Euler’s Formula and Special Relativity
The Truth Series Book One
Group Study Section 1
BY DR. THOMAS STARK, ANOTHER PSEUDONYM FOR MIKE HOCKNEY
**Introduction**
What is the greatest scientific mystery of modern times, the mystery that would stump even Sherlock Holmes? It is this … why, despite the greatest intellectual effort in scientific history over many decades, involving the most knowledgeable scientists there have ever been, in larger numbers than there have ever been, with the best resources available to them in all of history, including vast, multi-billion-dollar particle accelerators, is science unable to reconcile its two greatest theories: quantum mechanics and Einstein’s general theory of relativity? How is it possible that two theories that have been fantastically successful, and fantastically well verified in all sorts of way, fail to communicate with each other? There must be something drastically wrong with one or both of these theories, or there is something drastically wrong with science itself. Why is science so incapable of figuring out what the problem is? Why is there no scientific research into why science cannot unify its two most successful theories?
Doesn’t it strike scientists as fundamentally suspicious that they can’t make any substantive progress? Doesn’t it make them call into question the entire basis of their science? How can the two jewels of science be so resistant to being placed in a single crown? How can they be so contradictory? Doesn’t it occur to scientists that something somewhere is seriously amiss with their enterprise? Where is the scientific investigation into why this paradox exists? Why does science refuse to look at itself in the mirror and confront some harsh truths about itself?
Scientists always say how open-minded they are. Where is the evidence? They seem amongst the most closed-minded people on earth, and most afflicted by groupthink. In religion, heretics are ostracized. In science, heretics have their funds withdrawn. So every practicing scientist is a good conformist and careerist.
The underlying reason for science’s problems is that there is a fundamental ingredient missing from science: the *tertium* *quid* (the third thing), which is the common substructure supporting both quantum mechanics and general relativity. (“Tertium quid” refers to an unidentified and more fundamental third element that is present in combination with two known elements.)
To understand what science’s tertium quid is, it’s necessary to consider the elementary issue that the vast majority of scientists shy away from, namely what preceded the Big Bang, what *caused* the Big Bang? The reason why scientists refuse to engage with this question is that they imagine they are being drawn into metaphysics, or even – God forbid! – religion. They believe they are being yanked out of their comfort zone into the arena of speculation and faith. It has never once occurred to them that science has a *necessary* *rational* *precursor*, i.e. you can’t have science unless an essential prior ingredient is in place.
Science does not exist in its right, as something wholly independent and *sui* *generis*. It is something derived from an older – indeed *eternal* – parent. That parent isn’t “God”. (As if!) It is *mathematics*.
Plato said that the sensible world is an inferior copy of the intelligible world of perfect, immutable, eternal Forms. What he would say today is that the sensible (empirical), scientific world is derived from the intelligible (rational), mathematical world.
Science is contingent and temporal. Mathematics is necessary and eternal. Science deals with truths of fact. Mathematics deal with truths of reason. If you want the *ultimate* *reasons* for things, you have nowhere else to go but mathematics. Because science deals with facts and not reasons (it is preoccupied with “how” rather than “why”), it cannot penetrate to the rational layer that explains all theories, including relativity theory and quantum mechanics, and why they succeed or fail. This deficiency is why science breaks down and becomes incoherent. A collection of disparate facts does not and cannot explain reality. Only reasons can explain reality. Moreover, these reasons must be necessary, absolute, infallible, immutable, complete, consistent, perfect and eternal. Only mathematics qualifies.
It’s an extraordinary thing, but every attempt to *rationally* justify the existence of “God” is much better understood as an attempt to justify the existence of mathematics. It’s not “God” that creates the universe, it’s math. It’s not God that is perfect, flawless and exists forever, it’s math. It’s not God that is unerring, all-powerful, all-knowing, all-seeing and ubiquitous, it’s math. “God” is simply the human attempt to turn math into a person to whom humans can emotionally relate. When you strip away all of the human characteristics that have been projected onto God, what remains is pure math. Math, not God, is what guarantees the “soul” and the “afterlife”. The soul is simply an immaterial mathematical singularity, defined by Euler’s Formula (as we shall demonstrate in this book), and the afterlife is inevitable since mathematics and mathematical souls are *eternal*, and reflect the most basic law of energy that energy can be neither created nor destroyed, which logically means that it has existed forever, can never cease to exist, and cannot be created out of nothing, as science bizarrely claims.
Science seems like Abrahamism at times with its claim that something can be produced from nothing at all, like a cosmic rabbit out of a magician’s hat.
Carl Sagan, the patron saint of science, said, “Extraordinary claims require extraordinary evidence.” Science never has, and never could, provide any evidence that existence can come from non-existence, hence it is hoist by its own petard. It is making demented claims, while failing to advance any evidence to support them. It therefore qualifies as an irrational quasi-religion. Science has committed itself to a belief that energy *can* be created out of nothing, provided it is energy that overall balances to zero. This flagrantly contradicts the law of the conservation of energy. Wikipedia says, “In physics, the law of conservation of energy states that the total energy of an isolated system remains constant – it is said to be conserved over time.” Plainly, the total energy is *not* being conserved over time, and the total energy is *not* remaining constant, if energy can be created out of non-existence. If energy can be created out of non-existence, even if it is required to balance to zero, this process should be happening all the time, everywhere, rendering stable existence impossible. Nothing could possibly prevent it.
Self-evidently, we do not live in such a universe.
The fact that science seriously argues that this is possible proves how systemically flawed science is. These flaws are abolished by eternal mathematics, which defines eternal mathematical energy, which can be neither created nor destroyed under any circumstances, and is the root of all energy observed in the contingent, temporal scientific world.
Science could not exist without mathematics. The temporal cannot exist without the eternal to support it. The contingent cannot exist without the necessary. The relative cannot exist without the absolute. Science rejects all three of these eternal truths of reason, while mathematics fully supports them. The biggest question of all for science is this: Was there a *mathematical* *world* before the scientific world … was the state that preceded and caused the Big Bang a state of pure analytic mathematics? Was mathematics the eternal, necessary world that produced the temporal, contingent Big Bang universe of science?
In this book, we are going to show you exactly where space and time come from, exactly where matter comes from, exactly what mind is, and exactly what reality is. All we require is one thing, the most powerful tool of analytic mathematics, Euler’s Formula: eix = cos x + i sin x.
We are going to link this formula to Einstein’s special theory of relativity and show that Einstein’s theory is: a) derived from Euler’s Formula, and b) a catastrophic misinterpretation of the mathematics that underlies relativity theory, stemming from the fact that Einstein supported the scientific philosophy of empiricism and materialism rather than the mathematical philosophy of rationalism and idealism.
All of the problems of science dissolve when it is understood that mathematics underpins science, that the eternal underpins the temporal, that the necessary underpins the contingent, that the absolute underpins the relative, that the rational underlies the empirical, that the intelligible underlies the sensible, and that mathematical idealism based on dimensionless mathematical atoms (monads) underlies scientific materialism based on dimensional scientific atoms.
Once these truths are understood, it becomes simplicity itself to demonstrate that the mind-matter problem first posed by Descartes is fully resolved by Euler’s Formula. Euler’s Formula leads directly to ontological Fourier mathematics based on monads, with mathematics supplying an eternal frequency domain of mind, and giving rise to a temporal, spatial domain of matter via the extraordinary mathematical properties of sine and cosine waves.
When the ontology of the Lorentz transformations – which provide the mathematical core of Einstein’s special theory of relativity – is applied to Euler’s Formula, we see exactly how Fourier mathematics works, and why it allows the mind to become a rigorous object of mathematics, wholly separate from the human body, and able to survive the death of the human body.
It’s all in the math. To understand reality, you simply have to understand that science is built on top of mathematics. When you get the scientific empiricist irrationalism out of the way, you are left with nothing but rationalist mathematics, which explains *everything* in the universe. There is nothing in existence that cannot be traced back to Euler’s Formula, which has been dubbed *The* *God* *Equation*. We don’t need God to create the universe. We *do*need the God Equation.
**The** **Singularity**
Imagine a world without space and time. What is such a world like? It’s like nothing you know, nothing you can easily comprehend. It’s the world of ontological mathematics, the mathematics of existence. When you strip out space and time, you are left with nothing but the bare building blocks of existence, from which space and time are subsequently constructed.
Without space and time, you have nothing to deal with but pre-space and pre-time, which are wholly mathematical. The Big Bang universe of space and time comes from the mathematical Singularity of pre-space and pre-time. Science is nothing but mathematics with space and time added. Without space and time, science reduces to mathematics.
