“Imaginary numbers are not imaginary and the theory of complex numbers is no more complex than the theory of real numbers. Complex numbers are as intuitive for an electronics engineer as -100 is for the average person with an overdrawn bank account.”

— Mordechai Ben-Ari

Source: Just a Theory: Exploring the Nature of Science (2005), Chapter 3, “Words Scientists Don’t Use: At Least Not the Way You Do” (p. 56)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Imaginary numbers are not imaginary and the theory of complex numbers is no more complex than the theory of real number…" by Mordechai Ben-Ari?

Mordechai Ben-Ari 28

Israeli computer scientist 1948

Related quotes

“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

“It has been generally believed that only the complex numbers could legitimately be used as the ground field in discussing quantum-mechanical operators. Over the complex field, Frobenius' theorem is of course not valid; the only division algebra over the complex field is formed by the complex numbers themselves. However, Frobenius' theorem is relevant precisely because the appropriate ground field for much of quantum mechanics is real rather than complex.”

Freeman Dyson (1923) theoretical physicist and mathematician

[The threefold way: algebraic structure of symmetry groups and ensembles in quantum mechanics, Jour. Math. Phys., 3, 1962, 1199–1215, https://books.google.com/books?id=nnyNUidX1OMC&pg=PA410] (p. 1200)

“A complex system can fail in an infinite number of ways”

John Gall (1925–2014) American physician

Source: General systemantics, an essay on how systems work, and especially how they fail..., 1975, p. 92, cited in: Erik Hollnagel (2004) Barriers and accident prevention. p. 182

“You can ask the question about these ancient topics, such as perfect numbers and amicable numbers… and ask, are these good problems… I'd like to give a small amount of evidence… that they are… [S]tudying them helped us develop all of elementary number theory and from elementary number theory we developed the rest of number theory, and also you can argue that from elementary number theory came algebra..”

Carl Pomerance (1944) American mathematician

"Paul Erdős and the Rise of Statistical Thinking in Elementary Number Theory" https://www.youtube.com/watch?v=5cU0g9dI1S8&t=9m40s (July, 2013) Erdős Centennial Conference, Budapest.

“Reducing complexity by order formation is the number one skill needed by all leaders in the twenty-first century”

Peter Kruse (1955–2015) German psychologist

Peter Kruse, Google's Think Quarterly, "Soft Values, Hard Facts" (March 2011) Think Quarterly http://www.thinkwithgoogle.co.uk/quarterly/data/peter-kruse-next-practice.html