Posted on 06/09/2002 5:39:56 PM PDT by aculeus
AMONG a small group of very smart people, the publication of ''A New Kind of Science,'' by Stephen Wolfram, has been anticipated with the anxiety aroused in literary circles by, say, Jonathan Franzen's recent novel, ''The Corrections.'' For more than a decade, Wolfram, a theoretical physicist turned millionaire software entrepreneur, has been laboring in solitude on a work that, he has promised, will change the way we see the world. Adding to the suspense, the book has been announced and withdrawn as the artist returned to his garret to tinker, ignoring the bad vibes and hexes cast by jealous colleagues hoping to see him fall flat on his face.
Now, weighing in at 1,263 pages (counting a long, unpaginated index) and 583,313 words, the book could hardly be more intimidating. But that is the price one pays for a first-class intellectual thrill. While experimenting with a simple computer program 20 years ago, Wolfram stumbled on something rather eerie: ''the beginning of a crack in the very foundations of existing science.'' Ever since, he has been following it deeper as it widens into a crevasse.
The normal thing would have been to dispatch regular reports from the field -- unreadable papers published in fashionable zines like Physical Review Letters or Physica D. Instead, Wolfram decided to do what Darwin did (and he would not shun the comparison). He is springing loose his vision all at once, in a book intended for nonscientists and scientists alike.
From the very beginning of this meticulously constructed manifesto, the reader is presented with a stunning proposal: all the science we know will be demolished and reassembled. An ancient error will be corrected, one so profoundly misguided that it has led science down the wrong avenue, until it is approaching a cul-de-sac. The mistake (as everyone who hated calculus will be happy to hear) is trying to capture the richness of the universe with mathematical equations -- Newton's, Maxwell's, Einstein's. All are based on an abstract, perhaps dubious idea -- that time and space form a seamless continuum. Whether dealing with an inch or a second, you can chop it in half and the half in half, ad infinitum. Thus things can be described with unlimited, infinitesimal precision.
This conceit works fine for simple phenomena like a planet's trajectory around the sun or a weight falling from the Leaning Tower of Pisa. But as scientists try to explain systems of greater complexity -- a hurricane, the economy of Portugal, a human or even a reptilian brain -- the calculations become ever more elaborate until one is left with an unwieldy array of symbols that do not explain much at all.
Wolfram believes that even his own field, theoretical physics (he got a Ph.D. from Caltech when he was 20), suffers from the problem. Equations can capture characteristics of individual particles with breathtaking precision. But put three or four particles together and the complications begin to overwhelm. The problem, he proposes, is that equations are the wrong tool for the job. They should be replaced with computer programs -- more specifically, the little snippets of software called algorithms.
That sounds absolutely ridiculous. Programs are just human inventions, marching orders for a machine. They serve well as a quick and dirty means of tricking a computer into approximating the smoothness of nature, roughing out reasonably good facsimiles of a scientist's perfect equations. But computers understand nothing but 1 or 0, with no gradations in between. Algorithms can mimic reality's grain as finely as the engineers can manage, but the simulation can never be as sharp as the real thing.
Wolfram contends that this, the common wisdom, gets things upside down: the algorithm is the pure, elemental expression of nature; the equation is an artifice. That is because the continuum is a fiction. Time doesn't flow, it ticks. Space is not a surface but a grid. A world like this is best described not by equations but by simple step-by-step procedures. By computer programs.
The universal operating system Wolfram imagines is not something horribly complicated like Windows. The key idea in the book is that simple, byte-size programs have the surprising ability to produce endlessly intricate behavior. His most basic example is a group of elegant little algorithms with a clunky name: cellular automata.
These have been kicking around in the popular science press for years. Start with a row of squares (the cells), some white and some black. Then transform the pattern according to a mindlessly simple rule. Here is an example: if either of a cell's neighbors is black, then make the cell itself black in the next round; otherwise, make it white. That is the whole program. Print each new generation below its progenitor and a pattern unfolds like a piano roll. Automate the procedure with a computer and watch what scrolls down the screen.
Most of these experiments -- Wolfram has tried them all -- settle into numbing repetition, churning out the same configuration again and again. But every now and then a rule takes flight and soars. What Wolfram calls Rule 30 sounds about as dull as can be: if a cell and its right-hand neighbor are white, the next time around make the cell the same color as its left-hand neighbor is now; otherwise, make it the opposite. Apply the rule to a single black square and the pattern that emerges looks every bit as random as the snow on a television tuned to an empty channel. You have to see it to believe it, and Wolfram obliges with stunning illustrations (including the book's goldenrod endpapers, spattered with output from Rule 30). The implication is that some computation like this may be the engine of entropy in the universe.
