. It was fun to pry the little tool off the bottom and twirl the metal strip at the top. You could make bets with your friends on whether you'ld really need a transfusion or not. But then they'd just say the doctors were trying to get rich. You should have known better than to try and be friends with collectivists. But capitalism marches on, today cheese spam, tomorrow, what, macadamia beer?

Arab insecurity

Just finished "Paper Money" by Adam Smith, written in 1981, just after the oil crises of the Seventies had made some of the Arabs filthy rich. Smith (or Goodman or whatever his REAL name is) assumes in 1981 that by 2000 the Arabs will pretty much own the whole world. It struck me that the Arabs probably thought they would, too. That feeling must have produced some heavy-duty letdown when the Berlin Wall came down, the Soviet Union broke up and prosperity, low interest rates and massive new oil discoveries broke the Arab near-monopoly. The Arabs in 1981 were really in the position that the DeBeers diamond monopoly may be in right now, if these stories ( I wish I had saved the link to them) about huge diamond discoveries in Canada are true. I suppose it would have made me go nuts with frustration if I were a twenty-something Saudi princeling named Bin Laden and I saw the power position my country had obtained go by the boards slowly but surely and the hated Americans gradually gather back into their hand all the good cards. Why, it might make me resort to fundamentalist Islam to compensate for my lost dream of bossing around the entire industrialized world. I might blame the Saudi hierarchy, as well as all the other not-sufficiently-fundamentalist regimes in the area. Now if I am alive at all, I'm hiding in a cold dirty cave somewhere in the mountains of southern Afghanistan or northern Pakistan, hunted like the dog I have turned into. Also, after thumbing my nose at the fool Clinton for eight years, bombing and murdering at will, this junior Bush has to come along and have the gall to declare all-out war not only on me but on my ideas and my lust for glory. Why, it's enough to make me fly a plane into a building!

Wolfram and Kamen

What is it about these guys, Stephen Wolfram and Dean Kamen, that enables them to get so much publicity, for very little? I am tempted to throw in Stephen Hawking, Bobby Fischer and Nietzsche, but no. I just ordered Wolfram's new book about a "New Science" - fifty dollars! Dean Kamen is selling his scooters that don't go any faster than a bicycle for $8,000. What is it? The press must be desperate for heroes. The word "genius" scatters itself liberally when any of these boys appear.

I should say, too, that I am extremely unlikely to buy a Segway, but since I've already plumped for Wolfram's book, I hope it has more substance to it. I've always been intrigued by cellular automata, fractals and all that. Maybe you could put the program that produced the universe on a 3.5" floppy. Making it produce anything would be the hard part, since everything is already deeply involved in becoming something else. As den Beste may have mentioned, at least one would hope that the program was well written. But that brings up another thought. What if it isn't all that good and can be easily improved? Would we be duty-bound to improve it and start the better version off with a little seed matter and step back and see what happens? This could be better than cloning.

[5/19/2002 7:13:22 AM | Robert Speirs]
Not us

Just finished listening to Fox News Sunday. Tony Snow got the whole war thing together in ten words: "We have met the enemy, and he is NOT us."! Take that, Pogo! What a great summary of the enlightenment that has - finally - come over this country after decades of self-loathing and guilt tripping. Makes me confident and happy. It also makes a fitting memorial to the thousands who died on Sept. 11.

OK, OK, I know, this blog is supposed to be about puzzles. I did finish the quasi-cryptic by Lewis in the Nation, dated May 20, number 2846. The Nation is a weekly, I guess. I wouldn't subscribe to it on a bet. But the weekly pressure does perhaps explain the sketchy nature of the cryptic puzzle. Lewis doesn't bother with any fancy "distort the solution before you enter it into the diagram" business. All the entries are the same as the clue solutions. Some other differences appear from the usual Cox/Rathvon and Maltby puzzles. Lewis is addicted to multi-word answers, therefore to very long answers, and to spilling entries over from one numbered slot to the next, sometimes to three or more. Every other letter is unchecked. That makes it difficult to guess words. The occasional obscure clue - this puzzle had one extreme obscurity - could remain unfilled-in even when all the cross-checked letters have been entered. Luckily, I knew enough about Ethiopia to figure out this one. Next time, who knows?

I enjoyed this one more than I expected to, but don't seem to be impelled to rush out and acquire each puzzle as it comes out, as I do for the other cryptics. Nevertheless, Lewis does offer a change of pace from the monthlies. Most entertaining clue? 6 down, but then I'm a sucker for - well - conundrums!
[edit]
[5/17/2002 2:59:19 PM | Robert Speirs]
Another good one

Yesterday, I finished the June 2002 Atlantic puzzle, "Layers" by Cox and Rathvon. It was one of the cleverest yet. The words are all entered conventionally into the diagram. The diagram, however, has two separate parts, an outside layer and a core, with one square in the middle. The clues are arranged so that some of the answers from the outside layer, when arranged according to the numbering scheme given, provide the clues for the core layer. Not only that, but the diagram entries from the core layer are entered in numbered squares. Then you enter each letter in a crostic-like row to give you one final clue, which tells you how to complete the final center box. So it is indeed "layered". Quite an achievement. The clues were challenging, although there was a good proportion of three and four-letter entries, which tend to be easier. This I find excusable, given the intricacy of the overall scheme. The cross-clues in the diagram were quite helpful, with the desirable balance pleasingly maintained.

