if you took an engineering course that covered fourier transform, z transform, or laplace transform, then you have seen an introduction to harmonic analysis on the circle and the real number line.
typically when I see mentions of harmonic analysis together with differential geometry I start thinking of fourier transform on more fancy shapes (on the sphere, for example, the replacements for complex exponentials are called spherical harmonics)
my PhD was EE in signal processing and I took some extra math classes at the graduate level, and continue to read some of this for fun and profit.
I still cant understand most of the terminology in the fields medal citations. that probably requires a more thorough couple of years of graduate education in mathematics.
math is by far the furthest of the sciences in terms of depth of human discovery.
rank correlation between GDP and life expectancy (child mortality would have been maybe a bit better). uses a 20 year window in both directions per year. bootstraps for 5% and 95% quantiles of the rank correlation.
there looks to be a max around 1992, and steady downhill in correlation since then.
this seems unlikely to be an artifact of the analysis, though 1992 is eerily close to 20 years from the last date. 2013 is the last year where we have at least 15 years total symmetriclaly around the given year to include in the correlation for that year.
Yes, but it can be more of a pain keeping track of pairs. In production though, this is what's done. And given a fault, the debug binary can be found in a database and used to gdb the issue given the core. You do have to limit certain online optimizations in order to have useful tracebacks.
This also requires careful tracking of prod builds and their symbol files... A kind of symbol db.
I thought that what constitutes a measurement is well understood; it's just the entanglement between the experiment and the observer, and the process is called decoherence - and the collapse itself is a probabilistic process as a result.
AFAIK an EoT is not required to design experiments to determine if it's a real physical phenomenon vs. a mathematical trick; people are trying to think up those experiments now (at least for hidden variable models of QM).