Other rules have the opposite effect: seed them with a random jumble of cells and, after a few iterations, they begin generating complex order. Some of the output resembles intricately varied stalactites; some looks like tracks of colliding particles in a high-energy accelerator lab. Think of stars and galaxies emerging from the confusion of the Big Bang, or life from the primordial sea.
Most pleasing to the eye are rules generating nested patterns like those of a crystal or a snowflake, or the markings on a seashell, the branching of a leaf, the spiral of a pine cone. Other patterns swirl like clouds, smoke or turbulent streams of water.
Wolfram believes he has clinched the deal with what, for many scientists, will be the meat of the book: a proof that a simple cellular automaton can be programmed to perform any conceivable computation (making it equivalent to what the British mathematician Alan Turing called a universal computer). If you buy all this, then a simple algorithm like those described in the book could constitute the machine code of the universe, the platform on which all the other programs run.
One idea after another comes spewing from the automata in Wolfram's brain. Maybe it is not evolution but algorithms that generate biological complexity. Maybe, if everything arises from computations, it makes perfect sense to think of the weather and the stock market as having minds of their own. Maybe free will is the result of something called ''computational irreducibility'' -- the fact that the only way to know what many systems will do is to just turn them on and let them run.
All this is laid out clearly and precisely. Any motivated reader should be able to plow through at least a few hundred pages before the details become too burdensome. Then one can just marvel at the pictures. (It's evident why Wolfram, who adds depth to the term ''control freak,'' published this work himself. Some illustrations contain hundreds of checkered cells per inch, requiring ''careful sheet-fed printing on paper smooth enough to avoid significant spreading of ink.'')
Probably only scientists will read the 348 pages of notes (though these can be very amusing, providing us with Wolfram's thoughts on subjects like ''clarity and modesty,'' ''whimsy'' and ''writing style''). Many may already be thumbing through the index, whetting their knives. At least in the main text, Wolfram often gives the impression that he has the field -- sometimes called physics of computation -- all to himself. Some of his colleagues will find their work acknowledged in the notes; others may not.
Yet Wolfram has earned some bragging rights. No one has contributed more seminally to this new way of thinking about the world. Certainly no one has worked so hard to produce such a beautiful book. It's too bad that more science isn't delivered this way.
George Johnson contributes science articles to The Times. His new book, ''A Shortcut Through Time,'' will be published next year.
This guy isn't claiming you can simulate the universe with a Turing machine. He says the universe IS a Turing machine.
BUMP
Oh, puh-leaze...
The article you link doesn't even support the claim you make for it. You claim "fence-sitters", plural, while the article just just quotes a single person suggesting intelligent design, and you claim that people who were "on the fence" were "swung over" to a view of intelligent design, but there's no indication that Myers wasn't already in that camp to start with.
A the reporters slant is fatuous anyway -- he suggests that there was a hasty meeting to deal with the "shocking" discovery that humans have about the same number of genes as mice (and other mammals), and yet this fact has been known for decades (and is no real surprise).
The reporter was pushing really hard for a interesting "angle", and just ended up sounding silly.
So, while by no means a new idea, I can see where the notion that "(t)he mistake ... is trying to capture the richness of the universe with mathematical equations -- Newton's, Maxwell's, Einstein's" might have some practical value.
Who's Dave?
I can't speak for Dave, but personally I wasn't "working hard" to "avoid" anything. You asked how an algorithm could be implemented without equations, and I gave the answer: By using state tables. Finite State Machines (FSMs) can implement any computable algorithm without equations or other high-level programming constructs, merely by looking up the current state and input values in the state table and then changing state/outputs to the new values listed in the table.
State tables are especially appropriate for the sort of cellular automota that Wolfram is talking about.
How you read some psychological motivation into my answer, I'll never know, but I submit that it says more about your state of mind than it does about mine.
What would a state table look like for F=m*a?
It would look like the state table for a multiplier circuit. That's basic circuit design fundamentals. Here's a Harvard EE/CS assignment that asks for that very thing as a 5-point question: http://www.eecs.harvard.edu/cs141/asst/ass6.pdf (Pre-lab problem #2). That's for a simplified circuit (4-bit integer multiplier), but the floating-point state table isn't all that much harder once you've got the basics.
So a state table can be used to represent the results of an equation? Kinda of like using really big multiplication tables when you want to multply. Doesn't that blow up on you?
