The day is divided into 64 hours, the hour into 64 minutes, and the minute into 64 seconds. One octal hour is roughly a third of a traditional hour, and the same goes for minutes and seconds.
The week is divided into 8 days (0-7). There are no months, just a continuous series of dates, from 0 to 364/365, which in base 8 is 554/555. This way, one can tell by the date number what week number and what day of week it is. The date 344 (in base-8) tells you that it is week 34, day 4.
Furthermore, if we would like to specify the time of day on a particular date, we can simply put a comma on the date number, and continue with numbers for the hour, the minute and so on, because all measures are defined in the octal format. The following two lines give exactly the same amount of information, in the traditional notation and Octal Time respectively:
In the traditional notation, there are seven separate measures: Month, date, week, day of week, hour, minute and second. And for some reason, they hardly leverage the fact that we have one overwhelmingly dominant radix, namely base 10. If they were, 200 minutes would be defined as 2 hours, and so on with the other measures. As it is, I don't immediately know how many hours 200 minutes is. I have to stop for a moment and do a calculation in my head:
But why!? Why does our system for measuring and understanding time waste so much of my time by putting such trivial mathematical obstacles in my way at every turn!? This is not just plain stupid, it has an actual impact on all of our lives. A good understanding of time is crucial both for managing how we spend our waking hours, and for more profound things like coming to terms with our own lives as we progress from youth toward old age and eventually death. We would all benefit, both individually and societally, from a time system that promotes intuitive comprehension of time: of durations and relative positions in time from pre-history to the far future.
Our system for measuring time should be quick and easy, optimized for intuitiveness and usefulness, not for traditionalism, or whatever the traditional system is optimized for.
Changing to decimal time in one form or another would be a great improvement. But I have come to realize that the decimal radix is part of the problem. If we were to choose a radix based on how easy and intuitive it makes our dealing with numbers, base 10 would be out of the question.
A common suggestion for a better radix is 12, with the reason given that this number can be evenly divided in a lot of different ways – by 2, 3, 4 and 6, whereas 10 can only be evenly divided by 2 and 5. Some even take this reasoning a lot further, promoting a return to base 60, which the Babylonians used in their time. 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30.
But switching to a radix based on this criteria would only be a very small improvement. The only thing it would make easier is dividing more numbers evenly. But not repeatedly, mind you. For instance, multiplying or dividing 10 by 2 or 5 is easy, but it rapidly gets more complicated as you repeat the operation:
Multiplication and division by 5 Multiplication and division by 2
390625 256
78125 128
15625 64
3125 32
625 16
125 8
25 4
5 2
1 1
0.2 0.5
0.04 0.25
0.008 0.125
0.0016 0.0625
0.00032 0.03125
0.000064 0.015625
0.0000128 0.0078125
0.00000256 0.00390625
There are patterns here, but they are not easy for a human brain to learn by heart, or to apply in practice.
The series for base 12 or base 60 would demonstrate the same problem, only with more complicated patterns.
In bases with more than one factor, the only number that scales easily is the base number itself. In base 10, multiplication and division by 10 requires hardly any effort. You only have to shift the decimal point one place to the right or to the left.
In base 8, there are three numbers that are made effortless to multiply or divide with: 2, 4 and 8. The base number is of course the easiest, but the three-step patterns for 2 and 4 are easy enough to learn and make use of. The series below are in base 8, using all the normal number symbols except 8 and 9. This is why half of 10 is 4, etc.
Multiplication and division series, in base 8
By 10 By 4 By 2
10000 10000 10000
4000
2000 2000
1000 1000
400 400
200
100 100 100
40
20 20
10 10
4 4
2
1 1 1
0.4
0.2 0.2
0.1 0.1
0.04 0.04
0.02
0.01 0.01 0.01
0.004
0.002 0.002
0.001 0.001
0.0004 0.0004
0.0002
0.0001 0.0001 0.0001
Just like it is easy to multiply or divide any number by 10 in any base, the octal numeral system makes it easy to multiply or divide any number by 2 or 4. Whatever number one starts with, you get a three-step pattern to any series of multiplication or division by 2 or 4.
One would get the same kind of benefit from using any number that is the power of another number. For instance, 16, which is 2 to the fourth power, or 27, which is 3 to the third power.
