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A New Kind of Science
First things first - have I read this book? Hell, no, and if anybody else says THEY have in the next year, they're lying thru their teeth. This book is so dense that if Wolfram had added a single additional page, the whole thing would have imploded into a black hole. That's got to be the only reason he quit writing and finally went to press.
I've been waiting for years for ANKOS to come out. I ordered my copy Tuesday when it was released, got it on Thursday and I've been skimming it like mad since. To give you some idea of how engrossing this book is, I was reading it Friday morning at 4 AM in the bathroom of a Motel 6, curled up in a bedspread on the tile floor to keep from disturbing my wife and stepdaughter during a trip to my stepson's graduation. I've got four college degrees, one in math and two from MIT, and bottom line - this sucker's gonna take a while to digest. However, it's theoretically straightforward enough that anybody with a high enough level of obsession and a few years to stay glued to it can follow it in its entirety. In ANKOS, Wolfram certainly comes across as arrogantly cocky but in the final analysis is he a crank or a revolutionary genius? Who knows, but it's going to be a new nerd pastime for the next decade to argue that point.
ANKOS is 1250+ pages divided into 850 pages of breezy exposition followed by 350 pages of fine-print notes. The exposition is composed of 12 chapters and the notes have about a paragraph per page of topic- and name-dropping technobabble to let you know where to go next for more details on whichever of Wolfram's tangents strike your fancy. Topping the whole thing off is a 60+ page index with thousands of entries in even smaller typeface than the notes.
Despite its length, ANKOS is not a rigorous mathematical proof of anything as much as it is a superficial survey of a vast new intellectual landscape. And what a landscape Wolfram has laid before us. It's all about cellular automations, which have traditionally been relegated to the realm of mathematical recreations. Start with a black square in the center grid square (cell) on the top line of a sheet of graph paper. Think up a few rules about whether a square gets colored black or white on the next line down depending on the colors of its neighbors. Apply these rules to the squares on the next line of the sheet of graph paper. Repeat. Watch what happens. Sounds simple. It isn't.
The first short chapter outlines Wolfram's central thesis: That three hundred years of mathematics based on the equals sign have failed to provide true insight into various complex systems in nature, and that algorithms based on the DO loop can succeed in this endeavor where mathematics has failed. The reason, claims Wolfram, is that deceptively simple algorithms can produce heretofore undreamed of levels of complexity. He claims that while frontier intellectual efforts such as chaos theory, fractals, AI, cybernetics and so forth have hinted at this concept for years, his decade of isolation studying cellular automata has taken the idea of simple algorithms or rules embodying universal complexity to the level of a new paradigm.
The second chapter outlines what Wolfram calls his crucial experiment: the systematic analysis of the 256 simplest rule sets for the most basic cellular automatons. He discovers this "universe" of rules is sufficient to produce his four so-called "classes" of complex systems: order, self-similar nested patterns, structures and most importantly, true randomness. The first two lead to somewhat familiar checkerboard-type patterns and leaf-type fractals; the last two, unforeseen unique shapes and unpredictable sequences. Wolfram stresses that the ability of simple iterative algorithms to produce complex and unique non-fractal shapes as well as truly random sequences of output is in fact a revolutionary new discovery with subtle and profound implications.
The third chapter expands his initial 256-rule-set universe of simple algorithms with many others Wolfram has researched for years in the dead of night while others slept. Rule sets involving multiple colors beyond black-and-white, rule sets that update only one grid square instead of a whole row, rule sets that embody full-blown Turing machines, rule sets that substitute entire sets of patterned blocks into single grid cells, that tag end point grid squares with new patterns, that implement "registers" and "symbols" - Wolfram has examined them all in excruciating detail. And no matter how complex the rule set is he explores, it ends up generating still more and more unexpected complex behavior with many notable features as the rule sets are implemented. This ever-escalating spiral of complexity leads Wolfram to believe that cellular automatons are a viable alternative to mathematics in modeling - in fact, embodying - the inherent complexity of the natural world.
