Mind Matters Natural and Artificial Intelligence News and Analysis

TagImaginary numbers (as essential)

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Abstract Computer generated Fractal design. 3D Illustration of a Beautiful infinite mathematical mandelbrot set fractal.

Recent Research: Imaginary Numbers Are Part of the Real World

If we try to leave them out of quantum mechanics, our description of nature becomes faulty

Imaginary numbers, beginning with the square roots of minus numbers, are part of the world in which we live, even though we can’t quite picture them. Try it. The square root of 1 is 1 (1 × 1 = 1). But what’s the square root of -1? It can’t be -1 because if we multiply -1 × -1, we still get 1. The two minus numbers cancel each other out. That’s why the square root of -1 is written as i. Now, here’s the odd part: Imaginary numbers are not just a conundrum; they are part of a science description of the world in which we live in: Though imaginary numbers have been integral to quantum theory since its very…

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Man's hand holding white blank styrofoam ball with handwritten imaginary number formula against the white background.

Why Would a Purely Physical Universe Need Imaginary Numbers?

Our computers and the entire modern world depend on them, says science writer Michael Brooks in an excerpt from his new book

In an excerpt from his new book, The Art of More: How Mathematics Created Civilization, science writer Michael Brooks offers the intriguing idea that the modern world arose from imaginary numbers: Imaginary numbers are not imaginary at all. The truth is, they have had far more impact on our lives than anything truly imaginary ever could. Without imaginary numbers, and the vital role they played in putting electricity into homes, factories, and internet server-farms, the modern world would not exist Michael Brooks, “Imaginary Numbers Are Reality” at Nautilus (February 9, 2022) Imaginary numbers, are we recall from school, are the square roots of minus numbers. Two plus numbers, multiplied, result in a plus number. But so do two minus numbers.…

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Alien Planet with Moons

Recent Science Papers Support Science Fiction Premises

There isn’t a crystal clear boundary; both science and science fiction achievements require imagination

Good science fiction should start with science fact. But, of course, science is a dynamic enterprise that includes many current mysteries and uncertainties so there is plenty of room to develop an imaginative theme while exploring the edges. Here are five edges that a reader or writer may want to explore: ➤ It might indeed be possible to go through a wormholes to a distant galaxy, according to a recent paper. A wormhole, first envisioned by Einstein and Rosen in 1935, “is a special solution to the equations describing Einstein’s theory of general relativity that connects two distant points in space or time via a tunnel.” (LiveScience) It has long been considered at best hypothetical and at worst impossible but…