Inspirational Mathematics Quotes

A mathematical formula for happiness:Reality divided by Expectations.There were two ways to be happy:improve your reality or lower your expectations.

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.

The ‘Muse’ is not an artistic mystery, but a mathematical equation. The gift are those ideas you think of as you drift to sleep. The giver is that one you think of when you first awake.

The axiom of equality states that x always equals x: it assumes that if you have a conceptual thing named x, that it must always be equivalent to itself, that it has a uniqueness about it, that it is in possession of something so irreducible that we must assume it is absolutely, unchangeably equivalent to itself for all time, that its very elementalness can never be altered. But it is impossible to prove. Always, absolutes, nevers: these are the words, as much as numbers, that make up the world of mathematics. Not everyone liked the axiom of equality––Dr. Li had once called it coy and twee, a fan dance of an axiom––but he had always appreciated how elusive it was, how the beauty of the equation itself would always be frustrated by the attempts to prove it. It was the kind of axiom that could drive you mad, that could consume you, that could easily become an entire life. But now he knows for certain how true the axiom is, because he himself––his very life––has proven it. The person I was will always be the person I am, he realizes. The context may have changed: he may be in this apartment, and he may have a job that he enjoys and that pays him well, and he may have parents and friends he loves. He may be respected; in court, he may even be feared. But fundamentally, he is the same person, a person who inspires disgust, a person meant to be hated.

Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite.

It is not knowledge, but the act of learning, not the possession of but the act of getting there, which grants the greatest enjoyment.

We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.

At times there's something so precise and mathematically chilling about nationalism. Build a dam to take away water AWAY from 40 million people. Build a dam to pretend to BRING water to 40 million people. Who are these gods that govern us? Is there no limit to their powers?

We are mathematical equations where your life is the sum of all choices you've made until now. The good news is you can change the equation so that you start making a difference in your life.

Naturally, we are inclined to be so mathematical and calculating that we look upon uncertainty as a bad thing...Certainty is the mark of the common-sense life. To be certain of God means that we are uncertain in all our ways, we do not know what a day may bring forth. This is generally said with a sigh of sadness; it should rather be an expression of breathless expectation.

Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to; to have a break-through idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.

The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game-- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.

(existential mathematics...) the degree of slowness is directly proportional to the intensity of memory; the degree of speed is directly proportional to the intensity of forgetting.” –p. 39

Both for practical reasons and for mathematically verifiable moral reasons, authority and responsibility must be equal - else a balancing takes place as surely as current flows between points of unequal potential. To permit irresponsible authority is to sow disaster; to hold a man responsible for anything he does not control is to behave with blind idiocy. The unlimited democracies were unstable because their citizens were not responsible for the fashion in which they exerted their sovereign authority... other than through the tragic logic of history... No attempt was made to determine whether a voter was socially responsible to the extent of his literally unlimited authority. If he voted the impossible, the disastrous possible happened instead - and responsibility was then forced on him willy-nilly and destroyed both him and his foundationless temple.

Faraday was asked: "What is the use of this discovery?" He answered: "What is the use of a child - it grows to be a man.

I was advised to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.

As he soars, he thinks, suddenly, of Dr. Kashen. Or not of Dr. Kashen, necessarily, but the question he had asked him when he was applying to be his advisee: What's your favorite axiom? (The nerd pickup line, CM had once called it.) "The axiom of equality," he'd said, and Kashen had nodded, approvingly. "That's a good one," he'd said. The axiom of equality states that x always equals x: it assumes that if you have a conceptual thing named x, that it must always be equivalent to itself, that it has a uniqueness about it, that it is in possession of something so irreducible that we must assume it is absolutely, unchangeably equivalent to itself for all time, that its very elementalness can never be altered. But it is impossible to prove. Always, absolutes, nevers: these are the words, as much as numbers, that make up the world of mathematics. Not everyone liked the axiom of equality––Dr. Li had once called it coy and twee, a fan dance of an axiom––but he had always appreciated how elusive it was, how the beauty of the equation itself would always be frustrated by the attempts to prove it. I was the kind of axiom that could drive you mad, that could consume you, that could easily become an entire life. But now he knows for certain how true the axiom is, because he himself––his very life––has proven it. The person I was will always be the person I am, he realizes. The context may have changed: he may be in this apartment, and he may have a job that he enjoys and that pays him well, and he may have parents and friends he loves. He may be respected; in court, he may even be feared. But fundamentally, he is the same person, a person who inspires disgust, a person meant to be hated. And in that microsecond that he finds himself suspended in the air, between ecstasy of being aloft and the anticipation of his landing, which he knows will be terrible, he knows that x will always equal x, no matter what he does, or how many years he moves away from the monastery, from Brother Luke, no matter how much he earns or how hard he tries to forget. It is the last thing he thinks as his shoulder cracks down upon the concrete, and the world, for an instant, jerks blessedly away from beneath him: x = x, he thinks. x = x, x = x.

I noticed that the [drawing] teacher didn't tell people much... Instead, he tried to inspire us to experiment with new approaches. I thought of how we teach physics: We have so many techniques - so many mathematical methods - that we never stop telling the students how to do things. On the other hand, the drawing teacher is afraid to tell you anything. If your lines are very heavy, the teacher can't say, "Your lines are too heavy." because *some* artist has figured out a way of making great pictures using heavy lines. The teacher doesn't want to push you in some particular direction. So the drawing teacher has this problem of communicating how to draw by osmosis and not by instruction, while the physics teacher has the problem of always teaching techniques, rather than the spirit, of how to go about solving physical problems.

Going back to the basis, the phrase ‘Fight Like A Girl’, and we’ve all heard that growing up. And by that they mean that you’re some kind of weakling and have no skills as a male. It’s said to little boys when they can’t fight yet, and it ridicules us. By the time we were born, the most of us hear things which program you to accept and know that you are less than your male counter part. It comes apparent in the way you’re paid for your job, it comes apparent when yóu are not allowed to go outside after a certain hour because you stand a good chance of getting raped while no one says that to your boyfriend. While women, anywhere, live in some kind of fear, there is no equality and that is mathematically impossible. We cannot see that change or solved in our lifetimes, but we have to do everything that we can. We should remind ourselves that we are fifty-one percent. Everyone should know that fighting like a girl is a positive thing and that there is not inherently anything wrong with us by the fact that we are born like ladies. That is a beautiful thing that we should never be put down because of. Being compared to a woman should only make a man feel stronger. It should be a compliment. In this world we’re creating it actually is. I remember this one guy who came to our show in Texas or something and he had painted his shirt “real men fight like a girl”, and I cried, because he was going away in the army next day. He bought my book because he wanted something he could read over there. I just hoped that this men, fully straight and fully male can maintain and retain all of those things that make him understand us, and what makes him so beautiful. A lot of military training is step one: you take all those guys and put them in front of bunch of hardcore videogames where you kill a bunch of people and become desensitised. But that is NOT power! I will not do that. I will not become less of a human being and I refuse to give up my femininity because that’s bullshit. I’m not going to have to shave my head and become all buff and all that to be able to say “now I’m powerful” because that’s bullshit. All of this, all of us, we are power. You don’t have to change anything to be strong.

[...] confusing time with its mathematical progression, as the old do, to whom all the past is not a diminishing road but, instead, a huge meadow which no winter ever touches.

A wall is happy when it is well designed, when it rests firmly on its foundation, when its symmetry balances its part and produces no unpleasant stresses. Good design can be worked out on the mathematical principles of mechanics.

David Hilbert, the towering mathematical intellect of the previous thirty years, had put it thus:9 ‘Mathematics knows no races … for mathematics, the whole cultural world is a single country’,

A lot of scientific evidence suggests that the difference between those who succeed and those who don't is not the brains they were born with, but their approach to life, the messages they receive about their potential, and the opportunities they have to learn.

It is by a mathematical point only that we are wise, as the sailor or fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.

By simple mathematics giving is key to the world you seek to live in. If I take I alone gain. If I give or share then two at least are enriched.

To be a scholar study math, to be a smart study magic.

Every time a student makes a mistake in math, they grow a synapse.” There

Education makes your maths better, not necessarily your manners.

But then, the sky! Blue, untainted by a single cloud (the Ancientes had such barbarous tastes given that their poets could have been inspired by such stupid, sloppy, silly-lingering clumps of vapour). I love - and i'm certain that i'm not mistaken if i say we love - skies like this, sterile and flawless! On days like these, the whole world is blown from the same shatterproof, everlasting glass as the glass of the Green Wall and of all our structures. On days like these, you can see to the very blue depths of things, to their unknown surfaces, those marvelous expressions of mathematical equality - which exist in even the most usual and everyday objects.

Many parents have asked me: What is the point of my child explaining their work if they can get the answer right? My answer is always the same: Explaining your work is what, in mathematics, we call reasoning, and reasoning is central to the discipline of mathematics.

Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.

Teaching mathematics, like teaching any art, requires the ability to inspire the student. Inspiration requires marketing, and marketing requires stirring communication.

The distance between your Dreams and Reality is inversely proportional to your Efforts.

If all the tough situations in our life are problems, mathematics thought us to solve any problem. Just need a formula which you need to derive on your own.

Some people are awe-inspired by majestic mountains, some by poetry and others by abstruse mathematics. But whatever the source, we all need a little awe in our lives.

Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?

Worth as I use it here is immeasurable, not as in mathematics towards infinity. But that it can not be measured. There are no measurable parameters for it! Certainly not a material-communal measurable parameter for it! Such, it is what the being holds that cannot and should never be traded. When it is there, every essence of your being knows it, and takes commands from it that will be able to override any personal or imposed sense of value.

History, Geology, Psychology, Philosophy, Chemistry, Physics, Theology, Mathematics, Technology, Sociology, Biology, and the list goes on and on. If all this body of knowledge exist for human consumption, why would I specialize in only one field?

That this blind and aging man forged ahead with such gusto is a remarkable lesson, a tale for the ages. Euler's courage, determination, and utter unwillingness to be beaten serves, in the truest sense of the word, as an inspiration for mathematician and non-mathematician alike. The long history of mathematics provides no finer example of the triumph of the human spirit.

the global impact of pure science rises above all national boundaries, and the sheer timelessness of pure mathematics transcends the limitations of his twentieth-century span. When Turing returned to the prime numbers in 1950 they were unchanged from when he left them in 1939, wars

I was not born happy. As a child, my favourite hymn was :'Weary of earth and laden with my sin.' At the age of five, I reflected that, if I should live to be seventy, I had only endured, so far, a fourteenth part of my whole life, and I felt the long-spread-out boredom ahead of me to be almost unedurable. In adolescense, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics.

India was China's teacher in religion and imaginative literature, and the world's teacher in trignometry, quandratic equations, grammar, phonetics, Arabian Nights, animal fables, chess, as well as in philosophy, and that she inspired Boccaccio, Goethe, Herder, Schopenhauer, Emerson, and probably also old Aesop.

