"Nature is written in that great book which ever is before our eyes - I mean the universe - but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth."
If you want to debate the existence of God with scientists, you do not go armed with a "holy" book. You have to bring your knowledge of the science of the soul. Your science has to be better than theirs. You have to show them where they are in error.
The first motto of the Illuminati (under Grand Master Pythagoras) was: "Number rules the universe." Mathematics is the basis of organization, hence of life, hence of mind. A universe that did not operate according to mathematics would be incomprehensible, irrational, and nothing but random chaos from which no life and no consciousness could ever emerge.
So, the ultimate question, as Pythagoras realized, was: where does mathematics come from? How and why does the cosmos understand mathematics? Moreover, if the cosmos is based on mathematical rules and humanity can understand mathematics then it follows that humanity can unlock the secrets of the cosmos and read the Mind of God. Science is how humanity uses mathematics to comprehend the universe. But science historically made one catastrophic mistake: it let empirical data be its sole guide rather than empirical data and mathematical logic.
The cosmos did not design itself according to data; it was designed on the basis of logic. If you wanted to understand a computer program, would you study the output of the program or the code of the program itself? Scientists have attempted to work back from the data to the program; philosophers have tried to understand the program with little regard to its output. The proper approach is to come at the problem from both angles at the same time. But logic will certainly provide the best starting point. If we can understand the logic of the designer (whether we are referring to "God" or "Nature"), then we can unravel his design. We have to attempt to walk in the designer's shoes. How would we do the design? What would our guiding principles be? There can be no doubt that one day a program will be designed whose output is a perfect simulation of the world we see around us. It will reveal what happened at the Big Bang - and before. We will be able to run the simulation backwards and forwards. The program's logic will be the same as that used by the Designer, and will be awesomely perfect. It will be based on the most elegant mathematical concepts. If we did but know it, all of the answers already exist in our minds. We "simply" have to extract them.
Design rule number one: Use ALL of mathematics. Why? Because why would you use only a subset? By using all of mathematics, every possibility remains open; by using a subset, certain options are rendered impossible. You would have to be able to calculate all of the consequences of excluding certain numbers before you proceeded with your design. What would limited mathematics provide that was superior to unlimited mathematics? What would be the sufficient reason for using a subset of mathematics rather than its entirety?
So, Nature is based on "complete" mathematics, but, strangely, no mainstream mathematician or scientist has ever defined what complete mathematics is. And therein lies the Achilles heel of science. You can't begin to understand the cosmos until you understand what complete mathematics is.
The question can be framed in two other ways: 1) Does the cosmos reflect all conceivable numbers and, if so, what are all the conceivable numbers? If the cosmos doesn't reflect all conceivable numbers then why not? What would be the sufficient reason for preferring some numbers over others, for using some and ignoring others? 2) How many dimensions are required to accommodate all conceivable numbers? Why would the cosmos use anything more than the minimum number of dimensions?
So, you cannot begin cosmology until you have fully defined the instrument that cosmology is based on: complete mathematics. Unfortunately, cosmologists have let data rather than logic guide them. And thus, after many attempts and theories involving anything up to 26 dimensions, they have arrived at 11-dimensional "M" Theory as their latest candidate for explaining everything. This is probably the most complex mathematical theory ever devised. Yet it is unquestionably wrong because it isn't based on mathematical completeness. Not a single M theorist can explain why the cosmos should be based on the rather peculiar number of 11 dimensions, as the theory requires. If 11 dimensions isn't the minimum number of dimensions required for complete mathematical expression then M-theory is in error. We know exactly what the right number is - it can be worked out with simple logic - and it isn't 11. M-theory claims that the extra "hidden" dimensions are curled up so infinitesimally small that they will never be directly detected. Why would Nature operate in such a way? This sounds more like metaphysics than science. It bears all the hallmarks of forcing a theory to fit any relevant data by inventing ingenious but faintly ridiculous tricks. The theory's complexity derives from having to accommodate all of the trickery involved. When you discover that M-theory can be subdivided into five distinct 10-dimensional "superstring" theories, and one 11-dimensional "supergravity" theory, it begins to seem as though scientists are spending their time trying to make rival theories fit together rather than solving the real mystery.
The best theory for analyzing mathematical completeness is Einstein's special theory of relativity which concerns itself with the most magical entity of all...
We take light so much for granted, yet all of the profoundest enigmas are encapsulated by light. In science class at school, everyone learns that light is the visible part of the electromagnetic spectrum, but "light" can also refer to the entire electromagnetic spectrum, visible and invisible, and that's the sense in which we will use the term. Particles of light are called photons, from the ancient Greek word photos, meaning light. (An alternative designation is luxon, from the Latin word lux, meaning light.)
Consider this quotation from a popular science book:
"If you could attach a clock to a light beam it would not tick at all. We say that to a photon, time does not go by at all (maximum time dilation) and the whole Universe has zero size (maximum length contraction)!!"
Jim Al-Khalili (Black Holes, Wormholes & Time Machines)
This statement is made rather matter-of-factly, and the writer doesn't dwell on it as he rushes on to more conventional material. But what could be more radical and mind-blowing than what he has just said? Shouldn't he have written his entire book on this subject alone? He has hurried past the astounding fact that light does not experience space or time. This is a startlingly good example of how eminent scientists can so dismally fail to appreciate the implications of what their discoveries are screaming at them.
Photons have no mass. So, immediately we are presented by the baffling question of what a massless particle is. When we think of particles, we usually imagine (no matter how inaccurately) tiny, hard balls which, of course, have mass. They are solid, substantial, tangible entities, the building blocks of the real world. We could theoretically touch each and every one of them. But how can you touch a particle with no mass? What would you be touching? Is it a scientific fiction to call a photon a particle given that, in essence, we define particles as having mass and yet a photon has no mass?
So, putting it all together, a photon has no mass, and experiences neither time nor distance. It is not "dimensional" in any conventional sense. Are bells starting to ring?
A photon comprises a combination of electric and magnetic fields, oscillating at right angles to each other, travelling at 300,000 km per second (in our frame of reference, but not in its own).
Visible light - "white light" - isn't white at all. It's a blend of all the colours of the rainbow, as experiments with prisms showed long ago. But what is colour? If we had a miraculous super microscope and we trained it on a beam of white light, would we initially see "white photons" and then, as we increased the magnification, would these decompose into tiny, discrete red, orange, yellow, green, blue, indigo and violet photons whizzing around in a rainbow jumble? If white photons don't actually exist but the colour white is instead a composite phenomenon of photons of many different colours then we are acknowledging that we are able to see a colour that isn't "real", that is constructed from an underlying reality. In fact, colour isn't a primary property of objects; it's a derived, secondary property. Photons are distinguished by frequency, wavelength and energy content, not by "colour". Colour is a mental construction - it's how our brains interpret photons of different frequencies i.e. it exists in our minds, not in the world. A hypothetical computer mind might simply analyze and register the numerical values of the frequency or wavelength of photons, and the question of colour wouldn't arise. If we all had the genes for colour blindness, the expression "the sky is blue" would never have occurred to us. That shows how dependent colour is on our perceptual apparatus. The visual cortex of our brain ignores photons of ultra-violet light, infrared light, radio waves, microwaves etc. They are all around us, but they're invisible because our eyes didn't evolve the means to "see" them. What else is hidden from our senses?
The next equally bewildering enigma of photons is that they all travel at the same speed. Even if there were an infinite number of them, each and every one would travel at an identical speed. Even more bafflingly, no matter what speed an observer is travelling at, any measurement he takes of the speed of light will always yield the same result. An observer travelling at 99.99% of the speed of light isn't 0.01% slower than the speed of light; he's the full speed of light slower i.e. if he turns on a torch, the light beam will still shoot away at light speed. Light, in itself, has no concept of relative speed. It doesn't care whether something is stationary or moving at 99.99% light speed - from light's point of view, both situations are the same. Light will escape from either situation at its usual speed. Therein lies one of existence's greatest enigmas.
If a woman in a car is travelling at 99 mph, she is travelling at 99% of the speed of another car travelling at 100 mph. That's the common sense view of the world. Light does not obey common sense. In fact, common sense is often your worst enemy if you want to understand the essence of existence.
It is reason that revealed all of the mysteries of light to humanity, not common sense, not our five senses. Had we followed the dictates of common sense and our eyesight, we would never have penetrated the ultimate secrets of light.
Many people have difficulty contemplating the human soul. They think that an immortal, massless entity with no dimensions that exists outside space and time is inherently preposterous. But they are perfectly willing to accept the existence of light. Yet what is light? Einstein's special theory of relativity says that it is an immortal, massless entity with no dimensions that exists outside space and time.
Hasn't the penny dropped yet? Since Einstein, we have had scientific proof, verified by countless experiments, that something completely uncontroversial and unquestioned - light - has exactly the "physical" attributes commonly assigned to the soul. So, is it any longer tenable to assert that the concept of the soul is scientifically ridiculous? If it is then the concept of light must be equally ridiculous. If we took one further step of attributing mind to light, the theory of light would become the theory of souls.
We have already said that many things exist, e.g. ultraviolet light, that affect us and yet are invisible to us. Their existence is revealed by reason, followed by experiments. How would we know if a light beam contained mind or not? Science does not attribute independent mind to anything, not even to human beings. "Mind", for scientists, is something that mysteriously emerges from matter and is entirely defined by, and dependent on, matter. The once-popular, quasi-scientific theory of behaviourism regarded the human mind as completely irrelevant. All that was important to a behaviourist was that if you applied a stimulus to a human being, you would get a certain measurable and predictable output: some type of behaviour. The stimulus and the resultant behaviour could be studied scientifically. The ingredient that existed between the stimulus and the observed behaviour - the human mind - was deemed of no consequence. It was nothing but a "black box".
Which scientific equation has "mind" explicitly written down as a variable, along with the x, y's and z's? There is no such equation. Science cannot investigate light's hypothetical "soul" properties because it doesn't have the "vocabulary" for doing so. That, of course, does not mean that those properties are not there. Invariably, science ignores something if it cannot find the right theoretical means of describing it.
Science, when it finally embraces r >= 0, will undergo a new Copernican revolution. Philosophy, religion and science will come together in a coherent, integrated whole. There will be no place for faith, common sense, or the deceptive evidence of our five senses. Our senses are directed at utility - what is useful to us in our everyday existence - not at truth.
Think of light with two aspects: inner and outer. The outer is probed by science. The inner is nothing less than the domain of the soul.
The universe can be comprehended rationally and intuitively. It cannot be comprehended through the sort of commonplace thinking that imprisons most humans in their humdrum, unenlightened lives where blind faith is regarded as the extension of common sense. Christians, Muslims and Jews believe in a common sense world, and anything beyond common sense - such as the nature of God, the soul, the afterlife etc - is placed in the arena of faith, whereby you have no choice but to believe what some prophet said in some ancient book.
