This comment is hidden.
Show Comment
DeWayfarer · 61-69, M
They still don't know definitively how the Sumerians figured out their π tables. Lots of assumptions though. And therefore myths. Why did they even pick the sexagesimal number system (base 60) is how this should be approached.
@DeWayfarer 1. Sixty is unusually divisible.
60 can be divided evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. That makes it excellent for trade, land measurement, rations, weights, fractions, calendars, and later astronomy. A base-10 system handles halves and fifths neatly, but not thirds, quarters, sixths, or twelfths nearly as well. Sexagesimal notation became especially powerful for calculations involving fractions.
2. It may have emerged from a mixed counting tradition, not a clean “choice.”
The Mesopotamian system was not pure base 60 in the modern mathematical sense. It retained decimal features: Babylonian sexagesimal digits were written using unit marks and ten-marks, so ten remained embedded inside the notation. That suggests base 60 may have grown from a compromise or layering of older counting systems rather than from one deliberate reform.
3. It fit administrative life.
Early Mesopotamian states needed accounting systems for grain, labor, land, animals, weights, and payments. A number like 60 is useful because it allows many equal subdivisions without messy remainders. That matters in a bureaucratic economy.
4. It became culturally sticky once embedded in tables and institutions.
Once scribes, merchants, temples, and astronomers used sexagesimal tables, the system acquired institutional inertia. Later Babylonian mathematics and astronomy inherited it, and from there it passed into Greek, Islamic, medieval, and modern scientific traditions — hence 60 minutes in an hour, 60 seconds in a minute, and 360 degrees in a circle.
60 can be divided evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. That makes it excellent for trade, land measurement, rations, weights, fractions, calendars, and later astronomy. A base-10 system handles halves and fifths neatly, but not thirds, quarters, sixths, or twelfths nearly as well. Sexagesimal notation became especially powerful for calculations involving fractions.
2. It may have emerged from a mixed counting tradition, not a clean “choice.”
The Mesopotamian system was not pure base 60 in the modern mathematical sense. It retained decimal features: Babylonian sexagesimal digits were written using unit marks and ten-marks, so ten remained embedded inside the notation. That suggests base 60 may have grown from a compromise or layering of older counting systems rather than from one deliberate reform.
3. It fit administrative life.
Early Mesopotamian states needed accounting systems for grain, labor, land, animals, weights, and payments. A number like 60 is useful because it allows many equal subdivisions without messy remainders. That matters in a bureaucratic economy.
4. It became culturally sticky once embedded in tables and institutions.
Once scribes, merchants, temples, and astronomers used sexagesimal tables, the system acquired institutional inertia. Later Babylonian mathematics and astronomy inherited it, and from there it passed into Greek, Islamic, medieval, and modern scientific traditions — hence 60 minutes in an hour, 60 seconds in a minute, and 360 degrees in a circle.
DeWayfarer · 61-69, M
@FrogManSometimesLooksBothWays 60/10 comes out even. Yet that that doesn't explain so high a base. You can justify anything divisible by ten using that reasoning.
The number system had to come first. Without numbers you can have no math.
I believe it was once said that anything over ten was considered many. There again no math would be possible.
The Sumerian number system is THE absolute oldest known number system using math.
The number system had to come first. Without numbers you can have no math.
I believe it was once said that anything over ten was considered many. There again no math would be possible.
The Sumerian number system is THE absolute oldest known number system using math.