Nice essay Paul,
very nice observation on water as product of combustion. Hadn't thought of "hydrogen + oxygen so why not fire" re: water...
Need to think about the y = 1/x cubed thing.
As well as a way of mapping physics I have uncovered a new way of looking at math, of translating it into English.
I don't know if this will work but an attempt just here:
What is "squaring", "cubing"?
"cubing" seems like "acceleration"? Miles per second PER second? Two to power 3 is 2 times 2 times 2; or 2 of 2 of 2?
Now that graph "decelerated" didn't it: it fanned out SPLAT into a trumpet!
What is "x axis"?
It is a converging definition of x? How do you know each value for x is linear re: preceding values? By feedback loops referring back to previous values?
What is "rotate about x-axis"?
A particular plot on a y-axis x-axis point is a Y-self-reference x-self-reference mutual reference?
Perhaps rotation about x-axis of such a point is "area". But the next point along would be ?
What does "y = 1/...." mean?
Hold y constant to x as unity/... ?
Each "next point" of x-axis y-axis would be defined by feedback re both axises so relatively DE-mutualising their mutual self-reference so generating a FIXED definition of "x-axis" and of "y-axis".
Thus "Volume" is defined! Because volume was integrated by differentiating area!
You see, we have a series of disks for each rotated x-y point plot that is rotated about x-axis. AREA is "disk" and we have a SERIES of disks (so AREA is differentiated).
(AS in: "area" definition locally "distinguished"; relatively separated from definition of x-numbers say)
But volume is integrated:
A multiplicity of values of x and y that are self-referential and mutually referential. The mutual space is DEFINED as the very definition of x-axis and y-axis.
IT IS FILLED WITH PAINT!
Congratulations again Paul Martin!
Thank you I didn't know where I was going or where I came from but all the while I was already there in this exercise?
Why could he not calculate area? Because it was already calculated?
Why could he calculate volume?
Maybe because of a limit in defining it due to interference with how x and y axises define each other?
Re: "relatively": isn't that Peter Lynd's point?
That here "y = 1/..." means "y is moving relatively to x" so position can not be precisely determined...
Isn't "relative motion" the very definition of "locked together" so "FIXED position"?
I read up about axions as postulated particles that violate charge conjugation and parity re: colour forces.
Lee Smolin talks of quantized volumes and quantum geomtry...
Seems here we can see axions as localised "spheres" of volume-area in your math essay graph...
Little views of x-axis, y-axis?
"Charge conjugation" as x-axis, y-axis....?
run out of time....