‘New kind of science’ is not science at all

Originally published 8 October 2002

Stephen Wol­fram’s A New Kind of Sci­ence arrived ear­li­er this year in a bliz­zard of hype. As sig­nif­i­cant as the works of New­ton and Dar­win, said breath­less touts, and the author seems to agree.

Sci­ence has been bark­ing up the wrong tree for hun­dreds of years, he says. His “new kind of sci­ence” will set things straight, explain­ing every­thing from ele­men­tary par­ti­cle physics to the econ­o­my to the weath­er to human con­scious­ness and free will.

The uni­verse is not myr­i­ad par­ti­cles act­ed on by forces, mov­ing in con­tin­u­ous space and time, as described by all physi­cists since New­ton. Rather, Wol­fram states, the uni­verse is a com­put­er pro­gram — and the pro­gram might be incred­i­bly simple.

Not hard­ware, but software.

A stun­ning claim, and you may want to check it out. But you won’t read this doorstop of a book overnight. If you want to have a seri­ous go at it, set aside a cou­ple of months on a desert island.

Stephen Wol­fram was born in Lon­don, and edu­cat­ed at Eton, Oxford, and Cal­tech. He received a doc­tor­ate in the­o­ret­i­cal physics at age 20, hav­ing already made sig­nif­i­cant con­tri­bu­tions to par­ti­cle physics and cos­mol­o­gy. In 1981, at age 22, he received a MacArthur “genius award.”

In 1986, he found­ed his own com­pa­ny to devel­op and mar­ket Math­e­mat­i­ca, the world’s lead­ing soft­ware for sci­en­tif­ic com­put­ing, and made him­self a rich man. Mean­while, he was busy inves­ti­gat­ing a branch of com­pu­ta­tion­al math­e­mat­ics called cel­lu­lar automa­ta.

Cel­lu­lar automa­ta are the heart and soul of Wol­fram’s “new kind of sci­ence.” Let me give an example.

Imag­ine a grid of cells, like the squares on an end­less checker­board. Each cell can be in one of two pos­si­ble states, black or white.

Start with any pat­tern of black squares, per­haps some­thing very sim­ple. With each tick of the clock, let every square in the grid simul­ta­ne­ous­ly respond to the fol­low­ing rule: If a square has two black neigh­bors (among the eight adja­cent squares, includ­ing diag­o­nals), it stays the same col­or; if it has three black neigh­bors, it becomes black; any oth­er num­ber of black neigh­bors, it becomes white.

Set the clock run­ning — tick, tick, tick — and watch as amaz­ing, unpre­dictable and appar­ent­ly inex­haustible pat­terns evolve.

This par­tic­u­lar two-dimen­sion­al cel­lu­lar automa­ton, called the Game of Life, was invent­ed by the British math­e­mati­cian John Con­way in the late 1960s, and has giv­en com­put­er geeks end­less hours of fun.

Cel­lu­lar automa­ta can be of one, two, three, or more dimen­sions, have more than two pos­si­ble states for each cell, and evolve accord­ing to any con­ceiv­able rule. What they all have in com­mon is a grid of pix­els that change with every tick of the clock.

And here’s the kick­er: Even extreme­ly sim­ple cel­lu­lar automa­ta can quick­ly lead to pat­terns of aston­ish­ing complexity.

Wol­fram spent 10 years inves­ti­gat­ing cel­lu­lar automa­ta on his com­put­er, and describes them by the hun­dreds in his book. The pat­terns they gen­er­ate are indeed daz­zling, fre­quent­ly bear­ing uncan­ny resem­blances to pat­terns in nature, such as snowflakes, the stripes on zebras, the mark­ings of seashells, curl­ing smoke, or fluc­tu­a­tions of the economy.

These resem­blances are not acci­den­tal, Wol­fram states. The uni­verse is itself, per­haps, a cel­lu­lar automa­ton, a mul­ti­di­men­sion­al grid of dis­crete pix­els, tick­ing away accord­ing to some sim­ple rule or rules, yet to be determined.

Whoa! That’s one big jump. From the admit­ted­ly mind-bog­gling pat­terns that can be gen­er­at­ed with sim­ple com­put­er pro­grams to “a new kind of science.”

For one thing, the “sci­ence” is not as new as Wol­fram makes it seem. Cel­lu­lar automa­ta have been around for more than half a cen­tu­ry, and many peo­ple have inves­ti­gat­ed their prop­er­ties. Wol­fram is not the first to sug­gest that the uni­verse might be use­ful­ly described as a cel­lu­lar automaton.

For anoth­er thing, Wol­fram’s “new kind of sci­ence” hard­ly qual­i­fies as sci­ence. The book makes not a sin­gle pre­dic­tion that can be test­ed in the usu­al way. The uni­verse might be a cel­lu­lar automa­ton run­ning a sim­ple rule, but, as Wol­fram demon­strates, any num­ber of dif­fer­ent rules might lead to the uni­verse we live in. The only way to pre­dict what sort of uni­verse will evolve from a giv­en rule is to run the pro­gram from the begin­ning, which is equiv­a­lent to re-run­ning the uni­verse itself.

Wol­fram also demon­strates that all com­plex cel­lu­lar automa­ta are equal­ly com­plex, which means — if the uni­verse and every­thing in it are cel­lu­lar automa­ta — that the uni­verse, the human brain, and a bowl of Chee­rios are equal­ly com­plex. The human brain there­fore has as much chance of explain­ing the uni­verse as a bowl of Chee­rios has of explain­ing the human brain.

A New Kind of Sci­ence is not new and not sci­ence, but it is a daz­zling com­pendi­um of com­pu­ta­tion­al play, an impor­tant con­tri­bu­tion to the the­o­ry of cel­lu­lar automa­ta, and, yes, a work of genius.

Is the uni­verse a com­put­er pro­gram? Why not? All of our expla­na­tions are metaphor­i­cal. For New­ton, the uni­verse was a mechan­i­cal clock­work. As com­put­ers get ever more sophis­ti­cat­ed, and dom­i­nate our lives ever more com­plete­ly, it is inevitable that they will influ­ence the way we think about the uni­verse and ourselves.

So, if you wish, think of your­self as a pat­tern of flick­er­ing pixels.

But don’t expect cel­lu­lar automa­ta to replace the old kind of sci­ence any time soon. Iron­i­cal­ly, Wol­fram’s big book demon­strates rather con­vinc­ing­ly exact­ly why that’s not about to happen.