They were aware that the symbols of mythology and the the symbols of mathematical science were different aspects of the same, indivisible Reality. They did not live in a 'divided house of faith and reason'; the two were interlocking, like ground-plan and elevation on an architect's drawing. It is a state of mind very difficult for twentieth-century man to imagine- or even to believe that it could ever have existed. It may help to remember though, that some of the greatest pre-Socratic sages formulated their philosophies in verse; the unitary source of inspiration of prophet, poet, and philosopher was still taken for granted.

The ‘real’ mathematics of the ‘real’ mathematicians, the mathematics of Fermat and Euler and Gauss and Abel and Riemann, is almost wholely ‘useless’ (and this is true of ‘applied’ as of ‘pure’ mathematics). It is not possible to justify the life of any genuine professional mathematician on the ground of the ‘utility’ of his work.… The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are, at present at any rate, almost as ‘useless’ as the theory of numbers. It

Life is not mathematics and the human being is not made for the sake of politics. I want a change in the present social system and do not believe in mere party politics.

(which has inspired at least one novel, Apostolos Doxiadis's Uncle Petros and Goldbach's Conjecture29).

This is rather an awe-inspiring statement to get out of a straightforward uniqueness theorem in mathematics.

Diagnostic, comment-based feedback is now known to promote learning, and it should be the standard way in which students’ progress is reported.

Always give help when needed, always ask for help when you need it

Success is the circle, hard work is the perimeter of it. the diameter of success is the addition of radius and radius of success is the failures of it

The spirit of Edison, not Einstein, still governed their image of the scientist. Perspiration, not inspiration. Mathematics was unfathomable and unreliable.

A bird is like an instrument working according to mathematical law, and it is in the capacity of man to reproduce such an instrument

had explicitly been concerned to treat mathematics as if it were a chess game, without asking for a connection with the world. That question was, as it were, always left for someone else to tackle.

once i asked myself ," what is time? " , in a second or two , i find the answer - " 't' for tension , 'i' for imaginative character of time , 'm' as it is mathematically expressed , 'e' as it has elegance

The popular image of the lone (and possibly slight mad) genius-who ignores the literature and other conventional wisdom and manages by some inexplicable inspiration (enhanced, perhaps, with a liberal dash of suffering) to come up with a breathtakingly original solution to a problem that confounded all the experts-is a charming and romantic image, but also a wildly inaccurate one, at least in the world of modern mathematics. We do have spectacular, deep and remarkable results and insights in this subject, of course, but they are the hard-won and cumulative achievement of years, decades, or even centuries of steady work and progress of many good and great mathematicians; the advance from one stage of understanding to the next can be highly non-trivial, and sometimes rather unexpected, but still builds upon the foundation of earlier work rather than starting totally anew....Actually, I find the reality of mathematical research today-in which progress is obtained naturally and cumulatively as a consequence of hard work, directed by intuition, literature, and a bit of luck-to be far more satisfying than the romantic image that I had as a student of mathematics being advanced primarily by the mystic inspirations of some rare breed of "geniuses.

five suggestions that can work to open mathematics tasks and increase their potential for learning: Open up the task so that there are multiple methods, pathways, and representations. Include inquiry opportunities. Ask the problem before teaching the method. Add a visual component and ask students how they see the mathematics. Extend the task to make it lower floor and higher ceiling. Ask students to convince and reason; be skeptical.

there was no shame in admitting you didn't have the answer, it was a necessary step toward the truth. It was as important to teach us about the unknown or the unknowable as it was to teach us what had already been safely proven.

In adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics. Now, on the contrary, I enjoy life; I might almost say that with every year that passes I enjoy it more…very largely it is due to a diminishing preoccupation with myself. Like others who had a Puritan education, I had the habit of meditating on my sins, follies, and shortcomings. I seemed to myself - no doubt justly - a miserable specimen. Gradually I learned to be indifferent to myself and my deficiencies; I came to center my attention increasingly upon external objects: the state of the world, various branches of knowledge, individuals for whom I felt affection…And every external interest inspires some activity which, so long as the interest remains alive, is a complete preventive of ennui. Interest in oneself, on the contrary, leads to no activity of a progressive kind. It may lead to the keeping of a diary, to getting psychoanalyzed, or perhaps to becoming a monk. But the monk will not be happy until the routine of the monastery has made him forget his own soul. The happiness which he attributes to religion he could have obtained from becoming a crossing-sweeper, provided he were compelled to remain one. External discipline is the only road to happiness for those unfortunates whose self-absorption is too profound to be cured in any other way.

The human mind is an incredible thing. It can conceive of the magnificence of the heavens and the intricacies of the basic components of matter. Yet for each mind to achieve its full potential, it needs a spark. The spark of enquiry and wonder. Often that spark comes from a teacher. Allow me to explain. I wasn’t the easiest person to teach, I was slow to learn to read and my handwriting was untidy. But when I was fourteen my teacher at my school in St Albans, Dikran Tahta, showed me how to harness my energy and encouraged me to think creatively about mathematics. He opened my eyes to maths as the blueprint of the universe itself. If you look behind every exceptional person there is an exceptional teacher. When each of us thinks about what we can do in life, chances are we can do it because of a teacher. [...] The basis for the future of education must lie in schools and inspiring teachers. But schools can only offer an elementary framework where sometimes rote-learning, equations and examinations can alienate children from science. Most people respond to a qualitative, rather than a quantitative, understanding, without the need for complicated equations. Popular science books and articles can also put across ideas about the way we live. However, only a small percentage of the population read even the most successful books. Science documentaries and films reach a mass audience, but it is only one-way communication.

I've been thinking about all the things I might have done differently. All the choices I didn't make. All the decisions that made and unmade me, all the actions and inactions I did or didn't take. With the shades drawn and the garbage overflowing, I've been thinking about all the bold steps I never took, all the gut instincts I didn't listen to, all the people I let down. I've been thinking about the cruel mathematics of my life, looking at my sums and wishing I'd shown my work.

It turns out that even believing you are smart—one of the fixed mindset messages—is damaging, as students with this fixed mindset are less willing to try more challenging work or subjects because they are afraid of slipping up and no longer being seen as smart.

Grothendieck transformed modern mathematics. However, much of the credit for this transformation should go to a lesser-known forerunner of his, Emmy Noether. It was Noether, born in Bavaria in 1882, who largely created the abstract approach that inspired category theory.1 Yet as a woman in a male academic world, she was barred from holding a professorship in Göttingen, and the classicists and historians on the faculty even tried to block her from giving unpaid lectures—leading David Hilbert, the dean of German mathematics, to comment, “I see no reason why her sex should be an impediment to her appointment. After all, we are a university, not a bathhouse.” Noether, who was Jewish, fled to the United States when the Nazis took power, teaching at Bryn Mawr until her death from a sudden infection in 1935.

We don't know that we don't own or owe Anything (In mathematical terms we are sifar), so keep walking as long as your legs are moving towards the infinite. Your own Ego is the only obstacle in this journey, earlier you get rid of it sooner will you find the infinite peace.

Another misconception about mathematics that is pervasive and damaging—and wrong—is the idea that people who can do math are the smartest or cleverest people. This makes math failure particularly crushing for students, as they interpret it as meaning that they are not smart.

More often than not, at the end of the day (or a month, or a year), you realize that your initial idea was wrong, and you have to try something else. These are the moments of frustration and despair. You feel that you have wasted an enormous amount of time, with nothing to show for it. This is hard to stomach. But you can never give up. You go back to the drawing board, you analyze more data, you learn from your previous mistakes, you try to come up with a better idea. And every once in a while, suddenly, your idea starts to work. It's as if you had spent a fruitless day surfing, when you finally catch a wave: you try to hold on to it and ride it for as long as possible. At moments like this, you have to free your imagination and let the wave take you as far as it can. Even if the idea sounds totally crazy at first.

In my opinion, defining intelligence is much like defining beauty, and I don’t mean that it’s in the eye of the beholder. To illustrate, let’s say that you are the only beholder, and your word is final. Would you be able to choose the 1000 most beautiful women in the country? And if that sounds impossible, consider this: Say you’re now looking at your picks. Could you compare them to each other and say which one is more beautiful? For example, who is more beautiful— Katie Holmes or Angelina Jolie? How about Angelina Jolie or Catherine Zeta-Jones? I think intelligence is like this. So many factors are involved that attempts to measure it are useless. Not that IQ tests are useless. Far from it. Good tests work: They measure a variety of mental abilities, and the best tests do it well. But they don’t measure intelligence itself.

Mathematics is at the center of thinking about how to spend the day, how many events and jobs can fit into the day, what size of space can be used to fit equipment or turn a car around, how likely events are to happen, knowing how tweets are amplified and how many people they reach.

The paradox of quantum physics in the 21st Century, awakens us to the realisation that "nothing matters" in and of itself. That nothing can be stated with certainty; but everything is just a mathematical probability occurring in an instance of space-time convergence, which forms our objective reality in the present moment.

In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.

How do we learn? Is there a better way? What can we predict? Can we trust what we’ve learned? Rival schools of thought within machine learning have very different answers to these questions. The main ones are five in number, and we’ll devote a chapter to each. Symbolists view learning as the inverse of deduction and take ideas from philosophy, psychology, and logic. Connectionists reverse engineer the brain and are inspired by neuroscience and physics. Evolutionaries simulate evolution on the computer and draw on genetics and evolutionary biology. Bayesians believe learning is a form of probabilistic inference and have their roots in statistics. Analogizers learn by extrapolating from similarity judgments and are influenced by psychology and mathematical optimization.

In confronting the theoretical falsity and absurdity of that [Social Democrat] doctrine with the reality of the phenomenon, I gradually acquired a clear picture of its aims... At such times, I was overcome by dark forebodings and fear of something evil. I saw before me a teaching inspired by egoism and hatred, mathematically calculated to win a victory-but the triumph of which would be a mortal blow to humanity.

now I want to speak about the word ‘theory’. This was originally an Orphic word, which Cornford interprets as ‘passionate sympathetic contemplation’. In this state, he says, ‘The spectator is identified with the suffering God, dies in his death, and rises again in his new birth.’ for Pythagoras, the ‘passionate sympathetic contemplation’ was intellectual, and issued in mathematical knowledge. In this way, through Pythagoreanism, ‘theory’ gradually acquired its modern meaning; but for all who were inspired by Pythagoras it retained an element of ecstatic revelation. To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural even if untrue.