Space and time are defined by *extension*. When you remove space and time, you are necessarily left with the world of *non-extension*. This is a world outside science given that the whole of science is framed by space and time, and makes no sense without them.
Descartes, the first modern philosopher, famously divided the world into two incompatible substances: 1) matter (*res* *extensa* = extended substance), and 2) mind (*res* *cogitans* = thinking substance). Extended things never think, while unextended things do nothing but think.
Descartes said, “I am a being whose whole essence or nature is to think, and whose being requires no place and depends on no material thing.”
For Descartes, mind and body were two radically different things. This is the position known as “dualism”. When people imagine their mind or soul surviving death, they are, whether they realize it or not, subscribing to Cartesian dualism. Science, which is more or less synonymous with atheism, vigorously rejects this position. Science is exclusively about materialism, hence insists that mind is a product of matter, in some mysterious way that no scientist has ever explained or defined.
Descartes came close to being the most intelligent human being of all time. He just needed one further insight, which he was actually excellently positioned to make given that he was a mathematical genius as well as a philosophical genius. Mathematics was exactly what he needed to complete his depiction of reality. Indeed, he said, “With me, everything turns into mathematics. … Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.”
The mathematics of Descartes’ day was not sufficiently powerful for him to make the leap to ontological mathematics, i.e. to claim that ultimate reality is mathematical, and that mind and matter are two expressions or modes of mathematics, one being unextended (dimensionless), and the other extended (dimensional). Moreover, the religious climate of the day would not have accommodated such a radical suggestion, unless it were claimed that mathematics was God’s language, through which he executed his creative endeavors and his divine will.
Descartes clearly knew or intuited that there was more knowledge to be revealed when he said, “I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery.”
Leibniz, another mathematical and philosophical genius, and Descartes’ true successor, ventured even deeper into the world of ultimate rational reality than his illustrious predecessor. To complete their brilliant work, it needed others to continue down the road of mathematics, guided by the philosophy of rationalism. Instead, a catastrophe intervened. The person responsible was the man commonly regarded as the greatest scientist of all time … *Isaac* *Newton*.
Newton wasn’t a philosopher and wasn’t a rationalist. He was the most contradictory of people: a religious extremist and scientific empiricist rolled into one. He almost certainly suffered from autism, which characterizes many scientists to this day.
Newton added advanced mathematics to the “natural philosophy” of materialism and empiricism, and thus created modern science. He had nothing to say about the mind, except to deny that it was unextended, as Descartes and Leibniz insisted. He subscribed to the doctrine of the theological philosopher Henry More that the spiritual world was extended, just like the material world (hence, in More’s view, why mind and matter could interact).
Where Newton succeeded in mathematizing empirical natural philosophy, Descartes and Leibniz failed in mathematizing rational metaphysics. They were on the correct intellectual track, but could not convert their system into a practical and successful enterprise. Newton was on the wrong track but *could* convert his system into something practical and successful … thanks to mathematics.
Newton succeeded where Descartes and Leibniz failed because he relied on “extended” mathematics, whereas they needed a mathematics of the unextended, a much more difficult mathematical problem, much harder to visualize, and impossible to support via direct observational evidence.
Science is all about extended mathematics involving space, time and matter. What Descartes and Leibniz were trying to do, although they weren’t entirely conscious of it, was to construct an unextended mathematics, dealing with non-space, non-time and mind. Where Newton dealt with physics and matter, Descartes and Leibniz were concerned with metaphysics and mind. Mathematics in their day simply wasn’t developed enough to accommodate mind and metaphysics. Now it is, which means the game has totally changed. It is now possible to fully replace scientific materialism and empiricism with scientific idealism and rationalism. To put it another way, it is now possible to replace Newton’s conception of reality with that of Descartes and Leibniz. This will usher in the ultimate paradigm shift, and completely change how humanity sees reality. Science will become rational and logical rather than empirical and observational, and all of the irrational premises on which current science is built will vanish.
Philosophy, *bad* *philosophy*, is what is holding science back. Science doesn’t even recognize that it *is* a philosophy, such is its lack of self-awareness and intellectual integrity.
Science is emphatically not a rationalist philosophy. It is an empiricist philosophy, hence an irrationalist philosophy. Scientists believe that science is on the side of reason and logic. It’s not. Mathematics is. The reason and logic that appear in science are inherited from mathematics. When science does not use mathematical arguments, it descends into irrational farce. The vast majority of what scientists say about quantum mechanics and cosmology is little short of gibberish, and is provably false.
**The** **True** **Dualism**
When Descartes spoke of the dualism of mind and matter, he failed to grasp a more fundamental truth that is now all too apparent. The true dualism is between physics and metaphysics. Physics is empiricist mathematics that has matter as its subject. Metaphysics is rationalist mathematics that has mind as its subject. Mind versus matter is simply unextended mathematics (metaphysics) versus extended mathematics (physics), mathematics that can’t be visualized versus mathematics that can.
Mathematics is mind. Science is body. Mathematics is rationalism.
Science is empiricism. Mathematics is intelligible. Science is sensible. That’s reality in a nutshell.
Mathematics relies on reason and logic, and can be conducted without any reference to the senses. Science, by contrast, cannot do without the senses, and always privileges them over reason and logic. Religion, meanwhile, relies on the emotions and mystical intuitions, and has no connection with the senses (science), or reason and logic (mathematics).
Philosopher Gilbert Ryle ridiculed the idea of Cartesian mind as an entity capable of interacting with matter, and dismissed it as a category error, derisively referring to the Cartesian mind as “the ghost in the machine.”
There is no “ghost” if mind is mathematics (unextended mathematics), and matter is also mathematics (extended mathematics). There is then nothing to prevent their interaction since they are both aspects of mathematics.
Echoing Ryle, P. C. W. Davies and J. R. Brown wrote a book called *The* *Ghost* *in* *the* *Atom*. But there is no ghost in the atom any more than there is a ghost in a collection of atoms (a body, or a machine). Mathematics is the invisible entity that controls atoms, and mathematics is the most rational thing you can get. There is nothing mystical or ghostly about it. The “ghost” – the entity which is deemed so ridiculous by scientists – is in fact dimensionless mathematics, the opposite of anything “spooky”.
All dimensional things are controlled by dimensionless things. All physical things are controlled by metaphysical things. All matter is controlled by mind. All living bodies are animated by the living minds that direct them.
Plato and Aristotle knew that the world could be intelligible only if matter – the stuff we see and with which we interact – has invisible form controlling it, form being the entity that organizes and unifies a given collection of matter into a single, discrete object. Form provides the definition and actuality of the object. Without it, matter would be undefined and unintelligible … pure potentiality, and nothing else. Leibniz brilliantly carried forward these ideas in his conception of the monadic mind. It’s now clear that he, Plato and Aristotle were right all along.
Dimensionless mathematics is the unseen form of the world, while “matter” is what you get when mathematics is processed via the mathematical dimensions of space and time.
Mind is that which exists when space and time do not apply. Matter is that which exists when they do. How simple is that?!
The mind is immaterial and outside space and time. Mind is an unextended entity that links to extended matter via the well-known mathematical techniques developed by Joseph Fourier in the 18th century. The mind belongs to the ontological Fourier frequency domain, while matter belongs to the ontological Fourier spacetime domain.
There is no mystery here. The problem for humanity lies in the fact that so many people – including scientists – regard mathematics as unreal, abstract and merely a manmade language, rather than as real, concrete and nothing less than the language of Nature itself.
Math existed before the first human, and will still exist after the last human has perished. Mathematics is the language of eternity, of eternal form, of eternal intelligibility. Mathematics is the answer to eternal existence. It is mathematics, not God, that exists eternally, perfectly, immutably, absolutely and infallibly. Math necessarily exists forever. It is *impossible* for math not to exist.
Scientists are not rationalists. They are empiricists, i.e. *irrationalists*. That’s their central problem. That’s why they keep thinking of math as a ghostly subject that they can’t pin down rather than as the concrete foundation of science, and indeed of everything else.
Mathematics is the most concrete thing you can get. You can falsify science, but you can’t falsify mathematics. You can verify, but not prove, science, whereas mathematics is all about proof, hence has no need at all of verification.
In many ways, science, as currently conceived, is the opposite of mathematics. Science won’t achieve a final theory of everything until it realizes that science is merely an extension of unextended mathematics, and that unextended mathematics is where all the ultimate answers and explanations lie.