In chapter four, he begins this process, by linking cellular automatons to the natural world concept of numbers. Automatons that multiply and divide, that calculate prime numbers and generate universal constants like pi, that calculate square roots and even more complex numerical functions like partial differential equations - Wolfram details them all. Who needs conscious human minds like those of Pythagoras or Newton to laboriously work out over thousands of years the details of things like trigonometry or calculus? Set up dominos in just the right way, flip the first one and stand back - nature can do such calculations automatically, efficiently and mindlessly.
Chapter five broadens the natural scope of cellular automations from one-dimensional numbers to multi-dimensional entities. Simple X-Y Cartesian coordinates are left behind as Wolfram defines "networks" and "constraints" as the canvas on which updated cellular automatons flourish - always generating the ever-higher levels of complexity. More Turing machines and fractals such as snowflakes and biological cells forming organs spontaneously spring forth. So far we've seen some really neat sleight-of-hand that Martin Gardner or Michael Barnsley might have written. But we're only on page 200 of 850 with seven chapters to go, and Wolfram is just now getting warmed up.
Chapter six is where Wolfram begins to lay the foundation for what he believes is so special about his insights and discoveries. Instead of using rigid and fixed initial conditions as the starting points for the cellular automations he has described, he now explores what happens using random and unknown initial conditions in each of his previously defined four "classes" of systems. He finds that while previously explored checkerboard (Class 1) and fractal (Class 2) systems yield few surprises, his newly-discovered unique (Class 3) and random (Class 4) cellular automaton systems generate still higher levels of complexity and begin to exhibit behavior that can simulate any of the four classes - a telltale hint of universality. Furthermore, their behavior starts to be influenced by "attractors" that guide them to "structure" and self-organization.
With the scent of universality and self-organization in the air, Wolfram begins in chapter seven to compare and contrast his cellular automations to various real-world topics of interest. Billiards, taffy-making, Brownian motion, casino games, the three-body problem, pachinko machines - randomness is obviously a factor in all of these. Yet, Wolfram notes, while randomness is embedded in the initiation and influences the outcomes of each of these processes, none of them actually generate true randomness in the course of running the process itself. The cellular automations he has catalogued, particularly his beloved Rule 30, do. The realization that cellular automations can uniquely serve as an initiator or generator of true randomness is a crucial insight, leading to the difference between continuity and discreteness and ultimately to the origins of simple behaviors. How, you ask? Hey, Wolfram takes most of the chapter to lay it out in a manner that I'm still trying to follow: no way can I summarize it in a sentence or two.
By chapter eight, Wolfram believes he has laid out sufficient rationale for why you, me and everybody else should think cellular automations are indeed the mirror we should be looking in to find true reflections of the world around us. Forget the Navier-Stokes equations - if you want to understand fluid flow, you have to think of it as a cellular automation process. Ditto for crystal growth. Ditto for fracture mechanics. Ditto for Wall Street. Most definitely ditto for biological systems like leaf growth, seashell growth and pigmentation patterns. This is very convincing stuff - tables of Mathematica-generated cellular automation shapes side by side with the photos of corresponding leaves or seashells or pigment patterns found in nature. Yes, you've seen this before in all of the fractals textbooks. The difference between fractals and cellular automations: fractals are a way to mathematically catalog the points that make up the object while cellular automations are a way to actually physically create the object via a growth process. It's a somewhat subtle difference - and a key Wolfram point.