No sensible person would wish to conduct their life on such a dubious basis. All sensible people seek knowledge. Believing any old rubbish because "someone said so" is ludicrous. You must use your own intelligence to penetrate the deep mysteries of life. And, above all, your intelligence must be capable of transcending common sense and dogmatic belief.
Are you ready to escape from the jail of your mind?
"Common sense is the collection of prejudices acquired by age eighteen."
The greatest enemy of enlightenment is "common sense". In day-to-day life, common sense "works", which is why ordinary people revere it. Most managers, for example, are good at common sense i.e. knowing how to play the system, to obey the rules, to pander to higher managers, to avoid radical ideas, to highlight their modest successes and blame others for their failures, and to stick firmly within the domain of the conventional, acceptable and uncontroversial. Unfortunately, they're hopeless at everything else. All geniuses, on the other hand, can "see" far beyond the realm of common sense. They use imagination, intuition and visionary ideas as their guides, not the trivialities of common sense. What would you rather be - a middle manager with a comfortable common sense life, or a genius who has unlocked the door to the mysteries of existence? Tragically for humanity, most people aspire to be middle managers. That's the extent of their ambition, that's as far as their horizons stretch. These are the sort of people that Nietzsche branded as "Last Men."
A common sense person will choose blandness, banality, and conformity. A common sense person wants to be the same as everyone else, just a bit more successful. Only the exceptional are capable of rejecting the whole idea of conforming with the masses. Nietzsche described the conformist, brainwashed masses as the "common herd", spending their lives grazing on trivia.
Hard-nosed business people and many ordinary people celebrate common sense and sneer at "intellectuals". In many countries, "intellectual" is a term of abuse, and intellectuals are regarded as pointless, useless individuals, wasting their time on speculative, impractical nonsense. Yet if hostile aliens told us that they were about to exterminate our world unless we could show why humanity deserved continued existence, it would be the works of our greatest intellectuals and artists that we would provide as evidence. We wouldn't show the aliens spreadsheets, profit and loss accounts, managerial PowerPoint presentations, our bank accounts, our houses, our journey to work, our cars. No, we would show them the paintings and frescos of Michelangelo, Raphael and Da Vinci, the sculptures of Rodin, Degas and the ancient Greeks, the philosophies of Pythagoras, Plato, Aristotle, Heraclitus, Descartes, Leibniz, Hegel, Nietzsche, the works of the greatest mathematicians such as Gauss, Fourier, Euler, Riemann, Cantor, the scientific equations of Einstein, Dirac, Heisenberg, Schrödinger, Feynman, Clerk Maxwell; we would show them the work of Crick and Watson on DNA, we would tell them of Darwinism, of Freud, Jung and Adler, we would furnish them with the works of Shakespeare and Goethe, we would give them the poetry of Byron, Shelley, Yeats, Eliot, the music of Beethoven, Mozart and Wagner.
We wouldn't present the aliens with a list of the wealthy, celebrities, CEOs, bankers, lawyers, accountants, entrepreneurs, senior managers, hedge fund managers and top traders. Why not? Because, in truth, we all know that these people in no way reflect the glory of humanity; of human potential expressed to the maximum. So you have to ask yourself why they are accorded such importance in our society when, in the higher scheme of things, they are regarded as irrelevant and even shameful. The rewards they receive for their mediocre efforts have no relationship to their worth as human beings or their contribution to human excellence. But they are all masters of common sense and seizing business opportunities.
No true genius ever pays court to common sense. Human greatness does not live in the bland, sterile, commonplace, dumbed-down arena of common sense. Sure, common sense will help you to survive, but it will never take you anywhere near the truth of life. Common sense is the worst tool imaginable for understanding reality. It always leads people away from knowledge and towards prejudice, just as Einstein observed. What your common sense tells you is "out there" isn't there at all. Our common sense deceives us. Its function is to enable us to exist as animals on Earth - it does nothing to take us on our journey to divinity, to exist as souls in the celestial planes. The Abrahamic religions try to solve that gap via faith. The Gnostic religions understand that only knowledge can help us, but this is knowledge of no ordinary kind. This is transcendental knowledge, knowledge that takes us far beyond the confines of what our ordinary senses proclaim. Our senses are tuned into this world while our minds need to be tuned into that world. Gnosis is the supreme knowledge to be attained, knowledge of r >= 0.
Lesson One - if you want to "know", leave common sense behind. It can offer you nothing of substance and value. Common sense is "intelligence for dummies". Real intelligence makes no use of it.
"Long experience has taught me this about the status of mankind with regard to matters requiring thought: the less people know and understand about them, the more positively they attempt to argue concerning them, while on the other hand to know and understand a multitude of things renders men cautious in passing judgment upon anything new."
As Galileo observes, commonplace thinking leads to arrogance and prejudice - just look at the deranged Tea Party with their simplistic nostrums. These people are all rooted in common sense and hatred of any "fancy ideas."
"Everything you've learned in school as 'obvious' becomes less and less obvious as you begin to study the universe. For example, there are no solids in the universe. There's not even a suggestion of a solid. There are no absolute continuums. There are no surfaces. There are no straight lines."
Humanity, for the most part, lacks imagination. People can't see beyond what seems "obvious". They have such a strong attachment to common sense that they prefer it to reason. Their "gut instincts" are tied to common sense, not to reason. In a "fight or flight" situation, it will be a rare person who pauses to reason his way out of the dilemma.
Leibniz said that the best account of the world is the one that is "simplest in hypotheses and the richest in phenomena." If you were God, isn't this exactly the creative principle that you would employ i.e. the simplest solution that provides the most possibilities? The universe appears immensely complex, yet humanity, via science, seems to have made a remarkable degree of sense of much of it. If the universe is based on rational principles (i.e. is not some random, lawless, chaotic, incomprehensible arena), why should the exercise of reason be unable to reveal its secrets? If the principles of reason are universal then they apply to God as much as humanity; the better we become at reasoning, the more we become Godlike, as Plato and Aristotle were keen to assert. The biggest obstacle humans have is that our minds have evolved in a way that makes it difficult, though not impossible, for us to discern the true nature of reality. If common sense and the evidence of our senses on the one hand, and profound scientific, logical and mathematical reasoning on the other, are not aligned then this means that we are continually deceived by what we take for granted.
Ill-informed non-scientists often sneer at science. In truth, they have no comprehension of what science says and they refuse to budge from their common sense opinions by which they are permanently enslaved. Certain people have an enormous interest in maintaining a common sense set of opinions because, crucially, no one needs to be an expert to make pronouncements based on common sense. Common sense could be defined as Lowest Common Denominator thinking - i.e. the most basic, least sophisticated, least demanding level of thinking. Common sense thinking favours stupid people because it is infinitely closer to their view of the world than it is to the abstract, complex, visionary thinking of geniuses. Common sense is all about "dumbing down". Read the Koran, the Torah or the Bible and you will find no complex ideas at all. In the Bible, Jesus Christ delivers childish parables. In the Torah, Moses barks out simplistic rules and commandments (how does switching off electricity on the Sabbath, as many Jews do, bring them any closer to God?). In the Koran, "Allah" provides a fixed formula for life that requires Muslims to do nothing but obey - to "submit". Freethinking, dissidence and non-conformity are anathema in these religions.
Stupid people flock to such religions. They are designed for stupid people. They are successful because most people are stupid. They are dumbed-down religions for dumbed-down people. Plato complained that he had created the perfect state, but where were the perfect people? The tragedy of humanity is that it is held back by humanity. It has never turned to its greatest minds. It has never placed its trust in the most meritorious. It has never valued "heresy" - the ability to choose differently. Instead, it has burned the heretics.
If humanity were intelligent, the Abrahamic religions could not exist. In the future, when humanity is guided by Illumination and is on course to achieve its divine potential, the Abrahamic faiths will seem like a bad, far distant, primitive memory of horror, and no one will be able to comprehend that humans once held such absurd beliefs.
Once someone acknowledges that common sense is wrong then it follows that they are placing themselves at the mercy of experts, of the geniuses of the human race who have developed abstract and bewilderingly complicated techniques for understanding the truth of existence. If advanced mathematics is the language of Nature rather than common sense opinion then most people are screwed, right?
What's the point of hanging on to simplistic and false opinions? To comfort yourself? To pander to your vanity? Deep down, most people realize they don't have a clue about the mysteries of life. Some have a spiritual yearning that brings them to sites like this one, and they are to be applauded, yet the vast majority arrogantly dismiss anything they don't understand and bury their heads in the sand. They lap up the religions of faith because these don't demand anything difficult of them.
What is a believer? He is someone who thinks that he is a good person and that he is certainly going to heaven. Well, that's not a hard position to hold, is it? If you ask such a person about quantum mechanics, relativity theory, advanced mathematics, advanced philosophy, advanced theology, he won't have a clue what you're talking about, but what does he care? He's a believer. He's saved. God loves him. End of story.
Now you can see why the religions of faith have spread like a cancer across the globe. They require no knowledge. In fact, they despise knowledge. Never forget Martin Luther's insane declaration, "Reason is the Devil's whore." The Abrahamic faiths are all about common sense in day-to-day matters - obeying rules, laws and commandments set by the powers-that-be in the name of "God" - with the mysteries of life being consigned to a compartment marked, "No need to worry. If I believe in God I will be OK." They can then get on with the rest of their lives - watching junk TV, eating junk food, getting drunk, getting high, getting married, doing dreary jobs, waving the patriotic flag, shopping, going to church on the Sabbath, going to the baseball game or football match yada yada yada: all the sad, soulless nonsense that passes as the "glory" of humanity. In fact, most of us are sad robots on permanent Auto Pilot. We insult the glories of which we are truly capable, that we could attain if we succeeded in releasing our higher selves.
It's time to stop shopping, to stop believing, to stop being enslaved by common sense. It's time for humanity to turn to knowledge, to Gnosticism.
Ordinary people would like to think that common sense is the right tool for understanding the world, and that philosophers, scientists and mathematicians are wrong and perverse to seek "deeper" truths of reason that contradict common sense.
"All truths are easy to understand once they are discovered; the point is to discover them."
Galileo is being somewhat simplistic in this instance. There is no obligation for truths to be easy to understand. Why shouldn't they be paradoxical and mystical? Imagine that all truths were mathematical i.e. that you could not hope to comprehend the universe unless you were a skilled mathematician. At a stroke, almost all of humanity would be excluded from any hope of discovering the truth of their existence. After all, mathematics is one of the most hated subjects on earth, reviled by schoolchildren all across the globe. When did you ever see a mathematics celebrity? When did you ever see a prime-time TV programme about mathematics? In fact have you ever seen any TV programme on mathematics? If there were such a programme would you watch it or would you switch over (to watch yet another soap opera, rom com, panel show, reality TV show etc).
Robert Heinlein said, "Democracy can't work. Mathematicians, peasants, and animals, that's all there is - so democracy, a theory based on the assumption that mathematicians and peasants are equal, can never work. Wisdom is not additive; its maximum is that of the wisest man in a given group."
