Platonic Solids Quotes

Collection of famous quotes and sayings about Platonic Solids.

Quotes About Platonic Solids

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In Euclid's Elements we meet the concept which later plays a significant role in the development of science. The concept is called the "division of a line in extreme and mean ratio" (DEMR). ...the concept occurs in two forms. The first is formulated in Proposition 11 of Book II. ...why did Euclid introduce different forms... which we can find in Books II, VI and XIII? ...Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order to construct the Platonic solids... we must build the two-dimensional faces... It is for this purpose that Euclid introduced the golden ratio... (Proposition II.11)... By using the "golden" isosceles triangle...we can construct the regular pentagon... Then only one step remains to construct the dodecahedron... which for Plato is one of the most important regular polyhedra symbolizing the universal harmony in his cosmology. ~ Alexey Stakhov
Platonic Solids quotes by Alexey Stakhov
In this book, you will encounter various interesting geometries that have been thought to hold the keys to the universe. Galileo Galilei (1564-1642) suggested that "Nature's great book is written in mathematical symbols." Johannes Kepler (1571-1630) modeled the solar system with Platonic solids such as the dodecahedron. In the 1960s, physicist Eugene Wigner (1902-1995) was impressed with the "unreasonable effectiveness of mathematics in the natural sciences." Large Lie groups, like E8-which is discussed in the entry "The Quest for Lie Group E8 (2007)"- may someday help us create a unified theory of physics. in 2007, Swedish American cosmologist Max Tegmark published both scientific and popular articles on the mathematical universe hypothesis, which states that our physical reality is a mathematical structure-in other words, our universe in not just described by mathematics-it is mathematics. ~ Clifford A. Pickover
Platonic Solids quotes by Clifford A. Pickover
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You're reading something constructed using a rhetorical practice, something informed both directly and indirectly by the entire history of composition up until this point, from the Sophists to Derrida. But you're navigating it using pure logical statements, using spans of text or images that, when clicked or selected, get other files and display them on your screen. The text is based in the rhetorical tradition; the links are based in the logical tradition; and somewhere in there is something worth figuring out.

