Constant2 comments on The Futility of Emergence - Less Wrong

36 Post author: Eliezer_Yudkowsky 26 August 2007 10:10PM

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Comment author: Constant2 27 August 2007 12:27:49AM 12 points [-]

Okay, but that's really not how I have understood emergence. It delineates a subject matter, and does so in an abstract way that includes many specific examples which are purportedly alike in some important way. But I don't think this use necessarily implies that the explanation has thereby been given. It is, rather, usually an attempt to delineate a subject matter which can be further investigated. I believe that the hope is that a general theory of emergence is possible, though my impression is that there isn't even a generally agreed-upon definition of it, let alone a commonly accepted theory.

One common element that I have sometimes noticed is that an emergent phenomenon can be idealized and a simplified mathematical model constructed of it, which is not precisely correct but which is a very good approximation. The existence of such simple and very good models is remarkable and extremely lucky for us.

For example, an actual fluid such as water is really made up of molecules that interact, but there is a simple mathematical model for fluids which treats fluids as absolutely continuous and smooth all the way down, not composed of atoms but fluid at every scale. As I vaguely recall, this simple mathematical model can be adjusted by plugging in values for viscosity, compressibility, and so forth. It is not exactly the same as actual fluids (the resemblance breaks down completely on the scale of molecules) but it is very close at the macroscopic scale.

Similarly, we have the concept of the "ideal gas", which is only an approximation to real gases but on a macroscopic scale a very close and useful one.

That we can vastly simplify and idealize something without losing all that much predictive power seems to be a characteristic of many so-called emergent phenomena.