I just ran across this simple explanation by Miles Mathis of what calculus really is. It is quite simple, even if the author is a bit long winded and self congratulatory. Check it out.

Here's a TL;DR extract of the important bit. Please note that everything is a length, not just a point or a number.

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1 Δz 1, 2, 3, 4, 5, 6, 7, 8, 9….

2 Δ2z 2, 4, 6, 8, 10, 12, 14, 16, 18….

3 Δz

^{2}1, 4, 9, 16, 25, 36, 49 64, 81

4 Δz

^{3}1, 8, 27, 64, 125, 216, 343

5 Δz

^{4}1, 16, 81, 256, 625, 1296

6 Δz

^{5}1, 32, 243, 1024, 3125, 7776, 16807

7 ΔΔz 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

8 ΔΔ2z 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

9 ΔΔz

^{2}1, 3, 5, 7, 9, 11, 13, 15, 17, 19

10 ΔΔz

^{3}1, 7, 19, 37, 61, 91, 127

11 ΔΔz

^{4}1, 15, 65, 175, 369, 671

12 ΔΔz

^{5}1, 31, 211, 781, 2101, 4651, 9031

13 ΔΔΔz 0, 0, 0, 0, 0, 0, 0

14 ΔΔΔz

^{2}2, 2, 2, 2, 2, 2, 2, 2, 2, 2

15 ΔΔΔz

^{3}6, 12, 18, 24, 30, 36, 42

16 ΔΔΔz

^{4}14, 50, 110, 194, 302

17 ΔΔΔz

^{5}30, 180, 570, 1320, 2550, 4380

18 ΔΔΔΔz

^{3}6, 6, 6, 6, 6, 6, 6, 6

19 ΔΔΔΔz

^{4}36, 60, 84, 108

20 ΔΔΔΔz

^{5}150, 390, 750, 1230, 1830

21 ΔΔΔΔΔz

^{4}24, 24, 24, 24

22 ΔΔΔΔΔz

^{5}240, 360, 480, 600

23 ΔΔΔΔΔΔz

^{5}120, 120, 120

from this, one can predict that

24 ΔΔΔΔΔΔΔz

^{6}720, 720, 720

And so on.

Again, this is what you call simple number analysis. It is a table of differentials. The first line is a list of the potential integer lengths of an object, and a length is a differential. It is also a list of the integers, as I said. After that it is easy to follow my method. It is easy until you get to line 24, where I say, “One can predict that. . . .” Do you see how I came to that conclusion? I did it by pulling out the lines where the differential became constant.

7 ΔΔz 1, 1, 1, 1, 1, 1, 1

14 ΔΔΔz

^{2}2, 2, 2, 2, 2, 2, 2

18 ΔΔΔΔz

^{3}6, 6, 6, 6, 6, 6, 6

21 ΔΔΔΔΔz

^{4}24, 24, 24, 24

23 ΔΔΔΔΔΔz

^{5}120, 120, 120

24 ΔΔΔΔΔΔΔz

^{6}720, 720, 720

Do you see it now?

2ΔΔz = ΔΔΔz

^{2}

3ΔΔΔz

^{2}= ΔΔΔΔz

^{3}

4ΔΔΔΔz

^{3}= ΔΔΔΔΔz

^{4}

5ΔΔΔΔΔz

^{4}= ΔΔΔΔΔΔz

^{5}

6ΔΔΔΔΔΔz

^{5}= ΔΔΔΔΔΔΔz

^{6}

All these equations are equivalent to the magic equation, y’ = nx

^{n-1}. In any of those equations, all we have to do is let x equal the right side and y’ equal the left side. No matter what exponents we use, the equation will always resolve into our magic equation.

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