Mathematical Insight is Specialised Mystical Perception

I believe mystical insight is the capacity of fundamental consciousness in highly specific states to penetrate higher dimensions to access knowledge, understanding and perspective. It is direct, pure awareness and understanding, unmediated by brain based computations, symbolism or language. Rucker described it as an experience of the unity of the Absolute in a direct way. Davies describes ‘mystical vision,’ as a state and a perception that allows one to perceive aspects of reality, not perceivable through rational states of mind.


Mystical perception

Mystical perception can lead to astonishing insights and wisdom impossible for the everyday rational perceptions of even the most intelligent well educated person. It is experienced in its highest forms through life long, disciplined meditation practice and why some of the yogis and monks of India’s most sophisticated mystical schools have achieved the highest degree of insight and knowledge from this process. I believe that pure mathematical insight is a highly specific and specialised form of mystical perception that some gifted people can experience. You could imagine it in both its forms as a state of high quantum coherence 1 when the mind can compute in superposition not like a quantum computer factoring enormous amounts of numbers but in terms of higher consciousness, non-local mystical-like perception (discussed in Does consciousness emerge from the brain? Book Two: Section One). I argue mystical perception is possible because reality and consciousness are ultimately higher dimensional phenomena. In a higher dimensional universe the laws of nature and everything else exist eternally, outside of time and space, known as the Plutonic realm, the Akasha and what I call the information universe and therefore accessible to human consciousness.

Interestingly some people from all walks of life, races, creeds and education levels have the capacity to experience certain degrees of mystical insight, if only fleetingly and perhaps only a handful of times in their life. Some have been great poets, philosophers and others scientists—all of whom have been giants in their field. Davies lists many of science’s ‘finest’ thinkers like Heisenberg, Edington, Pauli, Schrodinger, Einstein and Jeans, as advocates of mysticism, I would add greats like Plato and Pythagoras, who were mystics, philosophers, scientists and mathematicians. Davies writes that physicists David Bohm and Brian Josephson believe that a ‘useful’ guide to the development of scientific theories is regular mystical insights created by quiet contemplative meditation. Rucker recalls how Godel, who he describes as the ‘greatest’ logician this century, advised him that this was the best way to gain deep mathematical intuition, where one could perceive infinite sets.


True intuition and higher dimensions

Remember how Einstein believed the basis of our ability to understand the universe comes from our ‘intuitive’ mind and the intellect is merely a ‘faithful servant,’ that organises and structures the insights. Physicists Polkinghorne, Davies and Weinberg describe how intuitive insights bring the greatest discoveries in science by the greatest thinkers and the rest do the intellectual grunt work to explain it. Weinberg called these scientist ‘magicians,’ as they arrived at some great new insight into nature outside of current knowledge, with no discernible logical steps.


I believe we are at an interesting transition in our evolution and history, where science has brought us to the threshold of higher dimensions with rational deduction but is faltering at the doorstep, confused and bewildered. Imagine that physicists discovered the higher dimensional quantum vacuum almost ninety years ago. Awestruck and somewhat intimidated by its strange non-classical behaviour, they agreed to deny its very existence and carry on as if it was Newtonian-like—the Copenhagen interpretation. Physics is in crisis to this day because of this and the ongoing misperception of what they have been dealing with, even though the mathematics shows its higher dimensional nature everywhere, which is often perceived as a problem to be eradicated. I believe we have come to a time where mystical insight is more necessary than ever to give theoretical physicists, mathematicians and philosophers the deepest possible guiding perspective to deal with the unimaginable complexity and abstraction of higher dimensions. If this is used to guide mathematical insight and rational deduction, we will be able to piece together the jigsaw of reality at the highest level of intellectual, scientific and metaphysical sophistication.

