Was walking to the bank and reading from that little art book I’ve been reading, and I remembered some of what I had intended to write last time.

Something else I’ve started reading – this is a very ambitious time for me! – is Roger Penrose’s The Road to Reality, which was displayed somewhat prominently in some UK bookstores. Not so in the US, but I did still find it at the library. This one I don’t intend to finish, but it’s still enriching to dip in. It’s a huge book meant to introduce a lay reader to the contemporary physicist’s view of the universe, but with somewhat more actual exposure to the math than such books usually have. Trying to pitch that sort of content to a genuinely “lay” reader is tough, and I can already tell that Penrose’s grip on what he’s not assuming us to already know is a bit shaky. He’s trying to do the right thing but the occasional aside that zooms way out of bounds is unencouraging, and, from browsing forward, I predict total comprehension failure at about the halfway point. But we’ll see.

Anyway, he starts with a discussion of “what is math, exactly?” and this discussion, though ultimately rather superficial, nonetheless was very helpful for me. The crazy Platonic dilemma, of individual horses vs. “horseness,” is much clearer and more apparently real when applied to mathematical (rather than semantic) abstractions. There are no squares or lines in the real world, only approximations. Yet when we talk about math, and geometry, we are talking about interactions and relations among things that have a certain kind of reality to us. Where, then, do the absolute and perfect squares and lines of mathematics exist? Penrose gives a funny little diagram of three worlds, each containing the next: the physical world, the mental world, and the Platonic world of forms – this last being the world of mathematics. The diagram, I take it, is in part a play on one of Penrose’s claims to fame, and is a little wacky for me, but the idea that the world of mathematics is neither the mind nor the world fits in well with what I’ve been thinking – it is in fact, in this inner cosmology I’m working out, the world of the mental program. As per my last entry.

The philosophy that tells us that there are multiple possible mathematical systems, each internally coherent, is easy to nod at, but our intuitive sense that (to use Penrose’s first example) Euclidean geometry is “the real deal” and non-Euclidean geometry is just “an interesting notion in math” is very strong. The idea that the real (real!) spatial universe might well be non-Euclidean is one of these affronts of modern physics that we are forced to write off as being simply beyond the pale of normal human experience, something that can be theorized about but which is fundamentally inassimilable. This idea that there are things which are true but, in practice, fundamentally inassimilable is a useful wedge for separating our model of the world from the world itself. Euclidean geometry too, as Penrose and Plato and others have pointed out, is not the world itself. Again: there are no perfect squares or lines in the real world. The mass of world-modeling accumulated under the name of “science” is still not truth – it is just as close an approximation of truth as we can muster. Math and science are not a collection of “facts” about the world, they are an independent structure, which through careful revision tends asymptotically closer to the actual world.

A computer game that plays poker – why did I think of this, of all things? – uses variables and routines and subroutines and formulae etc. to “model” the game of poker. The computer does not “know” anything about poker, per se. It has images stored away that look like cards, and it calls them up according to algorithms that mathematically mimic the play of poker, yet it has never heard of “cards” and wouldn’t recognize them if they were, um, fed into the disc drive. Conversely, a person who plays poker – even computer poker – would have no reason to recognize or understand nerdy jargon like “function cardValue (cardPlayed) {return cardArray[cardPlayed].value;}”. But what if the poker program itself was the person who played poker? It would know the game from both worlds at once, and so would have a hard time differentiating between the function “cardValue” and the value of a given card – which, you might argue, is not so problematic. But it would also have a hard time differentiating between the programming world in which the concept of “function” was meaningful, and the poker world in which it was not. What I am saying about art, basically, is that if computers could write poetry, it would be about functions, not about, um, poker. (Better computer example for poetry would be a flower simulator. Do they have that? Sort of.)

So back to the geometrical example: the feeling that a straight line is a valuable construct, that it is a useful notion, is deep deep down there in the roots of what humans do with their minds. Dogs, for example, do not care about squares. They don’t believe in them the way we do. Human interest in geometrical figures is a fairly low-level example of our interest in our own world-model; it has something to do with the way our brains have learned to perceive and evaluate space. Drawing a repeating pattern of parallels or diamonds on a stone axe is a way of prioritizing and sharing this world of forms, this mental model. Primitive art and folk art are heavily geometrical – this is the first tier of the human activity of projecting the mental model. Primitive man didn’t find squares in the wilderness and draw pictures of them; the squares arose from some substratum of his own mental program.

I’ve also done some reading about Pythagoras recently. Pythagoras attributed mystical importance to numbers and apparently taught that the world of numbers, not the physical world, was the “real” world. It is clear to us now that, in fact, the world of numbers is less real than the world outside us, but is one of the most versatile and durable things inside us for predicting and emulating that outer world. Compared to religion, say, mathematics makes much better predictions. So of course Pythagoras applied religious significance to it. It’s a running feature of all religion that it privileges its explanations over the everyday “apparent” explanations. This is because explanations exist only in the mental world, not in the outer world, so, accurate or inaccurate, believing in explanations will always involve a certain deprioritizing of the outward appearances of things.

Oh man.

This entry once again reveals that I don’t quite know how to say all this in a way that seems clear and concise. But I’m working around to it. Prepare for a few more rambles like this before this has been purged from my system.

One more shot. Though the five senses deliver data to us from physical reality, our cognitive experience of a coherent and comprehensible world is not actually an experience of the outer world, but rather of an inner model world. This model is constructed by our brain according to a program that combines and interprets the sensory data according to certain principles and assumptions. While at the lowest levels, regarding our perceptions of space, time, and matter, these principles are common to all humans, at higher levels these principles vary from culture to culture and even from individual to individual. Furthermore these principles are subject to revision and adaptation. All of the above may seem self-apparent, but when taken to heart, this description of the relationship between reality and experience sheds a clarifying light on many issues that continue to be discussed in a muddled and deluded way. E.g. the nature of art, the nature of science, the nature of culture, etc. etc.

I don’t doubt that some philosopher has said the same thing. Can anyone tell me what philosopher’s work I’m clumsily reenacting here?

Beth says (tentatively) that I shouldn’t post stuff like this until I’ve really worked it out for myself. My suspicion is that all this adds up to very little of value to anyone other than me. I think I’m just trying to express a shift in my personal understanding, which does not represent any actual new insight for the world. As with all learning I’ve ever done, there is a vital difference between having understood an idea and having incorporated it into one’s thought. I’ve just incorporated something into my thought.

But this website was supposed to be space for me to give vent to these sorts of things. The idea is that it is only incidentally public; I’m trying to inure myself to the idea that everything I do, potentially, is public, and that it’s really only a question of what I want to achieve rather than what’s appropriate. So I’m just posting stuff as I type it. I’ll take it down later if it embarrasses me that much. Reading it is your problem.