“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.”

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

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American cosmologist 1955

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“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 (1955) American cosmologist

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

“Quantum mechanics explains the physical stability of the atom by predicting its allowed discrete energy levels and defining the wave functions (also called atomic orbitals) associated with each energy level. The orbitals determine the probability density for finding the electrons at particular locations in the atom when the electrons are in a specific quantum state.”

David W. Oxtoby (1951) President of Pomona college

Principles of Modern Chemistry (7th ed., 2012), Ch. 5 : Quantum Mechanics and Atomic Structure

“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.”

John Dalton book A New System of Chemical Philosophy

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

“Discretion is the best form of calculation.”

Honoré de Balzac book The Girl with the Golden Eyes

La discrétion est le plus habile des calculs. <br class="br"> La Fille aux yeux d'or http://fr.wikisource.org/wiki/La_Fille_aux_yeux_d%E2%80%99or (The Girl with the Golden Eyes) (1835), translated by Ellen Marriage, ch. III. <br class="br">La Fille aux yeux d'or (1833)

“We have merely (!) to measure the volume V of a sphere of radius r or the sum \sigma of the angles of a triangle of measured are \delta, and from the results to compute the value of K.”

Howard P. Robertson (1903–1961) American mathematician and physicist

Geometry as a Branch of Physics (1949)

“Bohr had… discovered that the frequencies corresponding to very large integers could be calculated accurately from the classical mechanics; they were simply the number of times that an ordinary electron would complete the circuit of its orbit in one second when it was at a very great distance from the nucleus of the atom to which it belonged. This could only mean that when an electron receded to a great distance from the nucleus of its atom, it not only assumed the properties of an ordinary electron, but also behaved as directed by the classical mechanics. Yet the classical mechanics failed completely for the calculation of frequencies corresponding to small orbits.”

James Jeans (1877–1946) British mathematician and astronomer

Physics and Philosophy (1942)

“That classical theory had catastrophic implications for the constitution of matter was barely appreciated by Planck and others at the turn of the century, and played no substantial role in the development of quantum theory until Bohr's work 13 years later.
The lesson that could be drawn from this, and also from the development of general relativity, is that a crisis will only become creative if it is formulated in a mathematically precise manner. This conclusion has an echo in Bell's insistence on having quantum mechanics "fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist", but what it really calls for is a critique of the "orthodox" theory fully formulated in mathematical terms with nothing left to the discretion of the critic.”

Kurt Gottfried (1929) American physicist

Does quantum mechanics carry the seeds of its own destruction? (1991)

“Rapidly going over what I could recall of Jim Bursley's information about pathological curves confirmed the conjecture. The snowball curve, derived from an equilateral triangle, is a perimeter of infinite length enclosing a finite area. The angles or points of the perimeter are uncountable. An equilateral triangle projected integrally in the third dimension is a triangular pyramid of equal surfaces. The three-dimensional snowflake derived from this pyramid--hence its diamantine appearance--is a finite volume enclosed in a surface of infinite area. The convolutions of such a surface, to be gathered around its defined content extrude a number of discrete angles or points beyond all possibility of computation. The pressure on each point is infinitesimal, unmeasurably small; the total external pressure exerted on any part of the surface is an aggregate of infinitesimal values, itself infinitesimal.”

William Grey Walter (1910–1977) American-born British neuroscientist and roboticist

Source: The Curve of the Snowflake (1956), p. 126.

“2d. Saving space: (a) By the utilization of the large volume of space contained in the slopes of roofs… (b) by the reduction of floor thickness… (c) by the utilization of space (as on shipboard) for lockers, cupboards, closets, etc… (d) by the use of thin partitions… and (e) by elimination of corridors… so that the least possible area may be required for communication.”

Ernest Flagg (1857–1947) American architect

Introduction
Small Houses: Their Economic Design and Construction (1922)

“Heisenberg finds that facts of observation lead uniquely and inevitably to the theoretical structure known as matrix mechanics. This shows that the total radiation in any region of empty space can change only by a single complete quantum at a time. Thus not only in the photo-electric phenomenon, but in all other transfers of energy through space, energy is always transferred by complete quanta; fractions of a quantum can never occur. This brings atomicity into our picture of radiation just as definitely as the discovery of the electron and its standard charge brought atomicity into our picture of matter and of electricity.”

James Jeans (1877–1946) British mathematician and astronomer

Physics and Philosophy (1942)

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