State tables are pretty much the epitome of trading memory for performance. State tables are extremely fast (a single constant time op), but consume ungodly amounts of memory for all but the most trivial computations. Giant Look-Up Tables (GLUTs) are just one of the many interesting formats for universal computation. I always bring up GLUTs when trying to stretch people's brains about equivalence in computation. Most people's intuition says that you can't do anything interesting with a GLUT, but in fact you can do everything with a GLUT that you could with any other Turing machine, and this is relatively easy to see if you really think about it. An equation is basically a higher entropy encoding of the state table (if you want to look at it that way).
This is the only article on the subject that I was able to come up with. There were other discussions blunting the postulate that the gene-mapping projects were creation theories' coffin nails. You are correct that Myers doesn't say that he was "swung over," but God knows that there were Darwinists (not necessarily experts, but who embrace anything that casts doubt on the existence of a deity) who were licking their chops, thinking that the more we know about the creation, the less we will believe in a Creator.
the reporters slant is fatuous anyway -- he suggests that there was a hasty meeting to deal with the "shocking" discovery that humans have about the same number of genes as mice (and other mammals),
Not true. Here's Tom Abate's opening paragraph from the article:
Nowhere does Abate suggest that this was anything other than the previously scheduled annual meeting of the AAAS. Fact is that the recent completion of the Human Genome Project and what it did and didn't reveal was the main topic of conversation at the meeting, as would be expected.
Aftershocks of the human genome announcement rippled through San Francisco all weekend as the annual meeting of the American Association for the Advancement of Science brought thousands of thinkers here to mull the surprising fact that humans have only a few more genes than mice...
...and yet this fact has been known for decades (and is no real surprise).
So you're calling the reporter a liar? He is imagining researchers' surprise in the low amount revealed in the HGP? After a decade, untold thousands in man-hours and millions of dollars spent on the studies, they were blase about it revealing things they already knew? Are you sure you want to be on record with that opinion?
If I remember right, a theory of chaos states that nature gravitates to a position on the edge of chaos. Too much stability and stagnation and death occurs; too much chaos and nothing progresses or organizes.
An algorithm for evolution seems intuitive as well. Life emerges not from and into complete chance (chaos), but governed by certain limits, the possible variety is part of a process which could likely be modeled by algorithms.
In my years on the talk.origins newsgroup, and in the science community, I have yet to meet even a single case of the sort of "licking their chops to turn everyone atheist" evolutionists which you, and many other people, seem to believe are lurking in every corner.
...and yet this fact has been known for decades (and is no real surprise).
So you're calling the reporter a liar?
I never attribute to malice that which can be adequately explained by stupidity.
He is imagining researchers' surprise in the low amount revealed in the HGP? After a decade, untold thousands in man-hours and millions of dollars spent on the studies, they were blase about it revealing things they already knew?
On the issue of man/mice gene counts, yes.
Are you sure you want to be on record with that opinion?
Absolutely. From http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7505451&dopt=Abstract:
Proc Natl Acad Sci U S A 1993 Dec 15;90(24):11995-9Here we have a nine-year-old study that announced the same conclusion, and it only confirmed what had been known from more indirect estimates long before. And yet, the reporter describes it as somehow being a recent bit of "surprising" news so novel and amazing that it caused "aftershocks" to "ripple" through a science meeting "all weekend":Number of CpG islands and genes in human and mouse.
Antequera F, Bird A.
Institute of Cell and Molecular Biology, University of Edinburgh, Scotland.
Estimation of gene number in mammals is difficult due to the high proportion of noncoding DNA within the nucleus. In this study, we provide a direct measurement of the number of genes in human and mouse. We have taken advantage of the fact that many mammalian genes are associated with CpG islands whose distinctive properties allow their physical separation from bulk DNA. Our results suggest that there are approximately 45,000 CpG islands per haploid genome in humans and 37,000 in the mouse. Sequence comparison confirms that about 20% of the human CpG islands are absent from the homologous mouse genes. Analysis of a selection of genes suggests that both human and mouse are losing CpG islands over evolutionary time due to de novo methylation in the germ line followed by CpG loss through mutation. This process appears to be more rapid in rodents. Combining the number of CpG islands with the proportion of island-associated genes, we estimate that the total number of genes per haploid genome is approximately 80,000 in both organisms.
PMID: 7505451 [PubMed - indexed for MEDLINE]
[Original article] Aftershocks of the human genome announcement rippled through San Francisco all weekend as the annual meeting of the American Association for the Advancement of Science brought thousands of thinkers here to mull the surprising fact that humans have only a few more genes than mice...The reporter was clearly angling for a way to spin an otherwise dry scientific gathering as a dramatic, shake-up-the-world-of-science revolution. But his "hook" topic turns out to be a yawner (it's interesting that mice and humans -- and other mammals -- have similar numbers of genes, but it's hardly the sort of information that causes "aftershocks"), and something that had already been known for a long, long time.
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