Most people would be appalled by the idea that they were cut off from the truth because of lack of mathematical acumen, which is why the religions of faith are so much more popular than mathematics, science and philosophy. You don't have to be smart to "believe" - any fool can believe anything - but you do have to be smart to understand philosophy, science and mathematics.
"There are those who reason well, but they are greatly outnumbered by those who reason badly."
There are people who are proud to say that they despise mathematics, but only a fool would be pleased to be useless at mathematics. You might not have much aptitude for it, but you should not hold it in contempt, as most people do. Science - the most successful of all human endeavours, from which all of our technology is derived, is founded squarely on mathematics. The clowns who loathe mathematics wouldn't be so happy if someone took away all of their gadgets, yet without maths, science and technology there wouldn't be any gadgets - no LCD TVs, iPods, iPhones, iPads, cell phones, DVDs, playstations, cars, planes, medicines, electric guitars, light bulbs, internet, electricity etc.
The religions of faith couldn't care less about mathematics, science or technology. They say, "You'll be fine as long as you believe in Jesus/Allah/Jehovah. Screw mathematics." That's why cultures that promote faith are backward.
Islamic nations are hell-bent on returning to a pre-industrial existence like that of the Arabian desert of their prophet Mohammed. Will you find Einstein's theories or quantum mechanics in the Koran? "Who has need of these godless ideas?" is what the imams say. To a man, they are scientifically illiterate. If you listen to the stupid then you will become stupid. That's the inviolable Law of Dummies.
Islam represents the desire to be stupid. Islam is a belief system that God wants us to be dumb and to do nothing other than robotically obey the contents of a single book - the Koran. Islam is a belief system that proclaims that you deserve to die if you don't slavishly adhere to the Koran. The point of life, Muslims say, is to do nothing other than obey like machines. What an inspiring vision of life. What a celebration of human potential. For Islam, free will and freethinking are Satanic. They lead you away from the Koran, and hence towards hell-fire. That's your reward for thinking for yourself - hell. What God would punish people eternally for thinking? How can anyone doubt that it is in fact Islam that is Satanic, as are all religions that try to stop people from thinking.
If you want to become a genius then make sure your nation is run by geniuses. The Old World Order don't want the people to be smart. Nothing, in fact, could be more damaging to their agenda. Imagine that all schools were equally good: then money couldn't buy a better education and secure better life opportunities. That would be a catastrophe for the privileged elite. Their whole basis of power is that they can use their wealth to buy unassailable advantages over others. They want you to be stupid, to be "believers", to operate according to common sense.
Muslims would be happy to live in caves. Their religion was born in a cave, when Mohammed allegedly had the Koran dictated to him by the Angel Gabriel. It is a religion of caves, of anti-technology, anti-evolution, and anti-knowledge. It is a religion of dark places and cold stone. Women are expected to cover themselves from head to toe because, apparently, all Muslim men are permanently sexually inflamed and the slightest sight of a woman could incite them to the most extreme crimes. What a dismal and terrifying religion. It is a religion of the shadow, and the cave is the most suitable emblem for it. The Koran is the Book of Darkness.
A Christian pastor threatened to burn a few copies of the Koran because it was "of the Devil". What was the response? Did the Muslims ignore this man? No, they reacted with violent demonstrations full of snarling, murderous hate. People died. Thus proving the pastor's point. Islam's sole response to criticism is mass, rent-a-crowd protests and extreme, deadly violence. Is this a religion or a psychosis? Muslims are incapable of accepting free speech. They want to kill everyone who disagrees with the Koran. Therefore this is the deadliest of all religions. They howl in protest at the possibility of the Koran being burned, yet this same book advocates burning all people in eternal hell-fire if they fail to worship Allah. What's more outrageous: burning a book or burning the whole non-Islamic human race? What is the true scandal and provocation? When will Islam be put on trial for advocating the death and eternal punishment of all non-Muslims? Why should the intolerable be tolerated? Why should the intolerant be treated with tolerance? Why should Islam be appeased? Why isn't every Muslim spokesperson on earth asked one simple question: do you or do you not advocate that all non-Muslims should suffer hellfire, as the Koran decrees? If they say "yes", they have placed themselves outside the scope of tolerance and respect. If they say "no", they have placed themselves outside Islam.
If Christians say that Jews and Muslims (who explicitly reject
Jesus Christ) can go to heaven, then they have admitted
that Christ is pointless in terms of Salvation, hence there is no longer
any reason to be a Christian. If Muslims say that Jews and Christians
(who explicitly reject the Koran and Mohammed) can go to heaven, then
they have admitted that the Koran and Mohammed are pointless, hence
there is no longer any reason to be a Muslim. If Jews say that
Christians and Muslims (who explicitly reject the tenets of the Jewish
faith) can go to heaven, then they have admitted that God does not have a
unique Covenant with the Jews, and that all of the many Jewish laws and
prohibitions are pointless in terms of Salvation, hence there is no
reason to be a Jew. In other words, the inescapable logic of these
religions, if they wish to continue to have a point, is that only they are right and
everyone who disagrees with them is wrong, and will suffer
hellfire as punishment. In other words, these religions have inbuilt
hatred and contempt for others. They are guaranteed to create conflict because they are mutually exclusive. Why should such hateful and despicable
ideas be tolerated in the 21st century? These religions are an
intrinsic abomination. It is nauseating when a pope shakes hands with a
rabbi or imam when he believes that both are going to hell (and likewise
they think he is going to hell). What hypocrites! The last thing that
matters to these people is honesty.
These religions all speak of nothing but peace while their histories speak of nothing but violence. If you tell all those who disagree with you that they are going to hell, how can you expect peace and mutual respect? What part of "you're going to hell unless you agree with me" is peaceful or respectful? If you tell others that you are the Chosen People, why are you surprised when they hate you? The answer is real simple - stop calling yourselves that! But these people will never stop. They are imbued with hatred and contempt for others. Their rhetoric of peace is belied by their actions, by the extremist dogmas to which they subscribe, by the death and destruction they will dish out to "preserve" their beliefs.
In truth, the age of the Abrahamic faiths is over. Catholicism, permanently discredited by the child abuse scandal, is turning into an irrelevance before our eyes. Islam, an utterly backward religion, rages against modernity. The Jews are dying out and becoming increasingly inbred and retarded. By the end of this century, none of these religions will still exist.
The 9/11 hijackers are said to have offered up their blood sacrifice to Allah. What God would accept a "gift" of an aircraft full of screaming, terrified men, women and children?
The Jews are no better. Consider the tale of the great Jewish hero Joshua, the leader of the Hebrew conquest of Canaan:
Joshua 11:11: And they smote all the souls that were therein with the edge of the sword, utterly destroying them: there was not any left to breathe: and he burnt Hazor with fire.
Joshua 6:21: And they utterly destroyed all that was in the city, men and women, young and old, and ox, and sheep, and asses with the edge of a sword.
So was Joshua (actually "Yehoshua," meaning "Yahweh is salvation", and rendered as "Jesus" in Greek) a peaceful, gentle soul, considerate of others, merciful and compassionate? Or was he a genocidal, exterminatory maniac, fully supported by his equally savage God, Yahweh?
And never forget that this bloodstained, murderous religion of Joshua was also the religion of Jesus (Yehoshua) Christ.
The only reason Christians and Jews aren't living in caves is that, historically, their leaders were violent psychopaths who saw the need for more and more deadly weapons of war. They needed mathematicians, scientists and technologists to provide more effective killing power. Then, when capitalism and the industrial revolution came along, the fat cats saw that mathematics, science and technology could deliver even bigger profits via machines, gadgets, chemicals etc.
So, humanity's greatest achievement - science - has been fuelled by greed and violence. Imagine if a different fuel were used: the vision of the Venus Project, for example. What couldn't humanity achieve? Could we build a bridge to heaven? In Norse mythology, Bifröst was such a bridge, coming in the wondrous form of the rainbow. Where are our rainbow bridges? Where are our towers to the stars? Where are our portals to God?
"You cannot teach a man anything, you can only help him find it within himself."
There's a great deal of truth in this. Muslims, Christians and Jews cannot be taught while they cling to the words of their prophets and holy texts. Their minds are not receptive. They are locked down. Teaching is a two-way process; it requires someone with the ability to communicate and someone with the equally important ability to listen. Keeping an open mind is astonishingly difficult. Humanity, as a whole, is full of closed minds, narrow outlooks, and dangerous prejudices.
And it's getting worse.
Who will lead us out of the land of bondage in a great Exodus for the modern age?
E.X.O.D.U.S. - Pho'
The Illuminati have always accorded mathematics the highest possible status. Pythagoras regarded it as divine. Quite simply, it is the core language of the universe. It is the language by which the r = 0 and the r > 0 domains first communicated, and which defines their interactions in the past, now, and forever. It is woven into the fabric of the cosmos. Nature is living mathematics. Music is the sound of mathematics. Reason is the logic of mathematics. Consciousness is self-aware mathematics. Humanity is walking, talking, feeling, aspiring mathematics. God is the perfect culmination of mathematics. The universe is rational, ordered, and comprehensible only because it is mathematical. Without mathematics, existence would be impossible as anything other than immortal chaos and randomness, devoid of life and any possibility of anything meaningful ever happening. Mathematics is the first language of God. It is also the first language of all human beings, but it is carried in us unconsciously rather than consciously.
Completely stupid sports people who can't add two and two can nevertheless instinctively solve the most difficult mathematical problems. A dumb golfer who can strike a ball hundreds of yards in a high wind and make it land inches from a tiny hole hasn't achieved that feat by some random mechanism. His brain has unconsciously factored in the distance from the hole, the type of club needed, the weather conditions, wind speed, wind direction, force to be exerted on ball, desired trajectory etc. He does it all intuitively. If he got out a piece of paper and tried to perform an explicit mathematical calculation, he wouldn't have a clue where to begin. Yet he does the calculation effortlessly in his subconscious. If he didn't, he could never be a successful golfer. When he plays golf, the golfer is a mathematical wonder machine, performing prodigious calculations in the blink of an eye. Baseball players, hitting a ball or catching it, are the same. Football players, basketball players, ice hockey players…all of them are masters of instinctive mathematics, judging speeds, angles, forces, and trajectories with supreme ease. Inside us all, no matter how much we might consciously detest and fear mathematics, is a mathematical genius. If we could bring that unconscious genius into consciousness, humanity would bound forward with God-sized steps.
Otherwise, we are condemned to the kind of world where the inmates are running the asylum, guys like this: http://www.youtube.com/v/SsCe2LIYkNo
Consider these remarks about mathematics:
"Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them."
Jean Baptiste Joseph Fourier
"Everything of any importance is founded on mathematics."
"Mathematics and music are God's languages. When you speak them…you're speaking directly to God."
"One cannot understand...the universality of the laws of nature, the relationship of things, without an understanding of mathematics. There is no other way to do it."
"I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations,' are simply the notes of our observations."
Godfrey Harold Hardy
"The mathematician's patterns, like those of the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way."
Godfrey Harold Hardy
"Obvious is the most dangerous word in mathematics."
