If there's one thing I leaned doing a Ph.D. is if you dig deep enough, you find many foundational laws of nature rely on some necessary assumption that, if proven incorrect, would topple the whole thing
If there's one thing I leaned doing a Ph.D. is if you dig deep enough, you find many foundational laws of nature rely on some necessary assumption that, if proven incorrect, would topple the whole thing
Dennard scaling though did end in the mid 00s and this impacted Koomey’s law which talks about performance/watt and saw a similar petering out.
Apparently the bound at even a conservative rate puts the thermodynamic doubling limit at 2080. After that we’ll have to really hope smart people have figured out how to make reversible computing a thing.
This was a bit of a bummer for programmers working in single threaded languages who found that their code stopped getting faster for free.
https://ourworldindata.org/grapher/transistors-per-microproc...
variance/standard deviation (also btw, a sum of squares concept)
it marks the inflection points on the gaussian curves, but so what, the 2nd derivative points to something significant about the integral? not really. But even if we accept that it does, what does two standard deviations mean? a linear double on the x coordinates says what about the a hairy population density function? nothing.
or similar to Metcalfe's Law, the very widely used Herfindahl Index (also squares!). It's a cross between a hash and a compression, it says something about the original numbers, but wildly different scenarios can collide.
This "law" isn't somehow less true just because it was originally used as a sales tactic.
https://www-users.cse.umn.edu/~odlyzko/doc/metcalfe.pdf offers this and several other lines of evidence that the law is wrong, and O(n log(n)) is a more accurate scaling law.