The End of equations?
January 27, 2002 5:31 AM   Subscribe

The End of equations? Paul Dirac and Albert Einstein thought equations were things of beauty, Stephen Wolfram, by contrast thinks they are antiquated.
posted by none (10 comments total)
That fucker still hasn't published?
posted by techgnollogic at 5:43 AM on January 27, 2002

Maybe they are, maybe they arn't. But at the rate things are going we are going to have to wait untill the guy dies and we can get a look at his book post-humorously to find out...
posted by delmoi at 6:49 AM on January 27, 2002

posted by mattpfeff at 8:39 AM on January 27, 2002

posted by fuq at 10:41 AM on January 27, 2002

Take a look at the ego on this guy. Jeeeez.
posted by dr_emory at 11:26 AM on January 27, 2002

isn't a computer program, at some fundamental level nothing more than a bunch of equations?

i'm having trouble understanding what the big deal is
posted by juv3nal at 4:39 PM on January 27, 2002

We've spent four weeks now doing translation of reasonably straightforward problems into disturbingly obtuse equations in my linear programming class. There are quite a few modules in our mind that are repurposable for computational work; those that handle equations do not necessarily work best for all problems.

I was pretty young when I realized conditionals map terribly onto equations. Often, they become hidden in the solution, not apparent in the expression.

I think the moment of clarity came to me this quarter when I just exclaimed, looking at eight different variables with various subscript mappings and indexes and maximums, "I feel like I died and became a FORTRAN compiler. For gods sakes, we give better labels to *compilers*, and they're just software!"

Of course, there's cause for brevity: The more you have to write per variable, the less work you can do hand-resequencing equations.

posted by effugas at 7:24 PM on January 27, 2002

Two points. First, there's a school of thought that says that programs should be more like mathematical equations - that you lose nothing in expressibility, but gain accuracy and reliability. Hence functional programming.

Second, there's a wonderful book called The Computational Beauty of Nature that, I suspect, covers everything Wolfram is going to say. I'd recommend the book to anyone interested looking for unifying ideas across chaos theory, automata, fractals etc.
posted by andrew cooke at 3:29 AM on January 28, 2002

The difference between equations and programs is typically in retained state. In youre typical equation, you're expressing a relationship and there is typically no state (read: memory) in the relationship unless the relationship is recursive, whereby the state is implicit in the expression.

For example, if you had a function f(n) = n-1, and a function g(n) = n+1, you could express addition add(a, b) as { if b = 0, a; otherwise add(g(a), f(b)) }
You are defining add in terms of itself which for any fixed a and b gives you state in the expansion of the relationship.

State in software has been standard operating procedure for time immemorial and is a big thorn in the side of theoreticians who would prefer a purely functional language in which there is no state at all.

State (and side-effects) are an expressional flexibility, but also the cause for most bugs in software.
posted by plinth at 9:51 AM on January 28, 2002

This talk of functional programming reminds me that I'm currently skipping my Programming Languages lecture. Oops.

The prof tells me that the most advanced functional lang is ML. Apparently, they've got ML programs that run within 1.8 times the speed of the equivalent C program. It's beautiful, yes, but still harder to program in.
posted by Succa at 8:52 AM on January 29, 2002

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