The Golden Ratio and the Cross and Triangle of the Golden Dawn

If you've studied the Golden Ratio, you know that it is the most pleasing ratio to the human eye. Studies have been done that asked participants to choose the rectangle they liked the most, and they would almost unanimously choose a Golden Rectangle. I've even seen a fascinating study in human sexuality that showed that people with bodily proportions that are closest to the Golden Ratio are the most sexually attractive. On the flip side, body shapes that were exactly the Golden Ratio seemed alien and weird to subjects, as they are too perfect.

The Golden Ratio, also referred to by the Greek letter Phi, is a ratio that is found all through nature. It can be found in the spiral of a seashell, in many flowers and plants, as well as all over the human body. It can be found within many geometric shapes including, but not limited to, the ratio of line segments upon the pentagram. It is one of the most important concepts in the field of sacred geometry.

I was recently analyzing the Cross and Triangle in the context of looking for the Golden Ratio, as the figure seems pleasant to look upon, and so I presumed it must be present. I was delighted to find that my hypothesis was correct. At first I made some technical drawings, made some measurements, and found that according to my measurements the ratio of the height of the cross to the side of a triangle was the close to the Golden Ratio. Then the hard part was creating a mathematical model that more clearly demonstrates the presence of this Divine Proportion, which just required some initial creative thinking and a bit of trigonometry.

The model I'm using is one based on the cross being a sort of cubical cross (if you fold it up it forms a cube), otherwise known as a calvary cross of six squares, relating to Tiphareth via the number 6. This cross is then made to fit the borders of the triangle to the fullest, where the corners of the cross just touch the legs of the triangle, and the base of the cross is collinear with the base of the triangle. As such:

I then padded the cross with more squares and used the side of one of the squares composing the cross as the base unit for measurement. This is how I was able to calculate the size of the triangle, and various divisions therein, in respect to the cross. As such:

I then extracted the triangle formed at the bottom left vertex of the triangle from the extrapolated rectangle. Based on the fact that the height of the triangle, or the vertical leg, is 3 squares high, we can use the value of 3 units for that leg. The angle of the triangle vertex is 60 degrees, as it is the corner of an equilateral triangle. As the cross meets the triangle at 90 degrees, we can further derive that the top angle of this triangle is 30 degrees.

The rest is all trigonometry.

With these calculations, we can fill in the diagram with all lengths.

From the diagram with all the values, I think you can see where I have pulled the following values for the ratio of the side of a triangle to the height of the cross. Phi, the funny looking Greek letter if you're not used to looking at the characters of the Greek alphabet, is the character associated with the Golden Ratio.

So there you have it. The Golden Ratio (Phi) is approximately 1.61803, and the ratio of the side of a triangle to the height of the cross is about 1.61603. They are not EXACTLY the same, but they are super duper close. Make the triangle just an eency weency bit larger and you would have a more precise cross and triangle. Then again, I'm not sure we can get more exact than to 2/1000ths of a unit difference with tools we'd be using to make them.

The Efficacy of Revealed Truths (or Falsehoods)

This post is primarily going to focus on the distinction between a magician who has trained their rational mind, and one who has trained their mind to believe anything it experiences as reality. Something I have sought to maintain in my practice, and have encouraged in my peers and students, is seeking something more than a mere personal truth in my aspirations: objective truth.

The fact of the matter is that something can sound really good in your own head, yet when you speak of such things to others they make absolutely no sense at all. There is of course the possibility that the people you are talking to in such cases aren't competent enough to grasp the concepts you are laying in front of them, and no doubt the arrogant man will think this the case even when it is clearly not.

The same can be said of magical rituals. If a ritual works for you and does not work for anybody else, given the same degree of understanding and competency in the underlying energies and formulas and the will to make use of the ritual, then it probably isn't being properly communicated, as there must be some assumption made on the part of the person transmitting such a teaching upon what probably seems obvious to them. The other possibility is that the ritual really does nothing at all, and the person who believes in it has programmed a state of self-delusion through repetitive practice.

