Comment by ColinWright
7 years ago
In case people are wondering:
A global map with resolution
of 1.85 kilometers ...
1.85 km is roughly one Nautical Mile, which is roughly one arc-minute of a great circle. As such it's a natural unit of measure.
The original definition of the meter was 1 ten-millionth of the distance from the North Pole to the Equator via Paris, making the Earth's circumference 40 million meters. Divide by 360 degrees per circle, then by 60 arc-minutes per degree, and you get (40 x 10^6) / (360 x 60) which is about 1852 meters.
Just in case people were wondering ...
I was wondering how one would make a global map with a resolution of a nautical mile. Spacing dots a nautical mile apart on the equator is simple, but you can’t continue with a rectangular grid up north or south (by the time you’re at 60 degrees, the dots would be only half a mile apart)
A perfect solution doesn’t exist, and AFAIK no exact solution for the simpler “place N dots on a sphere in maximizing the minimum distance between dots” exists, but decent approaches exist. See http://web.archive.org/web/20120315152121/http://www.math.ni..., https://www.maths.unsw.edu.au/about/distributing-points-sphe...
See also gradian: https://en.wikipedia.org/wiki/Gradian
"one grad of arc along the Earth's surface corresponded to 100 kilometers of distance at the equator; 1 centigrad of arc equaled 1 kilometer."
i.e. both nautical miles and kilometres are derived from the size of the Earth. Plain old statute miles are just a mess, and best avoided.
Yup, so that will be the best thing once everyone switches to using grads for latitude and longitude.
No! Radians is the SI unit. I would possibly also accept fractions of a whole rotation.
The arbitrary factor of 400 (or 360), is simply not helpful for machine calculations.
2 replies →
Polar circumference. Earth is an ellipsoid.
Equatorial circumference is 40075 km. One arc-minute of equatorial longitude is about 1.855 km.
People who do crazy things with measurements cause a significant fraction (at least 15/360) of the many pains in my ass. Degrees need to die a painful death, and so can grads. There is nothing at all "natural" about them as a unit of measure, as they are arbitrary divisions of one rotation, by 360 and 400 respectively.
But I admit, even if not natural they may be more convenient for some calculations than other numbers.
> As such it's a natural unit of measure
As natural as the number 360, and 60.
I would argue the meter seems more natural, since it is related to 10 fingers ...
Given that you are already using degrees, arc-minutes, and arc-seconds in your specifications of latitude and longitude, it makes sense to use a unit of distances that meshes with them. Using meters makes less sense because it doesn't work well with the size of the Earth.
Difficulties with measurements and conversions are like a dead cat under the carpet - no matter how you push it about there's always an inconvenient lump and a bad smell. The Earth is inconveniently shaped, and you simply have to deal with it. The existing system of measurements may offend your sense of taste, but it has evolved over time to be useful to those who have to use it. Attempts to devise systems a priori and without taking into account the extensive experience of those who actually use them have always failed.
There's probably a reason for that.
I think "natural" was meant in the sense "it naturally follows" or "it's natural to assume", where it's meant to imply a natural path given your preexisting knowledge and conditions, not natural as in "this comes about in nature".
With that in mind, 360 is a fairly natural way to segment a circle for modern Humans.
60 is a very natural number.
You have twelve joints on the fingers of one hand. (Use the thumb to count.) You have five fingers (including the thumb) on the other hand to track multiples of 12 with. Voila, 60!
360 and 60 are quite handy, by virtue of having a lot of integer divisors. For a civilization where long division is unknown or limited to a few scribes, being able to divide things by common fractions easily is an important criterion in a system of measure.
> since it is related to 10 fingers
If your parent comment is correct. 10 finger thing will merely be an afterthought.