Derivation of the Zodiac from Pascal’s Triangle.
An exploration of the zodiac as a infinite pattern of expansion spiraling though space & time.
Doubling Theorem from Pascal’s Triangle
Adding each row creates a doubling theorem, one of the most basic forms
of exponential growth.
Fibonacci Sequence from Pascal’s Triangle
Adding each diagonal creates the Fibonacci sequence. The Fibonacci sequence represents one of the fundamental structures of spirals in nature. It relates too the golden mean spiral and is one of the most prevalent mathematical patterns in nature.
Repetition of the formulas.
Both sequences go into infinity, but have a pattern that emerges with their last digit. The doubling theorem creates a repeated pattern of 2 4 8 6. The Fibonacci sequence creates a pattern that is 60 numbers long.
What does it mean?
The real magic comes when we put these two repeated patterns on a circle. A pattern is created that matches up perfectly with all of the principles of the zodiac; modalities, elements, and polarities.
Modalities are three types of expression; cardinal, fixed, and mutable. The modalities in the zodiac match up with the Fibonacci sequence. Here there are four 0’s and eight 5’s. All perfectly placed. Every transition of 0-5 lines up to a cardinal point, every transition from 5-5 is fixed, and every transition from 5-0 is mutable.
The elements – earth, air, wind, and fire – correspond to the pattern we see from the doubling theorem. By looking at every 5th iteration, those that match up with the 0’s and 5’s of the Fibonacci sequence, we will see the exact pattern of the elements. Just like fire earth air and water repeating themselves around the zodiac, so does 2,4,8, and 6. (*I will note here that while the doubling theorem starts with a “1” this is replaced by a 6 after the first cycle and maintains a 6 into infinity.This is reflected in the diagram.)
Finally, we have polarities. The opposing poles of the chart wheal provide complementary elements to each other and in essence complete each other.. If you add up any two numbers diagonally they equal 10. This works for the Fibonacci sequence or the doubling theorem. It is a perfect mathematical representation of this dynamic. (*The exception is for for 0 and 0, of course, which show up matched up in the Fibonacci sequence and represents the start of each new cycle of modalities.)
“A pattern is created that matches up perfectly with all of the principles of the zodiac; modalities, elements, and polarities.”
We are spiraling though space and time. Contrary to common visual models of our solar system, we are not simply rotating around the sun. We are moving forward with the sun in a giant spiral which maintains a fairly consistent orbit. Pascal’s triangle is a simple mathematical array of binomial coefficients that has been studied for thousands of years. While there are many patterns and properties hidden inside, two properties provide a summation of the triangle itself at every new iteration. The horizontal and diagonal summations creates doubling equation and the Fibonacci sequence, respectively.
The Fibonacci sequence represents the basic patterning hidden behind spirals in the known natural world, and the doubling equation is one of the most basic examples of expansion in natural world as related to life.
So imagine, we are not rotating around the zodiac, instead we are spiraling though time and space and the equations that we are spiraling though create the pattern of the zodiac into infinity. This is similar to, yet slightly more complex, as the spiraling of petals on a flower or rings of a pinecone based off these fundamental principles. To phrase another way, at each moment we are at a different stage of this pattern, built off of Pascal’s triangle, and are affected by the energies of that vantage point.
The pattern itself perfectly matches the basic mathematical properties of elements, modalities, and polarities by which the zodiac was created; and is reflected in almost every known pattern in the natural world.
This is a diagram of a sprial, showing the last digit of the data points for every 5th iteration, or line, of Pascal’s triangle. When combined we see that they the create the same zodiac energy in the same spot of the sprial into infinity.
For years I looked to discover a theoretical basis for the 12 signs. They didn’t just come out of know where. Right? Over a few years of studying sacred geometry and astrology this theory slowly came together, and finally snapped into place in one very exciting afternoon. What is so fundamental about this? We are not rotating around the zodiac. Instead the zodiac is a code built into the nature of spirals. It reflects physical reality and extends a bridge to the philosophy of astrology. Furthermore it assumes constant evolution of the zodiac without the structure itself changing. This is fascinating because it says why we are affected by the energy. Its not just some cosmic wind that blows by, it is a fundamental shift of everything around us as we go though each phase of the cycle of our planet, spiraling though space & time. I will get into exactly why other planets might affect us as well in later blogs… Stay Tuned!
Want to stay up to date on articles and workshops?
Subscribe to my Awesome Newsletter.