Revisiting the Equations of Magick - Babalon Rising 2026

This is the third of four presentations I offered at the Babalon Rising Festival this year. It is based on a updated version of this post from back in 2008. This material will also be found in my new book Thelemic Sorcery, which I am currently in the process of writing.

Decades ago, I once asked a much more experienced magician who I had a lot of respect for what the limitations of magick were. The answer I got was something to the effect of “Well, does it have any limits?” There may be a sense in which that answer is true, since given nearly infinite time the probability shifts created by magick might allow us to do almost anything. However, it was an answer I found entirely useless. Real things have limits – this is precisely the point of the physical sciences – and understanding those limits is how we understand all phenomena. We cannot assume the omnipotence of the mind without any evidence, and likewise we cannot fall into the common skeptical assumption that if you can do anything paranormal you must be able to do everything that could possibly be described as paranormal.

That conversation proved valuable in motivating me to embark on my own exploration of magick’s exact practical limits One thing we do know is that numerous factors go into figuring out how successful a magical operation will be. One of the early attempts to quantify those factors was a series of equations published in Peter Carroll’s 1992 book Liber Kaos. The chaos magick movement in the 1980’s and early 1990’s represented a significant step forward for practical magick. Peter Carroll and Ray Sherwin first broke magick down to what they considered its essential components. They then approached magical experiments in a scientific way – or at least as scientifically as was practically achievable. Liber Kaos was released around the same time as my fateful conversation, and it proved to be a good starting point for my paranormal research.

Peter J. Carroll passed away on April 22nd of this year at the age of 73. I submitted the proposal for this talk prior to that date and had no idea that he would have passed by the time I would be presenting it at Babalon Rising. While the central thesis of this presentation has to do with places where I disagree with his formulation of magick, it is important to note that he was a true pioneer in this area. Prior to Liber Kaos nobody had ever even floated the idea of probability equations for magical operations. Without his work I would have had nothing to build on, and might never have arrived at any of these revisions.

Too many modern practitioners talk about the “chaos” in chaos magick as something akin to “anarchy.” But while the chaos magick system does reject hierarchy, the original meaning of the term referred to chaos theory, an emerging branch of mathematics. Chaos theory describes systems with arbitrarily large degrees of freedom, independent variables that are nonetheless loosely interlinked. Phenomena that conform to chaos theory principles operate as if any point in this network can act as a critical point, at which a small probabilistic influence can propagate itself into a much larger overall effect.

As it turns out, most natural systems, from living organisms to weather, tend to operate in this way. The point of chaos magick is that a small probability shift directed at the right critical point can produce large-scale effects. The classic example of this is called the butterfly effect, so named because according to chaos theory, a butterfly flapping its wings can influence the atmosphere such that a storm could develop on the other side of the world a few weeks later. This does appear to be a basic, foundational principle of how magick works. The simple probability shifts produced by psychic forces are small enough that they are hard to measure in simple experiments. They require amplification across an interconnected system over time to reach their full potential.

One of the main methods of chaos magick, sigil work, is adapted from the works of Austin Osman Spare, a magician and artist who originally studied magick with Aleister Crowley. It should come as no surprise that chaos and Thelemic magick are relatively compatible with a few key differences. In many ways chaos magick works like a simpler version of Thelemic sorcery, which is not surprising given that Crowley also experimented extensively with practical magick. Independent verification of those results in the context of more recent experimentation suggests something akin to consistent underlying principles.

Carroll’s first equation is written thus:

M = GL (1 – A) (1 – R)

All values on the right side of the equation range from 0 to 1. M, the magical effect, is obtained by multiplying G, gnosis, times L, the magical link, times 1 – A, conscious awareness, times 1 – R, subconscious resistance. This yields a value for M in the same 0 to 1 range.

Carroll’s second equation is written thus:

Pm = P + (1 – P) M^(1/P)

Pm represents the probability of success, with M from the first equation figured in and P representing the original unmodified probability value.

