I apologize for the length of this post. The subject matter is vital to our immediate situation. I hope you can find the time to look over the entire post and digest it.
These next four posts that I have been working on are all interrelated and all significantly related to what is happening in La Palma. I do not believe that the La Palma incident is going away. I am convinced that they are going to create the MegaTsunami. When exactly? I don’t know.
Science is a Religion • Autumn Asphodel
How Mainstream Science Became a Religion
13th September 2016
Contributing writer for Wake Up World
Mainstream science — despite all its claims of objectivity, and despite the fact it attempts to lay claim to the truth — is itself a religion.
Science places itself on a pedestal and assures everyone it has dispassionately arrived at its conclusions. Meanwhile, however, it is full of assumptions, denials and limitations, and makes the serious mistake of presenting its theories as facts.
Materialism, the driving force behind mainstream science, has been shown again and again to lack the capacity to explain the world around us, especially in relation to idealism or other theories that account for the energetic nature of reality. However, the errors and assumptions of mainstream science are gladly seized upon by technocrats, who are eager to use science and technology to further their own ambitions of control. The planned New World Order has a massive technocratic aspect, and includes forcing the vaccine, GMO, surveillance, geoengineering, carbon-driven global warming, SMART (Technology) and microchipping agendas onto an unsuspecting public.
Yet, despite this, we remain collectively bedazzled by materialism, a religion that has induced a certain faith in us. And up until recently, it has still been difficult for society at large to accept the fact that the unseen energetic realms of our reality are actually more powerful and more primal than the material realms we can see and touch … but that is starting to change.
Back to Ancient Athens – Materialism vs. Idealism
This is certainly not the first time we have struggled with the debate of whether the world can best be described by the philosophy of materialism; the ancient Greek philosophers and scientists thought long and hard about the issue.
Materialism vs. idealism is really the philosophical battle between the ideas that matter exists independently (and that consciousness doesn’t exist or is secondary), as opposed to the idea that consciousness, thought and energy are primary (and that matter is secondary) to existence. Democritus championed the materialist viewpoint (and his ideas were taken further by Aristotle), whereas Plato proposed the idea of idealism with his famous theory of the World of Forms or World of Ideas, which posits that non-physical (but substantial) forms (or ideas) represent the most accurate reality. According to Plato, our materialist reality is an inferior copy of a more perfect world. This is exactly in alignment with what various cultures, shamans, religions and spiritual traditions have been saying for millennia about the pre-eminence of energy, and the power of mind over matter.
Even many distinguished mainstream Western scientists over the last 100+ years have grasped the point that matter is not solid. Here are the very best and brightest of them alluding to the fact that energy is pre-eminent to matter:
“All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.” – Max Planck
“If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.” – Nikola Tesla
“The day science begins to study non-physical phenomena, it will make more progress in one decade than in all the previous centuries of its existence.” – Nikola Tesla
“The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts.” – Werner Heisenberg
“We may therefore regard matter as being constituted by the regions of space in which the field is extremely intense … there is no place in this new kind of physics for the field and matter, for the field is the only reality.” – Albert Einstein
“The field is the sole governing agency of the particle.” – Albert Einstein
“Everything we call real is made of things that cannot be regarded as real.” – Niels Bohr
Plato also wrote that the entire universe can be explained mathematically by numbers. This exactly aligns itself with the idea that we live in a holographic universe – a kind of computer simulation with digital numbers at its foundation.
The Renaissance: Reinforcing the Left-Brain Materialist View
The Renaissance was heralded as a golden age for humanity — and in many ways it was — but it also further cemented the left-brain materialist view of the world, which can be found in the works of Copernicus, Galileo, Descartes and Newton. Copernicus and Galileo famously proposed heliocentrism (the theory that the planets revolve around the Sun, which is located at the center of the Solar System) over the then-existing geocentric model (the theory that the Earth is at the center of all the celestial bodies) (Which is what the BIBLE, the Word of GOD tells us.), but as the recent rise of the flat earth movement has shown, there is a copious amount of evidence to suggest that the heliocentric theory is far from being complete and conclusive.
It was Descartes who famously claimed “I think, therefore I am” and gave birth to the falsehood that thinking, reason and logic is the base of our existence, when in fact being or consciousness is. Put simply, there is no brain to think without a consciousness that animates it.
Newton, for all the great work he did for physics, came up with a set of abstract, mathematically-based, mechanical formulae which he called “the laws of nature”. Though he was to live several centuries after Newton, genius inventor and true scientist Nikola Tesla made a very telling comment regarding the tendency of mainstream science and scientists to get stuck in a rut with their abstract mathematical theories. This statement could most definitely be applied to Einstein, who despite his brilliance in proposing the theory of relativity, worked for 3+ decades afterwards and could never come up with a more complete theory. Tesla said:
“Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.”
Darwinian Eugenics and Evolution
Charles Darwin, for those of you who didn’t know, was part of an elite family who favored eugenics (selective breeding), so it is not surprising therefore that his theory of evolution emphasized the virtues of dog-eat-dog competitiveness, survival of the fittest, and might-is-right – all habits and values of the psychopathic ruling class.
Those who insist that science is not a religion may be hard-pressed to explain why someone like Darwin chose to focus on those elements of Nature in this theory, instead of focusing on or even considering the incredible symbiosis and cooperation that is also evident in Nature – and to a greater extent than competition.
Today: The Insane and Never-Ending Search for the Smallest Particle
Fast forward to today, and it seems that science is a religion like never before. What’s happening at CERN with the Hadron Collider’s search for ever smaller and smaller particles seems like materialistic mainstream science desperately trying to justify itself and its outmoded theory, like a dog forever chasing its tail in vain.
In November 2014, a paper entitled Quantum Realism: The physical world as a virtual reality was published by Dr. Brian Whitworth Ph.D (Masters of Science in Information Systems), MA Hons (Psychology) and BSc (Maths). It contrasted the materialistic and idealistic views, which Dr. Whitworth framed as physical realism and quantum realism. When he matched these views to the data coming out of CERN, he found the quantum realism (simulation) model of reality fit the observations and facts much better. He writes:
“The Higgs boson is the virtual particle created by an invisible field to explain another virtual particle created by another invisible field to explain an actual effect (neutron decay). Given dark energy and dark matter, it explains at best 4% of the mass of the universe, but the standard model needs it, so when after fifty years CERN found a million, million, million, millionth of a second signal in the possible range, physics was relieved. There is no evidence this “particle” has any effect on mass at all, but the standard model survives.
“By piling fields upon fields, the standard model now has at least 48 point particles, 24 fitted properties, 5 overlapping invisible fields and 14 virtual particles that pop in and out of existence on demand, anywhere, anytime. And it isn’t finished yet, as each new effect needs a new field, e.g. inflation needs an inflaton field. If this approach, founded on physical realism, is preferred, it isn’t because of its simplicity, as it is hard to imagine anything more complicated! Chapter 4 suggests that while the fitted calculations work, their interpretation is a mythology on a scale not seen since Ptolemy’s epicycles.”
We are Blind to The Electromagnetic Spectrum
Materialism places so much stock in what we can apprehend with our 5 senses, especially sight, since it is the dominant sense for most people. Yet, of what we know exists in the full electromagnetic spectrum, we can only see a tiny range from approximately 700 nanometers (abbreviated nm) to 400 nm, between the infrared and ultraviolet rays. As this short video clip demonstrates, if the electromagnetic spectrum were a reel of film 2,500 miles long (stretching from California to Alaska), then the band of light visible to human beings would be around 1 inch long! If these numbers are correct, that means that we only perceive 0.0000000631313% of what is really there. So why, when we are so blind, does mainstream science place so much faith in our ‘5-senses reality’ and disregard the unseen as fantasy or imagination?
Because we can not see or feel the elecromagnetic forces/weapons that they are using on us and our environment, we are either totally unaware or cannot believe they exist. But, trust me, they are using them on us at this time. Not only on us, but on our EARTH. They are destroying our atmosphere, water, our land and everything on it!
Now you know why, to them that is not madness. They believe that we are living in a hologram and they want to design it to their specifications. They want to destroy it and build it back “better”.
Mainstream Science – Bogged Down by Fraud and Fakery
So far, I have discussed the reasons why mainstream science is ideologically or theoretically on the wrong track. I haven’t even begun to touch the ways in which science is horribly misguided and mistaken on a practical level. Sad to say, science has been totally corrupted by special interests who fund and determine the outcome of much of the research. The fraudulent scientific research of Big Pharma is rife, and has been acknowledged as untrustable by medical journal editors, professors, doctors, government officials and former Big Pharma insiders. Essentially, well-funded interests can pay for whatever “scientific result” they want for their agenda, slanting, distorting and omitting data in line with their goals. Simply put, a scientist discovering the “wrong” result will be quickly rejected and defunded.
This fake and fraudulent science, which is not true science at all but rather corporate junk science which passes under the rubric of science, is all pervasive. As Marcia Angell, former editor-in-chief of the esteemed New England Journal of Medicine (NEJM), had to say about the pervasive fraudulent scientific research:
“It is simply no longer possible to believe much of the clinical research that is published, or to rely on the judgment of trusted physicians or authoritative medical guidelines … I take no pleasure in this conclusion, which I reached slowly and reluctantly over my two decades as an editor of The New England Journal of Medicine.”
For a fuller discussion of this point, please see my articles:
- The Massive Flaw with the Scientific Hierarchy of Evidence,
- The Top 10 Tricks Used by Corporate Junk Science and
- Most Scientific Research of Western Medicine Untrustable & Fraudulent, Say Insiders and Experts
Happily, there are many true scientists standing outside of the fakery and putting forth alternative evidence to consider. The truth cannot be hidden forever.
Conclusion: Science is a Religion Which Requires Faith
Mainstream scientists will probably feel aghast to hear it, but the truth is that science is a religion with its own high priests – they just wear white coats rather than black gowns. It requires belief (faith) in theories (doctrine) which can never ultimately be proven (Evolution, Relativity, Big Bang) because they are full of assumptions and contradictions. There is always at least one question that can never be answered, and the constant redefinition of terms, omission of numbers and invention of new factors becomes, at a certain point, like twisting facts to suit existing theories, rather than twisting theories to suit facts (as the fictional character Sherlock Holmes liked to say.)
Terence McKenna humorously put it like this: “Modern science is based on the principle: ‘Give us one free miracle, and we’ll explain the rest.’ The one free miracle is the appearance of all the mass and energy in the universe and all the laws that govern it in a single instant from nothing.”
