{"id":1823,"date":"2014-05-30T15:04:45","date_gmt":"2014-05-30T19:04:45","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=1823"},"modified":"2016-12-10T04:26:41","modified_gmt":"2016-12-10T09:26:41","slug":"giulio-tononi-and-me-a-phi-nal-exchange","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=1823","title":{"rendered":"Giulio Tononi and Me: A Phi-nal Exchange"},"content":{"rendered":"

You might recall that last week I wrote a post<\/a> criticizing Integrated Information Theory\u00a0(IIT), and its apparent implication that a simple Reed-Solomon decoding circuit would, if scaled to a large enough\u00a0size, bring into being a consciousness vastly exceeding our own. \u00a0On Wednesday Giulio Tononi, the creator\u00a0of IIT, was kind\u00a0enough to send me\u00a0a fascinating\u00a014-page rebuttal, and to give me permission to share it here:<\/p>\n

Why Scott should stare at a blank wall and reconsider (or, the conscious grid)<\/a><\/strong><\/span><\/p>\n

If you’re interested in this subject\u00a0at all, then I strongly recommend reading Giulio’s response before continuing further. \u00a0 But for those who want the tl;dr: Giulio, not one to battle strawmen,\u00a0first restates\u00a0my own\u00a0argument\u00a0against IIT with crystal clarity. \u00a0And while he has some minor quibbles (e.g., apparently my calculations of \u03a6 didn’t use\u00a0the most recent, “3.0” version\u00a0of IIT), he wisely sets those aside in order to focus on the core question: according to IIT, are all sorts of simple expander graphs conscious?<\/strong><\/p>\n

There,\u00a0he doesn’t\u00a0“bite the bullet” so much as\u00a0devour a\u00a0bullet hoagie with mustard. \u00a0He affirms\u00a0that, yes, according to IIT,\u00a0a large\u00a0network of XOR\u00a0gates\u00a0arranged in a simple expander graph is\u00a0conscious. \u00a0Indeed, he\u00a0goes further, and says that the “expander” part is superfluous: even a network of XOR\u00a0gates\u00a0arranged in a 2D square grid is\u00a0conscious. \u00a0In my language, Giulio is simply pointing out here that a \u221an\u00d7\u221an square grid\u00a0has decent<\/em> expansion:\u00a0good enough to produce a \u03a6-value of about \u221an, if not the information-theoretic maximum of n (or n\/2, etc.) that an expander graph could achieve. \u00a0And apparently, by Giulio’s\u00a0lights, \u03a6=\u221an is sufficient\u00a0for consciousness!<\/p>\n

While\u00a0Giulio never mentions this, it’s interesting\u00a0to observe\u00a0that logic\u00a0gates arranged in a 1-dimensional line<\/em> would produce a tiny \u03a6-value (\u03a6=O(1)). \u00a0So even by IIT\u00a0standards,\u00a0such a linear array would not<\/em>\u00a0be conscious. \u00a0Yet the jump from a\u00a0line to a two-dimensional grid\u00a0is enough to light the spark of Mind.<\/p>\n

Personally, I give Giulio enormous credit for having the intellectual courage to follow his theory wherever it leads. \u00a0When the critics point out, “if your theory were\u00a0true, then the Moon would be made of peanut butter,” he doesn’t try to wiggle out of\u00a0the prediction,\u00a0but proudly replies,\u00a0“yes, chunky<\/em> peanut butter—and you forgot to add that\u00a0the Earth\u00a0is made of Nutella!”<\/p>\n

Yet even as we\u00a0admire Giulio’s honesty\u00a0and consistency, his stance\u00a0might also prompt\u00a0us, gently, to take another look at this peanut-butter-moon theory, and at what grounds we had\u00a0for believing\u00a0it in the first place. \u00a0In his response essay, Giulio offers four arguments\u00a0(by my count) for accepting\u00a0IIT despite, or even because\u00a0of, its conscious-grid prediction: one “negative” argument and three “positive” ones. \u00a0Alas, while your \u03a6-lage may vary, I didn’t find any<\/em> of the four\u00a0arguments persuasive. \u00a0In the rest of this post, I’ll\u00a0go through them one by one and explain why.<\/p>\n

I. The\u00a0Copernicus-of-Consciousness\u00a0Argument<\/strong><\/p>\n

Like many\u00a0commenters\u00a0on my last\u00a0post, Giulio heavily criticizes my appeal to “common sense” in rejecting IIT. \u00a0Sure, he says, I might find it “obvious” that a huge Vandermonde matrix, or its physical instantiation, isn’t conscious. \u00a0But didn’t people also find\u00a0it “obvious” for millennia that the Sun orbits the Earth? \u00a0Isn’t the entire\u00a0point of science to challenge<\/em>\u00a0common sense? \u00a0Clearly, then, the test of a theory of consciousness is not how well it upholds\u00a0“common sense,” but how well it fits the facts.<\/p>\n

The above position sounds\u00a0pretty\u00a0convincing: who could dispute\u00a0that observable facts trump personal intuitions? \u00a0The trouble is,\u00a0what are<\/em> the observable facts when it comes to consciousness? \u00a0The anti-common-sense view\u00a0gets all its force by pretending that we’re in a relatively late stage of research—namely, the stage of taking an agreed-upon scientific\u00a0definition of consciousness, and applying\u00a0it to test our intuitions—rather than in an extremely early stage, of agreeing on what the word\u00a0“consciousness” is even supposed to mean<\/em>.<\/p>\n

