Related:
It's big numbers all the way down. I would like to understand this stuff better than I do. But I enjoyed the author's comments:
For example, I remember explaining to some mathematicians why the Moon rises a bit later each day. I can easily imagine not remembering whether it’s earlier or later. But this is something one can work out from first principles if one knows the Moon orbits the same way the Earth turns. Given that fact, a good mathematician should be able to figure out pretty quickly about much later the Moon rises each day. If they can’t do that, no amount of (∞,1)-categorical expertise will impress me.
I also remember stumping people with the question “if a solar eclipse happens when the Moon comes between the Sun and the Earth, why isn’t there one every month?”
A more significant challenge: “Since all rocks come from material that formed the Earth about 3 or 4 billion years ago, how can we use radioactive dating to measure the age of rocks and get different answers for different rocks?”
And: “If hot air rises, why is it colder on mountain tops?”
Confusion over the movement of the Moon caused me to miss an occultation of the Pleiades. Experience tells me that the Moon rises about an hour later each day. But my first intuition on seeing this question is that the Moon's orbit should put it ahead, not late, when my position on the Earth's surface repeats after 24 hours. Of course, that's right, and that's why I need some more time to catch up with the Moon: the observer is late. How much more time? Well, after about 28 days the catching-up periods should add up to a full revolution, so I suppose it's about 1/28 of a day, 0.86 hours, or 51 minutes. I'll make some observations if my memory and the weather hold up (both poor prospects).
For solar eclipses, I'm not sure it is so far off to say there is about one (at least partial) eclipse every month, somewhere on Earth. The tilt of the Earth's axis should not be a factor in eclipse frequency, but if the Moon's orbit is tilted with respect to the Earth's orbit around the Sun, that would make alignments less frequent.
For the rocks I have no idea. I think with once-living material, the different carbon isotopes are kept in balance by metabolism, and when the creature dies there is a predictable shift as the less-stable isotope decays. Rocks should be pretty uniform to start with. Maybe it's a clue in the question that the rock-forming "material" is uniform, but different rocks were formed at different times. If they are sedimentary, like limestone, they might contain material from living creatures. I can't remember the difference between igneous and metamorphic, but one of them is something about lava cooling down. I'll guess that something about hot lava prevents some kind of radioactive decay from occurring, but I can't imagine how.