Last time, I talked about time and how we humans perceive time, and the difficulties we seem to have in dealing with periods of time longer than a single human lifespan.

And the longer the span of time, the more difficulty we have as well. We are not equipped to handle geological time scales, for instance. Perhaps this is part of the reason that it took us time to realize the truth of continental drift, for instance, and why there is resistance to believing the changes that can be wrought by natural selection.

There are other directions of speculation as well. Our view of time, our experience of time, leads us to believe that there is a local continuity, a local constancy, when extending that local constancy to a larger, longer constancy which clearly doesn’t make sense.

If today is the same as yesterday, for instance, then today will be the same as tomorrow, and the next day, and the day after that. (Mathematicians will recognize this as a sort of analytic continuation.)

My favorite observation along these lines involves an extension of the mathematical three body problem. The problem itself is to write down a formula for the motion of three bodies (think for instance of the Sun, the Earth and the Moon), in isolation from all others, that would allow us to predict their future positions. The problem has no such solution, and the best we can do is to make necessarily approximate numerical calculations. (And why the numerical calculations are necessarily approximate is another story and one that involves the birth of chaos theory.)

Extend this to the whole of the solar system, with not only the Sun and the planets, but all of the moons and asteroids and comets and unknown objects lurking in the Oort Cloud. All have mass and so all have an effect on each other.

And so how do we know, beyond extrapolating from the past, that the orbits of planets, and in particular the orbit of the Earth around the Sun, are stable? We suspect that they are. All of the calculations we’ve done support the hypothesis that they are, and they almost certainly will remain so for the short term, by some definition of short.

To be fair, this isn’t a real worry, but rather is just something I’m speculating on to illustrate the point.

And up to this point, we’ve only been discussing time scales that are long compared to human lifespans. We could also go the other direction and consider time scales that are short compared to ours, and I think this to some extent comes back to the same analytic continuation point I made above.

If our experience has taught us, as it has, that tomorrow will be like today in the same way that today is like yesterday, then how can things happen so quickly as to put paid to that? And we have explored this to some extent, in the occasional episode of Star Trek for instance.

Another manifestation of this is the clock speed of artificial intelligences. A near- or sub-human artificial intelligence, hopefully still some many years away, that thought much more quickly than we do, would still be a significant menace and formidable enemy.

And so, time and the speed of the passage of time might be a problem.