...the entire history of Western pedagogy [is] an oscillation between these two traditions, between the tradition of rhetoric as a means for obtaining power - language as just a collection of interconnected signifiers co-relating, without a grounding in "truth," and the tradition of seeking truth, of searching for a fundamental, logical underpinning for the universe, using ideas like the platonic solids or Boolean logic, or tools like expert systems and particle accelerators ... what is the relationship between narratives and logic? What is sprezzatura for the web? Hell if I know. My way of figuring it all out is to build the system and write inside it, because I'm too dense to work out theories. ~ Paul Ford
Platonic Solids quotes by Paul Ford
I have found that the platonic affection
in friendships and familial
love for children can be relied upon
with certainty to lift the bruised soul
and repair the wounded spirit ~ Maya Angelou
Platonic Solids quotes by Maya Angelou
We were born in a Jewish world, as part of a Jewish faith tradition. We had to translate ourselves into the neo-Platonic thinking Greek world; that took us about 400 years. Then, finally a man named Augustine, the Bishop of Hippo, recast Christianity in terms of neo-Platonic thought. ~ John Shelby Spong
Platonic Solids quotes by John Shelby Spong
Whenever you brown butter, some of it is lost - water evaporates, milk solids fall to the bottom of the pan, that kind of thing. It's possible that in browning the butter you ended up making the dough with too little butter. ~ Dorie Greenspan
Platonic Solids quotes by Dorie Greenspan
The Platonic world of ideas corresponds to Thinking and Sensation on the mystical level. ~ Carl Jung
Platonic Solids quotes by Carl Jung
Russian ladies, for the most part, cherish only Platonic love, without mingling any thought of matrimony with it; and Platonic love is exceedingly embarrassing. ~ Mikhail Lermontov
Platonic Solids quotes by Mikhail Lermontov
For those whose ganglia were formed pre-TV, the mimetic deployment of pop-culture icons seems at best an annoying tic and at worst a dangerous vapidity that compromises fiction's seriousness by dating it out of the Platonic Always, where it ought to reside. ~ Jonathan Lethem
Platonic Solids quotes by Jonathan Lethem
Surrender the vert platonic bond tying your soul to mine craft, the sky fades a pink shadow cast. ~ Bradley Chicho
Platonic Solids quotes by Bradley Chicho
Political rights do not originate in parliaments; they are, rather, forced upon parliaments from without. And even their enactment into law has for a long time been no guarantee of their security. Just as the employers always try to nullify every concession they had made to labor as soon as opportunity offered, as soon as any signs of weakness were observable in the workers' organizations, so governments also are always inclined to restrict or to abrogate completely rights and freedoms that have been achieved if they imagine that the people will put up no resistance. Even in those countries where such things as freedom of the press, right of assembly, right of combination, and the like have long existed, governments are constantly trying to restrict those rights or to reinterpret them by juridical hair-splitting. Political rights do not exist because they have been legally set down on a piece of paper, but only when they have become the ingrown habit of a people, and when any attempt to impair them will meet with the violent resistance of the populace. Where this is not the case, there is no help in any parliamentary Opposition or any Platonic appeals to the constitution. ~ Rudolf Rocker
Platonic Solids quotes by Rudolf Rocker
Because, you see, everything you know about the way this universe works is correct - except for the little problem that this isn't the only universe we have to worry about. Information can leak between one universe and another. And in a vanishingly small number of the other universes there are things that listen, and talk back - see Al-Hazred, Nietzsche, Lovecraft, Poe, et cetera. The many-angled ones, as they say, live at the bottom of the Mandelbrot set, except when a suitable incantation in the platonic realm of mathematics - computerised or otherwise - draws them forth. (And you thought running that fractal screen-saver was good for your computer?) ~ Charles Stross
Platonic Solids quotes by Charles Stross
Or do you mean like she might have some sort of chair-related dysfunction?" Her eyes lit up and she leaned in conspiratorially. "Or maybe the chairs offend her, because all chairs are imperfect shadows of the Platonic ideal of a chair. And so she's disinclined to sit. Philosophically. ~ Casey Matthews
Platonic Solids quotes by Casey Matthews
Demon comes from daimon, which means 'intelligence' or 'individual destiny', whereas angel means messenger. Originally daimones were always perceived as being positive entities. The Greek philosopher Plato introduced the division between kakodaemons and eudaemons, or benevolent and malevolent daimons, in the fourth century BCE. Seven centuries later in the third century CE, the Neo-Platonic philosopher Porphyry made an interesting distinction, this being essentially that the good daimones were the ones who governed their emotions and being, whereas bad daimones were governed by them. ~ Stephen Skinner
Platonic Solids quotes by Stephen Skinner
For love is a celestial harmony
Of likely hearts compos'd of stars' concent,
Which join together in sweet sympathy,
To work each other's joy and true content,
Which they have harbour'd since their first descent
Out of their heavenly bowers, where they did see
And know each other here belov'd to be. ~ Edmund Spenser
Platonic Solids quotes by Edmund Spenser
I've been wondering if in fact ideal platonic love isn't just an intensely concentrated form of what inspires the best teachers. ~ Edmund Marlowe
Platonic Solids quotes by Edmund Marlowe
a lost battalion of platonic conversationalists jumping down the stoops off fire escapes off windowsills off Empire State out of the moon ~ Allen Ginsberg
Platonic Solids quotes by Allen Ginsberg
We've tried being enemies. It sucked. We've tried being friends, and it's not enough. The way I feel about you isn't platonic anymore. It's primal. ~ Leisa Rayven
Platonic Solids quotes by Leisa Rayven
Not by the Platonic device of uniting the strong and fair with the strong and fair, regardless of sentiment and morality, nor yet by his other device of combining dissimilar natures (Statesman), have mankind gradually passed from the brutality and licentiousness of primitive marriage to marriage Christian and civilized. Few ~ Plato
Platonic Solids quotes by Plato
One could not imagine a process more open to the elephantine logic of the Bible-smasher than this: that the sun should be created after the sunlight. The conception that lies at the back of the phrase is indeed profoundly antagonistic to much of the modern point of view. To many modern people it would sound like saying that foliage existed before the first leaf ; it would sound like saying that childhood existed before a baby was born. The idea is, as I have said, alien to most modern thought, and like many other ideas which are alien to most modern thought, it is a very subtle and a very sound idea. Whatever be the meaning of the passage in the actual primeval poem, there is a very real metaphysical meaning in the idea that light existed before the sun and stars. It is not barbaric; it is rather Platonic. The idea existed before any of the machinery which made manifest the idea. Justice existed when there was no need of judges, and mercy existed before any man was oppressed.