Materialist science has tried to convince us that everything can be explained with solid atoms, but as various experiments have proven, only theories which account for consciousness, energy, non-locality and other phenomena make sense. Particles are probability distributions, not little hard things. Mainstream science falls well short again and again in describing and predicting our world — a holographic universe, a computer simulation which looks and feels real but which is composed of stuff which is not solid. Materialistic science is a religion – and the time is long overdue to give up the faith.
“Not only is the universe stranger than we imagine, it is stranger than we can imagine.” ~ Sir Arthur Eddington
Mathematics Rising
“The future of mathematics is more a spiritual discipline…”
I did some following up on the work of Vladimir Voevodsky and for anyone who might ask, “what’s actually going on in mathematics,” Voevodsky’s work adds, perhaps, even more to the mystery. Not that I mind. The mystery emerges from the limitless depths (or heights) of thought that are revealed in mathematical ideas or objects. It is this that continues to captivate me. And the grounding of these ideas, provided by Voevodsky’s work on foundations, reflects the intrinsic unity of these highly complex and purely abstract entities, suggesting a firm rootedness to these thoughts – an unexpected and enigmatic rootedness that calls for attention.
Voevodsky gave a general audience talk in March of 2014 at the Institute for Advanced Studies at Princeton, where he is currently Professor in the School of Mathematics. In that talk he described the history of much of his work and how he became convinced that to do the kind of mathematics he most wanted to do, he would need a reliable source to confirm the validity of the mathematical structures he builds.
As I was working on these ideas I was getting more and more uncertain about how to proceed. The mathematics of 2-theories is an example of precisely that kind of higher-dimensional mathematics that Kapranov and I had dreamed about in 1989. And I really enjoyed discovering new structures there that were not direct extensions of structures in lower “dimensions”.
But to do the work at the level of rigor and precision I felt was necessary would take an enormous amount of effort and would produce a text that would be very difficult to read. And who would ensure that I did not forget something and did not make a mistake, if even the mistakes in much more simple arguments take years to uncover?
I think it was at this moment that I largely stopped doing what is called “curiosity driven research” and started to think seriously about the future.
It soon became clear that the only real long-term solution to the problems that I encountered is to start using computers in the verification of mathematical reasoning.
Voevodsky expresses the same concern in a Quanta Magazine article by Kevin Hartnett.
“The world of mathematics is becoming very large, the complexity of mathematics is becoming very high, and there is a danger of an accumulation of mistakes,” Voevodsky said. Proofs rely on other proofs; if one contains a flaw, all others that rely on it will share the error.
So, at the heart of this discussion seems to be a quest for useful math-assistant computer programs. But both the problems mathematicians like Voevodsky face, and the computer assistant solutions he explored, highlight something intriguing about mathematics itself.
Hartnett does a nice job making the issues relevant to Voevodsky’s innovations accessible to any interested reader. He reviews Bertrand Russell’s type theory, a formalism created to circumvent the paradoxes of Cantor’s original set theory – as in the familiar paradox created by things like the set of all sets that don’t contain themselves. (If the set does contain itself then it doesn’t contain itself) This kind of problem is avoided in Russel’s type theory by making a formal distinction between collections of elements and collections of other collections. In turns out that within type theory, equivalences among sets are understood in much the same way as equivalences among spaces are understood in topology.
Spaces in topology are said to be homotopy equivalent if one can be deformed into the other without tearing either. Hartnett illustrates this using letters of the alphabet:
The letter P is of the same homotopy type as the letter O (the tail of the P can be collapsed to a point on the boundary of the letter’s upper circle), and both P and O are of the same homotopy type as the other letters of the alphabet that contain one hole — A, D, Q and R.
The same kind of equivalence can be established between a line and a point, or a disc and a point, or a coffee mug and a donut.
Given their structural resemblance, type theory handles the world of topology well. Things that are homotopy equivalent can also be said to be of the same homotopy type. But the value of the relationship between type theory and homotopic equivalences was greatly enhanced when Voevodsky learned Martin-Löf type theory (MLTT), a formal language developed by a logician for the task of checking proofs on a computer. Voevodsky saw that this computer language formalized type theory and, by virtue of type theory’s similarity to homotopy theory, it also formalized homotopy theory.
Again, from Hartnett:
Voevodsky agrees that the connection is magical, though he sees the significance a little differently. To him, the real potential of type theory informed by homotopy theory is as a new foundation for mathematics that’s uniquely well-suited both to computerized verification and to studying higher-order relationships.
There is a website devoted to homotopy type theory where it is defined as follows:
Homotopy Type Theory refers to a new interpretation of Martin-Löf’s system of intensional, constructive type theory into abstract homotopy theory. Propositional equality is interpreted as homotopy and type isomorphism as homotopy equivalence. Logical constructions in type theory then correspond to homotopy-invariant constructions on spaces, while theorems and even proofs in the logical system inherit a homotopical meaning. As the natural logic of homotopy, constructive type theory is also related to higher category theory as it is used e.g. in the notion of a higher topos.
Voevodsky’s work is on a new foundation for mathematics and is also described there:
Univalent Foundations of Mathematics is Vladimir Voevodsky’s new program for a comprehensive, computational foundation for mathematics based on the homotopical interpretation of type theory. The type theoretic univalence axiom relates propositional equality on the universe with homotopy equivalence of small types. The program is currently being implemented with the help of the automated proof assistant Coq. The Univalent Foundations program is closely tied to homotopy type theory and is being pursued in parallel by many of the same researchers.
In one of his talks, Voevodsky suggested that mathematics as we know it studies structures on homotopy types. And he describes a mathematics so rich in abstract complexity, “it just doesn’t fit in our heads very well. It somehow requires abilities that we don’t possess.” Computer assistance would be expected to facilitate access to these high levels of complexity and abstraction.
But mathematics is, as I see it, the abstract expression of human understanding – the possibilities for thought, for conceptual relationships. So what is it that’s keeping us from being able to manage this level of abstraction? Voevodsky seems to agree that it is comprehension that gives rise to mathematics. He’s quoted in a New Scientist article by Jacob Aron:
If humans do not understand a proof, then it doesn’t count as maths, says Voevodsky. “The future of mathematics is more a spiritual discipline than an applied art. One of the important functions of mathematics is the development of the human mind.”
While Aaron seems to suggest that computer companions to mathematicians could potentially know more than the mathematicians they assist, this view is without substance. It is only when the mathematician’s eye discerns something that we call it mathematics.
Mike Shulman has a few posts related to homotopy type theory on The n-Category Cafe site beginning with one entitled Homotopy Type Theory, I followed by II, III, and IV. There’s also one from June 2015 – What’s so HoTT about Formilization?
And here’s a link to Voevodsky’s Univalent Foundations.
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By David Grandy
Originally printed in the JANUARY-FEBRUARY 2006 issue of Quest magazine.
Citation: Grandy, David. “Science and the Occult: Where the Twain Meet.” Quest 94.1 (JANUARY-FEBRUARY 2006):13-17.
When I was in graduate school, one of my professors — an eminent historian of medieval science espoused in his lectures what one student affectionately tagged as “the Old Man River theory of scientific progress.” The professor asserted that in his research he found no evidence of social or cultural factors impinging on the development of medieval science: driven purely by intellectual thought, the science “just kept rolling along.” I suspect the professor would not have made this claim to a more sophisticated audience; although he had little patience with any attempt to explain science as nothing but a reaction to outside cultural forces, he was savvy enough to know that there is more to the story of science than just intellectual thought.
Like my professor, I enjoy science enough to see it as something truly remarkable. Perhaps, however, I am more inclined to admit that there is no clear line of demarcation between science per se and culture. Actually, this is not much of an admission: it has become a commonplace understanding among historians of science. Gone are the days that scholars of science portray it as humankind’s sole instrument of truth in a confused and superstitious world. Despite this, many people still talk as if modern science is wholly distinct from and clearly superior to such traditions as alchemy, astrology, magic, Cabala, and nineteenth century Spiritualism. These movements, so this line of thought goes, have all been repudiated by science and are therefore intellectual dead ends.
This outlook is rendered problematic by historical scholarship (most of it in the last fifty years) that indicates complex and subtle interactions between now discarded beliefs and contemporary scientific principles. This is to say that scientific theories often emerge from circumstances that later may be seen as scientifically dubious. A case in point is Isaac Newton’s law of universal gravity. The law, as presented in textbooks, consists of a straightforward factual statement (every body in the universe is attracted to every other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them) and a matching mathematical equation. Given only this much, students reflexively assume that Newtonian physics is a world apart from alchemy or magic. After all, there is a conciseness and clarity to the theory that is rarely found in other domains of human experience, let alone in the murky depths of alchemy. One is surprised then to learn that Newton invested much time and energy seeking to produce the Philosopher’s Stone, the ultimate aim of alchemy. What is more, this quest cannot simply be written off as an intellectual dead end because it appears to have played into Newton’s scientific thinking, quite possibly into his theory of gravity (Westfall 1985).
Today alchemy is considered an occult pursuit, and it is hard to imagine how it may have once figured into Newton’s formulation of universal gravity. What we tend to forget, however, is that while the law can be clearly and succinctly stated, it is not altogether obvious how gravity works. Most people today, following Newton, describe it as an action-at a distance force, but this introduces difficulties—at least it did for Newton. In explaining the tides, he proposed that the moon (and the sun) reaches across apparently empty space to tug on the earth. For some of his contemporaries, however, this explanation went nowhere because it afforded no understanding of the mechanism by which gravitational forces propagate. Indeed it introduced a puzzle for anyone (like René Descartes) wishing to evacuate the cosmos of non contact forces, the like of which bespoke astrological influences and alchemical sympathies and antipathies. Newton privately summed up his misgivings in this way:
That gravity should be innate, inherent, and essential to matter so that one body may act upon another at a distance through a vacuum without the mediation of any thing else by and through which their action or force may be conveyed from one to another is to me so great an absurdity that I believe that no man who has in philosophical matters any competent faculty of thinking can ever Fall into it. (Westfall 1980)
Newton later defended his law of gravity by arguing that its validity is secured by observable phenomena—one can empirically test its predictions. However, he added, no one can discover its causes—why nature behaves this way—and in this sense only is the law “occult” (Westfall 1971). This admission speaks volumes about science (or, more generally, about the human intellect—the failing is not specific to science) and permits understanding of why occult or pseudoscientific practices often flourish side by side with science. For those who want to know the why of things or the ultimate causes, scientific theories do not quite close the explanatory circle. Arthur Schopenhauer faulted science on this score, noting that investigation of its theories recalls the experience of “somebody who unexpectedly finds himself in a group whose members systematically introduce each other as a friend or cousin, as if by doing so, they have sufficiently explained themselves; the visitor, however, though expressing pleasure with each introduction, has always the unexpressed question on his lips: “But how, the deuce, did I turn up among all these people?” (Schopenhauer 1966).
