Mathematics Is Everywhere Quotes

God without dominion, providence, and final causes, is nothing else but Fate and Nature. Blind metaphysical necessity, which is certainly the same always and everywhere, could produce no variety of things. All that diversity of natural things which we find suited to different times and places could arise from nothing but the ideas and will of a Being necessarily existing.

The Couple Overfloweth We sometimes go on as though people can’t express themselves. In fact they’re always expressing themselves. The sorriest couples are those where the woman can’t be preoccupied or tired without the man saying “What’s wrong? Say something…,” or the man, without the woman saying … and so on. Radio and television have spread this spirit everywhere, and we’re riddled with pointless talk, insane quantities of words and images. Stupidity’s never blind or mute. So it’s not a problem of getting people to express themselves but of providing little gaps of solitude and silence in which they might eventually find something to say. Repressive forces don’t stop people expressing themselves but rather force them to express themselves; What a relief to have nothing to say, the right to say nothing, because only then is there a chance of framing the rare, and ever rarer, thing that might be worth saying. What we’re plagued by these days isn’t any blocking of communication, but pointless statements. But what we call the meaning of a statement is its point. That’s the only definition of meaning, and it comes to the same thing as a statement’s novelty. You can listen to people for hours, but what’s the point? . . . That’s why arguments are such a strain, why there’s never any point arguing. You can’t just tell someone what they’re saying is pointless. So you tell them it’s wrong. But what someone says is never wrong, the problem isn’t that some things are wrong, but that they’re stupid or irrelevant. That they’ve already been said a thousand times. The notions of relevance, necessity, the point of something, are a thousand times more significant than the notion of truth. Not as substitutes for truth, but as the measure of the truth of what I’m saying. It’s the same in mathematics: Poincaré used to say that many mathematical theories are completely irrelevant, pointless; He didn’t say they were wrong – that wouldn’t have been so bad. (Negotiations)

Codes and patterns are very different from each other,” Langdon said. “And a lot of people confuse the two. In my field, it’s crucial to understand their fundamental difference.” “That being?” Langdon stopped walking and turned to her. “A pattern is any distinctly organized sequence. Patterns occur everywhere in nature—the spiraling seeds of a sunflower, the hexagonal cells of a honeycomb, the circular ripples on a pond when a fish jumps, et cetera.” “Okay. And codes?” “Codes are special,” Langdon said, his tone rising. “Codes, by definition, must carry information. They must do more than simply form a pattern—codes must transmit data and convey meaning. Examples of codes include written language, musical notation, mathematical equations, computer language, and even simple symbols like the crucifix. All of these examples can transmit meaning or information in a way that spiraling sunflowers cannot.

Music was a kind of penetration. Perhaps absorption is a less freighted word. The penetration or absorption of everything into itself. I don't know if you have ever taken LSD, but when you do so the doors of perception, as Aldous Huxley, Jim Morrison and their adherents ceaselessly remind us, swing wide open. That is actually the sort of phrase, unless you are William Blake, that only makes sense when there is some LSD actually swimming about inside you. In the cold light of the cup of coffee and banana sandwich that are beside me now it appears to be nonsense, but I expect you to know what it is taken to mean. LSD reveals the whatness of things, their quiddity, their essence. The wateriness of water is suddenly revealed to you, the carpetness of carpets, the woodness of wood, the yellowness of yellow, the fingernailness of fingernails, the allness of all, the nothingness of all, the allness of nothing. For me music gives access to everyone of these essences, but at a fraction of the social or financial cost of a drug and without the need to cry 'Wow!' all the time, which is LSD's most distressing and least endearing side effects. ...Music in the precision of its form and the mathematical tyranny of its laws, escapes into an eternity of abstraction and an absurd sublime that is everywhere and nowhere at once. The grunt of rosin-rubbed catgut, the saliva-bubble blast of a brass tube, the sweaty-fingered squeak on a guitar fret, all that physicality, all that clumsy 'music making', all that grain of human performance...transcends itself at the moment of its happening, that moment when music actually becomes, as it makes the journey from the vibrating instrument, the vibrating hi-fi speaker, as it sends those vibrations across to the human tympanum and through to the inner ear and into the brain, where the mind is set to vibrate to frequencies of its own making. The nothingness of music can be moulded by the mood of the listener into the most precise shapes or allowed to float as free as thought; music can follow the academic and theoretical pattern of its own modality or adhere to some narrative or dialectical programme imposed by a friend, a scholar or the composer himself. Music is everything and nothing. It is useless and no limit can be set to its use. Music takes me to places of illimitable sensual and insensate joy, accessing points of ecstasy that no angelic lover could ever locate, or plunging me into gibbering weeping hells of pain that no torturer could ever devise. Music makes me write this sort of maundering adolescent nonsense without embarrassment. Music is in fact the dog's bollocks. Nothing else comes close.

