The mathematicians have pretty much answered this question. Point to Friend, and Kaj needs to read up on chaos theory. Chaos theory describes the types of systems that can’t be well modeled if the model system deviates even very slightly from the system of interest.
Ah, but which proportion of all existing systems are chaotic? And of those that are, how chaotic are they? To what degree can you still extract predictable properties from chaotic systems? The Wikipedia page on chaos theory says that
Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices. Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations. Everyday examples of chaotic systems include weather and climate.
but we still have useful models on all of those systems, even though they’re imperfect. Whether the models are useful enough depends on what we try do with them, and how accurate results we need. Chaos theory is evidence in favor of my friend’s intuition, to be certain, but it doesn’t seem to resolve the question by itself. A comprehensive review of different systems and phenomena and the limits of how well they can be modeled could go a long way in that direction, though. Anybody know of one?
All of this is coming from a book on chaos theory I read ~5 years ago, so take it for what it’s worth. As I recall:
Microscopic wind currents cause worldwide changes to the weather in about a month.
On a frictionless billiard table, extremely microscopic differences in initial conditions cause significant changes in the system after about a minute of collision, since each collision magnifies the difference between model and system results.
Plus, your claim was a claim about all systems. His claim was a claim about some systems. In general, you had the harder case to make.
Anyway, the wikipedia article was a good place to start, but probably not deep enough if these questions interest you greatly.
The mathematicians have pretty much answered this question. Point to Friend, and Kaj needs to read up on chaos theory. Chaos theory describes the types of systems that can’t be well modeled if the model system deviates even very slightly from the system of interest.
Ah, but which proportion of all existing systems are chaotic? And of those that are, how chaotic are they? To what degree can you still extract predictable properties from chaotic systems? The Wikipedia page on chaos theory says that
but we still have useful models on all of those systems, even though they’re imperfect. Whether the models are useful enough depends on what we try do with them, and how accurate results we need. Chaos theory is evidence in favor of my friend’s intuition, to be certain, but it doesn’t seem to resolve the question by itself. A comprehensive review of different systems and phenomena and the limits of how well they can be modeled could go a long way in that direction, though. Anybody know of one?
All of this is coming from a book on chaos theory I read ~5 years ago, so take it for what it’s worth. As I recall:
Microscopic wind currents cause worldwide changes to the weather in about a month.
On a frictionless billiard table, extremely microscopic differences in initial conditions cause significant changes in the system after about a minute of collision, since each collision magnifies the difference between model and system results.
Plus, your claim was a claim about all systems. His claim was a claim about some systems. In general, you had the harder case to make.
Anyway, the wikipedia article was a good place to start, but probably not deep enough if these questions interest you greatly.