You are a genius: Imaginary numbers

Monday, March 31, 2014

Imaginary numbers

When I was in high school, a professor from the local university was invited to deliver a guest lecture to the nerdiest of the math students. I sat in awe as Professor Sherwood introduced imaginary numbers and showed how they could be used to solve second-order differential equations. Could something this bizarre, outlandish and fascinating actually be true? As it turns out, yes. Three decades later, I use imaginary numbers to solve the differential equations that allow me to design cellular telephones.

The awestruck feeling I got in high school is still alive in me today. Now I get this feeling in the presence of the most brilliant philosophers. Material things, they say, are almost entirely irrelevant to the pursuit of wisdom, virtue and happiness. Could something this bizarre, outlandish and fascinating actually be true?

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It goes against the grain for me to do what so often happens, to speak inhumanly about the great as if a few millennia were an immense distance. I prefer to speak humanly about it, as if it happened yesterday, and let only the greatness itself be the distance.
Søren Kierkegaard

He who deems it important to keep aloof from the so-called rabble ... is as much to blame as a coward who hides himself from his enemy because he fears defeat.
Johann Wolfgang von Goethe

If, while hurrying ostensibly to the temple of truth, we hand the reins over to our personal interests which look aside at very different guiding stars, for instance at the tastes and foibles of our contemporaries, at the established religion, but in particular at the hints and suggestions of those at the head of affairs, then how shall we ever reach the high, precipitous, bare rock whereon stands the temple of truth?
Schopenhauer

When I speak of the purpose of self-culture, I mean that it should be sincere. In other words, we must make self-culture really and truly our end, or choose it for its own sake, and not merely as a means or instrument of something else. And here I touch a common and very pernicious error. Not a few persons desire to improve themselves only to get property and to rise in the world; but such do not properly choose improvement, but something outward and foreign to themselves; and so low an impulse can produce only a stinted, partial, uncertain growth. A man, as I have said, is to cultivate himself because he is a man. He is to start with the conviction that there is something greater within him than in the whole material creation, than in all the worlds which press on the eye and ear; and that inward improvements have a worth and dignity in themselves quite distinct from the power they give over outward things.
William Ellery Channing

Not without a slight shudder at the danger, I often perceive how near I had come to admitting into my mind the details of some trivial affair,—the news of the street; and I am astonished to observe how willing men are to lumber their minds with such rubbish,—to permit idle rumors and incidents of the most insignificant kind to intrude on ground which should be sacred to thought. Shall the mind be a public arena, where the affairs of the street and the gossip of the tea-table chiefly are discussed? Or shall it be a quarter of heaven itself,—an hypæthral temple, consecrated to the service of the gods? I find it so difficult to dispose of the few facts which to me are significant, that I hesitate to burden my attention with those which are insignificant, which only a divine mind could illustrate. Such is, for the most part, the news in newspapers and conversation. It is important to preserve the mind’s chastity in this respect. Think of admitting the details of a single case of the criminal court into our thoughts, to stalk profanely through their very sanctum sanctorum for an hour, ay, for many hours! to make a very bar-room of the mind’s inmost apartment, as if for so long the dust of the street had occupied us,—the very street itself, with all its travel, its bustle, and filth, had passed through our thoughts’ shrine! Would it not be an intellectual and moral suicide?
Henry David Thoreau

The longer I live, the more urgent it seems to me to endure and transcribe the whole dictation of existence up to its end, for it might just be the case that only the very last sentence contains that small and possibly inconspicuous word through which everything we had struggled to learn and everything we had failed to understand will be transformed suddenly into magnificent sense.
Rainer Maria Rilke

I worship freedom; I abhor restraint, trouble, dependence. As long as the money in my purse lasts, it assures my independence; it relieves me of the trouble of finding expedients to replenish it, a necessity which has always inspired me with dread; but the fear of seeing it exhausted makes me hoard it carefully. The money which a man possesses is the instrument of freedom.; that which we eagerly pursue is the instrument of slavery. Therefore I hold fast to that which I have, and desire nothing.
Jean-Jacques Rousseau

