Sure you could. “Blern, party of flebix.” 
I don’t accept that this shows they “used Pi without ever understanding the concept.” They used the fact that rolling a drum, or any other cylinder/prism-type object, measures off a regular distance. For all we know, the drum may have been eliptical, rectangular, or even star-shaped.
Don’t modern, high accuracy clocks also have regular leap seconds to get around this problem?
It’s not that simple, for the reasons I pointed out in post #12.
Blern, party of flebix point glargu glargu flebix slicto glargu flebix glargu slicto slicto slicto . . . (continues for an infinite period of time. Never gets to order his klergle-stuffed graglax.)
Tuckerfan - you been reading the thread? A non-rational number base simply doesn’t work for the ordinary purposes we need math for. Math is a pretty inherent part of our lives, and not having words to describe such ideas as “six pack” and “foursome” would end up causing major problems.
Except it wouldn’t ever happen in the first place.
In the OP, Tuckerfan wrote:
> Obviously, their symbols for numbers and operations will be different than ours,
> but it also seems likely to me that there’ll be problems figuring out things if they
> don’t use a base ten numbering system.
If a random intelligent race is communicating with another random intelligent race, they will use the binary system. There’s no way to know what number system an alien race that we have never seen would use for most purposes, so the binary system is the obvious number system to use for alien contact. It’s what we use for many purposes anyway. That’s how all calculations in a computer are done, for instance, so it’s much easier to figure out umpty-ump digits of pi in binary and send that if we think that sending umpty-ump digits of pi would convince aliens of anything.
---- If a random intelligent race is communicating with another random intelligent race, they will use the binary system. There’s no way to know what number system an alien race that we have never seen would use for most purposes, so the binary system is the obvious number system to use for alien contact.
The aliens might think that base 3 was a more obvious choice. There are alleged advantages to designing a computer that way, and prototypes have been built from time to time. Admittedly, it’s not clear how well these advantages would pan out in practice, even if we ignored our large investment in binary computation.
Tuckerfan appears to be making a variant of the QWERTY argument, sometimes pitched as “Path dependence”. Under this way of thinking, bad technologies can get “locked in” due to the costs of switch-over.
I dunno. It’s difficult to imagine a universe where primitive cultures did not find counting of over-riding importance.
Leap seconds help correct for the Earth’s rotational period not being a perfect 24 hours. There’s a chaotic up-and-down fluctuation in the period, as well as a longer-term upward trend as the Earth gradually loses angular momentum. Adding (or in very rare cases, subtracting) leap seconds once or twice a year helps keep our clocks synchronized with the actual phase angle of the Earth.
On the other hand, maintaining the vernal equinox at the same place in the calendar year is a different problem — certainly one that’s compounded, slightly, by the fact that the Earth’s rotational period is not perfectly constant. That makes the length of the Earth’s year, as measured in Earth days, even more erratic than it would have been otherwise. (I call it “erratic”, though the year-to-year discrepancies are about one part in a billion.) The year length is still a fluctuating number though, even assuming a perfectly tuned leap second policy.
I take it you don’t recognize the smilie as the non-base 10 symbol for “whoosh”?