Sometimes all it takes is a simple word, a mere nothing, a well-intentioned but over-protective gesture, like the gesture made, quite unwittingly, by the Mathematics teacher, for the pacific, docile, submissive person suddenly to vanish and be replaced, to the dismay and incomprehension of those who thought they knew all there was to know about the human soul, by the blind, devastating wrath of the meek. It doesn't usually last very long, but while it does, it inspires real fear.

theory'. This was originally an Orphic word, which Cornford interprets as 'passionate sympathetic contemplation'. In this state, he says, 'The spectator is identified with the suffering God, dies in his death, and rises again in his new birth.' For Pythagoras, the 'passionate sympathetic contemplation' was intellectual, and issued in mathematical knowledge. In this way, through Pythagoreanism, 'theory' gradually acquired its modern meaning; but for all who were inspired by Pythagoras it retained an element of ecstatic revelation.

How to describe the excitement I felt when I saw this beautiful work and realized its potential? I guess it's like when, after a long journey, suddenly a mountain peak comes in full view. You catch your breath, take in its majestic beauty, and all you can say is "Wow!" It's the moment of revelation. You have not yet reached the summit, you don't even know yet what obstacles lie ahead, but its allure is irresistible, and you already imagine yourself at the top. It's yours to conquer now. But do you have the strength and stamina to do it?

The researchers found that when students were given problems to solve, and they did not know methods to solve them, but they were given opportunity to explore the problems, they became curious, and their brains were primed to learn new methods, so that when teachers taught the methods, students paid greater attention to them and were more motivated to learn them. The researchers published their results with the title “A Time for Telling,” and they argued that the question is not “Should we tell or explain methods?” but “When is the best time do this?

There's been about a 100 billion people who have ever lived. Do you know how many people can exist? You take a look at the genes and find how many combinations of genes can make an authentic human being. And it is stupendously a larger number than the 100 billion. What it means is you are alive against stupendous odds. You are breathing air, observing sunsets, gazing into the night sky. Most people who could exist will never experience that. [Most people that could exist mathematically]. . .will never exist . . you are as special a living entity as there ever was.

But just what are imaginary numbers, you may now be asking yourself, and what on earth could it mean to raise e to an imaginary-number power? This chapter concerns mathematicians' long struggle to answer the first of these two questions. Later we'll take up the second one , which inspired Euler to devise the most radical expansion of the concept of exponents in math history. At this point, suffice it to say that affixing an imaginary exponent to a number has a dramatic effect on it-something lime what happens to a frog when it's tapped by a standard-issue magic wand.

Glad that you thus continue your resolve To suck the sweets of sweet philosophy Only, good master, while we do admire This virtue and this moral discipline, Let's be no Stoics nor no stocks, I pray, Or so devote to Aristotle's checks As Ovid be an outcast quite abjured. Balk logic with acquaintance that you have, And practise rhetoric in your common talk, Music and poesy use to quicken you, The mathematics and the metaphysics Fall to them as you find your stomach serves you. No profit grows where is no pleasure ta'en. In brief, sir, study what you most affect.

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.

It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true.

A few months ago I found a note tucked into a journal. I googled the quote. It was from a poem by Saadi, an Iranian poet who lived in the thirteenth century. It was from his masterpiece, 'Gulistan', or 'The Rose Garden', Wikipedia told me. Gulistan is 'poetry of ideas with mathematical concision', it said, possibly the most influential piece of Persian literature ever written. I read on and came across the the following lines: 'If one member is afflicted with pain, other members uneasy with remain. If you have no sympathy for human pain, the name of human you cannot retain.' That's the essence of The Kindness of Strangers.

Perhaps I don't know enough yet to find the right words for it, but I think I can describe it. It happened again just a moment ago. I don't know how to put it except by saying that I see things in two different ways-everything, ideas included. If I make an effort to find any difference in them, each of them is the same today as it was yesterday, but as soon as I shut my eyes they're suddenly transformed, in a different light. Perhaps I went wrong about the imaginary numbers. If I get to them by going straight along inside mathematics, so to speak, they seem quite natural. It's only if I look at them directly, in all their strangeness, that they seem impossible. But of course I may be all wrong about this, I know too little about it. But I wasn't wrong about Basini. I wasn't wrong when I couldn't turn my ear away from the faint trickling sound in the high wall or my eye from the silent, swirling dust going up in the beam of light from a lamp. No, I wasn't wrong when I talked about things having a second, secret life that nobody takes any notice of! I-I don't mean it literally-it's not that things are alive, it's not that Basini seemed to have two faces-it was more as if I had a sort of second sight and saw all this not with the eyes of reason. Just as I can feel an idea coming to life in my mind, in the same way I feel something alive in me when I look at things and stop thinking. There's something dark in me, deep under all my thoughts, something I can't measure out with thoughts, a sort of life that can't be expressed in words and which is my life, all the same. “That silent life oppressed me, harassed me. Something kept on making me stare at it. I was tormented by the fear that our whole life might be like that and that I was only finding it out here and there, in bits and pieces. . . . Oh, I was dreadfully afraid! I was out of my mind.. .” These words and these figures of speech, which were far beyond what was appropriate to Törless's age, flowed easily and naturally from his lips in this state of vast excitement he was in, in this moment of almost poetic inspiration. Then he lowered his voice and, as though moved by his own suffering, he added: “Now it's all over. I know now I was wrong after all. I'm not afraid of anything any more. I know that things are just things and will probably always be so. And I shall probably go on for ever seeing them sometimes this way and sometimes that, sometimes with the eyes of reason, and sometimes with those other eyes. . . . And I shan't ever try again to compare one with the other. .

I grow little of the food I eat, and of the little I do grow I did not breed or perfect the seeds. I do not make any of my own clothing. I speak a language I did not invent or refine. I did not discover the mathematics I use. I am protected by freedoms and laws I did not conceive of or legislate, and do not enforce or adjudicate. I am moved by music I did not create myself. When I needed medical attention, I was helpless to help myself survive. I did not invent the transistor, the microprocessor, object oriented programming, or most of the technology I work with. I love and admire my species, living and dead, and am totally dependent on them for my life and well being.

A Puritan twist in our nature makes us think that anything good for us must be twice as good if it's hard to swallow. Learning Greek and Latin used to play the role of character builder, since they were considered to be as exhausting and unrewarding as digging a trench in the morning and filling it up in the afternoon. It was what made a man, or a woman -- or more likely a robot -- of you. Now math serves that purpose in many schools: your task is to try to follow rules that make sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride. As you limp off with your aching mind and bruised soul, you know that nothing in later life will ever be as difficult. What a perverse fate for one of our kind's greatest triumphs! Think how absurd it would be were music treated this way (for math and music are both excursions into sensuous structure): suffer through playing your scales, and when you're an adult you'll never have to listen to music again. And this is mathematics we're talking about, the language in which, Galileo said, the Book of the World is written. This is mathematics, which reaches down into our deepest intuitions and outward toward the nature of the universe -- mathematics, which explains the atoms as well as the stars in their courses, and lets us see into the ways that rivers and arteries branch. For mathematics itself is the study of connections: how things ideally must and, in fact, do sort together -- beyond, around, and within us. It doesn't just help us to balance our checkbooks; it leads us to see the balances hidden in the tumble of events, and the shapes of those quiet symmetries behind the random clatter of things. At the same time, we come to savor it, like music, wholly for itself. Applied or pure, mathematics gives whoever enjoys it a matchless self-confidence, along with a sense of partaking in truths that follow neither from persuasion nor faith but stand foursquare on their own. This is why it appeals to what we will come back to again and again: our **architectural instinct** -- as deep in us as any of our urges.

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.

The springtime peak of productivity that is shown in the works of many writers and artists, as well as by those in both Lombroso's study and my own, fits with popular conceptions about the blossoming forth of life during springtime. But how do these findings make sense in light of the striking peaks for severe depressive episodes, and suicide itself, during these same months? And why should so many artists and writers have another peak of productivity during the autumn months? (This is shown in the works of many writers, as well as in the findings from both Lombroso's and my studies. Interestingly, there is some evidence that major mathematical and scientific discoveries tend to occur during the spring and fall as well. Indeed, autumn has been seen by many artist as their most inspiring season.

The predominant thoughts and feelings of a pregnant woman are lodged in some of the major chakras of the unborn baby. They will therefore affect the character of the unborn baby. To produce better babies, it is very important for a pregnant woman to see and hear things that are beautiful, inspiring, and strong. The feelings and thoughts should be harmonious and progressive or positive. Anger, pessimism, hopelessness, injurious words, negative feelings and thoughts should be avoided. It is advisable for a pregnant mother to read books that are inspirational like the biographies of great yogis or great people, books on spiritual teachings, mathematics, sciences, business and languages. All of these will have beneficial effects on the unborn baby and will tend to make the baby not only spiritual, but also sharp-minded and practical.

G. Stanley Hall, a creature of his times, believed strongly that adolescence was determined – a fixed feature of human development that could be explained and accounted for in scientific fashion. To make his case, he relied on Haeckel's faulty recapitulation idea, Lombroso's faulty phrenology-inspired theories of crime, a plethora of anecdotes and one-sided interpretations of data. Given the issues, theories, standards and data-handling methods of his day, he did a superb job. But when you take away the shoddy theories, put the anecdotes in their place, and look for alternate explanations of the data, the bronze statue tumbles hard. I have no doubt that many of the street teens of Hall's time were suffering or insufferable, but it's a serious mistake to develop a timeless, universal theory of human nature around the peculiarities of the people of one's own time and place.

There were also many cases of feedback between physics and mathematics, where a physical phenomenon inspired a mathematical model that later proved to be the explanation of an entirely different physical phenomenon. An excellent example is provided by the phenomenon known as Brownian motion. In 1827, British botanist Robert Brown (1773-1858) observed that wen pollen particles are suspended in water, they get into a state of agitated motion. This effect was explained by Einstein in 1905 as resulting from the collisions that the colloidal particles experience with the molecules of the surrounding fluid. Each single collision has a negligible effect, because the pollen grains are millions of times more massive than the water molecules, but the persistent bombardment has a cumulative effect. Amazingly, the same model was found to apply to the motions of stars in star clusters. There the Brownian motion is produced by the cumulative effect of many stars passing by any given star, with each passage altering the motion (through gravitational interaction) by a tiny amount.

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.

At the risk of repetitiveness I must once more mention here the Pythagoreans, the chief engineers of that epoch-making change. I have spoken in more detail elsewhere of the inspired methods by which, in their religious order, they transformed the Orphic mystery cult into a religion which considered mathematical and astronomical studies as the main forms of divine worship and prayer. The physical intoxication which had accompanied the Bacchic rites was superseded by the mental intoxication derived from philo-sophia, the love of knowledge. It was one of the many key concepts they coined and which are still basic units in our verbal currency. The cliche' about the 'mysteries of nature' originates in the revolutionary innovation of applying the word referring to the secret rites of the worshippers of Orpheus, to the devotions of stargazing. 'Pure science' is another of their coinages; it signified not merely a contrast to the 'applied' sciences, but also that the contemplation of the new mysteria was regarded as a means of purifying the soul by its immersion in the eternal. Finally, 'theorizing' comes from Theoria, again a word of Orphic origin, meaning a state of fervent contemplation and participation in the sacred rites (thea spectacle, theoris spectator, audience). Contemplation of the 'divine dance of numbers' which held both the secrets of music and of the celestial motions became the link in the mystic union between human thought and the anima mundi. Its perfect symbol was the Harmony of the Spheres-the Pythagorean Scale, whose musical intervals corresponded to the intervals between the planetary orbits; it went on reverberating through 'soft stillness and the night' right into the poetry of the Elizabethans, and into the astronomy of Kepler.

