Rule 110 Cellular Automata

Rule 110 Cellular Automata

Rule 110 is the remarkably simple one dimensional cellular automata discovered by Stephen Wolfram in A New Kind Of Science and proven Turing complete by Cook and Wolfram.


In short, the above simple mechanism is a simple type of computer capable of computing anything.

Rule 110 is not the only example of complexity (a computer) being ultimately reduced to a very simple structure.

Hecht-Neilson’s Cogent Confabulation partial theory proposes a simple underlying process that covers all vertebrae intelligence mechanisms.

And from a somewhat elaborate biological analysis Smith1 concludes that “the description-length of the biological blueprint for human intelligence” may be in the range of 6-81 kb (with a *4 or /4 uncertainty) – a remarkably small program. (Admittedly, this estimate is based on the questionable, in my view, assumption that chimps do not have most of the intelligence machinery that humans have. The contrary seems likely to me.)

We know that AGI can be coded in about a page of code if we accept exponential slowness. And we also can easily list countless algorithms that can be vastly sped up without writing a lot of code. Why should this problem be different? There are arguments why – but I have not seen one convincing enough to override the firm ground supporting Occam’s razor.

Many difficult math problems took more than a century to solve yet ended up with short solutions. The lack of success in AGI to date does not provide strong support for the conclusion that the solution is large. The motions of the planets where at first analyzed by Kepler thru numerous charts of raw data only to finally be simplified to one simple formula that can be expressed in a handful of characters. Einstein expressed the long unknown connection between matter and energy in five characters.

In On Intelligence, Hawkins summarizes Mountcastle’s2 paper on cerebral function which claims that not only is the cortex relatively uniform but it performs essentially the same algorithm throughout, even for different senses. Hawkins writes:

I hope you can appreciate how radical and wonderfully elegant Mountcastle’s proposal is. The best ideas in science are always simple, elegant, and unexpected, and this is one of the best. In my opinion it was, is, and will likely remain the most important discovery in neuroscience. Incredible, though, most scientists and engineers either refuse to believe it, choose to ignore it, or aren’t aware of it.

All this points to the urgency of understanding and/or solving the existential risks of AGI.

(1) Information Content of Human Intelligence – Warren D. Smith (2006)

(2) Vernon Mountcastle (1978), “An Organizing Principle for Cerebral Function: The Unit Model and the Distributed System”, The Mindful Brain (Gerald M. Edelman and Vernon B. Mountcastle, eds.) Cambridge, MA: MIT Press.

Leave a Reply