For the purposes of science, information had to mean something special. Three centuries earlier, the new discipline of physics could not proceed until Isaac Newton appropriated words that were ancient and vague—force, mass, motion, and even time—and gave them new meanings. Newton made these terms into quantities, suitable for use in mathematical formulas. Until then, motion (for example) had been just as soft and inclusive a term as information. For Aristotelians, motion covered a far-flung family of phenomena: a peach ripening, a stone falling, a child growing, a body decaying. That was too rich. Most varieties of motion had to be tossed out before Newton’s laws could apply and the Scientific Revolution could succeed. In the nineteenth century, energy began to undergo a similar transformation: natural philosophers adapted a word meaning vigor or intensity. They mathematicized it, giving energy its fundamental place in the physicists’ view of nature. It was the same with information. A rite of purification became necessary. And then, when it was made simple, distilled, counted in bits, information was found to be everywhere.

I thought. I thought of the slow yellow autumn in the swamp and the high honey sun of spring and the eternal silence of the marshes, and the shivering light on them, and the whisper of the spartina and sweet grass in the wind and the little liquid splashes of who-knew-what secret creatures entering that strange old place of blood-warm half earth, half water. I thought of the song of all the birds that I knew, and the soft singsong of the coffee-skinned women who sold their coiled sweet-grass baskets in the market and on Meeting Street. I thought of the glittering sun on the morning harbor and the spicy, somehow oriental smells from the dark old shops, and the rioting flowers everywhere, heavy tropical and exotic. I thought of the clop of horses' feet on cobblestones and the soft, sulking, wallowing surf of Sullivan's Island in August, and the countless small vistas of grace and charm wherever the eye fell; a garden door, a peeling old wall, an entire symmetrical world caught in a windowpane. Charlestone simply could not manage to offend the eye. I thought of the candy colors of the old houses in the sunset, and the dark secret churchyards with their tumbled stones, and the puresweet bells of Saint Michael's in the Sunday morning stillness. I thought of my tottering piles of books in the study at Belleau and the nights before the fire when my father told me of stars and butterflies and voyages, and the silver music of mathematics. I thought of hot, milky sweet coffee in the mornings, and the old kitchen around me, and Aurelia's gold smile and quick hands and eyes rich with love for me.

Let me then remind you that justice is an immutable, natural principle; and not anything that can be made, unmade, or altered by any human power. It is also a subject of science, and is to be learned, like mathematics, or any other science. It does not derive its authority from the commands, will, pleasure, or discretion of any possible combination of men, whether calling themselves a government, or by any other name. It is also, at all times, and in all places, the supreme law. And being everywhere and always the supreme law, it is necessarily everywhere and always the only law.

Geometry exist everywhere.It is necessary, however, to have eyes to see it, intelligence to understand it , and spirit to wonder at it.The wild Bedouin sees geometric forms but doesn't understand them ; the Sunni understands them but does not admire them; the artist, finally, perceives the perfection of figures, understands beauty, and admires order and harmony.God was the Great Geometer.He geometrized heaven and earth.

Ever since his first ecstasy or vision of Christminster and its possibilities, Jude had meditated much and curiously on the probable sort of process that was involved in turning the expressions of one language into those of another. He concluded that a grammar of the required tongue would contain, primarily, a rule, prescription, or clue of the nature of a secret cipher, which, once known, would enable him, by merely applying it, to change at will all words of his own speech into those of the foreign one. His childish idea was, in fact, a pushing to the extremity of mathematical precision what is everywhere known as Grimm's Law—an aggrandizement of rough rules to ideal completeness. Thus he assumed that the words of the required language were always to be found somewhere latent in the words of the given language by those who had the art to uncover them, such art being furnished by the books aforesaid.

Mere subtlety may qualify you as a sceptic but not as a philosopher. On the other hand, scepticism is in philosophy what the Opposition is in Parliament; it is just as beneficial, and indeed necessary. It rests everywhere on the fact that philosophy is not capable of producing the kind of evidence mathematics produces.

Music, in the precision of its form and the mathematical tyranny of its laws, escapes into an eternity of abstraction and an absurd sublime that is everywhere and nowhere at once.