Rucker discusses mystical insight or vision as a possible path to ‘ultimate’ knowledge. He argues that rational explanation used in the scientific approach can’t ‘lead’ us to this knowledge or mystery at the end of the universe. He points out that rational inquiry will always lead to an infinite regress and that the rules of logic converge in several different ways to demonstrate the impossibility of rational explanation. Davies supposes that the ultimate understanding of nature may require mystical vision or something like it, because rational inquiry can’t get us there. He describes how Godel’s incompleteness theorem in mathematical proofs and the halting problem in computation point to limits of how far logic and reason can take us. Rucker suggests that mystical thought and rational thought should be combined in the quest for knowledge and understanding, as they represent complementary ways of knowing that lead to higher order knowing.

Davies states that most scientists have a ‘deep mistrust’ of mysticism. He believes that mysticism is ‘no substitute’ for logical reasoning and scientific inquiry, as long as the latter can be ‘consistently’ applied. He thinks the scientific method should be ‘pursued’ as far as possible. I think, in terms of a guiding overview in theoretical physics, the reliance of the scientific method has taken us as far as it can and why physics is in crisis, as it stands on the edge of higher dimensions. Mystical-like perception in the form of mathematical insight, needs to be used now to guide the scientific method and reasoning to create the proofs and the mathematical models. Davies however, makes the mistake of thinking in terms of mystical insight versus rational explanation. He needs to apply the same reasoning to this as he did to reductionism versus holistic methods, arguing one isn’t better than the other, one shouldn’t be pursued and not the other. Both methods should be used together in the most appropriate way for the task.

This is exactly what happened in ancient mystical traditions. Mystics entered the mystical vision and had experiences, which they used as an overview to guide the process of rational explanation and model building. Over generations and thousands of years this process created the rigorous, repeatable body of knowledge along with explanatory models and philosophical interpretations. However even mystics were severely limited by language and mental images that cannot express what they experienced except as pale metaphors. However today we have modern mathematics, which makes a profound difference.

Weinberg described theoretical physicists as ‘hound’ dogs who have the ability to ‘sniff’ out a trail along the ground. I believe this is useful and equivalent to the left-brain linear approach but it leads to many dead ends and is slow and painful. However, if you were searching for something, surely it would be far more effective to have a helicopter with its more global expansive perspective, as well as the hounds on the ground. The perspective from the helicopter could guide the hounds to the most promising trails to follow. This type of higher perspective is missing in physics and why it is stuck. The hounds are more like the blind men feeling different parts of an elephant and arguing about what they have discovered without any idea what it really is. Mystical-like insight can supply this perspective to guide mathematical insight and the slog of deductive reasoning but only if physicists drop the unnecessary bias towards ways of knowing. Remember how Schrodinger pointed out that we have produced highly intelligent and educated scientists, who are philosophically immature. If we understand and embrace the philosophy and technology of mystical insight, then this ‘grotesque,’ as Schrodinger described it, imbalance can’t occur and science and humanity would benefit enormously.

However, I must emphasise that it is more than just philosophical maturity it’s also perceptual maturity, as we stand on the threshold of taking formal scientific understanding into a higher dimensional reality. Physicists don’t just face the daunting challenges of such a world and the mathematical complexity needed to describe it but the very real hardwiring of their brain that evolved to perceive the everyday physical, 3D world. Higher dimensions whether they like it or not are magical and weird compared to what we know and how we perceive and think, so we need all the help we can get!


Maths Information Platonic and Akashic Realms

Davies explains that almost all scientists believe that the underlying order of the universe can be expressed by mathematics, which is the very bedrock of science and is rarely questioned. He believes in the Platonic idea that we do not invent mathematics we discover it. Remember the Plutonic realm is a higher dimension, where archetypal patterns of pure form, mathematical relationships and constants of nature exists eternally outside of time and space. Because the laws of nature are expressed in mathematics, then they too are not invented but discovered. “Mathematical objects and rules enjoy an independent existence, states Davies, “they transcend the physical reality that confronts our senses.” 2 He lists Godel who proved mathematics couldn’t be based purely on logic and Penrose as Platonists. Davies quotes Penrose as saying “it is as though human thought is … being guided towards some eternal, external truth … which has a reality of its own.” 3

