Thursday, December 02, 2010

escaping infinity

I've previously mentioned a chain of reasoning similar to this: 1) everything that is real is material, i.e. subject to the usual scientific "laws"; 2) whenever a substance "means" another substance, that relationship is an isomorphism recognized/superimposed by a material brain; 3) there is no ultimate theoretical barrier to the possibility of inventing a sufficiently advanced computer/program that could process "meaningful content" (i.e. isomorphisms) as well as a brain.

Many varying objections apply. One category pertains to an insinuated reduction and comparison of exceedingly-complicated consciousness to the current generation of inflexible, literal-minded computers and programs. And although it's likelier than not that the computers and programs that would successfully imitate the brain would be laid-out much differently than ours, these objections still make some valid points: a computer with more or faster components is "merely" another computer and a program with rather chaotic and evolutionary qualities, broken into segments running in parallel, is "merely" another program.

For instance, assume (if you're an objector, purely for argument's sake) that in principle a brain could be adequately simulated by the appropriate computer and program named Q. Brains, at least after suitable training, can simulate Turing Machines, so Q can also. We know that a sufficiently clever/defective program can end up running for infinite time (nonterminating loops) regardless of how "smart" its host is. Despite its sophistication, Q remains susceptible to this threat. But if Q is susceptible, then by assumption the brain that it adequately simulates is susceptible. How absurd! Everyone knows that people don't suffer from infinite thought repetitions. Thus, the original assumption has led to a false conclusion and there must not be a Q.

My list of responses fit a standard akin to natural selection. The brain's, and by extension Q's, safeguards against infinity aren't perfect (that's impossible), but are good enough.
  • Distraction. Brains are exquisitely tuned to react to change. Whether an alarming signal arrives through the senses or a long-gestating answer to a dilemma bursts into flower, the typical course of thought is continuous transformation in unanticipated directions. In the face of the avalanche, perhaps the better question is how there can ever be a mental impression of a unitary and uninterrupted flow of logic. Healthy and normal brains display a moderate weakness, if not desire, for distraction. Meditation is difficult. For some, stopping their feet from tapping and their knees from bouncing is difficult!
  • Memoization. The importance of context shouldn't be underestimated. It's fueled by short-term memory, the "scratchpad", which contains a temporary record of recent brain work. Moreover, since retrieval strengthens a memory, any cycle in the brain work will tend to self-promote. Hence the brain is primed to store previous trips through the loop. The other ingredient is pattern-matching. Each trip, something in the end leads back directly to the start. It's not much of a leap for the brain to construct an isomorphism among these remembered trips, thereby detecting the similarity and extracting the common pieces. Finally, these pieces allow for a short-circuit or "unrolling" of the loop because the brain now knows that the start always leads eventually to the start once more. There's no more need to carry out the (infinite) loop; staying at the start has the same ultimate effect. The execution of the loop has been optimized out of existence or "memoized". Clearly, memoization works best for short or easily-generalized loops. Lengthy or subtle loops could evade notice perhaps indefinitely. Consider cases of asymptotic progress, in which someone is fooled into the belief that the destination is reachable because it grows closer.
  • Simulation. The power of simulation or imagination allows a brain to contend instead with a comparatively toothless and "imaginary" version of the infinite loop. At all times, the brain can maintain its metaphorical distance, its suspension of disbelief. Through simulation, the loop is closer to an object under manipulation than a dictator reciting irresistible commands. The loop can be stopped, resumed, replayed backward, etc. The brain halts momentarily after every operation to review and reconsider the result, so the danger of runaway computation is nonexistent. If the whole enterprise is carried out with tools such as writing implements or another suitable device (e.g. smart phone?), then the halt is accomplished by nothing more intricate than resting hands. In short, the vital difference in simulation is that the brain may treat the loop "code" as data. Strictly speaking, it never really switches between modes of perception and simulation. It perceives and simulates and perceives and simulates. Dynamic feedback is built-in.
  • Ruination. Undeniably, real instances of infinite loops don't run forever on devices. Assuming the loop accomplishes something cumulative, its effects are likely to start causing noticeable trouble, even to the point of a forced halt when memory or disk is full. Alternatively, the physical parts of the system will quit functioning eventually since that is what continuous wear and tear does. Earthy considerations also affect brains. Moreover, brains are notoriously prone to failure. Fatigue, hunger, boredom, illness, etc. will cause a loop-stuck brain to produce mistakes in processing the loop, and the mistakes could incorrectly terminate it (e.g. your ComSci classmates who played Halo all night fail to find the right outcome during a "paper trace" question on the final exam). Once again, the greater the complexity of the loop, the more this factor kicks in. As a system shaped by evolutionary forces, a brain is better at survival than flawless mental calculation. Robust error recovery and correction is a more realistic strategy.
It may appear silly to ponder why biological beings don't end up in infinite algorithmic loops. However, infinite behavioral loops surely aren't nearly as ridiculous. We usually call them habits.

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