If mathematics ability were rooted in biology and sex differences were fixed, then we wouldn’t expect to see these changes over time. What’s more, we would expect the differences to be the same everywhere. And they’re not.

Indeed, except for the very simplest physical systems, virtually everything and everybody in the world is caught up in a vast, nonlinear web of incentives and constraints and connections. The slightest change in one place causes tremors everywhere else. We can't help but disturb the universe, as T.S. Eliot almost said. The whole is almost always equal to a good deal more than the sum of its parts. And the mathematical expression of that property-to the extent that such systems can be described by mathematics at all-is a nonlinear equation: one whose graph is curvy.

In this very brief history of modern cosmological physics, the laws of quantum and relativistic physics represent things to be wondered at but widely accepted: just like biblical miracles. M-theory invokes something different: a prime mover, a begetter, a creative force that is everywhere and nowhere. This force cannot be identified by instruments or examined by comprehensible mathematical prediction, and yet it contains all possibilities. It incorporates omnipresence, omniscience and omnipotence, and it’s a big mystery. Remind you of Anybody?49

The study of invisible writings was a new discipline made available by the discovery of the bi-directional nature of Library-Space. The thaumic mathematics are complex, but boil down to the fact that all books, everywhere, affect all other books. This is obvious: books inspire other books written in the future, and cite books written in the past. But the General Theory** of L-Space suggests that, in that case, the contents of books as yet unwritten can be deduced from books now in existence. **There’s a Special Theory as well, but no one bothers much it much because it’s self-evidently a load of marsh gas.

In mathematics, however, as everywhere else, men are inclined to form parties, so that there arose schools of pure synthesists and schools of pure analysts, who placed chief emphasis upon absolute “purity of method,” and who were thus more one-sided than the nature of the subject demanded. Thus the analytic geometricians often lost themselves in blind calculations, devoid of any geometric representation, The synthesists, on the other hand, saw salvation in an artificial avoidance of all formulas, and thus they accomplished nothing more, finally, than to develop their own peculiar language formulas, different from ordinary formulas.

Man has no moral instinct. He is not born with moral sense. You were not born with it, I was not - and a puppy has none. We acquire moral sense, when we do, through training, experience and hard sweat of the mind ... What is "moral sense"? It is an elaboration of the instinct to survive. The instinct to survive is human nature itself, and every aspect of our personalities derives from it. Anything that conflicts with the survival instinct acts sooner or later to eliminate the individual and thereby fails to show up in future generations. The truth is mathematically demonstrable, everywhere verifiable; it is the single eternal imperative controlling everything we do.

There was no escaping math, after all. It was everywhere, especially in nature. You could go as far to say that math was nature. Pi describe the arc of a rainbow, the way ripples spread in a body of water, the dimensions of the moon and sun. Fractals could be observed in halved sections of red cabbage, the topography of deserts, the branching of lightning bolts. And take the old man glaring out from his shirt, Leonardo Fibonacci, who discovered that a basic number sequence predicted the arrangement of scales on a pinecone, the distribution of petals on flowers, the spiral of a snail shell, the furcation of veins in the human body, even the structure of DNA. When all the people were gone, the numbers would persist.

We must consider also whether soul is divisible or is without parts, and whether it is everywhere homogeneous or not; and if not homogeneous, whether its various forms are different specifically or generically; up to the present time those who have discussed and investigated soul seem to have confined themselves to the human soul. We must be careful not to ignore the question whether soul can be defined in a single account, as is the case with animal, or whether we must not give a separate account of each sort of it, as we do for horse, dog, man, god (in the latter case the universal, animal—and so too every other common predicate—is either nothing or posterior). Further, if what exists is not a plurality of souls, but a plurality of parts of one soul, which ought we to investigate first, the whole soul or its parts? It is also a difficult problem to decide which of these parts are in nature distinct from one another. Again, which ought we to investigate first, these parts or their functions, mind or thinking, the faculty or the act of sensation, and so on? If the investigation of the functions precedes that of the parts, the further question suggests itself: ought we not before either to consider the correlative objects, e.g. of sense or thought? It seems not only useful for the discovery of the causes of the incidental proprieties of substances to be acquainted with the essential nature of those substances (as in mathematics it is useful for the understanding of the property of the equality of the interior angles of a triangle to two right angles to know the essential nature of the straight and the curved or of the line and (the plane) but also conversely, for the knowledge of the essential nature of a substance is largely promoted by an acquaintance with its properties: for, when we are able to give an account conformable to experience of all or most of the properties of a substance, we shall be in the most favourable position to say something worth saying about the essential nature of that subject: in all demonstration a definition of the essence is required as a starting point, so that definitions which do not enable us to discover the incidental properties, or which fail to facilitate even a conjecture about them, must obviously, one and all, be dialectical and futile.

