Numberphile: '60'

[pokerfan]

The ancient Babylonians used a number system with base 60 (sexagesimal). Tablet image courtesy of Bill Casselman and Yale Babylonian Collection

Sixty is the smallest number divisible by the numbers 1 to 6. (There is no smaller number divisible by the numbers 1 to 5). 60 is the smallest number with exactly 12 divisors.

The Babylonian number system had a base of sixty, inherited from the Sumerian and Akkadian civilizations, and possibly motivated by the large number of divisors which 60 has. The sexagesimal measurement of time and of geometric angles is a legacy of the Babylonian system.

[Blues Heron]

1. very cool! here's a nice discussion of this tablet

at this link

http://johncarlosbaez.wordpress.com/2011/12/02/babylon-and-the-square-root-of-2/

[ProdigalJunkMail]

2. very cool...

but not base 60 in the classic sense...


The marks he made were still base10...


sP

[Orrex]

3. I suppose that this proves that Babylonians had 60 fingers

Or 30 at least.

Or maybe 6.



Very interesting, all the same!

[laconicsax]

4. I'm not terribly impressed by their ability to count to 60 on two hands.

I have a system to count to 100 on two hands that I've been using for about seven years.

[pokerfan]

5. I can count 1023 using two hands

[laconicsax]

6. I can multiply any two numbers with two hands...

And what's multiplication if not just fancy counting?


http://www.smbc-comics.com/index.php?db=comics&id=1914

[pokerfan]

7. multiplication is repeated addition...

smbc is great....

[laconicsax]

8. I had a good time looking up tetration last night when I read that one.

Stupid Wikipedia telling me that repeated tetration is actually called pentation and repeated pentation is hexation.

[daaron]

9. If a 4-shot espresso is a 'quad'.

What's a 6-shot espresso called?

A 'sex'! (Or a 'hex' - same thing).

[laconicsax]

13. I think it's called "rocket fuel"

I'm addicted to caffeine just like everyone else, but you have to draw the line somewhere...

[marble falls]

10. I like it a lot, it had a great beat and I can dance to it, I'll give it a 59.

[htuttle]

11. That's Numberwang!

[FreeBC]

14. /golfclap

[daaron]

12. 6 is the product of the two smallest prime numbers.

60 is two times the product of the three smallest primes (2*3*5 = 30).

Whoooaaa... Heavy, man.

Dig it in binary:

1*(2^5) + 1*(2^4) + 1*(2^3) + 1*(2^2) + 0*(2^1) + 0*(2^0) = 32 + 16 + 8 + 4 = (111100) base2

What's a left bit shift? Oh yeah, multiplication by 2:

1111000 = (120) base10

Like wow, man: (2*2*2)*(3*3)*5 = (2^3)*(3^2)*(5^1) = 8*9*5 = 8*45 = 360.

It must mean something.

[napoleon_in_rags]

16. It all means something.

"We are the music makers, we are the dreamers of dreams" -Willy Wonka.

In a long ago post I talked about set numbers, how any set of integers can be encoded in an integer, (sum(2^n for each n in set)). 60 is set number for {2,3,4,5} all the numbers up to six, excluding 1, 0. 10*6 = 60. So in this context I just made up, 60 is significant in that regard. But the real significant thing is that there are infinity of such systems where 60 is significant in its own way. Its all about what we put into it.

2+3+4+5 = 14, the fourteenth card of the Tarot:
http://en.wikipedia.org/wiki/Temperance_(Tarot_card)

In gematria, the significance of the number 60: (note 4th definition)
http://www.billheidrick.com/works/hgm1/hg0060.htm

[daaron]

18. Yes. It all means something.

Unfortunately, what that something is is utterly opaque.

[FiveGoodMen]

19. But since we don't understand the question...

...42 is all we've got.

[napoleon_in_rags]

20. The Information Age was born when meaning was discarded.

I mean really literally, they divorced message meaning from the bits and bytes needed to transmit it, and that was it. The thought doing that is so second nature to us today, but it was conceptually tough back then. Meaning is just a map from the bits and bytes of our experiences to some other proverbial bits and byte in our heads, and that map is different for different people, and I don't just mean "yo" to a rapper and "yo" to a Spanish speaker, I mean different to everybody, in more subtle ways. We literally create meaning by creating that stimulus response map in our heads.

So what did I say? Oh yes, temperance. Um, wikipedia:

Some Jungians say that Temperance represents the unconscious, which can guide us, they contend, to a deeper understanding of ourselves. The one foot on the land, the other in the water, represents the unification of the external and internal, conscious and unconscious, realms.

Yes, know thyself, the unification of conscious and unconcious mind. That's what I'm talking about. My meaning was that meaning can be created, and generally is, but at a subconscious level where we don't see it, so we consider meaning to be an absolute an external phenomenon when it is actually a totally internal one, unique to ourselves. Yeah, that's what I meant. I wasn't just drunkenly babbling bullshit, I swear!

Honest.

[napoleon_in_rags]

15. They did great work with pi too.

All lost to Europe during the dark ages. Reminds of of the tenuousness of knowledge, we would do well never to forget.

[pokerfan]

17. They certainly got the ball rolling

and came up with a value of 3.125 or 25/8.

The ancient Babylonians generally calculated the area of a circle by taking 3 times the square of its radius (pi=3), but one Old Babylonian tablet (from ca. 1900-1680 BCE) indicates a value of 3.125 for pi.

http://ualr.edu/lasmoller/pi.html

A good book on the subject is Beckmann's History of Pi is terrific and includes the black hole of progress in pi (and most everything else) from the Roman Empire to the Renaissance in a chapter aptly called 'Night.'