# „In the algebra of fantasy, A times B doesn't have to equal B times A. But, once established, the equation must hold throughout the story.“

"The Flat-Heeled Muse", Horn Book Magazine (1 April 1965)

## Citações relacionadas

### „The equation of motion holds at all times, it is in this sense eternal“

— Werner Heisenberg German theoretical physicist 1901 - 1976

Physics and Philosophy (1958)

Contexto: The equation of motion holds at all times, it is in this sense eternal, whereas the geometrical forms, like the orbits, are changing. Therefore, the mathematical forms that represent the elementary particles will be solutions of some eternal law of motion for matter. Actually this is a problem which has not yet been solved.<!-- p. 72

### „On symbolic use of equalities and proportions. Chapter II.

The analytical method accepts as proven the most famous [ as known from Euclid ] symbolic use of equalities and proportions that are found in items such as:

1. The whole is equal to the sum of its parts.

2. Quantities being equal to the same quantity have equality between themselves. [a = c & b = c => a = b]

3. If equal quantities are added to equal quantities the resulting sums are equal.

4. If equals are subtracted from equal quantities the remains are equal.

5. If equal equal amounts are multiplied by equal amounts the products are equal.

6. If equal amounts are divided by equal amounts, the quotients are equal.

7. If the quantities are in direct proportion so also are they are in inverse and alternate proportion. [a:b::c:d=>b:a::d:c & a:c::b:d]

8. If the quantities in the same proportion are added likewise to amounts in the same proportion, the sums are in proportion. [a:b::c:d => (a+c):(b+d)::c:d]

9. If the quantities in the same proportion are subtracted likewise from amounts in the same proportion, the differences are in proportion. [a:b::c:d => (a-c):(b-d)::c:d]

10. If proportional quantities are multiplied by proportional quantities the products are in proportion. [a:b::c:d & e:f::g:h => ae:bf::cg:dh]

11. If proportional quantities are divided by proportional quantities the quotients are in proportion. [a:b::c:d & e:f::g:h => a/e:b/f::c/g:d/h]

12. A common multiplier or divisor does not change an equality nor a proportion. [a:b::ka:kb & a:b::(a/k):(b/k)]

13. The product of different parts of the same number is equal to the product of the sum of these parts by the same number. [ka + kb = k(a+b)]

14. The result of successive multiplications or divisions of a magnitude by several others is the same regardless of the sequential order of quantities multiplied times or divided into that magnitude.

But the masterful symbolic use of equalities and proportions which the analyst may apply any time is the following:

15. If we have three or four magnitudes and the product of the extremes is equal to the product means, they are in proportion. [ad=bc => a:b::c:d OR ac=b2 => a:b::b:c]

And conversely

10. If we have three or four magnitudes and the first is to the second as the second or the third is to the last, the product of the extremes is equal to that of means. [a:b::c:d => ad=bc OR a:b::b:c => ac=b2]

We can call a proportion the establishment of an equality [equation] and an equality [equation] the resolution of a proportion.“

— François Viète French mathematician 1540 - 1603

From Frédéric Louis Ritter's French Tr. Introduction à l'art Analytique (1868) utilizing Google translate with reference to English translation in Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (1968) Appendix

In artem analyticem Isagoge (1591)

### „That’s the a, b, c of politics. It ain’t easy work to get up to q and z. You have to give nearly all your time and attention to it. p. 20“

— George Washington Plunkitt New York State Senator 1842 - 1924

Chapter 4, Reformers Only Mornin’ Glories

### „Let the letters a b c denote the three angular points of a rectilineal triangle. If the point did move continuously over the lines ab, bc, ca, that is, over the perimeter of the figure, it would be necessary for it to move at the point b in the direction ab, and also at the same point b in the direction bc. These motions being diverse, they cannot be simultaneous. There-fore, the moment of presence of the movable point at vertex b, considered as moving in the direction ab, is different from the moment of presence of the movable point at the same vertex b, considered as moving in the same direction bc. But between two moments there is time; therefore, the movable point is present at point b for some time, that is, it rests. Therefore it does not move continuously, which is contrary to the assumption. The same demonstration is valid for motion over any right lines including an assignable angle. Hence a body does not change its direction in continuous motion except by following a line no part of which is straight, that is, a curve, as Leibnitz maintained.“