The German mathematician Emmy Noether proved in 1915 that each continuous symmetry of our mathematical structure leads to a so-called conservation law of physics, whereby some quantity is guaranteed to stay constant-and thereby has the sort of permanence that might make self-aware observers take note of it and give it a "baggage" name. All the conserved quantities that we discussed in Chapter 7 correspond to such symmetries: for example, energy corresponds to time-translation symmetry (that our laws of physics stay the same for all time), momentum corresponds to space-translation symmetry (that the laws are the same everywhere), angular momentum corresponds to rotation symmetry (that empty space has no special "up" direction) and electric charge corresponds to a certain symmetry of quantum mechanics. The Hungarian physicist Eugene Wigner went on to show that these symmetries also dictated all the quantum properties that particles can have, including mass and spin. In other words, between the two of them, Noether and Wigner showed that, at least in our own mathematical structure, studying the symmetries reveals what sort of "stuff" can exist in it.

The legendary inscription above the Academy's door speaks loudly about Plato's attitude toward mathematics. In fact, most of the significant mathematical research of the fourth century BC was carried out by people associated in one way or another with the Academy. Yet Plato himself was not a mathematician of great technical dexterity, and his direct contributions to mathematical knowledge were probably minimal. Rather, he was an enthusiastic spectator, a motivating source of challenge, an intelligent critic, an an inspiring guide. The first century philosopher and historian Philodemus paints a clear picture: "At that time great progress was seen in mathematics, with Plato serving as the general architect setting out problems, and the mathematicians investigating them earnestly." To which the Neoplatonic philosopher and mathematician Proclus adds: "Plato...greatly advanced mathematics in general and geometry in particular because of his zeal for these studies. It is well known that his writings are thickly sprinkled with mathematical terms and that he everywhere tries to arouse admiration for mathematics among students of philosophy." In other words, Plato, whose mathematical knowledge was broadly up to date, could converse with the mathematicians as an equal and as a problem presenter, even though his personal mathematical achievements were not significant.

Let me return from history and draw my conclusion. What all this means to us at the present time is this: Our system has already passed its flowering. Some time ago it reached that summit of blessedness which the mysterious game of world history sometimes allows to things beautiful and desirable in themselves. We are on the downward slope. Our course may possible stretch out for a very long time, but in any case nothing finer, ore beautiful, and more desirable than what we have already had can henceforth be expected. The road leads downhill. Historically we are, I believe, ripe for dismantling. And there is no doubt that such will be our fate, not today or tomorrow, but the day after tomorrow. I do not draw this conclusion from any excessively moralistic estimate of our accomplishments and our abilities: I draw it far more from the movements which I see already on the way in the outside world. Critical times are approaching; the omens can be sensed everywhere; the world is once again about to shift its center of gravity. Displacements of power are in the offing. They will not take place without war and violence. From the Far East comes a threat not only to peace, but to life and liberty. Even if our country remains politically neutral, even if our whole nation unanimously abides by tradition (which is not the case) and attempts to remain faithful to Castalian ideals, that will be in vain. Some of our representatives in Parliament are already saying that Castalia is a rather expensive luxury for our country. The country may very soon be forced into a serious rearmament - armaments for defensive purposes only, of course - and great economies will be necessary. In spite of the government's benevolent disposition towards us, much of the economizing will strike us directly. We are proud that our Order and the cultural continuity it provides have cost the country as little as they have. In comparison with other ages, especially the early period of the Feuilletonistic Age with its lavishly endowed universities, its innumerable consultants and opulent institutes, this toll is really not large. It is infinitesimal compared with the sums consumed for war and armaments during the Century of Wars. But before too long this kind of armament may once again be the supreme necessity; the generals will again dominate Parliament; and if the people are confronted with the choice of sacrificing Castalia or exposing themselves to the danger of war and destruction, we know how they will choose. Undoubtedly a bellicose ideology will burgeon. The rash of propaganda will affect youth in particular. Then scholars and scholarship, Latin and mathematics, education and culture, will be considered worth their salt only to the extent that they can serve the ends of war.

