Decoding the "Ghost Whisperer" crystal ball puzzle

This puzzle is actually a function of number geometry, or "gematria" as it was originally developed by Pythagoras and preserved in the Hebrew Kabbalah mystery school.  Notice in the puzzle that all multiples of 9 are the same symbol. Then notice that when you take any other 2-digit number, add its digits together and subtract the result, you will still have a multiple of 9.  So, multiples of 9 are the only possible result while assigned only one symbol (the one you are expecting). All of the other symbols are just random filler to distract you.

Most mathematicians and scientists would just blow this off as an "quirk" of numbers, but it is actually an important properties of harmonics expressed using numbers.

In the book I discuss a ratio found in the 15th century Rosslyn chapel in Scotland which I named the "magic number." This is expressed as 1:81 = 1 / 81 = 0.012345679012345679...

The number 81 is a multiple of 9 and also sums together into 9.  When it is divided into 1, it creates all the other digits.  This is what you are seeing in this "8-ball" puzzle. You are seeing the periodicity of an octave (8) relative to the unison (1) expressed in the harmonic geometry of numbers. This is found in mathematics wherever periodicity is present, such as the fact that all "sphenic" (or square-free) numbers - those numbers which are the product of three distinct prime numbers - have exactly 8 divisors.

From this we see that the numbers 1 and 8 are the engine behind the square of 3, or resonance in 3-dimensional space. In other words 2^3 (=8) is the complement of 3^2 (=9) just as odd and even numbers are complements. This is a first principle of countability, which is why the triangle is so critical to structural stability and why triads work so well in music harmony.

As I explain in my book, the 9th partial (and its multiples) in the harmonic series is the only harmonic that synchronizes perfectly with all of the golden ratio amplitude proportions of the fundamental.  It does not matter what number base you operate in, the synchronization of 9 (or 81) with 1 is a fact of physics. It acts as an axis of stability around which a standing wave vibrates whether we're talking about sound waves, electromagnetic waves, atoms, the solar system or life.  Don't let anyone tell you it is just a silly trick of numbers.  Only the puzzle is a trick while the principle behind it is a profound truth.