On Fri, 11 Oct 2013 00:25:27 +1100, Chris Angelico wrote: > On Fri, Oct 11, 2013 at 12:09 AM, Roy Smith <r...@panix.com> wrote: >> BTW, one of the earliest things that turned me on to Python was when I >> discovered that it uses j as the imaginary unit, not i. All >> right-thinking people will agree with me on this. > > I've never been well-up on complex numbers; can you elaborate on this, > please? All I know is that I was taught that the square root of -1 is > called i, and that hypercomplex numbers include i, j, k, and maybe even > other terms, and I never understood where j comes from. Why is Python > better for using j?
Being simple souls and not Real Mathematicians, electrical engineers get confused by the similarity between I (current) and i (square root of -1), so they used j instead. Real Mathematicians are hardy folk completely at home with such ambiguity -- if you can deal with superscript -1 meaning both "inverse function" and "reciprocal" *in the same equation*, i vs I hold no fears for you. <wink> But seriously... I think the convention to use j for complex numbers comes from the convention of using i, j, k as unit vectors, i being in the X direction (corresponding to the real axis), j being in the Y direction (corresponding to the imaginary axis), and k being in the Z direction. For what it's worth, there is no three-dimensional extension to complex numbers, but there is a four-dimensional one, the quaternions or hypercomplex numbers. They look like 1 + 2i + 3j + 4k, where i, j and k are all distinct but i**2 == j**2 == k**2 == -1. Quaternions had a brief period of popularity during the late 19th century but fell out of popularity in the 20th. In recent years, they're making something of a comeback, as using quaternions for calculating rotations is more numerically stable than traditional matrix calculations. Unlike reals and complex numbers, quaternions are non-commutative: in general, q1*q2 != q2*q1. There are also octonions, eight-dimensional numbers which are non- commutative and non-associative, (o1*o2)*o3 != o1*(o2*o3), and sedenions, a 16-dimensional number. -- Steven -- https://mail.python.org/mailman/listinfo/python-list
