Derivative Math Quotes

There was, I think, a feeling that the best science was that done in the simplest way. In experimental work, as in mathematics, there was 'style' and a result obtained with simple equipment was more elegant than one obtained with complicated apparatus, just as a mathematical proof derived neatly was better than one involving laborious calculations. Rutherford's first disintegration experiment, and Chadwick's discovery of the neutron had a 'style' that is different from that of experiments made with giant accelerators.

Like most religious mathematicians from Pythagoras to Godel, Bolzano believes that math is the Language of God and that profound metaphysical truths can be derived and proved mathematically.

How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

From the age of 13, I was attracted to physics and mathematics. My interest in these subjects derived mostly from popular science books that I read avidly. Early on I was fascinated by theoretical physics and determined to become a theoretical physicist. I had no real idea what that meant, but it seemed incredibly exciting to spend one's life attempting to find the secrets of the universe by using one's mind.

Here are the basic principles of Constructivism as practiced by Kronecker and codified by J.H. Poincare and L.E.J. Brouwer and other major figures in Intuitionism: (1) Any mathematical statement or theorem that is more complicated or abstract than plain old integer-style arithmetic must be explicitly derived (i.e. 'constructed') from integer arithmetic via a finite number of purely deductive steps. (2) The only valid proofs in math are constructive ones, with the adjective here meaning that the proof provides a method for finding (i.e., 'constructing') whatever mathematical entities it's concerned with.

Like most of the giants who revolutionize math or science, Cantor was 100% a man of his time and place, and his accomplishments were the usual conjunction of extraordinary personal brilliance and courage* and just the right context of general problems and conditions that, in hindsight, tend to make intellectual advances seem inevitable and their authors almost incidental. *Naturally, the significant results that legitimize a mathematical theory take time to derive, and then even more time to be fully accepted, and of course throughout this time the Insanity-v.-Genius question remains undecided, probably even for the mathematician himself, so that he’s developing his theory and cooking his proofs under conditions of enormous personal stress and doubt, and sometimes isn’t even vindicated in his own lifetime, etc.

Look at stocks as part ownership of a business. 2. Look at Mr. Market—volatile stock price fluctuations—as your friend rather than your enemy. View risk as the possibility of permanent loss of purchasing power, and uncertainty as the unpredictability regarding the degree of variability in the possible range of outcomes. 3. Remember the three most important words in investing: “margin of safety.” 4. Evaluate any news item or event only in terms of its impact on (a) future interest rates and (b) the intrinsic value of the business, which is the discounted value of the cash that can be taken out during its remaining life, adjusted for the uncertainty around receiving those cash flows. 5. Think in terms of opportunity costs when evaluating new ideas and keep a very high hurdle rate for incoming investments. Be unreasonable. When you look at a business and get a strong desire from within saying, “I wish I owned this business,” that is the kind of business in which you should be investing. A great investment idea doesn’t need hours to analyze. More often than not, it is love at first sight. 6. Think probabilistically rather than deterministically, because the future is never certain and it is really a set of branching probability streams. At the same time, avoid the risk of ruin, when making decisions, by focusing on consequences rather than just on raw probabilities in isolation. Some risks are just not worth taking, whatever the potential upside may be. 7. Never underestimate the power of incentives in any given situation. 8. When making decisions, involve both the left side of your brain (logic, analysis, and math) and the right side (intuition, creativity, and emotions). 9. Engage in visual thinking, which helps us to better understand complex information, organize our thoughts, and improve our ability to think and communicate. 10. Invert, always invert. You can avoid a lot of pain by visualizing your life after you have lost a lot of money trading or speculating using derivatives or leverage. If the visuals unnerve you, don’t do anything that could get you remotely close to reaching such a situation. 11. Vicariously learn from others throughout life. Embrace everlasting humility to succeed in this endeavor. 12. Embrace the power of long-term compounding. All the great things in life come from compound interest.

with two constants a and n. Important special cases are the constant

My job is to draw little points on little graphs and to derive little information.

...in pure mathematics the mind deal only with its own creations and imaginations. The concepts of number and form have not been derived from any source other than the world of reality. The ten fingers on which men learned to count, that is, to carry out the first arithmetical operation, may be anything else, but they are certainly not only objects that can be counted, but also the ability to exclude all properties of the objects considered other than their number-and this ability is the product of a long historical evolution based on experience. Like the idea of number, so the idea of form is derived exclusively from the external world, and does not arise in the mind as a product of pure thought.