Man is but a reed, the most feeble thing in nature, but he is a thinking reed. The entire universe need not arm itself to crush him. A vapor, a drop of water suffices to kill him. But, if the universe were to crush him, man would still be more noble than that which killed him, because he knows that he dies and the advantage which the universe has over him; the universe knows nothing of this. All our dignity consists then in thought. By it we must elevate ourselves, and not by space and time which we cannot fill. Let us endeavor to think well; this is the principle of morality.
Blaise Pascal

Just as the eye which constantly shifts its gaze, now turning to the right or to the left, now incessantly peering up and down, cannot see distinctly what lies before it, ... so too man's mind when distracted by his countless worldly cares cannot focus itself distinctly on the truth.
Basil of Caesarea

It is so easy to be immature. If I have a book to serve as my understanding, a pastor to serve as my conscience, a physician to determine my diet for me, and so on, I need not exert myself at all. I need not think, if only I can pay: others will readily undertake the irksome work for me. The guardians who have so benevolently taken over the supervision of men have carefully seen to it that the far greatest part of them (including the entire fair sex) regard taking the step to maturity as very dangerous, not to mention difficult. Having first made their domestic livestock dumb, and having carefully made sure that these docile creatures will not take a single step without the go-cart to which they are harnessed, these guardians then show them the danger that threatens them, should they attempt to walk alone. Now this danger is not actually so great, for after falling a few times they would in the end certainly learn to walk; but an example of this kind makes men timid and usually frightens them out of all further attempts.
Immanuel Kant

The use of culture is that it helps us, by means of its spiritual standard of perfection, to regard wealth as but machinery, and not only to say as a matter of words that we regard wealth as but machinery, but really to perceive and feel that it is so. If it were not for this purging effect wrought upon our minds by culture, the whole world, the future as well as the present, would inevitably belong to the Philistines. The people who believe most that our greatness and welfare are proved by our being very rich, and who most give their lives and thoughts to becoming rich, are just the very people whom we call the Philistines. Culture says: “Consider these people, then, their way of life, their habits, their manners, the very tones of their voice; look at them attentively; observe the literature they read, the things which give them pleasure, the words which come forth out of their mouths, the thoughts which make the furniture of their minds; would any amount of wealth be worth having with the condition that one was to become just like these people by having it?”
Matthew Arnold

Find out the reason that commands you to write; see whether it has spread its roots into the very depths of your heart; confess to yourself whether you would have to die if you were forbidden to write. This most of all: ask yourself in the most silent hour of your night: must I write? Dig into yourself for a deep answer. And if this answer rings out in assent, if you meet this solemn question with a strong, simple “I must”, then build your life in accordance with this necessity; your whole life, even into its humblest and most indifferent hour, must become a sign and witness to this impulse.
Rainer Maria Rilke

A man cannot live intensely except at the cost of the self. Now the bourgeois treasures nothing more highly than the self (rudimentary as his may be). And so at the cost of intensity he achieves his own preservation and security. His harvest is a quiet mind which he prefers to being possessed by God, as he does comfort to pleasure, convenience to liberty, and a pleasant temperature to that deathly inner consuming fire. The bourgeois is consequently by nature a creature of weak impulses, anxious, fearful of giving himself away and easy to rule.
Herman Hesse

Most of the time man does not do what he wills, but what he has willed. Through his decisions, he always gives himself only a certain direction, in which he then moves until the next moment of reflection. We do not will continuously, we only will intermittently, piece by piece. We thus save ourselves from willing: principle of the economy of the will. But the higher man always experiences this as thoroughly immoral.
Otto Weininger

