Neurological evidence for chaos in the nervous system (2014)
nautil.us
nautil.us
We even reflect our nature in the societies and systems we build, which are all ultimately chaotic, myriad variables interplaying to produce complex and often unpredictable outcomes.
Those processes are very sensitive to the initial condition, but given the same seed, they'll evolve identically.
yes. things like the logistic map or lorenz system demonstrate mathematical chaos, while being utterly deterministic.
"chaos is random" is a popsci dilution / mangling.
The best example of this would be weather forecasting. A lot of weather bureaus can perfectly forecast the next 24 hours but become increasingly difficult to get it right the more into the future you get them to forecast.
More precisely, chaos is fully deterministic but that can't practically be usefully applied beyond a few iterations, because small measurement error on inputs blow up into giant uncertainty in outputs.
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.
"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."
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
Growing? Show me a biologist or psychologist (or chemist or physicist for that matter) who does not understand as a given that biological and neurological systems are so incredibly complex that they can be described as chaotic.
In fact, this is understood by all of us. We don't expect identical twins to think identical thoughts.
This is a long article saying nothing, making something mundane and obvious out to be a looming paradigm shift.