Cosmologist Max Tegmark believes that the universe is pure form expressed by mathematics and has created what he calls, the mathematical universe hypothesis. I agree and argue that maths is information, so the universe is higher dimensional information and it’s computing, which is the basis of Section Three: The information universe. Penrose was inspired by the Mandelbrot set. He argued that it was definitely an entity, an object that was discovered and exists, like Mt Everest and is not merely an invention of the human mind. Davies quotes mathematician and well known science writer, Martin Gardner, who agrees with Penrose and states that they both find it ‘incomprehensible’ that anyone could believe the Plutonic realm doesn’t have an independent existence. Penrose feels strongly that mathematics creates a belief in “some kind of ethereal, eternal existence.” 4 In the sixties when people were taking pure LSD they saw beautiful paisley patterns. These were reproduced on clothing, as backgrounds to music clips and as posters, etc. These patterns came to symbolise the psychedelic era. Twenty years later computers were visualising almost identical patterns in the form of Julia sets and even the Mandelbrot set. This is no coincidence as the human mind is deeply connected to the Plutonic realm. Through the catalytic effect of LSD people were able to directly experience and visualise the existence of these ‘mathematical objects’ and later through mathematics visualised by computers we have discovered the same independent ‘objects!’

Davies quotes Heinrick Hertz, who first discovered and produced radio waves in a laboratory as saying, “one cannot escape the feeling that these mathematical formulas have an independent existence of their own…” 5 Davies tells how when he asked the famous physicist Richard Feynman if he thought mathematics and the laws of physics had an independent existence, Feynman replied, in regards to a simple mathematical relationship, “…when you discover these things, you get the feeling they were true before you found them. So you get the idea that somehow they existed somewhere, but there is nowhere for such things… 6 Davies cites John Barrow as using this argument of independent discovery as evidence of some ‘objective element’ that is ‘independent’ of the investigator. Rucker sees mathematical objects occupying a mental space he called the Mindscape. He believes mathematicians explore the Mindscape, similar to Armstrong, Cousteau and Livingston exploring the physical universe. Sometimes different explorers will come across the same terrain and report their findings independently.


Weinberg discusses the ‘unreasonable effectiveness’ of mathematics, in his book Dreams of a Final Theory, as does Davies in Mind of God. Apparently this was the title of an essay on the intriguing coincidence that very often completely abstract mathematics, discovered by mathematicians who were exploring certain processes for their inherent beauty, discovered formulas or mathematical entities that turned out (sometimes decades later) to be the answer to practical problems in the real world or modelled real world processes. Many times these obscure mathematical techniques enabled profound advances in theoretical physics. Yet at the time they were discovered neither the mathematicians nor the physicists thought they were of any practical value. Schrodinger in Nature and the Greeks, described this situation as ‘impressive.’ In Strange Story of the Quantum the chronological discoveries by independent physicists and mathematicians often exhibited interesting coincidences, wrote Hoffman. Often two or more physicists would independently discover the same thing within weeks or even days of each other, or a mathematician, completely unaware of developments in theoretical physics would discover a new mathematical process just before or just after a need emerged for it. As I mentioned the answer to these so-called coincidences lies in the relationship between our consciousness and the higher dimensional information universe.

Princeton mathematician and logician Kurt Godel, who Rucker described, as ‘unquestionably’ the ‘greatest’ logician of the century, argues that mathematical intuition is a higher order sensory perception in a 1964 addendum to his paper, What is Cantor’s Continuum Problem?

Despite their remoteness from sensory experience, we do have something like a perception of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don’t see any reason why we should have less confidence in this type of perception, i.e., in mathematical intuition, than in sense perception…the set theoretical paradoxes are hardly anymore troublesome for mathematics than deceptions of the senses for physics…Evidently the ‘given’ underlying mathematics is closely related to the abstract elements contained in our empirical ideas. It by no means follows, however, that the data of this second kind, because they cannot be associated with action of certain things upon our sense organs, are something purely subjective, as Kant asserted. Rather, they, too, may represent an aspect of the objective reality, but, as opposed to the sensations, their presence in us may be due to another kind of relationship between ourselves and reality7