Forget the Big Bang universe of space, time and matter (the scientific universe). The thing that counts is the mathematical universe – the analytic Singularity – that preceded and caused the Big Bang universe. How can you understand the Big Bang universe of science if you do not understand its cause? Its cause was a mathematical universe – an analytic Singularity of eternal mental energy. What could be more logical?
The extended universe of space, time and matter was preceded by an unextended, immaterial universe outside space and time, i.e. a Singularity. To put it another way, the cosmic body (the physical universe of science) was created by the cosmic *mind* (the mental universe of mathematics), which *still *exists, and is completely controlling the physical universe.
To get to body from mind all you are required to do is add extension, and we shall mathematically explain exactly how it is done in this book.
No miracles are involved. No one needs to invoke gods, spirits, probabilities, indeterminism, chance, accident, or anything else. It is all pure, inevitable, inexorable, rational, deterministic mathematics.
When Einstein said that “God” does not play dice, he was incontestably correct. “God” is pure math, and pure math at all times obeys the principle of sufficient reason, i.e. for every fact, there is an exact reason why it is thus and not otherwise. Science once shared this understanding of reality before becoming disastrously misled by its empiricist philosophy. In a rational mathematical universe, unlike an irrational scientific universe, nothing ever happens for no reason. Explicable causality, not inexplicable probability, drives the physical universe.
The reason why Descartes’ apparently dualistic system isn’t dualistic at all is that it is based on mathematics, hence is monistic. Mind and matter can communicate because there is no obstacle to unextended and extended mathematics communicating with each other. In fact, the latter is entirely derived from the former. That’s what the Big Bang is all about. The extended, empirical universe of space, time and matter – which science studies – is born from a perfect, rational, analytic, unextended, mathematical Singularity – which mathematics studies. What stands beyond physics is metaphysics … and metaphysics is simply unextended mathematics. Metaphysics versus physics = rationalism versus empiricism = mind versus matter = unextended mathematics versus extended mathematics.
The “mind” is not something bizarre, mysterious and unfathomable. Mind is unextended mathematics, i.e. pure mathematics, shorn of “space”, “time”, “matter”, and human senses and experiences.
The unextended mathematical Singularity is the true version of Plato’s perfect, immutable, eternal domain of absolute, infallible Truth outside space and time. The Truth *is* mathematics. Mathematics is the language of existence, of perfection, of the eternal truths of reason, which, by definition, have applied forever, and can never *not* apply. What preceded the Big Bang was a purely mathematical state, not “God”, or anything religious, spiritual or mystical. And definitely not non-existence, as science would have you believe.
The mathematical Singularity is the perfect home of the Principle of Sufficient Reason, the True “God”. “God” is not a being who manifests perfect reason. God is perfect reason itself, and perfect reason creates beings since perfect reason is nothing less than Plato’s Form of Life. Mathematics *defines*life. Life is a mathematical property.
The reason why science breaks down as it explores the world of the Singularity – where quantum mechanics and general relativity are unified – is that it is using entirely the wrong tools, concepts and ways of thinking. Science keeps using extended, empirical thinking where it should be using unextended, rational thinking.
Leibniz – with his concept of monads (unextended minds) – was the man who got closest to understanding the true nature of reality. Three hundred years after Leibniz’s death, his monads can now be perfectly explained via mathematics. The key to Leibniz’s *Monadology* is Euler’s Formula, the most important equation ever devised. It is none other than the God Equation, the equation that explains the whole of existence. No other equation can do so. It is unique. It is sublime. It is divine.
**The** **God** **Equation**
The power of Euler’s Formula is well illustrated through Einstein’s famous special theory of relativity. Euler’s Formula is the true basis of Einstein’s theory, yet also reveals that Einstein committed several acute interpretive errors, which have plagued science ever since. Einstein misinterpreted his own theory precisely because he was thinking as an empiricist rather than as a rationalist.
Einstein said, “Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.” In fact, mathematics, not imagination, embraces the entire world, and is all there ever will be to know and understand.
Had he been more imaginative (!), Einstein would have realized this. Like all scientists, he suffered from a cataclysmic *lack* of imagination … a wholesale inability to imagine a world without space, time and matter. Sensing types, such as Einstein, are the opposite of intuitive types. Intuitives have enormously more powerful imaginations.
The most important component of Einstein’s special theory is the postulate that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. Nothing is more extraordinary than the absolute character of the speed of light. Einstein did not attempt to explain this singular fact of nature. He merely accepted it as true, and built his theory around it.
If, as Newton believed, the speed of light is *not* fixed then space and time *must* be fixed. If, by contrast, the speed of light *is* fixed then it’s space and time that are *not* fixed.
For Newton, the speed of light could go up to infinity. Infinity, in his thinking, was the speed deployed by God. Gravitational effects were instantaneous in Newton’s theory of gravity because God – who was equivalent to absolute space in Newton’s system – could literally transmit the necessary information infinitely fast.
When Einstein abolished infinite speed and made the speed of light the cosmic speed limit, it signified that all forces, including gravity, took time to be transmitted. It also meant that Einstein had killed off Newton’s God.
It never once occurred to Einstein that the fact, proclaimed by his own theory, that no material thing could ever be accelerated to light speed – and hence that light speed was an ontological boundary and barrier – indicated that light belonged to *a* *different* *category* *of* *existence* from matter. All material things travel slower than light speed. That immediately begs the question of how light can belong to the material world if it behaves differently from all material things. The answer, of course, is that it does *not* belong to material world, which is exactly why it exhibits entirely different behavior. Science is ideologically incapable of reaching this simple conclusion.
In Cartesian philosophy, there is only one thing that cannot be matter, and that is *mind*. The inescapable conclusion is thus that light is the agent of mind, and what indeed could possibly be a better candidate? The Singularity that precedes the Big Bang is a Singularity of *pure* *light*. Pure light = pure mathematics = pure mind. Light, ontologically, is what unextended mathematics actually is. The “Big Bang” is a light event, a mental event. In particular, the Big Bang involves the breaking of the perfect symmetry of light. “Matter” is broken light … *asymmetric* light, recalcitrant, sluggish thought.
In mathematical terms, as we shall see, the domain of light is ruled by the mathematical property of *orthogonality*. The material universe, by contrast, is ruled by the property of *non-orthogonality*. Dimensionless existence is orthogonal existence, while dimensional existence is non-orthogonal existence. It really is that simple.
Dimensionality flows from the loss of perfect orthogonality. If perfect orthogonality is restored (as it always is in the end), the physical universe is eradicated, and reality returns to the Singularity of pure light.
God did not say, “Let there be light.” Light is eternal. In fact, light *is* God, the *real* God.
So, is light actually mind, as we have asserted? Let’s see if light does indeed have exactly the properties that Descartes attributed to mind. To do so, light must be immaterial, massless, unextended, outside space and time, and be constantly in motion (because if thinking stopped, mind would cease to exist … a mind is simply that which thinks, and can do nothing else; it thinks *forever*).
The Cosmic Mind that controls the Physical Cosmos is a Singularity of light. Light controls matter. Matter is *made* from light, from the “breaking” of light. Ultimately, all that exists is light, and light is just ontological mathematics, i.e. mathematics exists *as* light. Mathematics is not some bizarre, unreal abstraction. Mathematics is light itself. The light from the sun is mathematics. We are bathed in pure mathematics every day. Mathematics is life. Mathematics is mind. The biggest mistake humanity ever made was in failing to understand what mathematics actually is. Without light, we would be dead. Without light, we would not exist. Nothing would exist.
The Grand Unified, Final Theory of Everything is the theory of light, which is simply mathematics! Everything comes from math, everything comes from light, everything comes from mind. “Matter” does not exist in its own right. It is simply a special mode of mind, resulting from specific mathematical properties of mind.
**Light** **and** **Immaterialism**
Matter can be defined as that which can never be accelerated to light speed, because it would require an infinite amount of energy to accomplish this. The only thing that is not subject to this prohibition is, of course, light itself. Light, therefore, does not belong to the material world. It belongs to a different category of existence, namely *mental* existence.
It is extraordinary that science considers light part of the material world when it self-evidently isn’t. It *interacts* with the material universe – exactly as mind interacts with body – but is not itself material (just as mind is not).
Light is that which matter can never reach in terms of speed, hence light is not the final material entity, but the first mental entity. It is separated from matter by the clearest of all ontological barriers.