E. T. Bell
"Mathematics as we know it and as it has come to shape modern science could never have come into being without some disregard for the dangers of the infinite."
"Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite."
Cassius J. Keyser
"In mathematics you don't understand things. You just get used to them."
John von Neumann
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
John von Neumann
"Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told that the young man had gone off to become a poet. Hilbert is reported to have remarked, 'I never thought he had enough imagination to be a mathematician.'"
"Mathematics is persistent intellectual honesty."
"God created infinity, and man, unable to understand infinity, created finite sets."
"Nature imitates mathematics."
"Mathematics is the science of patterns, and nature exploits just about every pattern that there is."
"The only reason that we like complex numbers is that we don't like real numbers."
"Mathematics is an escape from reality."
"The pursuit of mathematics is a divine madness of the human spirit."
Alfred North Whitehead
Relativity: the Relationship between the Dimensional and the Dimensionless.
Now we are going to undertake something radically ambitious: to attempt to explain Einstein's special theory of relativity in a reasonably simple form. You can't expect to understand the universe unless you have some sort of feel for what Einstein said. We will be providing a unique interpretation of his theory, revealing the underlying reality that he missed.
Einstein uses little more than high school mathematics, but don't be deceived: his equations are awesome in their implications. Even if you find the equations trivial, you will never find the interpretation of the equations trivial. They truly reveal the Mind of God.
Einstein's great achievement was to place on a firm scientific and mathematical footing what mystics had long known, but hadn't been able to express in well-defined, unambiguous, rigorous terms. The beauty of mathematics is that it can be absolutely precise. With an astonishingly successful theory such as quantum mechanics, no one disagrees with the mathematics. What they argue over is how to interpret the mathematical equations, to describe what the equations mean in terms of reality. So, although mathematics can't unambiguously provide all of the answers - due to the difficulty in translating mathematics into non-mathematical language - it can provide a uniquely accurate framework in which to attempt to provide the answers. Words, intrinsically, do not have sufficient accuracy; only equations do.
Language is an imprecise tool. It's all too easy to misunderstand what someone has said. Words are loaded with ambiguity. Mathematics provides precision, but it does not provide unambiguous meaning. We have to apply that final layer, but at least mathematics gives us a platform with which we can all agree, even if we disagree over the next steps. In contrast, conventional religions provide no commonly accepted platform - do Muslims, Jews and Christians worship the same God, as some of them claim, or three utterly different gods, as others claim? It is impossible to define anything in conventional religion and impossible to reach any rational conclusions. That's why "faith" plays such a critical role. "Believing" is what you do when you haven't a clue how to analyze something mathematically.
But even scientists and mathematicians can have problems with reasoning. Even they can succumb to "common sense" that blinds them to the truth.
Brilliant scientists, for example, refuse to accept dimensionless existence where physical dimensions shrink to zero and time stops, and infinite quantities which they believe would somehow tear nature apart or render it incomprehensible. Yet, over and over again, the mysteries of life are seen to revolve around zero and infinity, which are just the flip sides of each other. But while science recoils from them in horror, modern mathematics takes them in its stride (although, historically, even mathematicians found them far more problematic than ordinary mathematical concepts).
It's often thought that mathematics deals with the hypothetical and physics with the real, but one thing is becoming relentlessly clearer: mathematics, the queen of science, is more real than physics. Physics is deceptively real i.e. it is more closely associated with our common sense, with the evidence of our senses, and less with true reality. It is the other way around with mathematics. When physics comes closest to true reality, as in relativity theory and quantum mechanics, it is astonishingly mathematical and counter-intuitive. Common sense simply vanishes - it can't help you at all in relation to relativity and the quantum world. If you can't get beyond your common sense, you will never understand these subjects. Why haven't physicists cottoned on yet? It is mathematics, not physics, that defines the laws of nature.
In previous articles, we discussed how quantum particles are so astoundingly small, so much smaller than any human mind could ever conceive, so close to being dimensionless, to being "nothing", that they cannot be properly understood unless it is recognised that they flicker between dimensional and dimensionless existence. We showed that infinity rears its head spectacularly in the case of black hole singularities and the Big Bang singularity, neither of which can be fully understood by physicists since singularities involve division by zero, thereby producing a result of infinity, at which point the laws of physics are said to collapse.
It's time to discuss another example of zero and infinity appearing in science, perhaps the most bewildering and profound example of all since, paradoxically, it involves an entity that we recognise as finite. With this entity, zero, the finite and the infinite come together in an astonishing way that may define the nature of existence. We are talking about one of the most bizarre phenomena of all - the speed of light.
The unique status of the speed of light is the centrepiece of Einstein's special theory of relativity. Although the mathematics of the speed of light can be described with tremendous accuracy, the "meaning" of light speed defies any straightforward interpretation. It might be said that all of the problems that bedevil fundamental physics flow from a failure to comprehend light.
Einstein's theory says nothing less than that all photons are, in their frame of reference, outside space and time. They don't experience the passing of time and they don't experience the traversing of any distances. The universe, for photons, is a mystical dimensionless point. Even if there were an infinite number of photons, they would all inhabit this inconceivable singularity beyond the reach of time and space.
Can you begin to see? The realm of light, as described by Einstein's supremely well tested equations, is astonishingly similar to what we have described as the r = 0 dimensionless domain: the realm of the mental. Immediately, the profoundest of questions arises. Are light and thought the same thing? Are photons, when considered from the correct perspective, mental rather than physical? When the sun shines on us, are we being bathed in the "thoughts" of the sun as well as its light? If photons do not experience space and time, and they do not have any mass, how else would you characterise them except as some sort of mind-like entities?
Yet no scientist would ever claim that photons are mental. Why not? Isn't that what Einstein's equations hint at? How can photons be real, physical entities if an infinite number of them can inhabit a timeless, massless domain of zero size? Descartes famously defined thinking substance ("res cogitans") as non-physical, without extension. What would he have made of photons? In their own frame of reference they too are without extension.
Scientists don't ponder such questions. They are too scared of where this train of thought leads - to religion, to souls, to God. Rather than take a God's-eye-view of the universe, they lock themselves into safe, common sense territory. They ignore how the world looks to a photon and focus on how the world looks to us. And thus they have turned away from understanding how the cosmos truly works.
The reality is that human beings are children of two domains - the dimensional and the dimensionless, r > 0 and r = 0. The attempt by science to restrict us to the r > 0 domain, the material domain of solid objects with mass, is the most catastrophic misjudgement imaginable, and actually refuted by science itself which consistently points to the inescapable reality of dimensionless existence.
It is that fateful error that has sundered science from religion. It is that fateful error that must be corrected to get the human race back on track.
The key equations of Einstein's special theory of relativity are known as Lorentz transformations. They provide a mathematical means for calculating how mass, distance and time are related between different frames of reference.
In terms of the special theory of relativity, any observer moving at constant speed in a straight line can consider himself at rest and that everything else is moving relative to him. But any such observer, no matter what speed he is moving at, will always get the same answer when he measures the speed of light.
Relativity has astounding consequences. If one observer holding a 30cm ruler is travelling at 99.9% of light speed, a stationary observer would observe that same ruler to be much shorter than if he himself were holding it. But since the person travelling at 99.9% light speed can consider himself stationary then the same is true the other way around. So which of them actually has a shortened ruler? The answer is that neither does and both do. Each of them has a 30 cm ruler from their own point of view. If they came together, they would each agree that they had a 30 cm ruler. It's only when they're moving at near light speed with regard to each other that they start to radically disagree about the length of the ruler.
So, is length contraction a real phenomenon or just an elaborate illusion? If both observers are holding 30 cm rulers, and both agree about that when they are together, surely it's ridiculous to say that their rulers shrink relative to each other when they are moving apart at high speed. But that's exactly what happens. "Reality" changes according to the speed you're travelling at. Rulers that measure a certain length in one frame of reference measure a completely different length in a second frame of reference when viewed from the first frame of reference, and the effect gets more pronounced as the relative difference in speed of the two frames of reference increases. Isn't that astounding? Common sense tells us that things have definite, fixed dimensions: relativity says that they don't. Physicist David Bohm wrote, "The new order and measure introduced in relativity theory implies new notions of structure in which the idea of a rigid body can no longer play a key role. Indeed, it is not possible in relativity to obtain a consistent definition of an extended rigid body, because this would imply signals faster than light."
All of this is true except in one domain: the unique frame of reference of the speed of light itself. Here, all rulers always measure zero distance. No such thing as a 30 cm ruler is physically possible in this frame of reference.
All observers, no matter what speed they're travelling at, will always agree that a hypothetical ruler being carried at light speed will always measure zero distance. That result is built into Einstein's equations. Everything is measured with respect to the speed of light except the speed of light, which is measured with respect to itself, making it a unique reference frame. This is an example of one of the great enigmas of existence: self-reference. So often, paradoxes reduce to situations of self-reference. When a Cretan says, "All Cretans are liars," is his statement true, false, or undecidable? Gödel's famous Incompleteness Theorem is the logical consequence of the enigma of self-reference.
In a self-referential frame of reference, zero and infinity come to the fore. So, all distances between photons are zero, their mass is zero, and time passes infinitely slowly i.e. time has stopped. And consider this paradox: given that speed = distance divided by time, if time never passes then no matter what distance is covered, the time elapsed is always zero, hence we are dividing by zero, hence the speed of a photon always equals infinity, in its own frame of reference. But equally, since all distances experienced by a photon are always zero, then no matter what time elapses, the speed of a photon will always be zero. So, what is the speed of a photon in its own frame of reference? Is it zero or infinity, or somehow neither and both? Is it simultaneously all possible speeds from zero to infinity? Such is the enigma of light speed. The mystery is compounded when we add in the result employed by Einstein that the speed of light in a vacuum is invariant for all observers in any frame of reference other than that of light itself.
Self-reference continues to baffle scientists, philosophers, mathematicians and logicians. They have all failed to understand why. It's because self-reference is the province of zero and infinity, the two numbers that cause conventional "laws" to collapse. A computer would go into an infinite loop trying to solve a problem of self-reference. It would never halt. In such a system, everything outside the self-reference is reduced to zero - it does not exist. It is nothing. Over and over again, the mystery of existence reduces to the mystery of infinity and zero. Everything that is most profound is contained in these supremely mysterious numbers.
We ourselves are units of self-reference. That's what the "self" is. We live permanently inside our own minds. Strictly speaking, we can never prove the existence of anything other than our own thoughts. "I think therefore I am" could equally well be stated as: "Only my thoughts exist. There is nothing other than my thoughts. All of 'reality' is but my thought, created by my thought." We break out of the infinite loop of self-reference - known philosophically as solipsism (from Latin solus "alone" + ipse "self", meaning the theory that the self is all that one truly knows to exist), by an assumption that an external world exists and that other minds exist. But we can never prove this. It will always be an assumption, the ultimate leap of faith.
If the centre of our existence - our self - is an infinite loop in some sense then how can it ever die? Sure, on its infinite journey it can take on many forms - different outward appearances (the self as phenomenon), but it can never perish as it is in itself (the self as noumenon). It is an immortal, transcendental self.
