Fourier Quotes

True greatness is when your name is like ampere, watt, and fourier—when it's spelled with a lower case letter.

The method of doubt must be applied to civilization; we must doubt its necessity, its excellence, and its permanence.

Despots prefer the friendship of the dog, who, unjustly mistreated and debased, still loves and serves the man who wronged him.

Matt laughed. "Close. That was last year. This year it's Obsessive Deovtion to Fourier Analysis Theory and Applications. And my personal favorite, Quantum Physics II: Romantic Entanglements of Energy and Matter." Julie turned her head to Matt. "You're a double major? Physics and math? Jesus..." "I know. Nerdy." He shrugged. "No, I'm impressed. I'm just surprised your brains fit in your head." "I was fitted with a specially desinged compression filter that allows excessive information to lie dormant until I need to access it. It's only the Beta version, so excuse any kinks that may appear. I really can't be held responsible.

The Civilized… murder their children by producing too many of them without being able to provide for their well-being. Morality or theories of false virtue stimulate them to manufacture cannon fodder, anthills of conscripts who are forced to sell themselves out of poverty. This improvident paternity is a false virtue, the selfishness of pleasure.

76. David Hume – Treatise on Human Nature; Essays Moral and Political; An Enquiry Concerning Human Understanding 77. Jean-Jacques Rousseau – On the Origin of Inequality; On the Political Economy; Emile – or, On Education, The Social Contract 78. Laurence Sterne – Tristram Shandy; A Sentimental Journey through France and Italy 79. Adam Smith – The Theory of Moral Sentiments; The Wealth of Nations 80. Immanuel Kant – Critique of Pure Reason; Fundamental Principles of the Metaphysics of Morals; Critique of Practical Reason; The Science of Right; Critique of Judgment; Perpetual Peace 81. Edward Gibbon – The Decline and Fall of the Roman Empire; Autobiography 82. James Boswell – Journal; Life of Samuel Johnson, Ll.D. 83. Antoine Laurent Lavoisier – Traité Élémentaire de Chimie (Elements of Chemistry) 84. Alexander Hamilton, John Jay, and James Madison – Federalist Papers 85. Jeremy Bentham – Introduction to the Principles of Morals and Legislation; Theory of Fictions 86. Johann Wolfgang von Goethe – Faust; Poetry and Truth 87. Jean Baptiste Joseph Fourier – Analytical Theory of Heat 88. Georg Wilhelm Friedrich Hegel – Phenomenology of Spirit; Philosophy of Right; Lectures on the Philosophy of History 89. William Wordsworth – Poems 90. Samuel Taylor Coleridge – Poems; Biographia Literaria 91. Jane Austen – Pride and Prejudice; Emma 92. Carl von Clausewitz – On War 93. Stendhal – The Red and the Black; The Charterhouse of Parma; On Love 94. Lord Byron – Don Juan 95. Arthur Schopenhauer – Studies in Pessimism 96. Michael Faraday – Chemical History of a Candle; Experimental Researches in Electricity 97. Charles Lyell – Principles of Geology 98. Auguste Comte – The Positive Philosophy 99. Honoré de Balzac – Père Goriot; Eugenie Grandet 100. Ralph Waldo Emerson – Representative Men; Essays; Journal 101. Nathaniel Hawthorne – The Scarlet Letter 102. Alexis de Tocqueville – Democracy in America 103. John Stuart Mill – A System of Logic; On Liberty; Representative Government; Utilitarianism; The Subjection of Women; Autobiography 104. Charles Darwin – The Origin of Species; The Descent of Man; Autobiography 105. Charles Dickens – Pickwick Papers; David Copperfield; Hard Times 106. Claude Bernard – Introduction to the Study of Experimental Medicine 107. Henry David Thoreau – Civil Disobedience; Walden 108. Karl Marx – Capital; Communist Manifesto 109. George Eliot – Adam Bede; Middlemarch 110. Herman Melville – Moby-Dick; Billy Budd 111. Fyodor Dostoevsky – Crime and Punishment; The Idiot; The Brothers Karamazov 112. Gustave Flaubert – Madame Bovary; Three Stories 113. Henrik Ibsen – Plays 114. Leo Tolstoy – War and Peace; Anna Karenina; What is Art?; Twenty-Three Tales 115. Mark Twain – The Adventures of Huckleberry Finn; The Mysterious Stranger 116. William James – The Principles of Psychology; The Varieties of Religious Experience; Pragmatism; Essays in Radical Empiricism 117. Henry James – The American; The Ambassadors 118. Friedrich Wilhelm Nietzsche – Thus Spoke Zarathustra; Beyond Good and Evil; The Genealogy of Morals;The Will to Power 119. Jules Henri Poincaré – Science and Hypothesis; Science and Method 120. Sigmund Freud – The Interpretation of Dreams; Introductory Lectures on Psychoanalysis; Civilization and Its Discontents; New Introductory Lectures on Psychoanalysis 121. George Bernard Shaw – Plays and Prefaces

The peoples of civilization see their wretchedness increase in direct proportion to the advance of industry.

There cannot be a language more universal and more simple, more free from errors and obscurities...more worthy to express the invariable relations of all natural things [than mathematics]. [It interprets] all phenomena by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes

the family is a group that needs to escape from itself...

