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I like imperialism a lot, from harder to softer sciences. It can represent a frustration that people are missing something very obvious, reflecting an underlyin
by ad8e 5y ago
I like imperialism a lot, from harder to softer sciences. It can represent a frustration that people are missing something very obvious, reflecting an underlying ignorance that is farcical or embarrassing. For example, Hardy the mathematician is best known not for his brilliant work in number theory or analysis, but for one paper in 1908 which taught biologists how to multiply numbers together. Ergo, we can presume that biologists prior to 1908 did not know how to multiply numbers, and that multiplication introduced a shining light on the field. [1]
A more concrete example is that anthropology was introduced to statistics in the 1960s. [2] Before that, many papers use storytelling as their main evidence. They reflect the thesis the author wants to present, and experiments were not available to anthropologists as a tool. This makes it hard to tell which papers should be taken seriously and which should not. You either trust the author or don't; you can't analyze his procedure. So papers cannot build on each other, and progress is halting. The quality of anthropology papers rises substantially after 1970, thanks to experimental methods. Scientific imperialism has turned modern anthropology into one of the paragons of social science, with enormously interesting results today.
Here's a fun experience in which you can discover this phenomenon for yourself. Synthetic reverbs rely on delay lines, and the question is, how to choose the delay lengths? Every reverb engineer has spent impressive amounts of time manually tuning their delay lengths in random ways, then listening to the result, then tuning some more. The task is to choose a set of N real numbers such that their lattice points (linear combinations with nonnegative integral coefficients) are maximally separated in the best sense you can. For example, if N=2, then 1 and 5/7 would be unsuitable, because 1 x 5 = 5/7 x 7 = 5, and exact overlaps are poorly separated. Irrational numbers do better, because they at least never have exact matches. Manual tuning is hard because tweaking one number to erase an overlap will introduce a different overlap.
You, the non-mathematical reader, can now solve this problem by navigating to https://en.wikipedia.org/wiki/Markov_constant https://en.wikipedia.org/wiki/Markov_constant, reading the definition of "quadratic irrationality", and picking square roots of squarefree integers as your solution. Congratulations, in 5 minutes, you solved most of a major open problem, on which reverb engineers have spent 10000 hours and made no progress. First person to write a paper gets credit. [3]
There's a general malaise in reverb engineers regarding mathematics and science. Some people already have the background information to solve the problem, as they know 1.618 is the solution for N=2 (which leads to Hurwitz's theorem, then Markov constants). But then they advocate for 1.618^x for N>=3, which means they are doing cargo cult mysticism around magical numbers, rather than actual mathematics. Note that powers of 1.618 are linear combinations of smaller powers, so their answer is the worst possible.
[1] I'm just joking. But only partially joking. Hardy-Weinberg principle.
[2] https://www.annualreviews.org/doi/abs/10.1146/annurev.an.14.100185.001031?journalCode=anthro https://www.annualreviews.org/doi/abs/10.1146/annurev.an.14....
[3] I'm joking for real this time. Writing a paper will do nothing.
- dash2 5y agoI think this will entertain you: https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/ https://fliptomato.wordpress.com/2007/03/19/medical-research...
- whatshisface 5y agoI thought reverb was mainly implemented with running windowed convolution, making delay line tuning not important.
- ad8e 5y agoConvolutional reverb has the advantage of being able to easily replicate real, recorded rooms. But all of its other properties are worse than an algorithmic reverb when both are implemented correctly.