Over a hundred years ago, the young H.G. Wells, full of enthusiasm for science but sensing its limitations, stated:
Science is a match that man has just got alight. He thought he was in a room in moments of devotion, a temple and that his light would be reflected from and display walls inscribed with wonderful secrets and pillars carved with philosophical systems wrought in harmony. It is a curious sensation, now that the preliminary sputter is over and the flame burns up clear, to see his hands lit and just a glimpse of himself and the patch he stands on visible, and around him, in place of all that human comfort and beauty he had anticipated darkness still.
Wells did not mean to dismiss science; throughout the first half of the 20th century he was one of its leading advocates. He did, however, appreciate that while science has the capacity to improve human life in many ways, it also, as Wells’ mentor T.H. Huxley put it, gives us a cosmos that “works through the lower nature of man, not for righteousness, but against it.” In other words, a purposeless, uncaring, accidental cosmos: That is why, in Huxley’s mind, science had the mandate of “building up an artificial world in the cosmos.” The universe was neither congenial with nor sympathetic to humankind’s interests; indeed, it had no capacity to be. As William James, a contemporary of Wells, noted at the turn of the twentieth century: “Nature has no one distinguishable ultimate tendency with which it is possible to feel a sympathy. In the vast rhythm of her processes, as the scientific mind now follows them, she appears to cancel herself.”
When combined with the earlier thought that scientific explanations fail to offer ultimate answers, this consideration—that, as physicist Steven Weinberg insisted, the universe is “pointless”—makes it unsurprising that many people today, in their search for life clarifying meaning, look away from science. Of course, some scientists portray science as having religious value—thereby one reads God’s Book of Nature—but since the Enlightenment this characterization has lost ground to the view that no human endeavor can publicly decide the question of God’s existence or purpose. Implicit in this outlook is the positivistic intuition that science concerns the logical extraction of laws and predictive consequences from verifiable sense data. That is, science is a way of putting ourselves in a situation where hypotheses can be confirmed or rejected on the basis of procedures that keep one firmly anchored to physical facts and the unbiased analysis thereof. So disciplined, science presumably makes no unwarranted inferences or metaphysical leaps.
The positivistic outlook has now worn thin. There is, as Edwin Burtt put it in his 1920s critique of logical positivism, “no escape from metaphysics.” Indeed, any escape attempt will be driven by considerations that open onto ultimately undecided issues of ontology and epistemology metaphysical considerations. Philosophically speaking, this fact blurs the line between science and the occult; historically speaking, the line has always been blurred.
Only since Newton have battle lines been drawn, for, as noted above, Newton was deeply involved in alchemy, not to mention biblical prophecy and symbolism. He believed, like Freemasons and Rosicrucian’s since, that new knowledge issues up from older, larger understandings. But despite his immersion in what we now regard as occult or pseudoscientific pursuits, he spoke in a positivistic vein, implying that he had developed a method for reading the text of nature without metaphysical interpolation. Given the explanatory success of his science and the immense prestige it brought him, many came to regard Newtonian physics as a bulwark against what Freud later called “the black tide of mud . . . of occultism” (Jung 1963). This attitude, however, did not eliminate belief in the occult. For one thing, some who developed occult systems after Newton saw themselves as scientific pioneers à la Newton, and it is only in retrospect that their systems have been deemed occult. During the latter part of the eighteenth century and throughout the nineteenth century, Mesmerists conducted experiments, phrenologists subjected the human head to rigorous measurement, Spiritualists kept careful record of what occurred during seances, and all these groups invoked scientific terminology to report their findings.
What is more, many who worked in these movements had formal scientific training and a few were prominent scientists. Anton Mesmer earned his doctorate in medicine at the University of Vienna and, inspired by Newton’s law of universal gravity, sought to harness a life force, putatively filling the cosmos, for healing purposes. William Crookes (discoverer of the element thalium and inventor of the Crookes tube), Oliver Lodge (knighted for his contributions to wireless telegraphy), and Arthur Russell Wallace (who independently formulated the theory of natural selection and co-announced it with Darwin) all affirmed the essential truth of Spiritualism, though they acknowledged that the movement had its share of charlatans. In their minds, Spiritualistic principles, far from contradicting science, were a welcome corrective to its bleak materialistic orientation. Moreover, the late nineteenth century discovery of X-rays and Becquerel rays (radioactivity) was taken by some as evidence of an unseen world of spirits existing just beyond the ken of our physical senses.
For many believers, Spiritualism held forth the heady prospect of demonstrating the reality of spiritual phenomena by scientific means. Sir Arthur Conan Doyle, for example, depicted Spiritualism as “infinitely the most important thing in the world” because it was “the first attempt ever made in modern times to support [religious] faith by actual provable fact.” This sentiment is not unlike that expressed two centuries earlier by Joseph Glanvill when he portrayed scientific investigation of demons and witches as “a kinde of America,” a new frontier of knowledge” (Clark 1999). Along with fellow scientists Robert Boyle and Henry More, Glanvill studied and theorized about witchcraft in the same way he did about the possibility of the vacuum, magnetic action at a distance, and the nature of light.
In the nineteenth century, perhaps no scientific theory sparked more occult thought than organic evolution. At first glance this is surprising, for organic evolution is often misconstrued as a counterweight to the idea that humankind has a divine origin. Nevertheless, the prospect of humankind’s unlimited evolutionary ascent within the cosmos fired the imagination of scientist and occultist alike. On the one hand, the evolutionary process, being blind and non teleological, does not aim for improvement or perfection, let alone anything like salvation or immortality. But on the other, theorists often could not refrain from dramatizing it. In the closing paragraph of his Origin of Species, Charles Darwin insisted that “[t]here is a grandeur in this [evolutionary] view of life,” and elsewhere he portrayed nature (i.e., natural selection) as “infinitely more sagacious than man” and “all seeing” and “infinitely wise” (Young 1985). Huxley, Darwin’s “bulldog,” equated evolution with “the cosmic process . . . it is full of wonder, full of beauty, and, at the same time, full of pain.” The pain, however, could be blunted through the exercise of visionary evolution: thanks to Darwin, humankind could now knowingly evolve and thereby outmaneuver a great deal of unnecessary hardship and catastrophe. With this thought in mind and almost as if he were gazing into a crystal ball, H.G. Wells spelled out the promise of evolutionary biology:
We are creatures of the twilight. But it is out of our race and lineage that minds will spring, that will reach back to us in our littleness to know us better than we know ourselves, and that will reach forward fearlessly to comprehend this future that defeats our eyes.All the world is heavy with the promise of greater things, and a day will come, one day in the unending succession of days, when beings, beings who are now latent in our thoughts and hidden in our loins, shall stand upon this earth as one stands upon a footstool, and shall laugh and reach out their hands amid the stars. (Wells 1914)
Given the ease with which it could be dramatized, evolutionary biology attracted occultists. The most notorious was Helena Petrovna Blavatsky, who co founded the Theosophical Society in 1875. Her books, Isis Unveiled (1877) and The Secret Doctrine (1888), blended religion (particularly Hinduism), contemporary science, and mythology into a seamless whole and opened up unsuspected vistas on the past and future. She spoke of cosmic cycles and the evolutionary ascent of “seven root races,” the fifth of which is the human race. The whole process, she emphasized, was governed by the law of karma and therefore was not, as many scientists believed, random or mindless. Curiously, Blavatsky seems not to have expected most educated people to embrace her outlook, even after giving it a scientific gloss. Occult understanding, she declared, is reserved for the few, and most scientists—Darwin himself—failed to grasp the cosmic and spiritual import of the evolutionary drama. They saw the outer, naturalistic shell of that process but ironically missed its rich inner vibrancy–life itself.
Rudolf Steiner, an erstwhile Theosophist who went on to found Anthroposophy, similarly posited an evolutionary drama of cosmic proportions. His cosmology, like Blavatsky’s, is complex, even dizzying, and reiterates ancient motifs now deemed occult or superstitious. Betraying a Pythagorean fondness for certain basic numbers, Steiner talked of the seven states of consciousness, the seven life kingdoms or conditions, the four elements, the three creative functions, the ten cabalistic sephiroth, the nine angelic orders, and so on. These orders, kingdoms, functions, and elements are linked to the planets or zodiacal constellations in a vast system of evolving consciousness. Like many other occultists at the turn of the twentieth century, Steiner felt that he was pulling back the curtain on materialistic science so that all could see its spiritual context.
Given its propensity to stretch the mind and summon up hope of improved if not fully transfigured living circumstances, science finds common cause with the occult. And while science may seek to distance itself from the occult, the gap between the two will never be clearly defined. To be sure, science may be delineated by its emphasis on objectivity, empirical data, and mathematics, but these characteristics merely mark a distinctive approach to nature: they do not decide what nature ultimately is or what it means. Answering these questions entails interpretative passage beyond secure scientific understandings, and here, in the realm of interpretation, science and the occult often reestablish contact.
A contemporary case in point is quantum physics. In the last century, probably no scientific development has sparked greater occult interest than quantum physics, but it is not because quantum physics explicitly points toward occult agencies or influences. It is because quantum physics, while affording incredibly accurate predictions about atomic phenomena, challenges traditional scientific assumptions about physical reality and thereby clears a space for renewed debate about a whole spectrum of issues: the nature of light, extrasensory perception, human free will, God’s omniscience, and so on. Some of these issues will be deemed occult by scientific purists, but even they cannot escape the charge that their worldview is, at some level, interpretative or metaphysical. Albert Einstein understood this principle better than most: “physical [scientific] concepts,” he wrote, “are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world.” As long as the world remains open to pluralistic interpretation, science and the occult will enjoy uneasy companionship.
Throughout history scientific theories have been proven wrong over and over again, and yet the world continues to accept and embrace them and continue on as if nothing has changed. They continue to teach debunked theories in our school demanding they be accepted as fact. The ignorant masses are lead along by their noses, afraid to accept they have been fooled an unable to sort through the lies to find the truth.
Newton’s Law of Gravity Proven Wrong: Einstein May Be Next …
Newton’s “Law of Gravity” has been in question since the research on black holes started showing much more progress, with the first-ever picture of a black hole. But now it has been declared wrong and Einstein’s hypothesis to be the best explanation of how gravity works.
Any theory to be considered the law in physics should be applicable everywhere in the universe to be truly considered which came out to be the limitation of law of gravity when it came to the black hole, stated the California professor.
According to the theory of General Relativity, proposed by Sir Albert Einstein, gravity results from how mass warps space and time. Greater the object’s mass, stronger its gravitational pull. This describes gravity not as a force, but as a result of the curvature of space-time caused by the uneven distribution of mass.
