Happy New (Marathi) Year!
I will speak in “aaeechee bhaashaa” (lit.: mother’s language).
“gudhi-paaDawyaachyaa haardik shubhechchhaa.” (lit.: hearty compliments [on the occasion] of “gudhi-paaDawaa” [i.e. the first day of the Marathi new year [^]].)
I am still writing up my notes on scalars, vectors, tensors, and CFD (cf. my last post). The speed is good. I am making sure that I remain below the RSI [^] detection levels.
BTW, do you know how difficult it can get to explain even the simplest of concepts once mathematicians have had a field day about it? (And especially after Americans have praised them for their efforts?) For instance, even a simple idea like, say, the “dual space”?
Did any one ever give you a hint (or even a hint of a hint) that the idea of “dual space” is nothing but a bloody stupid formalization based on nothing but the idea of taking the transpose of a vector and using it in the dot product? Or the fact that the idea of the transpose of a vector essentially means nothing than more than taking the same old three (or number of) scalar components, but interpreting them to mean a (directed) planar area instead of an arrow (i.e. a directed line segment)? Or the fact that this entire late 19th–early 20th century intellectual enterprise springs from no grounds more complex than the fact that the equation to the line is linear, and so is the equation to the plane?
[Yes, dear American, it’s the equation not an equation, and the equation is not of a line, but to the line. Ditto, for the case of the plane.]
Oh, but no. You go ask any mathematician worth his salt to explain the idea (say of the dual space), and this modern intellectual idiot would immediately launch himself into blabbering endlessly about “fields” (by which he means something other than what either a farmer or an engineer means; he also knows that he means something else; further, he also knows that not knowing this fact, you are getting confused; but, he doesn’t care to even mention this fact to you let alone explain it (and if you catch him, he ignores you and turns his face towards that other modern intellectual idiot aka the theoretical physicist (who is all ears to the mathematician, BTW))), “space” (ditto), “functionals” (by which term he means two different things even while strictly within the context of his own art: one thing in linear algebra and quite another thing in the calculus of variations), “modules,” (neither a software module nor the lunar one of Apollo 11—and generally speaking, most any modern mathematical idiot would have become far too generally incompetent to be able to design either), “ring” (no, he means neither an engagement nor a bell), “linear forms,” (no, neither Picasso nor sticks), “homomorphism” (no, not not a gay in the course of adding on or shedding body-weight), etc. etc. etc.
What is more, the idiot would even express surprise at the fact that the way he speaks about his work, it makes you feel as if you are far too incompetent to understand his art and will always be. And that’s what he wants, so that his means of livelihood is protected.
(No jokes. Just search for any of the quoted terms on the Wiki/Google. Or, actually talk to an actual mathematician about it. Just ask him this one question: Essentially speaking, is there something more to the idea of a dual space than transposing—going from an arrow to a plane?)
So, it’s not just that no one has written about these ideas before. The trouble is that they have, including the extent to which they have and the way they did.
And therefore, writing about the same ideas but in plain(er) language (but sufficiently accurately) gets tough, extraordinarily tough.
But I am trying. … Don’t keep too high a set of hopes… but well, at least, I am trying…
BTW, talking of fields and all, here are a few interesting stories (starting from today’s ToI, and after a bit of a Google search)[^][^] [^][^].
A Song I Like:
(Marathi) “maajhyaa re preeti phulaa”
Music: Sudhir Phadake
Lyrics: Ga. Di. Madgulkar
Singers: Asha Bhosale, Sudhir Phadke