The principle of equality sums up the teachings of moralists. But it also contains something more. This something more is respect for the individual. By proclaiming our morality of equality, or anarchism, we refuse to assume a right which moralists have always taken upon themselves to claim, that of mutilating the individual in the name of some ideal. We do not recognize this right at all, for ourselves or anyone else. We recognize the full and complete liberty of the individual; we desire for him plentitude of existence, the free development of all his faculties. We wish to impose nothing upon him; thus returning to the principle which Fourier placed in opposition to religious morality when he said: "Leave men absolutely free. Do not mutilate them as religions have done enough and to spare. Do not fear even their passions. In a free society these are not dangerous.

Social progress and changes of historical period take place in proportion to the advance of women toward liberty, and social decline occurs as a result of the diminution of the liberty of women.

The philosophers say that the passions are too lively, too fiery; in truth they are weak and languid. All around one sees the mass of men endure the persecution of a few masters and the despotism of prejudices without offering the slightest resistance... their passions are too weak to permit them to derive audacity from despair.

Under civilization poverty is born of superabundance itself.

the root of the opposition to liberalism cannot be reached by resort to the method of reason. This opposition does not stem from reason, but from a pathological mental attitude, from resentment and from a neurasthenic condition that one might call a Fourier complex, after the French socialist of that name

… Fourier's great mathematical poem ... {Referring to Joseph Fourier's mathematical theory of the conduction of heat, one of the precursors to thermodynamics.}

Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..." Klapaucius thought, and thought some more. Finally he nodded and said: "Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit." "Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming: Come, let us hasten to a higher plane, Where dyads tread the fairy fields of Venn, Their indices bedecked from one to n, Commingled in an endless Markov chain! Come, every frustum longs to be a cone, And every vector dreams of matrices. Hark to the gentle gradient of the breeze: It whispers of a more ergodic zone. In Reimann, Hilbert or in Banach space Let superscripts and subscripts go their ways. Our asymptotes no longer out of phase, We shall encounter, counting, face to face. I'll grant thee random access to my heart, Thou'lt tell me all the constants of thy love; And so we two shall all love's lemmas prove, And in bound partition never part. For what did Cauchy know, or Christoffel, Or Fourier, or any Boole or Euler, Wielding their compasses, their pens and rulers, Of thy supernal sinusoidal spell? Cancel me not--for what then shall remain? Abscissas, some mantissas, modules, modes, A root or two, a torus and a node: The inverse of my verse, a null domain. Ellipse of bliss, converge, O lips divine! The product of our scalars is defined! Cyberiad draws nigh, and the skew mind Cuts capers like a happy haversine. I see the eigenvalue in thine eye, I hear the tender tensor in thy sigh. Bernoulli would have been content to die, Had he but known such a^2 cos 2 phi!

It appears to me," said the daguerreotypist, smiling, "that Uncle Venner has the principles of Fourier at the bottom of his wisdom; only they have not quite so much distinctness in his mind as in that of the systematizing Frenchman.

To speak frankly, the family bond in the civilized regime causes fathers to desire the death of their children and children to desire the death of their fathers.

Condon, quick on his feet, replied that the accusation was untrue. He was not a revolutionary in physics. He raised his right hand: “I believe in Archimedes’ Principle, formulated in the third century B.C. I believe in Kepler’s laws of planetary motion, discovered in the seventeenth century. I believe in Newton’s laws.…” And on he went, invoking the illustrious names of Bernoulli, Fourier, Ampère, Boltzmann, and Maxwell.

Love in the Phalanstery is no longer, as it is with us, a recreation which detracts from work; on the contrary it is the soul and the vehicle, the mainspring, of all works and of the whole of universal attraction.

Derrière la série de Fourier, d'autres séries analogues sont entrées dans la domaine de l'analyse; elles y sont entrees par la même porte; elles ont été imaginées en vue des applications. After the Fourier series, other series have entered the domain of analysis; they entered by the same door; they have been imagined in view of applications.

Wisdom, virtue, morality, all these have fallen out of fashion: everybody worships at the shrine of commerce.

Philosophy was right to vaunt liberty; it is the foremost desire of all creatures. But philosophy forgot that in civilized societies liberty is illusory if the common people lack wealth. When the wage-earning classes are poor, their independence is as fragile as a house without foundations. The free man who lacks wealth immediately sinks back under the yoke of the rich. The newly freed slave takes fright at the need of providing for his own subsistence and hastens to sell himself back into slavery in order to escape this new anxiety that hangs over him like Damocles' sword. In thoughtlessly giving him liberty without wealth, you merely replace his physical torment with a mental torment. He finds life burdensome in his new state... Thus when you give liberty to the people, it must be bolstered by two supports which are the guarantee of comfort and industrial attraction...

You know what I believe? I remember in college I was taking this math class, this really great math class taught by this tiny old woman. She was talking about fast Fourier transforms and she stopped midsentence and said, ‘Sometimes it seems the universe wants to be noticed.’ “That’s what I believe. I believe the universe wants to be noticed. I think the universe is improbably biased toward consciousness, that it rewards intelligence in part because the universe enjoys its elegance being observed. And who am I, living in the middle of history, to tell the universe that it—or my observation of it—is temporary?

The experiment, so far as its original projectors were concerned, proved, long ago, a failure; first lapsing into Fourierism, and dying, as it well deserved, for this infidelity to its own higher spirit. Where

Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy. Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.

Charlie Black: Fourierism was tried in the late nineteenth century… and it failed. Wasn’t Brook Farm Fourierist? It failed. Tom Townsend: That’s debatable. Charlie Black: Whether Brook Farm failed? Tom Townsend: That it ceased to exist, I’ll grant you, but whether or not it failed cannot be definitively said. Charlie Black: Well, for me, ceasing to exist is — is failure. I mean, that’s pretty definitive. Tom Townsend: Well, everyone ceases to exist. Doesn’t mean everyone’s a failure.

