Collected Essays (56 page)

I’d been kind of waiting for Wolfram to write his book before I wrote my
own
book about the meaning of computation. So once he was done, I was ready to brush the lint of bytes and computer code off myself, step into the light, and tell the world what I learned among the machines. The result:
The Lifebox, the Seashell, and the Soul
(Thunder’s Mouth Press, 2005).

Where did I get my book’s title? I invented the word “lifebox” some years ago to describe a hypothetical technological gizmo for preserving a human personality. In my book title, I’m using “Lifebox” as shorthand for the universal automatist
thesis
that everything, even human consciousness, is a computation.

The
antithesis
is the fact that nobody is really going to think that a wised-up cell-phone is alive. We all feel we have something that’s not captured by any mechanical model—it’s what we commonly call the soul.

My
synthesis
is that gnarly computation can breathe life and soul into a lifebox. The living mind has a churning quality, like the eddies in the wake of a rock in a stream—or like the turbulent patterns found in cellular automata. Unpredictable yet deterministic CAs can be found in nature, most famously in the patterns of the Wolfram-popularized South Pacific sea snail known as the textile cone. Thus the “seashell” of my book title. (You an search my blog for “cone shell” for information about these venomous mollusks.)

Coming back to Wolfram’s
A New Kind of Science
, a lot of people seem to have copped an attitude about this book. Although it sold a couple of hundred thousand copies, many of the reviews were negative, and it’s my impression that people are not enthusiastically taking up his ideas. Given that I think these ideas are among the most important new intellectual breakthroughs of our time, I have to wonder about the resistance.

I see three classes of reasons why scientists haven’t embraced universal automatism. (1)
Dislike the messenger
. Thanks to the success of his
Mathematica
software, Wolfram is a millionaire entrepreneur rather than a professor. Perhaps as a result, he has a hard-sell writing style, an iconoclastic attitude towards current scientific practice, and a sometimes cavalier attitude towards the niceties of sharing credit. (2)
Dislike the form of the message
. Some older scientists resent the expansion of computer science and the spread of computational technology. If you hate and fear computers, you don’t want to hear the world is made of computations! (3)
Dislike the content of the message
. Wolfram’s arguments lead to the conclusion that many real-world scientific questions are impossible to solve. Being something of a perennial
enfant terrible
, Wolfram is prone to putting this as bluntly as possible, in effect saying that traditional science is a blind alley, a waste of time. Even though he’s to some extent right, it’s hardly surprising that the mandarins of science aren’t welcoming him with open arms.

One thing that sets my book off from Wolfram’s is the goal. At this point in my life, I don’t worry very much about convincing anyone of anything. To me the real purpose of writing a science book is to achieve personal enlightenment. And to get new ideas for science fiction novels.

On the enlightenment front,
The Lifebox, the Seashell, and the Soul
ends with a discussion of six keys to happiness, drawn from considerations involving six successively higher levels of gnarly computation. And these will make a nice note upon which to end this article.

Computer science
. Turn off the machine. Nature computes better than any buzzing box.

Physics
. See the gnarl. The world is doing interesting things all the time. Keep an eye on the clouds, on water, and on the motions of plants in the wind.

Biology
. Pay attention to your body. It’s at least as smart as your brain. Listen to it, savor its complexities.

Psychology
. Release your thoughts from obsessive loops. Avoid repetition and go for the gnarl.

Sociology
. Open your heart. Others are complex as you. Each of us is performing much the same kind of computation. You’re not the center.

Philosophy
. Be amazed. The universe is an inexplicable miracle.

Note on “Adventures in Gnarly Computation”

Written in 2005.

Appeared in
Isaac Asimov’s SF Magazine
, October 2005.

This short essay is adapted from
The Lifebox, the Seashell, and the Soul: What Gnarly Computation Taught Me About Ultimate Reality, the Meaning of Life, and How To Be Happy.
It’s always nice to publish a bit of science in
Asimov’s
, and my fellow SF writers seemed to enjoy the material.

Web Mind

The Web As a Model For the Mind

My
Web Mind
column is meant to be a clear-channel broadcast of a mad scientist’s wild ideas. Like the good Dr. Frankenstein, one of my pet interests is the creation of life. For the first few columns I’m going to be talking about how (and why) you might go about making a computer copy of your mind.

This summer I read a terrific book by Margaret Wertheim called
The Pearly Gates of Cyberspace
(W. W. Norton, 1999).

She starts with this idea:
the invention of pictorial perspective paved the way for Newtonian physics
. This happened because perspective provides a tool for mapping unbounded three-dimensional space onto a finitely large two-dimensional canvas: the whole world in a square meter of cloth! Each object of the world gets assigned to one particular location upon the picture plane and, looking from the picture back out at the world, we can then see that the individual objects are contained in an all-encompassing world-space. Perspective teaches us to think of each object’s location as mapped into a mathematical (x, y, z) triple of coordinate numbers—and this is the space of mathematical physics.

It’s fascinating to think that a new trick of artists made it possible to invent physics. Art matters! Accustomed as we are to seeing photographs, the perspective mapping of the world onto a square of paper seems obvious, even trivial, but it took people a long time to come up with it. And it was impossible for people to do modern physics until they had the idea of a unified underlying space. So, yes, maybe the invention of perspective really did lead to physics.