These equations demonstrate two key properties of magical operations. First off, to obtain a significant probability shift G and L need to be very high and A and R need to be very low. The way the factors are multiplied together means that any deficient factors in the operation tend to compound each other and dramatically limit the effect. Second, increasing the value of P by engaging in all possible mundane actions that will make success more likely is essential to obtaining any sort of dramatic success.

The first problem that I ran into with this construction is the idea that one must almost completely suppress conscious awareness of magical operations in order to make them work successfully. As a person with a nearly eidetic memory, I am always fully aware of my magical operations. In theory, that should mean everything I do would automatically have an M value of 0. However, I quickly realized experimentally that this is not the case. I concluded that the significance of A must have been determined based on an incorrect interpretation of the data behind it.

Carroll’s model of the mind is highly Freudian, positing that the conscious mind is a small subset of our actual cognition. The reason we do not recall our memories all at once is that there is an active process that shuttles information into the conscious mind from the vast unconscious mind. This process prevents us from recalling traumatic memories, acting as a sort of “psychic censor.” This is the result of an error on Freud’s part that has unfortunately permeated all forms of psychoanalysis. The error is easy to see when you understand Freud’s history, but it nevertheless has caused a great deal of mischief in the field of psychology.

Before formulating his psychoanalytic theories, Freud worked with patients using hypnosis. He eventually abandoned that method because he found that the “fixes” it produced for mental illness seemed promising at first but did not last over time. But he also made the observation that patients seemed to be able to recall any event in their lives when questioned about it under hypnosis, whereas they had no such memories when they were questioned while fully awake. Freud concluded that memories were stored in the brain intact, but a “repression mechanism” of some sort was responsible for blocking recall due to traumatic childhood events. The problem is that while he was able to obtain a lot of information from patients under hypnosis, he never checked any of it to see if it was accurate.

It turns out that under hypnosis the brain basically makes stuff up. The mechanism that hypnosis turns off is not repression, but rather the “checksum” or if you will “bullshit detector” that we run against our memories. You likely have had the experience of trying to remember something, recalling something, and then realizing that what you are remembering did not happen the way you are recalling it. That second realization is the process that checks for false memories and blocks them. But if you were directed to recall the same thing under hypnosis, you would just remember it wrong and that memory would now be stored as if it were accurate. This is what happened with many of the “Satanic panic” cases in the 1980’s. Because of how the brain works, “recovered memories” are incredibly unreliable, especially when “recovered” under hypnosis by therapists asking leading questions.

The brain does not store memories in full. It stores key “touchpoints” and then reconstructs the rest of the memory from those points. It then writes the current result back into memory. You may have had the experience of coming across a photograph of an event that you remember from your early childhood. If so, you probably have noticed that some of the details from your memory no longer match the photo. That is because the memory has shifted over time. Because of the reconstruction process memories usually do not remain accurate. One of the reasons that the human brain can hold so much information is that it uses this “good enough” form of encoding.

The Freudian idea of a vast, unconscious mind that we are usually unaware of follows from the assumption that memories are stored intact but blocked by an active process. The problem with this is that modern neuroscience has found no evidence of the Freudian “repression mechanism” or unconscious mind. The brain does engage in a fair amount of unconscious processing, but this processing is related to autonomic functions and conditioning, not censoring contents of cognition. It should be pointed out that the behaviorists who argued that all of cognition was nothing more than a collection of conditioning loops made the opposite error, so neither side of that debate was entirely correct and both reflected the limited understanding of brain processes during the mid-twentieth century.

Carroll unfortunately buys into the Freudian idea of the unconscious mind and equates the repression mechanism with his psychic censor. He proposes that conscious awareness of magical operations must be reduced to bypass this censor and get the objective into the unconscious mind, which does all the actual psychic work of setting the magick in motion. R, unconscious resistance, is formulated similarly, in that the resistance it models resides in this same unconscious realm. But since unconscious processing is just conditioning, not cognition, it is unclear how any of that is supposed to work from the perspective of today’s understanding of the brain.