Having established some credibility for his ideas, Wolfram stretches that credibility to the limit in chapter nine, where he applies his cellular automation ideas to fundamental physics. It was practically inevitable he would do this - his first published paper as a teenager was on particle physics, and that's the field he got his PhD in from Cal Tech at age 20 before going on to write the Mathematica software program and make his millions as a young businessman. Despite his solid background in physics, this seems at first blush to be pretty speculative stuff. He shifts his focus on the cellular automations from randomness to reversibility, and describes several rule-sets that both lead to complexity and are reversible. This behavior is an apparent violation of the Second Law of Thermodynamics. From Wolfram's way of thinking, if the universe is indeed some kind of ongoing cellular automation, then it may well be reversible and the Second Law must not be the whole story, so there must be something more we have yet to learn about the nature of the universe itself. He continues extensive speculations on what this may be, and how space, time, gravity, relativity and quantum mechanics must all be manifestations of this underlying Universal Cellular Automation. The rule set for this ultimate automation, which Wolfram believes might ultimately be expressed as only a few lines of code in Mathematica, takes the place of a mathematically-defined unified field theory in Wolfram's world. This is mind-blowing stuff, but ultimately boils down to Wolfram's opinion. I have great difficulty in comprehending space and time and matter and energy as "mere" manifestations of some cellular automation - if so, what is left to be the "system" on which the automation itself is running? I'm reduced to one of Clarke's Laws: The universe is not only stranger than we imagine, it is stranger than we CAN imagine ...
Wolfram shifts from Kubrick-style religion back to mere philosophy in chapter ten, where he explores how cellular automations are perceived by the human mind. Visual image perception, the human perception of complexity and randomness, cryptography, data compression, statistical analysis, and the nature of mathematics as a mental artifact are all explored. The chapter ends on a discussion of language and the mechanics of thinking itself. Wolfram reaches no real concrete conclusions on any of these, except that once again cellular automation is a revolutionary new tool to use in achieving new insights on all of these topics.
Chapter eleven jumps from the human mind to the machine mind by exploring not the nature of consciousness but the nature of computation instead. He goes here into somewhat deeper detail on ideas he has introduced earlier, about how cellular automations can perform mathematical calculations, emulate other computational systems, and act as universal Turing machines. He focuses on the implications of randomness in Class 4 systems and the universality embodied in systems like that of his Rule 110. His arguments lead up to a closing realization, what he does not call but may one day be named Wolfram's Law.
The final chapter, chapter twelve, discusses what all of Wolfram's years of isolation and work have led him to conclude. He calls it the Principle of Computational Equivalence. What follows is an unavoidably oversimplified distillation of Wolfram's thoughts on the PCE. If indeed cellular automations are somehow at the heart of the universe around us, then the human effort to reduce the universe to understandable models and formulas and simulations is ultimately doomed to failure. Because of the nature of cellular automation computation, there is no way to come up with a shortcut method that will deduce the final outcome of a system in advance of it actually running to completion. We can currently compute a rocket trajectory or a lens shape or a skyscraper framework in advance using mathematics merely because these are ridiculously simple human efforts. New technologies based not on mathematics but instead on cellular-automations like wind-tunnel simulators and nanobot devices will be exciting technological advances but will not lead to a fundamentally new understanding of nature. Issues that humans define as undecidability and intractability will always limit the level of understanding we will ultimately achieve, and will always have impacts on philosophical questions such as predestination and free will. To conclude with Wolfram's own final paragraph in the book:
"And indeed in the end the PCE encapsulates both the ultimate power and the ultimate weakness of science. For it implies that all the wonders of the universe can in effect be captured by simple rules, yet it shows that there can be no way to know all the consequences of these rules, except in effect just to watch and see how they unfold."
As noted above, 350+ pages of notes follow this exposition, and trust me, there's no way they can be summarized. To mention one nugget I found amusing as I envisioned Wolfram working towards endless dawns on ANKOS, he thinks sleep has no purpose except to allow removal of built-up brain wastes that cannot be removed while conscious. So much for dreaming.
So what is the bottom line on ANKOS? It is a towering piece of work and an enduring monument to what a focused and disciplined intellect can achieve. It is very thought provoking. It will definitely lead to new work and progress on cellular automation theory and some interesting technological applications we should all look forward to with anticipation. But is it the next Principia, the herald of a new scientific revolution?