Regulators lent a helping hand. On a spring afternoon in late April 2004, five members of the Securities and Exchange Commission gathered in a basement hearing room to meet a contingent of representatives from Wall Street’s big investment banks to talk about risk. The banks had asked for an exemption for their brokerage units from a regulation that limited the amount of debt they could hold on their balance sheets. The rule required banks to hold a large reserve of cash as a cushion against big losses on those holdings. By loosening up these so-called capital reserve requirements, the banks could become more aggressive and deploy the extra cash in other, more lucrative areas—such as mortgage-backed securities and derivatives.

Merrill Lynch had circulated internal memos about the risks in Citron’s portfolio as early as 1992, but those warnings didn’t stir action, let alone caution. Clearly, many senior people within the bank knew that what they were doing was wrong, yet they let it continue, selling him riskier and riskier derivatives and collecting their fees and commissions each time. Orange County had become one of Merrill’s top-five clients, as well as one of the largest purchasers of derivative securities in the world. The bank wasn’t willing to jeopardize the loss of that business, no matter how precarious and unsuitable Citron’s investments were. His own lawyer later argued that the sixty-nine-year-old Citron tested at a seventh-grade level in math, had a severe learning disability, and had long been suffering from dementia. Citron himself admitted that he lacked a basic understanding of what he had done and that he had simply been following the advice of his bankers. They’d held his hand and led him to the slaughter.

To apply first principles thinking to the field of value investing, consider several fundamental truths. Understand and practice the following if you want to become a good investor: 1. Look at stocks as part ownership of a business. 2. Look at Mr. Market—volatile stock price fluctuations—as your friend rather than your enemy. View risk as the possibility of permanent loss of purchasing power, and uncertainty as the unpredictability regarding the degree of variability in the possible range of outcomes. 3. Remember the three most important words in investing: “margin of safety.” 4. Evaluate any news item or event only in terms of its impact on (a) future interest rates and (b) the intrinsic value of the business, which is the discounted value of the cash that can be taken out during its remaining life, adjusted for the uncertainty around receiving those cash flows. 5. Think in terms of opportunity costs when evaluating new ideas and keep a very high hurdle rate for incoming investments. Be unreasonable. When you look at a business and get a strong desire from within saying, “I wish I owned this business,” that is the kind of business in which you should be investing. A great investment idea doesn’t need hours to analyze. More often than not, it is love at first sight. 6. Think probabilistically rather than deterministically, because the future is never certain and it is really a set of branching probability streams. At the same time, avoid the risk of ruin, when making decisions, by focusing on consequences rather than just on raw probabilities in isolation. Some risks are just not worth taking, whatever the potential upside may be. 7. Never underestimate the power of incentives in any given situation. 8. When making decisions, involve both the left side of your brain (logic, analysis, and math) and the right side (intuition, creativity, and emotions). 9. Engage in visual thinking, which helps us to better understand complex information, organize our thoughts, and improve our ability to think and communicate. 10. Invert, always invert. You can avoid a lot of pain by visualizing your life after you have lost a lot of money trading or speculating using derivatives or leverage. If the visuals unnerve you, don’t do anything that could get you remotely close to reaching such a situation. 11. Vicariously learn from others throughout life. Embrace everlasting humility to succeed in this endeavor. 12. Embrace the power of long-term compounding. All the great things in life come from compound interest.

AI Brain, PIRANDOM > Circlet + Diadem × Ring > Itemizer × Abstracter, Explained : 1111 < 11 < 1, I utilized dependency injection in code for the following. Phi divides into the Pythagorean theorem, and Pi divides into the Sort where Phi is 7 and the Cognitive domain is the point in time, Pythagoras is the Affective domain in space, and Pi is then injected to the fibonacci sequence for time within the range of 7 and 4 at 10 radians to form 3.14 respectively. In conclusion, If I ran this code in a video test to derive a model view projection matrix then this is the only code I would need to create the math core and automate calls to the pixel and vertex shaders Inna GPU.

IT POPS, A new discovery, by: Jonathan Roy Mckinney IT POPS is relative to space time in that it has two major components that follow the 3 laws of thermodynamics. The PIrandom creator injects an object with the relative XYZ coordinates in a model view projection that are derived by utilizing the correct Matrix math 11,10,10,10. Once Injected, the two way hash coin creator in time will create the entropy required to derive random shapes and reverse or abstract them into full objects for a complete wire frame like Michaelangelo could carve an Angel out of marble.

