Monday, October 14, 2019

How to understand calculus in an hour

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 = ΔΔΔΔz3
4ΔΔΔΔz
3 = ΔΔΔΔΔz4
5ΔΔΔΔΔz
4 = ΔΔΔΔΔΔz5
6ΔΔΔΔΔΔz
5 = ΔΔΔΔΔΔΔz6

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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