That such a surprisingly powerful philosophical method was taken seriously can be only partially explained by the backwardness of German natural science in those days. For the truth is, I think, that it was not at first taken really seriously by serious men (such as Schopenhauer, or J. F. Fries), not at any rate by those scientists who, like Democritus2, ‘would rather find a single causal law than be the king of Persia’. Hegel’s fame was made by those who prefer a quick initiation into the deeper secrets of this world to the laborious technicalities of a science which, after all, may only disappoint them by its lack of power to unveil all mysteries. For they soon found out that nothing could be applied with such ease to any problem whatsoever, and at the same time with such impressive (though only apparent) difficulty, and with such quick and sure but imposing success, nothing could be used as cheaply and with so little scientific training and knowledge, and nothing would give such a spectacular scientific air, as did Hegelian dialectics, the mystery method that replaced ‘barren formal logic’. Hegel’s success was the beginning of the ‘age of dishonesty’ (as Schopenhauer3 described the period of German Idealism) and of the ‘age of irresponsibility’ (as K. Heiden characterizes the age of modern totalitarianism); first of intellectual, and later, as one of its consequences, of moral irresponsibility; of a new age controlled by the magic of high-sounding words, and by the power of jargon. In order to discourage the reader beforehand from taking Hegel’s bombastic and mystifying cant too seriously, I shall quote some of the amazing details which he discovered about sound, and especially about the relations between sound and heat. I have tried hard to translate this gibberish from Hegel’s Philosophy of Nature4 as faithfully as possible; he writes: ‘§302. Sound is the change in the specific condition of segregation of the material parts, and in the negation of this condition;—merely an abstract or an ideal ideality, as it were, of that specification. But this change, accordingly, is itself immediately the negation of the material specific subsistence; which is, therefore, real ideality of specific gravity and cohesion, i.e.—heat. The heating up of sounding bodies, just as of beaten or rubbed ones, is the appearance of heat, originating conceptually together with sound.’ There are some who still believe in Hegel’s sincerity, or who still doubt whether his secret might not be profundity, fullness of thought, rather than emptiness. I should like them to read carefully the last sentence—the only intelligible one—of this quotation, because in this sentence, Hegel gives himself away. For clearly it means nothing but: ‘The heating up of sounding bodies … is heat … together with sound.’ The question arises whether Hegel deceived himself, hypnotized by his own inspiring jargon, or whether he boldly set out to deceive and bewitch others. I am satisfied that the latter was the case, especially in view of what Hegel wrote in one of his letters. In this letter, dated a few years before the publication of his Philosophy of Nature, Hegel referred to another Philosophy of Nature, written by his former friend Schelling: ‘I have had too much to do … with mathematics … differential calculus, chemistry’, Hegel boasts in this letter (but this is just bluff), ‘to let myself be taken in by the humbug of the Philosophy of Nature, by this philosophizing without knowledge of fact … and by the treatment of mere fancies, even imbecile fancies, as ideas.’ This is a very fair characterization of Schelling’s method, that is to say, of that audacious way of bluffing which Hegel himself copied, or rather aggravated, as soon as he realized that, if it reached its proper audience, it meant success.

Because the number system is like human life. (emphasis added) First you have natural numbers. The ones that are whole and positive. The numbers of a small child. But human consciousness expands. The child discovers a sense of long, and do you know what the mathematical expression is for longing?’ He adds cream and several drops of orange juice to the soup. ‘The negative numbers. The formalization of the feeling that you are missing something. And human consciousness expands and grows even more, and the child discovers the in between spaces. Between stones, between pieces of moss on the stones, between people. And between numbers. And do you know what that leads to? It leads to fractions. Whole numbers plus fractions prouce rational numbers. And human consciousness doesn’t stop there. It wants to go beyond reason. It adds an operation as absurd as the extraction of roots. And produces irrational numbers.’ He warms French bread in the over and fills the pepper mill. ‘It’s a form of madness. Because the irrational numbers are infinite. They can’t be written down. They force human consciousness out beyond the limits. And by adding irrational numbers to rational numbers, you get real numbers.’ I’ve stepped into the middle of the room to have more space. It’s rare that you have a chance to explain yourself to a fellow human being. Usually you have to fight for the floor. And this is important to me. ‘It doesn’t stop. It never stops. Because now, on the spot, we expand the real numbers with imaginary square roots of negative numbers. These are numbers we can’t picture, numbers that normal human consciousness cannot comprehend. And when we add the imaginary numbers to the real numbers, we have the complex number system. The first number system in which it’s possible to explain satisfactorily the crystal formation of ice. It’s like a vast, open landscape. The horizons. You head toward them, and they keep receding. That is Greenland, and that’s what I can’t be without! That’s why I don’t want to be locked up

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.

Count how many days you have lived! It's easy Math. You will soon realize the worth of living.

Whatever else happens, stay busy. (I always lean on this wise advice, from the seventeenth-century English scholar Robert Burton, on how to survive melancholy: “Be not solitary, be not idle.”) Find something to do—anything, even a different sort of creative work altogether—just to take your mind off your anxiety and pressure. Once, when I was struggling with a book, I signed up for a drawing class, just to open up some other kind of creative channel within my mind. I can’t draw very well, but that didn’t matter; the important thing was that I was staying in communication with artistry at some level. I was fiddling with my own dials, trying to reach inspiration in any way possible. Eventually, after enough drawing, the writing began to flow again. Einstein called this tactic “combinatory play”—the act of opening up one mental channel by dabbling in another. This is why he would often play the violin when he was having difficulty solving a mathematical puzzle; after a few hours of sonatas, he could usually find the answer he needed.

Are you ready to transform yourself? Are you ready to be one of the Special Ones, the Illuminated Ones? Are you ready to play the God Game? Only the strongest, the smartest, the boldest, can play. This is not a drill. This is your life. Stop being what you have been. Become what you were meant to be. See the Light. Join the Hyperboreans. Become a HyperHuman. Only the highest, only the noblest, only the most courageous are called. A new dawn is coming... the birth of Hyperreason. It’s time to enter Hyperreality.

Never forget, when you come to AC/GS, you are entering the dark, mysterious, complex, daunting, forbidding – but infinitely inspiring and perfect world – of INTJs. We can take you from Cimmeria to Hyperborea. Do not expect an easy ride. Don’t bring emotionalism and irrationalism. Let the most powerful ideas in the world wash over you and enlighten you. And then help us make our vision even brighter, enough to light up this whole benighted world.

That, you see, was the trouble. I am speaking of your attitude towards the subject of architectural design. You have never given it the attention it deserves. And yet, you have been excellent in all the engineering sciences. Of course, no one denies the importance of structural engineering to a future architect, but why go to extremes? Why neglect what may be termed the artistic and inspirational side of your profession and concentrate on all those dry, technical, mathematical subjects? You intended to become an architect, not a civil engineer.

Skeptical Empiricism and the a-Platonic School The Platonic Approach Interested in what lies outside the Platonic fold Focuses on the inside of the Platonic fold Respect for those who have the guts to say “I don’t know” “You keep criticizing these models. These models are all we have.” Fat Tony Dr. John Thinks of Black Swans as a dominant source of randomness Thinks of ordinary fluctuations as a dominant source of randomness, with jumps as an afterthought Bottom-up Top-down Would ordinarily not wear suits (except to funerals) Wears dark suits, white shirts; speaks in a boring tone Prefers to be broadly right Precisely wrong Minimal theory, considers theorizing as a disease to resist Everything needs to fit some grand, general socioeconomic model and “the rigor of economic theory;” frowns on the “descriptive” Does not believe that we can easily compute probabilities Built their entire apparatus on the assumptions that we can compute probabilities Model: Sextus Empiricus and the school of evidence-based, minimum-theory empirical medicine Model: Laplacian mechanics, the world and the economy like a clock Develops intuitions from practice, goes from observations to books Relies on scientific papers, goes from books to practice Not inspired by any science, uses messy mathematics and computational methods Inspired by physics, relies on abstract mathematics Ideas based on skepticism, on the unread books in the library Ideas based on beliefs, on what they think they know Assumes Extremistan as a starting point Assumes Mediocristan as a starting point Sophisticated craft Poor science Seeks to be approximately right across a broad set of eventualities Seeks to be perfectly right in a narrow model, under precise assumptions

Sixteenth-century Danish nobleman and astronomer Tycho Brahe was the greatest naked-eye astronomer and an interesting character. His colorful past included being kidnapped by his uncle, being given an island, constructing a state-of-the-art and gorgeous observatory, being evicted from his island only to have his observatory destroyed by the islanders after his departure, and wearing a metal prosthetic nose after having the tip of his own nose cut off during a mathematics-inspired duel. Brahe died in 1601 as a result of a burst bladder after he held his pee too long.

There's been about 100 billion people who have ever lived. Do you know how many people can exist? You take a look at the genes and find how many combinations of genes can make an authentic human being. And it is stupendously a larger number than the 100 billion. What it means is you are alive against stupendous odds. You are breathing air, observing sunsets, gazing into the night sky. Most people who could exist will never experience that. [Most people that could exist mathematically]. . .will never exist . . you are as special a living entity as there ever was

There's been about 100 billion people who have ever lived. Do you know how many people can exist? You take a look at the genes and find how many combinations of genes can make an authentic human being. And it is stupendously a larger number than the 100 billion. What it means is you are alive against stupendous odds. You are breathing air, observing sunsets, gazing into the night sky. Most people who could exist will never experience that. [Most people that could exist mathematically]. . .will never exist . . you are as special a living entity as there ever was.

In one study, researchers at the National Institute for Mental Health gave people a 10‐minute exercise to work on each day for three weeks. The researchers compared the brains of those receiving the training with those who did not. The results showed that the people who worked on an exercise for a few minutes each day experienced structural brain changes. The participants’ brains “rewired” and grew in response to a 10‐minute mental task performed daily over 15 weekdays (Karni et al., 1998).

GODMAN QUOTES 15 ***Equation of life*** In the syllable of wise words we remain inexhaustible. Worse encounter is turning a hunter to be the hunted The mathematics of life is an equation of solving an endless problem. In absence of faults figures are born... in truth of notes they are kept. In the language of humility a heavy word is accepted without pain. Our hope in words is found in reading the words of courage. You are the vocabulary of the words you acquired in the syllable of the word you read. It treats our fancy to know it… that life is what we define it according to our experience in it. True champions are not worth in currency. Conquer my heart and I will conquer your world.

