Written in Los Angeles and sent to silicon.com via a London hotel LAN a day later.

There seems to be a very good reason why artificial intelligence is advancing far more slowly than we expected.

Some months ago, I was working on an industrial problem that resulted in defining a formula for the relative intelligence of machines. This formula originated from the starting point of trying to quantify and understand the nature of artificial intelligence.

Based on entropic measures, this delightfully elegant formula was the final result:

Ir ≈ KN log2[1 + AS ( 1 + PM)]

Where: A, S, P, and M are weighting properties for the contributions of the Actuators or output mechanism, Sensors or input mechanism, Processor and Memory functions for the compute power, and N is the number of clock cycles.

Not only is this formula in line with our natural world experience of intelligence, it also confirms two essential and observed properties:

  1. With zero processor or memory power, intelligence is still possible.
  2. With zero sensor or actuator power, intelligence is impossible.

This proposition flies in the face of the conventional wisdom of those worried about the singularity – the point at which machines take over because they outsmart us. Here, people generally assume that machine intelligence is growing exponentially by way of the product PM and Moore’s Law. The estimated difference is shown below.


A spread of published predictions about processors and memory compared with our logarithmic modelImage: Peter Cochrane

If we now make a couple of big assumptions to further approximate Ir we can make further interesting observations.

Iff – if and only if: PM >> 1 and AS PM >> 1, then:

Ir ~ KN log2[AS PM)]

We now observe that the progress of actuators, sensors, processing power and memory technology is exponential with time ~ eat, est, ept and emt, then the growth in intelligence looks like this:

Intelligence rate of growth ~ k.a.s.p.t …(9)

This finding implies that overall machine intelligence is growing linearly with time. So the obvious question is what happens when a large number of intelligent machines are networked? If they are sufficient, and their numbers grow exponentially, then, and only then, will we see an exponential growth in intelligence.

This growth will probably be furnished by the cloud, with a large population of fixed and mobile computers, but more importantly, mobile phones laden with all forms of sensory capability. That development gives a whole new meaning to mobile intelligence.