Problem: Maths (& Physics) have too many cases where a symbol is used, confusingly, to mean multiple different things, leading to ambiguity and headaches.
Sensible solution: Use a key or just simply clarify the meaning in context, so v here is velocity, or v here is an arbitrary vector, or v here is specifically final velocity, or v here is the harmonic function for the complex part of a complex function f(z) for the purposes of the Cauchy-Riemann & Laplacian equations, or v here is the potential V(x) differentiated with respect to time (yes i have seen this once, it was disgusting).
My solution: add new characters. invent new scripts. steal syllabaries, acquire abjads, and abduct alphabets until we have enough squiggly lines to give literally everything its own unique symbol. This will help nobody and ruin everything. I will not rest until I am doing theoretical physics with these bad boys:
[Image ID: The 120 base Sitelen Pona of Toki Pona. They are simple, black and white, cartoonish, almost child-like drawings that act as logographic characters for the base words of the conlang Toki Pona. Each one has its corresponding name/word in Latin script beneath. End ID]
Thank you for coming to my TED Talk.
Handmade piece embroidered by Palestinian refugee women, INAASH Association for the Development of Palestinian Camps, Lebanon, 1970s [The Association for the Development of Palestinian Camps Collection, The Palestinian Museum Digital Archive, The Palestinian Museum, Birzeit]
Need a nice notation for injective and surjective functions, I propose the following
→= for injection (parallel lines from the branches of the arrow) because injections map distinct inputs to distinct outputs so visually it's = not >
→• for surjection (filled circle at the tip of the arrow) because filled circles indicate "is included in" in other contexts and a surjection includes all elements of the codomain
Notation is not sketching, and its products are not "sketches". I avoid the word "sketch", detest the French equivalent, croquis. The words reek of Beaux-Arts aestheticizing ideology. "Sketch" suggests something that will be followed by a more elaborate version of the same, and then by schematic drawings, design development drawings and, likely, many forms of conventional representation. What I am doing here is thoughts on paper. The current state of technology still requires the hand. But I could imagine using emerging technologies or the movement of my eyes alone, providing thought could somehow materialize itself in front of the eyes.