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totally out of date  as of 2012, their fastest machine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 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 1001000 times
faster by cost. This statement is a generally
accepted, slightly revised 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 1000 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, 10471054, 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, 203217, 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.
