Quantum Magick?


Do what thou wilt shall be the whole of the law.

``The word of Aiwaz must put forth a perfect presentation of the Universe as Necessary, Intelligible, Self-subsistent, as Integral, Absolute and Immanent. It must satisfy all intuitions, explain all enigmas, and compose all conflicts. It must reveal Reality, reconcile Reason with Relativity; and, resolving not only all antimonies in the Absolute, but all antipathies in the appreciation of Aptness, assure the acquiescence of every faculty of mankind in the perfection of its pleniary propriety.''

(Crowley, Book 4)

Introduction

I begin to suspect that ``mainstream science'' and ``magick'' meet somewhere in the realms of energy. (Let me just remind myself again that ``the laws of magick are the laws of nature'' so they presumably meet everywhere, if I but knew it.) To a physicist, energy is the primal Stuff. Since the increasing success of mathematical models in predicting the behaviour of interacting systems of energy, it has become in many quarters almost tautological that the goal of modern science is the Discovery Of The Equation By Which All May Be Known. I think there's a case to be argued that this belief was at its most widespread and virulent, at least among physicists, just at the end of the previous AEon and the birth of the electronic and information ages. The whole joy of mathematics is that is it observer-independent, obeying the eternal laws of its own self-consistency. Using the tools of pure mathematics physical science could confidently talk about reality independent of any particular observer and therefore eternal, absolute, true. The very same mathematics that gave us atom bombs and laptop computers tells us that reality is relative, massively interconnected in a vest web of relationships, runs on probabilistic laws and only unifiable by going to higher dimensions. Cabalists among you may amused to note that one current theory (that of ``superstrings'') --- quite credibly asserts this number to be ten.

A signal or vibration may be understood in various ways. We may speak of velocity, a vector combining rate and direction and motion, or frequency, the rate of vibration or oscillation. In one domain, a signal consisting a single frequency may be represented by a sine wave extending from +infinity to -infinity, in another by a single `spike' (or `delta function.') In mathematics, these various domains are connected via well-defined operations known as `transforms.' The technique first encountered by most is the `Fourier Transform' in which a complex signal may be decomposed into a superposition, or vector sum, of a number of individual sine waves. A branch of applied calculus, transform mathematics is a very powerful tool. In `Signal Processing' (encountered mostly by electrical engineers and physicists) a signal once obtained from an input device (such as a microphone or aerial) may be digitised and passed through a Fourier transform. This switches the information from time domain to frequency domain. Noise and static may be attenuated by reducing the signal's amplitude at higher frequencies before performing a second Fourier transform (back into time domain) and hence to the output device (loudspeaker, etc.)

Why is this interesting? Well, I've tried to indicate how operations may be performed on the signal when in one domain, before transform and use in another. In terms of my own practice, such ideas have given me a useful basis for interacting with my energetic system. Performing a ``Sanskrit transform'' results in the perception of experience as being delivered through a number of primary discrete sites of energetic activity, the `chakras.' A ``Qabalistic transform''imparts a Sephirotic view of ones micro-macrocosm, but again, feeling and sensation is delivered through the energy body, which in some way seems to ``carry the reality'' in ``transform space.'' These transforms are very useful, as we know. Experience indicates that meditation on or more active work with aspects of the chakras is over time reflected by changes in other aspects of one's reality. Each transform presents the user with a different toolkit for interacting with the energy. The results of using multiple transform techniques to produce hybrid offspring are a matter of ongoing research.

Quantum Theory: some implications

Quantum mechanics (QM) is the branch of modern physics dealing with the Very Small. It has only been in this century that the theory of `atoms' as the `fundamental, non-divisible building blocks of matter' has been able to be tested. Atoms were indeed observed, but were soon discovered to be composite objects. As physicists probed deeper and deeper into the atom, all pre-existing concepts about the nature of matter had to be discarded. The investigation of physical reality at quantum distances has revealed a very strange realm in which time cannot really be said to exist, everything is connected to almost everything else, and the mathematical description of reality is given in terms of probability matrices, a superposition of possibilities in which the act of making a measurement or observation so affects the system that the observer experiences fundamental, mathematically unbreakable limitations on the limits to certainty, on what may be known and what must, by the very act of knowing one thing, be itself unknowable. To quote the physicist David Bohm,

Ultimately the entire universe has to be understood as a single undivided whole, in which analysis into separately and independently existent parts has no fundamental status.

