A Quote by Roger Ascham
Mathematical Mark all mathematical heads, which be only and wholly bent to those sciences, how solitary they be themselves, how unfit to live with others, and how unapt to serve in the world.
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Mark all mathematical heads which be wholly and only bent on these sciences, how solitary they be themselves, how unfit to live with others, how unapt to serve the world.
Marke all Mathematicall heades, which be onely and wholy bent to those sciences, how solitarie they be themselues, how vnfit to liue with others, & how vnapte to serue in the world.
The mathematical question is "Why?" It's always why. And the only way we know how to answer such questions is to come up, from scratch, with these narrative arguments that explain it. So what I want to do with this book is open up this world of mathematical reality, the creatures that we build there, the questions that we ask there, the ways in which we poke and prod (known as problems), and how we can possibly craft these elegant reason-poems.
Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
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.
If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.
It seems perfectly clear that Economy, if it is to be a science at all, must be a mathematical science. There exists much prejudice against attempts to introduce the methods and language of mathematics into any branch of the moral sciences. Most persons appear to hold that the physical sciences form the proper sphere of mathematical method, and that the moral sciences demand some other method-I know not what.
One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?
The world looks like a multiplication-table, or a mathematical equation, which, turn it how you will, balances itself.
To my mind it is wholly irresponsible to go into the world incapable of preventing violence, injury, crime, and death. How feeble is the mindset to accept defenselessness. How unnatural. How cheap. How cowardly. How pathetic.
The only way to know everything is to learn how to think, how to ask questions, how to navigate the world. Students must learn how to teach themselves to use new tools, how to talk to unfamiliar people, and basically how to be brave.
The world has been set up in such a way that we don't even realise how ingrained certain things are, like how much we live in a patriarchal society or how institutional racism is ingrained in how we see the world. We don't realise how many things are being set in stone, in our heads.
The ocean is the only alien and potentially hostile environment on the planet into which we tend to venture without thinking about the animals that live there, how they behave, how they support themselves, and how they perceive us. I know of no one who would set off into the jungles of Malaysia armed only with a bathing suit, a tube of suntan cream, and a book, and yet that's precisely how we approach the oceans.
I certainly believe we all suffer damage, one way or another. How could we not,except in a world of perfect parents, siblings, neighbours, companions? And then there is the question on which so much depends, of how we react to the damage: whether we admit it or repress it,and how this affects our dealings with others.Some admit the damage, and try to mitigate it;some spend their lives trying to help others who are damaged; and there are those whose main concern is to avoid further damage to themselves, at whatever cost. And those are the ones who are ruthless, and the ones to be careful of.
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