Are Numbers Real? Quotes

“the two disciplines are inherently different in this way. One (math) is a collection of facts, which we are able to establish because we fix the rules, and the other (science) is a collection of models and theories, which we can test against data, but can never call the actual truth.”
― Brian Clegg, Are Numbers Real?: The Uncanny Relationship of Mathematics and the Physical World

“like Max Tegmark (see here) suggest that the link between the math and reality will never be good enough—that the predictions will prove wrong if we ever get to analyze what appears to be a black hole up close.”
― Brian Clegg, Are Numbers Real?: The Uncanny Relationship of Mathematics and the Physical World

“Astronomers have observed many objects in deep space that behave from indirect evidence as if they were black holes. The evidence is strong, but remains indirect. We have never observed a black hole.”
― Brian Clegg, Are Numbers Real?: The Uncanny Relationship of Mathematics and the Physical World

“But from the Earth’s point of view, time on the ship is passing slowly, so that when t has elapsed on the ship, 4t has gone by on the Earth.”
― Brian Clegg, Are Numbers Real?: The Uncanny Relationship of Mathematics and the Physical World

“Descartes was responsible for analytical geometry, a mechanism for translating from geometrical forms to the equivalent algebraic equations and vice versa.”
― Brian Clegg, Are Numbers Real?: The Uncanny Relationship of Mathematics and the Physical World

“We tend to remember Descartes for two things—proclaiming “I think, therefore I am,” and having the so-called “Cartesian coordinates” named after him, where we specify locations on a chart with x and y values. But this was just a tiny part of his work, which took in everything from theories on light to attempts to take a scientific view on the soul.”
― Brian Clegg, Are Numbers Real?: The Uncanny Relationship of Mathematics and the Physical World

“Yet to avoid scaring his audience, or more likely to make his methods less obvious, Newton painstakingly translated as much of his work as he could into old-fashioned geometry for his masterpiece, the Principia.”
― Brian Clegg, Are Numbers Real?: The Uncanny Relationship of Mathematics and the Physical World

“Newton made the calculations that would enable him to establish his laws of motion and gravity in a new, mysterious mathematics, the method of fluxions, that dealt with the infinitesimally small.”
― Brian Clegg, Are Numbers Real?: The Uncanny Relationship of Mathematics and the Physical World

“stick with √2, or write out as many decimal places of the diagonal’s length as we require, such as 1.414213452 … but these were not options that were available to the whole-number obsessed Pythagoreans. We now call a number like this irrational because it can’t be made from the ratio of two whole numbers, but for the Pythagoreans it seemed to literally be an assault on the foundations of rationality.”
― Brian Clegg, Are Numbers Real?: The Uncanny Relationship of Mathematics and the Physical World