Whereas, Newton’s “law of Universal Gravitation” states gravity as a force. The law further states that every particle attracts every other particle in the universe with a force (gravity) which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
We all have heard of the story of how Newton came up with the idea of gravity. An apple fell on his head while he was sitting under the tree which gave him something to think upon, i.e. how did the apple fall? From there the discovery of gravity started which stated gravity being a force due to which any two bodies in the universe attract each other. The law of universal gravitation came into existence in 1687. Since then it has been the explanation of gravity and gravitational force and has been taught in the entire world which now has been scientifically disproved. Even though it is only one law that has been disproved, but due to this single law, every aspect of gravitation and the related concept are going to take a new course which can be the beginning of a new era in the field of physics.
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Mathematics and Occultism – Anthroposophy
Anthroposophical Movement
Weekly News for English-speaking Members of the Anthroposophical Society
VOL. V. No. 28 | 8th July. 1928 |
Published at the Offices of the Anthroposophical Society in Great Britain, 46, Gloucester Place, London, W.I, England. Subscriptions: Great Britain and Dominions, 15s. yearly, 3s. 9d. quarterly. Single Copies, 3d. America, $4.00 yearly, $1.00 quarterly. All rights reserved.
Mathematics and Occultism
By Rudolf Steiner.
IT is well known that the inscription over the door of Plato’s school was intended to exclude anybody who was unacquainted with the science of Mathematics, from participating in the teachings of the Master. Whatever we may think of the historical truth of this tradition, it is based upon the correct understanding of the place that Plato assigned to mathematics within the domain of human knowledge. Plato intended to awaken the perceptions of his disciples by training them to move in the realm of purely spiritual being according to his “Doctrine of Ideas.” His point of view was that Man can know nothing of the “True World” so long as his thought is permeated by what his senses transmit. He demanded that thought should be emancipated from sensation. Man moves in the World of Ideas when he thinks, only after he has purged his thought of all that sensuous perception can present. The paramount question for Plato was, “How does Man emancipate himself from all sense-perception?” He considered this to be an all-important question for the education of the spiritual life.
Of course, it is only with difficulty that Man can emancipate himself from material perceptions, as a simple experiment on one’s own self will prove. Even when the man who lives in this every-day world does withdraw into himself and does not allow any material impressions of the senses to work upon him, the residues of sensuous perception still linger, in his mind. As to the man who is as yet undeveloped, when he rejects the impressions which he has received from the physical world of the senses, he simply faces nothingness — the absolute annihilation of consciousness. Hence certain philosophers affirm that there exists no thought free from sense-perception. They say, “Let a man withdraw himself ever so much within the realm of pure thought, he would only be dealing with the shadowy reflections of his sense-perceptions.” This statement holds good, however, only for the undeveloped man. When he acquires for himself the faculty of developing organs which can perceive spiritual truths (just as Nature has built for him organs of sense), then his thought ceases to remain empty when it rids itself of the contents of sense-perception. It was precisely such a mind emancipated from sense-perception and yet spiritually full, which Plato demanded from those who would understand his Doctrine of Ideas. In demanding this, however, he demanded no more than was always required of their disciples, by those who aspired to make them true initiates of the Higher Knowledge. Until Man experiences within himself to its full extent what Plato here implies, he cannot have any conception of what true Wisdom is.
Now Plato looked upon mathematical science as a means of training for life in the World of Ideas emancipated from sense-perception. The mathematical images hover over the border-line between the material and the purely spiritual World. Let us think about the “circle”; we do not think of any special material circle which perhaps has been drawn on paper, but we think of any and every circle which may be represented or met with in Nature. So it is in the case of all mathematical pictures. They relate to the sense-perceptible, but they are not exhaustively contained in it. They hover over innumerable, manifold sense-perceptible forms. When I think mathematically, I do indeed think about something my senses can perceive; but at the same time I do not think in terms of sense-perception. It is not the material circle which teaches me the laws of the circle; it is the ideal circle existing only in my mind and of which the concrete form is a mere representation. I could learn the identical truths from any other sensible image. The essential property of mathematical perception is this: that a single sense-perceptible form leads me beyond itself; it can only be for me a representation of a comprehensive spiritual fact. Here again, however, there is the possibility that in this sphere I may bring through to sense-perception what is spiritual. From the mathematical figure I can learn to know super-sensible facts by way of the sense-world. This was the all-important point for Plato. We must visualise the idea in a purely spiritual manner if we would really know it in its true aspect. We can train ourselves to this if we only avail ourselves of the first steps in mathematical knowledge for this purpose, and understand clearly what it is that we really gain from a mathematical figure. “Learn to emancipate thyself from the senses by mathematics, then mayest thou hope to rise to the comprehension of ideas independently of the senses”: this was what Plato strove to impress upon his disciples.
The Gnostics desired something similar. They said, “Gnosis is Mathesis.” They did not mean by this that the essence of the world can be based on mathematical ideas, but only that the first stages in the spiritual education of Man are constituted by what is super-sensible in mathematical thought. When a man reaches the stage of being able to think of other properties of the world independently of sense-perception in the same way as he is able to think mathematically of geometrical forms and arithmetical relations of numbers, then he is fairly on the path to spiritual knowledge. They did not strive for Mathesis as such, but rather for super-sensible knowledge after the pattern of Mathesis. They regarded Mathesis as a model or a prototype, because the geometrical proportions of the World are the most elementary and simple, and such as Man can most easily understand. He must learn through the elementary mathematical truths to become emancipated from sense in order that he may reach, later, the point where the higher problems are appropriately to be considered. This will certainly mean, for many, a giddy height of human perceptive faculties. Those, however, who may be considered as true Occultists have in every age demanded from their disciples the courage to make this giddy height their goal: — “Learn to think of the essence of Nature and of Spiritual Being as independently of sense-perception as the mathematician thinks of the circle and its laws, then mayest thou become a student of Occult Science” — this is what everyone who really seeks after Truth should keep before his mind as if written in letters of gold. “Thou wilt never find a Circle in the World, which will not confirm for thee in the realm of sense what thou hast learned about the Circle by super-sensible mathematical perception; no experience will ever contradict thy super-sensible perception. Thus dost thou gain for thyself an imperishable and eternal knowledge when thou learnest to perceive free of the senses.” In this way did Plato, the Gnostics and all Occultists conceive mathematical science as an educational means.
We should consider what eminent persons have said about the relation of mathematics to natural science. Kant and many others like him, for example, have said that there is as much of true science as there is mathematics in our knowledge of Nature. This implies nothing else than that by reducing to mathematical formulae all natural phenomena, a science is obtained transcending sense-perception — a science which, although expressed through sense-perception, is visualised in the spirit. I have visualised the working of a machine only after I have reduced it to mathematical formulae. To express by such formulae the processes presented to the senses is the ideal of mechanics and physics and is increasingly becoming the ideal of chemistry.
But it is only that which exists in space and time and has extension in this sense, which may be thus mathematically expressed. As soon as we rise to the higher worlds where it is not only in this sense that Extension must be understood, the science of Mathematics itself fails to afford any immediate expression. But the method of perception which underlies mathematical science must not be lost. We must attain the faculty to speak of the realms of Life and Soul, etc., quite as independently of the particular objective entity, as we are able to speak of the “circle” independently of the particular circle drawn upon paper.
As it is true that only so much of real knowledge exists in Natural Science as there is Mathematics in It, so it is true that on all the higher planes knowledge can be acquired only when it is fashioned after the pattern of mathematical science.
Now, within the last few years, mathematical science has made considerable progress. An important step has been taken within the realm of mathematics itself, towards the super-sensible. This has come about as the result of the Analysis of Infinity which we owe to Newton and Leibnitz. Thus another branch of mathematical science has been added to that which we call “Euclidian.” Euclid expresses by mathematical formulae only what can be described and constructed within the field of the “finite.” What I can state in terms of Euclid about a circle, a triangle or about the relations of numbers, is within the field of the finite, it is capable of construction in a sense-perceptible manner. This is no longer possible with the Differential Calculus with which Newton and Leibnitz taught us to reckon. The Differential still possesses all the properties that render it possible for us to calculate with it; but in itself as such, it eludes sense-perception. In the Differential, sense-perception is brought to a vanishing point and then we get a new basis — free from sense-perception — for our reckoning. We calculate what is perceptible by the senses through that which eludes sense-perception. Thus the Differential is an Infinitesimal as against the finitely sensible. The “finite” is mathematically referred back to something quite different from it, namely to the real “infinitesimally small.” In the Infinitesimal Calculus we stand on an important boundary line. We are mathematically led out beyond what is perceptible to the senses, and yet we remain so much within the real that we calculate the “Imperceptible.” And when we have calculated, the perceptible proves to be the result of our calculation from the imperceptible. Applying the Infinitesimal Calculus to natural processes in Mechanics and Physics, we accomplish nothing else, in fact, than the calculation of the sensible from the super-sensible. We comprehend the sensible by means of its super-sensible beginning of origin. For sense-perception, the Differential is but a point, a zero. For spiritual comprehension, however, the point becomes alive, the zero becomes an active Cause. Thus, for our spiritual perception, Space itself is called to life. Materially perceived, all its points, its infinitesimally small parts, are dead; if, however, we perceive these points as differential magnitudes, an inner life awakens in the dead “side-by-side.” Extension itself becomes the creation of the extensionless. Thus did life flow into Natural Science through Infinitesimal Calculus. The realm of the senses is led back to the point of the super-sensible.
It is not by the usual philosophical speculations upon the nature of differential magnitudes that we grasp the full range of what is mentioned here, but rather by realising in true “self-knowledge” the inner nature of our own spiritual activity when from the infinitely small we attain an understanding of the finite through Infinitesimal Calculus. Here we find ourselves continually at the moment of the genesis of something sense-perceptible from something no longer sense-perceptible. This spiritual activity in the midst of super-sensible proportions and magnitudes has become in recent years a powerful educational means for the mathematician. And for what has been accomplished in the realms lying beyond the limits of ordinary physical perception by intellects such as Gauss, Riemann and our contemporary German thinkers Oskar Simony, Kurt Geissler, as well as many others, we are indebted precisely to this. Whatever may be objected in particular against these attempts: the fact that such thinkers extend the conception of space beyond the three-dimensional compass; that they reckon in terms that are more universal and more comprehensive than the space of the senses; these are simply the results of mathematical thought emancipated by Infinitesimal Calculus from the shackles of sense-perception.
In this way important indications have been set for Occultism. Even when mathematical thought ventures beyond the limits of sense-perception, it yet retains the strictness and sureness of true thought-control. Even if errors do creep in this field, they will never act so misleadingly as do the undisciplined thoughts of the non-mathematical student when he penetrates into the realms of the super-sensible.