In another sense: if a ritual works and then another person, or group of people, is given the same ritual and then it no longer has any potency, then it never was a proper ritual to begin with. There has been some recent statements on the internet that making rituals publicly available somehow makes them therefore no longer effective. This is based on a false assumption that magic only works if nobody else is using the same names and ritual formulas. While I'm not personally a fan of making all things available to anyone and everyone that wants them, just because they want them and not because they have proven their understanding of the rudiments necessary to do something useful with them, said rituals and teachings should remain effective for those that do understand them even when they are in the possession of those that perhaps do not.

The proof that this assumption is false can be formed by anyone who has performed a ritual that is in the public domain. Certainly the most popular of the Golden Dawn rituals that has leaked out even beyond Golden Dawn style groups would be the Lesser Banishing Ritual of the Pentagram. Anyone who has devoted the time and energy to practicing this ritual, attaining a proper understanding of the symbols, names, and colors used in the context of the ritual, and has taken the time to really allow their consciousness and state of being to be transformed by this rite know that it still works, despite it haven been published in countless books and websites.

If something works, then it works. We could also look to all the mathematical and scientific methods that have been published in countless ways. Despite these ideas being given unto the masses throughout the entire world, they still work. I can add 2+2 in China and it will equal the same 4 as it does in America. I can measure the mass of an object in South America or on the moon, and it remains constant. I can do an LBRP, you can do an LBRP, and someone we've never met can do an LBRP, and the methods when properly employed STILL WORK.

Isis was Published on the Walls of Ancient Egypt, yet Still Serves as a Powerful Spiritual Archetype Even Today

The same can be said of the Neophyte Initiation. While there are slight variations of the 0=0 Initiation Ceremony from Golden Dawn order to Golden Dawn order, they are all still effective in the hands of a properly trained Hierophant even though Israel Regardie published one form of the ritual decades ago. Any Neophyte who has been properly initiated can tell you this.

The same truth I'm trying to express here can be seen by the masses of religious people throughout the world. If you are of X religion, you are certainly taught names of your god(s). These names are generally not a secret, with few exceptions, but are specifically transmitted to people of that given faith. The same can be said of prayers and methods of praying. Do the Divine Names, prayers, and praying methods become less effective as more people use them? I don't think so. In fact, an argument could be made that they probably become MORE effective, assuming they were worth anything to begin with.

I firmly hold that for someone to ultimately be successful on this path of the Golden Dawn, that one must develop a strength in both hemispheres of the brain and balance between the left and the right. The two extremes of one or the other are not good. Unbalanced intuition creates a state of mind where a person believes everything they experience to be the ultimate truth and the fullness of reality, with little or no care for tradition and objective reality, tradition, or known truths. Unbalanced logic would be likened to an armchair magician, and I don't think I need to explain the shortcomings of such an individual.

In my opinion, the perspective that "magic" only works when the techniques are kept secret to a select few is based on a foundation of mental imbalance. I think it is extremely easy to convince ourselves that we are supremely powerful magicians if we cut ourselves off from the outside world, cut ourselves off from reality. When our magic only appears to work when nobody is aware of it, I tend to think this is actually a state of delusion and is an imbalance in intuition.

The fact of the matter is, even with Golden Dawn teachings and rituals being published, only the people who are actually doing the work are going to understand it anyway. Thus the teachings still remain secret, behind of veil that can only be parted by the diligent, hidden in plain sight for those with eyes to see and those with ears to hear.

The Ruby Tablet

A quick post to make you aware of a wonderful effort by Darcy Kuntz. The Ruby Tablet, an online magazine featuring reprints of articles from esoteric magazines and journals from the past with the intention of covering Alchemy, Hermetics, Kabbalah, Enochian, Rosicrucian etc. This first run is a trial and is donation based. There is a link where you can donate what you think the magazine is worth to keep it running. The Golden Dawn Research Trust has gone to great lengths to see that more than just the Regardie black-brick is available for the independent student and temple; and is well worth your time and donation.

Thoughts on Numerology

Pi - Max and Sol discussing numerology

I am a mathematician, and as such I have always been drawn to the esoteric study of number. To my delight, I have directly experienced the power and objective nature of the quality of numbers and have led others to these same experiences. I have a firm belief in the spiritual power of numbers.

However, I start to sway my acceptance of occult practices of number once they start jumping to conclusions with erroneous or entirely missing logic. I truly believe that all things, when properly understood, can be understood through the lens of logic. Additionally, I have sought to uncover universal truths with my work in numbers.