Zero and infinity, the flip sides of each other, are at the heart of existence. Everything else is defined with respect to them. The finite can exist only in relation to the infinite. That is the key to comprehending the cosmos. The self - a unit of self-reference - is born of infinity and, like energy, can be neither created nor destroyed. It endures eternally, as all infinities do. Self-reference in tandem with the universal property of mind cannot help but give rise to self-awareness and consciousness. Hegel describes the critical event where one unit of self-reference encounters another such unit. At that stage, each is forced to concede that it is not alone, that the universe is not solipsistic. If the universe were solipsistic then one unit of self-reference would be able to control all other units of self-reference since they would be nothing but its own creations. If it can't control them then it can conclude that a) it is able to create things of which it has no knowledge and over which it has no control (implying a kind of insanity) or b) these things of which it has no knowledge and over which it has no control actually have independent existence i.e. the universe consists of many and not one. So, the unit of self-reference comprehends that it is not alone. And then, as Hegel so brilliantly illustrated, it is plunged into a life or death struggle to avoid being "negated" by this rival. We arrive at the famous master-slave dialectic. Before "death" arrives, one of the units of self-reference submits to the other and becomes the other's slave. From then on it struggles to be equal to the "master". The master, meanwhile, has nothing but contempt for the cowardly slave.
The master-slave dialectic goes on every single day in our contemporary world. Every day, the Old World Order remain the masters, and the rest of us remain their slaves. Why? Because we do not have the guts to overthrow them. We are indeed pathetic cowards. Six billion of us; six thousand of them, and yet we do nothing. If that's not a definition of cowardice, what is?
Do you dream of being an eternal slave? If not, wake up and buckle up. It's time to fight to be human, to no longer be the master's slave. The OWO can easily be swept aside. Their wealth can be removed from them by the will of the people and then they will be rendered powerless, like Samson without his hair. What will these six thousand do against six billion? Do you think hedge fund managers will be manning the barricades, or grabbing the nearest Kalashnikov?
These people are sustained by the illusion of power (represented by money) not by real power - the ability to personally fight and defeat others in mortal combat. At the dawn of humanity, the most violent men were the masters. They would literally kill you if you dared to fight them. Now the masters are the Wizards of Oz, ruling by tricks and deceptions. They can be defeated by nothing more strenuous than pulling back the curtain. The real horror is this - only the Illuminati are prepared to pull back the curtain. The rest of the human race are terrified. Why? Because if they do draw back that magic curtain - both infinitely heavy and infinitely light - then they will have no choice but to take responsibility for their lives. They will have to be creators rather than followers. They will have to be decision-makers rather those who obey orders. In other words, they will have to look in the mirror and for the first time ask themselves the biggest question of all: is being a slave all they are truly capable of?
Make no mistake, the world economy will temporarily collapse if the OWO are overthrown. That is inevitable since the world economy is theirs, completely defined by them. But if the people have the guts and the merit, they can rebuild it incredibly quickly. Look at two of the world's greatest powers: Germany and Japan. At the end of WWII, both nations were in ruins, their people horribly traumatized and demoralised. Their economies were destroyed, millions were dead and wounded, the cities had been reduced to smoking rubble, they were under occupation by their enemies. The situation simply could not have looked any bleaker and more desperate. These nations could have sunk into centuries of despair. But they didn't. The people of both countries were clever, resourceful and talented. They worked incredibly hard and in a matter of years they were back to being leading nations of the world once more. The fall of the OWO will certainly cause economic hardships for a time, but nothing in comparison with what the Germans and Japanese endured and overcame just a few decades ago.
Truly, there is nothing to fear. Just as adversity brought out the best in the German and Japanese people after the war, so it will bring out the best in all of the world's people when they have no choice but to build the world anew after the end of the OWO's reign.
Relativistic Length Contraction
If a stationary observer is holding a ruler and is observing another person moving at constant speed with regard to him, holding the same type of ruler, he will notice that the other person's ruler appear to have shrunk, and the faster the other person goes, the greater the shrinkage becomes.
The degree of contraction can be calculated by a so-called Lorentz transformation: Equation A) Lm = Lr √(1-(v2/c2))
Where Lr is the length of a ruler at rest and Lm is its "moving" length when travelling at velocity v. The speed of light - the "natural speed" of the cosmos, the speed by which everything else is defined, is designated as c.
Using equation A, when an observer called Jill is travelling at 0.866 of the speed of light, then the ruler she is holding appears to Jack, a stationary observer, to be only half its normal length i.e. a 30 cm ruler would appear to be only 15 cm long, although still showing 30 divisions.
If Jill could travel at the speed of light then the length of her ruler would appear, to Jack, to shrink to zero. (That's what you get if v = c in equation A: Lm = Lr √(1-(v2/c2)) = Lr √(1-(c2/c2)) = Lr √0 = 0.) That's one way of explaining why no human will ever attain light speed: you would literally vanish, not just theoretically but actually. At the speed of light itself, it can be said that relativity vanishes and is replaced by the absolute. In the domain of the absolute, nothing can have any physical dimensions! We have crossed the mystical barrier from r > 0 to r = 0.
At light speed, all distances are zero, whether measured by a hypothetical observer "travelling" at that speed, or any observer in any other frame of reference. Of course, at light speed, the idea of travelling anywhere ceases to be meaningful. You are simultaneously everywhere.
Above light speed, the ruler would have an "imaginary" length since v is greater than c, hence √(1-(v2/c2)) becomes the square root of a negative number, and the square root of a negative number belongs to the domain of so-called imaginary numbers, the astounding significance of which we shall be highlighting shortly.
The Time Equation
Equation B) Tm = Tr/(√(1-(v2/c2)))
When an observer called Jill is travelling at 0.866 the speed of light, then the clock she is holding appears to Jack, a stationary observer, to count time at only half its normal rate i.e. the passage of one second for him, takes two seconds for Jill. Her time is flowing more slowly than his; Jill's time is expanding, dilating, taking longer to flow. Since Jill's clock counts time twice as slowly then one year of her time is equal to two years of Jack's time.
If Jill could travel at the speed of light then her clock would appear, to Jack, to have completely stopped; her time would be passing infinitely slowly. (That's what you get if v = c in equation B: Tm = Tr /(√(1-(v2/c2)) = Tr /(√(1-(c2/c2)) = Tr /√0 = ∞. Jill's clock shows no movement. No time passes. That's one way of explaining why no human can ever attain light speed: you would literally leave time, not just theoretically but actually. In the domain of the absolute, nothing can experience the passing of time as we understand it, since clocks do not tick! We have crossed the mystical barrier from r > 0 to r = 0.
At light speed, all clocks take an infinite time to tick, whether measured by a hypothetical observer travelling at that speed, or any observer in any other frame of reference.
Above light speed, the clock would start counting imaginary time since v is greater than c, hence √(1-(v2/c2)) becomes the square root of a negative number.
(Note that whereas the term √(1-(v2/c2)) was used as a multiplier in equation A, it was used as a divisor in equation B. This shows that the length contraction and time dilation effects work in the opposite directions, in a directly proportionate manner: as length contracts, time proportionately dilates. It is this perpetual balance between space and time that ensures that no matter what speed an observer is travelling at, he will always obtain the same measurement for the speed of light: time and space continually adjust themselves to ensure that result.)
The Mass Equation
Equation C) Mm = Mr/√(1-(v2/c2))
Travelling at 0.866 of the speed of light, Jill's mass would double. At light speed, her mass would be infinite! This is the usual reason given for explaining why no human can ever attain light speed. It would require all the energy in the cosmos:
Mm = Mr/√(1-(v2/c2)) = Mr/√(1-(c2/c2)) = Mr/0 = ∞
(Above light speed, Jill's mass would be "imaginary" - the most effective diet in the cosmos, perhaps.)
Once again, we see zero and infinity representing the limiting cases of scientific equations. However, unlike in the case of black holes, scientists do not assert that the laws of physics mysteriously fall apart at this "infinity/zero" point where the speed of light reigns. They are quite happy to admit that gluons, gravitons and photons can sensibly exist at this point. In other words, scientists, for reasons known only to themselves, accept dimensionless existence in this context, yet in the very similar context of black holes they say that there's something wrong with the equations rather than simply acknowledging that mass (a property of dimensionality) can be converted into masslessness (a property of dimensionlessness).
The logic of black holes would seem to imply that dimensional particles with mass are subjected to such enormous compression in the black hole singularity that they are converted into dimensionless particles without mass i.e. a black hole singularity is "made" of massless, dimensionless particles such as photons, gluons and gravitons. Not a single scientist to our knowledge has ever proposed such an obvious thing, and many of the most renowned of black hole scientists confess that they have no idea what a black hole is made of i.e. what becomes of all the massive particles that have been crushed together, what new form they take. Instead they continue to talk about there being something wrong with black hole theory since it gives birth to infinities. But it's precisely when infinity appears in an equation that we are being shown that the gap between r > 0 and r = 0 is being bridged.
One of the radical consequences of Einstein's relativity theory, is that the earth can once more be defined as the centre of the universe, if that's what we choose. Any frame of reference is as valid as any other. We choose to say that the sun is at the centre of our solar system because it yields a much simpler way of understanding and tracking planetary motion, not because the sun actually is the centre of the solar system in any absolute sense. We could make any planet the centre if we wanted. We could make the moon or an asteroid the centre, but these would result in far greater complexity.
Returning to the extraordinary enigma posed by Einstein's special theory of relativity, if, in their own terms, photons are stationary and outside space and time then how come, in our terms, they are anything but? We perceive them as travelling at 300,000 km per second i.e. they are travelling very rapidly through space. How can both views be right? This is the central paradox of relativity. There is no single perspective from which to view the universe. The view you have of the cosmos is completely different depending on whether or not you have mass and what speed you are travelling at. Time and space aren't fixed, aren't absolute, but are dependent on mass and speed. Massless particles don't experience space and time from their perspective, particles with mass do. Similarly, particles travelling at light speed don't experience space and time from their perspective; particles travelling at any other speed do.
The particular speed that particles travel at relative to light speed determines how they experience space and time. There is no absolute space and time. Relative to a stationary observer on planet earth, a person moving at close to light speed will seem to live in a world in which time passes much more slowly and a ruler will measure much shorter distances than on earth. Yet, amazingly, the person moving at near light speed can claim that it is the person on earth who has the short ruler, and may also believe that it is the person on earth who has the slow clock (though this turns out to be false). Such is the mystery of relativity. (If you are interested in delving further into some of the incredible time puzzles of relativity, Google "The Twin Paradox".)
John Gribbin, in Schrödinger's Kittens and the Search for Reality, provides a summation of the main points we have raised:
"So what happens when we push this time-dilation business to the limit? Getting back to the original question that Einstein asked about light, how does the Universe 'look' to a beam of light (or a photon, if you prefer), or to a person riding on a light beam? And how does time flow for a photon?
