[pygy_]

The limitation for weather forecast is floating point precision, which lead predictions to diverge with reality because the small losses of precision add up to large discrepancies as time passes, in chaotic systems.

If we could compute with Real numbers, we would get much better predictions.

[posterboy]

> If we could compute with Real numbers, we would get much better predictions.

This is a paradox. The real numbers are in some technical sense not computable. I get what you mean though, analog computers. However, there are still limits to the precision.

[chaoticmass]

Good point. Relevant article: http://lampx.tugraz.at/~hadley/uncomputable_numbers.html

"almost every number is uncomputable"

"This means that predicting the weather arbitrarily far into the future is impossible without knowing the current conditions (temperature, air pressure, humidity, wind speed, etc.) to arbitrary precision. Since the quantities that describe the weather are real numbers, they are uncomputable. No finite computer program can calculate the weather arbitrarily far into the future."

[darkmighty]

I love this kind of argument. It is of course very simple that every real number is uncomputable -- real numbers have greater cardinality than the integers. So if you had a program (which can be described by a finite sequence of integers) capable of producing each real, you would have a finite integer sequence for each real, contradiction.

Note though that quantum mechanics adjusts this notion of real numbers in classical mechanics. A full quantum description of our world in theory requires only finitely many bits, because the quantum state is finite. But then measurements in quantum mechanics are non-deterministic, so impossibility of perfect prediction is still true :P

[chaoticmass]

Even then, measurements can never be 100% accurate, and we can never have enough measurements.