**Light** **and** **Masslessness**
“The word ‘mass’ is given two meanings in special relativity: one (‘rest mass’ or ‘invariant mass’) is an invariant quantity which is the same for all observers in all reference frames; the other (‘relativistic mass’) is dependent on the velocity of the observer.” – Wikipedia
The photon – the particle of light – has zero rest mass. The rest mass of an object is the inertial mass it possesses when it is at rest, i.e. not moving in space. Everything in the material world has a non-zero rest mass. Light does not, hence light cannot belong to the material world. Once again, we see that light belongs to a different category of existence. The only alternative to material existence is mental existence. There is no other type of existence.
There are only minds and bodies; the mental and the material. Photons – the light carriers – belong to the mental, not the physical.
Before Einstein, an object’s mass was regarded as a constant. Its rest mass was its mass in *all* *circumstances*, regardless of speed. Einstein’s special theory of relativity ushered in the notion of relativistic mass (i.e. dynamic, non-rest mass), different from rest mass, and which would keep changing as velocity kept changing.
If light speed is fixed, space and time cannot be fixed. If space and time are not fixed then mass cannot be fixed either since mass is implicitly defined with respect to space and time. The condition of light speed being fixed is the criterion for mental existence. The condition of material existence is space and time not being fixed, ergo light does not belong to material existence.
John Wheeler wrote, “Mass tells spacetime how to curve, and spacetime tells mass how to move.” This shows how intimately mass is related to space and time. Mass is just an aspect of spacetime. You cannot have physical mass without spacetime. Likewise, you cannot have physical mass in non-spacetime (a singularity). Light has no physical mass because it is not in spacetime.
Light *interacts* with spacetime. It is not *part* of spacetime. When we perceive light, we unavoidably perceive it from a spacetime perspective, which gives us a wholly false notion of its true nature. *We* are in spacetime. Light isn’t. We can’t help but perceive all things as being in spacetime – we are permanently wearing spacetime goggles – even if they are *not* in spacetime. If we were wearing green goggles, everything would appear green, including everything that wasn’t green. The task is to try to conceive of light from its own perspective, not ours, i.e. to mentally remove our spacetime goggles. Only math can accomplish this transformation of perspective.
Nothing is more detrimental to our ability to think about ultimate reality than our spacetime goggles … the basis of materialism and empiricism. If we could take off our spacetime goggles, no one would be a materialist or empiricist, and everyone would have a radically different conception of light. Light doesn’t move through spacetime. Spacetime moves through light!
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Any object in motion has kinetic energy. According to Einstein, an object’s mass increases as its energy increases. Therefore, the mass of an object is at its *minimum* when it is stationary. Its mass would be at its *maximum* if it could travel at light speed, but Einstein’s equations show that its mass would then have to be *infinite*. However, this is a contradiction since light itself does not have infinite mass. In fact, it has no mass.
In special relativity, an object’s dynamic mass, m, is calculated via the following equation:
m = m0/√(1 – (v2/c2))
where m0 is the rest mass, v is the object’s velocity through space, and c is the speed of light.
When v = 0 (i.e. the object is stationary in space), m = m0. As v increases, so does m. If v = c, m is infinite. Nothing in the material world has infinite mass, hence no material thing can be accelerated to light speed. It would require infinite energy to do so. This proves that there is a definitive ontological boundary between matter and light (mind). They do not belong to the same category of existence. It’s therefore a category error to treat light as part of the material world. Science, since it refuses to accept the existence of mind as a real entity, independent of matter, continuously commits this category error, with fatal consequences for the coherence of its theories.
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There is a fundamental problem with Einstein’s equation. Light moves at light speed, yet does not have infinite mass. In fact, it has no mass. This means that in order for anything material to travel at light speed, it would have to cease to be material and become mental, i.e. it would have to undergo an ontological phase transition. We see exactly the same phase transition in the formation of black hole singularities. Massive stars implode to nothing at all. They leave spacetime entirely.
Any material thing approaching light speed would become so massive that it would collapse into a singularity, just like a huge star. Every moving object would thus have its dynamic equivalent of the Schwarzschild radius.
Wikipedia says, “The Schwarzschild radius … is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light. An example of an object where the mass is within its Schwarzschild radius is a black hole. Once a stellar remnant collapses to or below this radius, light cannot escape and the object is no longer directly visible outside, thereby forming a black hole. It is a characteristic radius associated with every quantity of mass.”
This means that the material world of mass is completely bounded and contained by the immaterial mental world of no mass. When anything in the material world becomes too massive, it leaves material existence and becomes mental. Nothing material can travel at the speed of light because only mental things travel at that speed. To reach light speed, a material object does not need infinite energy. Rather, it needs to leave the spacetime world of matter, and it inevitably does so as soon as its mass reaches a certain critical point (determined by what we might designate as its “Schwarzschild velocity”).
The material world exists *inside* the mental world, in the sense that any means you use to leave the material world will necessarily involve your undergoing a phase transition to mental existence. When people wonder what space is expanding into, the answer is that it’s expanding into *mind*, not into non-existence. You can escape from the material world to the mental world, but you cannot escape from the mental world to anywhere beyond that. There is nowhere beyond the mind! The mind is the true universe. The false universe is the material construct – the Matrix – that resides within the mind, created entirely by mathematics.
All of these conclusions are implicit in the special theory of relativity, yet they are scrupulously avoided and ignored by small-minded, dim-witted, unimaginative and unintuitive scientists, who are entirely ruled by their senses, and never once consider the possibility of dimensionless, mental existence … even though it’s staring them right in the face via their own equations!
Scientists hate rationalism, hate reason and hate logic. The only conclusions they entertain are those compatible with materialism and empiricism. That makes science a closed-minded faith, the opposite of what it purports to be.
Descartes
“The visible world is merely an illusion that hides the real mathematical reality of things. Mathematics exists separately from human beings and is prior to the creation of the universe itself.” – Descartes
This is the classic Platonist view of mathematics that it pre-exists everything else i.e. is the cause of everything else. It implies, for those of a Creationist inclination, that God is a mathematician and uses mathematics to create something from nothing and order it into the cosmos, although mathematics is of course entirely absent from Abrahamic texts, notwithstanding the laughable claims of Kabbalists that the Torah is full of mathematics (what they mean is that numerology can be applied to the words of the text).
“I shall bring to light the true riches of our souls, opening up to each of us the means whereby we can find within ourselves all the knowledge we may need for the conduct of life and the means of using it in order to acquire all the knowledge that the human mind is capable of possessing.” — Descartes
Descartes was the first modern philosopher and declared of himself, “I am a spectator rather than an actor in the comedies of life.”
In terms of revealing the secrets of the universe, his greatest contribution was to divide the universe into mind and matter, distinguished in terms of what he called “extension” (length, breadth and height). While the material world was entirely concerned with extension, the mental world was unextended, hence “outside” the material world. Although this definition worked wonderfully in terms of clarifying the difference between mind and matter – and remains the ultimate definition – it created an enormous problem: how could they interact since they were so different and did not occupy the same space?
This conundrum created two radically different philosophical schools: materialism and idealism. Materialism was championed by science and denied that the independent mental domain existed at all: it wasn’t extended hence it wasn’t there. After all, it was impossible to detect with the human senses. No one could see it, hear it, touch it, smell it or taste it. What experiment could possibly reveal its existence? How could you collect any scientific data regarding it? Wasn’t it just exposing the reality that the immaterial, unextended domain of the soul and God was a fantasy?
Science is, at core, pure empiricism, materialism and atheism. These terms are all effectively synonymous. Although there are scientists who profess their belief in God, these are intellectually dishonest individuals who are trying to have their cake and eat it. If you accept the materialist paradigm, you have left no room for God, the soul or even for free will. You have placed the whole universe, including human beings, within an inexorable chain of physical cause and effect determined by scientific forces. Since no one claims that the laws of science have free will and can “do their own thing” whenever they feel like it, there is therefore no conceivable mechanism by which free will can operate.
Kant, an idealist, addressed the Cartesian problem by declaring that while there was only one universe (the mental one), it had two aspects: a noumenal universe of “things in themselves”, which was entirely unknowable, and a phenomenal universe of these things in themselves as they appearedto our senses, which had all the characteristics of the material world, without of course being material. We understand the world so well because it is in fact created by our own minds. Since we can’t ever escape from our minds, we can never see things as they truly are, free of the constructions our minds have imposed on them, free of the systemic illusion to which we are prey.
So, for Kant, the phenomenal world corresponded to the world of science ruled by deterministic laws of cause and effect (created by our minds and NOT inherent in any alleged external material world). However, the unknowable noumenal domain afforded Kant the opportunity to claim that it was there that God, the soul and free will existed, although, as he admitted, we could never know anything about them. This was an ingenious and highly influential scheme that explained the scientific world while, unlike scientific materialism, leaving legitimate room for the free will that we all believe ourselves to have.
