Mathematical Analysis Quotes

Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry ... if mathematical analysis should ever hold a prominent place in chemistry
an aberration which is happily almost impossible
it would occasion a rapid and widespread degeneration of that science. ~ Auguste Comte

I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary
being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived. ~ George Boole

But that would mean it was originally a sideways number eight. That makes no sense at all. Unless..." She paused as understanding dawned. "You think it was the symbol for infinity?"
"Yes, but not the usual one. A special variant. Do you see how one line doesn't fully connect in the middle? That's Euler's infinity symbol. Absolutus infinitus."
"How is it different from the usual one?"
"Back in the eighteenth century, there were certain mathematical calculations no one could perform because they involved series of infinite numbers. The problem with infinity, of course, is that you can't come up with a final answer when the numbers keep increasing forever. But a mathematician named Leonhard Euler found a way to treat infinity as if it were a finite number- and that allowed him to do things in mathematical analysis that had never been done before." Tom inclined his head toward the date stone. "My guess is whoever chiseled that symbol was a mathematician or scientist."
"If it were my date stone," Cassandra said dryly, "I'd prefer the entwined hearts. At least I would understand what it means."
"No, this is much better than hearts," Tom exclaimed, his expression more earnest than any she'd seen from him before. "Linking their names with Euler's infinity symbol means..." He paused, considering how best to explain it. "The two of them formed a complete unit... a togetherness... that contained infinity. Their marriage had a beginning and end, but every day of ~ Lisa Kleypas

The further we analyse the manner in which such an engine performs its processes and attains its results, the more we perceive how distinctly it places in a true and just light the mutual relations and connexion of the various steps of mathematical analysis; how clearly it separates those things which are in reality distinct and independent, and unites those which are mutually dependent. ~ Ada Lovelace

So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality. ~ Henri Poincare

Mathematical Analysis is ... the true rational basis of the whole system of our positive knowledge. ~ Auguste Comte

In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language. ~ Georg C. Lichtenberg

The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression,more exact,compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex world wide states that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write. ~ H.G.Wells

Like Molière's M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole's 'The Mathematical Analysis of Logic'. ~ Ernest Nagel

The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking. ~ John Von Neumann

I think we can end the divisions within the United States. What I think is quite clear is that we can work together in the last analysis. And that what has been going on with the United States over the period of that last three years, the divisions, the violence, the disenchantment with our society, the divisions - whether it's between blacks and whites, between the poor and the more affluent, or between age groups, or in the war in Vietnam - that we can work together. We are a great country, an unselfish country and a compassionate country. And I intend to make that my basis for running. ~ Robert Kennedy

The knowledge that is suited to our situation and powers, the whole compass of moral, natural, and mathematical science, was neglected by the new Platonists; whilst they exhausted their strength in the verbal disputes of metaphysics, attempted to explore the secrets of the invisible world, and studied to reconcile Aristotle with Plato, on subjects of which both these philosophers were as ignorant as the rest of mankind. ~ Edward Gibbon

Sculptors feel that somebody else is using their hands, that they couldn't possibly be doing this. ~ Kurt Vonnegut Jr.

Believe nothing merely because you have been told it. Do not believe what your teacher tells you merely out of respect for the teacher. But whatsoever, after due examination and analysis, you find to be kind, conducive to the good, the benefit, the welfare of all beings - that doctrine believe and cling to, and take it as your guide." - The Buddha The Occult (Hidden) Teachings The teachings and knowledge that appear hidden are ~ Michael Eggleston

The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth. ~ Hermann Weyl

For it is not cell nuclei, not even individual chromosomes, but certain parts of certain chromosomes from certain cells that must be isolated and collected in enormous quantities for analysis; that would be the precondition for placing the chemist in such a position as would allow him to analyse [the hereditary material] more minutely than [can] the morphologists ... For the morphology of the nucleus has reference at the very least to the gearing of the clock, but at best the chemistry of the nucleus refers only to the metal from which the gears are formed. ~ Theodor Boveri

Science ignores the spiritual realm because it is not amenable to scientific analysis. As importantly, the predictive success of Newtonian theory, emphasizing the primacy of a physical Universe, made the existence of spirit and God an extraneous hypothesis that offered no explanatory principles needed by science. ~ Bruce Lipton

When we ask for advice, we are usually looking for an accomplice ~ Saul Bellow

I extend that to the abortion issue, I extend that to the so-called gay rights issue, I think this is a freedom principle and consistent with the analysis in the economic area as well. ~ William Weld

Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration. ~ Octavio Paz

I didn't want to get into acting just to play bystanders. I feel a bystander enough in my own life. And I do think that theatre can contribute to a certain analysis and commentary on our own world. ~ Elliot Cowan

Think as you work, for in the final analysis, your worth to your company comes not only in solving problems, but also in anticipating them. ~ Tom Lehrer

A mathematical point is the most indivisble and unique thing which art can present. ~ John Donne

Once you have mathematical certainty there is nothing left to do or to understand. There will be nothing left but to bottle up your five senses and plunge into contemplation. While if you stick to consciousness, even though the same result is attained, you can at least flog yourself at times, and that will, at any rate, liven you up. Reactionary as it is, corporal punishment is better than nothing. ~ Fyodor Dostoyevsky