Plato and the Gnostics only recognised in mathematical science a good means of education, and no more than this is here implied about the mathematics of the infinitely small; nevertheless to the Occultist it does present itself as a good educational means. It teaches him to effect a strict mental self-education where sense-perceptions are no longer there to control his wrong associations of ideas. Mathematical science teaches the way to become independent of sense-perception, and at the same time it teaches the surest path; for though indeed its truths are acquired by super-sensible means, they can always be confirmed in the realm of the senses. Even when we make a mathematical statement about four-dimensional space, our statement must be such that when we leave the fourth dimension out and restrict the result to three dimensions, our truth will still hold good as the special case of a more general proposition.
No one can become an Occultist who is not able to accomplish within himself the transition from thought permeated with sense to thought emancipated from sense-perception. For this is the transition where we experience the birth of the “Higher Manas” from the “Kama Manas.” It was this experience which Plato demanded from those who wished to become his disciples. But the Occultist who has passed through this experience must go through one still higher. He must also find the transition from thought emancipated from sense-perception in form, to formless thought. The idea of a triangle, of a circle, etc., is still qualified by form, even though this form is not an immediately sensible one. Only when we pass over from what is limited by finite form to that which does not yet possess any form, but which contains within itself the possibility of form-creation, only then are we able to understand what is the realm of Arupa in contrast to the realm of Rupa. On the lowest and most elementary plane we have an Arupa reality before us in the Differential. When we reckon in Differentials we are always on the border-line where Arupa gives birth to Rupa. In Infinitesimal Calculus, therefore, we can train ourselves to grasp the idea of Arupa and the relation of this to the Rupa. We need but once integrate a differential equation with full consciousness; then we shall feel something of the abounding power that exists on the borderline between Arupa and Rupa.
Here, of course, it is at first only in an elementary manner that one has grasped what the advanced Occultist is able to perceive in higher realms of being. But one here has the means to see at least an idea of what the man who is limited to sense-perception cannot even divine. For the man who knows nothing beyond sense-perception, the words of the Occultist must at first seem devoid of all meaning.
A science which is gained in realms where the support of sense-perception is necessarily removed, can be understood in the most simple manner at the stage where man emancipates himself most easily from such perception. And such is the case in mathematics. The latter, therefore, constitutes the most easily mastered preliminary training for the Occultist who will raise himself to the higher worlds with definite enlightened consciousness and not in dim sensuous ecstasy or in a semi-conscious longing. The Occultist and the Mystic live in the super-sensible with the same enlightened clearness as the elementary geometrician enjoys in the realm of his laws of triangles and circles. True Mysticism lives in the light, not in the darkness.
When the Occultist, who starts from a point of view like that of Plato, calls for research in the mathematical spirit, he can easily be misunderstood. It might be objected that he overrates the mathematical spirit. This is not the case. Such an overrating rather exists on the part of those who admit exact knowledge only to the extent to which mathematical science reaches. There are students of natural science at the present time who reject as not being scientific in the full sense of the word any statement which cannot be expressed in numbers or figures. For them vague faith begins where mathematics end; and according to them, all right to claim objective knowledge ceases at this point. It is precisely those who oppose this overrating of mathematics itself who can most thoroughly value the true enlightened research which advances in the spirit of mathematics even where mathematical science itself ceases. For in its direct meaning mathematical science after all has to do only with what is quantitative; where the qualitative begins, there its domain ends.
The point is, however, that we should also be able to research (in the exact sense of the word) in the domain of the qualitative itself. In this sense Goethe set himself with particular emphasis against an overrating of mathematics. He did not want to have the qualitative bound and fettered by a purely mathematical method of treatment. Nevertheless, in all things he wanted to think in the spirit of the mathematician, according to the model and pattern of the mathematician. This is what he says: — “Even where we do not require any calculation, we should go to work in such a manner as if we had to present our accounts to the strictest geometrician. For it is the mathematical method which on account of its thoroughness and clearness reveals each and every defect in our assertions, and its proofs are really only circumstantial explanations to the effect that what is brought into connection has already been there in its simple, single parts and in its entire sequence; that it has been perceived in its entirety and established as incontestably correct under all conditions.” Goethe wishes to understand the qualitative in the forms of plants with the accuracy and clearness of mathematical thought. Just as one draws up mathematical equations in which one only has. to insert special values in order to include under one general formula a multiplicity of single cases, so does Goethe seek for the primordial plant which is qualitatively all-embracing in spiritual reality. Of this he writes to Herder in 1787: “I must further assure you that I am now very near to the secret of the generation and organization of the plant, and that it is the very simplest thing that can be imagined … The prototype of the plant (Urpflanze) will be the most wonderful creation of the world, for which Nature herself shall envy me. With this model and the key thereto one can then discover plants without end, which will necessarily be consistent, that is to say, which — even if they do not exist — could yet exist.” That is to say, Goethe seeks the as yet formless protoplant, and he endeavours to derive therefrom the actual plant-forms just as the mathematician gets from an equation the special forms of lines and surfaces. In these realms Goethe’s trend of thought was really tending towards true Occultism. This is known to those who learn to know him intimately.
The point is that by the self-training above-mentioned, Man should raise himself to a perception emancipated from the senses. It is only through this, that the gates of Mysticism and Occultism are thrown open to him. Through the schooling in the spirit of mathematics lies one of the paths to the purification from life in the senses. And just as the mathematician is consistent in life, just as he is able to construct bridges and bore tunnels by virtue of his training — that is to say, he is able to command the quantitative reality, in the same way, only he will be able to understand and rule the qualitative, who can make himself master in the ethereal heights of sense-free perception. This is the Occultist. Just as the mathematician builds the shapes of iron into machines according to mathematical laws, so does the Occultist shape life and soul in the world according to the laws of these realms which he has understood in the spirit of mathematical science. The mathematician is led back to real life through his mathematical laws; the Occultist no less so through his laws. And just as little as he who is ignorant of mathematics is able to understand how the mathematician builds up the machine, even so little can he who is not an Occultist understand the plans by which the Occultist works upon the qualitative forms of life and soul.
Mathematical Occultism & Occult Mathematics (part I) 09/15 …
1. Concentration 2. Memory 3. Imagination 4. Reason 5. Intuition 6. Discrimination 7. Victory Exercising the mind through problem-solving sharpens the Sword on the Magician’s table. Studying mathematical theories grows new brain cells into organized stuctures for higher cognition. Where to begin: Symbolic Logic & Set Theory. Mathematics was used by the Pythagorean Brotherhood as a means to an end, but was not the goal itself. The true goal: to develop mental perception of the spiritual world. Sense-free thinking and how the intellect becomes clairvoyant. Mathematics takes us up to the treshhold of the spiritual world, but no farther. Mathematics is a means of occult education, where we use the same style of mathematical thinking to cognize the spiritual world. Mathematical alchemy encodes thought-forms into our astral body which allow us to grow organs of super-sensible perception. Plant alchemy & the mathematics of life: fractals. Mineral alchemy & geometric structure. Developing sense-free thinking through mathematical theories. Mathematical structures as worlds of thought-forms. Dimensionality and the spiritual worlds. Developing fourth-dimensional awareness. Mathematical concentration: definitions, examples, theorems. Mathematical meditation: free association, visualization of geometric objects, visualization of analytical constructions.
Math & Mysticism · Avant.org
PDF SPECIAL COURSES OF INSTRUCTION: OCCULT MATHEMATICS Series …
Ancient Mathematical Origins of Modern day Occult Practices
Eugenia Victoria Ellis, PhD, AIA
Drexel University
I take the train to work each day. Inevitably I spy someone puzzling over a game of Sudoku. Often I hear someone referring to their house or office as having “good” or “bad” Feng Shui. Pop icons such as Madonna are taking up Cabala.
Surprisingly, these three popular interests are based on occult practices that have mathematical
origins in the Lo Shu, the ancient Chinese magic square of three (figure 1).
ICONOGRAPHY, ICONOLOGY AND ICONS
The research method I am using has two interconnected approaches: the first is an analysis based on the historical evidence of the cultural context surrounding the modern day practice; in reconstructing its history, the practice is to be considered as a source in itself.1
In other words, iconographic evidence is used as an historical source. This is a highly objective method whereby the practice itself has no merit in the analysis.
This research method begins with the image related to the practice and looks for symbolic elements of continuity between it and other images, gives credence to images of antiquity that can serve as threads linking symbolic content throughout historical time, and then recontextualizes the image within its present-day use.
In order to do this it is necessary to distinguish between the practice as a phenomenon in itself, the
iconographic content that may be present in the activity, and its iconology or essential meaning.
The practice is a physical phenomenon that is a product of an activity and is influenced by the prevailing cultural milieu; which determines it as a cultural artifact. It is this phenomenal aspect that allows for its subjective analysis. The distinguishing characteristic between iconography and iconology is basically that iconography is analysis, whereas iconology is synthesis. Through nalysis, iconography identifies, describes and classifies images within their own historical,
cultural and symbolic context. Iconology, on the other hand, is a synthetic process that looks at images as cultural symptoms, or symbols, which transcend time due their presence throughout historical time. While iconography systematically identifies a theme, iconology interprets the theme and is more concerned with its continuity as a way of understanding the hidden symbolic, dogmatic, or mystical meanings of an image. In other words, iconology renders visible the invisible aspects of iconography.
The term icon derives from the Greek word eikon, which embraces all sorts of images, including sculpture and even mental images. In art history, the term icon designates a wood-panel painting of a sacred subject intended for cult veneration. By extension, the term applies to sacred images in general, including mosaics and miniatures.
Because of their portability, icons could be opened and shut, be carried in parade throughout the city, and even accompany troops to battle. Icons entered mainstream medieval life by becoming part of their popular culture. In spite of the Old Testament prohibition of image veneration, the Christian origin of icons goes back at least to 200 AD when, according to the apocryphal Acts of John, an icon of St John the Evangelist was venerated in private with candles and wreaths.
(The ActsofJohn is an early 2nd-century Christian collection of Johannine narratives and traditions, long known in fragmentary form. The traditional author was said to be one Leucius Charinus, a companion and disciple of John) This is not a valid biblical work it has never been verified authentic and was a book for Gnostics and contains mystical sections out of the ordinary and cont congruent with the biblical books.
What is Gnosticism? According to Webster, it is “an occult salvational system . . . stressing [knowledge of spiritual things] as essential . . . combining ideas derived especially from mythology, ancient Greek philosophy, ancient religions, and eventually, from Christianity”. [Webster’s New World Dictionary, Simon & Schuster, Inc., 1988, p.577].
