Post
Binary Brain
One enticing theory for how our brain works is to compare it to an everyday computer whose CPU combines, analyzes and interprets a series of signals to produce a cohesive system. Like a computer’s 0’s and 1’s, neurons’ all-or-none firing activity could be the brain’s ‘bit’.
However, in his book “Shadows of the Mind”, Roger Penrose argues that due to some problems where computers incorrectly evaluate certain problems and humans do not, our brains are not computers.
Penrose’s argument is based on Godel’s Theorem and the so-called halting problem. The halting problem is a relatively simple mathematical procedure and was best explained by John R. Searle in “The Mystery of Consciousness”:
How exactly does Penrose use the unsolvability of the halting problem to prove we are not computers?
As long as we know of a set of computational procedures A that it is sound then we know that there are some computations, Ck(k), that do not stop (My note: imagine a halting number as that which would break a basic “for” loop). (A computation Ck(k) would be the k-th computation performed on the number k. So, if k equals 8, then Ck(k) would be the eighth computation on the number 8.) But the proof of the unsolvability of the halting problem demonstrates that the set of computational algorithms A is insufficient to ascertain that the computation Ck(k) does not stop. So A cannot encapsulate our understanding. Since A can be any set of computational algorithms, it follows that we are not computers carrying out an algorithm.
And from Penrose himself:
Human mathematicians are not using a knowably sound algorithm in order to ascertain mathematical truth.
The most obvious argument against the unsolvability of the halting problem is that a computer could be programmed to recognize and accept those values on which it would normally halt. However, and due to mathematics far beyond my comprehension, this point is apparently null to Penrose (apparently, his rebuttal follows a similar logic as that described above but much more complex).
The gist of it is that there are mathematical procedures for which a computer (that analyzes the procedure based solely on a preprogrammed algorithm) halts whereas a human can discern that it is, in fact, true and non-halting (or vice versa).
Are we just computers? Is there something else happening up there, something that cannot be entirely through computers alone?
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Comments
Interesting. When one thinks about it, it becomes obvious that the manner in which thought is often realized seems, indeed, very binary in politics, society, etc: True/false, right/wrong, left/right, friend/foe, war/peace. There are definitely a lot of people who think in terms of 1s and 0s – black and white. I have the impression that this is something that exists in nature, which might be best summed up in the Eastern concept of yin-yang – positive and negative forces and the tension between them.
Living in multiple dimensions, however, we have the ability to think on multiple levels as well, evidenced in the sciences – physics, mathematics. Making a decision is choosing to halt the process on a 1 or 0: Pick a side, cast a vote, buy a car. But humans are also well known for our capacity for abstract thought – philosophy (abstract reasoning), art – dreaming about the future, recalling the past. We definitely plumb the gray areas, so I’m inclined to think there’s quite something else going on up there.
Concensus is that we use only a small portion of the brain’s capacity. Genius we might recognize in those who naturally use far more, like Hawking. I tend to think the brain can be trained to a point (education), but creative and original thought is often not very much encouraged on a large scale. (Gee, wonder why.)
Creative people and free thinkers are often viewed as dangerous or subversive to the establishment. They appear to have escaped being programmed to think in those black and white terms. In short, while it is possible to program the brain (and it’s done all the time), we obviously have something computers don’t: Sentience.
QD
Jul 6, 07:12 AM #
I would tend to disagree that there is any sign of a binary essence of human cognition or behavior. Interestingly enough, my work in advertising research (though not directly working with the creative, but rather in the testing of its effectiveness) has helped hone my sense of just how fuzzy we are.
For instance, we have found that responses to questions whose design are to categorize those interviewed into various groups, e.g. by demographics or purchasers/users of types and/or brands of product, give distributions which don’t match available and prevailing statistics about those criteria. Further, tweaking the wording of the question, if only apparently slightly, can significantly change those results. In that case, we would have industry data vs. data from the first version of the question vs. data from the second version, all conflicting. Often, the variance is little more than we might expect naturally, and so isn’t statistically significant. Sometimes, though, it is.
Even anecdotally, you can, for instance, ask 10 people what a “blue” state means versus a “red” state (this is a dip into the cultural myopia that is being an “American”, I realize), and you’ll get a variety of answers. There will be similarities, but not true equivalence across all 10 answers (most likely).
I have used that sort of binary decision structure (though, technically, it’s not binary, but the fact that it’s a single decision among several options is the key) as a metaphor as well. It’s a handy model, but only as a model. Just as electrons are (by current best understanding) not quite in well-defined orbits about a nucleus, but rather occupy probability waves, so too do many other systems have (as far as I can tell) intrinsic fuzziness. What we can say about them, we can only say with some measure of probability.
As to the computability question, this sounds very much along the lines of the P vs. NP problem, even if tangentially. I’ll have to (a) read Penrose and (b) trust his greater education and, maybe, wisdom, in this regard…for now. It might be that we need to develop a fuzzier metaphor for what is a “computer” and what is not. For all his supposed self-aggrandizement, I think I might still want to see what Stephen Wolfram’s A New Kind of Science yields on that subject. If the universe is itself a computer, does that necessarily imply that all processes which are dynamic subsets of the universe inherit that behavior, i.e. everything is at least a piece of, or maybe a simulacrum of, that computer in which it exists? While our understanding and terminology and logic might still require work (it might be ludicrous to assert otherwise), maybe there’s a fundamental connection between computing and cognition, or more generally, between computing and other processes (e.g. is DNA replication not the processing of input via a codified process?), which connection makes it unlikely that we wouldn’t find silicon-based, conventional computing similar to other things.
It’s dangerous, I’ll allow, or at least potentially defeating, to quickly redefine our perceptions of reality to fit the model we want them to fit. That is, before we decide that, yes, erosion is a type of computer, we should be careful about what it is we’re deciding sets computers apart from non-computers. I find this issue of demarcation to be broad and intrinsic to almost any field of study or comtemplation. There are several well-discussed examples, such as the delineation of “science” from “non-science”; see this manuscript at the Galilean Library.
Daniel Black
Aug 10, 10:14 AM #
what the fuck
megan imabitch
Oct 4, 06:45 AM #
Neurons aren’t really always binary anyway, any more than genetics is. Depolarization, hyperpolarization, inhibitory, the number and frequency of firing, cumulative, bleaching, graded potentials, gated channels, resting potential, refractory periods, interneurons, bundling, clustering. That’s probably just a few ways.
c
Jul 3, 09:37 AM #
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