As I went through this puzzle, I felt a keen sense of anticipation, thinking, "I wonder if they're really going to be able to carry it through?" They did not disappoint. This is a definite nine out of ten. That brings up an interesting point. How should puzzles be rated, for difficulty, cleverness, entertainment value? What should the standards be? I'll be pontificating on this in future posts and solicit any comments anyone may have.

Most entertaining clue: 12 Down. Yes, I know it's easy, but I found it fun anyway.
[edit]

[5/15/2002 7:02:58 PM | Robert Speirs]

Not us

Just finished listening to Fox News Sunday. Tony Snow got the whole war thing together in ten words: "We have met the enemy, and he is NOT us."! Take that, Pogo! What a great summary of the enlightenment that has - finally - come over this country after decades of self-loathing and guilt tripping. Makes me confident and happy. It also makes a fitting memorial to the thousands who died on Sept. 11.

OK, OK, I know, this blog is supposed to be about puzzles. I did finish the quasi-cryptic by Lewis in the Nation, dated May 20, number 2846. The Nation is a weekly, I guess. I wouldn't subscribe to it on a bet. But the weekly pressure does perhaps explain the sketchy nature of the cryptic puzzle. Lewis doesn't bother with any fancy "distort the solution before you enter it into the diagram" business. All the entries are the same as the clue solutions. Some other differences appear from the usual Cox/Rathvon and Maltby puzzles. Lewis is addicted to multi-word answers, therefore to very long answers, and to spilling entries over from one numbered slot to the next, sometimes to three or more. Every other letter is unchecked. That makes it difficult to guess words. The occasional obscure clue - this puzzle had one extreme obscurity - could remain unfilled-in even when all the cross-checked letters have been entered. Luckily, I knew enough about Ethiopia to figure out this one. Next time, who knows?

I enjoyed this one more than I expected to, but don't seem to be impelled to rush out and acquire each puzzle as it comes out, as I do for the other cryptics. Nevertheless, Lewis does offer a change of pace from the monthlies. Most entertaining clue? 6 down, but then I'm a sucker for - well - conundrums!

Another good one

Yesterday, I finished the June 2002 Atlantic puzzle, "Layers" by Cox and Rathvon. It was one of the cleverest yet. The words are all entered conventionally into the diagram. The diagram, however, has two separate parts, an outside layer and a core, with one square in the middle. The clues are arranged so that some of the answers from the outside layer, when arranged according to the numbering scheme given, provide the clues for the core layer. Not only that, but the diagram entries from the core layer are entered in numbered squares. Then you enter each letter in a crostic-like row to give you one final clue, which tells you how to complete the final center box. So it is indeed "layered". Quite an achievement. The clues were challenging, although there was a good proportion of three and four-letter entries, which tend to be easier. This I find excusable, given the intricacy of the overall scheme. The cross-clues in the diagram were quite helpful, with the desirable balance pleasingly maintained.

As I went through this puzzle, I felt a keen sense of anticipation, thinking, "I wonder if they're really going to be able to carry it through?" They did not disappoint. This is a definite nine out of ten. That brings up an interesting point. How should puzzles be rated, for difficulty, cleverness, entertainment value? What should the standards be? I'll be pontificating on this in future posts and solicit any comments anyone may have.

Most entertaining clue: 12 Down. Yes, I know it's easy, but I found it fun anyway.

Maltby comes through

I've just finished Richard E. Maltby, Jr.'s effort, called "Heads or Tails, Revisited" from the June 2002 Harper's. It was much more enjoyable than I had feared. One entered the Across answers in standard fashion. Each Down column, however, had one 8-letter word and one 6-letter, plus a few threes thrown in as filler. All the fun was in the eights and sixes. The sixes were clued normally, but entering the solution in the diagram required you to find a group of three consecutive letters in the solution that matched a group of three in an eight letter word - any eight-letter Down word, not just the one in the same column. Each of the eight-letter clues gave you a word of the form "X is X", with each X representing a group of three letters. An example, not from the puzzle, would be "theistic". If a six letter word contained either of the same three letter groups (the or tic), for instance "rather", you would replace "the" with "tic" and enter the result - raticr - in the diagram. It sounds clumsy, but in practice works very well. At first glance it looks inelegant that so many of the eight-letter words project beyond the main body of the puzzle, leaving five letters in each apparently unchecked. This is not really so, however, as the matching of groups of three letters that may be unchecked directly to other groups of three in the six-letter words provides a perfectly adequate cross-checking mechanism. Good on yer, Maltby!

Star clue: 46 across, one of those that isn't too hard, but makes you feel clever when you get it. And that's the whole idea, isn't it, preening one's plumage?