Read and decide for yourself. Only time, and a lot of it, will tell.
To read it yourself, you can purchase A New Kind of Science at bn.com. You can read your own book reviews in this space by submitting your reviews after reading the book review guidelines.
it was me.
Fuck all of you motherfucking LambdaMOOers! Fuck you hard and fuck you well! That's right! Fuck y'all!
Does anybody know if NetBSD has been ported to this yet?
Give us a break. This story is a repeat of
the earlier one:
(the 420 Hemp Fest); Ann Arbor, MI (the Hash Bash); and
Washington, D.C. (buildup towards the July 4th Smoke-In).
Original Source(s)
Conventional wisdom: The most common tale is that 420 is the
police radio code or criminal code (and therefore the police call)
in certain part(s) of California (e.g. in Los Angeles or San
Francisco) for having spotted someone consuming cannabis
publicly, i.e. pot smoking in progress; that local cannabis users
picked up on the code and began celebrating the number temporally
(esp. 4:20 a.m., 4:20 p.m., and April 20); that the number became
nationally popularized in the late 1980s and, more ferverently, in
the early- to mid-1990s; and is colloquially applied to a variety of
relaxed and/or inspired contexts, including not only pot
consumption but also a good time more generally (in contrast to
the drug war surrounding).
Conventions are legends: 420 is not police radio code for
anything, anywhere. Checks of criminal codes (including those of
the City of San Francisco, the City of Los Angeles, Los Angeles
County, the State of California, and the federal penal code) suggest
that the origin is neither Californian nor federal (the two best
guesses). For instance, California Penal Code 420 defines as a
misdemeanor the hindrance of use (obstructing entry) of public
lands, and California Family Code 420 defines what constitutes a
wedding ceremony (Marco). One state does come close: The
Illinois Department of Revenue classifies the Alcoholic Liquor Act
under Part 420, and the Cannabis and Controlled Substances Tax
Act are next, under Part 428. (RB 5/19/99)
True story?: According to Steven Hager, editor of High Times,
the term 420 originated at San Rafael High School, in 1971,
among a group of about a dozen pot-smoking wiseacres who
called themselves the Waldos. The term 420 was shorthand for the
time of day the group would meet, at the campus statue of Louis
Pasteur, to smoke pot. ``Waldo Steve,'' a member of the group who
now owns a business in San Francisco, says the Waldos would
salute each other in the school hallway and say ``420 Louis!'' The
term was one of many invented by the group, but it was the one
that caught on. ``It was just a joke, but it came to mean all kinds of
things, like `Do you have any?' or `Do I look stoned?' '' he said.
``Parents and teachers wouldn't know what we were talking about.''
The term took root, and flourished, and spread beyond San Rafael
with the assistance of the Grateful Dead and their dedicated cohort
of pot-smoking fans. The Waldos decided to assert their claim to
the history of the term after decades of watching it spread, mutate
and be appropriated by commercial interests. The Waldos contacted
Hager, and presented him with evidence of 420's history, primarily
a collection of postmarked letters from the early '70s with lots of
mention of 420. They also started a Web site, waldo420.com. ``We
have proof, we were the first,'' Waldo Steve said. ``I mean, it's not
like we wrote a book or invented anything. We just came up with a
phrase. But it's kind of an honor that this emanated from San
Rafael.'' Maria Alicia Gaura for the San Francisco Chronicle,
4/20/00 p. A19; and thanks to Noah Cole for the submission
Alternate explanations
There are a variety of other explanations, all much more interesting
than police code, and many plausible. Some are more likely uses
of the 420/hemp connection rather than sources of it, such as the
score for the football game in Fast Times at Ridgement High,
42-0.
Known Myths: It isn't police code (see above). There are 315
chemicals in marijuana, not 420. And although tea time in
Amsterdam is rumored to be 4:20, it is actually 5:30 (Gerhard
den Hollander).
