A cautionary note

A cautionary note

One of the constraints laid down by DARPA at the recent Physical
Intelligence proposers workshop was that the model of intelligence
that was to be proposed had to have a physical implementation. It
seemed odd to some of the attendees that this should be a hard
constraint, since many models of intelligence have a perfectly
reasonable implementation as software.

I have long held something of a nuanced view on this point. On the
one hand, I never agreed with the philosophers and others who claimed
that embodiment was necessary for true intelligence, meaning, the
aboutness of symbols, or any of the rest. The people in the
Matrix were really intelligent thinking creatures even though their
bodies had nothing to do with the world they thought they were

On the other hand, the need to interact with a robot body and cope
with the real world has had a very salubrious effect in terms of
keeping AI researchers “honest” in the sense of not making simplifying
assumptions about the task to be accomplished (for the researchers who
did in fact use robots, that is).

Even a simulated world can turn out to have assumptions built in which
are either unknown to the writers or operate quite differently from
how they are believed to. An interesting example comes from my
experience doing molecular dynamics simulations at Nanorex.

The point of molecular dynamics is to simulate the atoms as if they
were point masses (which the nuclei very much are), with a set of
made-up forces between them to stand for the interactions of the
electrons. These forces can be thought of as springs; it’s of great
concern to find a formulation that matches the real forces but that’s
beside the point of this story.

The point of the story is that when you take a group of atoms with no
external source of energy and no sink, i.e. perfectly insulated, it
doesn’t get hotter and it doesn’t get colder. Energy is conserved in
a closed system.

The problem is, of course, that the numerical simulation doesn’t quite
conserve energy; there are various forms of “leakage” ranging from
round-off error to discreteness of timesteps. So molecular dynamics
simulations have a “thermostat” — a piece of code that sums up the
energy in the model and damps down the motion if the energy is too
high, or vice versa. For ordinary chemistry, this works fine.

We were trying to simulate molecular machines, however, and one
typical “experiment” would be to have a bearing, turn a shaft in it,
and see how much heat it would generate. So we couldn’t use the
thermostat to clamp the heat, since we were trying to simulate a
situation where the heat would vary.

So I tried to write a simulator which conserved energy at the very
lowest level, so energy conservation would be a property of the model
and we wouldn’t need a thermostat. It didn’t work — it’s quite
difficult to get “spring-like” forces with efficient implementations and
yet also follow some constraint like being conservative. On the other
hand, I thought I could get away with another microscopic property of
physics, namely being reversible. In real physics, the trajectories of
atoms are described just as accurately by the equations running
backwards in time as forwards. So it seemed that I should have a
system that matched physics to that extent, and on the average, as
much energy would be gained as lost, since there were exactly as many
energy-gaining trajectories as energy-losing ones — they were the
same ones in reverse!

So what happened? It turned out that you could take any random
assortment of atoms at all, let the simulation run, and it would get
hotter. No energy sources, no apparent way for this to happen, but
hotter it would get. Never colder, even though there were, as noted,
exactly as many possible cooling trajectories as warming ones.
Totally unlike physics, of course, since in the real world, energy is

But I had an ace up my sleeve: since I had made the system reversible,
I could let my atoms get hot and then reverse all their velocities.
And lo and behold: the system cooled off. It found one of those
energy-losing trajectories because it was exactly the reverse of the
energy-gaining one it was on before. But put the system an any random
state, and it would always warm up, never cool down.

I finally figured out what was going on, but I’ll let readers chew
over it as a meaty puzzle and tell you my conclusion next week.

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  2. Anonymous June 12, 2009 at 2:15 pm - Reply

    Wild guess: When you say that the system started in any random state – were there any
    restrictions on that state? For instance, were the nuclei started in the lowest energy positions,
    but with random velocities, or conversely, with zero initial velocities but randomly displaced
    positions? Either of these would give an initial state that couldn’t normally be produced by
    simulating for some time, then reversing velocities.

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