synthetic zero

June 16th, 2010

Ayn Rand was wrong. Of course, it’s difficult to summarize one’s thinking in a tweet limited to 140 characters; my friend Lisa Plaxco asked me to elaborate, so I’ll attempt to do so in this blog post. Let me start with where I agree with Rand. I agree that blind faith, or believing things without reason, is both unnecessary and in many ways problematic.

But there are so many points at which she goes wrong. Perhaps one of the most fundamental has to do with her conflation of propositional logic and ordinary meaning. As Einstein famously said, “As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.” Einstein understood the fundamental issue here, which is that to conflate a description of reality with reality itself is to make a very elementary mistake.

Ordinary concepts and propositions simply do not map into the Objectivist conceptual structure: for example, take the assertion that all propositions are either true or false. I remember bringing this up with a classmate of mine in my freshman year at Harvard… he was a physics major and a big fan of Rand. Very smart guy, so I decided to explore this issue with him, because I thought he could appreciate the argument.

The basic argument I made was this: if all propositions are either true, or false, let’s take a simple proposition such as “the apple is red.” Is this true, or false? What if you had an apple and you slowly, ever so slowly, changed it from red to orange? At what point would the proposition cease to be true, and become false?

Or let’s take a statement such as “It is hot today.” Is it true, or false? If you slowly lower the temperature, half a degree at a time, when it does it magically transform from being true to false? Could it be that this statement varies in truth value depending on who is saying it? Could it be that statements can be approximately true, or somewhat true and somewhat false, or true depending on context, depending on who is speaking, who is listening?

Yes, obviously. It’s amazingly, painfully clear that ordinary use of language and concepts can’t possibly map neatly onto propositional, mathematical logic. Propositional logic is an idealized system, it doesn’t relate directly to the way we think or communicate in everyday terms.

I made this argument and my classmate indicated that my arguments seemed quite intriguing, though I wasn’t sure if he was convinced or not. Interestingly, four years later I ran into him in Palo Alto — he was going to grad school at Stanford. He greeted me very warmly, and we got into a conversation about logic and AI. It turned out that he had graduated from Harvard summa cum laude after writing his thesis: on fuzzy logic! I was glad he had found my argument at least somewhat persuasive.

Of course, interestingly, we went on to discuss AI some more, and I was telling him that I thought neural network models were quite promising. He thought that was interesting, but he challenged me: doesn’t it seem as though our thought process is inherently serial, not massively parallel? So I said, okay, but right now, you’re seeing, you’re hearing, you’re feeling the wind on your skin, you’re talking, all at once. Isn’t that obviously massively parallel? He had to agree.

The interesting thing about all this is that we have a cognitive habit which is deeply ingrained: we create internal models which simplify things in some way, which make it easier to think about things conceptually, and then we make the fundamental error of conflating the map with the territory. Of course, any map must necessarily be a simplification of reality in order for it to be useful; but it is inherently a simplification, that is to say, it must leave out massive amounts of detail. As Borges alluded in “On Exactitude in Science“:

In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.

Leaving out details is of course necessary for information processing; but it is incredibly sloppy and rationally inexcusable to forget that this is what any conceptual system does.

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June 6th, 2010

Doubt is often used in a perjorative sense: that is, many religions, for example, place “doubt” in opposition to “faith” — and even in ordinary psychology, people often think of doubt in a negative way, as in self-doubt, and so on. But from a Buddhist, particularly Zen, perspective there’s another way of looking at doubt, which is more a questioning of ordinary assumptions we tend to make about the world, about our existential condition, but one can use this in not a negative but rather a constructive sense.

The sort of doubt I am talking about is essentially: doubt that the surface impression you have of the world, of your idea of who you are, what your position is in the world, etc., is the whole story. For example, you might think that your life is at a dead end, that you have exhausted all options, or that certain situations are intolerable for various reasons, unworkable. But there’s a form a doubt which is to say: check again. Are you really sure about that?

This is a kind of liberating doubt; the doubt of the scientist, who takes every hypothesis provisionally, who has a sort of skepticism that she has ever reached the final story.

If you pursue this doubt to its utmost, it actually deconstructs everything we ordinarily use to prop up our world, so that there is nothing left to lean on: except the fundamental universal ground of being. And when you get to that you realize that this can never be taken away; it is complete and sustaining and inexhaustible. It doesn’t need anything and is beyond time and conditions, while not being separated from time and conditions.

And this can lead you to an unshakable confidence. This great doubt is then the same as ultimate confidence. Rather than a confidence based on believing in tenets or dogma, hoping for this or that story to be true, it is a confidence that doesn’t depend on belief, but rather a thoroughgoing checking and re-checking of our existential condition which takes apart every individual thing while repositioning them in the context of the always already present, vast, inconceivable, timeless, supportive, and irreducible ground of being.

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