Technology compounding

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
1	Way I did this:
2	1. Create a set of technologies, and base "progress level" which you can think of as a growth trajectory
3	2. Growth in each tech increases as a function of previous period + RAND()*RANDBETWEEN(0,1) - to introduce some random punctuated growth
4	3. If cumulative growth in all technologies raises the average to be > average of the period where everything started, a new technology automagically emerges!
5
6
7		Progress level	0.20	0.51	0.81	1.01	1.02	1.23	1.43	1.39	1.58	1.67	1.79	2.02	2.02	2.17	2.27	2.36	2.27	2.49	2.55	2.76	2.89	2.86	3.06	3.29
8	Period/ Technologies	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
9	1	0.50	0.50	0.50	1.33	1.87	1.87	2.20	2.64	3.39	3.81	4.16	4.16	4.16	4.24	4.24	4.24	4.70	4.70	4.70	5.12	5.12	5.28	5.89	6.41	7.28
10	2	0.50	0.93	1.63	2.58	2.58	2.58	2.58	2.72	2.72	2.98	3.70	4.17	4.17	4.17	4.28	4.28	4.31	4.31	4.31	4.31	4.90	4.90	4.90	4.90	4.90
11	3	0.50	0.50	1.27	1.27	1.27	1.27	1.27	1.88	1.88	1.88	1.88	1.88	1.88	2.87	3.49	4.13	4.13	4.48	5.02	5.72	5.72	5.72	5.72	5.96	5.96
12	4	0.50	1.06	1.66	1.66	1.66	1.66	1.73	1.73	2.13	2.81	3.58	3.58	3.58	4.57	4.57	4.57	4.57	5.21	5.45	6.44	6.44	6.50	7.29	7.29	7.29
13	5	0.50	0.52	0.52	0.52	0.57	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.82	1.40	1.40
14	6			0.50	0.50	1.13	1.13	1.96	1.96	1.96	1.96	1.96	1.96	2.96	2.96	2.96	3.25	3.55	3.55	3.55	3.55	3.90	4.21	4.21	4.21	4.73
15	7									0.50	0.50	0.95	1.47	2.01	2.01	2.01	2.01	2.01	2.01	2.59	2.59	3.53	3.99	4.37	4.73	5.54
16	8											0.50	0.50	0.75	0.75	1.31	1.31	1.31	1.46	2.05	2.12	2.58	2.58	2.58	2.58	2.58
17	9														0.50	0.50	0.50	0.50	0.85	0.85	0.85	0.85	0.85	0.94	0.94	0.94
18	10																		0.50	0.72	1.69	1.69	2.16	2.16	2.16	2.43
19	11																				0.50	0.50	0.50	0.91	0.91	0.91
20	12																							0.50	1.16	1.46
21
22	Therefore:
23	1. Assess average technological progress in each age - by definition indexed to 1st period
24	2. Growth rate according to this model declines over time - mostly because I've made the growth rate in tech linear. This isn't a philosophical point, I just didn't care to play formulae with google sheets that much.
25
26	Period/ Technologies	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
27	Average	0.50	0.70	1.01	1.31	1.51	1.52	1.73	1.93	1.89	2.08	2.17	2.29	2.52	2.52	2.67	2.77	2.86	2.77	2.99	3.05	3.26	3.39	3.36	3.56	3.79
28	Growth		40.53%	44.13%	29.38%	15.55%	0.66%	13.44%	11.41%	-2.00%	10.31%	4.24%	5.72%	9.74%	0.19%	5.68%	3.83%	3.17%	-3.02%	7.90%	1.98%	6.96%	4.13%	-1.07%	5.87%	6.49%
29
30
31	Number of technologies	5	6	6	6	6	6	6	6	7	7	8	8	8	9	9	9	9	10	10	11	11	11	12	12	12
32	Factorials	120	720	720	720	720	720	720	720	5040	5040	40320	40320	40320	362880	362880	362880	362880	3628800	3628800	39916800	39916800	39916800	479001600	479001600	479001600
33	Combination of 2	10	15	15	15	15	15	15	15	21	21	28	28	28	36	36	36	36	45	45	55	55	55	66	66	66
34	Combination of 3	10	20	20	20	20	20	20	20	35	35	56	56	56	84	84	84	84	120	120	165	165	165	220	220	220
35
36
37	Takeaways: how we reached Childhood's End
38	- If a new technology emerges when one reaches saturation, or the combined technological might of the rest reaches a certain threshold, there will be new emergences of technology
39	- Without enough ability to recombine though, the combinations to explore to find the new technology and its applications shoot past us
40	- Recombinations require someone to get on top of [X] number of fields, where [X] can vary according to the current state of technology
41	- This makes no mention of recombinations - where we effectively 'retire' older technologies when some others make enough progress that they're subsumed into others - e.g., natural philosophy
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100