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It's the other way around: real numbers are imaginary. All numbers are imaginary. Numbers are very useful concepts, and can be used in various ways to describ
by mkl 4y ago
It's the other way around: real numbers are imaginary. All numbers are imaginary. Numbers are very useful concepts, and can be used in various ways to describe parts of reality. These descriptions can stop making sense if inappropriate kinds of numbers are used (e.g. -5 makes perfect sense as a displacement, but not as a count, and 5i makes perfect sense as part of a description of simple harmonic motion, but not as a displacement).
The use of the word "imaginary" to describe parts of complex numbers is quite unfortunate [1], because it misleads people into thinking there's something fake or weird about them, leading to confusion and entire articles trying to convince people they're valid. They're a totally normal, expected, and widely used feature of number systems as we understand them today.
The name they've got comes from how surprising and foreign they seemed to the people who first encountered them. Irrational numbers were similarly surprising and foreign to the people who first encountered them. Today we're perfectly comfortable working with irrational numbers like π, but the original reaction lives on in other meanings of "rational" and "irrational": based reasoning, and not based on reasoning, respectively.
"Imaginary" seems like a tougher hurdle, and while the article says "imaginary numbers" many times, mathematicians and physicists don't really. We talk about complex numbers, and describe complex numbers with 0 real part as "pure imaginary". "Imaginary" and "real" are just labels for the axes of the complex plane, and neither is literal in this context.
[1] As is the word "complex", which most commonly now means "complicated", but is used here with another meaning: made up of multiple parts.
- wruza 4y agothe original reaction lives on in other meanings of "rational" and "irrational": based reasoning, and not based on reasoning, respectively Doesn’t it simply mean “cannot be written as a ratio”? Edit: the parent is correct, they were called absurd numbers originally.
- mkl 4y agoI wasn't too clear in that sentence, but I mean the definitions about thinking. Colloquially: "rational" = "clear-headed", "irrational" = "crazy".
- TMWNN 4y ago>It's the other way around: real numbers are imaginary. All numbers are imaginary. I'm not sure whether <https://scp-wiki.wikidot.com/scp-033 https://scp-wiki.wikidot.com/scp-033> and <https://scp-wiki.wikidot.com/scp-1313 https://scp-wiki.wikidot.com/scp-1313> are evidence for, or against, your proposition.