In discussions about technological singularity and its connection to AI, graphs are often shown that depict an exponential growth in technological advancement. Often the y-axis is labeled "number of important inventions" or something similar. This sounds quite subjective and is certainly hard to qualify.

Is there a more objective way to quantify "how much technology and scientific insight a society has"?


The number of published paper per year is a good indicator. In the year 2006 around 1 million academic papers were published, in the year 2017 around 2 million per year. The cumulative sum is estimated with around 60 million papers right now. The papers can be divided into subjects like math and physics so it is possible to tell exactly how much knowledge a society has about a topic.

To draw a connection to AI it is possible to filter out only papers which are about Artificial intelligence. That means, only knowledge which is stored in a PDF file can be seen as real knowledge. For example, about the topic AGI, all the scientists have published in the year 2018 around 257 papers, according to Google Scholar. They know only what it is written in these documents. That means, if you meet one of the scholars in real life, he can only answer questions about his published paper, not more. The progress is not exponential like in the Moore's law. Every year the increase in the output is around 30%.

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  • $\begingroup$ Very interesting. We can probably trace this back in time from the Foundation of the Royal society back to Euclid and Pythagoras! $\endgroup$ – DukeZhou May 7 '18 at 18:58

Moore's Law is the most famous example, breaking it down from the standpoint of computing power.

Here, specifically, Moore's is talking about one of the "bounds of rationality" in regard to problems solving / solution checking.

"His reasoning was a log-linear relationship between device complexity (higher circuit density at reduced cost) and time"

This is just a quickie answer, but a highly salient subject, worth exploring more fully!

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  • $\begingroup$ Great answer! But how would this work for times before computers? It might be out of the scope of ai.se, but this method doesn't quantify progress before CPUs etc were invented, e.g. in the Enlightenment period or earlier $\endgroup$ – ahemmetter May 5 '18 at 19:29
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    $\begingroup$ perhaps computational power? from pen-paper calculations to abacus to something Babbage invented $\endgroup$ – k.c. sayz 'k.c sayz' May 5 '18 at 20:37
  • $\begingroup$ @ahemmetter I don't think pre-integrated circuit era is out of scope at all --I've mentioned water clocks in numerous answers to other questions. Minimax pre-dates modern computing by a couple of decades. $\endgroup$ – DukeZhou May 7 '18 at 18:57

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