The concept of absolute time—meaning a time that exists in “reality” and tick-tocks along independent of any observations of it—had been a mainstay of physics ever since Newton had made it a premise of his Principia 216 years earlier. The same was true for absolute space and distance. “Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to anything external,” he famously wrote in Book 1 of the Principia. “Absolute space, in its own nature, without relation to anything external, remains always similar and immovable.” But even Newton seemed discomforted by the fact that these concepts could not be directly observed. “Absolute time is not an object of perception,” he admitted. He resorted to relying on the presence of God to get him out of the dilemma. “The Deity endures forever and is everywhere present, and by existing always and everywhere, He constitutes duration and space.”45 Ernst Mach, whose books had influenced Einstein and his fellow members of the Olympia Academy, lambasted Newton’s notion of absolute time as a “useless metaphysical concept” that “cannot be produced in experience.” Newton, he charged, “acted contrary to his expressed intention only to investigate actual facts.”46 Henri Poincaré also pointed out the weakness of Newton’s concept of absolute time in his book Science and Hypothesis, another favorite of the Olympia Academy. “Not only do we have no direct intuition of the equality of two times, we do not even have one of the simultaneity of two events occurring in different places,” he wrote.

The goal was ambitious. Public interest was high. Experts were eager to contribute. Money was readily available. Armed with every ingredient for success, Samuel Pierpont Langley set out in the early 1900s to be the first man to pilot an airplane. Highly regarded, he was a senior officer at the Smithsonian Institution, a mathematics professor who had also worked at Harvard. His friends included some of the most powerful men in government and business, including Andrew Carnegie and Alexander Graham Bell. Langley was given a $50,000 grant from the War Department to fund his project, a tremendous amount of money for the time. He pulled together the best minds of the day, a veritable dream team of talent and know-how. Langley and his team used the finest materials, and the press followed him everywhere. People all over the country were riveted to the story, waiting to read that he had achieved his goal. With the team he had gathered and ample resources, his success was guaranteed. Or was it? A few hundred miles away, Wilbur and Orville Wright were working on their own flying machine. Their passion to fly was so intense that it inspired the enthusiasm and commitment of a dedicated group in their hometown of Dayton, Ohio. There was no funding for their venture. No government grants. No high-level connections. Not a single person on the team had an advanced degree or even a college education, not even Wilbur or Orville. But the team banded together in a humble bicycle shop and made their vision real. On December 17, 1903, a small group witnessed a man take flight for the first time in history. How did the Wright brothers succeed where a better-equipped, better-funded and better-educated team could not? It wasn’t luck. Both the Wright brothers and Langley were highly motivated. Both had a strong work ethic. Both had keen scientific minds. They were pursuing exactly the same goal, but only the Wright brothers were able to inspire those around them and truly lead their team to develop a technology that would change the world. Only the Wright brothers started with Why. 2.

Maybe there was symmetry everywhere, and the patterns of our days held no less certainty than the mathematical patterns of the universe. Maybe, in order to see the patterns, one simply needed to take a few steps back, turn the page upside down, approach everything from a different angle.

Consequently we have only to discover these laws of nature, and man will no longer have to answer for his actions and life will become exceedingly easy for him. All human actions will then, of course, be tabulated according to these laws, mathematically, like tables of logarithms up to 108,000, and entered in an index; or, better still, there would be published certain edifying works of the nature of encyclopaedic lexicons, in which everything will be so clearly calculated and explained that there will be no more incidents or adventures in the world. en—this is all what you say—new economic relations will be established, all ready-made and worked out with mathematical exactitude, so that every possible question will vanish in the twinkling of an eye, simply because every possible answer to it will be provided. en the ‘Palace of Crystal’ will be built. en ... In fact, those will be halcyon days. Of course there is no guaranteeing (this is my comment) that it will not be, for instance, frightfully dull then (for what will one have to do when everything will be calculated and tabulated), but on the other hand everything will be extraordinarily rational. Of course boredom may lead you to anything. It is boredom sets one sticking golden pins into people, but all that would not matter. What is bad (this is my comment again) is that I dare say people will be thankful for the gold pins then. Man is stupid, you know, phenomenally stupid; or rather he is not at all stupid, but he is so ungrateful that you could not find another like him in all creation. I, for instance, would not be in the least surprised if all of a sudden, A PROPOS of nothing, in the midst of general prosperity a gentleman with an ignoble, or rather with a reactionary and ironical, countenance were to arise and, putting his arms akimbo, say to us all: ‘I say, gentle- man, hadn’t we better kick over the whole show and scatter rationalism to the winds, simply to send these logarithms to the devil, and to enable us to live once more at our own sweet foolish will!’ at again would not matter, but what is annoying is that he would be sure to find followers—such is the nature of man. And all that for the most foolish reason, which, one would think, was hardly worth mentioning: that is, that man everywhere and at all times, whoever he may be, has preferred to act as he chose and not in the least as his reason and advantage dictated. And one may choose what is contrary to one’s own interests, and sometimes one POSITIVELY OUGHT (that is my idea). One’s own free unfettered choice, one’s own caprice, however wild it may be, one’s own fancy worked up at times to frenzy—is that very ‘most advantageous advantage’ which we have overlooked, which comes under no classification and against which all systems and theories are continually being shattered to atoms. And how do these wiseacres know that man wants a normal, a virtuous choice? What has made them conceive that man must want a rationally advantageous choice? What man wants is simply INDEPENDENT choice, whatever that independence may cost and wherever it may lead. And choice, of course, the devil only knows what choice.