The whole difference between construction and creation is exactly this: that a thing constructed can only be loved after it is constructed; but a thing created is loved before it exists, as the mother can love the unborn child. In creative art the essence of a book exists before the book or before even the details or main features of the book; the author enjoys it and lives in it with a kind of prophetic rapture. He wishes to write a comic story before he has thought of a single comic inciden ~ G.K. Chesterton
Platonic Solids quotes by G.K. Chesterton
I loved him. In a completely platonic, best friend, would not even go there if you were the last guy on earth, sort of way. ~ Theresa Smith
Platonic Solids quotes by Theresa Smith
In eighteenth-century Britain, many female friends enjoyed intense relationships, which they celebrated in romantic terms. Some probably compensated for stiff and formal relations with parents by forging close bonds with same-sex friends. In one case, Eleanor Butler and Sarah Ponsonby ran away from their families in Ireland to set up home together in Wales, where they would live in mutual harmony for more than fifty years. Known as the Ladies of Llangollen, they attracted visitors from far and wide who venerated their romantic story with never a hint that the friendship might be anything other than platonic ~ Wendy Moore
Platonic Solids quotes by Wendy Moore
Moreover, it is not entirely without significance that true love was, in Platonic philosophy
but also, as you know, in a whole sector, a whole domain of Christian spirituality and mysticism
the form par excellence of the true life. Since Platonism, true love and the true life have traditionally belonged together, and to a large extend Christian Platonism will take up this theme. ~ Michel Foucault
Platonic Solids quotes by Michel Foucault
The trouble with wanting to do the right thing is that frequently the right thing today is the wrong thing for tomorrow, or the wrong thing for the people who are standing between you and your perfect, platonic future. ~ Seanan McGuire
Platonic Solids quotes by Seanan McGuire
It is too late in the day for men of sincerity to pretend they believe in the Platonic mysticisms that three are one, and one is three; and yet that the one is not three, and the three are not one. ~ Thomas Jefferson
Platonic Solids quotes by Thomas Jefferson
From his companions, and set forth to walk, Perhaps grown wearied of their Corinth talk: Over the solitary hills he fared, Thoughtless at first, but ere eve's star appeared His phantasy was lost, where reason fades, In the calm'd twilight of Platonic shades. Lamia beheld him coming, near, more near - Close to her passing, in indifference drear, His silent sandals swept the mossy green; So neighbour'd to him, and yet so unseen ~ John Keats
Platonic Solids quotes by John Keats
The Keynesian world is a world in which there are two distinct classes of actors: the skilled investor, 'who, unperturbed by the prevailing pastime, continues to purchase investments on the best genuine long-term expectations he can frame', and, on the other hand, the ignorant 'game-player'. It does not seem to have occurred to Keynes that either of these two may learn from the other, and that, in particular, company directors and even the managers of investment trusts may be the wiser for learning from the market what it thinks about their actions. In this Keynesian world the managers and directors already know all about the future and have little to gain by devoting their attention to the misera plebs of the market. In fact, Keynes strongly feels that they should not! This pseudo-Platonic view of the world of high finance forms, we feel, an essential part of what Schumpeter called the 'Keynesian vision'. This view ignores progress through exchange of knowledge because the ones know all there is to be known whilst the others never learn anything. ~ Ludwig Lachmann
Platonic Solids quotes by Ludwig Lachmann
There is little of the true philosophic spirit in Aquinas. He does not, like the Platonic Socrates, set out to follow wherever the argument may lead. ~ Bertrand Russell
Platonic Solids quotes by Bertrand Russell
Descriptive geometry has two objects: the first is to establish methods to represent on drawing paper which has only two dimensions,-namely, length and width,-all solids of nature which have three dimensions,-length, width, and depth,-provided, however, that these solids are capable of rigorous definition.
The second object is to furnish means to recognize accordingly an exact description of the forms of solids and to derive thereby all truths which result from their forms and their respective positions. ~ Gaspard Monge
Platonic Solids quotes by Gaspard Monge
I found myself in an unknown universe, whirling far into space. African servants, dogs in hats, platonic ideals, sparkling conversation, and ivy-coated quadrangles with womanizing captains, dueling earls, actors. I met Father Cyprien de Gamache, her majesty's wily confessor; William, a poet, who claimed to be Shakespeare's son; and a giggling dwarf called Jeffry, who'd been presented to the queen in a pie. I met the ladies-in-waiting, too, who hardly looked my way, busy as they were, bickering over who went where and when, who wore what and when, who fetched what and why, who said what and to whom, and who gave her the right to say that. ~ Danielle Dutton
Platonic Solids quotes by Danielle Dutton
It is true that we instinctively recoil from seeing
an object to which our emotions and affections are committed
handled by the intellect as any other object is handled. The first
thing the intellect does with an object is to class it along with
something else. But any object that is infinitely important to us and
awakens our devotion feels to us also as if it must be sui generis and
unique. Probably a crab would be filled with a sense of personal
outrage if it could hear us class it without ado or apology as a
crustacean, and thus dispose of it. "I am no such thing," it would
say; "I am MYSELF, MYSELF alone."
The next thing the intellect does is to lay bare the causes in
which the thing originates. Spinoza says: "I will analyze the actions
and appetites of men as if it were a question of lines, of planes,
and of solids. ~ William James
Platonic Solids quotes by William James
Love is the feeling we have for those we care deeply about and hold in high regard. It can be light as the hug we give a friend or heavy as the sacrifices we make for our children. It can be romantic, platonic, familial, fleeting, everlasting, conditional, unconditional, imbued with sorrow, stoked by sex, sullied by abuse, amplified by kindness, twisted by betrayal, deepened by time, darkened by difficulty, leavened by generosity, nourished by humor, and "loaded with promises and commitments" that we may or may not want or keep. ~ Cheryl Strayed
Platonic Solids quotes by Cheryl Strayed
The ordinary logic is also jealous of the explanation of negation as relation, because seeming to take away the principle of contradiction. Plato, as far as we know, is the first philosopher who distinctly enunciated this principle; and though we need not suppose him to have been always consistent with himself, there is no real inconsistency between his explanation of the negative and the principle of contradiction. Neither the Platonic notion of the negative as the principle of difference, nor the Hegelian identity of Being and Not-being, at all touch the principle of contradiction. For what is asserted about Being and Not-Being only relates to our most abstract notions, and in no way interferes with the principle of contradiction employed in the concrete. Because Not-being is identified with Other, or Being with Not-being, this does not make the proposition 'Some have not eaten' any the less a contradiction of 'All have eaten. ~ Plato
Platonic Solids quotes by Plato
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