“Although mathematics originates in the human mind, its remarkable effectiveness in explaining the world does not extend to the mind itself. Psychology has proved unusually resistant to the mathematization that works so well in physics.”

Source: Quantum Reality - Beyond The New Physics, Chapter 1, The Quest For Reality, p. 2

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Nick Herbert23

American physicist 1936

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“Either mathematics is too big for the human mind, or the human mind is more than a machine.”

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As quoted in Topoi : The Categorial Analysis of Logic (1979) by Robert Goldblatt, p. 13

“The definition of random in terms of a physical operation is notoriously without effect on the mathematical operations of statistical theory because so far as these mathematical operations are concerned random is purely and simply an undefined term. The formal and abstract mathematical theory has an independent and sometimes lonely existence of its own. But when an undefined mathematical term such as random is given a definite operational meaning in physical terms, it takes on empirical and practical significance. Every mathematical theorem involving this mathematically undefined concept can then be given the following predictive form: If you do so and so, then such and such will happen.”

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“Among all the studies of natural causes and reasons Light chiefly delights the beholder; and among the great features of Mathematics the certainty of its demonstrations is what preeminently (tends to) elevate the mind of the investigator. Perspective, therefore, must be preferred to all the discourses and systems of human learning. In this branch [of science] the beam of light is explained on those methods of demonstration which form the glory not so much of Mathematics as of Physics and are graced with the flowers of both.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

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“Fifty years ago Kurt Gödel… proved that the world of pure mathematics is inexhaustible. … I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics.”

Freeman Dyson book Infinite in All Directions

Source: Infinite in All Directions (1988), Ch. 3 : Manchester and Athens
Context: Fifty years ago Kurt Gödel... proved that the world of pure mathematics is inexhaustible. … I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics. If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed, I would feel that the Creator had been uncharacteristically lacking in imagination.

“Johann Herbart’s work on education and particularly mathematical psychology influenced me. I think mathematics is the pure instance of construct functioning—the model of human behaviour.”

George Kelly (psychologist) (1905–1967) American psychologist and therapist

Attributed to George A. Kelly in Hinkle (1970, p. 91), as cited in: Fay Fransella and Robert A. Neimeyer. "George Alexander Kelly: The man and his theory." International handbook of personal construct psychology (2003): 21-31.

“It was funny, though, how the human mind would cast doubt even on itself in order to explain away unusual and unconventional things it had seen vividly and unmistakably. It left you in the middle, the human mind did.”

Fritz Leiber book Our Lady of Darkness

Source: Our Lady of Darkness (1977), Chapter 15 (p. 83)

“The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics.”

Benjamin Peirce Linear Associative Algebra

§ 2.
Linear Associative Algebra (1882)
Context: The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.

“Pure mathematics proves itself a royal science both through its content and form, which contains within itself the cause of its being and its methods of proof. For in complete independence mathematics creates for itself the object of which it treats, its magnitudes and laws, its formulas and symbols.”

Christian Heinrich von Dillmann (1829–1899) German educationist

Source: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 94.

“Psychology of Management, as here used, means, the effect of the mind that is directing work upon that work which is directed, and the effect of this undirected and directed work upon the mind of the worker.”

Lillian Gilbreth (1878–1972) American psychologist and industrial engineer

Source: Psychology of management, 1914, p. 1

“Reality contains not only evidence, but also the means (such as our minds, and our artefacts) of understanding it. There are mathematical symbols in physical reality. The fact that it is we who put them there does not make them any less physical.”

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Source: The Fabric of Reality (1997), Ch.3

“Although mathematics originates in the human mind, its remarkable effectiveness in explaining the world does not extend to the mind itself. Psychology has proved unusually resistant to the mathematization that works so well in physics.”

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Nick Herbert23

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