I have thought for the longest time, you simply cannot integrate with a delta. For any delta you chose, there is always something smaller.
IMO, that reflects nature. Universe->galaxy clusters->galaxies->solar systems->planets & their moons->atmosphere/crust/core->molecules->atoms->electrons/protons/neutrons->quarks, etc.
What this means is all the engineering formulas that are derived from integration are inaccurate at best and possibly completely wrong.
The question is, how accurate does it need to be? That is the difference between math and engineering. For engineering the figures need not be more accurate than what it is possible to build.
With the kind of math used to develop the energy systems we do have, it's a wonder they function at all.
I've been thinking the same for some time. My years of studying Tesla's work has shown me that what he was doing was mimicking natural phenomena: wireless energy transmission is how the sun transmits energy to the earth; millions upon millions of volts in a spark gap discharge is how lightning occurs, etc.
Someone (I think it was Eric Dollard) said "mother nature doesn't do math". Take that as a given and it follows that she doesn't do Euclidean geometry either. Look around you. What looks "natural" and what looks "man made"? Straight lines, near perfect circles, triangles, cubes, etc. are man made. Natural objects don't fit that model. What does fit her objects is fractals - self similar reproduction from smaller to larger scales. The veins in a leaf look similar to the branches of a tree and the limbs of a tree look similar to the roots. The sun, planets and moons of a solar system look similar to our current model of an atom.
My belief is that Phi is the closest we have to a basis for man made mathematical constructs of nature. The clearest example is the structure of a nautilus sea shell. When you start running fractal models of Phi and its derivatives they produce some very, very interesting 3D models that seem to have, to my eyes at least, an inherent instability which could explain the nearly infinite variability of nature's designs.
How to translate that into engineering is, however, beyond my abilities. My gut feeling is that it is only a matter of perspective but that change in perspective changes everything. Like a picture with two images entwined and you can see either - young or old woman?
