Real numbers are imaginary, and imaginary numbers are real.
[I]maginary numbers describe a physical state of something, so as much as a number can exist, these do. But … real numbers, [being ideal], are imaginary.
Posted on Friday, 3 August 2012
Real numbers are imaginary, and imaginary numbers are real.
[I]maginary numbers describe a physical state of something, so as much as a number can exist, these do. But … real numbers, [being ideal], are imaginary.
(I changed some parts that I don’t agree with but the phrasing and initiative are his.)
The “rational” numbers are ratios and the “counting” numbers are, um, what you get when you count. But “real” and “imaginary” numbers have nothing to do with reality or imagination (each is both real and ideal in the same sense).
How about we start referring to them this way?
√−1
becomes “twisting numbers”. This derives from the “twisting” feeling one gets when multiplying numbers from ℂ. For example 3exp{i 10°} • 5exp{i 20°} = 15exp{i 30°}
, they spiral as they multiply outwards. Keep multiplying numbers off the zero line and they keep twisting. Tristan Needham coined the word “amplitwist” for use in ℂ.Just to give a few examples of other acceptable numbers systems:
42 notes