It is easy to compress the passions by violence. Philosophy suppresses them with a stroke of the pen. Locks and the sword come to the aid of sweet morality, but nature appeals these judgments; she regains her rights in secret. Passion stifled at one point reappears at another like water held back by a dike; it is driven inward like the fluid of an ulcer closed to soon.

The deep study of nature is the most fruitful source of mathematical discoveries. By offering to research a definite end, this study has the advantage of excluding vague questions and useless calculations; besides it is a sure means of forming analysis itself and of discovering the elements which it most concerns us to know, and which natural science ought always to conserve.

Leibniz’s brilliant monadic system naturally gives rise to calculus (the main tool of mathematics and science). But it was not Leibniz who linked the energy of monads to waves – that was done later following the work of the French genius Jean Baptiste Joseph Fourier on Fourier series and Fourier transforms. Nevertheless, Leibniz’s idea of energy originating from countless mathematical points and flowing across a plenum is indeed the first glimpse in the modern age of “field theory” that now underpins contemporary physics. Leibniz was centuries ahead of his time. Leibniz’s system is entirely mathematical. It brings mathematics to life. The infinite collection of monads constitutes an evolving cosmic organism, unfolding according to mathematical laws.

Ontological Fourier mathematics is the complete mathematical explanation of Cartesian philosophy. It converts a substance dualism into a dual-aspect substance monism. There is only one substance - mathematics - but it can exist both dimensionlessly (as mind) and dimensionally (as matter, the product of mind). Mind adds the framing dimensions of space (extended real numbers) and time (extended imaginary numbers) to the unextended real and imaginary numbers of the frequency domain. (Ontologically, frequencies are not in space and time. They are instead the source of space and time).

Illuminism is based on Euler’s Formula. Euler’s Formula is the basis of Fourier mathematics. Fourier mathematics is the basis of quantum mechanics. Quantum mechanics is the basis of the scientific world. Therefore Euler’s Formula is the basis of the scientific world, and the basis of everything.

More pertinent, however, is that capitalism tends to stultify the worker’s creativity, his human urge for self-expression, freedom, mutually respectful interaction with others, recognition of his self-determined sense of self, recognition of himself as a self rather than an object, a means to an end. Karl Marx called it “alienation.” Capitalism alienates the worker—and the capitalist—from his “fundamental human need” for “self-fulfilling and creative work,” “the exercise of skill and craftsmanship,”8 in addition to his fundamental desire to determine himself (whence comes the desire to dismantle oppressive power-relations and replace them with democracy). Alternative visions of social organization thus arise, including Robert Owen’s communitarian socialism, Charles Fourier’s associationist communalism, Proudhon’s mutualism (a kind of anarchism), Marx’s communism, Bakunin’s collectivist anarchism, Kropotkin’s anarchist communism, Anton Pannekoek’s council communism, and more recently, Murray Bookchin’s libertarian municipalism, Michael Albert’s participatory economics, Takis Fotopoulos’s inclusive democracy, Paul Hirst’s associationalism, and so on. Each of these schools of thought differs from the others in more or less defined ways, but they all have in common the privileging of economic and social cooperation and egalitarianism.

Claro que si uno tuviera un receptor con paso de banda estrecha, y escuchara solo un mínimo margen de frecuencias, estaría obligado a aceptar la constante de tiempo larga. Jamás podríamos detectar una modulación rápida. Eso era una simple consecuencia del Teorema Integral de Fourier, estrechamente vinculado con el Principio de Incertidumbre de Heisenberg.

Ignorant as regards the unity of man with himself, the world is still more ignorant in respect to the two other unities - unity of man with God and the universe.

Civilization is the subordination of the individual to the welfare of the community.

Everything that exists is moral to the extent that it produces an equilibrium.

The unity of man and nature is the fundamental principle of a sound society.

The character of a society can be measured by the way it treats its most vulnerable members.

Civilization is built upon the unhappiness of others.

Fourier's scheme of changing, by means of phalansteries, the water of all the seas into tasty lemonade was surely a phantastic idea. But Bernstein, proposing to change the sea of capitalist bitterness into a sea of socialist sweetness, by progressively pouring into it bottles of social reformist lemonade, presents an idea that is merely more insipid but no less phantastic.

Neoclassical Assumptions in Contemporary Prescriptive Grammar,” “The Implications of Post-Fourier Transformations for a Holographically Mimetic Cinema,” “The Emergence of Heroic Stasis in Broadcast Entertainment” —’ ‘ “Montague Grammar and the Semantics of Physical Modality”?’ ‘ “A Man Who Began to Suspect He Was Made of Glass”?’ ‘ “Tertiary Symbolism in Justinian Erotica”?

Furious, the beast writhed and wriggled its iterated integrals beneath the King’s polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann’s Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out, fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier-—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, “Hurrah! Victory!!

Charles Fourier, in France, and Robert Owen, in England, propounded the original idea of socialism in the 1820s. It was to achieve the unrealized demands of the French Revolution, which never reached the working class. Instead of pitting workers against each other, a cooperative mode of production and exchange would allow them to work for each other. Socialism was about reorganizing society as a cooperative community.

