I dedicate a good amount of thought to what I'd do were I in control of human customs and behaviour. One topic that I regularly revisit is time, and how time is time is hopelessly mismanaged; there's a league of difference between true time and what I call ``historical time'', the latter a quagmire of historical mistakes, arbitrary decisions, and other such nonsense. However, base sixty is pleasant.
The decimal base has nice qualities, and I prefer the number one hundred in many ways in my personal life, but decimal isn't actually particularly pleasant. Further, those common representations of it wouldn't require many changes to maximize confusion between symbols; however, base sixty is too big.
Were I in control, time would be represented uniformly in base sixty, with base thirty as another of the preferred bases. A better world would be accustomed to using bases and symbols dedicated to the situation, but these two are the focus. Base thirty is pleasant, product of the first three primes.
Thirty symbols is a good count for what humans could reasonably recognize immediately and what could be expressed without any symbol resembling another, in any way. Base sixty could use an over bar to reserve space when being expressed with base thirty. Base sixty of seconds maps well to the current ideas of time: sixty cubed is two and one half days, another is one hundred and fifty, and then nine thousand. An average human lifespan could be measured by three or four counts of this quintic unit.
See my pleasing patterns articles, for some of my ideas on what base thirty symbols would look like.