Scientists of course dismissed Kant’s dualistic philosophy, just as they had previously dismissed Descartes’. They said that the so-called noumenal universe was, by definition, unknowable and beyond any form of detection, hence was an entirely spurious, redundant and empty concept. They also rejected the notion that the scientific universe was a creation of our minds rather than exactly what it seemed to be: an external material world obeying scientific laws that come from outside rather than inside our minds.
What Kant had effectively done was to recast the Cartesian philosophy in slightly different terminology, and with one radical twist. Descartes had proposed two domains, mental and physical. The physical domain was exactly as scientific materialists conceived it: an objective, external reality subject to inexorable scientific laws. The mental domain, on the other hand, was unextended and scientifically undetectable. Scientific materialism immediately dispensed with it altogether – especially since no one who supported Descartes could convincingly explain how mind and matter interacted.
Kant’s noumenal universe is much the same as Descartes’ mental domain – outside space and time, unextended and undetectable. However, whereas the mental domain, for Descartes, was strictly for consciousness (“I think therefore I am.”), the mental, noumenal domain for Kant is for everything. Every phenomenal object has a noumenal counterpart. Kant’s extraordinary innovation was to say that our minds operate mentally on these mental objects (noumena) in a coherent, systematic and predictable way that turns them all (other than minds themselves) into phenomenal rather than noumenal objects i.e. into objects in space and time, subject to the inexorable cause and effect of scientific law.
Kant said that space and time provide the conditionsfor sensory experience: “The formal principle of our intuition (space and time) is the condition under which anything can be an object of our senses.” This means that spatial and temporal relations are only experienced by the passive, receptive part of the mind, which Kant called intuition, as opposed to the active part concerned with intellect.
In other words, everything, for Kant, is actually mental, including space and time. Minds impose the systematic illusion of a scientific, lawful, objective, material universe.
One way of thinking about Kant’s noumena and phenomena is within the context of Plato’s domain of Forms and his Demiurge (“the public craftsman”). For Plato, the Demiurge took the eternal Forms and imprinted them on the universal clay (matter) to fashion a material copy of the perfect domain of mental Forms. For Kant, Plato’s well-defined Forms are replaced by the mysterious noumena – seeds of ideas, we might say. Our own minds take the role of the Demiurge. We fashion the noumena into the stuff of the phenomenal world not by stamping them on matter but by applying mental categories and intuitions to them, most especially of causality, space and time.
Rather than have a strict Cartesian mind-matter dualism, Kant has one mental world that manifests itself dualistically: 1) things as they mentally are in themselves (which are never observed and are unknowable, especially minds themselves), and 2) things as they appear to our senses – as material objects of science located in space and time and subject to causality.
Kant had thus unified mind and matter by claiming that everything is in fact mental, but then divided them again as knowable mind-created, “material” phenomena and unknowable mental noumena. He had resurrected the material world but it was no longer actually material but “phenomenal” – of the order of appearance rather than reality i.e. a grand illusion.
As we have observed, scientific materialists were unimpressed and ignored all such talk. For them, the scientific world was absolutely real and no kind of mind-created phenomenon. Nevertheless, Kant’s scheme – known as transcendental idealism because it pointed to the existence of higher truths that transcended our experience – was so intellectually ingenious and imposing that it caused an explosion of interest in idealism, led by great German geniuses, and culminating in the awesome Illuminatus Hegel.
Idealism addresses the Cartesian problem of mind-matter dualism by taking the opposite stance to materialism. Idealists say that the only reality we actually experience is the mental one. The only knowledge we have about the world is mental. We are nothing but entities that experience ideas, thoughts, feelings, sensations, impressions, intuitions: all mental rather than material states. If you removed our ideas of the world, you would have removed the world. Our ideas of the world ARE the world. So, whereas the materialists abolished the Cartesian mental world, the idealists abolished the Cartesian material world.
According to materialism, there is an objective world independent of our minds controlled by scientific laws of cause and effect that are equally independent of our minds. A scientific materialist can happily think of the universe as containing no minds at all, including his own. Science is about revealing the “objective truth” of a kind of dead, mindless, mechanical universe. Science has made no inroads at all into explaining life, mind or consciousness. All of its great successes concern the universe as a cemetery, or as a great clockwork mechanism incapable of exhibiting free will, desire or passion.
According to idealism, our minds create the universe and there is no objective universe “out there”. The laws of science are created by our minds and do not exist outside them. (It is in fact extremely difficult for materialists to account for the existence of scientific laws – if they are part of the extended material world, they must somehow be material. So where are they are? What are they? Where are they stored? How can they affect everything all over the universe? How can any material thing “know” what laws to obey and indeed how to obey them? Where did these laws come from? Where were they before the Big Bang? In fact, how can laws exist at all? Why shouldn’t the material world be a completely random, lawless place?
Everything in the material world decays and runs down, but not the laws themselves which always stay the same, hence are of a totally different and alien kind from the rest of the material world. Why are they immune to change when nothing is? No materialist has ever accounted for the laws of matter. Scientists talk of the heat death of the universe being caused by entropy and the Second law of Thermodynamics, but of course the Second Law of Thermodynamics is not itself subject to any decay and heat death i.e. laws are of a wholly category from what they control. Why?
A Platonic dualism has been invalidly introduced by science: eternal, immutable, perfect laws contrasted with transient, physical, imperfect objects relentlessly running out of usable energy. But scientific materialism rejects Plato, so it is therefore presented with a challenge so great that it has never once addressed it: are the laws of materialism themselves material? If they’re not then how can they exist since only matter exists? If they are then why aren’t they subject to material decay like all other matter? It’s not clear that any scientist has ever grasped the magnitude of this problem. By itself, this philosophical problem destroys the whole ideology of scientific materialism. Scientific materialism cannot be true because it cannot explain its own laws. It can’t explain what they are ontologically, hence they are like magic. They’re from fairyland!
People take scientific materialism seriously not because of its philosophical coherence but because it works pragmatically and its successes have indeed been wondrous.
Materialism and idealism can both make strong cases that the opposing school is false, yet neither has ever landed a knockout blow. Isn’t that astonishing? How can two so radically different views somehow bothbe powerfully true and persuasive? Surely this points to the need for a tertium quid – a third thing – that reconciles the opposing schools. Illuminism is precisely that tertium quid, and it fulfils the task through the ultimate truth: mathematics.
Unfortunately, Illuminism has two immense obstacles to overcome. On the one hand, scientific materialism has been staggeringly successful in terms of technology, manufacturing, the military-industrial complex and medicine. It has authentically changed our world beyond recognition. To any thinking person, science is immensely persuasive. It’s no surprise that someone like Richard Dawkins, a fervent atheist and materialist, is so widely admired. Yet even Dawkins and his followers can do nothing to dent the confidence of the second obstacle, the irrationalists i.e. the Jews, Christians, Muslims and Karmists.
The Abrahamists have actually become more fanatical and irrational as science has grown stronger. They are in much greater denial than ever before. They hate reason and prize irrational faith with a great passion. A medieval thinker such as Dante was aware of no serious conflict between science and religion. In fact, the two disciplines seemed in beautiful and perfect harmony, united by reason. It is in the present day that the gulf between mainstream religion and science has become unbridgeable. It is no longer rationally possible to think that Abrahamism has anything in common with science. If you accept the scientific facts then you cannot be an Abrahamist. Abrahamism has been formally refuted as a logical possibility in the scientific world. Many Abrahamists have therefore cultivated an extreme distaste for science. They are perfectly aware that if science is true their beliefs are false. Rather than abandon the beliefs with which they were brainwashed since birth, they have chosen to abandon reason. Like Luther, they have declared that reason is the Devil’s whore.
Nowhere is the abyss between science and Abrahamism clearer than in the case of Darwinian evolution. The situation couldn’t be simpler. If evolution is true, the Creator God of Abrahamism does not exist. The whole point of evolution is that it requires no Creator. It is a self-propelling process. Natural selection has nothing to do with truth or morality. It cares only about reproductive success, about the passing on and spread of particular genes, hence Dawkins’ famous and brilliant book The Selfish Gene.