The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules ... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms. ~ Kurt Godel

Remember that codes are more than a filing system. Every project needs a systematic way to store coded field data and a way to retrieve them easily during analysis. ~ Matthew B. Miles

To talk about communication theory without communicating its real mathematical content would be like endlessly telling a man about a wonderful composer, yet never letting him hear an example of the composer's music. ~ John R. Pierce

Isn't the initial loss that does for him, but the stupid plays he makes in an effort to deny that the loss has happened. The great economic psychologists Daniel Kahneman and Amos Tversky summarised the behaviour in their classic analysis of the psychology of risk: ~ Tim Harford

I am no longer an advocate of elaborate techniques of security analysis in order to find superior value opportunities. ~ Benjamin Graham

Perhaps I was mad, as I thought at moments; perhaps I was not like other men? But I was able to do the same things the others did; with a little effort and industry I could read Plato, was able to solve problems in trigonometry or follow a chemical analysis. These was only one thing I could not do: wrest the dark secret goal from myself and keep it before me as others did who knew exactly what they wanted to be- professors, lawyers, doctors, artists, however long this would take them and whatever difficulties and advantages this decision would bear in its wake. This I could not do. Perhaps I would become something similar but how was I to know? Perhaps I would have to continue my search for years on end and would not become anything, and would not reach a goal. Perhaps I would reach this goal but it would turn out to be an evil, dangerous, horrible one? ~ Hermann Hesse

Psychoanalysis is right to be mistrustful. One of its rules runs: whatever disturbs the continuation of the work of analysis is a resistance. ~ Sigmund Freud

The detective story, as created by Poe, is something as specialised and as intellectual as a chess problem, whereas the best English detective fiction has relied less on the beauty of the mathematical problem and much more on the intangible human element. [ ... ] In The Moonstone the mystery is finally solved, not altogether by human ingenuity, but largely by accident. Since Collins, the best heroes of English detective fiction have been, like Sergeant Cuff, fallible. ~ T. S. Eliot

They had lived to see their simple patriotism derided, their morality despised, their savings devalued. They caused no trouble. Millions of pounds of public money wasn't regularly siphoned into their neighbourhoods in the hope of bribing, cajoling or coercing them into civic virtue. If they protested that their cities had become alien, their children taught in overcrowded schools where 90 per cent of the children spoke no English, they were lectured about the cardinal sin of racism by those more expensively and comfortably circumstanced. Unprotected by accountants, they were the milch-cows of the rapacious Revenue. No lucrative industry of social concern and psychological analysis had grown up to analyse and condone their inadequacies on the grounds of deprivation or poverty. ~ P.D. James

What Ruef discovered was a ringing endorsement of the coffeehouse model of social networking: the most creative individuals in Ruef's survey consistently had broad social networks that extended outside their organization and involved people from diverse fields of expertise. Diverse, horizontal social networks, in Ruef's analysis, were three times more innovative than uniform, vertical networks. In groups united by shared values and long-term familiarity, conformity and convention tended to dampen any potential creative sparks. The limited reach of the network meant that interesting concepts from the outside rarely entered the entrepreneur's consciousness. But the entrepreneurs who built bridges outside their "islands," as Ruef called them, were able to borrow or co-opt new ideas from these external environments and put them to use in a new context. ~ Steven Johnson

Understanding does not come through analysis;understanding comes only when the mind is very quite,unburdened,no longer seeking success and therefore being thwarted,afraid of faluire. ~ Jiddu Krishnamurti

Insight depends on the multi-dimensional analysis of the input in its various aspects, on extracting relevant messages from irrelevant noise, identifying patterns in the mosaic until it has become saturated, as it were, with meaning. ~ Arthur Koestler

We have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed. ~ James Newman

Whatever may be the merits of a religious system, its effects upon the mass of mankind must depend in an important degree upon its teachers. All instruction and all truth, except simple mathematical truth, is modified by the medium through which it is conveyed. ~ Benjamin Robbins Curtis

Open your eyes, Mac." "What do you mean?" "Words can be twisted into any shape. Promises can be made to lull the heart and seduce the soul. In the final analysis words mean nothing. They are labels we give things in an effort to wrap our puny little brains around their underlying natures, when ninety-nine percent of the time the totality of the reality is an entirely different beast. The wisest man is the silent one. Examine his actions. Judge him by them. He thinks you have the heart of a warrior. He believes in you. Believe in him. ~ Karen Marie Moning

Anything is easy to the man who sees ... The open eye of the open mind
that has more to do with real detective work than all the deduction and induction and analysis ever devised. ~ Samuel Hopkins Adams

A logical analysis of reflexive usages in French shows, however, that this simplicity is an illusion and that, so far from helping the foreigner, it is more calculated to bother him. ~ Edward Sapir

The transmission of SARS, Dwyer said, seems to depend much on super spreaders - and their behavior, not to mention the behavior of people around them, can be various. The mathematical ecologist's term for variousness of behavior is "heterogeneity," and Dwyer's models have shown that heterogeneity of behavior, even among forest insects, let alone among humans, can be very important in damping the spread of infectious disease.

