Einstein Math Quotes

The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.

In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began.

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.

Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy -- it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head.

I am encouraged as I look at some of those who have listened to their "different drum": Einstein was hopeless at school math and commented wryly on his inadequacy in human relations. Winston Churchill was an abysmal failure in his early school years. Byron, that revolutionary student, had to compensate for a club foot; Demosthenes for a stutter; and Homer was blind. Socrates couldn't manage his wife, and infuriated his countrymen. And what about Jesus, if we need an ultimate example of failure with one's peers? Or an ultimate example of love?

Come back down here, heat supply,” I commanded. “I’m going to close my eyes and you are going to tell me about math so I can fall asleep. Tell me some theorems. Is that what you called them? Tell me how Einstein knew e equals mc squared. And start with once upon a time . . . okay?” “You’re a little bossy, you know that?” “I know. I have to be. It’s to make up for not being born with a calculator. Now share your wisdom, Infinity.” “Once upon a time—” I giggled and Finn immediately shushed me, continuing on with his “story.

The importance of C.F. Gauss for the development of modern physical theory and especially for the mathematical fundament of the theory of relativity is overwhelming indeed; also his achievement of the system of absolute measurement in the field of electromagnetism. In my opinion it is impossible to achieve a coherent objective picture of the world on the basis of concepts which are taken more or less from inner psychological experience.

As the story goes, Albert Einstein’s wife Elsa remarked, upon hearing that a telescope at the Mount Wilson Observatory was needed to determine the shape of space-time: “Oh, my husband does this on the back of an old envelope.

As Einstein once wrote (more ringingly in German than in this English translation by one of us [DG]) to honor Isaac Newton: Look unto the stars to teach us How the master’s thoughts can reach us Each one follows Newton’s math Silently along its path.

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell. ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.

Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of tiny particles suspended in a liquid: Einstein showed that these movements satisfied a clear statistical law. This was like a conjuring trick, easy when explained: before it, decent scientists could still doubt the concrete existence of atoms and molecules: this paper was as near to a direct proof of their concreteness as a theoretician could give. The third paper was the special theory of relativity, which quietly amalgamated space, time, and matter into one fundamental unity. This last paper contains no references and quotes to authority. All of them are written in a style unlike any other theoretical physicist's. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.

Literature, music, law, politics, science, math: Our culture is an edifice built of externalized memories.

Math was nature’s playbook.

Then again, Einstein (pretty good at math) was also quite clear when he concluded, There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.

Albert Einstein had Max Talmud, his first mentor. It was Max who introduced a ten-year-old Einstein to key texts in math, science, and philosophy. Max took one meal a week with the Einstein family for six years while guiding young Albert. No one is self-made.

As Albert Einstein said years ago, “The significant problems we face today cannot be solved at the same level of thinking we were at when we created them.” Developing the capacity to deal with the challenge of living in a stressful, ever-changing world is now more important than ever.

But by 1912, Einstein had come to appreciate that math could be a tool for discovering—and not merely describing—nature’s laws. Math was nature’s playbook. “The central idea of general relativity is that gravity arises from the curvature of spacetime,” says physicist James Hartle. “Gravity is geometry.

On the Electrodynamics of Moving Bodies” Now let’s look at how Einstein articulated all of this in the famous paper that the Annalen der Physik received on June 30, 1905. For all its momentous import, it may be one of the most spunky and enjoyable papers in all of science. Most of its insights are conveyed in words and vivid thought experiments, rather than in complex equations. There is some math involved, but it is mainly what a good high school senior could comprehend. “The whole paper is a testament to the power of simple language to convey deep and powerfully disturbing ideas,” says the science writer Dennis Overbye.