— Immanuel Kant German philosopher 1724 - 1804

Section III On The Principles Of The Form Of The Sensible World

### „In February 1917, it was found that a static solution with a positive curvature—the solution A—was not possible without the λ. In fact the curvature is proportional to λ (in solution A, λ is equal to the curvature; in B… it is three times the curvature). Thus, at the time when we had only the two static solutions A and B, and thought that these were the only possible ones, here was a plausible physical interpretation of the meaning of λ: it was the curvature of the world, and the square root of its reciprocal, the radius of curvature, could be conceived as providing a natural unit of length.“

— Willem de Sitter Dutch cosmologist 1872 - 1934

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

### „Manufacture was all the time sheltered b protective duties in the hoe market, by monopolies in the colonial market, and broad as much as possible by differential duties.“

— Karl Marx, livro The German Ideology

Fonte: The German Ideology (1845/46), pp. 183

### „It is vain futility to analyze the algebra of time.“

— Dejan Stojanovic, livro The Creator

“The Day,” p. 57

The Creator (2000), Sequence: “The Whisper of Eternity”

### „Once upon a time there was a fairy godmother, but the rest of the time there was none. This story is about one of those other times.“

— Diane Setterfield, livro The Thirteenth Tale

Fonte: The Thirteenth Tale

### „[B]efore Descartes, some of the ancients made the essence of matter consist in solid extension. But this opinion, of which all the Cartesians have made much, has at all times been victoriously combated…“

— Julien Offray de La Mettrie French physician and philosopher 1709 - 1751

Fonte: The Natural History of the Soul (1745), Ch. III Concerning the Extension of Matter

### „It must not be forgotten that the rules of Courts of equity are not, like the rules of the common law, supposed to have been established from time immemorial. It is perfectly well known that they have been established from time to time — altered, improved, and refined from time to time. In many cases we know the names of the Chancellors who invented them.“

— George Jessel (jurist) British politician 1824 - 1883

In re Hallett's Estate (1880) 13 Ch.D. 696, 710.

### „In the beginning of 1917, two solutions of the field equations for a homogeneous isotropic universe had been found, which I… call the solutions "A" and "B."… at that time only static solutions were looked for. It was thought that the universe must be a stable structure… In one of these solutions (B) the average density was zero, it was empty; the other one (A) had a finite density…. In B, to get the real universe, we should have to put in a few galactic systems, in A we should have to condense the evenly distributed matter into galactic systems. The universe A… has an average density, but no expansion. It is therefore called the static universe. B, on the other hand… expands, and it could only parade in the garb of a static universe because there is nothing in it to show the expansion. B is therefore called the empty universe. Thus we had two approximations : the static universe with matter and without expansion, and the empty one without matter and with expansion. The actual universe… has both matter and expansion… In 1917… the actual value of the density was still entirely unknown, and the expansion had not yet been discovered.“

— Willem de Sitter Dutch cosmologist 1872 - 1934

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

### „I have said more than once, that I hold space to be something purely relative, as time; an order of coexistences, as time is an order of successions.“

— Gottfried Leibniz German mathematician and philosopher 1646 - 1716

J'ay marqué plus d'une fois, que je tenois l'espace pour quelque chose de purement relatif, comme le temps; pour un ordre des coëxistences, comme le temps est un ordre des successions.

Third letter http://www.physics.ubc.ca/~berciu/PHILIP/TEACHING/PHYS340/EXTRA/FILES/Leibniz-ClarkeA.pdf to Samuel Clarke, February 25, 1716

### „I would write a book, or a short story, at least three times — once to understand it, the second time to improve the prose, and a third to compel it to say what it still must say.“

— Bernard Malamud American author 1914 - 1986

Address at Bennington College (30 October 1984) as published in "Reflections of a Writer: Long Work, Short Life" in The New York Times (20 March 1988)

Contexto: I have written almost all my life. My writing has drawn, out of a reluctant soul, a measure of astonishment at the nature of life. And the more I wrote well, the better I felt I had to write.

In writing I had to say what had happened to me, yet present it as though it had been magically revealed. I began to write seriously when I had taught myself the discipline necessary to achieve what I wanted. When I touched that time, my words announced themselves to me. I have given my life to writing without regret, except when I consider what in my work I might have done better. I wanted my writing to be as good as it must be, and on the whole I think it is. I would write a book, or a short story, at least three times — once to understand it, the second time to improve the prose, and a third to compel it to say what it still must say.

Somewhere I put it this way: first drafts are for learning what one's fiction wants him to say. Revision works with that knowledge to enlarge and enhance an idea, to re-form it. Revision is one of the exquisite pleasures of writing: The men and things of today are wont to lie fairer and truer in tomorrow's meadow, Henry Thoreau said.

