Forward to the Past

RANT#18: Harkening back to Rants 4, 5 and 6 when I complained about being ignored by the ortho-physics community over their lack of interest in my findings on higher dimensional Argand diagrams and how I couldn't find anything about it on the Web, well here we go again on all three counts. There's good news and bad news. I pulled a 1985 Dover edition of a 1964 title "A history of Vector Analysis" and started re-reading it and came to realize a lot of my thinking had been influenced by it. It's author is Michael J. Crowe, now an Emertius Professor of History of Science at Notre Dame. Since he published just a year after I got my PhD I figured he was a lot older than I but to my surprise I Goggled him to find he's a year younger. The good news is that I highly recommend the book if you want to see the face of the human side of math rather than the sterilized presentation of the subject. The bad news is that I thought I could catch his interest with an email about my vector "discovery" only to be once again unacknowledged. As for the "discovery" (which I still believe is original) it turns out that the best reference to higher dimensional "Argand" diagrams followed Monsieur Argand (1806)by the Irishman Sir Willian Rowan Hamilton of Quantum Mechanical operator fame. His discovery (invention?) of a early variety of vectors he called Quaternions was driven by a passion for understanding the imaginary quantity (square root of minus one). So he developed (c. 1848) a four component real number quantity consisting of a scalar and three component vector with multipliers labeled i, j, and k whose properties were that their squares were equal to minus one. In my Phenomenal Universe paper I borrowed Hamilton's quaternion by suggesting that the scalar was a radial measure of a set of real x, y, and z axes (like the Pythagorian theorem with r^2 = x^2 + y^2 + z^2. Not that the quaternion isn't curious enough but a quote by Hamilton is doubly perplexing since my thrust is that my three dimension Argand diagram collapses into 4 dimensional spacetime (with an added parallel imaginary dimension to the negative time axis. Anyway the quote is: "Time is said to have only one dimension, and space to have three dimensions. […] The mathematical quaternion partakes of both these elements; in technical language it may be said to be "time plus space", or "space plus time": and in this sense it has, or at least involves a reference to, four dimensions. And how the One of Time, of Space the Three, Might in the Chain of Symbols girdled be." — William Rowan Hamilton (Quoted in R.P. Graves, "Life of Sir William Rowan Hamilton"). How he jumped from one real and three virtual to three real and one virtual leaves me perplexed - but there you have it.