Which historical developments led to mankind becoming ingenious towards todays exponential growth?
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I believe what you are talking about is the rate of accumulation of knowledge, aka information. There's a relatively new branch of history called Informationalist History that studies this.
As an example, Douglas S. Robertson has classified all societies based on the amount of information, in bits, that a typical member has access to. Each is categorized based on the enabling invention that allowed humans access to that amount of information.
Where h is the amount of info one mind can hold, and is probably in the vicinity of 5Mb (5*106 bits).
- Level 0 - 107 bits (h) - Pre-Language
- Level 1 - 109 bits - Language
- Level 2 - 1011 bits - Writing
- Level 3 - 1017 bits - Printing
- Level 4 - 1025(?) bits - Computers
The exponent on that number of bits is the important thing. How far one society outclasses another can be gauged by the difference in those exponents.
In Robertson's view, this is why Native Americans, the most advanced of whom barely had writing, had no hope of competing with Europeans with printing presses, but under the right conditions could actually replace a society of Europeans with no printing press a few years earlier. Being a couple of orders of magnitude back can perhaps be dealt with. However, be several back and you'll be lucky if they bother to treat you as the same species.
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