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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 Δz2 1, 4, 9, 16, 25, 36, 49 64, 81
4 Δz3 1, 8, 27, 64, 125, 216, 343
5 Δz4 1, 16, 81, 256, 625, 1296
6 Δz5 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 ΔΔz2 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
10 ΔΔz3 1, 7, 19, 37, 61, 91, 127
11 ΔΔz4 1, 15, 65, 175, 369, 671
12 ΔΔz5 1, 31, 211, 781, 2101, 4651, 9031
13 ΔΔΔz 0, 0, 0, 0, 0, 0, 0
14 ΔΔΔz2 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
15 ΔΔΔz3 6, 12, 18, 24, 30, 36, 42
16 ΔΔΔz4 14, 50, 110, 194, 302
17 ΔΔΔz5 30, 180, 570, 1320, 2550, 4380
18 ΔΔΔΔz3 6, 6, 6, 6, 6, 6, 6, 6
19 ΔΔΔΔz4 36, 60, 84, 108
20 ΔΔΔΔz5 150, 390, 750, 1230, 1830
21 ΔΔΔΔΔz4 24, 24, 24, 24
22 ΔΔΔΔΔz5 240, 360, 480, 600
23 ΔΔΔΔΔΔz5 120, 120, 120
from this, one can predict that
24 ΔΔΔΔΔΔΔz6 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 ΔΔΔz2 2, 2, 2, 2, 2, 2, 2
18 ΔΔΔΔz3 6, 6, 6, 6, 6, 6, 6
21 ΔΔΔΔΔz4 24, 24, 24, 24
23 ΔΔΔΔΔΔz5 120, 120, 120
24 ΔΔΔΔΔΔΔz6 720, 720, 720
Do you see it now?
2ΔΔz = ΔΔΔz2
3ΔΔΔz2 = ΔΔΔΔz3
4ΔΔΔΔz3 = ΔΔΔΔΔz4
5ΔΔΔΔΔz4 = ΔΔΔΔΔΔz5
6ΔΔΔΔΔΔz5 = ΔΔΔΔΔΔΔz6
All these equations are equivalent to the magic equation, y’ = nxn-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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I'm afraid you lost me at the rate of change of the rate of change of Z (#7)
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