I don't regret the years I put into my work. Perhaps I regret the fact that I was not two men, one who could live a full life apart from writing; and one who lived in art, exploring all he had to experience and know how to make his work right; yet not regretting that he had put his life into the art of perfecting the work.

### „I just sat there thunderstruck. I realized that's exactly what I had been doing for over a decade with my story. I was writing heroic fantasy, while at the same time I was satirizing heroic fantasy.“

— Patrick Rothfuss American fantasy writer 1973

Interview with Fantasy Book Critic (25 May 2007)

Contexto: Anyway, I was listening to Beagle answer a question on the panel, he said something along the lines of, "I'd never want to write The Last Unicorn again. It was excruciatingly hard, because I was writing a faerie tale while at the same time writing a spoof of a faerie tale."

I just sat there thunderstruck. I realized that's exactly what I had been doing for over a decade with my story. I was writing heroic fantasy, while at the same time I was satirizing heroic fantasy.

While telling his story, Kvothe makes it clear that he's not the storybook hero legends make him out to be. But at the same time, the reader sees that he's a hero nonetheless. He's just a hero of a different sort.

### „Though Wallis was advanced for his times and accepted negative numbers, he thought they were larger than infinity but not less than zero. In his Arithmetica Infinitorum (1655), he argued that since the ratio a/0, when a is positive, is infinite, then, when the denominator is changed to a negative number, as in a/b with b negative, the ratio must be greater than infinity.“

— Morris Kline American mathematician 1908 - 1992

Fonte: Mathematical Thought from Ancient to Modern Times (1972), p. 253.

### „As a matter of fact, others are ready to help. There is for instance the Weather; and there is the Law of Gravity; and last but not least, Time. These are tough fellows. Night and day, always at it. And at it still. No one is a match for them.</b“

— Halldór Laxness, livro Kristnihald undir Jökli (bók)

Kristnihald undir Jökli (Under the Glacier/Christianity at Glacier) (1968)

### „I was led, many years ago, to regard Algebra as the Science of Pure Time“

— William Rowan Hamilton Irish physicist, astronomer, and mathematician 1805 - 1865

Preface, Lectures on Quaternions: Containing a Systematic Statement of a New Mathematical Method of which the Principles were Communicated in 1843 to the Royal Irish Academy... (1853) pp. 1-4 https://books.google.com/books?id=PJIKAAAAYAAJ&pg=PA1. Hamilton makes reference to the article "Theory of Conjugate Functions, or Algebraic Couples; with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time" (Read November 4th, 1833, and June 1st, 1835) Transactions of the Royal Irish Academy Vol. XVII, Part II (Dublin, 1835) pp 293-422.

Contexto: The difficulties which so many have felt in the doctrine of Negative and Imaginary Quantities in Algebra forced themselves long ago on my attention... And while agreeing with those who had contended that negatives and imaginaries were not properly quantities at all, I still felt dissatisfied with any view which should not give to them, from the outset, a clear interpretation and meaning... It early appeared to me that these ends might be attained by our consenting to regard Algebra as being no mere Art, nor Language, nor primarily a Science of Quantity; but rather as the Science of Order in Progression. It was, however, a part of this conception, that the progression here spoken of was understood to be continuous and unidimensional: extending indefinitely forward and backward, but not in any lateral direction. And although the successive states of such a progression might (no doubt) be represented by points upon a line, yet I thought that their simple successiveness was better conceived by comparing them with moments of time, divested, however, of all reference to cause and effect; so that the "time" here considered might be said to be abstract, ideal, or pure, like that "space" which is the object of geometry. In this manner I was led, many years ago, to regard Algebra as the Science of Pure Time: and an Essay, containing my views respecting it as such, was published in 1835.... [I]f the letters A and B were employed as dates, to denote any two moments of time, which might or might not be distinct, the case of the coincidence or identity of these two moments, or of equivalence of these two dates, was denoted by the equation,B = Awhich symbolic assertion was thus interpreted as not involving any original reference to quantity, nor as expressing the result of any comparison between two durations as measured. It corresponded to the conception of simultaneity or synchronism; or, in simpler words, it represented the thought of the present in time. Of all possible answers to the general question, "When," the simplest is the answer, "Now:" and it was the attitude of mind, assumed in the making of this answer, which (in the system here described) might be said to be originally symbolized by the equation above written.

### „The Greek world will continue in almost constant cultural revolution from the time of Homer to the day Rome brings Greece to its knees in the second century B. C. …the longest trajectory of fluid development in any society known to history.“

— Thomas Cahill American scholar and writer 1940

Fonte: Sailing the Wine-Dark Sea: Why the Greeks Matter (2003), Ch. III The Poet: How to Party