"To answer the second question first - it doesn't. The Lorentz transformations tell us that time stands still for an object moving at the speed of light. From the point of view of the photon, of course, it is everything else that is rushing past at the speed of light. And under such extreme conditions, the Lorentz-Fitzgerald contraction reduces the distances between all objects to zero. You can either say that time does not exist for an electromagnetic wave, so that it is everywhere along its path (everywhere in the Universe) at once; or you can say that distance does not exist for an electromagnetic wave, so that it 'touches' everything in the Universe at once.
"This is an enormously important idea, which I have never seen given due attention. From the point of view of a photon, it takes no time at all to cross the 150 million km from the Sun to the Earth (or to cross the entire Universe), for the simple reason that this space interval does not exist for the photon. Physicists seem to ignore this remarkable state of affairs, because they know that no material object can ever be accelerated to the speed of light, so no human (or mechanical) observer is ever going to experience this strange phenomenon. Perhaps they are simply so stunned by what the equations say that they have not fully thought out the implications. As I hope to persuade you, though, this curious behaviour of space and time from the point of view of photons may help to resolve all the outstanding mysteries of quantum physics." Even Gribbin hasn't gone far enough in highlighting the infinitely strange world of the photon. In its frame of reference, not only does the photon not experience the passing of time or the traversing of any distances, it has no mass, no size, no dimensions. All photons are exactly the same in these respects. How can one photon be distinguished from another? None can be individuated in time because no time passes, and none can be straightforwardly individuated spatially because there are no distances between them to be measured.
Moreover, is it valid for Gribbin to say, "From the point of view of the photon, of course, it is everything else that is rushing past at the speed of light"? Gribbin is treating a photon as if it is an ordinary observer located in space and time, but it isn't. It's not in time at all, and all distances experienced by it are zero, so how can anything be "rushing past" it? Rushing from where to where, and in what time? If, as Gribbin says, "…you can say that distance does not exist for an electromagnetic wave, so that it 'touches' everything in the Universe at once," there is nothing left that can rush past it. Given that Gribbin is an excellent writer and scientist, this example shows how easy it is to get confused by relativity. But, to his immense credit, Gribbin has realized the critical importance of viewing existence from the point of view of photons. Therein lies the key to mind and religion.
Returning to the central point, doesn't this bizarre world of photons sound exactly like the dimensionless r = 0 domain, outside space and time? In fact, there's only one difference. Despite being so hard to define in terms of any concrete existence, photons do possess real energy in the physical world.
What is the conclusion? When dimensionless, purely mental energy is converted into dimensional energy, it appears initially as massless, sizeless, unindividuated "particles" such as photons. The link between thought and light (electromagnetic radiation) is a close one, and the differences are exceptionally subtle.
One of the keys to establishing the reality of the r = 0 dimensionless domain to skeptical scientists is to show how it can realistically give rise to dimensional existence. We have now done so. Light is the bridge between the dimensionless and the dimensional. Light is a hybrid of the dimensionless and the dimensional, with one foot in each domain. Light, although part of dimensional reality, also exists in a twilight zone of dimensionlessness where one photon cannot be readily distinguished from another. Light might be said to be "physical thought". Photons might be said to be like brain cells in a cosmic brain, blazing with illumination. Enlightenment is therefore almost a literal expression rather than merely metaphorical.
In a black hole singularity, time doesn't pass and there is no distance between any particles within the singularity. Light can't escape from the singularity. Imagine that all of the countless black holes in the universe sucked in all of the matter around them and then came together in one vast, cosmic black hole. This Super Singularity would contain everything in the universe. It would be the reverse of the original Big Bang Singularity from which everything emerged in the first place. It would be timeless, spaceless, dimensionless. It would be the r = 0 Genesis Singularity, the most remarkable entity in existence - God in himself, as Absolute Idea.
We are used to thinking of black holes as being created by processes of collapse, leading to extraordinary concentrations of mass in little or no volume. However, there is another way to form a black hole that scientists never seem to mention. In the hypothetical case in which a particle with mass were accelerated to light speed, time would stop, distance would vanish and it would acquire infinite mass (and hence be infinitely dense since it occupied zero volume). Are those not exactly the same characteristics as those of black holes? So, our existence is in some sense bounded by black holes. If enormous entities with mass collapse catastrophically, black holes are the outcome. If any mass is accelerated to the hypothetical maximum of light speed, black holes are the outcome (since an infinite mass would be concentrated in zero volume). Mass and black holes go together. Black holes are concerned with what happens when mass has been compressed so much that its "dimensional integrity" has become unsustainable and it's starting to enter the dimensionless domain.
Our universe is a bizarre hybrid of the infinite and finite, the dimensionless and the dimensional, r > 0 and r = 0. If mass is the essence of r > 0, thought is the essence of r = 0, and light is the bridge between the two domains. In the centre of black holes, light cannot escape and mass is no longer recognizable in dimensional terms. Physicists are unable to say what a black hole singularity is made of. Light, mass, dimensionality and dimensionlessness, infinity and finitude all come together in black holes, the dimensional portals to the dimensionless domain.
But there's something else to think about. Light can't escape from a black hole, but nor can it escape from its own domain. If (from its perspective) it exists in a domain of zero dimensions, to where can it escape? It has nowhere to go. When we say that light can't escape from a black hole, we're talking about light relative to our perception of it, but, relative to itself, light is unaffected by a black hole since light is outside space and time. It is everywhere at once.
Light Hole versus Black Hole
A black hole, in conventional scientific terms, is where an enormous amount of mass is accumulated at a single dimensionless point - a singularity - giving rise to infinite density. Time stops. All distances are reduced to zero.
The realm of light - the arena for photons and all other particles travelling at light speed - is where time stops and distances are zero i.e. it has the same characteristics as a black hole singularity, the one glaring difference being that the realm of light - the Light Hole, so to speak - has no mass. (But, of course, we should always bear in mind that Einstein's most famous equation, E = mc2, makes mass and energy different forms of the same thing, related by the square of light speed.)
In other words, the Light Hole is the massless equivalent of a black hole. The Light Hole is the defining speed limit of the universe. Black holes are the mass limit of the universe. If particles accelerated to light speed acquire infinite mass (i.e. ALL of the mass created by the Big Bang) then by accelerating the cosmos to light speed, we would be combining the Light Hole and the Genesis Singularity in one entity. Isn't it remarkable that the physical universe always returns to itself? If you push it too far in any direction, you invariably come back to a dimensionless domain outside space and time, associated with zero and infinity. The physical dimensional universe - the finite - is hard-wired to the dimensionless mental universe - the infinite. The wiring is provided by light.
The term "black hole" is one that has validity only from the perspective of observers not travelling at light speed, but, to something that is travelling at light speed, there's no such thing as a black hole. Moreover, the expression "travelling at light speed" is meaningless from the point of view of any particle travelling at light speed because it's not actually travelling anywhere since it's not in space and time, and all distances are zero.
When the finite and the infinite come together, paradox is inevitable. Alfred Weber, discussing Hegel's approach to the infinite and the finite, said: "The contradiction found in the idea of being is resolved in the notion of becoming. Being becomes, i.e., determines itself, limits itself, defines itself. But determinate or finite being continues ad infinitum; the finite is infinite; nothing compels thought to assign limits to it. Here we have a new contradiction, which is resolved in the notion of individuality (being-for-self, Fürsichsein). The individual is the unity of the finite and the infinite. To consider these two terms as excluding each other is to forget that the infinite, excluded by the finite, would be limited by the finite, or would be finite itself. If the infinite begins where the finite ends, and if the finite begins where the infinite ends, so that the infinite is beyond the finite, or the finite on this side of the infinite, it would not really be the infinite. The infinite is the essence of the finite, and the finite is the manifestation of the infinite, the infinite existing. Infinity determines itself, limits itself, sets boundaries to itself; in a word, it becomes the finite by the very fact that it gives itself existence. Existence is possible only under certain conditions, in certain modes, or within certain limits. Existence is self-limitation. Existence is finite being. Finite being, the individual, the atom, is infinity existing in a certain manner, limited infinity: quality becomes quantity."
There are a couple of key phrases here: 1) "The individual is the unity of the finite and the infinite." That's a perfect description of the union of a mortal body and an immortal soul. 2) "Infinity determines itself, limits itself, sets boundaries to itself; in a word, it becomes the finite by the very fact that it gives itself existence." This is the appropriate response to the scientists who think that infinities are some threat to the fabric of the cosmos, that infinity represents a potentially fatal puncture of the finite. In fact, it is the nature of the infinite to set boundaries to itself and become finite. A circle is a perfect symbol of infinity represented in a finite form. Infinity is never a threat to the finite. Indeed it is the origin of the finite. There is no such thing as uncontrolled infinity. When an equation of physics produces an infinite result, it is a sign that something fascinating is happening: that the interface of r > 0 and r = 0 has been reached. It is no cause for the horror that afflicts physicists when they see infinity rearing its head. The final challenge facing mathematicians and physicists is to produce a technique for seamlessly integrating infinity with the finite rather than treating infinity as some sort of disastrous discontinuity. Everything between, and including, minus infinity to plus infinity is part of a smooth continuum. We never reach the "end of the world" and fall off the edge.
Some people ask the question: Why isn't the speed of light infinite? As we have seen, it can be interpreted as infinite in its own frame of reference. It appears as finite in our frame of reference for exactly the reason just stated: infinity limits itself. Space and time are finite dimensions. Therefore anything perceived from the perspective of these dimensions will appear finite. If we wore green goggles, we would see everything as green. Similarly, if we wear space-time goggles, everything appears in terms of space and time, of finite quantities. It cannot be emphasized enough that infinity filtered through finite dimensions must appear as finite.
The electromagnetic wave equation that describes light is time-dependent. If light speed was infinite, it would have no time-dependence since it would be everywhere at once. Hence the equation would fall apart, and the whole universe would be permanently blindingly bright. Light, as we understand it, would not exist. Space and time allow the infinite to be tamed, to provide scope for the type of lives we lead.
Space and time are finite filters through which everything, including the infinite, is forced to appear finitely. The infinite speed of light is converted into the constant finite speed with which we are familiar.
Our universe is an extraordinary arena in which, just as Hegel contends, the infinite is able to become finite, to become individual and self-limiting. But via black holes and the Light Hole, the finite returns to the infinite. Individuation is extinguished in black holes - one thing cannot be distinguished from another. The same is true in the dimensionless realm of photons in their own frame of reference. In some sense, all photons are the same. Leibniz said that the universe is based on an infinite number of dimensionless mental entities called monads. Just like photons, they are in some sense all the same since they are not differentiated in space or time. We could just as easily treat infinite separate monads as one Monad. Thus infinity becomes finite and indeed singular. The many and the one are intimately and inextricably related.
We could almost talk of a single Photon, the light of the entire cosmos concentrated in one single super light particle. If the Monad is the Mind of God then the Photon is his Divine Light with which he illuminates existence.
