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Wondering if anyone has ever tried to make a calendar where everything is a power of 2, so maybe the day is divided into 16 and the hour is divided into 64, etc.

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    Are you asking if anyone has ever designed one or if anyone has gone as far as trying to put one into action? – Steve Bird Feb 17 '19 at 22:01
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    There are novelty clocks that display the time in binary format. But a binary "calendar" like you picture it would not make sense. None of the units of measure would equal any of those used in the "real" world, significantly reducing its usefulness for anything but "gag" value. Also, you'd be basing your units on the length of day... which is variable. (That's why the "real" clock changed from GMT, day-length based, to UTC, constant seconds, in 1972.) – DevSolar Feb 18 '19 at 8:22
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    Calendars are made for a purpose, following the seasons, weather, regular floods etc and generally based on lunar/solar cycles. Ancient calendars are generally based on the lunar cycle (4 weeks -> 1 months), but they are not really good to reproduce the solar cycle, so the length of months are adjusted to improve it. I don't see how a random choice like "let's make a binary calendar because it is easier to code ..." would be useful for everyday use. That being said it is easy to imagine that one eg inside a software or for own entertainment is using crazy techniques to measure time. – Greg Feb 18 '19 at 16:28
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    I'm voting to close this question as off-topic because it has nothing to do with history. – Mozibur Ullah Feb 19 '19 at 9:05
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    I disagree that it has nothing to do with history. If the question were "has anyone created a calendar based on 13", there'd be a clear historical answer in the affirmative. So I think it's still a matter of history, even if the answer is that no one in history ever did it. – Gort the Robot Feb 21 '19 at 18:23
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The core issue is that the purpose of a calendar is to track astronomical events, and in particular, their relations. The three that are universally tracked are the three that are obvious to anyone:

  • The rotation of the Earth
  • The movement of the Moon around the Earth
  • The movement of the Earth around the Sun.

The issue is that these time periods do not relate to each other in powers of two. The second is roughly 29 times the first. The third is roughly 13 times the second and 365 times the first. None of those ratios is remotely a power of two. This means that any calendar that uses powers of twos isn't going work for tracking these cycles, and thus would be basically useless on Earth.

(For units of time less than a day, it would work as well as anything as everything less than a day is fairly arbitrary.)

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  • 1 second is a typical healthy adult heartbeat, or quite close.(Yes, I know Björn Borg and Michael Phelps are around 30 bpm - but they are truly exceptional.) After that what divisions make sense for the 86,400 seconds in a day. the values 12, 24, and 60 have many more divisors than most numbers, 60 in particular having 3 distinct prime divisors: 2, 3, and 5. The approximate value of a heartbeat has been refined to be a nearby value that gives divisions of the day that exactly divide into a very very large number of subdivisions. This aids marine navigation in particular. – Pieter Geerkens Feb 19 '19 at 5:44
  • One can track astronomical events with any calendar, no matter the base its numbers are in. Marine navigation has used different types of calendars in the past (just think cultures). And further comlicating things: Modern day marine and other navigation uses coordinate transformations, e.g. from spherical to cartesian and there's the binary because you won't do x/y/z with pen & paper, while spherical can well be done that way, has been done for centuries. – a_donda Apr 25 at 20:02
  • Lots of calendars reflect terrestrial phases as well, not just astronomical ones. – Aaron Brick Apr 25 at 20:06
  • "astronomical" may be an imperfect description. The point is that the various real world time measurements that are convenient to use don't fit into nice ratios with each other. – Gort the Robot Apr 26 at 20:40
  • @GorttheRobot The answer is too superficial and opinion based. The purpose of a calender is not astronomy, it is a convenience for humans, stemming from early agriculture, maybe earlier to track herd movement (speculative). Astronomomy is the base of such calender simply because seasons. Astronomers have more sophisticated methods to track time. The other answers fit better. – a_donda Apr 27 at 18:47
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Question: Has anyone created a binary calendar? Wondering if anyone has ever tried to make a calendar where everything is a power of 2, so maybe the day is divided into 16 and the hour is divided into 64, etc.

Short Answer:
Yes, Swedish-American engineer John W. Nystrom in 1863 as part of his tonal system proposed a universal system based on hexadecimals. The tonal system was a hexadecimal system for not only time and dates (including your calendar) but distance, weight, measurements, volume, geography and even coinage.. It was on the same scale and proposed as an alternative to the metric system. The Metric system was invented during the age of reason (1799) and based on 10's, as humans have 10 digits on their hands and feet. The motivation of the tonal system was to create a universal system based upon natural phenomenon of human discernible sound, which breaks down into 8 octaves, rather than being motivated by the digits on the human hand. The tonal system was developed in a time when the world was becoming obsesesed with sound. To that end, hexadecimal tonal system evolved independent and prior to computers.