For this reason, the A and R factors require some revision to line them up with the findings of modern neuroscience. While it is true that you can be aware of magical operations as they are running, you also cannot obsess over them if you want them to work. I have seen many failures along these lines, in my own work and in the work of others. It seems that being overly attached to the outcome of an operation is the real problem, so A should stand for Attachment rather than awareness. It is true that a person who can completely forget an operation runs no risk of obsessing over it, so perhaps this is what was originally observed and misinterpreted.

R requires less revision, in that it works fine if the “subconscious” qualifier is removed. Conditioning loops can create “subconscious resistance,” and in such cases Carroll’s formulation of R remains correct. However, resistance does not just arise from this sort of unconscious processing. Resistance arising from mixed emotions regarding your magical intent is just as problematic. Both types of resistance should be covered by the single R factor. The commonality is incoherence across the magician’s field of consciousness, which limits the development of single-pointed will. That is, it disrupts the clarity of the quantum information transmitted to the target of the spell and therefore reduces the resulting probability shift.

Carroll’s equations completely omit the significance of energy work, which to me is such an obvious part of magical success I have trouble imagining how it could have been missed. For me, when I was first learning ceremonial forms, studying Qigong and integrating those practices into my magick made an enormous difference. For the first time I felt like the rituals were really working, and my experimental results bore that out soon after. If magick is represented as quantum information transmitted to a target, energy work corresponds not to the message itself but to the power with which it is transmitted. As I will discuss in more detail in my talk on Programming the Universe, both of these components are necessary for tangible magical success.

Since energy work represents a factor that does not appear in Carroll’s equations, I represent it as an additional 0-to-1 variable called E for Energy, which is multiplied by G and L. Those three revisions produce my first equation, shown here. It is written thus:

C = GLE (1 - A) (1 - R)

The result of this equation C is called the Casting Value. It represents an overall measure of how perfectly the magical operation was performed.

As in Carroll’s original version, G is Gnosis, the degree to which consciousness expands and shifts. Notable, gnosis does not refer to all shifts in consciousness, but those that manifest in a certain way. Studies of advanced meditators have identified various physiological markers that correspond to the subjective state of Samadhi, “absorption” in English. This is the gnostic state to target for magical success, and this is how mysticism and magick are connected in Thelemic practice.

I once encountered a chaos magician who insisted that all you needed to do to produce gnosis was hyperventilate, because feeling dizzy represented a shift in consciousness. However, I can state from personal experience that dizziness does not make my magick more effective in any way. Assuming this individual made that observation from their own practice, I would assert that they were instead elevating E, since breathing and energy work are closely related, and were simply able to cultivate gnosis due to basic mystical awareness on their part.

L here represents the quality of the magical link to the target of the spell, just as in Carroll’s version. Sorcery employs two kinds of links, similarity and contagion. A similarity link is an image or symbol resembling or representing the target in some tangible way. A contagion link uses something that the target has been in contact with, or part of their body such as hair or fingernail clippings. When casting an operation on yourself, the value for L is always 1.

Once you have calculated C for a specific operation, you then multiply it by S, representing Magical Strength. This value is different for everyone and is based on a combination of natural ability and sustained daily magical practice. This is important because like all human skills, magical ability is a combination of natural aptitude and practice. You do not need to have extraordinary aptitude to get good at magick. It does help, but many people with very high aptitude wind up becoming intuitive psychics and the like because they can get results without any formal technique. That means people with lower aptitude who engage in dedicated practice and training can surpass many natural talents over time.