If Fourierism could be realised (which it surely cannot) out of a dream, the destinies of our race would shrivel up under the unnatural heat, and human nature would, in my mind, be desecrated and dishonored — because I do not believe in purification without suffering, in progress without struggle, in virtue without temptation. Least of all do I consider happiness the end of man’s life. We look to higher things, have nobler ambitions.

but in areas and with titles, I’m sure you recall quite well, Hal: “Neoclassical Assumptions in Contemporary Prescriptive Grammar,” “The Implications of Post-Fourier Transformations for a Holographically Mimetic Cinema,” “The Emergence of Heroic Stasis in Broadcast Entertainment”—’ ‘ “Montague Grammar and the Semantics of Physical Modality”?’ ‘ “A Man Who Began to Suspect He Was Made of Glass”?’ ‘ “Tertiary Symbolism in Justinian Erotica”?

The almost timeless curvature of the space of ideas obeys neither chronology nor history. So the thoughts of Sade and Fourier are like anticipated repercussions of the theories of Marx and Freud, of which they are a much more radical critique avant la lettre than any that were to follow, exerting their effects only posthumously. To reread the world of ideas against the grain of the ideology of the Enlightenment, the ideology of a chronological order of events.

The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms.

E per tutto il giorno mi riempivano la testa di stronzate che volevano farmi tenere a mente, come ad esempio le equazioni per calcolare la distanza fra il posto dove ci trovavamo e quelle in cui volevano farci andare loro, e naturalmente quelle per tornare indietro; cazzate come le coordinate coassiali, il calcolo dei coseni, la trigonometria sferoide, l'algebra di Boolean, gli antilogaritmi, l'analisi di Fourier, quadrati e matrici. Mi dissero che io avrei dovuto fare da riserva al computer di riserva.

As for the socialists, I quite agree with you that various of them, yes, and some of their chief men, are full of pure and noble aspiration, the most virtuous of men and the most benevolent. Still, they hold in their hands, in their clean hands, ideas that kill, ideas which defile, ideas which, if carried out, would be the worst and most crushing kind of despotism. I would rather live under the feet of the Czar than in those states of perfectibility imagined by Fourier and Cabet, if I might choose my ‘pis aller.

Roughly speaking what Fourier developed was a mathematical way of converting any pattern, no matter how complex, into a language of simple waves. He also showed how these wave forms could be converted back into the original pattern. In other words, just as a television camera converts an image into electromagnetic frequencies and a television set converts those frequencies back into the original image, Fourier showed how a similar process could be achieved mathematically. The equations he developed to convert images into wave forms and back again are known as Fourier transforms.

Feminism is a combination of social and political movements with a common goal to define, develop, and demand political, social, and fiscal rights for women. I'm sorry to tell you that a man coined the term. Charles Fourier, Utopian French Philosopher, came up with the word. Of course he did. It was 1837 when no one listened to women. I'm willing to bet his girlfriend coined it half an hour before, but no one took it seriously until he said it and then mansplained it to her. He didn't have a wife because he thought traditional marriage was damaging to women's rights. He was also a queer positive, socialist.

Great mathematical geniuses such as Pythagoras, Plato, Descartes, Leibniz, Fourier and Gödel all recognized that mathematics is ontological. ‘Real’ mathematics is ontological mathematics that tells us about reality; it’s not abstract mathematics that has no connection with reality, as most professional mathematicians seem to believe. Reality is 100% mathematical. Above all, Fourier mathematics is the key to the mystery of the universe because it’s the answer to the mystery of mind and matter and how they interact. Mind is the Fourier frequency domain and matter is the inverse Fourier spacetime domain, and the two domains are absolutely tied together in feedback loop. The universe, finally, is a hologram and holography is all about Fourier mathematics.

Morgan’s argument that prehistoric societies practiced group marriage (also known as the primal horde or omnigamy—the latter term apparently coined by French author Charles Fourier) so influenced Darwin’s thinking that he admitted, “It seems certain that the habit of marriage has been gradually developed, and that almost promiscuous intercourse was once extremely common throughout the world.” With his characteristic courteous humility, Darwin agreed that there were “present day tribes” where “all the men and women in the tribe are husbands and wives to each other.” In deference to Morgan’s scholarship, Darwin continued, “Those who have most closely studied the subject, and whose judgment is worth much more than mine, believe that communal marriage was the original and universal form throughout the world….

Reality is based on unobservable mathematical points (singularities). That’s the secret of existence. What’s at the centre of a black hole? – a singularity. What was the Big Bang? – a singularity event. What is the Big Crunch? – when spacetime returns to a singularity. What is light made of? – photonic singularities (immaterial and dimensionless; according to Einstein’s special theory of relativity, photons have no mass, are maximally length contracted to zero, and time has stopped for them). The whole universe is made of light. It comes from light and returns to light. Light is all about points – singularities. Light is the basis of thought, the basis of mind, and the basis of matter. Everything is derived from light, and light is nothing but mathematical points defined by the generalised Euler Formula, and it creates the visible world via Fourier mathematics.

When Pribram encountered Bernstein's work he immediately recognized its implications. Maybe the reason hidden patterns surfaced after Bernstein Fourier-analyzed his subject's movements was because that was how movements are stored in the brain. This was an exciting possibility, for if the brain analyzed movements by breaking them down into their frequency components, it explained the rapidity with which we learn many complex physical tasks. For instance, we do not learn to ride a bicycle by painstakingly memorizing every tiny feature of the process. We learn by grasping the whole flowing movement. The fluid wholeness that typifies how we learn so many physical activities is difficult to explain if our brains are storing information in a bit-by-bit manner. But it becomes much easier to understand if the brain is Fourier-analyzing such tasks and absorbing them as a whole.

