It has been a while since I've found time for Xanga. I still don't, but here is a letter I wrote to First Things magazine that never got a response (mildly frustrating). So, I'll just post it here to see if it piques anyone's interest. The article I criticize is making the point that 3 dimensions are uniquely suited for Intelligence and Life As We Know It, but makes a big blunder when it stumbles into an area I know quite a bit about.
While I enjoyed the June 2001 article by Stephen M. Barr, "Anthropic Coincidences", I am writing to correct what I believe is a factual error. Mr. Barr claims that "complex neural circuitry, as is needed in a brain, would not be possible in one or two dimensions. ... one finds that the wires have to intersect each other many times, leading to short circuits."
Statements of the form "there is no such thing as X" are always hard to prove, and I wish to mention several counterexamples for 1 and 2 dimensions drawn from literature and real life. There is a detailed counter-example for 2 dimensions in the fascinating book, "The Planiverse" by Alexander K. Dewdney, published by Poseidon Press, a division of Simon & Shuster, ISBN 0-671-46362-4 (0-671-46363-2 Pbk.). Diagrams are essential to effective communication of technical description, and the book is full of them, but I will give a brief overview.
First, 2D computer circuits are vastly simplified by integrating a tiny battery into each ciruit element. A NAND gate with battery does not require any cross-overs. An XOR gate is constructed from 4 NAND gates with no crossovers. A "crossover circuit" contructed from 3 XOR gates allows signals to cross an intersection without the benefit of a third dimension. Since each crossover requires 12 NAND gates, 2D computer designers will find that using an asynchronous design instead of a distributed clock will greatly reduce the gate count. This crossover circuit technique has been used in real 3D chip design to reduce the number of layers required since each additional layer adds significant cost. Mr. Dewdney also provides his Planiverse creatures with crossovers for fluid transfer by means of "zipper valves" and nerve impulses by means of a 3 neuron crossover connection.
Second, 1D communication is described in the classic, "Flatland" by Edwin A. Abbott. The inhabitants of Lineland communicate with each other by means of vibrations which are transmitted through all the participants. Each inhabitant has a unique and recognizable voice. This vision is not fleshed out in detail in Abbott's book, but I will point out that modern network protocols with linear topologies use this principle. IBM Token Ring, for example, transmits all packets of information through all devices in the ring. Each device has its own unique address and ignores, but passes on, packets with addresses it is not interested in.
There *is* a mathematically proven unique aspect to three dimensions. Knots can exist only in three dimensions. How knots relate to intelligence is far from obvious, however. And please note that virtual knots can be simulated by a 2D computer - even if they cannot exist physically in 2D.
Posted 12/13/2009 at 8:59 PM