Originally Posted by Xei
That isn't my explanation at all, sorry if I wasn't clear. The point of the majority of the post I made was to explain this: even with an extremely simple model that doesn't take into account random events like the one you mentioned, it's still chaotic. When I described the logistic map, I did so fully: you have one very simplified term for the births per year (r*current population) and another very simplified term for the deaths per year (r*current population^2), and even with this extremely simplified, deterministic model of a biological population, its behaviour is very complex. If you have access to some kind of simple programming language I recommend you try this for yourself... type in x = 0.5 (this is the starting population as a proportion of the maximum that the environment can support; you can choose any other number between 0 and 1), and r = 2.5 (for example). Then write x = r*x*(1x), and repeatedly perform that operation... pretty soon x will stabilise (to 0.6). Now change the value of r. Just above 3 will give you a cycle of two populations; at 3.5 it will jump about 4 different values; then as you get close to r = 4 it will start jumping all over the place, and will be highly sensitive to the initial values of r and x.
What does r stand for in this equation?
x is the maximum population for the environment.
nextpopulation = r*maximumpopulation*(1maximumpopulation)
Oh wait, is it just a number representing the resources?
I'll try it in C++.
I'm not sure why that equation was chosen though.
I mean what if you just had 1+1 ?
It doesn't get more complicated.
And it is only taking in to account a few factors.
And if you had all the factors perfectly figured out (hypothetically) than the equation would not get more complicated as it goes on.
Originally Posted by Xei
It's a popular science program, albeit quite an advanced one, so they were speaking informally to get the important message across. You are correct that if you knew literally everything to infinite accuracy about an idealised situation, you could predict everything about its future; however this is inconsequential. One of them did explain 'unpredictability' properly; no matter how accurately you know the initial configuration, it soon becomes useless. Imagine the error in your calculation multiplies by 10 each generation (so, exponential). Say your initial error is 0.0000000001, which is like knowing the circumference of the Earth to the nearest millimetre. Within only 10 generations, the error is 1 (analogous to knowing the circumference of the Earth is between zero and double what it actually is), and a few generations later it's totally useless. Now imagine we invest billions in extensive research to reduce the error by an entire factor of ten, which would be like learning the circumference of the Earth to the nearest tenth of a millimetre. How many generations does it take now before our measurement is useless? 100? Nope, it's just 11. No matter how accurately you know everything about the situation, extremely quickly it becomes completely useless, and from that point onwards you can know nothing useful at all.
Ok, but what if we have computers in the future that can predict it perfectly accurately?
Especially if we have AI, it will be less prone to error than humans, or will build AI which is less prone to error.
Originally Posted by Xei
To know anything useful about the future of the system after an arbitrary point would require infinite accuracy, and that is simply practically impossible. This is kinda obvious from a human perspective; we'll never be able to build instruments that are free from error. Microscopes, for instance, can only distinguish objects larger than the wavelength of light they're using. I'm not sure how serious you were about knowing absolutely everything about the start of the universe.
Well, I'm not sure if we could figure out the start of everything.
I was just speaking theoretically. And it would probably be easier to figure out every variable at a given instant, like now, and trace it back to the beginning hehe
Originally Posted by Xei
However, all of this does in fact go beyond just human error: since the start of the 20th century, we have known that uncertainty is an inherent part of the universe; this is the uncertainty principle. Randomness is in fact a real thing, and hence chaos is intrinsic too.
Hm, I'm not so sure about this. I know quantum physics basically says this. But I think eventually we'll figure out the rules to that too. I have no proof of it or anything, I don't even really get it, but it's just what I think.


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