When feasible, I still use my CPOC (Constituent, Process, Observable, Causality) method for designing and constructing simulations. My claim is that any given system can (usually) be equivalently described in any one of those four “languages”. When I first make that claim, many in the (whatever) audience balk. But I side-step most objections by a) hand-waving about possible isomorphisms between various formalisms and b) submitting a caveat that I really just want them to model agnostically, with as little preloaded bias as possible … so it doesn’t really matter if the claim is rigorously true in every (or any) case.
Last weekend, a friend told me about the recent kerfuffle over Numberphile’s proof that the sum of the natural numbers comes to -1/12. (I personally like this discussion the best.) I didn’t believe it, then, but hadn’t run across it, and wanted to keep an open mind. In any case, my friend and I then launched into a discussion about Platonists vs. the constructivists. I suggested that none of these results are “real” in any sense. They are all just artifacts of the way we’ve formulated the questions we’re asking. My friend lands on the other side, that these results have some (ontological) reality, existence, and we discover them … at least some of them. (Of course, I knew he felt that way, which I why I chose to be a constructivist for this conversation. To be honest, I’m agnostic and try to think either way depending on the circumstances.)
The superstitious tend to assert that things come in 3′s. So, to validate that, I also noticed these 2 blurbs this morning:
- How the language you speak changes your view of the world
- “Is There Something Mysterious About Math?”
Of course, this flows right along the lines of my previous post about Lee Rudolph’s comments on Hardy’s “astonishingly beautiful complex”. So, the superstition is really just a cognitive bias.
Anyhoo… Near the end of Scott’s post, one of my old saws was evoked: the extent to which the content of our minds/brains is separated from the environment in which we’re embedded. This topic also came up with my friend over the weekend. Our discussion was largely about the very natural language of humans, that of things, objects, “nouns”, as contrasted with the language of behaviors, processes, or “verbs”. W.r.t. the equivalency of models written in different languages, I can confidently assert that a system can be equivalently described in terms of states (objects) versus state transitions (processes). In that discussion, one of the examples I used was a human (or any organism). We think if it as an object. But given that our skin is semi-permeable, our cells die off and are replaced, we eat, defecate, etc., where I end and you begin is really not very well defined. A human is, I argued, more accurately described as a large cluster of processes. It’s not an object at all.
But that was all simply background for what I want to point out in this log entry, related to Scott’s post and all the rest. I tend to think that math is only mysterious where everything else is mysterious, at that border between what’s inside versus what’s outside our selves. Hence, when we talk about a proof or disproof of something that’s intuitive, we’re really talking about a) our own internal, isolated, ways of thinking and b) the socially constructed “complex” providing the medium for our inter-individual communications. Often, when something is counter-intuitive to one person but intuitive to another, perhaps it’s because one person’s internal “complex” (or “landscape”) is more like the socially agreed upon “complex” that is the body of math as a whole.
Finally, one of my ongoing (though still agnostic) assertions is that our brains/minds are really rather flat. What’s inside us is directly defined by what comes in and what goes out. You are mostly a naively traceable, albeit stigmergic, product of the stimulus you received from your environment. (Now, I have an alternative ongoing assertion: that we are all little isolated universes of thought, which is tragic, actually, because that means when someone dies, a universe of knowledge dies with them. Hence, though it may be counter-intuitive, the idea that we’re predetermined bags of meat, defined completely by our stimulus, is more optimistic than that alternative. If the alternative is true, just think of the knowledge we lose when a species goes extinct. Ugh. That perspective is profoundly depressing.)
I don’t commit to Tononi’s (though I 1st read about it in a book he co-authored with Gerald Edelman) Integrated Information Theory of consciousness either. But Scott Aaronson’s criticism is unsatisfying. It took me awhile to realize why (and I’m still not sure). But the basic idea is that the organization of something like a DVD player (and the math behind something like a codec) is an artifact of consciousness.
I’ve long been convinced that our artifacts (combustion engines, dams, scissors, cities, plowed fields, etc.) are simply extensions of our sensorimotor surfaces in the same way our hands and feet (and eardrums and retina) are extensions of our brains. E.g. the brain of a person born color blind is different, in a fundamental way, from the brain of a person born with all the color receptors. Similarly, a person born in the ubiquitous presence of smartphones has a fundamentally different brain than one born, say, in the 1930s.
Hence, although Scott’s argument works for the necessary but insufficient conclusion, I think it’s wiser to suggest that IIT’s Φ doesn’t measure the extent to which some thing (artifact, living or dead) is conscious. It measures the extent to which the cause(s) of the thing were conscious. I add the parenthetical plural of cause to indicate that perhaps an efficient cause of the thing (the agent) is conscious, but the material cause is not. It seems fairly clear that the DVD player would not have emerged without humans having created it. But to evoke Robert Rosen, when the thing being considered is its own cause, both the thing and its cause are conscious.
The interesting next step, of course, is when/if the intelligent design yahoos will pick up on this. It seems rather obvious that an eyeball doesn’t just “fall together”… it must be painstakingly developed, just like the DVD player. The trick is that the DVD player is not its own cause, whereas the eyeball is (… or almost is, to the extent that eyeballs are extensions of the nervous system of the animal). This is what led Rosen’s critics to accuse him of vitalism … and is the heart of our modern forms of anthropo- and bio-centrism. Where the intelligent design guys are clearly misguided, the ideas of pan-psychism or … pan-life-ism, is not as clearly wrong.)