Now, some Abrahamists seek to claim that their Creator God created the evolutionary process. But this is untenable, and indeed spectacularly so. Why would a Creator God establish a process so savage, so amoral, so far from truth and goodness, that it looks like pure evil? The brutal and bloody law of the jungle is what you would expect in hell, not heaven. If “God” were responsible for evolution then he would be Satan, not God. He would have created an arena of endless killing and pain, for no apparent reason. How can a moral God create a process devoid of morality?
Is a shark an immoral serial killer, or does it simply kill to live? Humans are killers par excellence. They kill for fun! A God who sets in motion a perpetual death machine of mind-boggling cruelty cannot be God. When “God” ordered Abraham to kill his own innocent son for no reason at all, he made it clear to all people possessed of reason that he was not God.
Since evolution requires no one to get it started – it’s just part of the fabric of the universe – why would God invent a system that makes him look superfluous? Is he actively trying to baffle and bewilder people? Is he perverse? If so, he cannot be God.
If God is the true Creator, why didn’t he simply create, just as it says in the Bible? Why didn’t he create one planet, one moon and one sun, and put humanity on the planet? What point in Creation is served by the countless planets, moons, stars and galaxies that litter the infinite universe? The universe is so incomprehensibly large (and expanding) that there are things out there that humanity will NEVER see. So why are they there? For whose benefit? What do they have to do with Adam and Eve on Earth, the alleged centrepiece of God’s universe?
The hypothesis of a Creator God cannot be sustained in the face of evolution and an infinite universe. Only someone insanely opposed to reason would continue to support the concept of a Creator God. What’s the difference between irrational people and mad people? Can we distinguish between the two? If you reject reason, can you even be called human or are you just an animal?
Descartes, a supreme rationalist, expressed the view that mathematics provides the fundamental structure shared by all branches of knowledge. That being the case, why does neither the Torah, Bible nor Koran refer at all to mathematics? If mathematics is the key to existence, the last place where you will discover the secrets of reality is in the Abrahamic holy texts. Can anyone point to even one item of worthwhile knowledge offered by the three books allegedly authored by the Creator of the universe? Does God hate knowledge, or does he hate the idea of human beings having knowledge? The books of Abrahamism are irrational texts of anti-knowledge and hatred of intellect. They contain no intellectual sustenance at all. They are books of Pavlovian dominance and submission.
Reason
Given that Descartes believed in two essentially separate domains of matter (extended) and mind (unextended), he could not conceive of a vacuum existing in the material world. If a vacuum contained “nothing”, it would be unextended, hence mind-like: an impossibility in the physical world of extension. Therefore, Descartes argued for the existence of a “plenum” – a completely full material universe, with no empty space whatever. He also rejected the concept of indivisible atoms. If they existed in the material world then, no matter how small, they were extended, hence divisible. Instead, he referred to infinitely divisible “corpuscles” (although he never considered what should happen if they reached their indivisible limit: Leibniz did and made them his dimensionless “monads”).
These corpuscles, Descartes said, had “primary”, objective qualities, intrinsic to themselves, of extension, motion, mass, volume, position, number etc. They also had “secondary”, subjective qualities that were not intrinsic to them but resulted from the effects they had on the human senses. These secondary qualities were colour, smell, taste, the sounds they caused us to hear and the way they felt to touch. In other words, all of our sensory information is secondary, subjective and unreliable. Think of colour. It can be radically changed by the prevailing conditions. In a red-lit room, everything appears reddish. As it gets darker, our colour vision fades to black and white (just look around your room before you go to sleep – there’s no colour!)
Descartes’ material universe was thoroughly mechanistic, mathematical and predictable, and gave a huge boost to scientific thinking. He advised researchers to divide all big problems into smaller ones (the reductive, analytical approach), to argue from the simple to the complex and to check everything carefully.
As a rationalist, Descartes thought that only pure reason yielded reliable knowledge, and reason relied on mathematics and logic. He was dismissive of the knowledge we get from our unreliable senses. No sure knowledge could come from such a dubious source.
The opposing school to rationalism is empiricism, which asserts that only our senses can yield knowledge about the external world. How can staying in a room using your pure reason tell you anything about a frog? You can learn about frogs only by gathering information about them via your senses. Without that information, reason is superfluous.
Rationalism and idealism are a natural alliance while empiricism and materialism represent the opposite alliance.
In order to explain the source of irrationality, Descartes contrasted will and intellect. He asserted that, driven by will, we often choose to believe confused, unclear ideas. Will power, it seems, has primacy over reason. This is a critical point. Abrahamists are irrational because reason, it appears to them, takes them down the road of atheism and certain death whereas Abrahamism promises them eternal life in paradise, albeit without any rational basis. Is it any wonder that legions of ill-educated, fearful people find reason rather less appealing than irrational faith? Our free will often leads us into absolute irrationality. It is never emphasized enough that only a small proportion of humanity is guided by reason. The rest are controlled by will. Therefore, there’s little point addressing the masses with rational arguments. You must target their emotions and will if you want to win the debate. Moses, Jesus and Mohammed were classic irrationalists making crude appeals to emotion and will, and using threats of extreme and indeed eternal pain for anyone who disobeyed them.
Humans are creatures of will, not of reason and intellect. Will is emotional and full of desire. If we want to evolve as a species, we must learn to moderate our will and increase our reason.
Imagine we were programming artificial intelligences that we wanted to be something like us. We certainly wouldn’t make them exclusively logical and rational. But here is the big question – how do you programme will into a machine? How do you make machines irrational? Aren’t will and irrationality what truly separate man and machine?
How can humanity progress without increased reliance on reason? Can increased will lead to any evolution? Or does it just drag us back to the jungle, and even further back to the primordial slime? A huge amount of capitalist advertising is directed straight at the will and emotions. Capitalism revolves around the will and emotions, not around reason. Abrahamism revolves around the will and emotions.
We can’t take the path to divinity unless we embrace reason. We have no choice.
** Platonism**
“Platonism”, derived from Pythagoreanism, is used to describe the stance of those mathematicians who assert that mathematics pre-exists humanity, is indeed eternally coded into the universe, and determines its structure. Mathematics is thus “real” and has independent existence. As far as Descartes was concerned, all human knowledge might one day be mathematized. Although Descartes wasn’t an Illuminatus, he shared exactly the same vision as the Illuminati – a complete mathematical explanation of existence. If mathematics is indeed universal and integral to existence, any rational alien race would also be mathematical. The only language in which we would be able to infallibly communicate with them would be mathematics.
So, is mathematics something that rational people discover about the universe, or is something that rational minds invent? The latter option seems inconceivable and yet if it were true it would surely lend maximum support to Kant’s hypothesis that minds create reality. If a mind can construct something as complex as mathematics, what couldn’t it invent?
The position that mathematics is an invention of mind is known as “formalism” or “relativism”. It asserts that mathematics is something akin to an enormously more elaborate version of chess. It has its rules and immensely complex games can be played, but they have no connection with reality. We use the initial rules to create additional yet consistent rules, but all we are ever doing is playing a more and more sophisticated game.
An argument has been advanced that mathematics is a “closed” system, hence cannot yield any knowledge about anything other than itself. There are no avenues for introducing non-mathematical parameters, hence mathematics can never provide “new” knowledge. This argument is actually key to the entire Illuminist project because Illuminism asserts that mathematics is indeed a closed system but it further asserts that there is nothing at all external to mathematics i.e. mathematics is EVERYTHING. To say that mathematics is closed is not to place any limitations on its explanatory power since there’s nothing outside it, nothing else to which it would have to open itself.
Illuminism declares that everything that exists and all authentic knowledge of everything that exists are entirely defined mathematically. Mathematics is IT. There’s nothing else. By the end of this series of books, we hope we will have persuaded you of this astounding fact.
Just look at the best theories of science: almost entirely expressed mathematically. If mathematics is simply a formalism, a self-consistent game, then the same must also be true of the most successful scientific theories, which means that we know nothing of the world and it might as well be Kant’s noumenal universe (about which we must remain silent).
Just look at computers and computer simulations – wholly mathematical. Where would we be without our computers? Has anything proved as successful as applied mathematics?
The abstract work of Bernard Riemann on non-Euclidean curved spaces would once have seemed to be mathematics in the purest formalist sense, with no connection with external reality (assumed to be entirely Euclidean), yet this work became the bedrock of Einstein’s general theory of relativity and is used in the cosmological theories describing the evolution of the universe.
“Platonist” mathematics is what we define as ontological mathematics.