17 = 8 ???
ummm.... no

Reduction of numbers is not a system into which I place any confidence. In fact, the more I read on the subject and the means authors have come to their conclusions, the stronger my opinion that it is an illegitimate form of sacred mathematics. The problem is that so many place this as the core of their practice in numerology for no apparent reason.

Reduction of numbers is simply this: if I have a number such as 63, the idea is that this number is also equivalent to 9 because 6 + 3 = 9.

However, this does not work in other numeric systems. Take 63 as a binary number.

BINARY

63 base 10 is the same as 111111 base 2.

Yet the addition of 1+1+1+1+1+1 in binary yields 110 (6 in decimal). Yet this practice always calls for a single number, so lets further break it down to 10 (2 in decimal). Again we reduce this number down to 1 (1 in decimal). At no point was calculated a form of 9, which was arrived at by reduction of the decimal form of 63 by reducing the binary equivalent. In fact, by reducing any binary number down to a single digit, you will always arrive at 1.

HEXADECIMAL

Take this same number to a higher base, say hexadecimal (base 16), and you will arrive at yet a different conclusion. 63 in hexadecimal is written as 3F. Adding thus yields the result: 3 + F = 12 (18 in decimal). By further reduction 1 + 2 = 3 (also 3 in decimal). Again, no output of 9. Reducing any hexadecimal number down to a single digit will offer 15 possibilities (because you won't reduce down to 0).

Conclusion? Reduction of numbers is completely different, depending on the numbering system you are using. Further, there is no real connection between the number 17 and 8, for example, because 8 is incomparable with 17. 8+8 = 16, likewise 8x2 = 16. 8+8+8 = 8x3 = 24. 17 is no multiple of 8.

However, 63 does have a relationship with the number 9, but not because of number reduction.
9+9+9+9+9+9+9 = 9x7 = 63. The number 63 could equally be said to have a relation with the number 3, 7, and 21, and this is a truth that permeates even the base of the number system being used.

In my opinion, the reduction of numbers is based on a misinterpretation of modern numbers using a primitive structure of math. Nowadays, we have a system of numbers that has placement value. In other words, the 3 found in 103 is 3 x 1, because the first number has a placement value of 10^0 (which is 1). The 1, while the digit itself is less than 3, actually has a greater value because of its location on the number, being in the hundreds place or 10^2, meaning 100. This is actually a very modern innovation in mathematics that is brought to you by the number zero, which serves as a placeholder.

Cuneiform Numbers

Prior to modern mathematics (we've been using zero in the context we are today for only a few hundred years) numbers were arranged and interpreted quite a bit different. There was no place holder, so numbers were usually determined by what was present, by adding all numeric symbols present representing the whole number. This was true of Babylonian Cuneiform, Egyptian Hieroglyphics, Hebrew and Greek numbering systems as well as others.

We don't use this system anymore, and a number written in modern time has a specific context in which it is written. It is erroneous to assume that 10 = 1 on the terms that 0 has no value. Beyond this, 10 is a specific number with its own value and energy. Aside from the erroneous nature of this practice, there is no need to reduce the number.

BIRTH DATES

However, while this practice is certainly not based on universal truths, I am willing to admit there is a possibility that this practice has its place within minds that have been conditioned to be affected by these numbers in these ways. Birth dates are a major part of numerology, in particular the reduction of birth dates. For example, someone born on April 24th would be a number 6 (2+4=6), and this would in theory say something about a person's personality.

I think the only way this could be possible is if we are talking about a person that lives in a society whose main numeric mode is the decimal system, and historically this has not always been the case. Additionally, these numbers have to be something they observe. I think the date of birth in the context of their numbers only has an affect on a person in as much as it is a number which they celebrate every year, and not all cultures do. I believe if this is true that a person could be lied to about their birthday their entire lives and that corresponding number would then be the one in question affecting their psychological makeup.

While I believe in the possibility, I think it is also a bit of a stretch to narrow down to a mere 9 personalities, even down to 31. I still place no confidence in the reduction of numbers, but I can see how on an unconscious level a mind might under certain circumstances interpret 24 to be 6 and how that could affect the psychological makeup on a subtle level if and only if one were to regularly identify with that number. It certainly is not a universal or consistent truth (is it even a truth at all then?), so it is of little use to me.