When we see civilization elated with this declining and decrepit phase of its career, we are reminded of a faded belle who, boasting of her attractions in her fiftieth year, excites at once the remark that she was fairer at twenty-five. So it is with civilization, which, dreaming of perfection and progress, is constantly deteriorating, and which will find but too soon in its industrial achievements new sources of political oppression, crimes and commotions.

Frances Wright was a writer, founder of a utopian community, immigrant from Scotland in 1824, a fighter for the emancipation of slaves, for birth control and sexual freedom. She wanted free public education for all children over two years of age in state-supported boarding schools. She expressed in America what the utopian socialist Charles Fourier had said in France, that the progress of civilization depended on the progress of women. In her words: I shall venture the assertion, that, until women assume the place in society which good sense and good feeling alike assign to them, human improvement must advance but feebly. . . . Men will ever rise or fall to the level of the other sex. . . . Let them not imagine that they know aught of the delights which intercourse with the other sex can give, until they have felt the sympathy of mind with mind, and heart with heart; until they bring into that intercourse every affection, every talent, every confidence, every refinement, every respect. Until power is annihilated on one side, fear and obedience on the other, and both restored to their birthright—equality.

So they rolled up their sleeves and sat down to experiment -- by simulation, that is mathematically and all on paper. And the mathematical models of King Krool and the beast did such fierce battle across the equation-covered table, that the constructors' pencils kept snapping. Furious, the beast writhed and wriggled its iterated integrals beneath the King's polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann's Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F_1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, "Hurrah! Victory!!

There is a class of writers who are ever boasting of the progress of civilization and of the human mind in modern times. If we were to credit their pretensions, we should be led to believe that the science of society had reached its highest degree of perfection, because old metaphysical and economic theories have been somewhat refined upon. In answer to their boasts of social progress, it is not sufficient to refer to the deeply-rooted social evils which exist, and which prey upon our boasted civilized social order. We will mention but a single one, the frightful increase of national debts and of taxation.

Dedicating my energies to the study of the social organisation which is in the future to replace the present condition of things, I’ve come to the conviction that all makers of social systems from ancient times up to the present year, 187-, have been dreamers, tellers of fairy-tales, fools who contradicted themselves, who understood nothing of natural science and the strange animal called man. Plato, Rousseau, Fourier, columns of aluminium, are only fit for sparrows and not for human society. But, now that we are all at last preparing to act, a new form of social organisation is essential. In order to avoid further uncertainty, I propose my own system of world-organisation. Here it is.” He tapped the notebook. “I wanted to expound my views to the meeting in the most concise form possible, but I see that I should need to add a great many verbal explanations, and so the whole exposition would occupy at least ten evenings, one for each of my chapters.” (There was the sound of laughter.) “I must add, besides, that my system is not yet complete.” (Laughter again.) “I am perplexed by my own data and my conclusion is a direct contradiction of the original idea with which I start. Starting from unlimited freedom, I arrive at unlimited despotism. I will add, however, that there can be no solution of the social problem but mine.

Despite the popularity of this view, the DeValoises felt it was only a partial truth. To test their assumption they used Fourier's equations to convert plaid and checkerboard patterns into simple wave forms. Then they tested to see how the brain cells in the visual cortex responded to these new wave-form images. What they found was that the brain cells responded not to the original patterns, but to the Fourier translations of the patterns. Only one conclusion could be drawn. The brain was using Fourier mathematics—the same mathematics holography employed—to convert visual images into the Fourier language of wave forms. 12 The DeValoises' discovery was subsequently confirmed by numerous other laboratories around the world, and although it did not provide absolute proof the brain was a hologram, it supplied enough evidence to convince Pribram his theory was correct. Spurred on by the idea that the visual cortex was responding not to patterns but to the frequencies of various wave forms, he began to reassess the role frequency played in the other senses. It didn't take long for him to realize that the importance of this role had perhaps been overlooked by twentieth-century scientists. Over a century before the DeValoises' discovery, the German physiologist and physicist Hermann von Helmholtz had shown that the ear was a frequency analyzer. More recent research revealed that our sense of smell seems to be based on what are called osmic frequencies. Bekesy's work had clearly demonstrated that our skin is sensitive to frequencies of vibration, and he even produced some evidence that taste may involve frequency analysis. Interestingly, Bekesy also discovered that the mathematical equations that enabled him to predict how his subjects would respond to various frequencies of vibration were also of the Fourier genre.

T'is but too true, that for five and twenty centuries since the political and moral sciences have been cultivated, they have done nothing for the happiness of mankind. They have tended only to increase human perversity, to perpetuate indigence, and to reproduce the same evils under different forms. After all their fruitless attempts to ameliorate the social order, there remains to the authors of these sciences only the conviction of their utter incompetency. The problem of human happiness is one which they have been wholly unable to solve. Meanwhile a universal restlessness attests that mankind has not attained to the destiny to which nature would lead it, and this restlessness would seem to presage some great event which shall radically change its social condition. The nations of the earth harassed by misfortune, and so deceived by political empirics, still hope for a better future, and resemble the invalid who looks for a miraculous cure. Nature whispers in the ear of the human race, that for it is reserved a happiness, the means of attaining which are now unknown, and that some marvelous discovery will be made, which will suddenly dispel the darkness that now enshrouds the social world.