Truth in the world resides only in mathematical proofs and physics labs. Everywhere else, it’s really a matter of opinion, and if it manages to become group opinion, it’s undeservedly crowned as capital-T Truth.

PageRank, the algorithm that gave rise to Google, is itself a Markov chain. Larry Page’s idea was that web pages with many incoming links are probably more important than pages with few, and links from important pages should themselves count for more. This sets up an infinite regress, but we can handle it with a Markov chain. Imagine a web surfer going from page to page by randomly following links: the states of this Markov chain are web pages instead of characters, making it a vastly larger problem, but the math is the same. A page’s score is then the fraction of the time the surfer spends on it, or equivalently, his probability of landing on the page after wandering around for a long time. Markov chains turn up everywhere and are one of the most intensively studied topics in mathematics, but they’re still a very limited kind of probabilistic model. We can go one step further with a model like this: The states form a Markov chain, as before, but we don’t get to see them; we have to infer them from the observations. This is called a hidden Markov model, or HMM for short. (Slightly misleading, because it’s the states that are hidden, not the model.)

Here in Alpha City, we have a common saying: “What we call ‘sky’ is merely a figment of our narrative.” The most dreamy-eyed among us seem to adorn themselves and their aspirations in that proverb and you’ll see it everywhere: in advertisements on the sides of streetcars and auto-rickshaws, spelled out in studs and rhinestones on designer jackets, emblazoned in the intricate designs of facial tattoos—even painted on city walls by putrid vandals and inspiring street artists. There is something glorious about kneading out into the doughy firmament the depth and breadth of one’s own universe, in rendering the contours of a sky whose limits are predicated only upon the bounds of one’s own imagination. The fact of the matter is that we cannot see the natural sky at all here. It is something like a theoretical mathematical expression: like the square-root of ‘negative one’—certainly it could be said to have a purpose for existing, but to cast eyes upon it, in its natural quantity, would be something akin to casting one’s eyes upon the raw elements comprising our everyday sustenance. How many of us have even borne close witness to the minute chemical compounds that react to lend battery power to our portable electronics? The sky is indeed such a concealed fixture now. It is fair to say that we have purged our memories of its true face and so we can only approximate a canvas and project our desires upon it to our heart’s dearest fancy. The most cynical among us would ostensibly declare it an unavoidable tragedy, but perhaps even these hardened individuals could not remember the naked sky well enough to know if what they were missing was something worthwhile. Perhaps, it’s cynical of me to say so! In any case, we have our searchlights pointed upwards and crisscrossing that expanse of heavens as though to make some sensational and profane joke of ourselves to the surrounding universe. We beam already video images of beauty pageants and dancing contests with smiling mannequins who look like buffoons. And so, the face of space cloaks itself behind our light pollution—in this respect, our mirrored sidewalks and lustrous streets do little to help our cause—and that face remains hidden from us in its jeering ridicule, its mocking laughter at this inexorable farce of human existence.

When one thinks clearly and begins a rational, logical examination of Einsteinian physics, you discover that the errors are everywhere and require a multitude of excuses, exclusions, exceptions, embellishments and the occasional recourse to the esoteric or to editing the laws of the universe, to get the equations to balance. After all, if Einsteinian theories and equations violate the laws of the universe, it’s clearly because the principles of mathematics, physics and logic are wrong… or so relativists would have you believe.

a ‘Divine mathematics,’ with which one could create the richest possible reality by the most economical means, and this, it now seemed to me, was everywhere apparent: in the beautiful economy by which millions of compounds could be made from a few dozen elements, and the hundred-odd elements from hydrogen itself; the economy by which the whole range of atoms was composed from two or three particles; and in the way that their stability and identity were guaranteed by the quantal numbers of the atom itself – all this was beautiful enough to be the work of God.

