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Nature's primary algorithm is massive parallel computation, at a scale that beggars us all. "The Book" is all around us. The algorithms that nature cares abou

Nature's primary algorithm is massive parallel computation, at a scale that beggars us all. "The Book" is all around us. The algorithms that nature cares about are woven into the fabric of the physical world. Our algorithms are just poor approximations, intended to make simulation tractable on discrete computers. For example, this site occasionally carries posts about making water look realistic in games. Those posts usually acknowledge that the graphics approach they describe is cheating compared to actually solving the Navier-Stokes equations. But the NS equations are just a mathematical expression of reality. We then cook that mathematical expression down even more, in order to arrive at a collection of algorithms (finite-difference approximations, domain partitioning, numerical solvers) that attempt to embody the math. Yet problems that today we would consider impossibly hard to solve computationally-- for example, fully resolving the flow of water around a sailboat, not to mention the wind in its sails, and the stresses in the mast-- nature solves billions upon billions upon billions of times a second.

stiff 13y ago
Tl;dr algorithms are representations of processes occurring in reality. That's really all I could understand from this. I would love to hear what would "algorithms being woven into the fabric of the physical world" even mean?
- dmlorenzetti 13y ago
  By "woven into the fabric" I mean that the physical world executes what we think of as algorithms, as part of its natural existence. We write an equation that represents viscosity, but nature just executes viscosity because of the way the atoms interact. Or rather, viscosity emerges because of the way things interact. There is no equation, there is no computational organization, there is no unit testing, there's just doing-- at massive scale. By the way, I would say not all algorithms occur in reality, and when they do, nature isn't necessarily very good at them. For example, sort and binary search just don't seem that high up on the list of things the physical world cares about. The natural sorting process by which dirt in a container separates out into various gradations of size, corresponds to bubble sort-- not an especially efficient algorithm.
shardling 13y ago
That's not at all what "The Book" means, though! The idea is that a proof from "The Book" feels perfect in the same way that, say, listening to Bach does. Less natural, more transcendental.
iyulaev 13y ago
"All models are wrong, but some [models] are useful." - George E. P. Box
mikeash 13y ago
For all we know, nature is a very slow, serialized computation. http://xkcd.com/505/ http://xkcd.com/505/
krichman 13y ago
Well, I downvoted. This is psuedo-philosophical nonsense that seems to be saying something profound, but isn't really. Nor does it add to a discussion on interesting algorithms. We could just as easily say that nature is a poor approximation of math, like shadows on a cave wall are poor approximations of the real object.
- dmlorenzetti 13y ago
  In what way is a "discussion on interesting algorithms" not already pseudo-philosophical? But OK, I'll do it your way: An interesting class of algorithms is finite-difference approximations [1]. Even more interesting are algorithms for designing such approximations [2]. A key insight to making these algorithms work is that Taylor series approximations can be used to study the truncation errors of discrete approximations to continuous phenomena. However these techniques, by themselves, mainly interest me in the context of the physical problems they are meant to address. Since those problems come from the physical world, I would argue that the algorithms themselves don't satisfy the formal criteria set forth in the original question, of what algorithms god would write down in a book. [1] See LeVeque, "Finite Difference Methods for Ordinary and Partial Differential Equations". [2] See Hamming, "Numerical Methods for Scientists and Engineers".
  - krichman 13y ago
    You are right. By purposefully misinterpreting "god" to be literal, you have won the discussion of what he would write in a book. Your answer is the best. Congratulations.

stiff 13y ago

Tl;dr algorithms are representations of processes occurring in reality. That's really all I could understand from this. I would love to hear what would "algorithms being woven into the fabric of the physical world" even mean?

dmlorenzetti 13y ago
By "woven into the fabric" I mean that the physical world executes what we think of as algorithms, as part of its natural existence. We write an equation that represents viscosity, but nature just executes viscosity because of the way the atoms interact. Or rather, viscosity emerges because of the way things interact. There is no equation, there is no computational organization, there is no unit testing, there's just doing-- at massive scale. By the way, I would say not all algorithms occur in reality, and when they do, nature isn't necessarily very good at them. For example, sort and binary search just don't seem that high up on the list of things the physical world cares about. The natural sorting process by which dirt in a container separates out into various gradations of size, corresponds to bubble sort-- not an especially efficient algorithm.

shardling 13y ago

That's not at all what "The Book" means, though! The idea is that a proof from "The Book" feels perfect in the same way that, say, listening to Bach does. Less natural, more transcendental.

iyulaev 13y ago

"All models are wrong, but some [models] are useful." - George E. P. Box

mikeash 13y ago

For all we know, nature is a very slow, serialized computation. http://xkcd.com/505/ http://xkcd.com/505/

krichman 13y ago

Well, I downvoted. This is psuedo-philosophical nonsense that seems to be saying something profound, but isn't really. Nor does it add to a discussion on interesting algorithms. We could just as easily say that nature is a poor approximation of math, like shadows on a cave wall are poor approximations of the real object.

dmlorenzetti 13y ago
In what way is a "discussion on interesting algorithms" not already pseudo-philosophical? But OK, I'll do it your way: An interesting class of algorithms is finite-difference approximations [1]. Even more interesting are algorithms for designing such approximations [2]. A key insight to making these algorithms work is that Taylor series approximations can be used to study the truncation errors of discrete approximations to continuous phenomena. However these techniques, by themselves, mainly interest me in the context of the physical problems they are meant to address. Since those problems come from the physical world, I would argue that the algorithms themselves don't satisfy the formal criteria set forth in the original question, of what algorithms god would write down in a book. [1] See LeVeque, "Finite Difference Methods for Ordinary and Partial Differential Equations". [2] See Hamming, "Numerical Methods for Scientists and Engineers".
- krichman 13y ago
  You are right. By purposefully misinterpreting "god" to be literal, you have won the discussion of what he would write in a book. Your answer is the best. Congratulations.