Sixties Songs: For instance, Bob Dylan's famous Rainy Day
Women #12 and 35 is a possible reference, or source --
12x35=420. And Stephen Stills wrote (and Crosby Stills Nash
although it is possible to hypothesize that these
deaths, too, had their purpose, since 420 has been, since time
immemorial, the number associated with fraud, deception and
trickery. (Comet 2/14/98) Comet's best guess is that this
refers to something in Indian mythology or numerology, since
the book is set in India and frequently involves Indian history,
culture, and religion. Given the high interest in Eastern
religion among the phish/dead community, this seems a likely
origin of 420's current significance.
Temporal Significance: Hands on analog clock at 4:20 look
like position of doobie dangling from mouth Larry in
Tuscan and Alex Mack 5/19/99). Disruptive students are out
of detention and safetly away from school by 4:20, also
rumored to be the time that you should dose to be peaking
when the Dead went on stage Hart. The Waldos were a
group of teens back in the 70's that lived in San Rafael, CA.
420 was the way they talked about pot in front of teachers,
non-smoking family members etc. Also it was the time of day
they could just go relax, and get baked. (PhunkCellar)
Jamaicans purportedly worked till 4 then walked home then
lit up. They would talk 420 like our parents talked about after
5. That's when partying began Larry in Tuscan). Albert (not
Abbie) Hofmann supposedly first encountered LSD at 4:20
p.m. on 4/19/1943 (Bart Coleman citing Storming Heaven by
Jay Stevens, recommended by Mickey Hart in Planet Drum).
Surrealist painter Miro was born April 20, 1893. And
www.filmspeed.com says the propoganda film Reefer
Madness has a copyright date of April 20, 1936 (i.e. 4/20).
(Patrick Woolford)
Misc: Could be that it comes from hydroponics, the practice
of cultivating plants in water often used by indoor marijuana
cultivators, since 4 is used for H on a calculator (420/H20).
(Nick Lowe 3/30/00) The number 80 (eight) is quatre vingt
(pronounced cah-truh vahn), meaning four (times} twenty.
Dan Nijjar 1/27/00 (No connection yet between the number
80 and pot. A quarter pound is roughly 120 grams, rounding
quarter-ounces to 7.5.) The titanic was supposed to arrive
4/20/1912. (Thanks to RB.) Perhaps the heavy use of vt420
terminals in the Berkeley area is to blame? (BTW, 420 in
binary code is 110100100.)
Ubiquitous?
Now there's a 420 Pale Ale. One of the late-97/early-98 Got
Milk ads featured a character eating cookies without milk and
then passing a sign that reads Next Rest Area 420 miles (as Ross
Bruning). Reportedly, all of the clocks in the movie Pulp Fiction
are stuck on 4:20. Shirts with the number 420 on the red-and-blue
interstate highway shield (Interstate 420?) have show up on the
sitcom Will and Grace (Paul Risenhoover 5/14/99) and in several
videos. UPS' labelling software has a 420 postal code legend for
next-day/2-day deliveries (which is how Phish tickets are sent).
(Jack Lebowitz 10/3/98) MTV's 1997 Viewer's Choice Award (for
the MTV Video Awards) was decided by calls to
1-800-420-4MTV. And by May of 1998, the number was
appearing in so many ads (eg Copenhagen 5/14/98 Rolling Stone
p54, Corvette p55 5/98 Car -), Homer mentions to
Flanders that Barney's birthday is April 20th. Also, the jackpot sign
in one part of the casino says $420,000. There are a couple less
concrete ones, but these two have to be legit, especially since they
decided to air THAT particular episode on 4/20/99. (Submitted by
Matt Meehan 4/21/99) And (as of Fall '99) the 60 free minutes that
Working Assets Long Distance offers, at the 7 cents per minute
rate, is $4.20 free. There's even a band named 420, and another
names . In the first fifteen pages of Karel Capek's novel War with
the Newts, a man diving under wonder stayed down for four
minutes and twenty seconds. Grant Garstka 1/6/00 At the
suggested retail price ($3.96) and Michigan (6%) sales tax, a deck
of Uno cards costs $4.20. Nic Boris 4:20 marks the first downbeat
of the drums in Led Zeppelin's epic Stairway to Heaven. (Dan
Harris) The bill authorizing force after the World Trade Center
attacks of 9/11/01 passed 420 to 1, and news reports in following
months noted many times that there are (or were then, anyway) 420
airports in the U.S. Allan Morris And don't forget that Adolf Hitler
was born on April 20, macabely celebrated (or at least
referenced) via the Columbine High School shootings.
