Monday, December 04, 2006

The Zen of Referential Transparency

Here's another interesting connection between Buddhist philosophy and math: this blog post by metaperl draws a connection between Haskell's lack of state variables, and Eckhard Tolle's belief that "the only thing that is real is the present moment."

I'm not familiar with Tolle, but this is a part of Zen thinking as well. You could choose to look at the past and future only as memories and projections that exist now, rather than as independent realities. I'm not claiming to know something that arcane about the universe. But it makes sense, using category theory as a metaphor, that you could choose to view the past and present and future as three real objects; or you could choose to look at the currently existing traces of the past, and currently existing precursors of the future as categorical arrows, and merely define the past and future in terms of those.

A pure function will return the same value every time it is called with the same arguments; this is convenient because it makes them timeless in a sense. If you define some function

f(x) = x+4,

you can say that f(2) = 6; and it's always true. If f(2) gets called 10 times during a program's execution, you only have to really do the addition once; after that you know it as a timeless fact. Even calculating it the once is bending to necessity; after all, it was already true before we calculated it.

But if we have some other function, g(), and we pass the result of f into it

g(x) = x * 7
print g(f(2))

Well, g(6) = 42 no matter what, and g(f(2)) = 42 no matter what. They're both universal timeless facts about this little system. But in practice the computer has to calculate f(2) in order to know what to feed to g, so that g(f()) relationship works like time. f is "before" g, even though they're both mathematically fixed, static, and unchanging.

My feeble understanding of Zen is that one can learn, among other things, to experience time as an artificial construct of this sort, and not as something fundamental. It's a pretty hard to nail down what's concretely different in this perspective, though, because it's probably isomorphic to the more conventional view of time as a mighty river, but supposedly there is a psychospiritual benefit to changing one's perspective in this way.

Some links:
An article about Zen, Time, and Bohm's interpretation of quantum physics
A prior post of mine on dependent origination and category theory

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