An extreme representative of this view is Ted Kaczynski, infamously known as the Unabomber. Kaczynski was a child prodigy who enrolled at Harvard at 16. He went on to get a PhD in math and become a professor at UC Berkeley. But you’ve only ever heard of him because of the 17-year terror campaign he waged with pipe bombs against professors, technologists, and businesspeople. In late 1995, the authorities didn’t know who or where the Unabomber was. The biggest clue was a 35,000-word manifesto that Kaczynski had written and anonymously mailed to the press. The FBI asked some prominent newspapers to publish it, hoping for a break in the case. It worked: Kaczynski’s brother recognized his writing style and turned him in. You might expect that writing style to have shown obvious signs of insanity, but the manifesto is eerily cogent. Kaczynski claimed that in order to be happy, every individual “needs to have goals whose attainment requires effort, and needs to succeed in attaining at least some of his goals.” He divided human goals into three groups: 1. Goals that can be satisfied with minimal effort; 2. Goals that can be satisfied with serious effort; and 3. Goals that cannot be satisfied, no matter how much effort one makes. This is the classic trichotomy of the easy, the hard, and the impossible. Kaczynski argued that modern people are depressed because all the world’s hard problems have already been solved. What’s left to do is either easy or impossible, and pursuing those tasks is deeply unsatisfying. What you can do, even a child can do; what you can’t do, even Einstein couldn’t have done. So Kaczynski’s idea was to destroy existing institutions, get rid of all technology, and let people start over and work on hard problems anew. Kaczynski’s methods were crazy, but his loss of faith in the technological frontier is all around us. Consider the trivial but revealing hallmarks of urban hipsterdom: faux vintage photography, the handlebar mustache, and vinyl record players all hark back to an earlier time when people were still optimistic about the future. If everything worth doing has already been done, you may as well feign an allergy to achievement and become a barista.

As you know, there was a famous quarrel between Max Planck and Einstein, in which Einstein claimed that, on paper, the human mind was capable of inventing mathematical models of reality. In this he generalized his own experience because that is what he did. Einstein conceived his theories more or less completely on paper, and experimental developments in physics proved that his models explained phenomena very well. So Einstein says that the fact that a model constructed by the human mind in an introverted situation fits with outer facts is just a miracle and must be taken as such. Planck does not agree, but thinks that we conceive a model which we check by experiment, after which we revise our model, so that there is a kind of dialectic friction between experiment and model by which we slowly arrive at an explanatory fact compounded of the two. Plato-Aristotle in a new form! But both have forgotten something- the unconscious. We know something more than those two men, namely that when Einstein makes a new model of reality he is helped by his unconscious, without which he would not have arrived at his theories...But what role DOES the unconscious play?...either the unconscious knows about other realities, or what we call the unconscious is a part of the same thing as outer reality, for we do not know how the unconscious is linked with matter.

It was a perfect school for Einstein. The teaching was based on the philosophy of a Swiss educational reformer of the early nineteenth century, Johann Heinrich Pestalozzi, who believed in encouraging students to visualize images. He also thought it important to nurture the “inner dignity” and individuality of each child. Students should be allowed to reach their own conclusions, Pestalozzi preached, by using a series of steps that began with hands-on observations and then proceeded to intuitions, conceptual thinking, and visual imagery. 56 It was even possible to learn—and truly understand—the laws of math and physics that way. Rote drills, memorization, and force-fed facts were avoided.

10. About these coincidences, the data and mathematicians are clear: Such things happen all the time. Then again, Einstein (pretty good at math) was also quite clear when he concluded, There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle. 11. I’m going with B, everything.

Let’s be honest. You’re not Einstein, but don’t let assholes like that teacher make you feel stupid. You’re plenty smart, and good at other stuff. You know that, right?” “Yeah.” “Don’t just say yeah like a fucking mope. Let me hear you say it. Say you know you’re good at stuff.” “I’m good at stuff.” “That’s right. You’re good at stuff. Fuck that math teacher,” he said.

Imagine waking up tomorrow and discovering that all the world’s ink had become invisible and all our bytes had disappeared. Our world would immediately crumble. Literature, music, law, politics, science, math: Our culture is an edifice built of externalized memories. If memory is our means of preserving that which we consider most valuable, it is also painfully linked to our own transience. When we die, our memories die with us. In a

Grossmann went home to think about the question. After consulting the literature, he came back to Einstein and recommended the non-Euclidean geometry that had been devised by Bernhard Riemann.11 Riemann (1826–1866) was a child prodigy who invented a perpetual calendar at age 14 as a gift for his parents and went on to study in the great math center of Göttingen, Germany, under Carl Friedrich Gauss, who had been pioneering the geometry of curved surfaces. This was the topic Gauss assigned to Riemann for a thesis, and the result would transform not only geometry but physics.

