I see you keep building an optimal and geometrically-and-colored notation from scratch! It does feel more intuitive than the conventional one. I also remember watching 3b1b's video and it making a lot of sense to me.
Yeah, the hypersquare is optimized for certain aspects. Conceptual clarity, color-coded semantic redundancy and memorability. For exponentiation and roots, it's great stuff for writing out an expression and deeply pondering relationships and learning to visualize them and manipulate them mentally, without confusion or uncertainty.
Or for creating teaching material, pretty-typing important final or in-between results or problem-relevant expressions as orientation anchors. Stating lemmas and theorems etc.
But it's not optimized for speed. Especially, if you have to grab two different pens for a symbol. And I keep hunting on my desk finding the right color again! So that's why, I haven't mirrored all the 3b1b-stuff or even restated basic laws in this notation. It's a pain in the butt and I'm sick of it.
For logarithms, the uncolored square is still strictly superior, but exponentiation is charmingly quick to write out and radicands can always be stated as reciprocal/multiplicative-inverse exponents.
So the next post will be the opposite of that approach and will focus on how you can write expressions faster and more cleanly by getting rid off +, -, x, two-line fraction-statements, parentheses, fast-encode polynomials as numbers to an unknown base, how to add polymorphism support into notation, how to work in-place to save on equation transformations, how to quick-encode expression-components etc.
That'll make any following deep dives and insights easier to write out.
I see you keep building an optimal and geometrically-and-colored notation from scratch! It does feel more intuitive than the conventional one. I also remember watching 3b1b's video and it making a lot of sense to me.
Yeah, the hypersquare is optimized for certain aspects. Conceptual clarity, color-coded semantic redundancy and memorability. For exponentiation and roots, it's great stuff for writing out an expression and deeply pondering relationships and learning to visualize them and manipulate them mentally, without confusion or uncertainty.
Or for creating teaching material, pretty-typing important final or in-between results or problem-relevant expressions as orientation anchors. Stating lemmas and theorems etc.
But it's not optimized for speed. Especially, if you have to grab two different pens for a symbol. And I keep hunting on my desk finding the right color again! So that's why, I haven't mirrored all the 3b1b-stuff or even restated basic laws in this notation. It's a pain in the butt and I'm sick of it.
For logarithms, the uncolored square is still strictly superior, but exponentiation is charmingly quick to write out and radicands can always be stated as reciprocal/multiplicative-inverse exponents.
So the next post will be the opposite of that approach and will focus on how you can write expressions faster and more cleanly by getting rid off +, -, x, two-line fraction-statements, parentheses, fast-encode polynomials as numbers to an unknown base, how to add polymorphism support into notation, how to work in-place to save on equation transformations, how to quick-encode expression-components etc.
That'll make any following deep dives and insights easier to write out.
Hey, this is clever!