„When we attempt to conceive the number of particles in an atmosphere, it is somewhat like attempting to conceive the number of stars in the universe; we are confounded with the thought. But if we limit the subject, by taking a given volume of any gas, we seem persuaded that, let the divisions be ever so minute, the number of particles must be finite; just as in a given space of the universe, the number of stars and planets cannot be infinite.“

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— John Dalton, buch A New System of Chemical Philosophy

Quelle: A New System of Chemical Philosophy (1808), Ch. III On Chemical Synthesis

Übernommen aus Wikiquote. Letzte Aktualisierung 3. Juni 2021.

John Dalton

englischer Naturforscher und Lehrer 1766 - 1844

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„We seem to inhabit a universe made up of a small number of elements-particles-bits that swirl in chaotic clouds, occasionally clustering together in geometrically logical temporary configurations.“

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— Timothy Leary American psychologist 1920 - 1996

Quelle: Chaos & Cyber Culture

„We begin with the number one in counting all things. It is impossible that this one can ever be reduced to zero. Because just as something cannot be made of nothing, one cannot be made from zero. Ki is like the number one. Ki is formed from infinitely small particles, smaller than an atom. The universal ki condensed becomes an individual, which further condensed becomes the one point in the lower abdomen, which in turn infinitely condensed never becomes zero, but becomes one with the universe. Thus we understand the essence of ki.“

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— Koichi Tohei Japanese aikidoka 1920 - 2011

11 : The definition of ki
Ki Sayings (2003)

„There is a smallest unit of space. Its minimum value is given by the cube of the Planck length… If you take a volume of space and measure it to a very fine precision… It has to fall into some discrete series of numbers, just like the energy of an electron in an atom. …we can calculate the discrete areas and volumes from the theory.“

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— Lee Smolin American cosmologist 1955

"Loop Quantum Gravity," The New Humanists: Science at the Edge (2003)

„There are 1011 stars in the galaxy. That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers.“

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— Richard Feynman American theoretical physicist 1918 - 1988

from a 1987 class, as quoted in David L. Goodstein, "Richard P. Feynman, Teacher," Physics Today, volume 42, number 2 (February 1989) p. 70-75, at p. 73
Republished in the "Special Preface" to Six Easy Pieces (1995), p. xx.

„The number of rational hypotheses that can explain any given phenomenon is infinite.“

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— Robert M. Pirsig, buch Zen und die Kunst ein Motorrad zu warten

Quelle: Zen and the Art of Motorcycle Maintenance (1974), Ch. 9; in Ch. 22 (see below) Pirsig recounts finding that Henri Poincaré had made a similar statement decades earlier.

„That from the outset they expect or even impose all the properties of finite numbers upon the numbers in question, while on the other hand the infinite numbers, if they are to be considered in any form at all, must (in their contrast to the finite numbers) constitute an entirely new kind of number, whose nature is entirely dependent upon the nature of things and is an object of research, but not of our arbitrariness or prejudices.“

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— Georg Cantor mathematician, inventor of set theory 1845 - 1918

Letter to Gustac Enestrom, as quoted in Georg Cantor : His Mathematics and Philosophy of the Infinite (1990) by Joseph Warren Dauben ~ ISBN 0691024472

„Black holes set a limitation on the number of species of elementary particles—quarks, leptons, neutrinos—which may exist. And black holes lead to a fundamental limitation on the rate at which information can be transferred for given message energy by any communication system.“

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— Jacob Bekenstein Mexican-Israeli physicist 1947 - 2015

[Black holes and everyday physics, General relativity and gravitation, 14, 4, April 1982, 355–359, 10.1007/BF00756269]

„When we run over libraries, persuaded of these principles, what havoc must we make? If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: For it can contain nothing but sophistry and illusion.“

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— David Hume, buch An Enquiry Concerning Human Understanding

Section 12 : Of the Academical or Sceptical Philosophy Pt. 3
An Enquiry Concerning Human Understanding (1748)