Einstein was no great mathematician. He struggled with maths. He says this himself. In 1943 he replied in the following way to a nine-year-old child with the name of Barbara who wrote to him about her difficulties with the subject: ‘Don’t worry about experiencing difficulties with maths, I can assure you that my own problems are even more serious!’2 It seems like a joke, but Einstein was not kidding. With mathematics, he needed help: he had it explained to him by patient fellow students and friends, such as Marcel Grossman. It was his intuition as a physicist that was prodigious.

Over the years, this revealing “Zurich Notebook” has been dissected and analyzed by a team of scholars including Jürgen Renn, John D. Norton, Tilman Sauer, Michel Janssen, and John Stachel.17 In it Einstein pursued a two-fisted approach. On the one hand, he engaged in what was called a “physical strategy,” in which he tried to build the correct equations from a set of requirements dictated by his feel for the physics. At the same time, he pursued a “mathematical strategy,” in which he tried to deduce the correct equations from the more formal math requirements using the tensor analysis that Grossmann and others recommended.

The fundamental problem with learning mathematics is that while the number sense may be genetic, exact calculation requires cultural tools—symbols and algorithms—that have been around for only a few thousand years and must therefore be absorbed by areas of the brain that evolved for other purposes. The process is made easier when what we are learning harmonizes with built-in circuitry. If we can’t change the architecture of our brains, we can at least adapt our teaching methods to the constraints it imposes. For nearly three decades, American educators have pushed “reform math,” in which children are encouraged to explore their own ways of solving problems. Before reform math, there was the “new math,” now widely thought to have been an educational disaster. (In France, it was called les maths modernes and is similarly despised.) The new math was grounded in the theories of the influential Swiss psychologist Jean Piaget, who believed that children are born without any sense of number and only gradually build up the concept in a series of developmental stages. Piaget thought that children, until the age of four or five, cannot grasp the simple principle that moving objects around does not affect how many of them there are, and that there was therefore no point in trying to teach them arithmetic before the age of six or seven.

The Roman general wanted to spare Archimedes, because he was so valuable—sort of like the Einstein of the ancient world—but some stupid Roman soldier killed him.” “There you go again,” Hazel muttered. “Stupid and Roman don’t always go together, Leo.” Frank grunted agreement. “How do you know all this, anyway?” he demanded. “Is there a Spanish tour guide around here?” “No, man,” Leo said. “You can’t be a demigod who’s into building stuff and not know about Archimedes. The guy was seriously elite. He calculated the value of pi. He did all this math stuff we still use for engineering. He invented a hydraulic screw that could move water through pipes.” Hazel scowled. “A hydraulic screw. Excuse me for not knowing about that awesome achievement.” “He also built a death ray made of mirrors that could burn enemy ships,” Leo said. “Is that awesome enough for you?” “I saw something about that on TV,” Frank admitted. “They proved it didn’t work.” “Ah, that’s just because modern mortals don’t know how to use Celestial bronze,” Leo said. “That’s the key. Archimedes also invented a massive claw that could swing on a crane and pluck enemy ships out of the water.” “Okay, that’s cool,” Frank admitted. “I love grabber-arm games.” “Well, there you go,” Leo said. “Anyway, all his inventions weren’t enough. The Romans destroyed his city. Archimedes was killed.

Albert Einstein, considered the most influential person of the 20th century, was four years old before he could speak and seven before he could read. His parents thought he was retarded. He spoke haltingly until age nine. He was advised by a teacher to drop out of grade school: “You’ll never amount to anything, Einstein.” Isaac Newton, the scientist who invented modern-day physics, did poorly in math. Patricia Polacco, a prolific children’s author and illustrator, didn’t learn to read until she was 14. Henry Ford, who developed the famous Model-T car and started Ford Motor Company, barely made it through high school. Lucille Ball, famous comedian and star of I Love Lucy, was once dismissed from drama school for being too quiet and shy. Pablo Picasso, one of the great artists of all time, was pulled out of school at age 10 because he was doing so poorly. A tutor hired by Pablo’s father gave up on Pablo. Ludwig van Beethoven was one of the world’s great composers. His music teacher once said of him, “As a composer, he is hopeless.” Wernher von Braun, the world-renowned mathematician, flunked ninth-grade algebra. Agatha Christie, the world’s best-known mystery writer and all-time bestselling author other than William Shakespeare of any genre, struggled to learn to read because of dyslexia. Winston Churchill, famous English prime minister, failed the sixth grade.