Since I think this point is extremely important—and of general interest,\u00a0beyond just IIT—I’ll expand on it with\u00a0some analogies.<\/p>\n

Suppose I told you that, in my opinion,\u00a0the \u03b5-\u03b4 definition of continuous functions—the one you learn\u00a0in calculus class—failed to capture the true meaning\u00a0of continuity. \u00a0Suppose I told you that I had a new, better<\/em> definition of continuity—and amazingly, when I tried out my definition on some examples, it turned out that\u00a0\u230ax\u230b\u00a0(the floor function) was continuous, whereas x2<\/sup>\u00a0 had discontinuities, though only at\u00a017.5 and 42.<\/p>\n

You would probably ask what I was smoking, and whether you could have some. \u00a0But why? \u00a0Why shouldn’t<\/em> the study\u00a0of continuity produce counterintuitive results? \u00a0After all, even the standard<\/em> definition of continuity leads to\u00a0some famously weird results, like that\u00a0x sin(1\/x)<\/a>\u00a0is\u00a0a continuous function, even though\u00a0sin(1\/x)<\/a>\u00a0is discontinuous. \u00a0And it’s not as if\u00a0the standard definition is God-given: people had been using words like\u00a0“continuous” for centuries\u00a0before Bolzano, Weierstrass, et al. formalized the\u00a0\u03b5-\u03b4\u00a0definition, a definition\u00a0that millions of calculus students still find\u00a0far from intuitive. \u00a0So why shouldn’t<\/em> there be a different, better definition of “continuous,” and why shouldn’t it reveal that a step function is continuous while a parabola is not?<\/p>\n

In my view, the\u00a0way\u00a0out of this conceptual jungle is to realize that, before\u00a0any formal definitions, any \u03b5’s and\u00a0\u03b4’s, we start with an\u00a0intuition<\/em>\u00a0for we’re trying to capture by the\u00a0word\u00a0“continuous.” \u00a0And if we press hard enough on what that intuition involves, we’ll find that it largely\u00a0consists of\u00a0various “paradigm-cases.” \u00a0A continuous function<\/em>, we’d say, is a function like 3x, or x2<\/sup>, or sin(x), while a discontinuity<\/em> is the kind of thing that the function 1\/x has at x=0, or that\u00a0\u230ax\u230b has at every integer point. \u00a0Crucially, we use the paradigm-cases to guide our choice of a formal definition—not vice versa! \u00a0It’s true that, once we have<\/em>\u00a0a formal definition, we can then apply it to “exotic” cases like x sin(1\/x), and we might be surprised\u00a0by the results. \u00a0But the paradigm-cases are different. \u00a0If, for example, our definition told us\u00a0that x2<\/sup>\u00a0was discontinuous, that wouldn’t be a “surprise”; it would just be\u00a0evidence that we’d picked\u00a0a bad definition. \u00a0The definition failed at the only task for which it could have succeeded: namely, that of capturing what we meant.<\/p>\n

Some people might say that this is all well and good in\u00a0pure math, but empirical science has no need for squishy intuitions and paradigm-cases. \u00a0Nothing could be further from the truth. \u00a0Suppose, again, that I told\u00a0you that\u00a0physicists since Kelvin had gotten the definition of temperature all wrong, and that I had a new, better definition. \u00a0And, when I built a Scott-thermometer that measures\u00a0true<\/em> temperatures, it delivered the shocking result that boiling water is actually colder than ice<\/em>. \u00a0You’d probably tell me where to shove my Scott-thermometer. \u00a0But wait: how do you know that I’m not the Copernicus of heat, and that future generations won’t celebrate my breakthrough while scoffing at your small-mindedness?<\/p>\n

I’d say\u00a0there’s an excellent\u00a0answer: because what we\u00a0mean<\/em> by heat is “whatever it is\u00a0that boiling water has more of\u00a0than ice” (along with dozens of other paradigm-cases). \u00a0And because, if you use a thermometer to check whether boiling water is hotter than ice, then the term for what you’re doing is\u00a0calibrating your\u00a0thermometer<\/em>. \u00a0When the clock strikes 13, it’s time to fix the clock, and when the thermometer says boiling water’s colder than ice, it’s time to replace\u00a0the thermometer—or if needed, even the entire theory on which the thermometer is based.<\/p>\n

Ah, you say, but doesn’t\u00a0modern physics define\u00a0heat in a completely different, non<\/em>-intuitive way, in terms of\u00a0molecular motion? \u00a0Yes, and that turned out to be a superb\u00a0definition—not only\u00a0because it was precise, explanatory, and applicable to cases far beyond our everyday\u00a0experience, but crucially, because\u00a0it matched\u00a0common sense\u00a0on the paradigm-cases<\/em>. \u00a0If it hadn’t<\/em> given sensible results for boiling water and ice, then the only possible conclusion would be that, whatever new quantity physicists had defined, they shouldn’t call it\u00a0“temperature,”<\/em> or claim that their quantity\u00a0measured the amount of “heat.” \u00a0They should call their new thing something else.<\/p>\n

The implications for the consciousness debate are\u00a0obvious. \u00a0When we consider whether to accept IIT’s equation of\u00a0integrated information with consciousness,\u00a0we don’t start with\u00a0any agreed-upon, independent notion\u00a0of consciousness against which the new notion\u00a0can be compared<\/em>. \u00a0The main\u00a0things we start with, in my view, are certain paradigm-cases that\u00a0gesture\u00a0toward what we mean:<\/p>\n