„Now it is one great object of this work, to shew the importance and advantage of ascertaining the relative weights of the ultimate particles, both of simple and compound bodies, the number of simple elementary particles which constitute one compound particle, and the number of less compound particles which enter into the formation of one more compound particle.“

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— John Dalton, buch A New System of Chemical Philosophy

Quelle: A New System of Chemical Philosophy (1808), Ch. III. On Chemical Synthesis

„The law of small numbers is not really a law. It is a sarcastic name describing the misguided attempt to apply the law of large numbers when the numbers aren't large.“

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— Leonard Mlodinow, buch The Drunkard's Walk

Quelle: The Drunkard's Walk, Chapter 5, The Dueling Of Large And Small Numbers, p. 99

„Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way"…. This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics.“

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— John C. Baez American mathematician and mathematical physicist 1961

„Just as negative and fractional rational numbers are formed by a new creation, and as the laws of operating with these numbers must and can be reduced to the laws of operating with positive integers, so we must endeavor completely to define irrational numbers by means of the rational numbers alone. The question only remains how to do this.“

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— Richard Dedekind German mathematician 1831 - 1916

p, 125
Stetigkeit und irrationale Zahlen (1872)

„A pure elastic fluid is one the constituent particles of which are all alike, or in no way distinguishable. Steam, or aqueous vapour, hydrogenous gas, oxygenous gas… and several others are of this kind. …Whatever …may be the shape or figure of the solid atom abstractedly, when surrounded by such an atmosphere it must be globular; but as all the globules in any small given volume are subject to the same pressure, they must be equal in bulk, and will therefore be arranged in horizontal strata, like a pile of shot.“

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— John Dalton, buch A New System of Chemical Philosophy

Quelle: A New System of Chemical Philosophy (1808), Ch. II. On the Constitution of Bodies, Sect. 1. On the Constitution of Pure Elastic Fluids

„In fact, as we shall see in the next section, most attempts to explicitly measure military power are mere tabulations of forces of various sorts: the numbers of men underarms, the number of weapons of a given type, etc. This is in itself an evasion of the problem since it says nothing about the actual capabilities of the forces of one country to deal with another.“

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— Andrew Marshall the director of the United States Department of Defense's Office of Net Assessment 1921 - 2019

Problems of Estimating Military Power (August 1966)

„We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.“

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— Carl Friedrich Gauss German mathematician and physical scientist 1777 - 1855

Letter to Friedrich Wilhelm Bessel (1830)

„The number 2 thought of by one man cannot be added to the number 2 thought of by another man so as to make up the number 4.“

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— Simone Weil French philosopher, Christian mystic, and social activist 1909 - 1943

Oppression and Liberty (1958), p. 82

„We strongly condemn all attempts to rewrite history, reduce the number of victims and minimize contribution to the defeat of Nazism and fascism, as well as attempts to rehabilitate those ideologists.“

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— Ivica Dačić Serbian politician 1966

Quelle: "Ivica Dacic: Serbia and Russia are more than just historical friends and allies" in The State Duma http://duma.gov.ru/en/news/51667/ (2 June 2021)

„I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realised that, by pure thought alone, it could prove eternal truths of the universe.
Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers.“

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— Marcus du Sautoy British professor of mathematics 1965

In "Life lessons" http://www.theguardian.com/science/2005/apr/07/science.highereducation?fb_ref=desktop The Guardian (7 April 2005)

„This is the universe! And I'm placing stones one by one on that. Like I'm increasing the number of stars one by one… I'm making the universe. It's like I'm a God. I'm going to become a God! On this Go Board.“

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— Yumi Hotta, Hikaru no Go

In the anime, Hikaru says this when he plays in a Go tournament for the first time.
Hikaru no Go

„Only if the third necessary thing could be given us. Number one, as I said: quality of information. Number two: leisure to digest it. And number three: the right to carry out actions based on what we learn from the interaction of the first two.“

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— Ray Bradbury, buch Fahrenheit 451

Quelle: Fahrenheit 451

John Dalton

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