"If you hold mean transmission rate constant," he told me, "just adding heterogeneity by itself will tend to reduce the overall infection rate." That sounds dry. What it means is that individual effort, individual discernment, individual choice can have huge effects in averting the catastrophes that might otherwise sweep through a herd. An individual gypsy moth may inherit a slightly superior ability to avoid smears of NPV as it grazes on a leaf.

An individual human may choose not to drink the palm sap, not to eat the chimpanzee, not to pen the pig beneath mango trees, not to clear the horse's windpipe with his bare hand, not to have unprotected sex with the prostitute, not to share the needle in a shooting gallery, not to cough without covering her mouth, not to board a plane while feeling ill, or not to coop his chickens along with his ducks. "Any tiny little thing that people do," Dwyer said, if it makes them different from one another, from the idealized standard of herd behavior, "is going to reduce infection rates. ~ David Quammen

When you make loving others the story of your life, there's never a final chapter, because the legacy continues. You lend your light to one person, and he or she shines it on another and another and another. And I know for sure that in the final analysis of our lives- when the to-do lists are no more, when the frenzy is finished, when our e-mail inboxes are empty- the only thing that will have any lasting value is whether we've loved others and whether they've loved us. ~ Oprah Winfrey

The more complex the world situation becomes, the more scientific and rational analysis you have to have, the less you can do with simple good will and sentiment. ~ Reinhold Niebuhr

The initial small step is simple: Rather than making a sweeping determination to tackle the Great Books (all of them), decide to begin on one of the reading lists in Part II. As you read each book, you'll follow the pattern of the trivium. First you'll try to understand the book's basic structure and argument; next, you'll evaluate the book's assertions; finally, you'll form an opinion about the book's ideas. You'll have to exercise these three skills of reading - understanding, analysis, and evaluation - differently for each kind of book. ~ Susan Wise Bauer

Finally, we arrive at the question of the so-called nonpolitical man. Hitler not only established his power from the very beginning with masses of people who were until then essentially nonpolitical; he also accomplished his last step to victory in March of 1933 in a "legal" manner, by mobilizing no less than five million nonvoters, that is to say, nonpolitical people. The Left parties had made every effort to win over the indifferent masses, without posing the question as to what it means "to be indifferent or nonpolitical."

If an industrialist and large estate owner champions a rightist party, this is easily understood in terms of his immediate economic interests. In his case a leftist orientation would be at variance with his social situation and would, for that reason, point to irrational motives. If an industrial worker has a leftist orientation, this too is by all mean rationally consistent - it derives from his economic and social position in industry. If, however, a worker, an employee, or an official has a rightist orientation, this must be ascribed to a lack of political clarity, i.e., he is ignorant of his social position. The more a man who belongs to the broad working masses is nonpolitical, the more susceptible he is to the ideology of political reaction. To be nonpolitical is not, as one might suppose, evidence of a passive psychic condition, but of a highly active attitude, a defense against the awareness of social responsibility. The analysis of th ~ Wilhelm Reich

In writing the first edition of Japan's International Relations we aimed to provide a comprehensive analysis of Japan as a normal state, rather than as an aberrant or abnormal state. ~ Glenn D. Hook

As long as we remain self-reflective and keep looking at who and what we are, as long as we keep our analysis that way, then there's no freedom. We're just trying clothes on in front of a mirror and admiring them. ~ Frederick Lenz

I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go. ~ Winston S. Churchill

Black people are not the descendants of kings. We are - and I say this with big pride - the progeny of slaves. If there's any majesty in our struggle, it lies not in fairy tales but in those humble origins and the great distance we've traveled since. Ditto for the dreams of a separate but noble past. Cosby's, and much of black America's, conservative analysis flattens history and smooths over the wrinkles that have characterized black America since its inception. ~ Ta-Nehisi Coates

We each possess the ability to engage in self-healing through contemplation and self-analysis. ~ Kilroy J. Oldster

Science is not about making predictions or performing experiments. Science is about explaining. ~ Bill Gaede

Experimentation without mathematical explanation is blind; mathematical explanation without experimentation is empty. ~ Bill Bryson

Significance unfortunately is a useful means toward a personal ends in the advance of science - status and widely distributed publications, a big laboratory, a staff of research assistants, a reduction in teaching load, a better salary, the finer wines of Bordeaux. Precision, knowledge, and control. In a narrow and cynical sense statistical significance is the way to achieve these. Design experiment. Then calculate statistical significance. Publish articles showing "significant" results. Enjoy promotion.

But it is not science, and it will not last. ~ Stephen Thomas Ziliak

Am unhappy, - very unhappy, for other things." "What other things? Can you tell me some of them?" How much I wished to reply fully to this question! How difficult it was to frame any answer! Children can feel, but they cannot analyse their feelings; and if the analysis is partially effected in thought, they know not how to express the result of the process in words. Fearful, however, of losing this first and only opportunity of relieving my grief by imparting it, I, after a disturbed pause, contrived to frame a meagre, though, as far as it went, true response. ~ Charlotte Bronte