I had two great passions at the time: one magical and ethereal, which was reading, and the other mundane and predictable, which was pursuing silly love affairs. Concerning my literary ambitions, my successes went from slender to nonexistent. During those years I started a hundred woefully bad novels that died along the way, hundreds of short stories, plays, radio serials, and even poems that I wouldn't let anyone read, for their own good. I only needed to read them myself to see how much I still had to learn and what little progress I was making, despite the desire and enthusiasm I put into it. I was forever rereading Carax's novels and those of countless authors I borrowed from my parent's bookshop. I tried to pull them apart as if they were transistor radios, or the engine of a Rolls-Royce, hoping I would be able to figure out how they were built and how and why they worked. I'd read something in a newspaper about some Japanese engineers who practiced something called reverse engineering. Apparently these industrious gentlemen disassembled an engine to its last piece, analyzing the function of each bit, the dynamics of the whole, and the interior design of the device to work out the mathematics that supported its operation. My mother had a brother who worked as an engineer in Germany, so I told myself that there must be something in my genes that would allow me to do the same thing with a book or with a story. Every day I became more convinced that good literature has little or nothing to do with trivial fancies such as 'inspiration' or 'having something to tell' and more with the engineering of language, with the architecture of the narrative, with the painting of textures, with the timbres and colors of the staging, with the cinematography of words, and the music that can be produced by an orchestra of ideas. My second great occupation, or I should say my first, was far more suited to comedy, and at times touched on farce. There was a time in which I fell in love on a weekly basis, something that, in hindsight, I don't recommend. I fell in love with a look, a voice, and above all with what was tightly concealed under those fine-wool dresses worn by the young girls of my time. 'That isn't love, it's a fever,' Fermín would specify. 'At your age it is chemically impossible to tell the difference. Mother Nature brings on these tricks to repopulate the planet by injecting hormones and a raft of idiocies into young people's veins so there's enough cannon fodder available for them to reproduce like rabbits and at the same time sacrifice themselves in the name of whatever is parroted by bankers, clerics, and revolutionary visionaries in dire need of idealists, imbeciles, and other plagues that will prevent the world from evolving and make sure it always stays the same.

qualitative market research in Myanmar Address Ramakrishna Paramhans Ward, PO mangal nagar, Katni, [M.P.] 2nd Floor, Above KBZ Pay Centre, between 65 & 66 street, Manawhari Road Mandalay, Myanmar - Phone +95 9972107002 +91 7222997497 Subjective Statistical surveying in Myanmar: Revealing Bits of knowledge for Business Development In the present globalized commercial center, understanding buyer conduct and market elements is urgent for organizations to flourish. Myanmar, with its quickly developing economy, presents special open doors and difficulties for organizations hoping to lay out areas of strength for an in the district. As organizations look to acquire an upper hand, the meaning of subjective statistical surveying in Myanmar couldn't possibly be more significant. This article digs into the significance of qualitative market research in Myanmar and how it tends to be instrumental in driving business development in the powerful Myanmar market. Myanmar, previously known as Burma, has seen critical political and monetary changes as of late, prompting expanded unfamiliar speculation and development across different areas. This change has brought about shifts in buyer inclinations, buying power, and market patterns. To explore this advancing scene effectively, organizations should participate in thorough subjective statistical surveying to acquire nuanced experiences into buyer conduct, inclinations, and social impacts. qualitative market research in Myanmar centers around understanding the "whys" behind buyer conduct, digging into the basic inspirations, feelings, and insights that drive dynamic cycles. Dissimilar to quantitative exploration, which gives mathematical information and factual examination, subjective examination offers a more profound comprehension of customer perspectives and inclinations, making it priceless for organizations looking to fit their techniques to the Myanmar market. One of the critical benefits of subjective statistical surveying in Myanmar is its capacity to uncover social subtleties and context oriented factors that impact buyer conduct. Given Myanmar's different ethnic gatherings, dialects, and cultural standards, a nuanced comprehension of nearby traditions and customs is fundamental for organizations meaning to resound with the interest group. Subjective examination procedures, for example, inside and out interviews, center gatherings, and ethnographic investigations empower scientists to dive into these social complexities, giving organizations noteworthy bits of knowledge for item improvement, promoting methodologies, and brand situating. Also, subjective examination assumes a significant part in distinguishing arising patterns and market holes that may not be obvious through quantitative information alone. By connecting straightforwardly with buyers and key partners, organizations can acquire subjective experiences into advancing business sector elements, possible undiscovered portions, and moving customer inclinations. This, thus, enables organizations to adjust their contributions and methodologies proactively, remaining on the ball in Myanmar's quickly changing business sector scene. As well as illuminating vital business choices, subjective statistical surveying encourages a more profound association among organizations and the nearby local area. By effectively including Myanmar purchasers in the examination cycle, organizations show a promise to understanding and tending to their requirements, cultivating trust and brand reliability simultaneously. This human-driven approach is especially relevant in Myanmar, where individual connections and local area ties hold huge influence over customer conduct.

ANYTHING x ZERO = ZERO | AT THE SAME TIME | ANYTHING WITH ZERO = ABSOLUTE.

Khwarizmi’s major contribution was to combine Euclid’s theories with Indian mathematics. The sheer clarity of his writing, and the simple way he managed to explain complex ideas, inspired generations of subsequent mathematicians and initiated rapid developments in algebra, geometry and trigonometry across the Islamic world: Indian innovations such as linear and quadratic equations, geometrical solutions, tables of sines, tangents and co-tangents suddenly became accessible to all.

Pythagoras (550 BCE), with his theory of numbers, had been a source of inspiration for those who sought harmony in the Universe. His aim was to show in his philosophy that there was a high, structural, divine order to the Universe. This was a natural habitat for the souls. Mathematics was the tool to investigate this order.

This is important because our behavior is affected by our assumptions or our perceived truths. We make decisions based on what we think we know. It wasn’t too long ago that the majority of people believed the world was flat. This perceived truth impacted behavior. During this period, there was very little exploration. People feared that if they traveled too far they might fall off the edge of the earth. So for the most part they stayed put. It wasn’t until that minor detail was revealed—the world is round—that behaviors changed on a massive scale. Upon this discovery, societies began to traverse the planet. Trade routes were established; spices were traded. New ideas, like mathematics, were shared between societies which unleashed all kinds of innovations and advancements. The correction of a simple false assumption moved the human race forward.

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.

If our 14 billion year cosmic history were scaled to 1 year, then 100,000 years of human history would be 4 minutes, and a 100 year life would be 0.2 seconds.

With God the impossible IS possible Statistical, scientific and mathematical square root, pi and deviations have no relevance to God Finite becomes Infinity Probability becomes Yes, Yes and Amen.

Mighty men of science and mighty deeds. A Newton who binds the universe together in uniform law; Lagrange, Laplace, Leibnitz with their wondrous mathematical harmonies; Coulomb measuring our electricity... Faraday, Ohm, Ampère, Joule, Maxwell, Hertz, Röntgen; and in another branch of science, Cavendish, Davy, Dalton, Dewar; and in another, Darwin, Mendel, Pasteur, Lister, Sir Ronald Ross. All these and many others, and some whose names have no memorial, form a great host of heroes, an army of soldiers – fit companions of those of whom the poets have sung... There is the great Newton at the head of this list comparing himself to a child playing on the seashore gathering pebbles, whilst he could see with prophetic vision the immense ocean of truth yet unexplored before him...

The mystical approach to studying creativity suggests that creativity is the result of divine inspiration or is a spiritual process. In the history of mathematics, Blaise Pascal claimed that many of his mathematical insights came directly from God. The renowned 19th century algebraist Leopold Kronecker said that “God made the integers, all the rest is the work of man” (Gallian, 1994). Kronecker believed that all other numbers, being the work of man, were to be avoided; and although his radical beliefs did not attract many supporters, the intuitionists advocated his beliefs about constructive proofs many years after his death. There have been attempts to explore possible relationships between mathematicians’ beliefs about the nature of mathematics and their creativity (Davis and Hersh, 1981; Hadamard, 1945; Poincaré, 1948; Sriraman, 2004a). These studies indicate that such a relationship does exist. It is commonly believed that the neo-Platonist view is helpful to the research mathematician because of the innate belief that the sought after result/relationship already exists.

The cult of the genius also tends to undervalue hard work. When I was starting out, I thought "hardworking" was a kind of veiled insult-something to say about a student when you can't honestly say they're smart. But the ability to work hard-to keep one's whole attention and energy focused on a problem, systematically turning it over and over and pushing at everything that looks like a crack, despite the lack of outward signs of progress-is not a skill everybody has. Psychologists nowadays call it "grit," and it's impossible to do math without it. It's easy to lose sight of the importance of work, because mathematical inspiration, when it finally does come, can feel effortless and instant.

But it didn't really happen in the space of a footstep, Poincare explains. That moment of inspiration is the product of weeks of work, both conscious and unconscious, which somehow prepare the mind to make the necessary connection of ideas. Sitting around waiting for inspiration leads to failure, no matter how much of a whiz kid you are.

Before going to bed, they take a few minutes to read over the mathematical or literary work they did during the day—especially if they’ve reached a plateau or feel stuck. The mind then works all night to close the loop, and they wake up in the morning with “inspiration.” It seems magical, but it isn’t so much magical as it is the result of effective priming of the mental pump. The OTT principle and prioritization with a list

mathematical problems solved; feature problems solved...

Since the development of mathematics is often inspired and guided by aesthetic considerations, mathematics can be described as “amphibious”: It is both a science and one of the humanities.

It was not just joy. There was something more, something deeper: After all, what could be more mysterious, what could be more awe-inspiring, than to find that the structure of the physical world is intimately tied to the deep mathematical concepts, concepts which were developed out of considerations rooted only in logic and the beauty of form?

The issue, then, is not, What is the best way to teach? but, What is mathematics really all about?... Controversies about…teaching cannot be resolved without confronting problems about the nature of mathematics.

However, mathematics-inspired books such as Agatha Christie’s Ten Little Indians (with its valuable, realworld lessons on subtraction) are fair game.

The continuous transformation of a school into an elite Science, Technology, Engineering and Mathematics (STEM) institution prepares students to become 21st century-ready. STEM embeds college-, career-, and citizen-ready skills into the curriculum. For our nation, we must succeed. Yet we cannot step into this new world without inspiration and commitment. So we cobble together ideas and actions to create our own recipe for success.

With the coming of Nazi-inspired racial laws, many promising Jewish graduate students were also dismissed from the universities. Castelnuovo organized special courses in his home, and in the homes of other Jewish former professors, to enable the graduate students to continue their studies. In addition to writing books on the history of mathematics, Castelnuovo spent the last of his eighty-seven years examine the philosophical relationship between determinism and chance and trying to interpret the concept of cause and effect.

