“We often resort to something called Hilbert space, which is described as n-dimensional—it’s like modern sex, any number may be played with.”

— James Blish , book The Quincunx of Time

Source: The Quincunx of Time (1973), Chapter 10, “Weinbaum on Sinai” (p. 116)

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James Blish 30

American author 1921–1975

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“At the most elemental level, reality evanesces into something called Schröedinger's Wave Function: a mathematical abstraction which is best represented as a pattern in an infinite-dimensional space, Hilbert Space. Each point of the Hilbert Space represents a possible state of affairs. The wave function for some one physical or mental system takes the form of, let us say, a coloring in of Hilbert Space. The brightly colored parts represent likely states for the system, the dim parts represent less probable states of affairs.”

Rudy Rucker (1946) American mathematician, computer scientist, science fiction author and philosopher

Source: The Sex Sphere (1983), p. 133-134

“Why is space-time doomed? There are many reasons, among which: In string theory we can change the dimension of space-time by changing the strength of the string force. Thus, the so-called II-A string theory, which semi-classically describes closed strings moving in ten-dimensional flat space for very weak coupling is dual for strong coupling to a theory, called M-theory, that at low energies is described by eleven-dimensional supergravity. By increasing the string coupling we can grow an extra dimension. How can the spatial continuum be fundamental if the number of spatial dimensions can be so changed?”

David Gross (1941) American particle physicist and string theorist

"Einstein and the Search for Unification", p. 11 https://books.google.com/books?id=rEaUIxukvy4C&pg=PA11, in The legacy of Albert Einstein: a collection of essays in celebration of the year of physics (2007)

“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.”

John C. Baez (1961) American mathematician and mathematical physicist

“The concepts which now prove to be fundamental to our understanding of nature—a space which is finite; a space which is empty, so that one point [of our 'material' world] differs from another solely in the properties of space itself; four-dimensional, seven- and more dimensional spaces; a space which for ever expands; a sequence of events which follows the laws of probability instead of the law of causation—or alternatively, a sequence of events which can only be fully and consistently described by going outside of space and time—all these concepts seem to my mind to be structures of pure thought, incapable of realisation in any sense which would properly be described as material.”

James Jeans book The Mysterious Universe

Source: The Mysterious Universe (1930), p. 122, 1937 ed.

“For whatever reason, we find it easier to "read" Hilbert Space patterns in terms of time. Yet the patterns exist outside of time. Thinking timelessly is not some unusual skill; when you remember last night's supper you sense a whole and not a chew-by-chew replay. To know a novel's action is to grasp the four-dimensional spacetime whole described.”

Rudy Rucker (1946) American mathematician, computer scientist, science fiction author and philosopher

Source: The Sex Sphere (1983), p. 135

“Light signals alone provide the metrical structure of the four-dimensional space-time continuum. The construction may be called light axioms.”

Hans Reichenbach (1891–1953) American philosopher

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

“My real speciality is the mathematical analysis of Hilbert Space operators. But this was no time to come on like an ivory-tower idealist.”

Rudy Rucker (1946) American mathematician, computer scientist, science fiction author and philosopher

Source: The Sex Sphere (1983), p. 18

“God may not play dice with the universe, but something strange is going on with the prime numbers.”

Paul Erdős (1913–1996) Hungarian mathematician and freelancer

Referencing Albert Einstein's famous remark that "God does not play dice with the universe", this is attributed to Erdős in "Mathematics : Homage to an Itinerant Master" by D. Mackenzie, in Science 275:759 (1997), but has also been stated to be a comment originating in a talk given by Carl Pomerance on the Erdős-Kac theorem, in San Diego in January 1997, a few months after Erdős's death. Confirmation of this by Pomerance is reported in a statement posted to the School of Engineering, Computer Science & Mathematics, University of Exeter http://empslocal.ex.ac.uk/people/staff/mrwatkin//kac-pomerance.txt, where he states it was a paraphrase of something he imagined Erdős and Mark Kac might have said, and presented in a slide-show, which subsequently became reported in a newspaper as a genuine quote of Erdős the next day. In his slide show he had them both reply to Einstein's assertion: "Maybe so, but something is going on with the primes."
Misattributed

“Albert Gleizes did not know Montmartre, had never seen anything of Picasso or Juan Gris, never heard Maurice Princet construct an infinite number of different spaces for the use of painters, but he described to me the absurdity of the museums in which mournful, extravagantly three dimensional crowds threaten to crush the visitor by jumping out of their frames.”

Jean Metzinger (1883–1956) French painter

Cubism was born

“Quantum phenomena do not occur in a Hilbert space. They occur in a laboratory.”

Asher Peres (1934–2005) Israeli physicist

[Asher Peres, Quantum theory: concepts and methods, Springer, 1995, 0792336321, 373]

“We often resort to something called Hilbert space, which is described as n-dimensional—it’s like modern sex, any number may be played with.”

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James Blish 30

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