One discovers... both from the consideration of the meaning of the mathematical equations and from the results of actual experiments, that the various particles have to be taken literally as projections of a higher dimensional reality which cannot be accounted for in terms of any force of interaction between them. [In other words:] We may regard each of the `particles' constituting a system as a projection of a `higher dimensional reality' rather than as a separate particle. [db80]

Hence, the mathematics may be viewed in various ways. When applied as a tool in Malkuth, QM has given rise to the modern semiconductor technologies behind the new computing and information infrastructure. When considered magickally, a workable interface between psi phenomena, consciousness, bioenergetics and synchronicity is established. We're getting quite near to where I've been trying to hasten us: the frontiers of science, where mathematics and mysticism almost visibly blur. Mathematics is the universal language of physicists, and as such perhaps the most powerful magickal language in daily use on this planet. A language in which `work' `force' `power' `acceleration' `field strength' `energy' `mass' and `current' all refer to well defined concepts, and observable quantities. Mathematics has provided the most effective magickal framework yet for enquiry into the nature and structure of matter (which we now know to be a form of energy, and vice versa.) I've mentioned interconnectedness a few times now, and will in a moment give a brief description of why I've been doing so.

Quantum mechanics is an ongoing revolution. An entirely new mathematics was developed, which made phenomenally accurate predictions of the behaviour of the observed physical realm at scales millions of times too small to see with a microscope. In fact, it goes down to the shortest distance which can be meaningfully said to exist. As I've mentioned, the first technological spinoffs --- typified by the microchip and consumer electronics --- have already begun to appear. Another effect of this revolution was to demolish existing physical reality maps, leaving a lot of people very confused. In the old world, matter was seen as composed of particles which clumped together to form visible matter, and interacted in ways resembling a tiny game of billiards. In order to know anything about the state of a physical system (or game of billiards) one must make an observation. If playing in the dark of our lack of knowledge, we must shine a light at the table. While once conceived of as waves of energy, propagating through an `ether' which filled all space and never actually moved itself, it was discovered that light can also sometimes give results which are inexplicable unless it is seem as a beam of separate particles known as `photons.' Now these particles impact the balls on the table and, even if only slightly, disturb them in the process. In observing/measuring the system (by looking at the light reflected from the table,) we have disturbed it. We also note that light has a 'wavelength', the distance in space traversed by the light as it goes through one oscillation of its electromagnetic field. In order to make more accurate observations, a shorter wavelength of light is necessary, which has a correspondingly higher energy, so increasing the disturbance caused by the impacting photons. This fundamental fact, that observation causes a disturbance means that we can never accurately know the state of a system before we observe it from the data gained by so doing. Strange perhaps, but true.

Among other things, Einstein is famous for his remark, `God does not play dice.' Quantum-level systems are described as superpositions of possibilities, which on observation resolve to a single observed actuality. However, it's not possible to predict which of the various outcomes will actually happen... only to assign probabilities. QM gives a method for calculating these probabilities, and this it does very well. Einstein believed that there were definite laws with definite outcomes somehow `hidden' behind this quantum facade. Moreover, QM seemed in places to predict outcomes clearly at odds with the universe as understood through Einstein's theories of relativity. The speed of light had been measured, and shown to be a constant, everywhere, in all directions regardless of the observer's velocity. \footnote{ This fact is key to Einstein's unification of space, time and gravity into a system which not only makes the similar predictions as Newton's laws of motion when applied to heavenly bodies, but better ones. A theory which unifies the curvature of spacetime with the presence of mass, and so explains why light rays are `bent' by stars.) } Quantum mechanics seemed to indicate the presence of interactions taking place at speeds greater than that of light's. In his attempt to indicate the inconsistencies which he perceived in the prevailing interpretation, he formulated what came to be known as the Einstein-Podolsky-Rosen (EPR) experiment. Three decades later John Bell formulated a theorem based on this experiment which when tested proved Einstein very wrong indeed. While energy cannot travel faster than c, the speed of light, some aspects of quantum state certainly can. This has some interesting ramifications.

