Full Circle: The complicated history of why there are 360 degrees in a circle
historytoday.com
historytoday.com
A bit of math shows that this unit is a milliradian (since sin 1/1000 ≈ 1/1000). The strange part is that there should be 6283.18... mils in a circle but that's too inconvenient, so they round it to 6400. In other words, they are using milliradians with the value of 3.2 for π.
Actually I don't think the article does a great job proving its thesis ("In school we learn there are 360 degrees in a circle, but where did the 360 come from? When it is pointed out that the Babylonians counted to base-60, rather than base-10 as we do, people often ask if there is a connection. The short answer is no.").
The article's conclusion is "So, although angles come from the Greeks, the 360 degrees comes from Babylonian astronomy". And it explains, more-or-less, how the Babylonians came to use 360 degrees for astronomy: because they had a habit of dividing things into 12 part, subdivided in 30. But that doesn't preclude they choose 12 and 30 (instead of, say, 13 and 28) because both are divisors of their base number 60.
Wikipedia points in that direction (but admits no-one really knows):
"Some ancient calendars, such as the Persian calendar, used 360 days for a year.[citation needed] The use of a calendar with 360 days may be related to the use of sexagesimal numbers."
"Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system.[7][8] The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree."
Another Wikipedia-quote agrees with your point of view:
"Another motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors,[note 1] making it one of only 7 numbers such that no number less than twice as much has more divisors" "
I believe the Babylonians actually use base 12, with the number 60 merely being a convenient multiple of 12. And I think the reason their counting system is base 12 is not because of its greater divisibility, but due instead to the way they used their fingers for counting. So, in the West, we count using each of our fingers and that’s how we arrive at a base 10 counting system. But in certain parts of the world, they use one thumb to count the separate segments of the fingers on the same hand. There are three segments in each of the 4 fingers, for a total of 12 (hence the base 12). And then the five fingers of the opposite hand are used to count how many groups of 12 have been counted. So 5 fingers on the second hand multiplied by 12 finger segments on the first hand = 60 in total.
* or not just crude but completely different; e.g. Babylonian and Roman hours varied in length each day as the time from sunrise to sunset was divided into twelve equal sections and sunset to sunrise implicitly the same. IIRC the constant-duration hour goes back only to marine navigation a few hundred years ago
So let's say there's 20 hours a day, since presumably we'd still want to have two daily clock rotations. Those hours could then be divided into 100 "minutes" with 100 "seconds" each.
If I'm doing my math right, this would mean:
• 1 alternate-universe hour = 1.2 current-universe hours
• 1 alternate-universe minute = 0.72 current-universe minutes
• 1 alternate-universe second = 0.432 current-universe seconds
I could very much deal with this. Current-universe seconds are a bit too long for the level of precision I want with that unit, and I don't think the < 30% change in the length of a minute or hour would matter much once I adapted. And, as a consequence, unit conversions would become so much easier!
I don't think we're lucky at all. :(
Perhaps you can get the Mars colonists to adopt a different system. The martian day is just close enough to the terrestrial day to make adapting the terrestrial system for it quite annoying.
Only when you also use that same base for everything else too. The decimal system works so well because it uses the same base as the number system we use (almost) everywhere.
And actually I don't really think the lack of divisors is really a problem in base 10. It may be different if you're used to imperial units, but when using the decimal system you don't think in fractions all that much. You either use more places after the decimal point, or move to a smaller unit.
I have lived in an Imperial system country, the modified version used in the USA, and multiple metric countries as well as using a mixture of cgs (SI) and mks depending on what work or study I was doing and still, for customary activity, find a dozen the most convenient. When doing science it doesn’t matter.
However, we'd no longer have the nice 1:10 ratio between seconds and human alpha waves...
Consider: You're asleep for ~ 1/3 of the day (hopefully), so you'd only have 7 units of time for everything you do while awake. This means many more events would have end up with weird start times, (e.g. 9:68 rather than 9:00 am). Just about every movie would be less than a single hour long.
The most expensive-per-minute cost/minute videos on TV are ads and nowadays the are all a minute long Or less. And most manage to fit in a problem, a little character development, a happy resolution & climax, and then even a little denouement!
It is possible that the base-60 numbering comes from this basic astronomical observation, or they may be mostly unrelated.
Babylonian math has roots in the numeric system started by the Sumerians, a culture that began about 4000 BCE in Mesopotamia, or southern Iraq, according to USA Today.
“The most commonly accepted theory holds that two earlier peoples merged and formed the Sumerians,” USA Today reported. “Supposedly, one group based their number system on 5 and the other on 12. When the two groups traded together, they evolved a system based on 60 so both could understand it.”
https://www.thoughtco.com/why-we-still-use-babylonian-mathem...
" For them, Venus was a single object and they observed its changing position, along with the other planets and the moon. These positions all lie on the same great circle, called the ecliptic, defined by the apparent motion of the sun as seen from the earth during the course of a year. "
Isnt the ecliptic basically a line (or very very skinny ellipse) from Earths perspective as we are on that great disc ourselves?
Also "For them, Venus was a single object" so for us its not??
The ecliptic, physically, is the plane of Earth's orbit around the Sun. It is so named because that is where eclipses happen, when the Moon crosses that plane. (Or other planets; we call that event a transit, but that's the same as a very annular eclipse.)
The projection of that plane as viewed on the sky from Earth is a great circle (or slightly offset, because the observer is on Earth's surface not at its center.) If the Earth were transparent, you could see the entire circle. In reality, you see a segment of it from horizon to horizon, as a line.
All the planets and the moon seem to stay near the ecliptic in the sky, because their orbits are within a few degrees of coplanar with Earth's.
Maybe we need to go metric with our circles too: https://en.wikipedia.org/wiki/Gradian
There is still another circle measurement, the mil which is 6400 for one turn. But I just learned by reading the wikipedia page, that there is not only the 6400 NATO mils I knew, but also 6000 Warsaw Pact mils or 6300 Swedish "streck"
The kilometre is the length of a centigrad of arc of the meridian through Paris, the circumference of the earth divided by 4 * 100 * 100
EDIT: I meant redefining pi instead of the radian.
Better yet, I think the unit of angle we should use is the 'full rotation' ('rot'?)
So instead of 360 degrees, or 2pi radians, we say 1 rot.
The many factors of 2pi in common equations imply we got this wrong.
> The second reason is that τ corresponds to one turn of a circle, and you may have noticed that “τ” and “turn” both start with a “t” sound.
e^(i * π) = -1, where i is the imaginary unit
would not in fact hold if we changed the definition of the radian. It's just the mathematically natural way of expressing arguments to trigonometric functions.
e^(2πi) = 1
e^jpi + 1 = 0
The reason for this form is that it doesn't just contain an imaginary unit and the two most popular constants but the additive and multiplicative identities.