I’m in annoying “foundationals” mode right now. It started when I decided to figure out *why* I found certain aspects of mathematics bothersome in school, and later on logic, along with various related things.
I realized that I learned BASIC before pre-algebra, so my expectations of variables and constants and logic were ‘set’ by the time I was in 5th grade in the way done in imperative programming languages.
So by the time pre-algebra then algebra came along, I’d already been messing in BASIC for a couple of years.
Suddenly, they want me to remove variables. Eliminate them. Gone. Seemed weird to me. Didn’t like it.
Then by the time I was in Calculus, I just couldn’t do it.. [that and I had senior-itis]. The way functions were handled and the way I understood functions were radically different.
I knew it takes time to step through changes. If you have a complicated statement, it has to go through a series of substeps to get there and sometimes those substeps matter, such as when you need to have each of those iterations cause something to happen on the screen.
I already thought of exponents as nested loops, even though they didn’t teach it that way.
I was always translating in my head between the ways mathematics does things and the way things were done in programming. [I was already messing with other languages at that point, even before I’d gotten my first PC].
Anyway, this always bugged me.
So, on occasion through the years, I tackle this conundrum and like to walk away with something novel under my belt that ties a few things together. This time I hope to ‘get it’ but who knows. It’s all steps in a process.
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Pi’s a theoretical construct. It’s useful as heck though to approximate the real world.
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I like zooming in and out. Looking real close then far away then up close again. Sometimes it’s dramatic jumps like this one other times it’s going step by step up and down the zoom levels.
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It’s sort of a constant for me 
🙂 I just have to think, “But what if…” and I’m there.
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You’re right of course Yeah a little QED shows the little tiny mirror machines doing their magic. Love his notation.
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True and even to go into the other extreme to the hard physicalist, they have to concede there’s no such thing as illusion if all is physical because they are processes in the brain that can be measured.
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Somewhere between “all is illusion” and “all is physical” is where most of these systems play out.
I like the interface between mathematics and engineering though.
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I’m fascinated by the little gaps. I remember in the early 80s drawing a circle on my Tandy Color Computer 2. I did the formula. It was an approximation of a circle. But it was on a TV screen and looked chunky.
I was fine with that, but I wondered then how small would those little squares have to be before it’d be smooth?
Then years later in geometry and trig when we investigated them further, I’d be tracing this circle with a compass and noticing the spots on the paper where the pencil dipped and curved. I noticed how the pencil lead fanned out on the paper.
It was a circle? yes, but it suffered from the same thing that bothered me about my blocky 8-bit graphics circle. Wasn’t perfect.
The math I used said it was but unless I go RIGHT into the center of the circle I drew, I couldn’t find it.
So, how do I get there?
How thin does the pencil or the pixel have to be?
So that’s the kind of stuff that occupied my brain as a kid a lot.
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Carburators are made of semi-precious metals that scrub the toxins out of the exhaust so that the environment doesn’t get toxic doesn’t it? I don’t know tricycles or carburators that well but I seem to recall.
Tricycles are hard to steer if I remember right.
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NEW SAMSUNG BOSE EINSTEIN CONDENSATE TV!
Oh it’d have marvelous resolution.
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