Wednesday, September 26, 2012

The Change of Taste in Good Science: Differential vs. Digital

In the science of the past, matter was modeled by continuous quantities, such as densities and pressures, which satisfied complicated differential equations. Now, good theories are like games with simple rules. “Rather than having to solve equations, and then study the meaning of the solutions, one can simply write a program and see the consequences presented directly as patterns on a screen.” (p136)

Smolin then goes on to say that “the computer is not only serving as a tool…it is itself serving as a metaphor.”  [But is not all form (such as that of the universe) an outgrowth of its function (i.e. the function as understood by humans at that time)? Therefore, whatever tools we use to understand become inextricable from the understanding itself?]

Back on Track:
(Regarding cosmology as analogous to biology) Smolin continues: Simple computer games can model the processes in biological populations in ways that ‘old’ differential mathematics could not. The key that we have discovered is – the right set of simple rules, repeated over and over again, can lead to the formation of enormously complex patterns and structures that reproduce themselves continually over time. The same math used to model the flow of waves through fluids (differential) cannot provide the results as would algorithmic systems (digital).

Old math keeps track of where the matter is, speaking a language of continuous function such as densities and flows. New science is discrete, speaking a language of on/off – a language of information.

Lee Smolin, The Life of the Cosmos, 1997, Oxford

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