The doctrinal core of Gnosticism is basically a form of mystical religious or philosophical doctrines which other adherents and some early Christian sects spread and which the early Church leaders vehemently rejected as heresy. Believers in Gnosticism are called Gnostics. The word “Gnostic” is derived from the greek word gnostiko or gnosis (inner mystic knowledge). The Gnostics believe that “gnosis” is subjective (internally perceived by the mind or feelings) knowledge of the divine element or spark in every man that needs to be discovered to be known. They believe the divine spark originally came from the “realm of light” (totally alienated from the world and the flesh), and is resident in the soul of man and is held there in captivity by the flesh (a product of demons). The only way to release the divine spark is through divine “revelation knowledge”, experienced within in the spirit. Also they believe that only when the unconscious spirit in man is awakened by revelation from the “realm of light” can he come to know his real self – the god within. Source
Ancient Mathematical Origins of Modernday Occult Practices page 2
Eugenia Victoria Ellis, PhD, AIA
This practice was recognized as an adaptation of pagan practices, certainly reflecting back to the origins of the word in Greek culture. The icon was venerated in pagan times with lit candles and incense, wreaths, and the placing of cushions before them for the worshippers. These painted icons were approachable, touchable gods that were a part of daily life. In contrast to the classical painting that depicted a staged story, the icon figure engaged the spectator directly through eye contact.2
In the 19th century Russian home, the traditional place for the display of icons was the krasnyi ugol
(fair corner), often the back corner of the reception or dining room. Visitors upon entering were expected to greet the icons placed there even before greeting their host.3
The ultimate example of Russian iconic tradition was the Spas nerukolvornyi, which was the imprint of Jesus’ face on white linen and the first icon to be hung in the corner in Russian culture.
The Spas nerukolvornyi is a two-dimensional representation or image, which was considered to present a higher dimensional reality, Christ’s Higher Self.
The 19th century Russian priest, Fr. Pavel lorensky (1882-1943) described the icon as the outline of a “heavenly vision,” which “because its outline coincides with a spiritual vision, is that
vision within our consciousness.”4
In other words, an icon originally was intended to be an outline, like Christ’s image on white linen, of a higher dimensional vision and not an imitative representation of it.
Today, icons are simple outline representations that stand for something else, an image shorthand for a larger idea. Icons proliferate: they appear on our computer desktop, they are present as ideal products of consumption, and they can be actors whose personae in themselves are iconic representations of today’s culture. However, in the study of popular culture, it is imperative that we consider the origins of our modern day practices so that we can (re)cognize these icons not as something “new” but as mimetic responses based on traditional conventions, surprisingly often dating back to antiquity.
SUDOKU, FENG SHUI AND CABALA
Sudoku is a relatively new invention and is a game that has recently begun to replace the crossword puzzle in certain newspapers. This number game was originally called “Number Place” and was developed by the retired architect and puzzle designer Howard Garns for Dell Pencil Puzzles and Word Games and first published in 1979. It was later discovered by the Japanese to be similar to the crossword puzzle, but as a number game was better suited for a language that is symbolic rather than phonetic. It was first introduced in Monthly Nikolist magazine in April 1984 and it rapidly became absorbed into popular Japanese culture.
The American name Number Place was translated into Japanese and then abbreviated as su (number, digit) doku (single, unmarried). Near the end of 2004, the retired Hong Kong judge Wayne Gould approached the editors of The Times to publish his computer-generated puzzles. On November 12, 2004 the British newspaper launched its first Sudoku puzzle. By April 2005, the transformed number game returned to America as a regular feature in the New York Post.5
Ancient Mathematical Origins of Modernday Occult Practices page 3
Eugenia Victoria Ellis, PhD, AIA
The puzzle itself is rather simple (figure 2). It consists of three-by-three grids of numbers within the larger three-by-three nine-square grid. The object of the game is to place the numbers one through nine in each three-by-three grid such that each number only appears once both horizontally and vertically in the overall 81-square grid. At the heart of this game is the three-by-three or nine square grid, which since ancient times, and across cultures, has been known as the magic square of three. However, the sudoku square is not magic, for if it were, it would be a mathematical square, not just a number square. For a square to be magic the numbers must sum horizontally, vertically and diagonally to the same magic number, the number of the square times the middle number. The first magic square was the square of three, which has the number five at its center and when multiplied by three, the number of the square, yields the magic number fifteen.
Legend has it that the first magic square was introduced on the back of a sacred turtle some
2,500 years ago when it appeared to the mythical Chinese King Yü from the waters of the Lo River.
It was depicted as knotted cords in a stylized dotted pattern composed of solid and open circles
connected by lines, arranged in nine groups containing one to nine units each: the open circles for yang odd numbers, the solid circles for yin even numbers. This diagram came to be called the Lo Shu, which means “Lo River Writing.”6
The positioning of the numbers were very specific, described by the Taoist Chên Luan in the sixth century AD: “2 and 4 make the shoulders, 6 and 8 make the feet; 3 is at the left, 7 is at the right; 9 is worn on the head and 1 is underfoot [literally: trodden by the shoes]; while 5 dwells at the center.” This mnemonic means of ciphering the order of the numbers of the magic square of three referred to a person, and most likely to a man or god considered as a microcosm of the universe.7
To the Old Chinese, the Lo Shu was a concise representation of the universe in a microcosm, an imago mundi that related to both the heavens and the earth through the harmonious balance of its numbers around the strong central number five, which was located at the center of the axis mundi, the cosmic axis connecting these two worlds.
The Lo Shu was associated with the sky and another name for it had been “The Celestial Numbers of the Nine Halls (or Palaces),” which were considered to be sky-dwellings visited by various celestial deities. The cult of T’ai-Yi (Han dynasty 202 BC-220 AD) believed that the Sky Emperor T’ai-Yi lived in a palace at the center of Heaven, at the top of the axis mundi, where he ruled the eight outer divisions of Heaven, in each of which he had a palace. In a like manner, the Chinese Emperor lived at the bottom of this cosmic axis, at the center of the Earth, and exerted his influence out in the surrounding eight directions.
The Lo Shu magic square became public knowledge in China in the tenth century AD after about thirteen hundred years of hidden, private or cultic use. It appeared at this time in the form of knotted cords in solid and open, yin and yang dots.8
The magic square’s survival into the tenth century was precisely because of its occult and hidden use, because there had been two significant book-burnings during the course of Old China’s recorded history: Shih Huang-ti, the first emperor of the Ch’in dynasty (221-207 BC), in an effort to ensure national unity had all books burned in 213 BC, except those on magic and divination for which he had a special affinity;9
Yang Ti, the second emperor of the Sui dynasty (589-618 AD), ordered the destruction of all occult books in 605 AD because they were in conflict with the Orthodox teachings of Confucius.10
By the tenth century the mysteries of the Lo Shu had been absorbed into the Chinese cultural fabric through popular use as a protective charm and as a magical means of divination. However, the diagram that had survived into the tenth century was derivative: it had lost its cosmological significance, it was no longer used for divination, its numbers were obscured because of the dotted pattern which prevented the recognition of its distinctive mathematical properties, and it had degenerated into merely a riddle. Sometime during the Sung dynasty (960-1280 AD) the
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cyclical workings of the Tao, which had been represented by the magic line that connected the
numbers in sequence in the magic square of three, were reduced to the notion of a circle cut in two by an S-shaped line. The Lo Shu itself was replaced by the symbol commonly known today as the YinYang. 11
Nowadays, the Lo Shu is often depicted as the Yin-Yang symbol surrounded by the eight trigrammatic kwa as it is currently used in the divinatory practice of Feng Shui.
Without going into great detail in this paper, Feng Shui involves a complex web of divinatory
calculations that begin with the magic square of three. In brief, the Lo Shu was an iconic representation used to mirror on earth the divine workings of the cosmos above. The celestial pole was fundamental to ancient Chinese astronomy and formed the basis of their cosmological thinking regarding microcosmic-macrocosmic relationships. Atop the celestial pole was the Imperial Star above the heavenly Central Palace where the sky emperor lived in the middle of his kingdom of eight surrounding “sky palaces.” This location mirrored the position of the emperor on earth, around whom feudal land-holding practices were modeled as squares within squares based on the nine-square grid of the Lo Shu. Chinese maps were drawn with the north arrow pointing down.
More than likely, this was so that the map could be co-ördinated with the emperor’s view looking
down on his kingdom. The Imperial Star was the pole star of the Great Bear constellation and is fixed, around which all the other stars revolve.
According to Confucian authority, the ruler on earth should govern by the sky emperor’s example:
“He who exercises government by means of his virtue may be compared to the pole star, which
keeps it place while all the stars turn around it.”12
The Lo Shu became public knowledge in tenth century China after the Chinese ceased to value it
as a magic square and no longer recognized its inherent potential as a symbol of the Universe in miniature. From the seventh to the fourteenth century there were considerable numbers of Persian and Arab merchants living in the port towns along the China coast. It is possible that these traders could have brought knowledge of the magic square to western Asia. In any event, the magic square of three was first published in the Islamic world around the year 900 AD in an Arabic treatise traditionally ascribed to Jābir ibn Hayyān (known to Europeans as Geber). It was presented as a charm and the square was comprised of letters that had numerical values, instead of numbers, called the abjad system.13
In the study of magic squares it is important to
acknowledge that number as we know it today,
represented by Arabic numerals,14 was not so in
ancient and medieval times. There were no
numerals in the Hebrew language; like the abjad system, each letter of the alphabet corresponded to a number (figure 3). In the Western world, “roman numerals” were used until the invention of the printing press in the Renaissance. And common to these numbering systems was no representation for zero.15 Therefore, when creating a magic square, the numbers not only summed to equal a magic number, but could also be read as a magic name.
The Arabic word for talisman is talsam. In casting out evil, the talsam brings good fortune. The first letters of certain names of God when written with abjad letter-numerals may take the place of the word itself. Or, the letter-numerals themselves may stand for their spiritual value. This is true of the badūh seal, which is believed by some Muslims to have been engraved by God on the seal stone of Adam’s ring. The badūh seal is the Lo Shu magic square of three written using the first nine abjad numbers, which is the form that was first published by Geber in 900 AD. It represents the planet Saturn, which is spelled zuhal in abjad letter-numerals that when summed equal 45 (z = 7+ h = 8 + l = 30), the magic sum of all the numbers in the square.16
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The badūh seal itself was the entire magic square of three. In later European occult circles this square’s magic path became known as “the seal of Saturn.”
