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##

Physical Limitations of OOPS

OOPS will scale to large problems in bias-optimal fashion,
thus raising the question:
Which are its physical limitations?
To give a very preliminary answer, we first observe
that with each decade computers become roughly 1000 times faster by cost,
reflecting Moore's empirical law first formulated in 1965.
Within a few decades *non*reversible computation will encounter
fundamental heating problems associated with high density computing
[4]. Remarkably, however, OOPS
can be naturally implemented using the *reversible* computing
strategies [12], since it completely resets all state
modifications due to the programs it tests.
But even when we naively extrapolate Moore's law,
within the next century OOPS will hit
the limit of [6]:
approximately operations per second on
bits for the ``ultimate laptop'' [34] with 1 kg of
mass and 1 liter of volume. Clearly, the Bremermann limit constrains
the maximal *conceptual jump size*
[69,70] from one problem to the next.
For example, given some prior code bias derived from solutions
to previous problems,
within 1 minute, a sun-sized OOPS (roughly
)
might be able to solve an additional problem that requires finding
an additional 200 bit program with, say, steps runtime.
But within the next centuries,
OOPS will fail on new problems that require
additional 300 bit programs of this type,
since the speed of light greatly limits the acquisition
of additional mass, through a function quadratic in time.

Still, even the comparatively modest hardware speed-up
factor expected for the next 30 years appears quite promising
for OOPS-like systems. For example,
with the 73 token language used in the experiments (Section 6),
we could learn from scratch (within a day or so)
to solve the 20 disk Hanoi problem ( moves),
without any need for
boosting task-specific instructions, or for incremental search through instances ,
or for additional training sequences of easier tasks.
Comparable speed-ups will be achievable much earlier by
distributing OOPS across large computer networks
or by using supercomputers--on the fastest current machines
our 60 tasks (Section 6)
should be solvable within a few seconds as
opposed to 4 days.

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** Up:** Experiments: 60 Successive Tasks
** Previous:** Future Research
Juergen Schmidhuber
2004-04-15

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