…Just walking one short path could make you feel hopeful, frustrated, bored, excited, or even nothing at all. And that this could change from one step to the next. You’re aware that you want to reach the center, and also aware that the labyrinth keeps taking you away from it. Just as you seem to be getting close, you turn and end up walking almost around its outer limits.... You love the labyrinth and you hate it at different moments, but you never feel like you’ve conquered it, because that would be ridiculous.... This is a path that is determined for you in advance, but no one can tell you what to think while you’re walking it. It’s not like a maze, you can’t get lost. No one’s playing any tricks on you. There aren’t any monsters lurking around any corners. You can see the end and yet, you walk calmly towards it, following perhaps the least logical route (in mathematical terms at least). Perhaps the labyrinth tells us why we don’t simply read the last pages of books. Why we don’t hurry through life looking for outcomes all the time, however many times we’re told that we should, and that we should be overtaking people and overcoming things as we go. The labyrinth doesn’t tell us how to live. It shows us how we do live.

Some students think their role in math classrooms is to memorize all the steps and methods. Other students think their role is to connect ideas. These different strategies link, unsurprisingly, to achievement, and the students who memorize are the lowest achieving in the world.

I'm still just as slow… At the end of the eleventh grade, I took the measure of the situation, and came to the conclusion that rapidity doesn't have a precise relation to intelligence. What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant. (Schwartz, 2001)

In this chapter we will look at the entire edifice of QFT. We will see that it is based on three simple principles. We will also list some of its achievements, including some new insights and understandings not previously mentioned. THE FOUNDATION QFT is an axiomatic theory that rests on a few basic assumptions. Everything you have learned so far, from the force of gravity to the spectrum of hydrogen, follows almost inevitably from these three basic principles. (To my knowledge, Julian Schwinger is the only person who has presented QFT in this axiomatic way, at least in the amazing courses he taught at Harvard University in the 1950's.) 1. The field principle. The first pillar is the assumption that nature is made of fields. These fields are embedded in what physicists call flat or Euclidean three-dimensional space-the kind of space that you intuitively believe in. Each field consists of a set of physical properties at every point of space, with equations that describe how these particles or field intensities influence each other and change with time. In QFT there are no particles, no round balls, no sharp edges. You should remember, however, that the idea of fields that permeate space is not intuitive. It eluded Newton, who could not accept action-at-a-distance. It wasn't until 1845 that Faraday, inspired by patterns of iron filings, first conceived of fields. The use of colors is my attempt to make the field picture more palatable. 2. The quantum principle (discetization). The quantum principle is the second pillar, following from Planck's 1900 proposal that EM fields are made up of discrete pieces. In QFT, all physical properties are treated as having discrete values. Even field strengths, whose values are continues, are regarded as the limit of increasingly finer discrete values. The principle of discretization was discovered experimentally in 1922 by Otto Stern and Walther Gerlach. Their experiment (Fig. 7-1) showed that the angular momentum (or spin) of the electron in a given direction can have only two values: +1/2 or -1/2 (Fig. 7-1). The principle of discretization leads to another important difference between quantum and classical fields: the principle of superposition. Because the angular momentum along a certain axis can only have discrete values (Fig. 7-1), this means that atoms whose angular momentum has been determined along a different axis are in a superposition of states defined by the axis of the magnet. This same superposition principle applies to quantum fields: the field intensity at a point can be a superposition of values. And just as interaction of the atom with a magnet "selects" one of the values with corresponding probabilities, so "measurement" of field intensity at a point will select one of the possible values with corresponding probability (see "Field Collapse" in Chapter 8). It is discretization and superposition that lead to Hilbert space as the mathematical language of QFT. 3. The relativity principle. There is one more fundamental assumption-that the field equations must be the same for all uniformly-moving observers. This is known as the Principle of Relativity, famously enunciated by Einstein in 1905 (see Appendix A). Relativistic invariance is built into QFT as the third pillar. QFT is the only theory that combines the relativity and quantum principles.

I walk around in a near-constant state of inspiration with a great hunger of knowledge, and I read everything I can about math and physics, often developing my own theories along the way.

Imperfection is a part of any creative process and of life, yet for some reason we live in a culture that has a paralyzing fear of failure, which prevents action and hardens a rigid perfectionism. It's the single most disempowering state of mind you can have if you'd like to be more creative, inventive, or entrepreneurial.

Essential to the order of things is the principle of correspondences. Hidden connections underlie diverse phenomena that impress the mind with similar qualities and associations, such as colour, shape, weight, movement and even names with similar sounds and spellings. The material world, operating as it does according to God's design, can be studied to understand His will (‘as above, so below’). The universe becomes a multilayered tableau of symbols. Chemicals and stars, for alchemists and astrologers, are symbolic and can be aligned with other symbols – mathematical, alphabetical, mythic and cosmic – all considered to be mystical. Humanity's divine spark inspires us to seek reunion with the Divinity. Toward this end, the Hermetist employs alchemy, astrology and magic too. Magical formulae are based on the correspondences already noted: a ritual to induce creativity might be addressed to the Sun and might entail lamps, gold, ‘Apollonian’ music and a sunny mood.

Beautiful Things come with Elegant Equations.

You can add new things to your life at every stage of your life: New ways, new habits, new ideas, new fears, and new stupidities! And remember, at every stage of your life, you can take something out of your life! You have the will to add and subtract! Make good use of this will, use this simple mathematics well to make your life better!

Scientism has done its best to undermine reason and logic. Those of us that belong to the Army of Reason have never left the battlefield. We soldier on, resisting the fierce current trying to push us back onto the shore. We do not deviate from our course. Our destination is clear. The stars shine on us. All is well with the world. The Empyrean lies before us. The fire of truth burns within us. Nothing shall ever quench it. Change is coming. The future is ours. De l’audace, encore de l’audace, et toujours de l’audace. Audacity, more audacity, and ever more audacity.

et al. (2000), Bonifaci et al. (2012), Tero et al. (2010), and Oettmeier et al. (2017). In Advances in Physarum Machines (Adamatzky [2016]), researchers detail many surprising properties of slime molds. Some use slime molds to make decision gates and oscillators, some simulate historical human migrations and model possible future patterns of human migrations on the moon. Mathematical models inspired by slime molds include a non-quantum implementation of Shor’s factorization, calculation of shortest paths, and the design of supply-chain networks. Oettmeier et al. (2017) note that Hirohito, the emperor of Japan between 1926 and 1989, was fascinated by slime molds and in 1935 published a book on the subject. Slime molds have been a high-prestige subject of research in Japan ever since.

Sometimes when I close my eyes, I can't see

With a narrow and open focus of altered states, many impossibles of yesterday have become possibles of today. Many technological and scientific inventions, innovations, and mathematical equations are products of altered states of mind.

The fact of zero He added nonstop: Did you know that zero was not used throughout human history! Until 781 A.D, when it was first embodied and used in arithmetic equations by the Arab scholar Al-Khwarizmi, the founder of algebra. Algorithms took their name from him, and they are algorithmic arithmetic equations that you have to follow as they are and you will inevitably get the result, the inevitable result. And before that, across tens and perhaps hundreds of thousands of years, humans refused to deal with zero. While the first reference to it was in the Sumerian civilization, where inscriptions were found three thousand years ago in Iraq, in which the Sumerians indicated the existence of something before the one, they refused to deal with it, define it and give it any value or effect, they refused to consider it a number. All these civilizations, some of which we are still unable to decipher many of their codes, such as the Pharaonic civilization that refused to deal with zero! We see them as smart enough to build the pyramids with their miraculous geometry and to calculate the orbits of stars and planets with extreme accuracy, but they are very stupid for not defining zero in a way that they can deal with, and use it in arithmetic operations, how strange this really is! But in fact, they did not ignore it, but gave it its true value, and refused to build their civilizations on an unknown and unknown illusion, and on a wrong arithmetical frame of reference. Throughout their history, humans have looked at zero as the unknown, they refused to define it and include it in their calculations and equations, not because it has no effect, but because its true effect is unknown, and remaining unknown is better than giving it a false effect. Like the wrong frame of reference, if you rely on it, you will inevitably get a wrong result, and you will fall into the inevitability of error, and if you ignore it, your chance of getting it right remains. Throughout their history, humans have preferred to ignore zero, not knowing its true impact, while we simply decided to deal with it, and even rely on it. Today we build all our ideas, our civilization, our software, mathematics, physics, everything, on the basis that 1 + 0 equals one, because we need to find the effect of zero so that our equations succeed, and our lives succeed with, but what if 1 + 0 equals infinity?! Why did we ignore the zero in summation, and did not ignore it in multiplication?! 1×0 equals zero, why not one? What is the reason? He answered himself: There is no inevitable reason, we are not forced. Humans have lived throughout their ages without zero, and it did not mean anything to them. Even when we were unable to devise any result that fits our theorems for the quotient of one by zero, then we admitted and said unknown, and ignored it, but we ignored the logic that a thousand pieces of evidence may not prove me right, and one proof that proves me wrong. Not doing our math tables in the case of division, blowing them up completely, and with that, we decided to go ahead and built everything on that foundation. We have separated the arithmetic tables in detail at our will, to fit our calculations, and somehow separate the whole universe around us to fit these tables, despite their obvious flaws. And if we decide that the result of one multiplied by zero is one instead of zero, and we reconstruct the whole world on this basis, what will happen? He answered himself: Nothing, we will also succeed, the world, our software, our thoughts, our dealings, and everything around us will be reset according to the new arithmetic tables. After a few hundred years, humans will no longer be able to understand that one multiplied by zero equals zero, but that it must be one because everything is built on this basis.