Everything that our present-day psychologist has to tell us—and here we refer not only to the systematic science but also in the wider sense to the physiognomic knowledge of men—relates to the present condition of the Western soul, and not, as hitherto gratuitously assumed, to “the human soul” at large.
Oswald Spengler

The will to power operating under a pure democratic disguise has finished off its masterpiece so well that the object's sense of freedom is actually flattered by the most thorough-going enslavement that has ever existed.
Oswald Spengler

The public, therefore, among a democratic people, has a singular power, which aristocratic nations cannot conceive; for it does not persuade others to its beliefs, but it imposes them and makes them permeate the thinking of everyone by a sort of enormous pressure of the mind of all upon the individual intelligence. In the United States the majority undertakes to supply a multitude of ready-made opinions for the use of individuals, who are thus relieved from the necessity of forming opinions of their own. Everybody there adopts great numbers of theories, on philosophy, morals, and politics, without inquiry, upon public trust; and if we examine it very closely, it will be perceived that religion itself holds sway there much less as a doctrine of revelation than as a commonly received opinion.
Alexis de Tocqueville

And I have known the eyes already, known them all—
The eyes that fix you in a formulated phrase,
And when I am formulated, sprawling on a pin,
When I am pinned and wriggling on the wall,
Then how should I begin
To spit our the butt-ends of my days and ways?
And how should I presume?
T. S. Eliot

I call that mind free, which masters the senses, which protects itself against animal appetites, which contemns pleasure and pain in comparison to its own energy, which penetrates beneath the body and recognises its own reality and greatness, which passes life, not in asking what it shall eat or drink, but in hungering, thirsting, and seeking after righteousness.

I call that mind free, which escapes the bondage of matter, which, instead of stopping at the material universe and making it a prison wall, passes beyond it to its Author, and finds in the radiant signatures which everywhere bears of the Infinite Spirit, helps to its own spiritual enlightenment.

I call that mind free, which jealously guards its intellectual rights and powers, which calls no man master, which does not content itself with a passive or hereditary faith, which opens itself to light whencesoever it may come, which receives new truth as an angel from heaven.

I call that mind free, which sets no bounds to its love, which is not imprisoned in itself or in a sect, which recognises in all human beings the image of God and the rights of his children, which delights in virtue and sympathizes with suffering wherever they are seen, which conquers pride, anger, and sloth, and offers itself up a willing victim to the cause of mankind.
William Ellery Channing

The craze for society, diversion, amusement, and luxury of every kind ... lead many to extravagance and so to misery. Nothing protects us so surely from this wrong turning as inner wealth, the wealth of the mind, for the more eminent it becomes, the less room does it leave for boredom. The inexhaustible activity of ideas, their constantly renewed play with the manifold phenomena of the inner and outer worlds, the power and urge always to make different combinations of them, all these put the eminent mind, apart from moments of relaxation, quite beyond the reach of boredom.
Schopenhauer

A taste for the best books, as a taste for whatever is best, is acquired; and it can be acquired only by long study and practice. It is a result of free and disinterested self-activity, of efforts to attain what rarely brings other reward than the consciousness of having loved and striven for the best.
John Lancaster Spalding

In his heart every man knows quite well that, being unique, he will be in the world only once and that no imaginable chance will for a second time gather together into a unity so strangely variegated an assortment as he is: he knows it but he hides it like a bad conscience—why? From fear of his neighbor, who demands conventionality and cloaks himself with it. But what is it that constrains the individual to fear his neighbor, to think and act like a member of a herd, and to have no joy in himself? Modesty, perhaps, in a few rare cases. With the great majority it is indolence, inertia. ... Men are even lazier than they are timid, and fear most of all the inconveniences with which unconditional honesty and nakedness would burden them. Artists alone hate this sluggish promenading in borrowed fashions and appropriated opinions and they reveal everyone’s secret bad conscience, the law that every man is a unique miracle.
Friedrich Nietzsche

You are a genius

Monday, March 31, 2014

Imaginary numbers

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