Magical strength S is measured as a probability value of 1 or greater. A value of 1 corresponds to 1-to-1 odds, that is, pure chance. A number higher than 1 represents the maximum probability shift that a particular magician can cause under ideal circumstances. A value of 10, for example, means that the magician can overcome 10-to-1 odds. That is, they can cause an event that is ten percent likely to occur if all other values in the equation for C are perfect. A value of 100 means that the magician can overcome 100-to-1 odds, that is, they can make an event that is 1% likely occur under such conditions.

Multiplying C times S yields M, the Magical Effect. To determine the likelihood of a given magical action succeeding, divide P, the natural Probability of the event, by M and then express the result as relative likelihood. If the odds of something happening are 1000 to 1 against and your M is 100, the result would be 10 to 1 against. Your operation may still not succeed at that likelihood, but your odds of success are greatly increased. A resulting value of 1-to-1 or greater should guarantee success.

In a group working, calculate M for each member of the group and add those values together for the total shift. The same can be done with spirits called on during the operation. A magician conjuring three spirits would add their own M to that of each spirit, so if all involved have M values of 10, the total M would be 40. Two magicians with M of 10 working with the same three spirits would have a total M of 50, and so forth. It is important to note that gnosis G will be the same for all magicians in the group working, and it usually declines when multiple magicians are involved just because some effort and attention is taken up by keeping everyone on the same page. This is irrelevant for spirits, since G does not affect them directly. Spirits do not require gnosis the same way human magicians do to influence probabilities.

I have heard statements in the magical community to the effect that each magician added to a working multiplies its results, but if that were true any magical group of medium size or larger could automatically do things like move small objects telekinetically, light candles psychically, and so forth simply due to the compounding probabilities. They could certainly win Powerball jackpots every time they cast for it. As such, the additive model falls much more in line with real-world measurements. It should be noted that this is in terms of physical world probabilities, the stuff of sorcery. Mystical effects are more subjective and shifts in consciousness are harder to measure than physical effects.

A final factor affecting all magical operations is the astrological condition under which the operation is performed. This is a value that either increases or decreases the final effect based on the quality of the astrological election. The range of this factor remains under investigation at the time of this writing. In my experience, a good election can double or triple the result and a bad one can divide it by a similar amount. The exact value has proved hard to determine, but I suspect that it lies within that range.

In older systems of magick such as the Scholastic Image Magic from the Picatrix, an image is engraved onto the proper material at the best electional moment and the magick is powered by the election, not any specific charge. With this sort of magick, a bad election can mean the operation will backfire, producing a result in the same sphere or influence as the desired result but harmful rather than helpful. In Thelemic sorcery this effect is mediated by complex charges that must be executed literally. This means that the worst an operation can do is nothing, at least if the charge is constructed and worded correctly.

One final condition especially relevant to Thelemic magick has to do with operations bound to a talisman or some other independent operation such as a magical child. Such operations yield about 80% of the probability shift of direct operation – that is, an operation linked directly to your sphere of consciousness. My working hypothesis is that some of the “power” of the operation has to go into sustaining an independent entity, whereas that expenditure is not necessary when the operation runs directly.

The trade-off is that your total magical power gets split between operations running directly off your sphere of consciousness, so as soon as you try to run multiple operations simultaneously the power of each decreases significantly. An independent operation is not limited in this way, so you can have as many of them running as you want – which is one of the real advantages of the magical child technique over most other methods. Also, you can create multiple independent operations of this sort running to accomplish the same task as long as you explicitly instruct them in the charge not to interfere with each other.

Working out equations of magick with real predictive power is an important step in creating a viable scientific model of paranormal phenomena. We are far behind the physical sciences in that regard, mostly because the scientific method has only been applied to magick since Crowley’s time, and even then not to nearly to the same degree as in any other science. We will get there, but it will take concerted effort to overcome magical secrecy and enact an effective system of experimentation and peer review. It may be that what I have laid out here is not the final form of these equations. I would actually be surprised if that turned out to be the case, given how early we still are in the modeling process. I look forward to a time when magick can be explored in the same manner as any other discipline, and with the same academic rigor.