Why Ten?

http://www.aish.com/spirituality/kabbala101/Kabbala_4_-_Why_10$.asp

This article is a bit confusing to me. It attempts to explain the foundation for the use of the number ten, as opposed to any other number.

What I did find interesting is that methematically, 10 is a "perfect" number not only because our numbering system is base-10, but also because 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 = 5 + 5 = 10.

To view the ten branches of the Tree of Life as "utterances", as opposed to simply "levels", makes more sense later, when he talks about "the deed" of creation. This article more or less lays a foundation for broader discussion.

http://www.tarotforum.net/showthread.php?t=92819

That's a nice link you give, kilts_knave.

Mathematically, by the way, 10 is not a perfect number, but rather a deficient number, in that its factors add to less than the number itself.

To take the triangular number of side ten (resulting in fifty-five), and then to use a base-10 representation of the total, reducing its representation by adding the digits used to return to ten, is all certainly very interesting, of course.

My guess is that had we evolved with a thumb and three fingers on each hand that we would be using base 8, we would regard that as a perfect number, intimately bound up with the very nature of divinity, and we would have amassed many thousands of years worth of explanations why that was so.
Our math would look a little different but it would work.

Additions of all the numbers of a base

"1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 = 5 + 5 = 10"

A few years ago I fiddled around with the properties of addition sequences such as this. With all the Even numbered bases (ie. 8, 10, 12, 78), what you wrote above is a fundamental property as far as I can figure (there are a few other interesting properties, but I'm not sure if others would care and can't remember them off the top of my head). The result of such additions as the one above will always be a "two digit" number each of which digits are the same ('5' and '5' in this case) and add up to the number of the base ('10' in this case). I worked out an equation after high school, but don't have it handy at the moment (later, I discovered the same equation in the first pages of a Dover advanced math book).

Take base 8 for another example: 0, 1, 2, 3, 4, 5, 6, 7, 10 (the '10' is used to represent '8' in a base 8 system - it signifies going up a digit the way the '1' followed by a '0' signifies going up a digit in base 10).

1 + 2 + 3 + 4 + 5 + 6 + 7 + 10 (8) =>
1 + 7 = 10 (8)
2 + 6 = 10 (8)
3 + 5 = 10 (8)
10 (8) = 10 (8)
and, 4 is left over.

Summing all of these, you get '44', and 4 + 4 = 10 (8)

Thank you JMD. I just googled "triangular number" and saw one of the equations I figured out on wikipedia. I also found some of the "perfect number" article interesting.

http://en.wikipedia.org/wiki/Perfect_number#Even_perfect_numbers
"other wrong assumptions were:

The fifth perfect number would have five digits in base 10 since the first four had 1, 2, 3, and 4 digits respectively.
<...>
The fifth perfect number <...> has 8 digits, thus refuting the first assumption."

Though it does seem likely kilts_knave is not using "perfect number" in the technical sense (pointed out to me).

jmd said:

Mathematically, by the way, 10 is not a perfect number, but rather a deficient number, in that its factors add to less than the number itself.

Click to expand...

I didn't really understand the mathematical or technical meaning of the term "perfect" (hence the quotation marks) when I referred to the number ten, above. Whoops.

But if this what you're talking about here, as with Pythagorean numerology, it may be a bit like comparing apples & oranges.

bradford said:

My guess is that had we evolved with a thumb and three fingers on each hand that we would be using base 8, we would regard that as a perfect number, intimately bound up with the very nature of divinity, and we would have amassed many thousands of years worth of explanations why that was so.
Our math would look a little different but it would work.

Click to expand...

And the 12 system (inches, pounds shillings pence - yes I am that old) seems to relate to a 'finger' counting system of using the thumb (so that's not counted as it is the 'counter') on each joint of the finger. One hand = 12 on the (say) left, then one joint on the right = 12, 2 joints on the right 24, plus one finger and one joint on the left, = 28 and so on.

Perhaps this is where we get that 3 and 4 and 3/4 are so important to us?