# „Now it is the practice of astronomers to assume that brightness falls off inversely with the square of the "distance" of an object—as it would do in Euclidean space, if there were no absorption… We must therefore examine the relation between this astronomer's "distance" d… and the distance r which appears as an element of the geometry.“

Geometry as a Branch of Physics (1949)

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##### Howard P. Robertson
amerikanischer Mathematiker und Physiker 1903 - 1961

## Ähnliche Zitate

### „Superficially at least the forces of electricity and magnetism seem to present the same kind of problem as gravitation. Experiment shows that two electrically charged bodies attract one another (or repel if their charges are of the same kind) with a force which conforms to the same mathematical law as the force of gravitation - both forces fall off inversely as the inverse square of the distance. The same is true of the magnetic force also; two magnetic poles attract or repel one another with a force which again follows the law of the inverse square of the distance.“

—  James Jeans British mathematician and astronomer 1877 - 1946

Physics and Philosophy (1942)

### „All the light which is radiated… will, after it has traveled a distance r, lie on the surface of a sphere whose area S is given by the first of the formulae (3). And since the practical procedure… in determining d is equivalent to assuming that all this light lies on the surface of a Euclidean sphere of radius d, it follows…4 \pi d^2 = S = 4 \pi r^2 (1 - \frac{K r^2}{3} + …);whence, to our approximation 4)d = r (1- \frac{K r^2}{6} + …), orr = d (1 + \frac{K d^2}{6} + …).</center“

—  Howard P. Robertson American mathematician and physicist 1903 - 1961

Geometry as a Branch of Physics (1949)

### „[T]he astronomical data give the number N of nebulae counted out to a given inferred "distance" d, and in order to determine the curvature… we must express N, or equivalently V, to which it is assumed proportional, in terms of d. …from the second of formulae (3) and… (4)… to the approximation here adopted, 5)V = \frac{4}{3} \pi d^2 (1 + \frac{3}{10} K d^2 + …);…plotting N against… d and comparing… with the formula (5), it should be possible operationally to determine the "curvature" K.“

—  Howard P. Robertson American mathematician and physicist 1903 - 1961

Geometry as a Branch of Physics (1949)

### „…the differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a curve, and cannot lead to an epistemological priority of Euclidean geometry, in contrast to the views of certain authors.“

—  Hans Reichenbach American philosopher 1891 - 1953

The Philosophy of Space and Time (1928, tr. 1957)

### „I had not thought of this regular decrease of gravity, namely that it is as the inverse square of the distance; this is a new and highly remarkable property of gravity.“

—  Christiaan Huygens Dutch mathematician and natural philosopher 1629 - 1695

(1691) quoted in Popular Astronomy, Vol. 56 (1948), pp. 189–190.

### „We underestimate the distance between ourselves and others. Not just inferential distance, but distances of temperament and ability, distances of situation and resource, distances of unspoken knowledge and unnoticed skills and luck, distances of interior landscape.“

—  Eliezer Yudkowsky American blogger, writer, and artificial intelligence researcher 1979

Beware of Other-Optimizing (April 2009) http://lesswrong.com/lw/9v/beware_of_otheroptimizing/

### „[T]he methods used for measuring Astronomical distances are in some applications absolutely the same as the methods of ordinary theodolite-surveying, and are in other applications equivalent to them…“

—  George Biddell Airy English mathematician and astronomer 1801 - 1892

Introduction
Popular Astronomy: A Series of Lectures Delivered at Ipswich (1868)

### „Although the classic theoretical foundation of distance measurement in physics is the 'rigid rod', nearly all distances in surveying, whether terrestrial or celestial, are made to depend on the properties of light. The two simplest properties so employed are the principle of propogation in straight lines and the principle that the intensity of light diminishes inversely as the square of the distance.“

—  Gerald James Whitrow British mathematician 1912 - 2000

p, 125
The Structure of the Universe: An Introduction to Cosmology (1949)

### „…the order of betweenness does not depend on mutual distances… betweenness is purely a relational order.“

—  Hans Reichenbach American philosopher 1891 - 1953

Quelle: The Philosophy of Space and Time (1928, tr. 1957)

### „The moon is not kept in her orbit round the earth, nor the earth in her orbit round the sun, by a force that varies merely in the inverse ratio of the squares of the distances.“

—  Thomas Robert Malthus British political economist 1766 - 1834

Quelle: An Essay on The Principle of Population (First Edition 1798, unrevised), Chapter XIII, paragraph 2, lines 19-22

### „This part of optics, when well understood, shows us how we may make things a very long distance off appear as if placed very close, and large near things appear very small, and how we may make small things placed at a distance appear any size we want, so that it may be possible for us to read the smallest letters at incredible distances, or to count sand, or seed, or any sort of minute objects.“

—  Robert Grosseteste English bishop and philosopher 1175 - 1253

De iride (On the rainbow) Note this prediction of optical scientific instruments like the telescope and microscope, not to be utilized until 250 years later.

### „In quantum theory, distance is inverse to energy, because you need particles of very high energy to probe very short distances. The inverse of the Planck energy is the Planck length.“

—  Lee Smolin American cosmologist 1955

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

### „From a careful determination of the amount of solar heat that which would fall per minute on an area of one square centimetre placed perpendicular to the radiation as it falls on Earth's surface and from a knowledge of the Earth's distance, we deduce that each square centimetre of the solar surface radiates on the average of about the rate of a nine horse-power engine.“

—  Gerald James Whitrow British mathematician 1912 - 2000

"Why the Sun Shines" (18 July 1957)

### „A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization (i) decays exponentially with this distance, and (ii) does so in accordance with one of two metrics, depending on the relation between the dimensions along which the stimuli vary. These empirical regularities are mathematically derivable from universal principles of natural kinds and probabilistic geometry that may, through evolutionary internalization, tend to govern the behaviors of all sentient organisms.“

—  Roger Shepard American psychologist 1929

Quelle: "Toward a universal law of generalization for psychological science," 1987, p. 1317

### „Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.“

—  Archimedes, buch On the Equilibrium of Planes

Book 1, Postulate 1.
On the Equilibrium of Planes

### „The straight line is regarded as the shortest distance between two people, as if they were points.“

—  Theodor W. Adorno, buch Minima Moralia

Nun gilt für die kürzeste Verbindung zwischen zwei Personen die Gerade, so als ob sie Punkte wären.
E. Jephcott, trans. (1974), § 20
Minima Moralia (1951)

### „A space representing the shortest distances for messages to travel…“

—  James Grier Miller biologist 1916 - 2002

Living Systems: Basic Concepts (1969)

### „Nevertheless, it remains conceivable that the measure relations of space in the infinitely small are not in accordance with the assumptions of our geometry [Euclidean geometry], and, in fact, we should have to assume that they are not if, by doing so, we should ever be enabled to explain phenomena in a more simple way.“

—  Bernhard Riemann German mathematician 1826 - 1866

Memoir (1854) Tr. William Kingdon Clifford, as quoted by A. D'Abro, The Evolution of Scientific Thought from Newton to Einstein https://archive.org/details/TheEvolutionOfScientificThought (1927) p. 55.

### „You do not reach the sublime by degrees; the distance between it and the merely beautiful is infinite.“

—  Anne Louise Germaine de Staël, buch Corinne

Bk. 4, ch. 3
Corinne (1807)

### „The organization of science into disciplines sets up a series of ghettos with remarkable distances of artificial social space between them.“

—  Kenneth E. Boulding British-American economist 1910 - 1993

Kenneth Boulding (1973) Image and Environment. p. ix
1970s