Truth in the world resides only in mathematical proofs and physics labs. Everywhere else it's really matter of opinion, and if it manages to become group opinion, it's undeservedly crowned as capital-T truth. And so you need to determine whatever the local version of truth is you're inhabiting.

Is it enough to live in a universe whose laws spontaneously create life? Or do you prefer ... God?” She paused, looking embarrassed. “Sorry, after all we’ve been through tonight, I know that’s a strange question.” “Well,” Langdon said with a laugh, “I think my answer would benefit from a decent night’s sleep. But no, it’s not strange. People ask me all the time if I believe in God.” “And how do you reply?” “I reply with the truth,” he said. “I tell them that, for me, the question of God lies in understanding the difference between codes and patterns.” Ambra glanced over. “I’m not sure I follow you.” “Codes and patterns are very different from each other,” Langdon said. “And a lot of people confuse the two. In my field, it’s crucial to understand their fundamental difference.” “That being?” Langdon stopped walking and turned to her. “A pattern is any distinctly organized sequence. Patterns occur everywhere in nature—the spiraling seeds of a sunflower, the hexagonal cells of a honeycomb, the circular ripples on a pond when a fish jumps, et cetera.” “Okay. And codes?” “Codes are special,” Langdon said, his tone rising. “Codes, by definition, must carry information. They must do more than simply form a pattern—codes must transmit data and convey meaning. Examples of codes include written language, musical notation, mathematical equations, computer language, and even simple symbols like the crucifix. All of these examples can transmit meaning or information in a way that spiraling sunflowers cannot.” Ambra grasped the concept, but not how it related to God. “The other difference between codes and patterns,” Langdon continued, “is that codes do not occur naturally in the world. Musical notation does not sprout from trees, and symbols do not draw themselves in the sand. Codes are the deliberate inventions of intelligent consciousnesses.” Ambra nodded. “So codes always have an intention or awareness behind them.” “Exactly. Codes don’t appear organically; they must be created.” Ambra studied him a long moment. “What about DNA?” A professorial smile appeared on Langdon’s lips. “Bingo,” he said. “The genetic code. That’s the paradox.” Ambra felt a rush of excitement. The genetic code obviously carried data — specific instructions on how to build organisms. By Langdon’s logic, that could mean only one thing. “You think DNA was created by an intelligence!” Langdon held up a hand in mock self-defense. “Easy, tiger!” he said, laughing. “You’re treading on dangerous ground. Let me just say this. Ever since I was a child, I’ve had the gut sense that there’s a consciousness behind the universe. When I witness the precision of mathematics, the reliability of physics, and the symmetries of the cosmos, I don’t feel like I’m observing cold science; I feel as if I’m seeing a living footprint ... the shadow of some greater force that is just beyond our grasp.

Mathematics is the science of the infinite. The great achievement of the Greeks was to have made the tension between the finite and the infinite fruitful for the knowledge of reality. The feeling of the calm and unquestioning acknowledgement of the infinite belongs to the Orient, but for the East it remained a mere abstract awareness that left the concrete manifold of existence lying indifferently to one side, unshaped and impervious. Coming out of the Orient, the religious feeling of the infinite, the apeiron, took possession of the Greek soul in the Dionysian-Orphic epoch that preceded the Persian Wars. Here the Persian Wars also mark the release of the Occident from the Orient. That tension and its overcoming became for the Greeks the driving motive of knowledge. But every synthesis, as soon as it was achieved, permitted the old antithesis to break out anew in deepened form. Thus, it determined the history of theoretical knowledge into our time. Indeed, today we are compelled everywhere in the foundations of mathematics to return directly to the Greeks.

Mathematics is the science of the infinite. The great achievement of the Greeks was to have made the tension between the finite and the infinite fruitful for the knowledge of reality. The feeling of the calm and unquestioning acknowledgement of the infinite belongs to the Orient, but for the East it remained a mere abstract awareness that left the concrete manifold of existence lying indifferently to one side, unshaped and impervious. Coming out of the Orient, the religious feeling of the infinite, the apeiron, took possession of the Greek soul in the DionysianOrphic epoch that preceded the Persian Wars. Here the Persian Wars also mark the release of the Occident from the Orient. That tension and its overcoming became for the Greeks the driving motive of knowledge. But every synthesis, as soon as it was achieved, permitted the old antithesis to break out anew in deepened form. Thus, it determined the history of theoretical knowledge into our time. Indeed, today we are compelled everywhere in the foundations of mathematics to return directly to the Greeks.

presented in an honest and straightforward manner. A little mathematical sophistication—and a little practice—allows you to recognize errors of randumbness, causuistry, and regression to the moon; once you get used to spotting phony patterns and false connections, you’ll begin to see them everywhere.