Bell's Theorem and Consciousness

If we take a guitar string and fix both its ends before plucking it, we will find that only a certain set of notes can be produced. These harmonics are defined by the geometry of the arrangement, since the only frequencies allowed are those that have antinodes (zero-points) at the two fixed ends. We could say that the set of notes has been quantised, that is, reduced to a finite set of discrete tones. The mathematics used when dealing with waves and vibrations is to a large extent that used when describing the structure of reality at the very small, quantum levels. An electron orbiting an atom may be represented as a sum of possible states of vibration using the techniques first developed by Fourier, as mentioned earlier. We find that an electron, like the guitar string, has a discrete set of possible states. One of the discrete variables used to represent the state of a subatomic particle is that known as `spin,' a peculiar quality which is quantised into one of only two values, `up' and `down.' For a closed system --- one not open to external influences --- we know that ``spin is conserved,'' meaning that the total sum of all spins in the system remains constant.

I'll now attempt to outline how Bell's Theorem makes use of this fact. Let us imagine an experimental setup in which we have two sub-atomic particles in close proximity to each other, one with spin `up' and one with spin `down' making the total spin of the system zero. We now allow these two particles to move away from each other, each moving towards a detector of some kind. In order to make a point, let's stretch out a bit and place one detector here in our lab and the other on the moon. Now, the first particle enters the detector in the lab, and we make an observation designed to measure its spin. Now, I said spin was peculiar, and so it is, for while spin may only be `up' or `down' this may be with respect to any arbitrarily chosen axis. This time, we place our axis running from two'o'clock to eight'o'clock --- the detector is designed to allow us to change this axis at will, we'll say. Now, observing the first particle we find that it's spin is either `up' (pointing to eleven'o'clock) or `down' (pointing to five'o'clock) --- we have no way of telling in advance which it will be, but we know that it must be one of these two. This time we find it's got spin `up' and so points to eleven'o'clock.

The experiment has been so arranged that the particle approaching the moon-side detector has not quite got there yet, but will do so in a shorter time than it would take a photon of light sent from the earth-side detector to the moon-side detector to arrive. Since spin is conserved, as soon as we observe the first particle to have spin `up' with an arbitrarily chosen axis so as to `point' to eleven'o'clock, we predict that the second particle will be observed to have spin `down' so as to `point' to five'o'clock. This is found to be the case --- but look what's happened! Somehow, the second particle has taken the correct alignment (enforced by our arbitrary choice of axis) in a time less than that necessary for a signal travelling at the speed of light to reach it from the first. The mathematics predicts that this will happen. Einstein, believing it impossible, thought he'd found a flaw in the maths. Observations since then have shown that in fact, the maths' predictions are found to be correct --- but Einstein's equations still hold. The speed of light is the absolute, universal limit to the speed at which energy may propagate through space, which is true, and will always be true. What we are coming to understand however is that quantum state is a form of information, and is not so limited. It is everywhere, at once. We should not see our two particles as being separate entities, but as a single system. When we observe this system, its entire, distributed quantum state changes, instantaneously. This `non-local' interconnectedness is I believe at the heart of the `new physics,' and interestingly brings physics increasingly close to the mysticism which it once so vigorously rejected. All things are in constant and continuous communication with everything else they've ever encountered, in a manner that totally transcends spacetime as we understand it. At a quantum level, the manifest universe must be seen as a complete, unitive, effectively indivisible whole. Is this beginning to sound familiar to anyone?

While this is so at very small distances, in the macroscopic world of cars, trees, chairs, planets and so on, reality seems pretty much to behave as first described by Newton. The `ten thousand things' can most certainly be seen as separate objects with no obvious connections to anything else... which is perhaps why these findings of modern physics have influenced the popular mind just about as much as mystic Daoism --- that is, hardly at all. Indeed, it's not immediately obvious that all this low-level weirdness is relevant at all to the nature of day-to-day reality. Of course, I wouldn't have brought you this far if I believed that to be the case.

