Transcript

OK, so we will pick up on the one topic that was not covered from two days ago because you guys needed to go play around with these cellular automata first. So I will work with the assumption that everybody here has now spent 48 hours playing with those.

But presumably because of the sleep deprivation, you've forgotten much of it by now. So we will cover some of it. OK, back to that issue of fractals and butterfly effects and that whole business that, by the time you look at chaotic systems that are determinist but aperiodical, that, when they seem to be lines crossing, getting back into the same spot, look closely enough and they're not going to actually be touching. And the centerpiece of why that matterswas that whole business of, these both appear to be the same. And take them out a decimal place and they're actually different. And a gazillion decimal places out. And the entire sort of rationale for thinking in that way is the notion that a very small difference here can make a difference one step to the left.