Base-4 timekeeping method to make more sense of our standard (thousands of years old and completely obsolete) clockPosted: 20/06 -09
Lately, beginning with getting really carried away with decimal time last year, I’ve been thinking a lot about timekeeping. Decimal time has the great advantage of making timekeeping intuitive for base-10 minds such as our own. But it doesn’t seem likely that we’ll see any revolutionary changes in society on this point, and even if we would have, I’d still have been unhappy, because I’ve realized that there is another, even more revolutionary step I’d much prefer: A step away from the base-10 numeral system. I’m not sure which alternative I prefer yet, but I think both base-8 and base-16 is far, far better. These have one huge advantage in common: They are multiples of 2. This is good for several reasons:
- Doubling and halving is by far the most intuitive way we have of dealing with numbers.
- In base-10, halving a number repeatedly becomes very hard very fast. Starting with 10, we get 10 — 5 — 2,5 — 1,25 — 0,625 — eh… That was four halvings. This is in stark contrast to the ease of halving in a base that is a multiple of 2. Take base-8, starting with 8, which in base-8 is written “10″, for reasons that should be obvious: 10 — 4 — 2 — 1 — 0,4 — 0,2 — 0,1 — 0,04 — 0,02 — 0,01 — 0,004 — etc. etc. That was 10 halvings, but you can go on forever without even having to think.
- Computers are base-2, and use multiples of 2 as byte-sizes. We all know how poorly this translates to base-10: 2 — 4 — 8 — 16 — 32 — 64 — 128 — 256. In base-8, this same series would read: 2 — 4 — 10 — 20 — 40 — 100 — 200 — 400. And in base-16: 2 — 4 — 8 — 10 — 20 –40 — 80 — 100. A numeral system with a base that is a multiple of binary is perfectly suited for our computer age.
But this post isn’t really about numeral systems, I’m just getting carried away again. Let me just point to a brilliant pro-base-16 book from 1862 by the Swedish-American John William Nystrom, and get on to what was the reason I started writing this post: I have found a close-to-perfect system for timekeeping that doesn’t demand a hopelessly improbable revolution. I romantically call it the base-4 timekeeping method. The premises are that our waking day is 16 hours long, and that 4 is the most intelligible number there is. Now, have the day split in four parts of four hours each, and each hour in four quarters, and you get a new map of the day that looks something like this (the bars are hatched up to 10:30, the time that this post was published):
A full day is 64 quarters long. You probably have a lot better sense of the length of a quarter than of a full hour, so calculating time in terms of quarters might be a good idea, in particular short spans. You gain a better grasp of the experienced duration of time that way, and, when placed on the map above, you know exactly how to weight time in relation to a full day. Timekeeping is made very simple.
You’re probably not convinced yet. But try to think about — for instance — how your waking time is budgeted on work, play, exercise etc., and I’m quite confident you’ll start seeing some benefits to the base-4 method.