Therein lies the key, I think, to Einstein’s brilliance and the lessons of his life. As a young student he never did well with rote learning. And later, as a theorist, his success came not from the brute strength of his mental processing power but from his imagination and creativity. He could construct complex equations, but more important, he knew that math is the language nature uses to describe her wonders. So he could visualize how equations were reflected in realities—how the electromagnetic field equations discovered by James Clerk Maxwell, for example, would manifest themselves to a boy riding alongside a light beam. As he once declared, “Imagination is more important than knowledge.”6

I'm not a geius guy, even and Albert Einstein isn't and Tesla, nobody is genius. From where you will know what's the IQ for Albert or Tesla in their time there wasn't such test and how such test can show how clever are you in case that the most questions are math, physics and mainly this how this two subjects will show that you are clever or dumb?? I strongly doubt about this if I know the answer sof the test and I fill it right so I must be the world clever man? No, I don't think so - That's bullshit! That I have written 8 books and now I'm working on some other books this doesn't make me clever, the most stuff are just search from the internet and put, the other is thoughts from me. Like thinking on some questions and that's all!

A more complex way to understand this is the method used by Hermann Minkowski, Einstein’s former math teacher at the Zurich Polytechnic. Reflecting on Einstein’s work, Minkowski uttered the expression of amazement that every beleaguered student wants to elicit someday from condescending professors. “It came as a tremendous surprise, for in his student days Einstein had been a lazy dog,” Minkowski told physicist Max Born. “He never bothered about mathematics at all.”63 Minkowski decided to give a formal mathematical structure to the theory. His approach was the same one suggested by the time traveler on the first page of H. G. Wells’s great novel The Time Machine, published in 1895: “There are really four dimensions, three which we call the three planes of Space, and a fourth, Time.” Minkowski turned all events into mathematical coordinates in four dimensions, with time as the fourth dimension. This permitted transformations to occur, but the mathematical relationships between the events remained invariant. Minkowski dramatically announced his new mathematical approach in a lecture in 1908. “The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength,” he said. “They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”64 Einstein, who was still not yet enamored of math, at one point described Minkowski’s work as “superfluous learnedness” and joked, “Since the mathematicians have grabbed hold of the theory of relativity, I myself no longer understand it.” But he in fact came to admire Minkowski’s handiwork and wrote a section about it in his popular 1916 book on relativity.

Einstein was distrustful of elaborate mathematics, odd as that sounds for a mathematical physicist. There was, Einstein considered, too much math around, and one could waste far too much time on it. His talent, despite the image in popular culture, lay not so much in mathematics – which he always found difficult – but in exceptional clarity of conceptual thinking. Einstein was never seduced by the easy flow of equations: he came to the hard labor of the math only when convinced the quest would be worth the effort.

Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell's equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein's field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul Dirac once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that "there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world.

String theory is potentially the next and final step in this progression. In a single framework, it handles the domains claimed by relativity and the quantum. Moreover, and this is worth sitting up straight to hear, string theory does so in a manner that fully embraces all the discoveries that preceded it. A theory based on vibrating filaments might not seem to have much in common with general relativity's curved spacetime picture of gravity. Nevertheless, apply string theory's mathematics to a situation where gravity matters but quantum mechanics doesn't (to a massive object, like the sun, whose size is large) and out pop Einstein's equations. Vibrating filaments and point particles are also quite different. But apply string theory's mathematics to a situation where quantum mechanics matters but gravity doesn't (to small collections of strings that are not vibrating quickly, moving fast, or stretched long; they have low energy-equivalently, low mass- so gravity plays virtually no role) and the math of string theory morphs into the math of quantum field theory.