Gnostic enlightenment is all about entering into union with the Monad via the cosmic light. Is there any more glorious image? Is it not infinitely more inspiring than the "vision" of the Abrahamic slave religions, where humanity is forever on its knees, with its eyes cast downwards through fear, worshipping a dim light far, far away, with which it will never come into communion.
4Di - Space is not 3D
The key to reality is the imaginary number, i. Imaginary numbers based on i are usually contrasted with so-called real numbers, which are the familiar numbers of the 3D world. (Numbers that contain both real and imaginary parts are known as "complex" numbers.)
How many dimensions of space are there? Three? That's what common sense says. Wrong. There are four. Why? Because mathematics says so, and maths always takes priority over common sense. Here's why there are four dimensions of space rather than three:
1) What is 1 x 1 (i.e. 1 "squared")? Answer = 1.
2) What is -1 x -1 (i.e. -1 squared)? Answer = 1.
Notice anything odd? Squaring 1 or -1 gives the same answer. In fact, squaring any negative number always gives a positive number. So, although there is a set of positive numbers and a matching set of negative numbers, there is no such matching set when it comes to the squares of positive and negative numbers. The squares are always positive, whether or not they are derived from positive or negative numbers. But why should the universe exclude a matching set of negative square numbers? This contravenes the Pythagorean principle of mathematical completeness.
All sorts of things that could be accomplished via negative square numbers are impossible in a universe in which only positive square numbers are possible. Why should negative square numbers be prohibited? Is there any fundamental mathematical reason for it, or is just a consequence of limited mathematical knowledge? If -1 is OK, what's wrong with -1 as a squared number? Symmetry demands that there should be a way of addressing this problem. There must be a set of negative squares forming the mirror image of the set of positive squares.
Mathematicians themselves were painfully slow to grasp what had to be done. Even when they stumbled upon the answer, it took them centuries to properly comprehend and develop it. They too were victims of the prejudices of common sense. They couldn't see anything physical that negative squares would apply to, so they largely ignored them.
The key to the problem of negative squares was i, the imaginary number. This is defined as the square root of -1. When i is squared the result is -1 i.e. i2 = -1. From i we can generate all of the negative squares e.g. 5i squared = -25; 10i squared = -100. Mathematical symmetry is restored at a stroke. Mathematics is "complete" once more.
But many mathematicians found the imaginary number bizarre and repulsive. One mathematician described it as, "void of meaning, or rather self-contradictory and absurd." Another said it was "uninterpretable", and another "an untrustworthy intruder." Another called it "fictitious." Such people thought it had no practical applications and was just some odd mathematical irrelevance. In fact, it is arguably the most important number of all, holding the key to breaking through the barriers of "common sense" that block our path to the truth.
In 1831, the brilliant German mathematician Gauss wrote of imaginary numbers, "If this subject has hitherto been considered from the wrong viewpoint and thus enveloped in mystery and surrounded by darkness, it is largely an unsuitable terminology which should be blamed. Had +1, -1 and the square root of -1, instead of being called positive, negative and imaginary (or worse still impossible) unity, been given the names, say, of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity."
You will never understand reality unless you appreciate the very real significance of the imaginary number. It is the crucial antidote to common sense. One might even call it the God Number since, as we shall see, it is the imaginary number that creates the scope for God, souls, heaven and an afterlife.
If x, y and z are the normal Cartesian coordinate axes (perpendicular to each other) of the three-dimensional space of common sense with which we are all familiar (left and right, backwards and forwards, up and down), then the "imaginary" axis for imaginary numbers is perpendicular to these three in a four-dimensional space (that we can't visualize, of course, since our senses are stuck in 3D).
It is precisely because we can't picture 4D-space that "common sense" is so shocked by it and tries to resist it. It seems intrinsically wrong. Yet it is fundamental and essential to a true understanding of the universe, as will become clear.
The starting point is the famous theorem of Pythagoras which states that in any right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In the famous "3,4,5" triangle, 32 + 42 = 52. So, the length of the hypotenuse = square root (side1 squared + side2 squared)
If two points (x1, y1) and (x2, y2) are placed on a 2D plane then we can calculate the distance between them by using Pythagoras' theorem: distance = square root ((x2-x1)2 + (y2-y1)2). This is the general technique for calculating the distance between any two points. The same technique can be extended to two points in any dimensional space. In 4D (including the "imaginary" axis), each point is specified by four points: (x1, y1, z1, w1) and (x2, y2, z2, w2).
Using mathematical terminology, we write ds2 = dx2 + dy2 + dz2 + dw2 where "d" is shorthand for the distance or difference between the respective coordinates (e.g. dx = x2 - x1).
However, because the values of "w" lie on the imaginary axis, this means that every value is multiplied by i, the imaginary number. If w1 = 2i and w2 = 8i then dw = 8i - 2i = 6i and dw2 = 6i2 = -36.
This ability of i to generate negative square numbers is one of the most important results conceivable. It is of such crucial significance because it means that in a 4D space, with one axis being imaginary, negative square numbers, which can be used in calculating distances between any two points, now become part of the mix. (In the traditional 3D universe, this is impossible - there are no negative squares involved in any distance calculations.)
To reflect that we have moved from 3D space to 4D space with an imaginary axis, we will henceforth use the designation "4Di".
Here are the astonishing consequences of reality being based on 4Di rather than 3D:
1) If the negative number produced by dw2 exactly balances the three positive numbers provided by dx2 + dy2 + dz2 then the overall result (ds2) will equal 0 i.e. it is possible, in 4Di space, for the distance between two different points (the
square root of ds2) to be ZERO! In 3D space, the only way to get the distance between two points to be zero is for the two points to be the same. In 4Di space, thanks to the imaginary axis, two points that may be very far apart if we compare their respective x, y, z and w coordinates, can actually be separated by no distance at all. Hence, at a non common-sense level, the two points, since no distance separates them, are actually the same despite being distinct. In quantum mechanics, we encounter the bizarre idea that a particle can be in two places at once. Here, we encounter the equally bizarre idea that two particles can be at the same place at once (in the sense of being at two distinct points but separated by no distance).
2) And if dw2 is larger (as a negative number) than the three positive numbers provided by dx2 + dy2 + dz2 then it means that the overall result ds2 will be less than 0 i.e. it is possible for the squared distance between two distinct points to be negative. (This means that the distance, the square root, will be imaginary.) In other words, in 4Di space, it is possible to get squared distances greater than zero (as in ordinary 3D space), less than zero and exactly equal to zero. Or, in terms of distance, to get real, imaginary and zero distances. In the 3D world of our everyday experience, this is impossible since the distance between two distinct points is always real. We can take a ruler and physically measure the distance in 3D space. But no "common sense" ruler will help us to measure an imaginary length or no length at all. Yet it turns out that imaginary and zero distances dictate our world.
3) If, to emphasize the different character of w compared with x, y and z, we write iw instead of w then d(iw)2 = -dw2. Hence our original equation of ds2 = dx2 + dy2 + dz2 + dw2 can be rewritten as ds2 = dx2 + dy2 + dz2 + d(iw)2 which, in turn, becomes ds2 = dx2 + dy2 + dz2 - dw2. So, the critical function of the imaginary axis is to introduce a negative sign into the calculation of distances, thus counteracting the normal positive signs. The squares of the three real spatial axes x, y and z have the same positive sign, while the square of the imaginary axis w is preceded by a negative sign. Our lives are dominated by the fact that one "square" axis in 4Di space has a different sign from the others. Our minds separate out the three positive axes and call them 3D "real" space.
To characterize the universe as a 4Di space rather than a 3D space is revolutionary. We now begin to see the glimmerings of something utterly profound: our ability to experience "reality" is severely restricted. If it is the case that our senses have evolved to be attuned to a 3D physical space but we actually inhabit a 4Di space then our senses will constantly deceive us since they are lacking awareness of an entire dimension. Hence much of our inability to grasp reality would stem from this problem. "Common sense" i.e. placing our trust in the direct evidence provided by our senses is our worst enemy because our senses are cut adrift from one of the four dimensions in which we live.
It's hard to believe that we could successfully ignore an entire dimension without disastrous effects. In fact, we don't. The effects of the "missing" dimension based on the imaginary spatial axis manifest themselves to us in an entirely different way from those associated with the traditional three spatial axes. We experience these effects as the basis of TIME.
Einstein himself, and everyone who followed him, failed to understand this astonishing truth: time has its origins in imaginary space. Time is not a primary dimension, but secondary, being based on distance. Or rather imaginary distance.
A light particle, a photon, has no mass. What governs its path and speed? Will it follow an "imaginary", "real" or "zero" distance path through 4Di space? In fact, it takes the simplest, shortest path of least resistance between two points. What is that path? It is the most obvious, least complicated option, the path of least resistance: the "zero" path i.e. where there is no distance between any points on this path.
The zero path traced out by a moving, massless particle through 4Di space has a unique significance: it is the limiting speed of the universe. No particle travelling along an imaginary path can ever exceed the speed of a particle following the zero path (i.e. the zero path speed is the speed limit for particles on imaginary paths) and no particle travelling along a real path can ever travel at less than that zero path speed. The zero path speed is the universal speed limit for any particle following any other path; it is the lowest speed attainable for any real path particle and the highest speed attainable for any imaginary path particle. We know this special speed by another name. It is the speed of light.
This unique speed is invariant. No matter what frame of reference is used, the speed of light always has the same value. Every observer, no matter what speed they are moving at, will always obtain the same value for the speed of light. Even someone travelling at 99.999% of the speed of light will, if they switch on a torch, find the light beam racing away from them at the speed of light, exactly as would happen if they were standing still. We can now understand why this should be so: light is following a unique, invariant zero path.
(Note that we are referring to the speed of light in a vacuum; light travels more slowly through other media such as water.)
Einstein famously wondered what would happen if he were travelling at the speed of light while holding a mirror in front of himself. Since both he and the mirror would be travelling at the speed of light, how could the light from his face catch up with the mirror in order to be reflected back? Wouldn't his reflection disappear? The answer he arrived at with the special theory of relativity was that a) he could never attain light speed and b) he would always see his reflection.
That the speed of light is constant in all frames of reference is one of the truly momentous facts of existence. Just consider how truly weird it is. If a man at the front of a train that is travelling at 100 kilometres per hour throws a rock out of the window at 50 kilometres an hour in the same direction as the travelling train, then a stationary observer will measure the rock as travelling away from him at 150 kilometres per hour i.e. the sum of the speed of the train and the speed of the rock. Likewise, common sense says that if a man travelling at 0.9 light speed switches on a torch and the light beam shoots away at light speed, then a stationary observer should measure the light beam as travelling at 1.9 times the speed of light, but common sense is completely wrong. Light, no matter who observes it in whatever context, is always measured to have exactly the same value in a vacuum. An observer standing still and an observer travelling at near light speed will both obtain exactly the same result for the speed of light. How can it be that relative motion between the stationary and moving observer makes no difference at all to how they measure the speed of light?
