## Mathematical exercise

Ever since the discovery of the memristor was announced at HP labs last year, I’ve been fascinated by its story and its promises. Now, its inventor Stanley Williams has given a presentation (available on YouTube) that goes in to some of the mathematical details and further predictions that he has for the device.

It’s a 45 minute presentation, but if you’re interested in the future of computing, I think you’ll enjoy it. I was impressed with the foresight of Leon Chua who in the late 1960s and early 70s discovered via mathematical exercise the “missing circuit element” that should relate flux to charge. If I were him, I think I’d have lost a little confidence in my work if my predictions hadn’t panned out after 40 years.

In addition to the neat math behind it (the memristor is the only fundamental circuit component that is time-variant, and therefore cannot be described in a single equality relationship), Williams makes some stunning claims about the potential of the memristor. For example, in strange agreement with Ray Kurzweil’s predictions, Williams shows a 3D cube of memristors on his slides. He predicts that we will soon have memory storage devices that last for “geologic time” (i.e. thousands or millions of years) but that can react at nanosecond switching speeds. What’s more, because the memory is passive (no energy required to sustain) the memristor is perfectly suited to low-power and low-heat systems: in other words, it just makes sense to stack them on top of each other. Williams calculates a theoretical limit of 1 petabit of storage per cubic centimeter (I think he said square centimeter in the presentation, but I assume he misspoke, since his slide shows a 3D cube?)

Another exciting part of the presentation comes near the end where Williams shows how the memristor may play a role in the next 10 years of computing achievements. He highlights the work of the HP photonics lab and claims that data transfer will soon be achieved through light (photons) for distances greater than a micrometer. With the remarkable ability of memristors to be both memory and logic gates (they naturally form the “implication” logic function which Bertrand Russell showed could represent logical operations in the most compact form), Williams envisions a computing device with hundreds or thousands of cores in a 3D matrix, with photonic message passing between devices. He estimates that in 10 years, the combination of these two technologies will increase our computation-per-dollar by 100 times.

And last but not least was the incredible insight, this time once again from Leon Chua, that the memristor behaves much like a human neuron. The HP lab that invented the memristor is already working on a prototype chip that will attempt to emulate the neurons in a brain, much like the Bluegene-L system has achieved. As Williams pointed out in his presentation, the key here is emulation, not simulation. Up until now, we have only been able to simulate the brain with our computing technology.