Quotes about tensor

A collection of quotes on the topic of tensor, equation, theory, mathematics.

Quotes about tensor

“Maxwell's equations… originally consisted of eight equations. These equations are not "beautiful." They do not possess much symmetry. In their original form, they are ugly…. However, when rewritten using time as the fourth dimension, this rather awkward set of eight equations collapses into a single tensor equation. This is what a physicist calls "beauty," because both criteria are now satisfied.”

Michio Kaku book Hyperspace

Source: Hyperspace (1995), Ch.5 Quantum Heresy

“Eight, sir; seven, sir;
Six, sir; five, sir;
Four, sir; Three, sir;
Two, sir; one!
Tenser, said the Tensor.
Tenser, said the Tensor.
Tension, apprehension,
And dissension have begun.”

Alfred Bester book The Demolished Man

Source: The Demolished Man

“I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen’s, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell’s equations.”

Kenneth E. Iverson (1920–2004) Canadian computer scientist

"Kenneth E. Iverson" http://keiapl.info/rhui/autobio.htm, autobiographical sketch from an unfinished work (ca. 2004), on his experience at Harvard with "a Masters program in Automatic Data Processing in 1955; in effect, the first computer science program."

Mathematics, Sense, Learning

“(…) the bottom line is that if you believe in an external reality independent of humans, then you must also believe that our physical reality is a mathematical structure. Nothing else has a baggage-free description. In other words, we all live in a gigantic mathematical object—one that’s more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names such as Calabi-Yau manifolds, tensor bundles and Hilbert spaces, which appear in today’s most advanced physics theories. Everything in our world is purely mathematical—including you.”

Max Tegmark book Our Mathematical Universe

Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (2014)

World, Mathematics, Reality, Appearance

“The field equation may… be given a geometrical foundation, at least to a first approximation, by replacing it with the requirement that the mean curvature of the space vanish at any point at which no heat is being applied to the medium—in complete analogy with… the general theory of relativity by which classical field equations are replaced by the requirement that the Ricci contracted curvature tensor vanish.”

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

Footnote
Geometry as a Branch of Physics (1949)

“The general theory of relativity considers physical space-time as a four-dimensional manifold whose line element coefficients g_{\mu \nu} satisfy the differential equationsG_{\mu \nu} = \lambda g_{\mu \nu} \qquad. \;. \;. \;. \;. \;. \; (1)in all regions free from matter and electromagnetic field, where G_{\mu \nu} is the contracted Riemann-Christoffel tensor associated with the fundamental tensor g_{\mu \nu}, and \lambda is the cosmological constant.”

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

"On Relativistic Cosmology" (1928)

“The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction.”

Hilary Putnam (1926–2016) American philosopher

in What is Mathematics, in [Hilary Putnam, Mathematics, matter, and method, Cambridge University Press, 1979, 0521295505, 60]

World, Law, Mathematics, Nature

“A new development began for relativity theory after 1925 with its absorption into quantum physics. The first great success was scored by Dirac's quantum mechanical equations of the electron, which introduced a new sort of quantities, the spinors, besides the vectors and tensors into our physical theories. …But difficulties of the gravest kind turned up when one passed from one electron or photon to the interaction among an indeterminate number of such particles. In spite of several advances a final solution of this problem is not yet in sight and may well require a deep modification of the foundation of quantum mechanics, such as would account in the same basic manner for the elementary electric charge e as relativity theory and our present quantum mechanics account for c and h.”

Hermann Weyl (1885–1955) German mathematician

Preface to the First American Printing (1950) Note: see Paul Dirac, The Principles of Quantum Mechanics (1947)
Space—Time—Matter (1952)

Problem, Success

“Before the spirit could seek into it, the mind must. She studied the tensor equations as once she studied the sutras, she meditated upon the koans of science, and at last she began to feel her oneness with all that was, and in the vision find peace.”

Poul Anderson book The Boat of a Million Years

Source: The Boat of a Million Years (1989), Chapter 19 “Thule”, Section 18 (p. 449)

Science, Peace, Study, Feeling