Imagine that the speed of light is 100 km per hour, and a man on a train travelling at 90 km per hour switches on a torch. We would expect a stationary observer to see the light beam travelling at 90 + 100 = 190 km per hour, but in fact the observer would see it travelling at 100 km per hour. How is this possible? Speed is distance over time. After one hour, the man on the train has travelled 90 km, and, relative to him, the light beam has travelled a further 100 km. So, he measures the speed of light to be 100 km divided by 1 hr = 100 km per hour. Relative to a stationary observer, the light beam has seemingly travelled 190 km in the hour so its value should be 190 km per hour, but it's still in fact 100 km per hour. As Einstein realized, the only credible way for this to be true for both the stationary and moving observers is for distance and time to change in some proportionate way as our speed alters so that it will still seem as if the light beam has travelled only 100 km in an hour.
For distance and time to alter as speed alters means that they are not primary, absolute properties of existence; they are dependent on how objects move. The ramifications are astounding. The idea that anything has definite, measurable dimensions in any absolute sense is rendered meaningless. An object viewed by a stationary observer will have different dimensions depending on the object's speed relative to that of light. So, what are its "true" dimensions? Can it be said to have any? Because we never move at speeds significant in relation to light speed we never notice any strange changes in the dimensions of objects as they move relative to us, but we would if the speed of light were similar to the speeds we move at. If light speed were 1000 km per hour, we would notice weird effects all the time. We would no longer have a vocabulary based on solid, unchanging objects with fixed dimensions.
When a particle moves in "Zero space", it does not experience time and it has no mass. What about particles moving through "imaginary" space? That's when they do experience time and they have a positive mass. What about particles moving through "real" space? That's when they experience "imaginary time" and have "imaginary mass".
In the language of relativity theory, the zone we live in is called "timelike" and only subluminal speeds are possible, while the zone associated with real space is called "spacelike" and only superluminal speeds are possible.
In a typical textbook treatment of Einstein's special theory of relativity, you will encounter the equation: ds2 = dx2 + dy2 + dz2 -c2dt2 where c is the speed of light. How does this compare with the equation we have used of ds2 = dx2 + dy2 + dz2 -dw2?
The equations are identical except for -dw2 (based on the imaginary axis) and -c2dt2.
The square root of -c2dt2 is icdt since (icdt)2 = i2 x c2 x dt2. In other words, the imaginary axis is at the heart of -c2dt2, just as it is at the heart of -dw2. In fact, the only difference between -c2dt2 and -dw2 is the constant c2.
The imaginary axis that we have labelled w uses units of distance i.e. spatial units. The speed of light, c, has units of distance divided by units of time (since speed = distance divided by time). Hence the time axis, t, multiplied by c has units of distance since (distance/time) x time = distance because the time units cancel out. Thus the term cdt has space rather than time units and is now on a par with dx, dy and dz, which are also measured in distance units.
So, dw is directly proportional to cdt since both are measured in distance units and c is a constant.
To state it explicitly, the time axis (t) and the imaginary axis (w) are directly related, via c the speed of light, the "natural speed" of the cosmos. We have thus demonstrated the astonishing fact that time is intimately related to imaginary space, the two being linked by the invariant speed of light. The mathematics of 4Di space are IDENTICAL to the mathematics of what the German mathematician Minkowski called 4D spacetime, where space and time are fused together, with time leading to squared distance expressions that have the opposite sign to the squared expressions of the conventional spatial axes of x, y and z. One of the central enigmas of existence can, in some sense, be attributed to this difference of a negative sign being matched against three positive signs, leading to real, imaginary and null zones instead of just real zones.
All of this stems from mathematical completeness, from the imaginary number i. Without it, all distances are real. With it, distances can be real, imaginary or zero. So, by ensuring that all of mathematics is used rather than a subset, we get the possibility of far more diverse phenomena. The Zero zone - the so-called infinitely narrow "luxon wall" - stands between the real and "imaginary" universes i.e. between the spacelike and timelike zones of existence.
We have shown that time is born of imaginary space. Without imaginary space there would be no such thing as time. 4Di space is the basic entity, not 4D spacetime.
Isaac Newton believed in absolute space and absolute time. He envisaged space as an infinitely large 3D container, with time being measured by a cosmic clock that ticked at the same rate everywhere in the universe. This is the common sense view of space and time, and it works very well in our everyday environment. For Newton, space and time existed independently of any objects i.e. if you removed everything from the universe, space would continue to exist and time would continue to tick by.
Leibniz, with his "relational" view of time and space, opposed Newton. According to the relational view, space and time would not exist if there were no objects. Time and space describe relations between objects, and without objects then there are no relations to describe.
Einsteinian physics replaced Newton's absolute space and time (each existing independently of the other) with a 4D spacetime where space and time are inextricably fused together. Einstein's system is Leibnizian since space and time are dependent on the contents of the universe and how those contents move with respect to each other.
The Einsteinian/Leibnizian view only becomes obvious when objects are travelling at near lightspeed, hence why science remained resolutely Newtonian for so long.
However, the Einsteinian view of 4D spacetime is itself not the full story and ought to be replaced by the more fundamental 4Di space involving three real spatial axes and one imaginary spatial axis. Time comes into existence only because of 4Di space i.e. time is not a fundamental property of the universe but rather a secondary characteristic derived from the imaginary component of space. If space were not a 4Di domain then time as we know it would simply not exist.
Time results from how 3D objects move through 4Di space. Its nature changes depending on what path an object takes through space. Time does not "tell" an object how to move; rather, a moving object tells time how to tick, or indeed not to tick at all in the case of particles such as photons.
Moving objects are the fundamental reality of the dimensional universe, and "space" (4Di) defines the mathematical set of relations that all moving objects obey, thus giving rise to the laws of physics. Space does not exist as an independent, absolute physical entity; it is a mathematical construct that is given the appearance of reality by how objects move with respect to each other. Time is not an independent, absolute physical entity either, which is why time has always been so hard to define. People have been baffled by time because they have always attempted to make it a primary property of the cosmos. Once time is understood as a function of the mathematics of space and, in particular, of imaginary space then everything becomes clear.
Even apparently stationary objects (in relation to space) are still moving - through time.
To reiterate, precisely as Leibniz first asserted, time and space do not exist in an absolute sense. Only moving objects exist. The dimensional universe, as we experience it, is the arena of physical objects in motion in space and/or time. There's nothing more to it.
What is crucial to understand is that the frame of reference of any massless entity is outwith space and time. Everything that happens in the cosmos is instantly reflected in this unique reference frame. All possible information about the physical universe is instantaneously captured in the light domain.
When we describe the physical universe in terms of 4Di rather than 3D, at a stroke we get to the heart of the difference between common sense and reality. Common sense says that only 3D exists, but 3D is mathematically incomplete because zero and imaginary distances between two distinct points are prohibited. Physically, this seems to make sense, but mathematically it's absurd. Why should zero and imaginary distances be excluded because of a mathematical feature that all negative numbers raised to an even power are positive? If another mathematical feature - imaginary numbers - can resolve this and allow a negative number to be generated when any such imaginary number is raised to an even power, why should nature ignore this complete version of mathematics in favour of a truncated version? Nature doesn't. Nature is mathematical. Nature obeys the laws of complete, not incomplete, mathematics. It includes ALL numbers, not a subset of numbers. Numbers such as zero, infinity and the imaginary number are as "real" as 1, 2 and 3. They cannot be ignored or excluded or treated as less real or indeed as unreal.
Anything not forbidden is compulsory. Imaginary numbers are not forbidden, hence are compulsory. They are embedded in nature, but our common sense chooses to interpret them as non-spatial: as time, in fact. So, the profound mystery of why space and time exist is now explained by the underlying mathematical truth that there are two different types of numbers: real and imaginary. Real numbers underlie our conventional understanding of space; imaginary numbers underpin time. But, fundamentally, we are dealing with a single entity: all the numbers of mathematics, the complete set, none ignored or excluded. Nature operates according to Absolute Mathematics. If it can exist mathematically then it will exist in reality. Anything not forbidden mathematically is compulsory.
Look at all of the things that fall into place when 4Di replaces 3D.
1) Instead of distances between two points always being real (as in 3D), it becomes possible to also have zero and imaginary distances. Three types of "reality" - three choices - become possible where only one was possible in 3D.
2) It transpires that Einstein's famous special theory of relativity is based precisely on this division of reality into three distinct aspects. However, Einstein talked of a 4D spacetime rather than 4Di space. 4D spacetime and 4Di space obey exactly the same mathematical rules and framework. We choose to emphasise 4Di because it shows that the basic reality is spatial rather than spatial plus temporal. Time is derived from imaginary space; it is a secondary feature, not a primary one. Time could not exist if there were no imaginary space. Imaginary space, because it leads to zero and imaginary distances rather than just real distances, provides the crucial factor that makes life as we know it possible.
3) To reiterate, there are three zones of spatial reality: zero, imaginary and real. In the zero zone - "Null Space" - all distances and times are by definition zero. Everything is interconnected. Everything is One. This is the centre of the cosmic mystery, the transcendent realm that mystics have intuitively grasped. Since each point in our familiar 3D space can be matched up with an imaginary coordinate that can ensure that any two points in 4Di space are separated by zero distance then in Null Space all things are inextricably brought together in a single cosmic unity. This is the most profound mystery of all, and it is brought about by mathematical completeness. It cannot be stressed enough that in 4Di space, but not in 3D space, there is a null zone in which all things are connected. Our world of everyday common sense is locked into the illusion of 3D "reality" and, in this incomplete representation of existence, the differences between things are emphasized rather than their unity: individuation is stressed over communion. The great religion of Hinduism has always stressed that, under the power of Maya, human life is essentially illusory, and Buddhism makes the same claim that our reality is an illusion. But the illusion is one of incompleteness rather than false reality. To the extent that we experience 3D rather than 4Di, our view of reality is distorted, but it's not fake or make-believe. It's inaccurate, not wrong. It is lacking complete information. The world is absolutely real, but the 3D representation of it omits a critical component. The Absolute Truth lies in 4Di. Reason can lead us there, but not our common sense which leads us astray, and certainly not faith, which is useless.
4) The real and imaginary zones are like mirror images of each other, with the Null zone providing the mirror, the infinitely narrow luxon wall.
5) The Null zone is an extraordinary place where particles have no mass or size; where everything is interconnected and no time passes. It is the realm of the inverse twins, zero and infinity. The most extraordinary fact of existence is that zero and infinity can exist at the heart of 4Di spatial reality. Physicists are horrified and baffled by the Null zone. They don't comprehend that it is the most critical feature of science and mathematics, and indeed of life itself. It is where the answer to every mystery ultimately lies.
So, have we provided the answer to mathematical completeness? Does 4Di accommodate all possible numbers? Is the cosmos four dimensional (three real space dimensions and one imaginary space dimension)?
No, we have committed an error. Although 4Di has the right "shape" - which is why Einstein's special theory of relativity works - it is not actually complete. Can you see what we have done wrong? Use your intuition. What number seems right for the total number of dimensions required for mathematical completeness? How many dimensions does the cosmos need?