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Detailed Answer
I think what you are asking is has anybody created a hexadecimal time system / with the resulting calendar. As you know binary is just a way to represent numbers as is Hex as is the decimal system. There is no inherent accuracy or inaccuracy as previous answers have intuited due to the numbering system as all three can represent any number positive or negative which the others can render. While Humans with 10 finger and 10 toes perhaps have an easier time counting using the decimal system, computers which think in on/off binary circuits handle binary better under the hood regardless of how the number is eventually represented. But really who wants to write long string of 1's and 0's to describe the date? So the happy medium between the two numbering systems is the hexadecimal. The sixteen based numbering system. 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

We all know the Romans used their own rather non intuitive numbering system which gave way to the wide spread arabic numerals (10 based). Similarly the old non intuitive imperial systems(which is still used in the US) evolved from the amalgamation of different local systems has largely been replaced by the 10 based Metric system invented 1799. Metric system coming out of the age of reason. The tonal system of the 1863 reflected a time when the world was obsessed by sound. The first telegraph(1830s), first phonograph(1857), and the first telephone(1876).

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  • Great find. Sound is not limited to eight octaves, but octaves are related by powers of two. – Aaron Brick Apr 26 at 3:57
  • @AaronBrick what’s the best way to put that? 8 Human discernible Octaves? I’m still looking into it? Any thoughts? Wish I could find a graphic for his calendar. – JMS Apr 27 at 18:13
  • A piano keyboard spans eight octaves. Humans can generally hear somewhat more, maybe nine to eleven octaves depending on age and probably other factors. The rough rule of thumb is 20Hz to 20KHz; log2(1000) =~ 10. – Aaron Brick Apr 27 at 21:14
  • That’s awesome. – Gort the Robot May 5 at 1:47
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Yes. Time in UNIX relies on a measure based on the seconds elapsed since the UNIX epoch. This measure is natively described using a datatype called time_t, which is an integer, originally 32 bits wide and now 64 bits wide in order to avoid the Year 2038 problem. By my calculation, the current time is 1011110001110111001110011101111.

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    Humorous, but clearly also a deliberate misreading of the question. The question is not about simple counting of an existing time unit, but about rebuilding the hierarchy of time and date units in ratios that are powers of two. – Pieter Geerkens Feb 6 at 6:15
  • Not a deliberate misreading. "everything is a power of 2". You can define "hour" and "day" as you see fit. – Aaron Brick Feb 6 at 15:24
  • That's not possible - day must correspond to the common meaning of "day", and thus is a prescribed number of seconds, and seconds likewise must correspond to a usual meaning of "second" as the approximate resting heart rate for a moderately fit and activ ehuman. – Pieter Geerkens Feb 6 at 16:57
  • @PieterGeerkens The question does not say anything about terrestrial solar days; this particular binary calendar is based on the second. You might as well deny that French Metrical Time was truly metric, since its months and hours have different lengths than we're used to. – Aaron Brick Feb 6 at 17:47
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    The answer makes absolutely sense. And the Unix is not the only example, just one of the earlier. Virtually everything today, from gps clocks to digital watches and position determination in WGS84, the usual cartesian coordinate system, uses digital representation. – a_donda Apr 25 at 20:03
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Just make a year be 225 seconds long. It matches well with the amount of seconds in a Gregorian calendar year. It's not useless. If it was, I wouldn't have mentioned it. It's purely binary and mathematically efficient. There is no leap year, day, second, anything.

This is purely just time since a specific date (ie. AD/CE 0001 Jan 01 @00:00:00 AM, UTC). My friend wanted me to recreate the calendar system, and I did it with relative ease.

64 seconds, 64 minutes, 16 hours, 32 days, 16 months (Binutes, bhours, bidays, bieks, bonths, beasons, byears, for example)

The year starts off at 0, like age. You're not 1 year old when you're born, so it waits a year until it says year 1. It's the same with the other measurements.

I used a spreadsheet to recreate the system, so I can easily enter an amount of (regular) time and it'll convert for me (I find minutes the most accurate when copy-pasting. More on that if you need).

Since the binary year is 33,554,432 seconds long, it closely matches a Gregorian calendar year averaging in 31,556,952 seconds.

I am aware of Leap years, so I accounted for that. I am NOT referring to a tropical year. And even if I'm still wrong, it's only up to a day off.

A binary year is NOT a Gregorian year, although they are both very close. If you still have anything to argue about, please tell me. I'll do my best to clarify anything as needed.

The link to the spreadsheet is here: https://docs.google.com/spreadsheets/d/1jOofsyw50huVG3bKXyGGfpfcMWqqsH2jCBZKa1-uTFY/edit?usp=drivesdk

The link to the current time since aforementioned epoch: https://www.timeanddate.com/countdown/to?p0=0&year=1&month=1&day=1&hour=0&min=0&sec=0

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