With such an illustrious reputation, it would be easy to assume Einstein rarely made mistakes—but that is not the case. To begin with, his development was described as “slow,” and he was considered to be a below-average student.16 It was apparent from an early age that his way of thinking and learning was different from the rest of the students in his class. He liked working out the more complicated problems in math, for example, but wasn’t very good at the “easy” problems.17 Later on in his career, Einstein made simple mathematical mistakes that appeared in some of his most important work. His numerous mistakes include seven major gaffes on each version of his theory of relativity, mistakes in clock synchronization related to his experiments, and many mistakes in the math and physics calculations used to determine the viscosity of liquids.18 Was Einstein considered a failure because of his mistakes? Hardly. Most importantly he didn’t let his mistakes stop him. He kept experimenting and making contributions to his field. He is famously quoted as having said, “A person who never made a mistake never tried anything new.” What’s more, no one remembers him for his mistakes—we only remember him for his contributions.

While standing above the world's largest particle accelerator, men and women like Philip could reveal the brilliant math they had been forging behind closed doors - mathematical physics attempting to answer the only question he and his colleagues found worth asking, the question that had eluded even Einstein: How do we unify the four forces of the universe into one law?

humans frequently believe things that they believe to be true but aren’t true, such as psychic healing and the one you call Einstein failing math and the foods you call Twinkies surviving on the shelf indefinitely.

The Polytechnic was a new sort of college dedicated to producing teachers and professors for various math or scientific disciplines, and it was one of the few universities in Europe to grant women degrees.

For the man on the street, science and math sound too and soulless. It is hard to appreciate their significance Most of us are just aware of Newton's apple trivia and Einstein's famous e mc2. Science, like philosophy, remains obscure and detached, playing role in our daily lives. There is a general perception that science is hard to grasp and has direct relevance to what we do. After all, how often do we discuss Dante or Descartes over dinner anyway? Some feel it to be too academic and leave it to the intellectuals or scientists to sort out while others feel that such topics are good only for academic debate. The great physicist, Rutherford, once quipped that, "i you can't explain a complex theory to a bartender, the theory not worth it" Well, it could be easier said than done (applications of tools

I reviewed some of his articles and knew Albert couldn’t manage all those mathematical calculations on his own. You were always better at math than him. Than most of us, actually.” I

From kindergarten through senior year of high school, Evan attended Crossroads, an elite, coed private school in Santa Monica known for its progressive attitudes. Tuition at Crossroads runs north of $ 22,000 a year, and seemingly rises annually. Students address teachers by their first names, and classrooms are named after important historical figures, like Albert Einstein and George Mead, rather than numbered. The school devotes as significant a chunk of time to math and history as to Human Development, a curriculum meant to teach students maturity, tolerance, and confidence. Crossroads emphasizes creativity, personal communication, well-being, mental health, and the liberal arts. The school focuses on the arts much more than athletics; some of the school’s varsity games have fewer than a dozen spectators. 2 In 2005, when Evan was a high school freshman, Vanity Fair ran an exhaustive feature about the school titled “School for Cool.” 3 The school, named for Robert Frost’s poem “The Road Not Taken,” unsurprisingly attracts a large contingent of Hollywood types, counting among its alumni Emily and Zooey Deschanel, Gwyneth Paltrow, Jack Black, Kate Hudson, Jonah Hill, Michael Bay, Maya Rudolph, and Spencer Pratt. And that’s just the alumni—the parents of students fill out another page or two of who’s who A-listers. Actor Denzel Washington once served as the assistant eighth grade basketball coach, screenwriter Robert Towne spoke in a film class, and cellist Yo-Yo Ma talked shop with the school’s chamber orchestra.

Hubble’s work confirmed his math—and refuted Einstein’s general theory of relativity. Furthermore, he deduced, if the universe was expanding equally in all directions, it must have initiated in a massive explosion from a single point. This meant that the universe is not infinitely old; it has a certain age, and that the moment of creation—which British astronomer Fred Hoyle later mockingly called the “big bang”—was analogous to God’s first command: Let there be light.

