Exponential laws in technology development?

November 14, 2016 2:19 PM

I recently learned about Haitz's law, the LED equivalent of Moore's law. Is there a good discussion somewhere of exponential laws in technology development? Do they apply broadly across modern (semiconductor) technology development? Is there an equivalent for digital camera sensors?
posted by pombe to Technology (4 answers total)

Best answer: Image sensors seem to follow the more common overlapping s-curve model of development if you go by the diagram in this article. Overlapping s-curves have been a part of the study of innovation for a long time. But I don't think they have a name or a law other than being called "overlapping s-curves"
posted by GuyZero at 2:38 PM on November 14, 2016

The "overlapping s-curve" is also called "sigmoid curve" or "sigmoid function", with one particular case being the "logistic function". The derivatives of these functions look like bell curves or the proposed "oil extracted per year" curve of peak oil.
posted by the antecedent of that pronoun at 5:15 PM on November 14, 2016 [1 favorite]

Best answer: I think that improvement of CPUs and LEDs will both also turn out to be sigmoid curves in retrospect. Misapplying the assumption that because a few points lie near a line on a log plot gets you results like "Researchers use Moore's Law to calculate that life began before Earth existed" which incidentally links to another supposed exponential law, "Koomey's Law", which I'd not heard of before now. This one pertains to power efficiency of integrated circuits.

I'm sad this 2007 article's screenshots of Alexa have gone missing, though the implied prediction of Facebook's near extinction by 2009 has not come to pass, alas. (This 2016 paper which discusses several exponential "laws" of technological progress also has graphs of Facebook and Twitter actual usage together with very plausible looking sigmoid curves fitted to them)

It's much easier to grasp why the adoption of a new technology would follow a sigmoid curve, because even when the technology is not displaced (like CD players, cough), it still reaches a saturation point where there are no new people to adopt the technology. It's harder to see why, particularly as an outsider to a technical field, there is some exhaustible supply of new advances within the technology that mean exponential increases in efficiency can't continue forever.

The "easy" examples come from basic thermodynamics. For instance, the thermodynamic efficiency of solar cells can never exceed a particular magic number, around 86%. And there's some limit to the amount of the earth's surface we can ever cover with them. But even so, the growth of solar power looks exponential right now. (the efficiency-over-time curves of PV panels in various technologies look decidedly non-exponential)
posted by the antecedent of that pronoun at 5:45 PM on November 14, 2016

When I give talks about technology and its development and near-future outcomes, I usually pair Moore's law with Koomey's Law. Koomey's says, basically, that for a given amount of processing, the power needed to complete it will halve every 18 months. So while batteries have to obey chemistry and physics, chips can successfully use their power more efficiently over time.
posted by griffey at 6:47 PM on November 14, 2016