On the other hand, some scientists are formalists and believe that mathematics is merely an invention of the human mind and it therefore has no external, independent existence. Davies believes that Godel’s Incompleteness Theorem I explained in Philosophy ‘put paid’ to this formalist belief. Godel outlined in a paper that by assuming the objective existence of mental objects, the consistency of mathematics could be proved wrote Rucker. Penrose asserted that mathematics represents the purist form of thinking processes, which defies the notion that our thinking is a form of digital computation. He argues convincingly that Godel’s theorem of non-computability, “…established that human understanding and insight cannot be reduced to any set of computational rules.” 8 Thus demonstrating that we perceive mathematics by non-computational means. In other words Penrose is constructing a framework for how we perceive in the manner Godel described. Penrose has explored the mechanisms of how our brain could use quantum processes to achieve this. I describe this in Book Two: Section One: The totality of mind, as the brain having the potential for quantum computation and being deeply entangled in the non-local information and intelligence of the universe.

Godel’s incompleteness theorem proved there is no complete set of theorems to prove all true statements. The point of all this is simply that the formalists can never disprove the existence of or know the Plutonic realm, the Mindscape, the Absolute or any number of other smaller infinite sets by rational means. However, we are discovering pieces of the infinite using mathematics, like the infinite amplituhedron, a higher dimensional object that encodes complex particle interactions in the real world.


Mathematical insight is mystical insight

I believe mathematical insight is a highly specialised form of mystical perception. I believe it is a form of perception as mathematicians like Cantor, Godel, Penrose, Rucker and scientists like Davies and Tegmark describe like a sixth sense that the human mind possesses. I argue it is also mystical as it is capable of penetrating the higher dimensional or Plutonic realm outside of time and space where mathematical objects, laws and relationships exist. It is specialised as it’s specific to this mathematical realm. The fact that so many of the deep and very difficult descriptions of phenomena like God, consciousness and the nature of reality obtained originally by mystical insight thousands of years ago, have now been rediscovered by mathematics, tells me that mathematical insight is a specialised form of mystical insight. Some examples are the Absolute, reflection principle and the set theory universe, higher dimensions, the amplituhedron, limits to knowledge and non-computational consciousness.


Mathematics is the foundation of science, it’s maths that has enabled us to discover the laws of nature, construct falsifiable theories and models of how nature works. It’s this mathematical infrastructure that has allowed us to construct incredible technologies to enable us to advance humanity in ways that no other knowledge system has been capable of, including mystical thought. If we were unable to perceive these higher mathematical truths and only had our ordinary senses and logic to rely on as Hume and Kant believed, we would be unable to ever advance beyond the level of the ancient Greeks, Romans, Chinese or Indians. We would be stuck with their technology and mysticism. All the mystical perception in the world experienced by the most talented, disciplined and spiritually advanced mystics could never achieve what mathematical insight has achieved.

What has been experienced with mystical perception can only be described in words using pale three dimensional analogies and poetry. As this never comes close to the actual experience, it’s impossible for others to appreciate and understand, except in mere intellectual or emotional ways, so can’t be applied effectively in the world. That’s why mystical teachings are easily misunderstood, trivialised or deliberately perverted and why traditionally they have been kept secret. Look how religions have perverted the underlying metaphysics and how thoroughly the commercialism and romanticism of the new age movement has mangled ancient shamanic and Eastern metaphysics.

However, mathematics can’t be perverted like language, it can be manipulated, interpreted and used in all sorts of different ways but the mathematical truths that are discovered, the absolutes that relate to the world as it is, are transcendental phenomena—unchanging and immutable and so are ultimately more robust in the face of erroneous interpretations, which are transient as science hones in on the greater truth. In other words a poor interpretation of mathematical truth will only last hundreds of years, whereas poor interpretations of mystical truth last thousands.