Love! How many legends were organized for it? It was said that it is the most mysterious human feeling that pushes us to do things we are not ready for and heedless of us. Despite the reality, and the difficulties, we do the impossible, and in the name of love, we do miracles. Just legends but the truth is that history did not mention that any miracle has happened thanks to love. Myths, of which there is no use but our consolation, and the justification of our blind rush behind unjustified, incomprehensible feelings, to do what we were not ready to do, and then we pay the price with a reassuring conscience, and with a comfortable mind, in the name of love. If we analyze these feelings, love, anger, hate, tranquility, fear, we will find that they are another face of pain, just chemical reactions inside our bodies, and hormones controlled by our mind, it decides when to kindle the fire of love in us, and when to make hate blind us. If you know how to motivate the mind to produce the hormone needed to produce the desired emotions, then you do not have to talk about anything anymore. It is all your emotions, which are yours. This inevitably makes human feelings subject to causation in the universe, unless our feelings are from another world, not causal. Therefore, the most magical words remain, those that come out of the mouth of a lover describing his love for his lover, “I love you without reason.” This is the impossibility desired, and in the subconscious, these words have charm and glamour, and the tongue of the lover says, “My love for you is not from this causal world, neither the color of your hair, nor your eyes, nor your body, nor your sweet voice, nor your way of speaking, nor anything that you possess is a reason why I love you, because my love for you is not causal, does not belong to this world.” A lie loved by the mind of the lovers, a legend among the millions which says, that nothing in this world can anticipate the feelings and moods of human beings before they occur, and more precisely, the private feelings and fluctuations, of an individual, to be precise, and not just of a large group of people, the more we try to customize it, the more difficult it becomes. And where the indicators of the collective mind, the demagogue, can give us an idea of the general direction and the future fluctuations of a society or group of people, not because of a weakness in the lines of defense of feelings, but rather because we know that the mob, the collective mind, and the herd, will force many to follow it, even if it violates what they feel, what they want at their core. The mind is designed for survival, and you know that survival’s chances are stronger with the stronger group, the more number, it will secrete all the necessary hormones, to force you to follow the herd. However, the feelings assigned to a particular person remain an impossible task, so many people are able to deceive each other by showing signs of expected trends and fluctuations that contradict the reality of what they feel. Humans and scientists have treated it as something unpredictable, coming from another world, a curse on science, as if it were a whiff of a magical spell cast on us from the immemorial. But in fact, emotions are causal, and every cause has a causative. Like everything else in this world, the laws of chaos and randomness apply to them. They can be accurately predicted, formulated into mathematical equations, and even manipulated. All it takes is to have something that contains all the cosmic events, a number we did not imagine, starting with the flutter of a butterfly, a breath of air, temperatures across the universe, a word a man says to his son, a donkey’s kick, a rabbit’s jump, and ending with the movement of stars and planets, and cosmic explosions, and beyond, and able to deal with them, and with the hierarchical possibilities of their occurrence.

The development of quantum mechanics in the late 1920s expanded the classical notion of fields in a way that would have shocked Newtonian physicists. Quantum fields do not exist physically in space-time like the classically inferred gravitational and electromagnetic fields. Instead, quantum fields specify only probabilities for strange, ghostlike particles as they manifest in space-time. Although quantum fields are mathematically similar to classical fields, they are more difficult to understand because, unlike classical fields, they exist outside the usual boundaries of space-time. This gives the quantum field a peculiar nonlocal character, meaning the field is not located in a given region of space and time. With a nonlocal phenomenon, what happens in region A instantaneously influences what occurs in region B, and vice versa, without any energy being exchanged between the two regions. Such a phenomenon would be impossible according to classical physics, and yet nonlocality has been dramatically and convincingly revealed in modern physics experiments. In fact, those experiments are independent of the present formulation of quantum mechanics, which means that any future theory of nature must also embody the principle of nonlocality. We’ll return to nonlocality again in chapter 16. Consciousness Fields Just as the individual is not alone in the group, nor any one in society alone among the others, so man is not alone in the universe. —Claude Levi-Strauss The idea that consciousness may be fieldlike is not new.2 William James wrote about this idea in 1898, and more recently the British biologist Rupert Sheldrake proposed a similar idea with his concept of morphogenetic fields.3 The conceptual roots of field consciousness can be traced back to Eastern philosophy, especially the Upanishads, the mystical scriptures of Hinduism, which express the idea of a single underlying reality embodied in “Brahman,” the absolute Self. The idea of field consciousness suggests a continuum of nonlocal intelligence, permeating space and time. This is in contrast with the neuroscience-inspired, Newtonian view of a perceptive tissue locked inside the skull.

Silly Putty?

More radically, how can we be sure that the source of consciousness lies within our bodies at all? You might think that because a blow to the head renders one unconscious, the ‘seat of consciousness’ must lie within the skull. But there is no logical reason to conclude that. An enraged blow to my TV set during an unsettling news programme may render the screen blank, but that doesn’t mean the news reader is situated inside the television. A television is just a receiver: the real action is miles away in a studio. Could the brain be merely a receiver of ‘consciousness signals’ created somewhere else? In Antarctica, perhaps? (This isn’t a serious suggestion – I’m just trying to make a point.) In fact, the notion that somebody or something ‘out there’ may ‘put thoughts in our heads’ is a pervasive one; Descartes himself raised this possibility by envisaging a mischievous demon messing with our minds. Today, many people believe in telepathy. So the basic idea that minds are delocalized is actually not so far-fetched. In fact, some distinguished scientists have flirted with the idea that not all that pops up in our minds originates in our heads. A popular, if rather mystical, idea is that flashes of mathematical inspiration can occur by the mathematician’s mind somehow ‘breaking through’ into a Platonic realm of mathematical forms and relationships that not only lies beyond the brain but beyond space and time altogether. The cosmologist Fred Hoyle once entertained an even bolder hypothesis: that quantum effects in the brain leave open the possibility of external input into our thought processes and thus guide us towards useful scientific concepts. He proposed that this ‘external guide’ might be a superintelligence in the far cosmic future using a subtle but well-known backwards-in-time property of quantum mechanics in order to steer scientific progress.

More radically, how can we be sure that the source of consciousness lies within our bodies at all? You might think that because a blow to the head renders one unconscious, the ‘seat of consciousness’ must lie within the skull. But there is no logical reason to conclude that. An enraged blow to my TV set during an unsettling news programme may render the screen blank, but that doesn’t mean the news reader is situated inside the television. A television is just a receiver: the real action is miles away in a studio. Could the brain be merely a receiver of ‘consciousness signals’ created somewhere else? In Antarctica, perhaps? (This isn’t a serious suggestion – I’m just trying to make a point.) In fact, the notion that somebody or something ‘out there’ may ‘put thoughts in our heads’ is a pervasive one; Descartes himself raised this possibility by envisaging a mischievous demon messing with our minds. Today, many people believe in telepathy. So the basic idea that minds are delocalized is actually not so far-fetched. In fact, some distinguished scientists have flirted with the idea that not all that pops up in our minds originates in our heads. A popular, if rather mystical, idea is that flashes of mathematical inspiration can occur by the mathematician’s mind somehow ‘breaking through’ into a Platonic realm of mathematical forms and relationships that not only lies beyond the brain but beyond space and time altogether. The cosmologist Fred Hoyle once entertained an even bolder hypothesis: that quantum effects in the brain leave open the possibility of external input into our thought processes and thus guide us towards useful scientific concepts. He proposed that this ‘external guide’ might be a superintelligence in the far cosmic future using a subtle but well-known backwards-in-time property of quantum mechanics in order to steer scientific progress.

Each and every person have always different knowledge but most of time the ideal is always same.

Allison Coudert has argued that Leibniz was almost certainly influenced by Jewish Kabbalah, with its own esoteric use of combinatorial procedures for exploring the mysteries of the Godhead through gematria and other arithmosophical theurgies.7 Despite the arcane sources of his inspiration, however, Leibniz was not alone among mainstream early modern philosophers in the quest for a “science of sciences,” nor was he alone among moderns in his quest for secret knowledge, as evidenced, for example, by Newton's vast writings on alchemy. Even Descartes, who argued for a rigid distinction between mind and matter, had insisted on their practical unity at the level of “the living.” As Deleuze puts it in his preface to Malfatti's work, “Beyond a psychology disincarnated in thought, and a physiology mineralized in matter,” even Descartes believed in the possibility of a unified field “where life is defined as knowledge of life, and knowledge as life of knowledge” (MSP, 143). This is the unity, Deleuze asserts, to which Malfatti's account of mathesis as a “true medicine” aspires. Deleuze explicitly refers to mathesis universalis at several key points in Difference and Repetition, particularly in connection with what he calls the “esoteric” history of the calculus (DR, 170). As Christian Kerslake has argued, Deleuze's reference here is not merely to obscure or unusual interpretations of mathematics, but to the decisive significance of Josef Hoëné-Wronski, a Polish French émigré who had elaborated a “messianism” of esoteric knowledge based on the idea that the calculus represented access to the total range of cosmic periodicities and rhythmic imbrications.8 The full implications

Happiness defies all laws of mathematical operations. The more you divide it , the more it multiplies. Then why do we find it so difficult to be happy. Is it because of the hustles of our daily or because of the futility of our aggressive endeavours. Lack of happiness can be traced back to 4 reasons. 1. Making relentless comparisons 2. Taking failure at heart 3. Chasing materialistic goals 4. Being inordinately futuristic Happiness is not a destination but a spiritual journey wherein the actions and soul unite with each other to actualize the purpose of our existence.

The point is that I loved math with a passion. I loved the order, the clarity of it, the absolute in it. And I think that my students felt that, for me, something more than mere math was involved, an attitude toward life itself. I liked a straight answer to a straight question, in just the way that I felt the beauty of a perfect equation or, even more, a geometric figure.

the Lord creates, but always for a purpose. Even color and music and beauty serve a purpose—to inspire awe and turn our eyes to the Lord. And creation operates according to laws—most of them mathematical, by the way. So embracing discipline is a way of embracing God.

You ask me if an ordinary person, by studying hard, would get to be able to imagine these things like I imagine. Of course. I was an ordinary person who studied hard. There's no miracle people — it just happens, they got interested in this thing and they learned all this stuff. They're just people. There's no talent, a special miracle ability to understand quantum mechanics or a miracle ability to imagine electromagnetic fields that comes without practice and reading and learning and study. So, if you say you take an ordinary person who's willing to devote a great deal of time and study and work and thinking and mathematics and time, then he's become a scientist.

Nothing begins as a single thing; everything starts as a package of things.

Naperville Community Unit School District 203 in Illinois, profiled in John J. Ratey’s book Spark, is a particularly inspiring example of how physical movement enhances cognitive ability. School officials implemented a district-wide PE curriculum that focuses on fitness as opposed to sports, and then had students take some of their hardest subjects after exercising. As a result, Naperville students achieved stunning results on the Trends in International Mathematics and Science Study (TIMSS), a standardized test administered every four years to students worldwide. In 1999 it was given in thirty-eight countries31, and Naperville students scored first in the world in science, and sixth in math—behind only math superstars such as Singapore, Korea, Taiwan, Hong Kong, and Japan. This is remarkable, since Naperville students are a cross-sampling of ordinary American students. The stunning results from Naperville echo other studies suggesting a strong link between exercise and learning. Researchers from Harvard32 and other universities reported in 2009 that the more physical fitness tests children passed, the better they did on academic tests.

Numerous research studies (Silver, 1994) have shown that when students are given opportunities to pose mathematics problems, to consider a situation and think of a mathematics question to ask of it—which is the essence of real mathematics—they become more deeply engaged and perform at higher levels.

In a TED talk watched by over a million people, Wolfram (2010) proposes that working on mathematics has four stages: Posing a question Going from the real world to a mathematical model Performing a calculation Going from the model back to the real world, to see if the original question was answered The first stage involves asking a good question of some data or a situation—the first mathematical act that is needed in the workplace.