The human nervous system consists some 10^{12} neurons, most of them in the brain and spinal column. Each neuron has a number of inputs from other neurons (typically between one and ten thousand), and a similar number of outputs. For a given pattern of inputs, a neuron will either do nothing, or `fire,' sending a pulse of current to each of its outputs. Neurons are modelled as having an input `threshold,' which the total input current must exceed in order for the neuron to fire. The connection between consciousness and the pattern of neural firings is not at all well understood. At the join between one neuron and another is a very small gap, across which an electric current is able to propagate. What is interesting is that this gap is so small --- about two to three hundred angstroms (two to three hundred millionths of a meter) --- that quantum fluctuations may be expected to influence perhaps up to a million neurons at any one time. \footnote{The idea being that the neurons are close to the threshold, and are only tipped over as a result of quantum-level interactions.} These fluctuations may be due to changes occurring elsewhere within the nervous system... or somewhere totally different, like, in a star a million light years away. It's quite possible.

Now, the role of quantum mechanics in consciousness is hotly disputed. Some philosophers assert that consciousness arises from `complex interactions' occurring between neurons, which could perhaps one day be reproduced on a computer... this is a `Strong AI (Artificial Intelligence)' viewpoint. Others are not so sure, and feel that consciousness and QM may be tightly bound together, and this is the side which I am here favouring. Many of you will be familiar with the phenomena termed `synchronicity' by Carl Jung, in which seemingly `random coincidences' take on a deep personal significance. Indeed, I expect that you have found that the practice of magick has rather increased the rate of these events... and that you have found yourself encountering other folk in strangely similar situations. At the quantum level, reality is an indivisible, massively interconnected whole. Each nervous system is embedded into this whole in such a way as that its very functioning would appear to impinge on the fabric of the whole, spreading `virtual vibrations' out across spacetime. As above, so below. Quantum structures within and without and a proven mechanism --- non local interactions --- for interfacing between the two. By acting so as to affect the patterns of interaction and vibration within our nervous systems we in so doing, affect the external quantum structure of the entire universe. In short, modern physics and magick would seem to be saying identical things. Surprise, surprise.

Before we make an observation, QM tells us that reality is `unformed'... it exists only as a superposition of probabilities. This truth is popularly known as the ``Schrodinger's Cat'' paradox. On making an observation, the ``wave function'' describing the set of possible states (itself a Fourier sum of all possibilities, as already mentioned) ``collapses'' and we're left with a single, observed state. This collapse is very mysterious, since it involves so-called `hidden variables' involved with the non-local nature of reality. Some people have suggested `consciousness' and `will' as elements playing crucial roles in determining the outcome of an observation.

Any event, such as an observation of quantum state, involves the union of an observer and a Fourier sum of possible outcomes. While only a discrete number of possible states may be said to exist in any one situation, each term in the Fourier series must be treated as being infinite in itself. Treating the observer as a point consciousness (and as a quantum detector, that's fair) we are here looking at the union of a point (hadit) with infinite possibility (nuit) --- which interact in a mysterious way in which both will and consciousness are potentially implicated.

Our interactions with the universe are becoming clearer. As I mentioned at the start, energy is the `primal stuff' of both physics and magick. What I've been trying to indicate is that modern physics has found that energy is at a quantum level strangely entangled with the nature of consciousness. As my kundalini teacher says, `Be aware of the energy. That's the kundalini energy, the awareness. The awareness is the energy. The energy is the awareness.' Awareness is observation, is making changes at the quantum-unity level of reality. As awareness increases, harmonics develop, a synergetic building of gestalt consciousness which tends to excite similar reactions in the surrounding outside world, delivering synchronicities. Acts of love under will --- nuit/hadit unions --- allow us to affect the fields of quantum probability, hastening the process. The `body of light' may be seen at one level as awareness of quantum reality beyond the body, \footnote{On another, the body's bio-electromagnetic fields are also perceptible as energy fields.} yet still bound into the body at the level of quantum interactions in the synaptic cleft between neurons. There is no obvious limit to the extent of this perception, for as it is written,

``For the seer hath no head; it has expanded into the universe, a vast and silent sea, crowned with the stars of night.''

(The Vision and the Voice, 5th AEthyr.)

I reminded us at the beginning that ``The laws of magick are the laws of nature.'' One of those laws is known to be, E = mc^{2}. The law as summarised by the symbol string ThELHMA is equally true when applied to the investigation of the interactions of energy, consciousness and spacetime. Let us all look forward to the day when this is more widely appreciated. Thanks for coming, and I hope you enjoyed the ride.

Love is the Law, Love under Will.