Incan Counting System Decoded?

Discovery News ^ | Feb 3 2004 | By Rossella Lorenzi

[Don Joe]

360 is pretty close to our present 365.24xxx days per year.

I wonder how much mass change of our planet there'd have to be to get the year to have 360 days in it?

There could be other reasons for the count being "off" by five odd days. Maybe the guy doing the counting was sick like a dog for two weeks, and by the time he got back to making his scritches on the stone, he misremembered a few days due to fever delirium. Or, maybe they counted accurately, but used an invalid endpoint, due to viewing the sun's yearly position from "Stone A" to "Crotch of Tree B", not taking into account that "Tree B" would be growing.

There are probably plenty of other reasons for getting the count wrong, I just pulled those two off the top of my head.

Or, maybe they said, "365.25? That's nuts, just round it down to 360, it'll work fine, and the math's a lot easier." (Or maybe some scribe copied it that way, thinking he'd be doing the world a favor.)

It doesn't necessarily mandate a change in the planet's mass.

Now, on the other hand, I've wondered about dinosaurs, whose bones weren't strong enough to support their weight, and flying dinosaurs, that didn't have the lift or bone structure sufficient to allow flight.

I'm thinking that two things may have been at play here, that I haven't read of anyone else considering. (Maybe they have, but I haven't read it.) If the world was spinning faster on its axis, then centrifugal force would make everything on the surface seem to weigh less than it does now. (Even today, you'll weigh less at the equator, where you're traveling at about a thousand MPH, than you will at the poles, traveling at 0 MPH.)

Also, if the air pressure was significantly higher, the air would be denser, which would of course make any lifting surface much more efficient.

[AdA$tra]

I heard SCO is suing the Incans for using Unix V code in that device.

[AdA$tra]

360 is pretty close to our present 365.24xxx days per year.
I wonder how much mass change of our planet there'd have to be to get the year to have 360 days in it?

I wonder if their system had leap years and leap seconds and all that other stuff that doesn't quite work in ours.

[Elsie]

(work in progress indeed!)

[Pyro7480]

I think it's more the fact that there are 360 degrees in a circle.

[William Terrell]

"Instead, all scholars based their calculations according to a base 10 counting system. But calculations made to base 40 are quicker, and can be easily reconverted to base 10," . . .

"How would one explain the many statements in the Spanish chronicles, both those written by Spaniards and by literate Andeans, who stated quite straightforwardly that the Inca used a base 10 counting system? This system is also attested in a mountain of early colonial documents that describe how the Inca organized their administrative system according to a base 10 counting system."

The answer to the last paragraph is found in the first.

[XEHRpa]

Where do you suppose we got our base-12 system?

I'm surprised no one has answered this yet. Think about it. Since the early days of commerce (and even within family units prior to that), people have needed to divide integral numbers of things into portions. To avoid inequity (or squabbles in the case of family units), one needs to group things in easily divisible quantities.

What is the smallest number of items that can be grouped into either 2 or 3 equal piles? The answer is 6. How about 2, 3 or 4 equal piles? The answer is 12. How about 2, 3, 4, or 5 equal piles? Of course, 60. How about 2, 3, 4, 5, or 6 equal piles? Also, 60. And how about 2, 3, 4, 5, 6 or 8 equal piles (we'll leave out lucky 7)? The answer is 360.

Though I have never read it anywhere, the answer always seemed obvious to me that selling things in groups of 12, 60 or 360 (wholesale) was to facilitate retail in smaller equal portions. It also makes figuring out what the subportion is worth easier.

It's all fractions!, which the schools think we no longer need.

[XEHRpa]

Oops. Correction:

2, 3, 4, 5, 6, or 8 piles => 120
2, 3, 4, 5, 6, 8, or 9 piles => 360
2, 3, 4, 5, 6, 8, 9, or 10 piles => 360

[Cronos]

Thanks! That was insightful!

[XEHRpa]

You're welcome. Usually, the easiest answer is the reason. Hundreds/thousands of years after the fact, it is sometimes difficult to ascertain what the simple explanation might have been at the time.

That's why I love history, and the history of technology. There are frequently links exposed that require a wider knowledge. For example, the fermented honey drink, mead, persisted in popularity for several centuries in Catholic countries after the Reformation vis a vis the Protestant countries. Why? The Catholic Church burned many more candles (eschewed by the Protestants), and accepted tithings in the form of wax from the poor. Poor peasants would get their wax by searching for beehives in the wild. What to do with all the leftover honey? Mead.

It is a little tough to figure it out without the wider historical context.

[_Jim]

Big Indian or

Little Indian???

One little - two little - three little Endians -

four little - five little - six little Endians -

seven little - eight little - nine little Endian boys!

[Consort]

The Dozenal Society explores dozenal arithmetic and tell about the advantages of base 12 on their Web sites.

[XEHRpa]

I went to their site, and am still trying to find where they actually say WHY it's better. But I took a stab in replies 87-88, which describes why it may have been historically preferable in a world of integers.

[Consort]

American Dozenal Society. Click on "FURTHER INFORMATION" at the bottom of the first page.

[XEHRpa]

Thanks. From the referenced page:

The primary advantage of 12 over 10 is that you cannot take a 1/3 or a 1/4 of 10 and get an even number, whereas, you can with 12. Nor can you write a third of 10 as a decimal. The number goes on forever, 3.3333. . . Being able to take a third and a forth of your base number and get an whole number is very handy. A secondary advantage is that 12 has more divisors, 1, 2, 3, 4, 6, &12 verses 1, 2, 5, & 10 for 10.

This hits on what I said, plus the fact that the numbers 60 and 360 takes it up another notch (as Emeril might say). POW!

[SunkenCiv]

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[SunkenCiv]

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