@Background Pony #B74E  
What does pi have to do with 60? Unless you mean 2pi radians = 60° x 6

Just a couple of notes regarding alleged arbitrariness.
 
1.)Look into moon phases and their length.
 
2.)Look into the factorization of 60 and the ease of operations it brings. Then proceed to compare them to 2, 6, 10, 16, 30, or the ever weird non-integer base system which have their own benefits and disadvantages over 2, 6, 10, 12, 16, and other more commonly used bases. Additionally, look into the nature of the circle, it’s relationship between pi and 60, and many other interesting things.

@RandomBlank  
Exactly, the clock/calender was partially arbitrary and then partially engineered (so that things came out to a year (as in there could’ve been 10 days in a week instead of 7 (arbitrary) but then forcing ~3 weeks per month instead 4 (engineered)) so it really doesn’t relate to the number system used, which is in basically all cases arbitrary or “convenient” (like 10’s). To develop a base and then try to due all the math available at that time with that base (and dozens of others) to see which one overall seems most convenient is just not going to happen. Besides, by the point math was created to a descent degree, the number system used in a culture is fairly fixed. Still, if ponies had a number system based on a multiple of 4 (whether base 4,8,12,16 etc) it’d probably be arbitrary, since using exactly 4 wouldn’t help in the way we use 10.
 
With all the numbers systems that have come and gone, perhaps base 10 remains strong due to it simply working well and not just because those who used base 10 happened to also become world powers.
 
Anyway, they use base 10, (canon) so debating what an equine race would actually use (if not a show created by people who use base 10) can only go so far.

@Techy Pony  
Oh, seconds, minutes and hours come from babylonian system. Week is biblical, and months were “engineered” first by Caesar, and then adjusted by one of the Popes.
 
Nevertheless, the numeric system is almost never “engineered” meaning things as advanced as scientific notation don’t happen as a consideration when a numeric system is being born. These systems generally evolve.
 
On a related note, check the decimal time system developed after French Revolution. It didn’t survive long, but there it was, a definitely real thing.

@RandomBlank  
You could always use scientific notation or something similar xD
 
I wouldn’t count clocks as any indication of what they count/do math with. We use arbitrary numbers for time for seconds, minutes, hours days, weeks, months and just sort of adjusted it to work out close to a year, however none of those numbers are a 10, 100, 1000 etc.

@Techy Pony  
Binary is awfully unwieldy for bigger numbers. Representing a million requires 20 digits. Considering 8-hour clocks that appeared in the earlier episodes, I wouldn’t be surprised if they use octal though.

@RandomBlank  
So basically I was right, people arbitrarily chose bases to count in and it just happened to be that base 10 was rather convenient, determined after success and failure rather than just picking a multiple of fingers?
 
I don’t think it’s any more convenient to double/half in hex than base 10 (just doing a few quick calculations), and it’s relation to binary doesn’t count since as you stated such things came way after the development of the system used.
 
It’s possible base 10 was used over base 16 because of finger counting, but such a reason is useless to ponies so there’s no reason for them to use a base of 4 or a multiple of 4. Heck, maybe they use binary because of binary type writters? XD

@Techy Pony  

 
That is a later phase, way after the number system is developed and established by the society. Number systems evolve early, before given civilization develops more advanced arithmetics.
 
The number system’s convenience comes from the number of natural factors of the base. The 60-based system of Mesopotamia was very convenient, with factors 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, but it failed through way unwieldy large base, and cultural/military domination of Rome with its own (horrible) system, only replaced by arabic which was (again) positional, provided a zero and the base 10, while not optimal, was widely accepted (through roman) and not overly unwieldy despite its meager set (2,5) of factors.
 
Hexadecimal is nice thanks to being directly related to binary, meaning operations like doubling, halving, and such are trivial, and while its three factors (2,4,8) aren’t much, the advantages outweigh the disadvantages by quite a bit.

@Background Pony #B74E
 
@RandomBlank  
Ah yes, forgot to count the 0 making it base 16.
 
 
@RandomBlank  
I know what you mean, but without personally using other bases it’s difficult to tell how much more useful they’d be. Also, I don’t think that fact of ‘absorbing the number’ (counting without having to consciously count 1,2,3,4…) would make much difference in arithmetic since you’re never counting, but processing numbers, usually all of which are far beyond what you can look at and just ‘absorb the number’.
 
Besides, I don’t think base 4 would be natural for ponies anyway. For humans, absolute basic counting may be eased by counting with fingers (though I think base 5 would be easier since you could count to 30 instead of 10 without counting in your head as well) but it does nothing to help arithmetic. For ponies they couldn’t count on hooves any easier than you could count on feet, you can’t sit and hold up your limbs when you want to count the lazy way. If anything I bet the base they count in would just come from some arbitrary base somepony came up. Perhaps a multiple of 4, perhaps a large base that way larger numbers could be written down without taking up as much space. I can imagine mouth writing is not as accurate and larger writing is necessary, so paper real estate is a factor worth considering.

Hexadecimal doesn’t go from 0 to 16. Here’s an example of what hexadecimal numerals may look like:

@Techy Pony
 
It’s base 16, which is quite convenient.  
Humans use base 10 only thanks to our 10 fingers. For equines base 4 would be the “natural origin” but base 4 being so low would be very inconvenient. Additionally, without knowing numbers humans can easily count to 4 “at a glance” (you need to actually count to distinguish 5 in a row from 6, your brain doesn’t automatically ‘absorb the number’ when you look at as many items/people). Equine brain is built differently - they can “absorb” counts of up to 12 easily, so base 4 would be far below ‘useful capacity’; base 16 would be much more functional.

@Techy Pony  
I suppose you might be close to right, for up to 15 they are all unique symbols. and there’s nothing particularly noteworthy of 15 in this case, specially since it’s actually a base 16.
 
And no one will ever believe me, but that was supposed to be a 5, not a 4.

I don’t think someone knows how numbers work, why would you try and give a unique symbol to numbers up to 15?
 
 
@Background Pony #B74E  
Given what I said, it actually seemb like it’s based 15, which is odd.

That looks like a base-4 number system, but it seemingly can’t support anything beyond 15 without additions.

You forgot R.

Ponyform?  
Ponyfied Cuneiform names…