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Basic Concepts of unTime

There are only 2 natural units of time necessary: Year and Day
(the lunar month, a natural unit of time, is not necessary)

Year one should start at 10,000 B.C.
We should begin counting the year at a date which preceeds history so that all dates worthy of memory are on the positive side of the timeline leaving no need for "A.D./B.C., B.C.E/C.E., etc.". So as to cause the least trouble for the western world, the year 1 should begin at 10,000 B.C. making the conversion a simple addition of 10,000. This starts the positive timeline before the beginning of the neolithic revolution (from hunting/gathering to agriculture), 10-12 thousand years ago.

Year zero should be before year 1 and previous years should be negative.
Regardless of where we begin counting the year, this should be implemented. We have a numeric system which deals with negative numbers. Let's just use that. The only complication is that there is no year zero. So, if we implement this with our current starting point (1 A.D.), 1 B.C. would be year zero, 2 B.C. would be -1, etc.

The days of the year should be noted from 1 to 366.
January 1st would be day 1 and December 31 would be day 365. By doing away with months we would not only lose an extra digit, but an entirely separate number.

Leap days should be added at the end of the year.
Always being 366, it would not disrupt the order of the other days.

The last day of the year should be considered an extra Sunday. In leap years, the last 2 days should be considered extra Sundays.
Each year, the days of the week would always correspond to the same numbers. This change could be made independently of the others. It would prevent the need for the 7 separate calendars we currently use. The extra day should be considered the New Year's holiday. There would be little secular transition for this. Easter and any religious holidays based on a day of the week would probably grow due to predictability. This works with the need for religions to have a 7-day week which is too powerful to attempt to change.

The days of the week should have single letters for abbreviation: U for Sunday, Q for Thursday
The seven day week is too entrenched to try to change. The fact that the days are named after norse gods and such is ridiculous but does not interfere with efficiency. That we cannot abbreviate them with single letters is just dumb. Let's just decide on some alternative letters for Sunday or Saturday and Tuesday or Thursday. I have to suggest U for Sunday making it unday and the Q for Thursday because the Q is how you make the th sound in unphonics. The U is probably ok with most people, but the Q would be more acceptable if it were an H going with the theme of using the second letter.

Time of day should be referenced as a fraction of the day.
This would eliminate the need for entirely separate numbers for hours, minutes, and seconds. And, it would do away with the bizarre corner we've painted ourselves into on this am/pm thing. As the unclock (above) shows, the day is simply extended to whatever amount of detail is preferred. Scientists would often deal with digits far from the decimal, but everyday life would only have 2 digits to refer to. Each percent of the day is about 15 minutes. So, a movie would usually be 6 cents, you would meet someone at .52 to go to lunch, etc. You would not even need to go to the third digit unless you were talking to your boss...or in a murder trial. The third digit would probably be refered to as a mil (1/1000) and the second as a cent (1/100).
Fractions of the Day:
.1 = 2h 24m
.01 = 14m 24s
.001 = 86.4s