The Home of the Soul
Descartes famously identified the pineal gland as where the mind or soul exists and interacts with the physical body. He imagined the soul as a “homunculus” – a little man – who receives all of the information flowing in from the senses and processes it all, adding his own reason and logic to make sense of it. It is as if our soul is in a private cinema watching the images being sent, via the eyes, from the external world. The soul itself does not interact with the external world while the body that does is in some sense just a human automaton. Behaviourist philosopher Gilbert Ryle referred to this model of a private soul inside a kind of mechanical man as the “ghost in the machine”.
For Descartes, Nature, in its material aspect, is an automaton, and he held that animals have neither souls nor feelings. They are just machines. In fact, even humans are just machines materially, meaning that doctors are not healers but mechanics and repairmen. In Descartes’ mechanistic universe, matter affects matter only through physical contact. Matter, motion and collisions are the only elements in this system. There is no “action at a distance” – no forces operating across space. It was a corollary of this position that if the motions of all particles were known, we would be able to know the future by calculating how the system would evolve with time. Everything, in principle, could be explained. This is still, more or less, the position adopted by scientific materialism.
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THE MYERS-BRIGGS MATHEMATICAL TYPES
What type of people can hope to understand mathematics? We contend that as a generality only four of the sixteen Myers-Briggs personality types can be seriously mathematically literate.
First of all, to be mathematically skilled you have to be an introvert. Our definition of introvert is a simple one. An introvert is someone who enjoys his own company and does not go out of his way to seek the company of others. An extravert, on the other hand, enjoys the company of others and goes out of his way to avoid being on his own. To be a mathematician, you must have tremendous concentration, which implies being on your own without distractions. An extravert, continually distracted by the company he cultivates, never has the time and opportunity to be a deep thinker. Profound thinking is almost exclusively reserved for people capable of being solitary for long periods.
Secondly, mathematicians are usually highly intuitive. They can tune in, so to speak, to the mathematical fabric of the universe. Numbers, shapes and patterns present themselves as gifts to intuitives.
Thirdly, mathematicians are highly likely to be thinkers. While entertainment is the terrain that appeals to feeling and sensing types, mathematics, science and philosophy appeal to thinkers. Thinkers like cold abstractions, vast patterns, ordered lists, organised building blocks, while entertainment types wallow in the sensations and feelings that words, images and action summon in their imagination.
The four psychological types that predominantly fill the ranks of mathematicians are: INTJ, INTP, INFP and ISTP.
ISTPs and INFPs are the second rank of mathematicians. In the ISTP case, these mathematicians are highly observant about the world they detect with their eyes and ears (they often love music), but they have a severe deficiency through their lack of intuition. INFPs are highly intuitive and can even feel mathematics to some extent, but they are hindered by their deficiency in terms of high-powered thinking.
INTJs and INTPs are the first rank of mathematicians. INTJs are incredibly intuitive and have enormous thinking power to accompany those intuitions. Similarly, INTPs have vast thinking capacity supported by great intuition. The difference between the INTJs and INTPs is that the former reach judgments much more quickly. They grasp the significance of an intuition almost instantly. Almost effortlessly, they see vast patterns forming in their minds, linking things that would seem to have no connection at all as far as other Myers-Briggs types are concerned. However, their certainty that they are right means that they are not overly concerned with proving their assertions, and proof is of course essential to the mathematical project. INTPs are the “details” people, the thinkers willing to dot the i’s and cross the t’s. They are mathematicians in the truest sense of the word, but they are not as quick to see and understand patterns as the INTJs. The ideal mathematician would be someone who was a perfect hybrid of INTJ and INTP.
In this series of books, we are not committed to providing laborious and intimidating mathematical proofs. Instead, we want to use just enough mathematics to provide solid conceptual foundations. In other words, this series is written from the INTJ perspective and we invite any INTPs who may be reading this to fill in all of the details we will of necessity omit. This book is about broad-stroke mathematical concepts, not mathematical proofs. If we adopted the INTP approach, this book would be the most daunting ever written and incomprehensible to anyone other than mathematicians. Our aim is to give an intelligent person, without a mathematical background, enough information to glimpse and grasp the mathematical basis of reality, and to appreciate its astonishing power, beauty and simplicity.
Although the mathematical foundations of existence are indeed simple, the concepts that flow from them are mind-bogglingly difficult and baffling. The contents of this series will provide the greatest intellectual challenge of your life.
Gottfried Leibniz, a Grand Master of the Illuminati and perhaps the greatest thinker of all time, declared that the best world is the one which is “simplest in hypotheses and richest in phenomena”. This is not just the formula for the best world but for the ONLY world. The world pursues the path of least resistance. It takes the shortest path it can between two points. It never expends energy gratuitously. From the world’s point of view, everything is as simple as it could possibly be. That might not seem the case from our perspective as human beings, but that’s the way it is.
By the end of this series, you will hopefully have a full understanding of the simple “hypotheses” from which the world is built and you will marvel at the astonishing complexity and richness that flows from them. Yet the apparent complexity is a product not of Nature but of the false “common sense” view of the world that humanity has constructed based on numerous fallacies. Even science, humanity’s most successful endeavour, is packed with errors caused by paying too much attention to our unreliable senses and not enough to our potentially infallible reason. For example, we see colours all around us yet a logical deconstruction of the concept of colour shows that the world does not objectively contain any colour at all. As neuroscientist Beau Lotto said, “Colour doesn’t exist. It is a construct of your brain. There is nothing literal about colour in the world.” If all human beings had the genes for total colour blindness, it would never even have occurred to anyone that the sky was blue or that there was any such phenomenon as colour.
What does it mean to assert that our genes are the “cause” of colour perception? The genes belong to us and not to the objects that allegedly exhibit the colour. Is Kant therefore right that our minds are creating their own reality independent of the true world? But no one can question the rational mathematical statement that 1 + 1 = 2. That is an eternal, incontestable, immutable truth. Reason, not our senses, reveals the absolute truths of existence. Our senses continually deceive us. They were not designed as organs of truth but as means for allowing us to adapt successfully to life on earth.
We see only a tiny portion of the electromagnetic spectrum – “visible light”. The rest of the spectrum is invisible to us. Until Scotsman James Clerk Maxwell’s revolutionary theory of electromagnetism arrived in the second half of the 19th century, we had no idea what light really was and knew nothing about any electromagnetic spectrum. Our senses failed to detect any such spectrum because it’s not what they were designed for. They evolved for reasons of survival, not reasons of truth or completeness. So why do scientists so slavishly revere the evidence of our senses and have such contempt for the exercise of the highest and purest reason?
Reason alone can reveal the absolute truth of existence, and what subject is the essence of reason? – *Mathematics*.
Although mathematics is conventionally regarded as an abstract tool, we shall introduce a second type of mathematics that we have labelled “ontological mathematics”. This means that is does not treat mathematical entities as mere paper abstractions and symbols but as things with real existence. Ontological mathematics might also be called the mathematics of energy since that’s what it’s fundamentally about. Numbers written on paper have no energy content. Numbers written in spacetime most certainly do. Manipulation of numbers on paper has no energy implications, but it does in spacetime. Things that can be done effortlessly on paper may not be possible ontologically because of these energy considerations: this is the fundamental difference between abstract and ontological mathematics.
Think of all the sub-atomic particles listed by scientists. Do any of these particles have any properties that cannot be characterised mathematically? There isn’t a single thing about them that isn’t defined by numbers, shapes, quantities, dimensions and mathematical formulae i.e. all the stuff of mathematics. So in what way are these objects of science rather than objects of mathematics? It’s only because we (humanity) have chosen to think of mathematics as fundamentally unreal and abstract that we perversely regard objects that are in every way defined mathematically, and which have no non-mathematical features, as objects of science rather than of mathematics.
Quantum mechanics, relativity theory and M-theory (the theory that is trying to harmonise quantum mechanics and relativity) are all astoundingly mathematical. Are these scientific theories or ontological mathematical theories? If we rebrand science as ontological mathematics then it becomes much clearer why abstract mathematics reflects science so well: “science” is just mathematics as reality rather than as abstraction.
There’s a gulf between conventional science and ontological mathematics in terms of three critical numbers: zero, infinity and the imaginary number, i. Conventional science, an expression of extreme philosophical materialism, asserts that zero, infinity and the imaginary number have no ontological reality within any region of space and time. Conventional science involves a hypothesis that only real numbers are ontological or have any bearing on reality. There is not a single rational reason why this should be the case: it is pure empiricist materialist dogmatism. Science refuses to address the issue of why it accepts only real numbers greater than zero and less than infinity. It gives no rational reason for rejecting zero, infinity, negative numbers and imaginary numbers beyond the simplistic one that they are not empirically detectable. Science thus enshrines empiricist materialism in how it regards mathematics. This is not a scientific but a philosophical stance, and indeed a faith-based position since the ontology of mathematics is not something that can be determined via fallible human senses.