The use of the magic square as a mystical device to communicate with the cosmos was eventually transformed into a tool to be used to gain control over one’s environment. Later developments of the Islamic magic squares resulted in their transformation into talismans or tools of magic by being conflated with their god and by being associated with astrology. However, the exact dates of this transformation are uncertain. Magic square amulets and charms were to be used for establishing friendships, preventing dreaming, casting out devils, etc. These magic squares work by being ingested or inhaled in a variety of ways, worn about the neck as a talisman, or engraved on a ring and worn on the finger.17
In the act of casting out evil spirits, magic circles (figure 4), squares and figures are sketched on the ground and then the demoniac person is seated in the center while an incantation is read.18
Circles have always played an important role in Arabic magic. The encircling of a person in danger is used as protection from evil spirits and wild animals. This can be done either verbally through phrases such as “I encircle you by God” or “I encircle you by the Qur’ān and what it contains,” often accompanied by circular gestures of the hand, or physically by drawing a magic circle on the ground while uttering powerful verses and magic formulae in preparation for the endangered person’s occupancy of the protected circle’s center.19
In the Islamic world, the pragmatic application of the magic square’s use for spells and protection gradually took precedence over its mystical and philosophical value, so that the magic square finally degenerated into being merely a magic charm or talisman. This seems to be the aspect of the magic squares that Europe inherited from the East during the Middle Ages. The exact origin of this transference has not yet been identified, however, it has been generally accepted that magic squares were transmitted to Europe via the Islamic world. These magic squares, however, were derivative and were disassociated from the religious and philosophical aspects of their inherent mathematical properties. Magic squares were seen solely for their magic or astrological properties and were gradually absorbed into the standard paraphernalia of the Renaissance magician.20
It is important to remember that numbers as we know them today did not exist at this time in the West—numbers in the East were represented by letters of the alphabet and what we recognize today as “roman numerals” were used in the West. This, together with the substitution of abjad letters for numbers to spell one of the names for God, made it possible to conflate numeric magic squares with acrostic magic squares and to substitute words for numbers using Islamic, Hebrew or Latin alphabets.
It may have been scholars in the Jewish communities of Spain, southern Italy and other Mediterranean lands that had commercial contacts in the Middle East and India, who were the
intermediaries through whom magic squares were brought to Europe. The earliest numerical magic square found in Europe was the magic square of three, discussed in the early twelfth century by Abraham ibn Ezra of Toledo. It was written with Hebrew letter-numerals in a style that became popular with the later Cabalists. The square’s constant numerical sum of 15 would have been written in Hebrew letters with יה or yōd and hē from right to left, the shortened form of the Tetragrammaton YHWH, the Divine name.
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The actual Hebrew letters would not have been written to avoid profaning the Divine Name, but the number’s true meaning would be a secret understanding, making the square itself a symbol for God. This method of interpreting letter numeral squares may have been influential in the development of gematria, a cabalistic method of interpreting the Hebrew scriptures by
interchanging words whose letters have the same
numerical value when added.
The earliest known European set of magic squares is found in a fifteenth-century Latin manuscript that is bound together with a fifteenth-century manuscript copy of Picatrix, presently located in the Jagiellonian Library in Cracow, Poland.
Picatrix itself was supposedly translated from Arabic sources in thirteenth-century Spain by
Jewish and Christian scholars at the court of Alfonso the Wise and is considered to be the
source of the Islamic astrological and cosmological lore that helped to build the tradition of the Cabala.
The Cracow set contains squares that can be identified as both Hindu and Islamic, and also squares that are garbled, which indicates that the manuscript’s scribe did not understand the content of what was being copied. This Cracow set is notable because it is the earliest known instance in Europe of magic squares dedicated to the Seven Planets.
It is important to note that the Cabala is believed to be an infallible science had by means of a nonhuman discipline and divine tradition. In other words, Cabala is knowledge direct from God without human intervention. In Renaissance Italy there was an enthusiastic interest in Jewish Cabala, because it was considered to be the most ancient manifestation of Christian truth and source of divine teachings of the ancient philosophers and theologians.21 The magic square or numerical acrostic was an integral part of the tradition of the Cabala. Contained within the magic squares were magic sums that named various gods and angels (Figure 5). These divine words were understood to have occult properties and secret powers that were used in ancient times in the performance of sacred rites and religious ceremonies. The “word” was more than the instrument of internal mystical union between man and God, but was also the instrument by which one could perform external miraculous activities in the world—works beyond human strength that, while constituted in nature, could hold power over it.
Due to the superstitious use of magic squares during the Renaissance and the discovery that their use did not effect miraculous wonders, together with an increasingly “rational” Western worldview, as early as the sixteenth-century in Germany magic squares lost their symbolic value and began to be viewed merely as problems in the mathematical arrangement of numbers.22 Over the next two hundred years, the ancient Islamic methods of making magic squares continued to be “discovered” by various Europeans, who augmented the existing squares with new inventions of their own. By the eighteenth-century in exoteric circles, magic squares had finally become mere mathematical recreations; however, in esoteric European circles, magic squares continued to circulate in hidden and occult manuscripts.
Two of these occult manuscripts were The Key of Solomon the King (1889) and The Book of Sacred
Magic of Abra-Melin the Mage: as delivered by Abraham the Jew unto his son Lamech, A.D. 1458 (1883), both translated by S. Liddell MacGregor Mathers.
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Mathers was a member of the Golden Dawn, a hermetic order in nineteenth century
England. According to the forward23 to The Key, it is a crucial text of Western ritual magic. Both The Key and the Book of Sacred Magic contain magic word squares. These Hebrew word squares are incorporated as part of the “First and Second Pentacles of Saturn” in The Key and comprise the entire third book of Sacred Magic as magical symbols. In Sacred Magic, the “Names arranged in the Squares represent generally the effect to be produced” or “appellations of the result to which the Square is to be applied.”24 These two books are excellent examples of how excerpts from a divinatory text, such as the Cabala, can be appropriated and transformed into magic or witchcraft, in this case “white magic.” (No such thing as white magic. All Magic is from the darkside)
Central to The Key is the act of encircling, similar to the Islamic magic tradition. In short, prior to the actual construction of the circle, the disciple must become clean in mind and body through prayer, ablution and fasting over a period of several days. The center is marked by a stake or sickle to which a cord is attached and the circumference of the circle is sketched on the ground with a knife blade at the end of the cord.
The intercardinal directions are marked and the crossing creates four regions within the circle: the east, west, north and south. Another circle is inscribed beyond the first, into which are written pentagrams with symbols and the names of the creator, which in turn protect the enclosure. At the perimeter of these circles a square is circumscribed, “square” with the cardinal directions. Beyond the first square is another square positioned such that the angles of the first square touch the centers of the sides of the second, so that the angles of the latter stretch toward the four corners of the universe. Each of these four corners becomes the center for another drawn circle, within which perfume is to be burnt.
Through this act of encircling, the disciple seated at its origin is protected within and oriented to the earth below and the universe above by becoming square with the world. This same act of encircling, with a similar underlying iconology but with a demoniacal twist, was central to “black magic” or witchcraft (figure 6).
MAGIC SQUARES AND VISUAL CULTURE
The construction of magic squares, the making of talismans and the process of encircling are geomantic magical procedures characteristically used throughout history and across cultures to bring cosmic harmony to the physical world. These methods were simply tools used by humans to project the divine onto the earthly as a way of “protecting” or bringing order to the built world.
The difficulty is in determining origins for these various icons that are mathematical (re)creations, words and magical devices all in one.
The talisman bears an icon that is the product of a magical procedure. The icon represented on the talisman could be the magic square itself, in itself a symbol, for instance the badūh seal, which in its entirety represents a Muslim God. The magic path of the magic square might be the sigil represented, for example, the “seal of Saturn” of the square of three, which due to its magic sum makes the square itself a symbol for God in the Hebrew tradition.
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Additionally, various other magic paths or significant relationships among the numbers of a magic square might become the basis for the construction of an icon to be represented on a talisman.
These talismanic aspects of magic squares seem to have survived well into 20th century Europe among many different groups of people, 25 the talisman itself having become disassociated from its numeric origins. The construction of the talisman and its active use for protection of the individual were means used to ensure one’s well-being and to bring good fortune to one’s immediate environment. The talismanic technique of encirling is a geomantic procedure that projects the divine from above to protect the earthly below.
This geomantic magical procedure creates auspicious conditions by guaranteeing alignment
of the microcosmic with the macrocosmic. (They fail to mention that this is all in relation to employing the aid of spirits, the spirits of the fallen and their progeny.)
The magic square is an arcane example of the superstitious and irrational that we moderns
consistently endeavor to banish from the common sense of our experience. The way we do this is through distancing ourselves by exorcising the primitive and occult aspects of our everyday lives to the margins, in spite of the fact that the essential meaning of these hidden aspects of our culture are regularly present in the images of our society. We are happy to play a crossword puzzle that does not involve words or mathematical ability. We would be unwilling to acknowledge that the mere act of completing the square might once have been a mystical experience intended to unite the puzzler with the divine. We are content with the knowledge that something like Feng Shui is an ancient practice that we have resurrected, and we recast the practice as being a truly contemporary part of life for a progressive society, unwilling to recognize this as a throw-back to a world that predated our forward-looking stride towards enlightenment and modernity. Eager for a new spirituality that could distance ourselves from everybody else and proclaim us as avant-gardes leading the way to a higher dimensional reality, we embrace ancient religions, which because of their esoteric nature have been hidden from popular view, and turn them into New Age fads.
Until recently, the visual artifact has largely been ignored, considered to be more or less decorative or superficial, and inferior to the printed word.
Nowadays, we are constantly bombarded with images and the virtual, reinforcing the notion that the image is ethereal, intangible and without meaning. However, the visual is not the invention of modern consumer culture; nor is it peculiar to modern politics and media. Iconic representations, logos and even branding form the vocabulary of images in almost every society, not only since the fifteen and sixteenth centuries when technology made it possible to reproduce and distribute images on paper, but even when we first scratched iconic images in the sand and carved representations in stone.
