And if intelligence is not the bottleneck... well... is superintelligence actually worth as much as we think it is? Is human intellect the apex of what biological systems can do, or is it merely the point past which intelligence stops being the bottleneck and the returns of higher intelligence drop off dramatically?
This is what motivated me to come up with a new definition of real numbers, namely, they are objects (I call them oracles) that answer Yes or No when asked if the number ought to be between two given rational numbers. Abstracting out what properties such an object should have, one can come up with a space of these oracles, define an arithmetic, and prove that they satisfy the axioms of real numbers.
For details: https://github.com/jostylr/Reals-as-Oracles/
In many ways, this is giving a definitional support to the use of interval analysis which is, of course, a very practical concern. It also brings our some cool stuff about mediants and continued fractions (nothing new about that, but nicely motivated).
It also fits in with the adjacent post about busy beaver numbers and its conclusion about knowing a number is in an interval.
Do you mean physically? Basic shapes like circles, squares and triangles allow us to hold irrational numbers in our hands as distances. Children playing with blocks can sense that root 2 does not conform nicely with other (rational) distances.
ones = number % 10
tens = number // 10
do_print = (ones + tens) == 10Not true! Economists have devoted person-millenia developing the theory of instrumental variables, which lets you extract causal relationships from historical non-experimental data.
That said, it's damn hard to find a good instrument. Many economists use it badly, and most doctors don't even know the theory.
I've seen much recent discussion on HN about robocalls not being resolved by the new STIR/SHAKEN protocol arising from the TRACED Act. I found this on https://regulations.gov and thought it would be of interest.
The big US providers have implemented the STIR/SHAKEN caller ID authentication framework as of mid-2021 but there was a 2-year extension to mid-2023 for small providers. The implementation appears to have been ineffective at stopping robocalls because of origination via the exempt small providers. The FCC has now passed a rule that a subset of small providers (those most likely to be originating illegal robocalls) must be in compliance by mid-2022.
TLDR - if this works there should finally be a dropoff in robocalls this summer.