A wise woman once said that children dread mathematics because the subject is nothing more than a subject. Without mathematics, you are powerless. Mathematics is everywhere. Math is in everything. (Devi)

He (Gauss) lives everywhere in mathematics

Zero is the ultimate nullibist and holenmerist entity. Zero is whole in every number, and whole in every part of mathematics. The universe that we all experience exists purely because zero is nullibist and holenmerist … because zero contains all numbers … because zero is exactly where “something” = “nothing”. Reality exists solely because something = nothing. Zero is everything. Zero contains everything. Zero is everywhere. Zero is whole everywhere, and whole in everything. Nothing rivals the incredible power and beauty of zero. It’s the ultimate expression of the Principle of Sufficient Reason (PSR) and Occam’s razor. What could be simpler than nothing? The universe of zero is the simplest possible universe and the best possible universe.

A Nullibist says God is nowhere (transcendent). A Holenmerist says God is everywhere and wholly in each part (immanent). Both views can be reconciled via a transcendent Fourier frequency Singularity, linked to the entire, immanent, Fourier spacetime domain. The frequency domain is “nowhere” in relation to spacetime, but is connected wholly to every part of spacetime. This amazing idea – ontological holography, to put it another way – was known to the ancients and medieval thinkers, but is completely avoided by modern scientists.

to stand for “periphery.” It is hard to ignore the ubiquity of pi in nature. Pi is obvious in the disks of the moon and the sun. The double helix of DNA revolves around pi. Pi hides in the rainbow and sits in the pupil of the eye, and when a raindrop falls into water, pi emerges in the spreading rings. Pi can be found in waves and spectra of all kinds, and therefore pi occurs in colors and music, in earthquakes, in surf. Pi is everywhere in superstrings, the hypothetical loops of energy that may vibrate in many dimensions, forming the essence of matter. Pi occurs naturally in tables of death, in what is known as a Gaussian distribution of deaths in a population. That is, when a person dies, the event “feels” the Ludolphian number. It is one of the great mysteries why nature seems to know mathematics.

Noether proved mathematically that equations will only exhibit this symmetry if they are associated with a quantity whose value does not change. In other words, for time translation symmetry to exist in the laws of mechanics, something must be conserved. That something is what we call energy. Noether’s theorem goes far beyond energy conservation. It shows that whenever equations contain a symmetry, some quantity must be conserved. For example, the laws of mechanics do not regard one location in space as being more special than any other. Billiard balls follow these laws irrespective of where in the universe they are. This means the laws of mechanics have a spatial symmetry as well as a temporal one. For this to happen, a quantity called momentum is conserved. This is linked to the idea of inertia—the familiar feeling of being thrown forward when the vehicle you’re in brakes suddenly. Put another way, this happens to ensure the laws of mechanics are the same everywhere in the universe. Other conserved quantities linked to symmetries include angular momentum and electrical charge.

In one form or another, calcium carbonate turns up everywhere—in coral reefs, in the pores of basalt, in the ooze at the bottom of the ocean. It’s the main component of limestone, which is one of the world’s most common sedimentary rocks. “There are vast amounts of limestone dust blowing around in the troposphere, where we live,” Keutsch observed. “So that makes it attractive. “It has near-ideal optical properties,” he went on. “It dissolves in acid. So I can say with certainty that it will not have the same ozone-depleting impact that sulfuric acid has.” Mathematical modeling has confirmed the mineral’s advantages, Keutsch told me. But until someone actually throws calcium carbonate into the stratosphere, it’s hard to know how much to trust the models. “There’s no other way around it,” he said. —

It is because, in mathematics, you realise that balance and symmetry is actually in everything, even when it feels like chaos or pain...... But I think La Presencia has given us the understanding that mathematical purity is everywhere. We are inside it. Nothing is random. Not life, not death. Not even randomness. Not even us two here making this dirt into a garden. All of it connects. Everything is part of this whole. This beautiful fabric. Heaven isn't somewhere else. Nor is everyone we have lost. We are tied to them. The strings are in us.