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betelguese_42 t1_j6c2mwk wrote

Reply to comment by breckenridgeback in ELI5: Why do imaginary numbers even need to exist? by Tharsis101

TLDR: The name imaginary numbers is bad and people would find it less futile if it was called Bob numbers

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Flaky-Proof5511 t1_j6cbvrs wrote

Didn't the YouTuber 3Blue1Brown suggested rotation numbers as a more user friendly name ?

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Magnetic_Syncopation t1_j6d9syu wrote

Another commenter mentioned that you can substitute calculations in electronic circuits that would normally use imaginary numbers instead with vectors. But it's a lot more work doing that, whereas imaginary numbers make calculations easier to do.

It seems like imaginary numbers provide a way of rotating between magnitudes in a sine/cosine way

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lunatickoala t1_j6chnor wrote

Imaginary number is a bad name for them... and intentionally so. It was meant to be derogatory. Mathematics has a history of people not liking new developments because people think of math as a very logical and objective thing and those developments can fly in the face of what they believe.

There's an apocryphal story that someone in the Cult of Pythagoras proved that the square root of two is irrational and they were so outraged by the idea that a number could be irrational that they took him to sea in a boat and returned without him. They believed that all numbers could be expressed as a ratio of two integers and an irrational number by definition is one that can't be expressed as a ratio.

The Ancient Greeks also didn't believe in the idea of zero or negative numbers and both were very controversial in the Western world for many centuries afterwards. In math today, the standard form for polynomials to put all the coefficients on one side and set it to zero because it's really useful. For example, Ax^2 + Bx + C = 0 for the quadratic polynomial where B and C are allowed to be zero and A/B/C are all allowed to be negative. But up until I think the 1500s, Western mathematicians didn't have a standard form but a family of forms specifically to avoid zeroes and negative numbers. Ax^2 + Bx = C, Ax^2 = Bx + C, Ax^2 = C, Ax^2 = Bx, etc.

Imaginary numbers first saw real use in the cubic equation because the people who found it realized that in some cases it involved taking the square root of a negative number, which people believed to be nonsensical. However, the cubic equation worked because the imaginary numbers cancelled each other out. Thus, they were called imaginary because people didn't think they were "real" and were only a mathematical trick that happened to work out and not something that's meaningful.

To get a feel for what it was probably like when irrational numbers, zero, negative numbers, and imaginary numbers were first introduced, look at the comments whenever 1+2+3+4+5+6+... = -1/12 comes up.

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otherestScott t1_j6d03us wrote

It’s not a bad name honestly, because “real numbers” also means something important in math and it excludes imaginary numbers

If we called them Bob numbers, you’d either have to change the name of “real numbers” to “non-Bob numbers” which isn’t great, or you would feel a lot less natural to exclude them.

It’s the same as rational vs irrational numbers. It’s not that pi or the square root of 2 is overly emotional, it’s just a convenient binary for mathematicians to use.

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Panceltic t1_j6cp5zt wrote

The same issue with grammatical gender. Instead of “masculine, feminine and neuter nouns” we could call them “Type A, B and C” and avoid many pointless discussions.

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