“My research work was based in pictures. I needed to visualise things and projective geometry was often most useful e. g. in figuring out how a particular quantity transforms under Lorentz transf[ormation]. When I came to publish the results I suppressed the projective geometry as the results could be expressed more concisely in analytic form.”

—  Paul Dirac

"Recollections of an Exciting Era," three lectures given at Varenna, 5 August 1972, quoted in Peter Galison, "The Suppressed Drawing: Paul Dirac's Hidden Geometry", Representations, No. 72 (Autumn, 2000)

Adopted from Wikiquote. Last update Aug. 9, 2024. History

Help us to complete the source, original and additional information

Do you have more details about the quote "My research work was based in pictures. I needed to visualise things and projective geometry was often most useful e. g…" by Paul Dirac?
Paul Dirac photo
Paul Dirac 23
theoretical physicist 1902–1984

Related quotes

Hans Reichenbach photo

“Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i. e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.”

Hans Reichenbach (1891–1953) American philosopher

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

“.. When an individual, e. g. higher forms of animals, thinks, it is always for his own advantage whether the resulting action or expression is favorable or not to the onlookers or observers.”

Isidro A. T. Savillo (1959) Filipino biologist

The Overpowering Influence of the Environment to Gene Expression, Biologybrowser.org, 2002 http://biologybrowser.org/node/1154589,

Joseph Louis Lagrange photo

“An ancient writer said that arithmetic and geometry are the wings of mathematics; I believe one can say without speaking metaphorically that these two sciences are the foundation and essence of all the sciences which deal with quantity. Not only are they the foundation, they are also, as it were, the capstones; for, whenever a result has been arrived at, in order to use that result, it is necessary to translate it into numbers or into lines; to translate it into numbers requires the aid of arithmetic, to translate it into lines necessitates the use of geometry.”

Joseph Louis Lagrange (1736–1813) Italian mathematician and mathematical physicist

Dans Les Leçons Élémentaires sur les Mathématiques (1795) Leçon cinquiéme, Tr. McCormack, cited in Moritz, Memorabilia mathematica or, The philomath's quotation-book (1914) Ch. 15 Arithmetic, p. 261. https://archive.org/stream/memorabiliamathe00moriiala#page/260/mode/2up

Girard Desargues photo

“I freely confess that I never had taste for study or research either in physics or geometry except in so far as they could serve as a means of arriving at some sort of knowledge of the proximate causes… for the good and convenience of life, in maintaining health, in the practice of some art,… having observed that a good part of the arts is based on geometry, among others that cutting of stone in architecture, that of sundials, that of perspective in particular.”

Girard Desargues (1591–1661) French mathematician and engineer

ca. 1640) as quoted by William Thompson Sedgwick, Harry Walter Tyler, A Short History of Science https://books.google.com/books?id=Wl8AAAAAMAAJ (1917

Algis Budrys photo

“Look, if I could guarantee what the results were going to be, I wouldn’t need a research program!”

Algis Budrys book Rogue Moon

Source: Rogue Moon (1960), Chapter 3, Section 2 (p. 57)

Spencer Tunick photo

“I make installations and the final result is a video projection and the photograph. If I didn’t make video projections, then call me one thing; if I didn’t make photos, then call me another. I’m in between an installation artist, video artist and photographer. And when you work with nude bodies, you’re immediately called a pornographer or a fashion photographer.”

Spencer Tunick (1967) American photographer

Spencer Tunick in: "Interview Spencer Tunick," at coolcleveland.com, 2004.

Jean Metzinger photo

“I sought refuge in my schoolbooks, among the flowers of Greek poetry, or the magical figures of geometry.”

Jean Metzinger (1883–1956) French painter

Cubism was born

Phillip Guston photo

“To answer your first question - most significantly the [ Federal Art Project ] project was my training ground in the real sense of the word. I feel very strongly about this. We were all poor, or most of us, and to have the time and opportunity to continue working - I was then in my twenties which is the important period - the crucial period for the young painter. This was most important and figures significantly in my own development. Although I feel that my personal image as a painter did not come about until I began my easel painting with personal imagery which was about 1941. The project kept me alive and working - it was my education.”

Phillip Guston (1913–1980) American artist

n.p.
1961 - 1980, Oral history interview with Philip Guston, 1965 January 29

Piet Mondrian photo

“the Cubists in Paris made me see that there was also a possibility of suppressing the natural aspect of form. I continued my research by abstracting the form and purifying the colour more and more. While working, I arrived at suppressing the closed effect of abstract form, expressing myself exclusively by means of the straight line in rectangular opposition; thus by rectangular planes of colour with white, grey and black. At that time, I encountered artists with approximately the same spirit, First Van der Leck, who, though still figurative, painted in compact planes of pure colour. My more or less cubist technique - in consequence still more or less picturesque - underwent the influence of his exact technique. Shortly afterwards I had the pleasure of making the acquaintance of Van Doesburg. Full of vitality and zeal for the already international movement that was called 'abstract', and most sincerely appreciative of my work, he came to ask me to collaborate in a review he intended to publish, and which he [Theo van Doesburg] was to call 'De Stijl.”

Piet Mondrian (1872–1944) Peintre Néerlandais

I was happy with an opportunity to publish my ideas on art, which I was engaged in writing down: I saw the possibility of contacts with similar efforts.
Quote of Mondrian c 1931, in 'De Stijl' (last number), p. 48; as cited in De Stijl 1917-1931 - The Dutch Contribution to Modern Art, by H.L.C. Jaffé http://www.dbnl.org/tekst/jaff001stij01_01/jaff001stij01_01.pdf; J.M. Meulenhoff, Amsterdam 1956, pp. 44-45
published in the memorial number of 'De Stijl', after the death of Theo Van Doesburg in 1931
1930's

Related topics