Thomas Edison described himself as being “not at the head of my class, but the foot.” Einstein graduated fourth in his class of five physicists in 1900.54 Steve Jobs had a high school GPA of 2.65; Jack Ma, the founder of Alibaba (the Chinese equivalent of Amazon), took the gaokao (the Chinese national educational exam) and scored 19 out of 120 on a math section on his second try;55 and Beethoven had trouble adding figures and never learned to multiply or divide. Walt Disney was a below-average student and often fell asleep in class.56 Finally, Picasso could not remember the sequence of the letters in the alphabet and saw symbolic numbers as literal representations: a 2 as the wing of a bird or a 0 as a body.57

With a great deal of effort, seeking help from friends better versed in mathematics than himself, Einstein learns Riemann’s math—and writes an equation where R is proportional to the energy of matter. In words: spacetime curves more where there is matter. That is it.

Einstein further explained that the pull of gravity actually slows time down. So if you were an astronaut on a long interstellar trip and your spacecraft passed close to a black hole (where the gravitational force is massive), time would slow down significantly. When you got back to Earth you might have aged several years, but your spouse and your friends would have already lived into old age. We can observe this effect in a much smaller way right here on Earth. If you lived in Dubai on the top floor of Burj Khalifa, the world’s highest tower, time would pass slightly faster for you than it would for someone living on the ground floor, just because gravity affects each of you differently. While a variance like this is too small for the human body to detect, it’s measurable with today’s technology. It gets even more bizarre. The math indicates that in space-time, past, present, and future are all part of an integrated four-dimensional structure in which all of space and all of time exist perpetually.

Various factors, it seems, contribute to what we call genius and the forms it may take: speed of thought (at which von Neumann, by all accounts, was exceptional), depth of understanding (at which, according to Wigner, Einstein excelled), originality, creativity, and so forth. Sometimes, too, genius may be narrow in its focus – as in the case of Einstein or Ramanujan – while at other times, as illustrated by von Neumann, and to an even greater extent by some Renaissance figures such as Leonardo da Vinci, it can range over many subjects.

Government alone cannot restore the economy to health. Innovation is a primary driver of economic growth. One way of measuring inventive creativeness is through patent applications. Chetty, along with Alex Bell, Xavier Jaravel, Neviana Petkova, and John Van Reenen, studied the childhoods of more than a million patent holders, linking family income with elementary test scores and other key factors. Children at the top of their third-grade math class were the most likely to become inventors—but only if they also came from a high-income family. High-scoring children who were from low-income or minority families were no more likely to become inventors than affluent children with mediocre scores. Successful inventors were also less likely to be women, Black, Latino, or from the Southeast. Chetty called these failed inventors the “lost Einsteins.” “If women, minorities, and children from low-income families were to invent at the same rate as white men from high-income (top 20%) families, the rate of innovation in America would quadruple,” the authors said. The most ominous finding by Chetty and his colleagues was the effect of Covid-19 on educational progress. Using a popular math program called Zearn, the economists plotted the achievement of children from upper-income families versus those from lower incomes. When schools shut down and instruction switched to remote learning, children in the upper-income tier suffered a small drop in the lessons completed, but low-income children fell in a hole—a 60 percent drop in the rate of progress in learning math. The long-term economic prospects for those children are dire. “We’re likely to see further erosion of social mobility the longer this lasts,” Chetty said. The American dream was drifting farther out of reach for another generation.

Einstein completely failed to address the elephant in the room, namely that light – from its own perspective – isn’t in any inertial reference frame. We can therefore legitimately say that it obeys entirely different laws of physics – those of non-locality (singularities) rather than locality (spacetime) – and, in fact, actually the laws of pure mathematics. Light is the non-inertial container for all inertial reference frames, and ensures that they are all part of an absolute system, not a relative system. It imposes a principle of absolutism, not a principle of relativism!