Phish-related Occurances
Whatever the origin, the number appears frequently... For the
summer 1997 tour, TicketMaster service charges were $4.20. In
the Fall 1997 Doniac Schvice Dry Goods section, a limited edition
Pollack poster printed on 100% hemp is order number 420P. The
Great Went was 420 miles from Boston (former home of Phish).
The official logo includes 4 gills and 20 bubbles (Gringo
11/12/98). As of 6/15/97, including covers and originals, Phish
had performed a total of 420 songs (thought its 486 by 4/24/98).
(David Steinberg). Lawnboy is 420megs of memory. Patrick
Walker Phish's The Vibration of Life underlies a whirling loop
with Seven Beats per second (which makes 420 beats per minute.)
Trey has used the altered line woke up at 4:20 in Makisupa
Policeman, which also often indirectly celebrates 420ing, e.g. by
mention of goo balls. One of the funniest shirts around takes light
jabs at both the 4:20 phenomenon and the rumored evolution
(collapse?) of the Phish.Net (especially rec.music.phish) from
being Gamehendge to Flamehendge, and beyond. The first day of
the Great Went started at 4:20 (with Makisupa Policeman. (The
second day started late, at 4:37.) Noah Cole The first single from
Slip Stitch and Pass was played on WBCN 10/14/97 at 4:20 pm.
An uproar at 12/31/96 can be heard on tape during the 2001, in
response to an enormous digital clock (which was counting down
to midnight) reaching 11:55:40 and reading -4:20. (Yoda)
During the 9-12-00 2001, Trey hits the first riff right at 4:20 into
the intro jam. (Cal 2/25/01) Some mail order tickets for the 1997
New Year's run were in section 420. The first Mass Pike toll
leaving Oswego was $4.20. (Camille Heath ) And the standard
shipping for The Phish Companion through Amazon was
originally $4.20.
420 Shows: Phish performed on April 20 in 1989, 1990, 1991,
1993, and 1994. The first day of the Great Went started at 4:20,
although that was called a soundcheck by Trey after three songs.
The Jazzfest Harry Hood 4-26-96 started at about 4:20 reported by
Trevor. At Big Cypress, David Bowie was playing at 4:20 a.m.
And the one event during the hiatus (10/8/00 - ?) featuring all
four members - for Jason Colton's wedding - was 12/1/01, 420
from: http://www.phish.net/faq/n420.html:
The review begins with a a grand statement about how the author hasn't even read the book -- the first inidcation that the reviewer is reviewing reactions and interviews, and not Wolfram's actual words.
But then again, this is Slashdot... ;)
All about me
Right. And since the effort to reduce the universe to formulas has been breathtakingly successful beyond the wildest dreams, while the cellular automata approach (and related new-age "Santa-Fe-style" chaos and complexity theories) have yet to solve their first problem of any significance, we have to conclude that the book's central thesis is a huge bunch of baloney.
"Skimming" is not reading, and the reviewer's opinion is meaningless if he hasn't had time to digest the book. The reviewer BEGINS by declaring his or her ignorance and lack of effort -- that's just plain irresponsible.
This is a book, not a TV show or a movie; it will still be available a month (and probably ten years) from now, giving a reviewer plenty of time to actually READ the book before commenting on it. Then the review might have some credibility.
All about me