Wertheim’s next step is the following: people used to have a notion of God as an entity that lived in physical space, but once Newtonian physics had made space into a Cartesian three-dimensional construct it seemed likely that God would have to live elsewhere. In the nineteenth century there was a feeling that God might live in the fourth dimension, but in post-Einsteinian physics has make all of the physical space dimensions into scientific constructs as well. Wertheim feels that we might now usefully ask ourselves if there is some tendency for present-day people to think of God as somehow located in cyberspace. Wertheim compares the science-fictional notion of making a software copy of oneself to the traditional religious notion of having a soul that goes to heaven, and suggests that if souls can be thought of as going into cyberspace, then perhaps some people might expect to find God in there as well.

Let’s pause here to specify what is meant by the word “cyberspace.” One can usually think of “cyberspace” as simply a sexy word for “the Web” or “the Internet.” A little more generally, you can speak of cyberspace as a manifold containing all the kinds of data that one might conceivably access via a computer. My feeling is that cyberspace exists more as a container that holds data, rather than saying that cyberspace has an existence in and of itself. That is, I’d say that cyberspace is something like a pure, idealized, pre-quantum-mechanical vacuum: a content-free domain of positional possibility. But, just as it makes sense to inquire about the spatial dimensionality of an empty vacuum, it makes sense to talk about the dimensionality of cyberspace, and we’ll get into this question below.

Before getting to that, I’d like to make some remarks about the structure of cyberspace and of the human mind, to look for similarities between the two, and to speculate about future developments in philosophy and science. In the most concise possible form, the main idea I’m going to investigate here is the following.

Web : Mind :: Perspective : Space.

Might it be that the newborn Web provides a mapping tool which will lead to a mathematics of the human mind? As Marshall McCluhan taught, the effects of new media are wide-ranging and unpredictable.

I have three reasons for thinking the Web is good for modeling the mind. First of all, the Web can display any type of media. Secondly, the Web has a hyperlinked structure reminiscent of mental associations. Thirdly, the Web and the mind’s pattern of links are mathematical fractals of a similar kind.

Regarding the first point, the Web, a. k. a. cyberspace, is a network containing all the kinds of data that one might conceivably access via a computer. In and of itself, the Web is not limited to any particular form of media. It can dole out printed words, sounds, images, movies, or active programs. Just like the mind.

The second point has to do with the fact that the Web pages by which we access Web data are written in hypertext (as in “Hypertext Markup Language,” a.k.a. HTML). One of the essential features of hypertext is that it contains hyperlinks: buttons you use to hyperjump to different locations in the hypertext. Later on, we’ll look at how this compares to the mind’s process of making associations.

And thirdly, I feel that the mind and Web are both fractals, specifically they are fractals of a similar kind of dimensionality. Before arguing this any further, I’d like to give you some background on fractals.

The word “fractal” was coined by Benoit Mandelbrot,
Fractals: Form, Chance and Dimension
(Freeman, 1977). It means a shape that has an exceedingly fragmented form, but which also has a certain kind of regularity. The regularity of a fractal lies in its self-similarity. If you select a small part of a fractal and magnify this part, then the magnified image will resemble the entire fractal shape itself.

Fractals can be either regular or random according to whether the small pieces of the fractal bear an exact or only a statistical resemblance to the whole form. The figure below shows three stages in the construction of a regular fractal called the Koch curve. We generate it by repeatedly replacing each line-segment by a little wiggle.

The Helge von Koch curve, a fractal of dimension 1.26.

The “dimension” of a regular fractal is given by this rubric:
If looking P times as hard at a shape shows Q times as much structure, then the fractal dimension of the shape is log Q / log P.
Each time you magnify the Koch curve by a factor of three, you see four times as many pieces, so I say it has dimensionality log 4/log 3. For a straight line, when I make it three times bigger I see three times as many pieces, so it has dimensionality log 3 / log 3 = 1. If I make a square three times bigger, I see 9 times as many pieces, and it turns out that log 9 / log 3 is 2.

Don’t worry much about the log function here, the basic point is simply that the bumpier and granular the fractal, the higher its dimension. And the maximum dimensionality of a fractal is bounded by the space that it sits in. The Koch curve is an unruly line in two-dimensional plane, and it’s thought of as having dimension 1.26. A mountain is a messy surface in three-dimensional space, and its dimensionality might be something like 2.1. If we had a sufficiently spiky fractal we might actually need a higher N-dimensional space to hold it without its part having to overlap.

Speaking of mountains, the parts of a mathematical fractal need not be perfect copies of the whole. It’s perfectly all right to have the patterns vary a bit from level to level. The idea is that a spur on a mountain looks quite a bit like the whole mountain, even though it isn’t an exact replica. The outcroppings on the spur in turn resemble the spur, even though they aren’t scale models of it. The outcroppings have mountainous little bumps on them, and the bumps have little jags, and if you get a magnifying glass you’ll find zigs and zags upon the jags.

Among the physical forms that are commonly thought of as being like fractals are the following.
Dimensions between 1 and 2
: coastlines, trees, river drainage basins.
Dimensions between 2 and 3
: mountains, clouds, sponges. Fractal forms are found within the human body as well. Among these are the circulatory system, the nervous system, the texture of the skin, the eye’s iris, the convoluted surface of the brain, and the spongy masses of the internal organs.

A tree is a particular kind of fractal that’s particularly important for the present discussion. If you look closely at a tree, you’ll readily notice that it has a trunk with big branches. There are subbranches coming off of the branches, and there are subsubbranches upon the subbranches, and so on through five to seven levels of branching.