Useless Effort Well Spent A topic that often comes up among seekers is the question of effort versus non-effort on the spiritual path (or no-path). Great teachers are divided on this. Some prescribe maximum effort in spiritual matters. Others say there is nothing to be done, that you are already That which you seek. Those who advocate effort admit their own realizations did not come as a result of their efforts. Those who say there is nothing to be done have usually realized this truth after diligent inquiry and meditation. What's a seeker to do (or not-do)? In thinking about this we might first inquire if effort and action are the same. Experience tells us no. Enjoyable activity often feels effortless, and doing nothing is sometimes difficult. Effort appears to be more a state of mind, a description of the way we do or not-do, not the what—more to do with thoughts about an action than the thing itself. Experience also tells us that when these thoughts of effort are absent—whether from activities or meditation—things generally go better. Which leaves the question of action versus non-action in spiritual matters. Should I practice meditation, read books, attend meetings, find teachers... or not? To do, or not to do? ... it may be that in the end Self-realization is all a matter of destiny, yet it does appear that yearning and intent might play a role. Again, observation teaches us that it's in the area of one's greatest interest and activity that providence is most visible—that opportunities materialize, coincidences occur, revelation happens. Einstein had no epiphanies about cubism. Picasso none about math. Which brings us back to the koan: "To do, or not to do?" The answer, I suppose, is "Yes." Act tirelessly without effort. Do nothing without being idle. Live life on the pinpoint of paradox and leave the rest to God. Advaita is right. You are already That which you seek, and there is nothing you can do to cause Self-realization. Hold this truth close as you effortlessly seek Self-realization with everything you've got, and Grace may befall you.

Though energy fields are invisible, they shape matter. Albert Einstein said that, “The field is the sole governing agency of the particle.” Many studies show that human beings are influenced by the energy fields of others. In a series of 148 1-minute trials involving 25 people, trained volunteers going into heart coherence were able to induce coherence in test subjects at a distance. They didn’t have to touch their targets to produce the effect. Their energy fields were sufficient. When you are in a heart coherent state, your heart radiates a coherent electromagnetic signal into the environment around you. This field is detectable by a magnetometer several meters away. When other people enter that coherent energy field, their heart coherence increases too, producing a group field effect. Not only are we affected by the fields of other people; we’re affected by the energies of the planet and solar system. A remarkable series of experiments, conducted by a research team led by Rollin McCraty, director of research at the HeartMath Institute, has linked individual human energy to solar cycles. McCraty and his colleagues track solar activity using large magnetometers placed at strategic locations on the earth’s surface. Solar flares affect the electromagnetic fields of the planet. The researchers compare the ebbs and flows of solar energy with the heart coherence readings of trained volunteers. They have found that when people are in heart coherence, their electromagnetic patterns track those of the solar system. 8.15. The heart coherence rhythms of a volunteer compared to solar activity over the course of a month. A later study of 16 participants over 5 months found a similar effect. McCraty writes: “A growing body of evidence suggests that an energetic field is formed among individuals in groups through which communication among all the group members occurs simultaneously. In other words, there is an actual ‘group field’ that connects all the members” together. The results of this research confirm a hypothesis McCraty and I discussed at a conference when I was writing Mind to Matter: Not only are these heart-coherent people in sync with large-scale global cycles, they’re also in sync with each other. McCraty continues, “We’re all like little cells in the bigger Earth brain—sharing information at a subtle, unseen level that exists between all living systems, not just humans, but animals, trees, and so on.” When we use selective attention to tune ourselves to positive coherent energy, we participate in the group energy field of other human beings doing the same. We may also resonate in phase with coherent planetary and universal fields. 8.16. The brain functions as receiver of information from the field. The Brain’s Ability to Detect Fields The idea of invisible energy fields has always been difficult for many scientists to swallow. Around 1900, when Dutch physician Willem Einthoven proposed that the human heart had an energy field, he was ridiculed. He built progressively more sensitive galvanometers to detect it, and he was eventually successful.

