IDSIA is located right above the Swiss Supercomputing Center CSCS. Some of their machines are doing 1,300 billion floating point operations per second. (Note of 2012: this text was written in 2001; by the time you read it, this number probably will be totally out of date - as of 2012, their fastest machine already did a Petaflop or a million billion FLOPS.)

Our brains are maybe 10,000 times faster than that. We have over 10 billion neurons, each with about 10,000 synaptic connections to other neurons. A frequent guess at the computational power per synapse is something like 100 multiplications per second.

On the other hand, each decade computers get roughly 100 times faster by cost. This statement is a generally accepted variant of Moore's law, first formulated in 1965.

Over the past three decades many people have extrapolated Moore's law to predict the date when machines will match brains. The most frequent estimate is 2020 plusminus a few years (underestimating synapses by a factor of 100 will cost a decade or so). Such an educated guess motivated Schmidhuber to study computer science.

Calculating machines were introduced by Wilhelm Schickard (1623), Pascal (1640), and Leibniz (1670). The first working general purpose computer was completed by Konrad Zuse in 1941. In the year 2041, only 100 years later, their fastest descendants will presumably outperform brains by a factor of a million, at least in terms of raw computing power. Compare Schmidhuber's law.

Where are the limits? How much can you compute with the "ultimate laptop" (S. Lloyd, Nature 406, 1047-1054, 2000) with 1 kg of mass and 1 liter of volume? Answer: not more than 10^51 operations per second on not more than 10^32 bits (compare H. J. Bremermann: Minimum energy requirements of information transfer and computing, International Journal of Theoretical Physics, 21, 203-217, 1982). The massively parallel laptop's temperature would be roughly 10^9 degrees Kelvin. As we compress it such that it approaches its Schwarzschild Radius (where it will become a black hole), it still cannot perform more than 10^51 operations per second. But now it may work in a serial fashion, as the communication time around the black hole horizon equals the time to flip a bit. Two additional centuries of Moore's law seem necessary to achieve the Bremermann limit.

Long before that, in 2141, roughly half a millennium after Schickard, and 200 years after Zuse, there should be affordable hardware with a million times the raw computational power of all current human brains combined.