Thursday, February 5, 2009

Meditation on Math

Mario Livio will be in town for the next couple of days, making appearances at PSU, Powell's Books, and the Linus Pauling House.

His newest book has sparked some discussion on the Wanderers list.

From Mario's chapter one (Mystery):
A few years ago, I was giving a talk at Cornell University. One of my PowerPoint slides read: "Is God a mathematician?" As soon as that slide appeared, I heard a student in the front row gasp: "Oh God, I hope not!"
I contributed this essay this morning...

Re: is God a mathematician (Cornell student: "oh God I hope not"), I'm thinking of Keith Devlin's book about non-human creatures and their significant processing powers in physical interaction with their environment

Some say "that's instinct" which means they don't have to think about it -- like humans don't have to think about thinking or using language (we "just do it" -- with practice).

So where is the line between language and not-language, between mathematics and not-mathematics?

With university trained faculties (a double meaning) we're conditioned to compartmentalize and see "math" (M) over here, "not math" (~M) over there, with walls between language and not-language (L|~L), thinking and not-thinking (T|~T).

That's a view I'm inclined to counter (see summary below).

When you get really into it, a theology can seem precise, rigorous and logical, no accident that many mathematicians were fervent in some faith or other.

That sense of seeking something beyond, but as a corporate process (with others) gives rise to debate, revisited threads, a set of concepts that interact, get fine tuned.

Adherents feel comforted by the "rigor" of their dogmas and enjoy reciting, reviewing, reinforcing their creeds.

I am not alone in thinking it makes sense to see "God" as yet one more operational signifier, at work (or not), within language games, like a "zero".

We also have uses for "time", "nature", "balance"... these are difficult words too, in the sense that it takes a lifetime to appreciate 'em (and then some).

I tend to like polytheisms when it comes to "balancing energies" e.g. the village elders and younger learners, future leaders, sit around the campfire and debate what to do next.

If we're in some routine period when the environment seems unchanging (rhythmic but constant), aren't being invaded or attacked, then those background patterns get taken for granted.

But humans themselves tend to evolve quickly (using memes more than genes) and that brings about change, including to the environment. Change becomes the accepted backdrop then.

In any case "pleasing the gods" is a psychological exercise in keeping the tribe viable.

A lot of western writers (Nietzsche, Freud, Norman O. Brown) will pick up Apollonian and Dionysian as their polarity, but is one polarity sufficient? Multiple antipodes suggests a sphere, a polyhedron, working to stay centered.

All of which is to say: I think natural processes, including that of humans doing their best to anticipate the future, adapt, keep an even keel, are mathematical processes, whether or not one uses the ideas of axioms and theorems.

Furthermore, thinking about God, deities of any kind, ancestors, projecting psychological qualities into various creatures and balancing them, is a kind of information processing, and therefore mathematical in nature.

Finally, I think we all experience not being fully in control, i.e. are part of a larger process in which we find ourselves that "has a life of its own" (Ouija board, invisible hand...) and there's this real phenomenon of prayers being answered, dreams coming true, thoughts proving reliable -- as well as the contrary.

Our sense that "God is a mathematician" derives from this sense of integrating into a larger picture that's also "thinking" (i.e. "doing the math") in some way. We find ourselves rewarded for thinking logically. We feel God must be too, or Nature, or... (something more than "just me" or "just we").

There's this prevalent stereotype of "religion" (which fits in some cases) as being primarily about believing something impossible / incredible, and making one's "faith" a test of one's willingness to sacrifice one's better judgment and/or powers of reason, on the altar of some cosmic fairy tale.

However this is just one of many Hollywood movie situations.

Having a belief system (ideology, paradigm) that's not adapted, not serving, is a cause of suffering for sure, so any strong tradition (science included) is going to have processes for surviving implosion, rebirth and reconstruction of the psyche. No one is immune from having to let go of old certainties from time to time. What once seemed reliable, no longer does.

Let's think of the American Dream as a shared fantasy, and with the added advantage of being secular in some way, even though there's some eye on a pyramid. Per those National Treasure movies, it's secular more in the sense of being "all traditions" (lots of heritage), not any one of them lording it over the others, no "official religion" backing an emperor, pope or king (for so long the pattern, democracy not trusted, thought of, or tried).

No "official science" either, lots of competing paradigms.

Still that need for balance. Plus the environment is changing. Plus we're aware it's a small planet. Our mathematics needs to be pretty strong, is my feeling. That heritage will serve us, is my hope. I say "our" as I'm including myself as one of the American dreamers here.

Per Hegel, there's a relationship between Logic and History we need to be thinking about. I've written a longish essay here, probably few have the patience. I'm doing the math, reasoning to a point where we see the future of the USA, lots of components and subsystems, as a mathematical challenge.

What I'm balancing against (countering), is this university-inspired notion that "mathematicians" are just this select group in the Ivory Tower, proud of how their discipline "has no meaning" in terms of reality.

Making the "real world" be something distant, exotic, is a literary conceit of many academic cultures, but that's for anthropologists to study, has nothing really to do with the ongoing computation.

I'm not saying "their" work (including some of "mine") is unimportant or irrelevant, merely that I don't choose to see "mathematics" as some esoteric process that takes place exclusively in some rarefied academic environment.

I know how to talk as if that were the case (i.e. I'm as "schooled" as the next guy), but I don't really believe it.

So, on with the math! In God we trust (or in Apollo or whatever).