Therefore, I believe mathematical insight is the practical side of mystical insight, as it allows sentient beings to unlock the mysteries of how nature works, which gives them the technology to advance materially, which is a crucial aspect of the evolution of sentience and provides the foundation for a spiritually mature and sustainable civilisation. On the other hand it will lead us to the truths of mystical perception, as it advances our understanding of the fundamental higher dimensional nature of reality and consciousness and provides the neurotechnology tools to improve brain function – eventually producing enlightenment, which reconnects us as individuals to mystical perception. It is also doing this indirectly and globally by creating the problems we face in the world today, due to the power of our technology to amplify the good and the bad within us. In turn out of survival, this is forcing us to face deep and hard questions about our humanity, particularly the destructive side and what we can do about it. This is the basis of Book Two: The Neuroscience and Technology of Enlightenment, and Book Three: Science and Our Spiritual and Technological Transformation.


Mystical states and scientific understanding

Talbot argues that scientists must transform from objective observers to participatory experiencers as quantum theory has demonstrated this is the case anyway. He gives the example of researchers of lucid dreams who have begun programs to actually induce lucid dreaming for themselves, so they experience the phenomena first hand. He suggests researchers of near-death-experiences NDEs and out-of-body-experiences OBEs in the future will devise means of travelling to these realms themselves as part of their research. I believe advanced neurotechnologies will play a crucial role in the experiential transformation of scientist’s interaction with any phenomena they study.

2-4Herbert questioned our reliance on classical ‘modes’ of perception stating we will figure out how to experience the quantum world directly. I believe that quantum theorists must transcend the limitations of their ordinary hardwired perceptions to be able to advance physics in a more balanced manner. I foresee a time in the future, when students specialising in mathematical and/or theoretical physics will need to be able to enter certain controlled states of heightened awareness––using meditative or neurotechnological techniques, to be able to understand advanced higher dimensional theories. Eventually some scientists will be able to use mystical perception to do their work.

When more scientist understand, value and utilise mathematical insight, altered states of consciousness and mystical perception, they will advance science into a true metaphysical science of higher dimensions and the rest will follow as they do now. In science the trend setters state what the current beliefs are and understanding and the rest just believe it and carry on with business, even if they mostly don’t understand, as in most cases they don’t need to.

Once we crack the higher dimensional issue and are able to unite quantum and relativity theory we will be able to develop a technology of real magic beyond our wildest dreams. When we can manipulate processes in a higher dimension to allow them to manifest or to direct processes in our lower dimensional world that’s technological magic and that’s where all sentient beings would end up. Mystical perception took us as far as it could and now mathematical perception is taking us to the next level. At this level we will understand the universe so profoundly we can unite with mystical perception in a way the whole of humanity will share in. This is our evolutionary destiny but there are no guarantees, as we could easily destroy ourselves in the process!



  1. Quantum coherence is a state where two particles are entangled and in superposition.  When particles are entangled they demonstrate non-local connection.  This means no matter how far these particles are separated they are still connected in an instantaneous way.  Superposition is the state particles are in when they are not being measured.  In superposition a particle is a distribution of probabilities of every state a particle could be in.  It is this property that scientists want to exploit in quantum computing which will allow massive parallel computation, not across processors but within each switch.  The superposition collapses down and is read as an output.  Coherence is this delicate state of superposition, which is the key to mind boggling computational ability.  Environmental noise in the form of heat, light and strangely enough observation can all destroy the coherence, creating decoherence. A quantum computation can’t leave a trail that could be seen otherwise the superposition state collapses and this can spread through the computer rendering all processing useless. It seems like a useful analogy to compare the delicate states of mystical insight to quantum coherence.  These states take a lifetime to train and stabilise even by the elite, the literature is full of references to the difficulty of accessing these states and maintaining them.  Anyone who has seriously practiced meditation will have experienced situations where they are in a state of knowing and then they realise this consciously and the state immediately collapses.  It is like the act of conscious observation destroys the state of superposition just like a quantum computer.  Is this evidence that our minds can quantum compute? Could it be that states of deep meditation or mystical insight are superposition quantum computing states and this is why they are so difficult to achieve and so easily perturbed?
  2. The Mind of God Science and the Search for Ultimate Meaning p141
  3. Ibid p142
  4. Ibid p144
  5. Ibid p145
  6. Ibid p146
  7. Infinity and the Mind The Science and Philosophy of the Infinite p164
  8. Shadows of the Mind p65