An unmixed evil to those who have touched them in any way
I have been advised by my adviser to study quaternions over the next little while. Yes indeed, today is the best day of my life. Quaternions are pretty much the reason I wanted to do pure algebra in the first place; that and category theory, so it's exciting that I am now being instructed to learn about this stuff. Be still my heart...
The title of this post is what Lord Kelvin had to say about quaternions, but for fear that you might form a negative impression of quaternions, I will also quote from Thomas Pynchon's Against the Day:
"the thing about a Quaternion 'is' is that we're obliged to encounter it in more than one guise. As a vector quotient. As a way of plotting complex numbers along three axes instead of two. As a list of instructions for turning one vector into another..... And considered subjectively, as an act of becoming longer or shorter, while at the same time turning, among axes whose unit vector is not the familiar and comforting 'one' but the altogether disquieting square root of minus one. If you were a vector, mademoiselle, you would begin in the 'real' world, change your length, enter an 'imaginary' reference system, rotate up to three different ways, and return to 'reality' a new person. Or vector..."
More fiction needs to incorporate hypercomplex numbers.
The title of this post is what Lord Kelvin had to say about quaternions, but for fear that you might form a negative impression of quaternions, I will also quote from Thomas Pynchon's Against the Day:
"the thing about a Quaternion 'is' is that we're obliged to encounter it in more than one guise. As a vector quotient. As a way of plotting complex numbers along three axes instead of two. As a list of instructions for turning one vector into another..... And considered subjectively, as an act of becoming longer or shorter, while at the same time turning, among axes whose unit vector is not the familiar and comforting 'one' but the altogether disquieting square root of minus one. If you were a vector, mademoiselle, you would begin in the 'real' world, change your length, enter an 'imaginary' reference system, rotate up to three different ways, and return to 'reality' a new person. Or vector..."
More fiction needs to incorporate hypercomplex numbers.