Fourier succeeded in proving a theorem concerning sine waves which astonished his, at first, incredulous contemporaries. He showed that any variation of a quantity with time can be accurately represented as the sum of a number of sinusoidal variations of different amplitudes, phases, and frequencies.

the simple algebraic equation ω+k3 = 0. This is called the dispersion relation of (1): with the help of the Fourier transform it is not hard to show that every solution is a superposition of solutions of the form ei(kx-ωt), and the dispersion relation tells us how the “wave number” k is related to the “angular frequency” ω in each of these elementary solutions.

Susurrus whispers through the grass and gorse, godling of the Martian wind, gene-spliced tyke of Zephyros and Ares. His story needs no Ovid, tells itself in the rustle of striplings and flowers he loves, the tale that he is: a zygote collaged from: spermatazoa flensed to nuclear caducei; a mathematical transform by the Fréres Fourier, Jean and Charles, flip of an axis changing Y to X; and the egg from which Eros hatched, is always hatching, offered up blithely to a god of war gone broody, Ares a sharper marksman than any brat with bow and arrow, no more to be argued with than the groundling Renart in a frum.

What is incredible about the Fourier idea is that any waveform can be constructed by adding waves of the simplest form together.

Fourier believed the world would eventually contain thirty-seven million poets equal to Homer, thirty-seven million mathematicians equal to Newton, and thirty-seven million dramatists equal to Molière—although, he admitted, these were only “approximate estimates.

Materialists simply cannot conceive of immaterial, non-sensory things. Yet the irony is that mathematics is entirely immaterial and non-sensory ... and is the core of scientific materialism! Work that one out. It’s mathematics that defines “immaterial substance” and does so via the God Equation, and Fourier frequency singularities. Of course, Hobbes had the excuse that he didn’t know any of that ... but modern scientists have no such excuse. They have complete access to Euler’s Formula and Fourier mathematics. What they lack is intelligence, imagination and a proper ontology and epistemology, and any understanding whatsoever of what mathematics actually is.

What the uncertainty principle really reflects is the fact that a quantum entity is neither a wave nor a particle but contains both attributes at the same time. The essence of this principle is the Fourier idea. One can create a wave pulse from adding a handful of pure waves of definite frequencies. Similarly, the particle-like property (a pulse) can emerge from the wave-like property and vice versa.

The uncertainty of being able to know both where a particle is and where it is going beautifully mirrors jazz improvisation. And isn't it mind blowing that the spectrum of vibrations that were amplified by inflation, those that led to the structure in our universe today, is the same as the spectrum of noise? Fundamental to it all is the Fourier addition of waves. The harnonic structure of the cosmic microwave background emerges from quantum noise, just as distinct beats and rhythms emerge from a fundamental waveform, an oscillation, a uniform repetition, a circle.

From this premise, the usual conclusions follow: humankind is now separated from the true and the real; its destiny is to arrive at the consummation intended for it by God; philosophers are here to help the rest of us understand what that consummation is. James’s particular conception of it was derived in part from his reading of Swedenborg and in part from a writer with whom Swedenborg was often paired in the nineteenth century, the French socialist Charles Fourier: ‘Man’s destiny on earth,’ as James expressed it in Substance and Shadow (1863), ‘…consists in the realization of a perfect society, fellowship, or brotherhood among men.’ The chief impediment to arriving at this redeemed state was belief in an independent selfhood (what Swedenborg called the ‘proprium’). James considered this belief ‘the great parental fount of all the evils that desolate humanity.’ Belief in selfhood was bad because it led some people to regard themselves as superior to other people.

A book on Fourier mathematics contains infinitely more true knowledge than of all the religious texts of the world put together.

si le verbe civiliser se trouve déjà avec la signification que nous lui prêtons chez les bons auteurs du XVIIIe siècle, le substantif civilisation ne se rencontre que chez les économistes de l’époque qui a précédé immédiatement la Révolution. Littré cite un exemple pris chez Turgot. Littré, qui avait dépouillé toute notre littérature, n’a pas pu remonter plus loin. Ainsi le mot civilisation n’a pas plus d’un siècle et demi d’existence. Il n’a fini par entrer dans le dictionnaire de l’Académie qu’en 1835, il y a un peu moins de cent ans… L’antiquité, dont nous vivons encore, n’avait pas non plus de terme pour rendre ce que nous entendons par civilisation. Si l’on donnait ce mot-là à traduire dans un thème latin, le jeune élève serait bien embarrassé… La vie des mots n’est pas indépendante de la vie des idées. Le mot de civilisation, dont nos ancêtres se passaient fort bien, peut-être parce qu’ils avaient la chose, s’est répandu au XIXe siècle sous l’influence d’idées nouvelles. Les découvertes scientifiques, le développement de l’industrie, du commerce, de la prospérité et du bien-être, avaient créé une sorte d’enthousiasme et même de prophétisme. La conception du progrès indéfini, apparue dans la seconde moitié du XVIIIe siècle, concourut à convaincre l’espèce humaine qu’elle était entrée dans une ère nouvelle, celle de la civilisation absolue. C’est à un prodigieux utopiste, bien oublié aujourd’hui, Fourier, que l’on doit d’appeler la période contemporaine celle de la civilisation et de confondre la civilisation avec l’âge moderne… La civilisation, c’était donc le degré de développement et de perfectionnement auquel les nations européennes étaient parvenues au XIXe siècle. Ce terme, compris par tous, bien qu’il ne fût défini par personne, embrassait à la fois le progrès matériel et le progrès moral, l’un portant l’autre, l’un uni à l’autre, inséparables tous deux. La civilisation, c’était en somme l’Europe elle-même, c’était un brevet que se décernait le monde européen

One of the greatest ideas of mathematics is that all time series one is likely to encounter in nature can be described as a superposition of periodic functions.

