How much faster is the theoretical rate of progress than the historical rate of progress?
score:2
Honestly, I'm not sure there are a lot of "innovations" that could have become popularized significantly before they did (that might be a decent question if it could be phrased properly).
One thing I've talked about here before is the Informationalist view of History. Since what you're talking about here is the acquisition and spread of knowledge, I think this is one case where it can be applied. Knowledge of course is a self-feeding cycle. The more you know, the more you can know. Given that's an exponential function, what needs to be analyzed here more than anything is the level of knowledge a society currently has, and in particular its means of distributing knowledge to people.*
For example, Europeans had actually set foot on North America and made some attempts to settle it long before Columbus. However, their settlements died out before the Printing Press was invented, which means that knowledge was much more difficult and expensive to distribute back then, so consequently orders of magnitude less people knew about it. Norse sailors knew about it. The Pope knew about it in as much as he'd need to occasionally send their parish new priests. However, almost nobody else heard about it until modern times. On the other hand, Columbus didn't even think he'd found anywhere new. However, his discoveries happened 50 years after the printing press, so all the educated of Europe ended up reading about it.
Likewise there had been several successfully suppressed popular reformist movements within the Catholic church prior to the invention of the Printing Press. However, Martin Luther posted a list of academic debate points, someone thought it might be worth printing them up with their newfangled German printing presses, and he backed into the protestant reformation. Threatening ideas that used to be suppressible by Church authorities no longer were in the new environment.
The first chapter of Douglass S. Robertson's The New Renaissance, makes a really good case for organizing human societies (or perhaps historical "Ages") by the amount of information available to any one person in them. I'll copy the basic gist here from a previous answer:
Where h is the amount of info one mind can hold, and is probably in the vicinity of 5Mb (5*106 bits), a society's information level is:
- 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. Knowledge is a self-feeding cycle, so this will of course show up in all kinds of little ways that we might collectively call "technology" or "rate of progress".
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. Think of it as like a fighter's weight class. A really good fighter can perhaps fight up a couple of weight classes, but too far over and its really not going to be possible for them to compete.
So as far as where we are now, that would be Robertson's Level 4. We probably haven't hit the limits on the amount of accessible bits to one person there yet, but when we do he was thinking the limit is probably going to be the limit on our ability to filter it all down to anything useful.
* - Mathematically, as numbers get larger, if one factor is exponential, all other factors fall away in importance, and can thus be ignored for the purposes of analysis.
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Source: stackoverflow.com
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