The number should be a power of 2, because this is by far the number that is easiest for humans to operate with. Doubling and halving is as easy as can be, whereas multiplying or dividing with some other prime requires effort, sometimes a lot of effort. Any base which is the power of 2 is optimized for the ease of doubling and halving, and is thus aligned with the fundamental strength of human mathematical ability.
Of all the alternatives, base 8 stands out as the most practical.
Using a base 16 numeral system, we would be able to express higher values with fewer symbols, but that would necessitate inventing six new symbols, or making a new use of old symbols, such as is the case with the convention for hexadecimal notation in computer science: The letters A-F represents the values 10-15. I don't think it is likely that I or anyone else will be able to select a set of symbols that everyone can agree on.
Using a base 2 is a real alternative, contrary to what one might at first think. Of course, if we use the symbols 0 and 1, a lot of values would need numbers so long they would be difficult to read, and generally waste our time. But since there are only two values in the base, the binary numeral system can be written in a new way, for instance as three part squiggly lines with tiny peaks and valleys to represent ones and zeroes. There would be 8 variations on such lines (which we quickly would begin to recognize as though they were symbols in a base 8 numeral system). The same principle could be applied to giving each number a name. For instance, ones could be represented by either "b" or "i", zeroes by either "o" or "m". That way, 010 could be pronounced "obo", 111 would be "ibi", and so on. Something like this definitely could work, and be practical. But it would be pretty weird. Besides, it is very easy to switch from octal numeral symbols to this system, which is half-binary, half-octal. So even if a binary radix is is preferrable in certain contexts, it doesn't have to be the dominant system, as it can live side by side with the octal system with no problem whatsoever.
The octal alternative is the only one that is neither too big, too small or too unfamiliar.
Computers work with binary numbers, which is why we see numbers like 32, 64, 128, 256 etc. all the time. In base 8, this same series would be rendered 40, 100, 200, 400 etc. Units like megabyte and gigabyte, which as they are currently defined are only approximatey a million and a billion bytes, respectively, could be redefined as precisely a million and a billion.
Numbers become a lot easier to represent as fractions of a circle. One eight of a circle is 45 degrees, which is a very easy angle to read and to construct. One tenths or a circle, 36 degrees, is anyones guess. This advantage is perhaps particularly useful in the context of the clock and the calendar.
The day of Winter solstice of 1970 is defined in OT as the New Year of Year Zero. Every fourth year after this is a leap year, except every 128th year, a number which in base 8 is "200".
The choice of the start of the calendar era is completely arbitrary. And since a change of numeral system would mean that all years would become unfamiliar anyway, it is a great opportunity to finally get rid of the outdated Christian designation. And the perfect candidate for a new start of a calendar era is the epoch of Unix time, or rather, the first winter solstice following it. This is a good choice because a small number is more practical than a large one, and because this is an age defined by computers.
Contrary to the epoch, the choice of where to start the year is not an abitrary one. There are several astronomical events that mark the passing of a year. The solstices and equinoxes are the most obvious ones. And of these, the winter solstice is the best alternative for two reasons:
Since the date changes on midnight, the darkest point of the day, the year should change on its darkest point (that is, the darkest point for those who live on the Northern hemisphere, which is a majority of the population of the Earth). darkest point of the year.
It is closest to the traditional New Year.
The pattern for determining leap years in the Gregorian calendar is accurate down to 0.0309581 percent of a day, or 26.75 seconds (traditional). The pattern in the octal calendar is accurate down to 0.0002919 of a day, or one quarter of a second (traditional). The Gregorian calendar is shifted backward by one day every 3300 years. The octal calendar is shifted forward by one day every 340 000 years. And the pattern is even quite a lot simpler.
In OT, there are no months. The year starts on date 08, and ends on the date 5548, or 5558 on leap years. The week is defined as eight days long.
Splitting the year into months makes it difficult to calculate the number of days between two dates that are in different months.
The reason the week should be eight days is that this makes it as easy as possible to tell from the date which week and which day of the week it is.
The calendrical solstices and equinoxes can be specified by adding a fraction to the year number. The last summer solstice was year 50.48, and the next autumnal equinox is 50.68. Because of the unevenness of the number of days in a year, it is not practical to specify all dates just by adding octimals (the octal version of decimals). The solstices and equinoxes are the only ones that unambiguously can be referred to in this way.
There are 1008 hours in a day, 1008 minutes in an hour, and 1008 seconds in a minute.
I haven't figured out what to do with time zones yet. 64 zones are too many, and 8 seems too few.