Abstract mathematics – which has no ideological hostility to zero, infinity and the imaginary number (or negative numbers for that matter) – is considered irrelevant to science in respect of these key numbers. Any scientist will tell you that nothing infinite can exist within any localised region of reality because it would literally destroy the fabric of existence in that region, and no such catastrophic tears are observed except, arguably, in the specific cases of the mysterious singularities associated with black holes and the Big Bang. Scientists maintain that there is something wrong with the existing scientific theories regarding singularities and their dreaded infinities and that these problems will be resolved by some new theory such as M-theory.
Scientists will also tell you that they associate zero with non-existence i.e. it is devoid of ontological significance. Descartes defined *res cogitans* (thinking substance) as having no extension i.e. it had no presence in the extended world of matter. Scientists, as strict materialists, have dismissed the Cartesian concept of independent thinking substance (mind). Mind, for scientists, is a mysterious aspect of matter. It cannot exist separately from matter, hence is some kind of material phenomenon or epiphenomenon. According to science, the Cartesian mind, the domain of zero, is pure nonsense. It simply isn’t there. Of all the catastrophic errors of science, this is the greatest because it turns out that zero is the quintessence of existence and completely defines it.
As for the imaginary number, i, this appears in a vast number of scientific equations, yet scientists regard it as purely instrumental i.e. it helps to produce the right answers but has no ontological reality. Mathematician Marcus du Sautoy declared, “Calculating with imaginary numbers is the mathematical equivalent of believing in fairies.” It seems extraordinary that extremely highly qualified individuals should accept “fairies” in the midst of some of the most successful theories and equations of all time and not conclude that either these theories and equations are the purest moonshine, or else imaginary numbers are anything but imaginary. It is poverty of both reason and imagination that makes mainstream scientists and mathematicians so blind to the ontological reality of imaginary numbers. There are no “fairies” in mathematics. Neither zero, infinity nor imaginary numbers are fairies. On the contrary, they are essential to existence. They are the most solid, substantial entities of them all, every bit as solid and ontological as real numbers.
So, Illuminism defines two types of mathematics: abstract (conducted purely in the mind or on paper) and ontological (that unfolds as reality itself) – the two are of course extremely closely related, with energy being what separates them. Ontological mathematics can be further divided into ontological mathematical materialism (science) and ontological mathematical idealism (the mathematics of zero and infinity).
The imaginary number belongs to mathematical materialism (though scientists haven’t grasped this yet). What this means is that the imaginary number has real existence in the physical world – which is why it appears in so many key equations of science. It is not an instrument for getting the right answer: it is part of the fabric of reality. In fact, it is the basis of time.
The two branches of ontological mathematics constitute a complete account of reality – a grand unified theory if you will. What the two branches achieve is the resolution of Cartesian dualism.
Descartes divided reality into two separate domains of mind and matter but could not give any plausible explanation of how the two domains interact. Despite being a brilliant mathematician and acknowledging that mathematical knowledge is the primary source of truth, Descartes failed to make the intuitive leap that would have made him a god amongst men. He didn’t grasp that mind belongs to the mathematical domain of zero and infinity while matter belongs to the mathematical domain of everything that exists between those two numbers, and that together they embrace everything that can possibly exist from zero to infinity in all directions. There is therefore no dualism at all between mind and matter: they are part of a seamless mathematical continuum and they communicate and interact effortlessly via their common language of mathematics. It’s the unique properties and qualities of zero and infinity that separate them from the rest of mathematics and make mind seem radically different from matter. In fact, the two domains are just different manifestations of ontological mathematics. There is no dualism, no mystery, no magic, no baffling enigma of how mind and matter interact. They are not two different substances but the same substance – mathematical substance.
Where science regards mathematics as an invaluable tool for revealing the secrets of the scientific world, Illuminism regards science as an invaluable tool for helping to reveal the secrets of the mathematical world. Mathematics is not only the answer to Cartesian dualism but also to the Kantian dualism of noumenon and phenomenon. In fact, these two dualisms are ultimately the same.
The noumenal realm was originally defined by Plato as the world of ideas apprehended by the philosophical, rational mind while the phenomenal realm was the world of sensory reality in which the unphilosophical and animalistic were permanently trapped i.e. their primitive minds could never take them to the noumenal domain. The tendency of modern philosophy is to support science in denying the possibility of knowledge gained independently of the senses. Kant famously asserted that although the noumenal world exists, it is entirely unknowable; we can only ever grasp phenomenal reality. Science agreed that we can know only the material world and simply denied that there was any noumenal world at all, just as it had previously denied that there was any Cartesian domain of mind and any religious domain of soul. Science, like Doubting Thomas, says no to anything it can’t empirically detect.
Illuminism, on the other hand, asserts that the noumenal domain not only exists, it is primary, the ground of existence. Moreover, phenomenal and noumenal reality are both fully knowable via mathematics – because all phenomena and noumena are mathematical entities.
Science, hitherto, has been the tool for probing the empirical, material, phenomenal world while metaphysics (literally “what comes after physics”) is the term traditionally applied to the study of the noumenal universe. Religion also makes comments about the noumenal universe but in a faith-based, irrational, idiotic way where the statements of prophets and holy texts are regarded as some sort of absolute “truth” revealed by “God”. We shall ignore the claims of mainstream religion since they are more or less absurd. The Western Abrahamic religions of faith quite literally have zero truth content, and the Eastern religions are far too mystical and imprecise. The “God” of Abrahamism is as far from truth, reason, logic, enlightenment and reality as you could get. He is the false God, the God of the stupid and irrational and all those who have contempt for the truth. “The truth shall set you free” is the most ironic statement conceivable in the mouth of an Abrahamist.
Science has proved spectacularly successful while metaphysics has been speculative and resulted in no definitive view or consensus, hence science has become the basis of modern rational thinking and has relentlessly promoted empiricism, materialism and atheism.
Illuminism asserts that the only way to save metaphysics is via mathematics since a) mathematics IS reality and b) mathematics is the only subject about which anything precise can be said. Science’s power derives from the fact that it uses mathematics and metaphysics doesn’t. Metaphysics should be rebranded as the “philosophy of ontological mathematics”, along the same lines as the philosophy of science.
One of the greatest tragedies of science is that most scientists are not only ignorant of philosophy but also actively hostile towards it. Such scientists dismiss the philosophy of science which seeks to philosophically clarify what the findings of science actually mean. One of the greatest philosophers of science was Thomas Kuhn and his book *The Structure of Scientific Revolutions* is a full-scale assault on the pretensions and delusions of scientists. It was Kuhn who introduced the famous concept of the “paradigm shift”. Even today, the vast majority of scientists have never read Kuhn, hence don’t realise how he fatally undermined much of the ideology and dogmatism of science.
Kuhn believed that scientists had a great deal to learn from the study of the history of science and Illuminism agrees entirely with this. In fact, the same is true of every subject. Unless you understand something’s history, you don’t have any deep understanding of it at all. You don’t know how it came to be where it is and what debates, controversies, dilemmas, difficulties and dialectics fuelled the journey. Scientists, sadly, are as ignorant of the history of science as they are of the philosophy of science – hence are much less effective at science itself. The teaching of science should always begin with the history and philosophy of the subject before people start learning science itself. The same is true of mathematics.
Although we are asserting that mathematics is the truth of reality, this book (and series) is not primarily a mathematics textbook. Rather, we will be examining the philosophy of particular mathematical concepts and showing how they define such apparently scientific phenomena as space and time.
Space and time go right to the heart of ontological mathematics and not a thing can be truly understood about the material world if a person is ignorant of the mathematical origins of space and time. It’s a fact that no one outside the Illuminati has ever understood space and time and, in this series, we will reveal the truth to everyone.
The primary tools for understanding ontological mathematics are abstract mathematics, science and philosophy. Ontological mathematics should be regarded as the grand synthesis of mathematics, science and philosophy, turning them into one unified subject rather than three separate subjects. In doing so, it addresses all of the questions of religion. It brings religion into the domain of facts, evidence, reason, logic and, above all, mathematics. All faith-based elements of religion are exposed as ignorant, irrational, superstitious, crazy nonsense that feeds the madness of stupid fanatics, with whom our world is plagued – particularly in the case of Orthodox Jews, Muslims (more or less all of them) and Christian Fundamentalists.
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