Thomson particularly admired Fourier’s agnostic theoretical method, based on mathematical models that were useful but at the same time noncommittal on the difficult question of the nature of heat.

This miracle of social concord would result not from direct conciliation, which would be impossible, but from the development of new interests, and especially from the amazement with which the minds of men would be filled on being convinced of the radical falseness of the civilized social order by comparison with the associative or combined, and of the errors in which the social world has been so long plunged - misled by speculative philosophy, which upholds and extols this order with all its defects to the entire neglect of the study of association.

Mathematicians find it easier to understand and enjoy ideas which are clever rather than subtle. Measure theory is subtle rather than clever and so requires hard work to master.

Distribution theory was one of the two great revolutions in mathematical analysis in the 20th century. It can be thought of as the completion of differential calculus, just as the other great revolution, measure theory (or Lebesgue integration theory), can be thought of as the completion of integral calculus. There are many parallels between the two revolutions. Both were created by young, highly individualistic French mathematicians (Henri Lebesgue and Laurent Schwartz). Both were rapidly assimilated by the mathematical community, and opened up new worlds of mathematical development. Both forced a complete rethinking of all mathematical analysis that had come before, and basically altered the nature of the questions that mathematical analysts asked.

Distribution theory was one of the two great revolutions in mathematical analysis in the 20th century. It can be thought of as the completion of differential calculus, just as the other great revolution, measure theory (or Lebesgue integration theory), can be thought of as the completion of integral calculus. There are many parallels between the two revolutions. Both were created by young, highly individualistic French mathematicians (Henri Lebesgue and Laurent Schwartz). Both were rapidly assimilated by the mathematical community, and opened up new worlds of mathematical development. Both forced a complete rethinking of all mathematical analysis that had come before, and basically altered the nature of the questions that mathematical analysts asked.

Fourier analysis, which makes it possible to represent any signal as a sum of sine waves of various frequencies.

... the development of mathematics, for the sciences and for everybody else, does not often come from pure math. It came from the physicists, engineers, and applied mathematicians. The physicists were on to many ideas which couldn’t be proved, but which they knew to be right, long before the pure mathematicians sanctified it with their seal of approval. Fourier series, Laplace transforms, and delta functions are a few examples where waiting for a rigorous proof of procedure would have stifled progress for a hundred years. The quest for rigor too often meant rigor mortis. The physicists used delta functions early on, but this wasn’t really part of mathematics until the theory of distributions was invoked to make it all rigorous and pure. That was a century later! Scientists and engineers don’t wait for that: they develop what they need when they need it. Of necessity, they invent all sorts of approximate, ad hoc methods: perturbation theory, singular perturbation theory, renormalization, numerical calculations and methods, Fourier analysis, etc. The mathematics that went into this all came from the applied side, from the scientists who wanted to understand physical phenomena. [...] So much of mathematics originates from applications and scientific phenomena. But we have nature as the final arbiter. Does a result agree with experiment? If it doesn’t agree with experiment, something is wrong.

notes, et saisit sa médaille pour parler de ses travaux. Que se passe-t-il à l’intérieur d’un échantillon de cet objet, si une de ses extrémités est chauffée et l’autre mise dans la glace d’un seau à champagne ? La réponse n’est toujours pas connue, mais elle illustre l’une des motivations de cet éternel chercheur, toujours très actif. Comment expliquer les effets macroscopiques de la matière à partir de ces composants microscopiques ? Comment décrire les systèmes qui ne sont pas à l’équilibre thermodynamique ? Ou, dans le cas présent, peut-on déduire l’équation de propagation de la chaleur, connue depuis Fourier au XIXe siècle, d’après le comportement des particules élémentaires à l’intérieur de l’échantillon ?

Early in the nineteenth century, Jean Baptiste Joseph Fourier was investigating what determines the temperature of terrestrial bodies such as the earth. He speculated that part of the answer was that atmospheric gases might inhibit heat from escaping, thereby warming the earth’s surface.

Fourier had predicted that capitalism would lead to “Commercial and Industrial Feudalism,” with producers in bondage to large corporations and banking houses.

In a book published in 1808, François Fourier identified commerce as ‘the source of all evil’ and the Jews as ‘the incarnation of commerce’.84 Pierre-Joseph Proudhon went further, accusing the Jews of ‘having rendered the bourgeoisie, high and low, similar to them, all over Europe’. Jews were an ‘unsociable race, obstinate, infernal…the enemy of mankind. We should send this race back to Asia, or exterminate it.’85 Fourier’s follower, Alphonse Toussenel, edited the anti-Semitic journal Phalange and in 1845 produced the first full-scale attack on the Jews as a network of commercial conspirators against humanity, Les Juifs: rois de l’époque: histoire de la féodalité financière. This became a primary source-book for anti-Semitic literature, in many languages, for the next four decades.

She is distinguished from a courtisane only in that she does not offer her body for money by the hour like a commodity, but sells it into slavery for once and all. Fourier's words hold good with respect to all conventional marriages: "As in grammar two negatives make one affirmative, so in matrimonial ethics, two prostitutions are considered as one virtue." Sexual love in man's relation to woman becomes and can become the rule among the oppressed classes alone, among the proletarians of our day—no matter whether this relation is officially sanctioned or not. Here

The uncertainty principle. The uncertainty principle, introduced by Heisenberg in 1927, states that the position of a particle cannot be determined, but provides a mathematical formula relating its uncertainty to the uncertainty of the particle's momentum. Now in QFT what we call particles are really fields, and since fields spread out, there is no precise "position". However there is a property of fields in general, known as Fourier's theorem, that relates the spatial spread of any field to the spread of its wavelengths. In QFT, the wavelength of a quantum is related to its momentum, and I still remember my moment of insight when I realized that Heisenberg's relation between the uncertainties of position and momentum is simply Fourier's theorem.

