Top 265 Differential Equations Quotes & Sayings - Page 5

How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasturenothing but years of effort can extract it. You can't hurry the process. Or pass from arithmetic to algebra; you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon.

Everyone can act. Everyone can improvise. Anyone who wishes to can play in the theater and learn to become 'stage-worthy.' We learn through experience and experiencing, and no one teaches anyone anything. This is as true for the infant moving from kicking and crawling to walking as it is for the scientist with his equations. If the environment permits it, anyone can learn whatever he chooses to learn; and if the individual permits it, the environment will teach him everything it has to teach. 'Talent' or 'lack of talent' have little to do with it.

Objects obey quantum laws- they spread in possibility following the equation discovered by Erwin Schodinger- but the equation is not codified within the objects. Likewise, appropriate non-linear equations govern the dynamical response of bodies that have gone through the conditioning of quantum memory, although this memory is not recorded in them. Whereas classical memory is recorded in objects like a tape, quantum memory is truly the analog of what the ancients call Akashic memory, memory written in Akasha, Emptiness- nowhere.

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds.

A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.

Seeing and playing with physical objects can enable access to symbolic ideas. When I studied physics and math at university it was all done through equations and textbooks whereas artists go to art school and start making stuff; they fling paint at the walls, they dance and bash things together with giant bits of metal. Our society has come to think of science as being a very abstractified thing, and art as being a materialized thing.

As Alaska zipped through something obvious about linear equations, stoner/baller Hank Walsten said, "Wait, wait. I don't get it." "That's because you have eight functioning brain cells." "Studies show that Marijuana is better for your health than those cigarettes," Hank said. Alaska swallowed a mouthful of fries, took a drag on her cigarette, and blew a smoke at Hank. "I may die young," she said. "But at least I'll die smart. Now, back to tangents.

Man is said to be a reasoning animal. I do not know why he has not been defined as an affective or feeling animal. Perhaps that which differentiates him from other animals is feeling rather than reason. More often I have seen a cat reason than laugh or weep. Perhaps it weeps or laughs inwardly - but then perhaps, also inwardly, the crab resolves equations of the second degree.

In the beginning no power differential existed between male and female. God empowered both with full rights and responsibility to rule outward over all creation, not over each other. As we know all too well, the fall changed everything, precipitating male rule over women and also the rule of some men over other men, a.k.a., patriarchy. Within patriarchy, women no longer derive their value from their Creator, but from men - father, husband, and sons. Within patriarchy, a woman's value is gauged by counting her sons.

A scientist's life, the author says, is indeed conflictual, formed by battles, defeats, and victories: but the adversary is always and only the unknown, the problem to be solved, the mystery to be clarified. It is never a matter of civil war; even though of different opinions, or of different political leanings, scientists dispute each other, they compete, but they do not battle: they are bound together by a strong alliance, by the common faith "in the validity of Maxwell's or Boltzmann's equations," and by the common acceptance of Darwinism and the molecular structure of DNA.

Challenger was lost because NASA came to believe its own propaganda. The agency's deeply impacted cultural hubris had it that technology-engineering-would always triumph over random disaster if certain rules were followed. The engineers-turned-technocrats could not bring themselves to accept the psychology of machines with abandoning the core principle of their own faith: equations, geometry, and repetition-physical law, precision design, and testing-must defy chaos.

In quantum mechanics there is A causing B. The equations do not stand outside that usual paradigm of physics. The real issue is that the kinds of things you predict in quantum mechanics are different from the kinds of things you predict using general relativity. Quantum mechanics, that big, new, spectacular remarkable idea is that you only predict probabilities, the likelihood of one outcome or another. That's the new idea.

Renormalization is just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr's orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number.

I once thought that if I could ask God one question, I would ask how the universe began, because once I knew that, all the rest is simply equations. But as I got older I became less concerned with how the universe began. Rather, I would want to know why he started the universe. For once I knew that answer, then I would know the purpose of my own life.

Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future... If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them... My own belief is that this is a more likely line of progress than trying to guess at physical pictures.

I mean you're given all these lessons for the unimportant things--piano-playing, typing. You're given years and years of lessons in how to balance equations, which Lord knows you will never have to do in normal life. But how about parenthood? Or marriage, either, come to think of it. Before you can drive a car you need a state-approved course of instruction, but driving a car is nothing, nothing, compared to living day in and day out with a husband and raising up a new human being.

I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen's, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell's equations.

Tell me it's never been done. Because the only real laws in this world-the only things we really know-are the two postulates of relativity, the three laws of Newton, the four laws of thermodynamics, and Maxwell's equation-no, scratch that, the only things we really know are Maxwell's equations, the three laws of Newton, the two postulates of relativity, and the periodic table. That's all we know that's true. All the rest are man's laws

Any high school boy or girl knows how to calculate the force with which a stone he or she throws will hit someone in the face, but nothing in those equations they use will tell them whether or not to throw it...To solve the problem of values we must know what is valuable. Consciousness is the most valuable commodity...To bring values into science, we need to connect science with what is valuable consciousness.

A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.

If time is treated in modern physics as a dimension on a par with the dimensions of space, why should we a priori exclude the possibility that we are pulled as well as pushed along its axis? The future has, after all, as much or as little reality as the past, and there is nothing logically inconceivable in introducing, as a working hypothesis, an element of finality, supplementary to the element of causality, into our equations. It betrays a great lack of imagination to believe that the concept of "purpose" must necessarily be associated with some anthropomorphic deity.

Grandad taught me that the alien signs and symbols of algebraic equations were not just marks on paper. They were not flat. They were three-dimensional, and you could approach them from different directions, look at them from different ways, stand them on their heads. You could take them apart and put them back together in a variety of shapes, like Legos. I stopped being scared of them.

In this acausal world, scientists are helpless. Their predictions become postdictions- Their equations become justifications, their logic, illogic. Scientists turn reckless and mutter like gamblers who cannot stop betting. Scientists are buffoons, not because they are rational but because the cosmos is irrational. Or perhaps it is not because the cosmos is irrational but because they are rational. Who can say which, in an acausal world?

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

There was a blithe certainty that came from first comprehending the full Einstein field equations, arabesques of Greek letters clinging tenuously to the page, a gossamer web. They seemed insubstantial when you first saw them, a string of squiggles. Yet to follow the delicate tensors as they contracted, as the superscripts paired with subscripts, collapsing mathematically into concrete classical entities - potential; mass; forces vectoring in a curved geometry - that was a sublime experience. The iron fist of the real, inside the velvet glove of airy mathematics.