Meaningful Number Coincidence

I have long been fascinated by the connections as between the two vowels I and O (as used in the English alphabet) and the two numbers 1 and 0 (which have a close structural similarity).

I is the 9th letter of the alphabet, whereas O is the 15th.

Now it is interesting how I as a pronoun is used to refer to the personal self. 9 as a number serves as a powerful symbol of integration (and indeed is the basis for the well known Enneagram personality system).

9 in the denary system relative to 10 is - 1. Now the negative direction psychologically is towards the unconscious (which is the basis for integration). The positive direction by contrast is towards the conscious (which is the basis for differentiation).

Now the importance of 9 can be understood more clearly when expressed in binary terms.

9 is then 1001. This is indeed a palindrome (reads the same in either direction). Indeed we could say that a palindrome is a mirror reflection of itself. As an integrated personality is likewise a mirror reflection of itself, number palindromes serve as important symbols of psychological integration.

1001 (i.e. 9) also is interesting in that that it contains both two 1's and two 0's. It is thus balanced in this sense.

By contrast differentiation involves taking a psychological direction to its extreme. In numerical terms this ca be expressed by ordering the digits in both ascending a descending order of importance.

Thus in ascending order we have 0011. In descending order we have 1100. Now when we get the difference of these two numbers (i.e. 1100 - 0011) we once again obtain 1001.

Now this numerical sequence symbolises perfectly a dynamic model of integration. Opposite characteristics of personality should first be clearly differentiated. Then these opposites should be recognised as complementary (which is integration).

Remarkably these very characteristics are inherent (in quantitative terms) in the number 9 (expressed in binary terms). Indeed it is the only number (in binary form) that possesses these unique characteristics.

Interestingly another fascinating number (with remarkable properties) is 153. Indeed it features in the Christian Gospels (because of its alleged mystical qualities). In binary form it is in fact written as a double 9 (10011001).

Now 9 has in mathematical terms certain unique properties. For example if the sum of digits of a number is divisible by 9, then the number itself is divisible by 9. For example the sum of digits of 153 = 1 + 5 + 3 = 9. This of course is divisible by 9 so therefore 153 is divisible by 9 (= 17).

Also if we take any number and then write down its mirror reflection or reverse (i.e. its digits written in opposite sequence), and then obtain the difference of these two numbers then this number will always be divisible by 9. Remarkably the resulting number will always show distinct palindromic tendencies (i.e. either be a palindrome or very close to a palindrome).

So I have just got 319724 (from a random number generator). The reverse is 427913.

The difference 427913 - 319724 = 108189. When divided by 9 this yields a palindrome i.e.12021.

Now once again 9 represent the negative direction of 10 ( - 1) and is symbolic of the unconscious process of integration (where there is no division between polarities).

11 represents the positive direction of 10 (+ 1) and is symbolic of the conscious process of differentiation (where positive and negative polarities are separated).

This again is remarkably replicated in number behaviour.

If a number has an odd number of digits then the difference of this number and its reverse will always be divisible by 11.

However if the number has an even number of digits then the sum of this number and its reverse will always be divisible by 11.

Now the number 319724 (already mentioned) has an even number of digits. Therefore the sum of this number and its reverse is divisible by 11.

319724 + 427913 = 747637. When divided by 11 we get 67967 (which again is a palindrome!)

The implication of this is that when a number has an odd number of digits the difference of this number and its reverse is always divisible by 99.

The number 9 has also close connections with another fascinating class of numbers dating from the Pythagoreans called amicable (or friendly) numbers. These numbers usually appear as pairs (or triples).

With amicable pairs the sum of divisors of each number is equal to the other number in the pair.

220 and 284 represent the best known amicable pair.

The sum of divisors of 220 = 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284.

The sum of divisors of 284 = 1 + 2 + 4 + 71 + 142 = 220.

Now the sum of amicable numbers is nearly always divisible by 9. For example 220 + 284 = 504 (which is divisible by 9). There are some rare exceptions to this rule (Like people, some numbers apparently are more friendly than others!).

Again I is the 9th letter and O the 15th letter (in the English alphabet).

Now we can demonstrate a fascinating connection between these numbers.

Once again the binary conversion of 9 is 1001. Now as well as a horizontal mirror image number (i.e. its reverse) we can obtain a vertical mirror image number. This is obtained by simply exchanging binary digits. The "lower" 0 now becomes the "higher" 1; the "higher" 1 becomes the "lower" 0.

Thus the vertical mirror image of 1001 is 0110 (i.e. 6). The sum of these = 1111 which in denary terms is 15. Thus O as the 15th letter of the alphabet is complemented in binary terms by a number comprising a repetition of the digit 1.

Thus the vertical mirror image complement of 9 is 6. Amazingly the very symbols we use for 9 and 6 are literally vertical mirror images of each other!

6 in fact is the best known example of another fascinating class of numbers studied by the Pythagoreans (viz. perfect numbers). 28, 495 and 8128 are the next three perfect numbers. Perfect numbers are the sum of their own divisors (not including the number itself). Thus 6 = 1 + 2 + 3.

Ken Wilber in Sex, Ecology and Spirit, in quoting Ramana refers to the pure fulfilment of causal emptiness as the I-I state. In other words all phenomenal polarities have now dissolved so that the witnessing self is inseparable from all that is witnessed.

Now this state can equally be expressed in terms of the qualitative binary system

Where it is accurately referred to as 1-1. Just as in quantitative terms 1-1 = 0 (i.e. a state of static emptiness), likewise in qualitative terms 1-1 = 0 (i.e. a state of dynamic emptiness or pure potential.

Thus the empty causal state represents in terms of dynamic experience the negation of all rational form (1) which is 0 (i.e. a state of pure intuitive emptiness).

A fuller expression of the causal state of emptiness would involve both the alphabetic formulation (I-I) and the digital formulation (1-1) which appear so similar to each other.