Bohemian Intellectual Mathematics and Occultism
Ramanujan12 Thead Start date: Sep 21, 2003
#1 Ramanujan12 “Bohemian” Intellectual Mathematics and Occultism There seems to be a difference in the cultural genre of mathematics in recent history. Going back to arround the mid 19th Century the Annals of Mathematcis have been archiving journals in “higher mathematics”, high-high mathematics actually the highest……so high that access to currents from the periods b4 the 1990’s have an specified-only-access system to protect this information from any undesireable institutions, researchers or mathematicians even. A kind of Euro-only and industry-centered mathematics cult appears to be coveting these publications and the Anals are just the surface-undergound front for a deepest level archive. There are mathematical mystics ammongst the background of academic society that dwells on a higher level of academic life. Many of these bohemian geniuses produced equations and some even had their knowledge stollen by these “mathemagical” cult groups. Hence mathematics as we know it is for the student, teacher, professional in the industry, but the secret stuff dwells on a high intuitive level of lexicography and semiotics. This is what I will reffer to as “intellectual mathematics”, a kind of late Avante Gardeism in function theory and analysis that flourished in the 1950’s, the 1960’s, 1970’s, and the 1980’s a bit too. Schools of analysis from Poland, underground fractal maths comming out of Russia and many other countries dealing with mathematical intuitions and model theories that our academies have no access to as text nor access mentally to know the language. What I am talking about here my friends is math as a non-industrial interest relations field, math as quasi-academic, independant and having a verry apparent philosophical, hermeneutic, semiotic, and linguistic repetoire. These texts may be on microfiche, they cannot be downloaded as PDF’s or anything else. However, there are allways intentional mistakes that have occured in the Springer Verlag monographs from the 1970’s, im not sure what publishing houses permitted this or who “disappeared” for making such publications available, but it can and has happened. Mathematical illuminaries are far beyond the calculus, the algebraic equations, differential geometry etc. all fall to pieces within these genesis level math systems. And the Kabbal that archives and progresses this secret knowledge have prodigies from outside academia to write texts for them, highly cryptic texts and symbols you aint ever seen, and believe me I have seen it all, everything from the halls of higher surface to the highest underground maths. It might be important for me to note that these 20th Century periodicals are not mathematics as we know it. Most of the value of these texts is their heuristic and crypto-interpretive stylism. All of the prised and respected mathematical foundations for QST and QFT all fall apart, and all of their field invariances, all of their incongential inconsistencies collapse with this coveted occult mathematics. Because durring those years (1950’s-1980’s), mathematicians and mystics basically devoted a culture on the outer limits of academic discourse that was extremally philosophical and the transformational grammar used to write these text underwrite the integrals, convergences, inversions, limit theorems, scalars, and analyticity in math as we know it. Intellectual mathematicians didn’t start with symbols and relations and go on to develop integrals, vector products, and calculative tensors, toplogy etc. they underwrote all that with language, with plane worlds; ie. their math was very wordy. And the words, itallics, brackets, all that they used to delineate their theorems were intellectually rendered from a philosophy of hermeneutics, interpretation and inversions for even inverse theories reduced to lexical discourses. This was the mathematics which founded number theory, this was the mathematics that was hijacked by the illuminised occult industrial-logicians math of calculator result methods. It is offten said that the highest math dwells in intuition, in descriptive propositions that are linked to a kind of mysticism, a mysticism that speeks in strange terms, deffines mathematical processes in a language that no mathematician can easilly decipher; without years of focus on that one text that managed to make it to the presses. Basically the purpose I am written this post is to inspire you. To inspire you to make up your own rules, re-engineer the theses on calculus and analysis and algebra to that of a Pythagorean mysterium or a Plotinus. I can just see the mathematicians as philosophical heretics, with pipe tobacco kits and long overcoats writting up abstract and yes deviant theories that nobody can understand. I hope this post inspires some to think outside the unit cube into the abstract unit box. Inspiration from Doob, Iwahori, Ward, and those without names recorded who could have changed the world. Specific Moral of the story is this: mathematics is a discourse, it is becoming a computational industrial discourse and wavering it’s intelligencia. Be creative, use your imagination, and have fun because thats the highest form of intuition, that is were your theorems will happen. If the occult circle of illuminised mathematicians allready have the TOE {using anti-gravity, UFO’s, ghosts, crop circles etc.} then it is up to us to take it back by writting the equations and monographic texts that will reallize TOE from the coming-to-itself of all abstractions of language, a theory for the origination of human language and semiote as radical discursive work. Good Luck –
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The maddeningly magical maths of John Dee
As an exhibition of notorious magician John Dee’s books continues, Philip Ball argues that he warrants a place in science’s history
Scholar, Courtier, Magician: The lost library of John Dee is showing at the Royal College of Physicians, London, until 29 July
“THE book of nature is written in the language of mathematics,” claimed Galileo. His full argument is actually more complicated than this, but philosophers, scientists and historians have seized on his statement to characterise “true” science: no branch of natural philosophy could call itself a science until it had become mathematical. “There is only that much genuine science in any science, as it contains mathematics,” asserted Immanuel Kant in the 18th century.
Physicist Steven Weinberg seems to agree. The birth of modern science in the “scientific revolution” of the 17th century was “the search for mathematically expressed impersonal laws that allow precise predictions of a wide range of phenomena”, he writes in his book To Explain the World: The discovery of modern science.
Yet Galileo had the good fortune to work on mechanics and astronomy: problems that can be conveniently mathematicised. Even today this maths-based definition still doesn’t accurately describe much of chemistry (for which reason Kant denied that it was science), biology, the earth sciences or medicine. There’s not a single equation in Charles Darwin’s On the Origin of Species.
“Dee’s work looks like mumbo-jumbo and mysticism. Yet it was mathematical“
One person who would have welcomed Galileo’s statement, had he not lived half a century too early to witness it, was the English scholar John Dee (1527-1608 or 1609). Yet Dee doesn’t appear in most histories of science, and some of Galileo’s champions might regard him with a degree of horror. Dee is more or less uncategorisable by today’s standards. Some of his Tudor contemporaries might have considered him a philosopher, an astrologer, perhaps even a magician – but they would have agreed that he was, above all, a mathematician.
And what did Dee do with maths? He cast horoscopes, practiced numerology and alchemy, and sought occult codes that would permit conversations with angels in the language used by Adam. Dee is, in short, the worst nightmare for those who want to tell the history of science along the same lines as Weinberg. To them, Dee’s work looks like mumbo-jumbo, superstition and mysticism. Yet it was fundamentally mathematical.
Dee’s eclectic interests are explored in an exhibition of his books at the Royal College of Physicians in London. These books are a few pitiful remnants of the legendary library at his home in Mortlake, west of London, before many of its contents were pilfered while he was travelling abroad. (The apocryphal story has it that the library was ransacked and torched by a mob who suspected him of demonic witchcraft.)
Among the volumes on display is the first English translation of the influential mathematical treatise by the ancient Greek writer Euclid, here called The Elements of Geometrie, published in 1570 by Henry Billingsley, Lord Mayor of London. It’s a gorgeous volume, with elaborate fold-out diagrams of polyhedra and intersecting planes, and Dee wrote the preface. That he was chosen for the task indicates the esteem in which his mathematical expertise was held.
What’s striking to modern readers about that essay is, first, that Dee considers it necessary to mount a defence of maths; and second, the breadth that he attributes to the discipline. Many people, Dee says, consider maths to be disreputable and allied with witchcraft. Indeed, some of the suspicion aroused by Nicolaus Copernicus’s De revolutionibus in 1543 came not from his heliocentric theory of the solar system, but from the fact that he used maths to deduce what he could not directly see. In Tudor times, maths books were often burned on suspicion of being “conjuring books”.
And maths really did have connections with the occult. Numerology was important to the Jewish mystical tradition called the Kabbalah, which Dee studied closely. Codes and cryptography were discussed in Steganographia (c. 1499) by the German abbot Trithemius, who was suspected of diabolical wizardry; it was this book that Dee examined to understand angelic communication. Even as late as 1651, Francis Bacon’s friend and biographer John Rawley was accused of conjuring when he used geometry to calculate the height of a steeple.
This kind of accusation isn’t fair, Dee argued. Maths is both useful and a source of hidden knowledge. He quotes the Italian Renaissance scholar Giovanni Pico della Mirandola: “By number, a way is had to the searching out and understanding of everything able to be known.” The wonders described in Dee’s preface were so captivating that, according to historian Peter Zetterberg, many readers were probably “disappointed by the Elements itself with its pedestrian tone and topics”.
In particular, Dee says, maths is a practical discipline, useful for technologies such as hydraulics and surveying (geometry, he reminds us, means “land measuring”). It was also needed to make ingenious mechanisms, a popular art at the time.
Practically minded “virtuosi” made their living by creating such devices for the princes and nobles of Europe, and Dee himself was said to have made a giant mechanical beetle for a play at Trinity College in Cambridge that astonished audiences. “And for these, and suchlike marvellous arts and feats naturally, mathematically and mechanically wrought and contrived, ought any student and modest Christian philosopher be counted and called a conjurer?” Dee asked.
“Copernicus aroused suspicion for using maths to deduce what he could not directly see“
Mechanisms like this were considered in those days to be allied with the tradition called natural magic, in which the invisible forces of nature were harnessed to work wonders. In 1648, the Englishman John Wilkins, Warden of Wadham College in Oxford – where he convened the group of philosophers who later became the Royal Society – published a book called Mathematical Magick. The title might lead you to expect either a collection of “think-of-a-number” party tricks or a treatise on numerology. In fact, it was a textbook of mechanisms: levers, wheels, pulleys, screws, clocks, windmills – even submarines.
Dee personifies this natural-magic tradition. For some he was the archetypal Elizabethan magus, using a crystal ball with the help of his shady sidekick Edward Kelley to speak with angels or demons. It’s possible that Shakespeare used Dee as the model for Prospero in The Tempest.
But the giants of the scientific revolution took him and his vision of mathematics seriously. Wilkins’s Mathematical Magick, inspired by Dee’s work, was one of the young Isaac Newton’s favourite books, and Dee’s preface was widely read throughout the 17th century. Robert Hooke defended Dee’s angelic discourses when they were published posthumously, saying that they must be encrypted intelligence messages sent to the British court while Dee was abroad.
Dee prefigured 17th-century scholarly occultists such as the Englishman Robert Fludd and the German Jesuit Athanasius Kircher, who discerned mystical “hidden knowledge” in nature’s workings while also exploring natural phenomena and mechanical inventions. If all this sounds a little like the mix we find in Isaac Newton too, you have got the right idea.
That’s why Dee is a noteworthy figure in the history of science. And his example stands as a warning: that if we cherry-pick from the time when Renaissance magic was morphing into modern science, we will never understand what that extraordinary time was really all about.
This article appeared in print under the headline “Count John Dee”
MY FINAL COMMENTS:
Look at how much of this stuff is fairly new, only introduced in the last 500 years. Folks will say that is due to progress. That is ego talking. THERE IS NOTHING NEW UNDER THE SUN. That is what GOD’s Word says. This has all been used before. The world has been moving in repeating cycles. The devil and his minions introduce the forbidden “knowledge” and use it on the masses, then they take it away. Take knowledge and lock it up until folks forget it ever existed, so they can bring it out again. Only this time, is the last time. We are at the end.