Some time ago I bumped into a book that forced me to discover a whole new world view, contrary to the ‘traditional’ view still predominant in our contemporary science, especially among the ‘theoretical physicists’ and mathematicians. It has a confusing name ‘realism’ (ha-ha-ha!) and it doesn’t mean what you think! What can be confusing about that, you may ask? The confusion is in the answer to the question: ‘what is real?’ The so called ‘realists’ don’t say that there is some kind of a ‘nature’ and there are some ‘natural phenomena’ out there that are real as one might think. Nothing of the kind! They claim that the icons, which may be drawings, cryptic symbols (hi, Russell and Whitehead) or ‘formulas’ that they chose for representation of the observed phenomena are ‘real’, the conjectured definitions of their behaviour under changing conditions are ‘real’ in the sense that they map onto something that necessarily can happen in reality. And, of course, the results of their arithmetical and not so arithmetical (but always tautological) manipulations with these icons that will be done by the selected few who ‘understand’ the ‘true meaning’ (of these icons) is real. Really? Are they? What you wrote on your wrinkled piece of paper is guaranteed to map onto something in the real world? You are saying that it is bound to exist because you used summation and multiplication derived from counting distinctely different items to electromagnetic fields flying across the Universe? Yeah! Right! I can see what kind of a ‘realist’ you are, ha-ha-ha!
    Back to my story about the book(s) I read. It’s a relatively old book, from 1992, by a British professor Simon L. Altmann, called “Icons and Symmetries” (from it I discovered his other book “Rotations, Quaternions and Double groups” and the book by Elie Cartan “The Theory of Spinors”). He, by his book, made me realise once again, that the way we draw or otherwise visually or symbolically ‘represent’ the observed phenomena influences our intuitions in a way that is not always productive and sometimes is outright wrong. His story was about Oersted, the cult of Hamilton, the ‘Rodrigues construction’ for consequitive rotations and on and on to spinors with a point that they are more fundamental than both types of vectors and why.
    The point that we should never forget is that whatever we draw, whatever we say or write about the observable phenomena are just metaphors. They are created by our brain and are some vague ‘approximation’ (of reality) constructed by it. Sometimes these metaphors are ‘spot on’ (or at least we still think so today), sometimes they are useful in some situations but lead to errors and misunderstandings in other… as in this case with polar and axial vectors that he is discussing.

When did it start? A long time ago…

    Commesurable and incommesurable, remember? The biggest secret of the universe that Pythagoreans were hiding from everybody, that the diagonal of a square is ‘incommesurable’ with its sides. Really? The problem can not be solved by bean counting means that there is something mysterious about it? Nope. Just NO, forget about it. Go back to reality and make an experiment. The experiment will show that it is “more than…” but “less than…” and forget about the rest, bean counter. But NOOOO (hi, Belushi), this is the ‘mystery of the Universe’. Why? Because of the properties that we assign to the Pythagorean ‘icons’ - their ‘numbers’.
    From what I know now it seems that Kirchhoff and Helmholtz were the main ‘founders’ of the school of formula jogglers in the German tradition that later produced Einstein with his ‘heuristic hypothesis’ of ‘photons’. I will look into it later and add something about that here.

‘Sicilian defence’ in the time of AlphaZero.

    As you sail in the sea of knowledge you constantly bump into terminology that had been created a long time ago by some people who had their own view of the world and motivations, they were surrounded by a different world with different stories (and sometimes were using them as metaphors to explain their ideas as in the case of Aristotle who cites “Cresphontes”, a play by Euripides that no longer exists, in one of his texts that I talked about). We use symbolic names or names of their authors for complex constructs or methods of thought. This is one of the features of our civilization and at the same time a mnemonic rule of producing ‘stenographic signs’ and using them to communicate ideas. The combination of words ‘Sicilian defence’ was invented by somebody, God knows when and for what reason, but it means a tree of sequences of chess moves. For a human it is a way of describing to another slightly educated human how the chess pieces can move or have moved, but besides that it means nothing. Unfortunately even the old books about mathematics have a lot of those ‘terms’. The ‘named’ formulas are particularly annoying, they are pretty much always named after somebody who wasn’t the author of the invention, but had enough influence to persuade ‘the scientific community’ that all credits should go to him/her (yes, I’m looking at you too, Ada Lovelace). In a sense, by repeating these names of formulas you connive the outrageous vanity of these people and carry them further to the next generation of unsuspecting kids who will afterwords have to figure it all out by themselves. Basically, I’m saying that lying to our kids is not exactly right, how about stopping doing it? Like, right now!

Oliver Heaviside, the man with painted nails.

    And then there was Oliver Heaviside with his ‘operational calculus’ and then there were ‘umbral calculus’ - a version of the same but for mathematicians… I will write about it some day.

What was useful

    The points that were particularly useful:

  1. This Hamilton’s BS mixing matrices-objects and matrices-transforms is just that - BS, as I always felt. It would be good to write about it separately, probably in conjunction with the time dimension explanations.
  2. The real method should be much stranger than what the ancient philosophers envisioned, namely: after our manipulations with formulas we come to a ‘conclusion’, then we return to the metaphysics of the phenomenon and fix it, then we go back to experiment and rebuild it based on the new metaphysics, then we change the metaphor based on the result of the new experiment. Sounds very strange. The name ‘meta-induction’ for description of this process comes to mind immediately.
  3. Distances as matrices and distances as graphs / trees are an idea that keeps coming to my mind over and over again. Maybe it’s time to write a paper about them.

    P.S. Hans Reichebach

        And of course Hans Reichenbach in his wonderful book “The rise of scientific philosophy” joked every ten pages of so about the habbit of ‘visualisation’ of the philosophers of the past. In case you are wondering what it is - he was talking about just that: creating ‘icons’ instead of real variables, then inventing all sorts of tautological ‘conclusions’ about the real things and phenomena based on the properties of these icons , ‘axiomatically’ introduced by the author. Example? The ‘photons’ of course, what else. Books:
    Simon L. Altmann - “Icons and Symmetries”
    Altmann - “Rotations, Quaternions and Double groups”
    Elie Cartan - “The Theory of Spinors”
    Penrose, Rindler - “Spinors and space-time. vv. 1,2”

    Later.