From: Raymond G. Van De Walker (rgvandewalker@juno.com)
Date: Tue Jun 22 1999 - 21:57:48 MDT
On Sun, 13 Jun 1999 19:16:20 +1000 "Timothy Bates"
<tbates@karri.bhs.mq.edu.au> writes:
>any chance of passing on the algorithm you sued to calculate this ;)
>
>> I calculated that a human-equivalent-intelligence (HEI) would fit
>into
>> several thousand cubic microns,
I have a canned response I sent to another correspondent- it got me
a signed book from Halperin!
Mr. Halperin, I'm a professional computer engineer, and an amateur but
trained philosopher and biologist, and I don't think that even advanced
nanotechnology can pack a human-equivalent brain into the volume of a
blood cell. (TFI p208 is wrong)
Let me show you the numbers: The human brain has 10 billion
neurons. Each neuron has between 30 and 10,000 synapses, with one
associated dendrite for each. If the axon is considered just another
connection, its organizational importance is merely to make distant
dendrites. Taking the geometric mean of the number of dendrites, say
that each cell has 300 dendrites. Then there are at roughly 3x10^12
synapses in the proposed human-equivalent brain.
Now, I thought about ways to reduce this by editing the system,
but they won't work. Like most real computing systems, the majority of
the logic (>95%) by weight or volume is I/O. (The cerebrum, cerebellum,
gyrii, and most of the encephalon) Neural networks are great for I/O:
they're robust and compact compared to the digital systems they replace.
You would not want to use anything else to construct the phenomenal
systems of a robot.
So, for a first approximation, let's say we can custom-design the
system so that we can store one synaptic weight per byte. This generously
assumes that the connection pattern (i.e. which neuron has the synapse)
is hard-wired or hard-coded into the simulation program. The synaptic
weights have to change, because that's how the system learns. Since they
change, they have to be recorded.
Therefore, the computer needs at least one byte per synapse,
3x10^12 bytes of storage.
Using Drexler's estimates for fluorine/hydrogen carbyne tapes,
this could be stored in at least 1500 cubic microns (Drexler roughly
estimated 2GBytes/cubic micron; see the notes for Engines of Creation,
p19)
Now, we want the brain to run at human speed. Let's say that
nanocomputers run 1 million times as fast as neurons; this is roughly
right, because I'll assume mechanical nanocomputers. Mechanical
nanocomputers would be more compact than quantum electronic computers.
They also have a speed that more closely matches the mechanical carbyne
tape drive. If we use the QE computers, they will run 100x faster, while
only being about 50x bigger, but the apparent advantage will be cancelled
because they will stall waiting for the tape drives. The result will be
a slower or larger computer than the mechanical systems. This might be
fixable; quite possibly an experienced nanoengieer could finesse this, if
such a person existed. However, note that it just divides the
computer-volume by 2, and the tape remains the same size.
So, to get at least human speed, we need roughly 1/1,000,000 the
number of processors, about 3x10^6. I assume that each one of these is
servicing a million simulated synapses. I'm going to throw in the CPUs
for free (I know pretty good CPUs that have as few as 7,000 gates; see
the web site for computer cowboys).
Using Drexler's estimates for random-access memory
(20MBytes/cubic micron), we can fit 305 of 64K computers in a cubic
micron. The computers therefore take roughly 9.8x10^4 cubic microns.
The computers' program memories are therefore the major system
expense. Can we get rid of them? Now let's say that the engineer goes
for broke, and designs a system with no computers. It's totally analog,
maybe with frequency-modulated hysteresis devices acting as neurons, and
carbyne pushrods acting as dendrites. In this case, the system volume
should grow substantially, because the dendrites have to physically
exist, each with a few thousand carbon atoms, rather than just being
simulated from 8 bits on <50 atoms of tape.
Possibly one could substitute a custom logic machine that _only_
processes neural nets? The problem with these is that they tend to be
larger and more complex than the computers they replace. Random logic is
bulkier and more power-hungry than the random-access memories that store
software. Faster, maybe, but then we might stall waiting for the tape,
right?
The computers therefore take about 9,800 cubic microns. The tape
storing the synapses takes about 1,500 cubic microns. Now remember, this
is a _low_ estimate. I actually think that the storage for a synapse
would have to store an address of a neuron as well, thus having 4 bytes
of address in addition to the byteof weight. This quintuples the tape
system to 7,500 cubic microns. Also, the tape drive and computers might
double in size. Drexler doubled them.
11,300 cubic microns is small. It's a cube about 22.5 microns on
a side, say a quarter-millimeter on a side, about 1/8 the size of a
crystal of table salt. 17,300 cubic microns (storing synaptic addresses)
is still small, about 25.9 microns on a side. Even 34,600 cubic microns
(double everything) is small, maybe 32.6microns on a side, the size of a
crystal of table salt.
<snip stuff about Halperin's book>
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