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 nonreversible 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 $10^{51}$ operations per second on $10^{32}$ 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 $2 \times 10^{30} kg$) might be able to solve an additional problem that requires finding an additional 200 bit program with, say, $10^{20}$ 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 $10^9$ 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 ($>10^6$ moves), without any need for boosting task-specific instructions, or for incremental search through instances $< 20$, 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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