The game is played by partners. Each child has a blank 100 grid. The first partner rolls two number dice. The numbers that come up are the numbers the child uses to make an array on their 100 grid. They can put the array anywhere on the grid, but the goal is to fill up the grid to get it as full as possible. After the player draws the array on their grid, she writes in the number sentence that describes the grid. The game ends when both players have rolled the dice and cannot put any more arrays on the grid

A particularly inspiring story was told by a mother whose autistic son just wanted to play with shapes and shadows. He was failing in his “Special Ed” program, where he was being forced to do things he didn’t want to do. She found that the more she encouraged him to do what he enjoyed, the more his shell cracked open. And when she followed his interests and made resources available to him to support those interests, he began to talk and to thrive. When he was three years old, she was told that he would never talk. At eleven years of age, he enrolled in a university and began studying mathematics.

Such results should prompt educators to abandon the traditional fixed ideas of the brain and learning that currently fill schools—ideas that children are smart or dumb, quick or slow. If brains can change in three weeks, imagine what can happen in a year of math class if students are given the right math materials and they receive positive messages about their potential and ability.

The modernist reaction to the Enlightenment came in the aftermath of the Industrial Revolution, whose brutalizing effects revealed that modern life had not become as mathematically perfect, or as certain, rational, or enlightened, as advances in the eighteenth century had led people to expect. Truth was not always beautiful, nor was it always readily recognized. It was frequently hidden from view. Moreover, the human mind was governed not only by reason but also by irrational emotion. As astronomy and physics inspired the Enlightenment, so biology inspired Modernism. Darwin’s 1859 book On the Origin of Species introduced the idea that human beings are not created uniquely by an all-powerful God but are biological creatures that evolved from simpler animal ancestors. In his later books, Darwin elaborated on these arguments and pointed out that the primary biological function of any organism is to reproduce itself. Since we evolved from simpler animals, we must have the same instinctual behavior that is evident in other animals. As a result, sex must also be central to human behavior. This new view led to a reexamination in art of the biological nature of human existence, as evident in Édouard Manet’s Déjeuner sur l’Herbe of 1863, perhaps the first truly modernist painting from both a thematic and stylistic point of view. Manet’s painting, at once beautiful and shocking in its depiction, reveals a theme central to the modernist agenda: the complex relationship between the sexes and between fantasy and reality.

the researchers found that the students who memorized more easily were not higher achieving; they did not have what the researchers described as more “math ability,” nor did they have higher IQ scores (Supekar et al., 2013). The

long time, step by step, to work through the same process or idea from several approaches. But once you really understand it and have the mental perspective to see it as a whole, there is often a tremendous mental compression. You can file it away, recall it quickly and completely when you need it, and use it as just one step in some other mental process. The insight that goes with this compression is one of the real joys of mathematics. (Thurston, 1990)

The brain researchers concluded that automaticity should be reached through understanding of numerical relations, achieved through thinking about number strategies (Delazer et al., 2005).

The problem with academia is that it is about being good at remembering things like chemical formulae and theories, because that is what you have to regurgitate. But children are not allowed to learn through experimenting and experience. This is a great pity. You need both.” One of the most powerful aspects of the Dyson story is that it evokes a point that was made in chapter 7; namely, that technological change is often driven by the synergy between practical and theoretical knowledge. One of the first things Dyson did when he had the insight for a cyclone cleaner was to buy two books on the mathematical theory of how cyclones work. He also went to visit the author of one of those books, an academic named R. G. Dorman.22 This was hugely helpful to Dyson. It allowed him to understand cyclone dynamics more fully. It played a role in directing his research and gave him a powerful background on the mathematics of separation efficiency. But it was by no means sufficient. The theory was too abstract to lead him directly to the precise dimensions that would deliver a functional vacuum cleaner. Moreover, as Dyson iterated his device, he discovered that the theory had flaws. Dorman’s equation predicted that cyclones would only be able to remove fine dust down to a lower limit of 20 microns. But Dyson quickly broke through this theoretical limit. By the end, his cyclone could separate dust smaller than 0.3 micron (this is approximately the size of the particles in cigarette smoke). Dyson’s practical engagement with the problem had forced a change in the theory. And this is invariably how progress happens. It is an interplay between the practical and the theoretical, between top-down and bottom-up, between creativity and discipline, between the small picture and the big picture. The crucial point—and the one that is most dramatically overlooked in our culture—is that in all these things, failure is a blessing, not a curse. It is the jolt that inspires creativity and the selection test that drives evolution.

But he needed to be certain before committing to something so—the word, certain, arrested his thoughts. A person can’t be absolutely certain about anything, not certainty in the sense of a mathematical proof. He wasn’t certain about Kate. He saw her, observed her, wanted to be with her. Somehow, he just knew. For reasons already set in his heart, the way he was wired, Josh knew Kate was a person he wanted in his life. She was the proof. Would it be the same way with God?

All the art experts, all the big galleries, if not maybe quite all of the humble folk who look at them, agree Jackson Pollock’s splatter paintings do indeed count as great art. And JP intended it to be art too. But what’s curious about most of the most radical artists of the post-Second World War period is that they came from nowhere to prominence with the support of . . . the CIA! Yes, the American secret services actively promoted (through books, funding schemes, newspapers and of course galleries) radical art as part of a labyrinthine strategy to undermine the Soviet Union. This was all part of a special strategy to win over intellectuals – including philosophers – described as ‘the battle for Picasso’s mind’ by one former CIA agent, Thomas Braden, in a television interview in the 1970s. Tom Braden was responsible for dispensing money under the heading Congress for Cultural Freedom. Naturally, most of the people he gave money to had no idea that the funds, and hence the artistic direction, actually came from the CIA. Intellectuals and great artists, after all, hate being told what to think. And what was the communist empire doing meanwhile? They were promoting, through galleries, public funding and so on, a very different kind of art supposedly reflecting communist political values. ‘Soviet realism’ was a kind of reaction to ‘Western Impressionism’ (all those dotty – pointilliste the art-experts call them – landscapes and swirling, subjective shapes) and ensured that people in the paintings looked like people, decent, hard-working types too, and what’s more were doing worthy things – like making tractors or (at least) looking inspirationally at the viewer. When Soviet art wasn’t figurative (as this sort of stuff is called), it was very logical and mathematical, full of precise geometrical shapes and carefully weighted blocks of colour.

As he learned more math, Brodt made the wonder-inspiring observation that mathematical laws seemed to be Someone's intention rather than just accidents in many concepts: infinity, unity being totality, irrational numbers in general and pi in particular as it illustrates such disparate occurrences as the relationship of height to base perimeter in the Great Pyramid of Giza and the course of any meandering river (over a surface smoothed for consistency). There was also the Fibonacci Sequence, that looping string of addends which, with their sums, describes the spirals on a nautilus shell, the distribution of leaves around a tree branch, and the genealogy of ants and bees. It all seemed too orderly, too regular and consistent to have occurred by chance. So many things in the world appeared as blotches, smears, or random spikes that these mathematically explained phenomena were extraordinary--he wanted to say mystical, but he wouldn't want to be caught using that word.

Unexpected intrusions of beauty in the timeline of your life sums up the mathematically operated Heisenberg's Uncertainty Principle.

Tensors represent the pinnacle of mathematical formalism. -- Albert Einstein

The CGPA system in the honours and master's levels seems erroneous, contradictory and discriminatory. If a CSE student writes his answers correctly, he gets full marks. If all the answers are correct, he even gets A+. On the other hand, a literature student never gets A+ even if all his answers are correct and to the points! This is nothing but irony that the teachers inspire the students of Mathematics, Business Administration to try harder to get A+ but the teachers of English and Bangla literature never inspire the students to study seriously to achieve A+! So, the students kind of know that the dream of getting A+ is never achievable. Sometimes, some teachers say that there is no 'perfect' answer in literature; that is why the students do not get A+. This idea is also flawed because it leads to another question- how much better answer should be considered as the best or perfect answer in literature? If there is no such thing as the best or perfect answer in literature, then why is it written in the syllabus that 4.00 means A+ for all the subjects including literature. In a word, the syllabus says that A+ in literature is achievable but the students never get it or I should say that the teachers never give A+ to the students! If a student gets 2 marks out of 2 by writing the answer- 1 + 1= 2, similarly a literature student deserves 5 marks out of 5 if he writes an answer without making any grammatical, spelling or such other mistakes. So, in my opinion, the solution is - if the CGPA system is same for all the departments, then there should be no discrimination in the marking system either. If it is not possible, there should be a new, separate or different CGPA system for the English and Bangla Language and Literature departments. Unfortunately, the same CGPA system is used differently in the different departments. Hence, it must be changed!

There is another remark to be made regarding the conditions of this unconscious work, which is, that it is not possible, or in any case not fruitful, unless it is first preceded and then followed by a period of conscious work. These sudden inspirations are never produced (and this is sufficiently proved already by the examples I have quoted) except after some days of voluntary efforts which appeared absolutely fruitless, in which one thought one had accomplished nothing, and seemed to be on a totally wrong track. These efforts, however, were not as barren as one thought; they set the unconscious machine in motion, and without them it would not have worked at all, and would not have produced anything.

Mathematics is a very broad and multidimensional subject that requires reasoning, creativity, connection making, and interpretation of methods; it is a set of ideas that helps illuminate the world; and it is constantly changing.

Every time a student makes a mistake in math, they grow a synapse.

The powerful thinkers are those who make connections, think logically, and use space, data, and numbers creatively.

The world was lifting itself up out of darkness and beginning to shine, and mathematics was how he could help. It was his contribution. It was what he could give, according to his abilities. He was lucky enough to live in the only country on the planet where human beings had seized the power to shape events according to reason, instead of letting things happen as they happened to happen, or allowing the old forces of superstition and greed to push people around. Here, and nowhere else, reason was in charge.

Bridging two cultures (Nigerian and American) and three professions and careers (Architecture, Business and Education) to literacy’s true freedom.

Maths should be practised, not memorized.

John von Neumann (1903–1957) was the second center of attraction at the Macy Conferences. A mathematical genius, he had written a classic treatise on quantum theory, was the originator of the theory of games, and became world famous as the inventor of the digital computer (inspired by Turing's pioneering theoretical work).

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.

To try to reduce democracy to technocracy, and to expel from it the Gospel inspiration together with all faith in the supra-material, supra-mathematical, and supra-sensory realities, would be to try to deprive it of its very blood. Democracy can only live on Gospel inspiration.

This concept is central to understanding what distinguishes the Arrowsmith approach: cognitive exercises do not teach content or skill in, say, mathematics; the aim is to forge new neural pathways in the brain so that later, when math is taught, number concepts actually make sense.

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better if for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.