This reminds me of an old story from the Harvard math department, concerning one of the grand old Russian professors, whom we shall call O. Professor O is midway through an intricate algebraic derivation when a student in the back row raises his hand. “Professor O, I didn’t follow that last step. Why do those two operators commute?” The professor raises his eyebrows and says, “Eet ees obvious.” But the student persists: “I’m sorry, Professor O, I really don’t see it.” So Professor O goes back to the board and adds a few lines of explanation. “What we must do? Well, the two operators are both diagonalized by . . . well, it is not exactly diagonalized but . . . just a moment . . .” Professor O pauses for a little while, peering at what’s on the board and scratching his chin. Then he retreats to his office. About ten minutes go by. The students are about to start leaving when Professor O returns, and again assumes his station in front of the chalkboard. “Yes,” he says, satisfied. “Eet ees obvious

It might surprise you to know that, for the most part, finance involves addition and subtraction. When finance people get really fancy, they multiply and divide. We never have to take the second derivative of a function or determine the area under a curve (sorry, engineers). So have no fear: the math is easy. And calculators are cheap. You don't need to be a rocket scientist to be financially intelligent.

Skin in the game can make boring things less boring. When you have skin in the game, dull things like checking the safety of the aircraft because you may be forced to be a passenger in it cease to be boring. If you are an investor in a company, doing ultra-boring things like reading the footnotes of a financial statement (where the real information is to be found) becomes, well, almost not boring. But there is an even more vital dimension. Many addicts who normally have a dull intellect and the mental nimbleness of a cauliflower—or a foreign policy expert—are capable of the most ingenious tricks to procure their drugs. When they undergo rehab, they are often told that should they spend half the mental energy trying to make money as they did procuring drugs, they are guaranteed to become millionaires. But, to no avail. Without the addiction, their miraculous powers go away. It was like a magical potion that gave remarkable powers to those seeking it, but not those drinking it. A confession. When I don’t have skin in the game, I am usually dumb. My knowledge of technical matters, such as risk and probability, did not initially come from books. It did not come from lofty philosophizing and scientific hunger. It did not even come from curiosity. It came from the thrills and hormonal flush one gets while taking risks in the markets. I never thought mathematics was something interesting to me until, when I was at Wharton, a friend told me about the financial options I described earlier (and their generalization, complex derivatives). I immediately decided to make a career in them. It was a combination of financial trading and complicated probability. The field was new and uncharted. I knew in my guts there were mistakes in the theories that used the conventional bell curve and ignored the impact of the tails (extreme events). I knew in my guts that academics had not the slightest clue about the risks. So, to find errors in the estimation of these probabilistic securities, I had to study probability, which mysteriously and instantly became fun, even gripping. When there was risk on the line, suddenly a second brain in me manifested itself, and the probabilities of intricate sequences became suddenly effortless to analyze and map. When there is fire, you will run faster than in any competition. When you ski downhill some movements become effortless. Then I became dumb again when there was no real action. Furthermore, as traders the mathematics we used fit our problem like a glove, unlike academics with a theory looking for some application—in some cases we had to invent models out of thin air and could not afford the wrong equations. Applying math to practical problems was another business altogether; it meant a deep understanding of the problem before writing the equations.

The Lorentz transformations, when properly understood, are revealing a mathematical relation between mind and matter. Descartes argued that mind is unextended and matter extended, yet can interact with each other. The Lorentz transformations show how this actually works. Light is unextended, and matter is extended, yet matter is wholly defined relative to light, and cannot exist without light. Because light is absolute, it is eternal and necessary. Because matter is relative, it is temporal and contingent. It’s all in the math. The Lorentz transformations mathematically prove that idealism is true and materialism false. Idealism is absolute, and materialism relative (dependent, derived, created, caused)

After evidence forced him to give up the beautiful polyhedra, Kepler, in later life, became convinced that the planets play music along their paths. In his 1619 book Harmony of the World he derived the planet’s tunes and concluded that “the Earth sings Mi-Fa-Mi.” It wasn’t his best work. But Kepler’s analysis of the planetary orbits laid a basis for the later studies of Isaac Newton (1643–1727), the first scientist to rigorously use mathematics.

Decades later, Widrow, recalling Wiener’s personality in a book, painted a particularly evocative picture of a man whose head was often, literally and metaphorically, “in the clouds” as he walked the corridors of MIT buildings: “We’d see him there every day, and he always had a cigar. He’d be walking down the hallway, puffing on the cigar, and the cigar was at angle theta—45 degrees above the ground. And he never looked where he was walking…But he’d be puffing away, his head encompassed in a cloud of smoke, and he was just in oblivion. Of course, he was deriving equations.