March 18, 2009

Middle World

This is part 1 of 5 in the series Brain - Time - Music - Computing.
Next: The Brain in Middle World

Dawkins remarks that brains have evolved to help animals survive within the orders of magnitude of size and speed at which their bodies operate. He calls Middle World (MW) this relatively narrow range of phenomena directly and intuitively accessible to perceptual and cognitive processes [2]. Dawkins invokes the human brain’s evolutionary entanglement with MW to explain humans' difficulty in grasping, and coping with, the physical realities of the universe outside of its familiar confines, from the sub-atomic scales of quantum physics to the universe-size scales of relativity. But the fundamental properties of MW can also help characterize the nature of the tasks at which brains came to excel, in particular the fundamentally dynamic nature of these tasks.

Everything in MW is subject to what the human brain perceives and understands as time, “the continuum of experience in which events pass from the future through the present to the past” (Wordnet). MW time (MWT) cannot be altered in any way: in particular, its flow cannot be slowed, stopped or reversed. The implications are deep. First, nothing in MW can ever happen again, every and any experience is that of an ever changing environment, by an ever changing observer. Exact reproduction of an experience, such as a musical performance, is a practical impossibility both for the performer and for the listener. Second, mathematical abstractions, such as randomness, synchrony, or infinity, do not exist in MW (David Cope discusses randomness in [1]). Mathematics define an idealized world of spatio-temporal invariants, which in some respects models aspects of MW, and aspects of the universe outside of MW that are difficult for MW-evolved brains to grasp.

Mathematics provide a framework for MW brains to characterize and manipulate invariants in a way that is consistent, completely and absolutely predictable, independent of time and space; in particular, these invariants are not sub ject to, and allow the abstraction of, the flow of MWT. The theory of computation came about to formalize actions and operations in the mathematical world, where they must abide by the principles of consistency, predictability, universality. This requires not only that the notion of time be abstracted, but also that the resulting abstract manifestation of time in computing be enforced as a strong invariant. The mathematical properties of computation, especially the abstraction and immutable crystallization of the flow of time, constitute major obstacles to the useful computational modeling of many important MW phenomena.

[1] David Cope. Computer Models of Musical Creativity. MIT Press, 2005.
[2] Richard Dawkins. The God Delusion. Houghton Mifflin Harcourt, 2006. See also Dawkins' TED Talk: The Universe Is Queerer Than We Can Suppose

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