That’s what I meant, phalanx,’ he repeated. ‘Phalanstère I expect you mean,’ said Tony Morland courteously, managing at the same time to put half a meringue away in one cheek like a monkey in his desire to impart information. ‘The theory of the phalanstère was begun and put into practice by Fourier, about 1832, but it was never much of a success. He wanted to organise society into bodies called phalanges, who were to live in phalanstère which were a square league. There is a lot more but you wouldn’t understand it. I know about it all because we did it last term.

Or if the hypothesis were offered us of a world in which Messrs. Fourier’s and Bellamy’s and Morris’s utopias should all be outdone, and millions kept permanently happy on the one simple condition that a certain lost soul on the far-off edge of things should lead a life of lonely torment, what except a specifical and independent sort of emotion can it be which would make us immediately feel, even though an impulse arose within us to clutch at the happiness so offered, how hideous a thing would be its enjoyment when deliberately accepted as the fruit of such a bargain?

The theory of Fourier series shows that such a sound can be decomposed as a sum of sine waves with various phases, at integer multiples of the frequency ν, as in Bernoulli’s solution (3.2.7) to the wave equation. The component of the sound with frequency ν is called the fundamental. The component with frequency mν is called the mth harmonic, or the (m – 1)st overtone.

So, which is it? Does matter create mind? Or does mind create matter? Scientific materialists have never made any progress whatsoever in explaining how matter produces mind. Mind can easily explain the production of matter – via autonomous Fourier immaterial frequency functions finding collective expression in a Fourier material spacetime world. It’s the collective rather than individual nature of this mental activity that makes it seem “physical”, and which gives rise to the delusion of the existence of matter. It’s all in the math.

The vital ingredient that was always missing from idealism and panpsychism was mathematics. Scientific materialism used math, and its rivals didn’t, and that’s why science became the dominant ideology. If idealism and panpsychism are able to use math too, they can replace science. Ontological Fourier mathematics with its dimensionless (mental) and dimensional (material) waves is how the gap is bridged between mind and matter

A thought in itself is in fact a sinusoidal wave, and, from this, everything else – the entire nature of existence – follows. Equating a thought to a sinusoidal wave that can be used in Fourier mathematics is the greatest intellectual breakthrough of all time. When its consequences are eventually understood by scientists, philosophers and mathematicians, it will revolutionize the human race like nothing before.

It’s often the case that brilliant ancient ideas are discarded by science, especially when they have any religious connotations. What ought to be done instead is to repurpose and reformulate these ancient ideas mathematically. So, for example, Aristotle’s Prime Mover can be recast as a Fourier frequency domain at the center of a Fourier spacetime domain. The Prime Mover is immaterial and outside space and time (it’s a Singularity), and controls the material world of spacetime. The latter is an ontological hologram projected by the former.

The frequency domain of mind (a mind, it must be stressed, is an unextended, massless, immaterial singularity) can produce an extended, spacetime domain of matter via ontological Fourier mathematics, and the two domains interact via inverse and forward Fourier transforms. An inverse Fourier transform converts a frequency (mind) function into a spacetime (material) function, and a forward Fourier transform does the opposite. So, mind can causally affect the material world, and matter can inform mind about its condition, its state. This is thus the long-sought answer to the world-historic problem of Cartesian substance dualism.

The soul is simply a transcendent quantum wavefunction of the mind that docks with the immanent quantum wavefunction of a spacetime body. Why would anyone find that baffling? One day, it will be regarded along the lines of 1 + 1 = 2. There will be children in the future who are taught this in primary school and who will never once doubt the existence of the eternal, monadic soul. It will be the most certain fact in their lives, with all the math to prove it.

A hole in a hole in a hole—Numberphile Around the World in a Tea Daze—Shpongle But what is a partial differential equation?—Grant Sanderson, who owns the 3Blue1Brown YouTube channel Closer to You—Kaisaku Fourier Series Animation (Square Wave)—Brek Martin Fourier Series Animation (Saw Wave)—Brek Martin Great Demo on Fibonacci Sequence Spirals in Nature—The Golden Ratio—Wise Wanderer gyroscope nutation—CGS How Earth Moves—vsauce I am a soul—Nibana

Že skoro libovolný opakující se vzor lze sestavit skládáním jednoduchých vln, si jako první uvědomil Francouz jménem Joseph Fourier, jeden z Napoleonových expertů na blízce příbuzné obory egyptologie, matematiku a vysoušení močálů. Za pomoci nechutně komplikovaných výpočtů se mu podařilo z těchto prostých složek vytvořit prakticky každý opakovaný vzor, jaký si dovedete představit.

Durante las últimas décadas, se ha facilitado el acceso a tecnologías de punta como la espectroscopía infrarroja transformada de Fourier (ftir, por sus siglas en inglés), la cromatografía líquida de alta resolución (hplc, por sus siglas en inglés) y la cromatografía de gases acoplada a espectrometría de masas (cg-ms, por sus siglas en inglés). Ahora los científicos son capaces de identificar lo que nuestros ancestros bebían al extraer las marcas químicas del residuo orgánico