FIELD EFFECTS Emotional contagion is just one explanation for the growth of meditation. Another is field effects. Everything begins as energy, then works its way into matter. Though energy fields are invisible, they shape matter. Albert Einstein said that, “The field is the sole governing agency of the particle.” Many studies show that human beings are influenced by the energy fields of others. In a series of 148 1-minute trials involving 25 people, trained volunteers going into heart coherence were able to induce coherence in test subjects at a distance. They didn’t have to touch their targets to produce the effect. Their energy fields were sufficient. When you are in a heart coherent state, your heart radiates a coherent electromagnetic signal into the environment around you. This field is detectable by a magnetometer several meters away. When other people enter that coherent energy field, their heart coherence increases too, producing a group field effect. Not only are we affected by the fields of other people; we’re affected by the energies of the planet and solar system. A remarkable series of experiments, conducted by a research team led by Rollin McCraty, director of research at the HeartMath Institute, has linked individual human energy to solar cycles. McCraty and his colleagues track solar activity using large magnetometers placed at strategic locations on the earth’s surface. Solar flares affect the electromagnetic fields of the planet. The researchers compare the ebbs and flows of solar energy with the heart coherence readings of trained volunteers. They have found that when people are in heart coherence, their electromagnetic patterns track those of the solar system. 8.15. The heart coherence rhythms of a volunteer compared to solar activity over the course of a month. A later study of 16 participants over 5 months found a similar effect. McCraty writes: “A growing body of evidence suggests that an energetic field is formed among individuals in groups through which communication among all the group members occurs simultaneously. In other words, there is an actual ‘group field’ that connects all the members” together. The results of this research confirm a hypothesis McCraty and I discussed at a conference when I was writing Mind to Matter: Not only are these heart-coherent people in sync with large-scale global cycles, they’re also in sync with each other. McCraty continues, “We’re all like little cells in the bigger Earth brain—sharing information at a subtle, unseen level that exists between all living systems, not just humans, but animals, trees, and so on.” When we use selective attention to tune ourselves to positive coherent energy, we participate in the group energy field of other human beings doing the same. We may also resonate in phase with coherent planetary and universal fields. 8.16. The brain functions as receiver of information from the field. The Brain’s Ability to Detect Fields The idea of invisible energy fields has always been difficult for many scientists to swallow. Around 1900, when Dutch physician Willem Einthoven proposed that the human heart had an energy field, he was ridiculed. He built progressively more sensitive galvanometers to detect it, and he was eventually successful.

During the 1919 solar eclipse, people go out to measure the positions of the stars and they find exactly what Einstein predicted. Einstein gets a telegram saying this, and somebody asked him, Professor Einstein, what would you have said if the observations didn’t agree with what your prediction of general relativity said should be happening? And Einstein said, “I’d be sorry for the dear lord; the theory is correct.” What he meant by that is the math is just so elegant, so beautiful, so powerful, that almost seemingly it can’t possibly be wrong.

Other research establishes the ability of one person to affect another through these fields. For instance, studies at the Institute of HeartMath in California have shown that one person’s electrocardiograph (heart) signal can be registered in another person’s electroencephalogram (EEG, measuring brain activity) and elsewhere on the other person’s body. An individual’s cardiac signal can also be registered in another’s EEG recording when two people sit quietly opposite one another.89 This interconnectivity of fields and intention is a marriage of subtle energy theory and quantum physics. As Dr. Benor pointed out, Albert Einstein has already proven that matter and energy are interchangeable. For centuries, healers have been reporting the existence of interpenetrating, subtle energy fields around the physical body. Hierarchical in organization (and vibration), these fields affect every aspect of the human being.90 Studies show that healing states invoke at least the subtle biomagnetic fields. For example, one study employed a magnetometer to quantify biomagnetic fields coming from the hands of meditators and yoga and Qigong practitioners. These fields were a thousand times stronger than the strongest human biomagnetic field and were located in the same range as those being used in medical research labs for speeding the healing of biological tissues—even wounds that had not healed in forty years.91 Yet another study involving a superconducting quantum interference device (SQUID) showcased large frequency-pulsing biomagnetic fields emanating from the hands of therapeutic touch professionals during treatments

In 1919, a solar eclipse took place that settled that question once and for all. This is the eclipse during which Einstein's theory of relativity was proven, as Einstein's math perfectly predicted the position of Mercury observed in the eclipse.

Einstein, however, had a better intuition for physics than for math, and he did not yet appreciate how integrally the two subjects would be related in the pursuit of new theories. During his four years at the Polytechnic,