I had a conversation with someone today who said he’s relearning logic from a categorical perspective. What struck me about this was not the specifics but the pattern:
Relearning _______ from a _______ perspective.
Not relearning something forgotten, but going back over something you already know well, but from a different starting point, a different approach, etc.
Have any experiences along these lines you’d like to share in the comments? Anything you have relearned, attempted to relearn, or would like to relearn from a new angle?
In my sophomore year, I learned numerical analysis purely from a implementational perspective. I learnt a little bit about error analysis and convergence but the focus was mostly on writing program that can solve problems. Later, in graduate school, I learned about the analysis part of the method. It was fun to finally understand why a method will fail to perform due to the nature of the problem and implementation of the algorithm. Also those graduate classes taught me how to leverage existing ideas to create new methods with improved convergence properties.
Lot of people out there need to relearn statistics from a Bayesian perspective! (the unkind version would omit the “re”).
relearning time series analysis from a frequency approach (my “mother tongue” is time domain)
Is there somebody who is truly bilingual?
Programming from a functional perspective! (I went BASIC -> C -> Perl -> C++ without touching LISP, so Haskell readjusted my brain.)
Relearning Fourier analysis from functional analysis perspective. Sines and cosines are “just” a very useful choice of basis.
Relearning inner product from differential geometry perspective. Change of coordinates just changes the representation of your inner product of choice, and to reach a truly different inner product, you must embed your space to a higher dimensional space.
I relearned (or at least enjoyed) linear algebra from a matrix perspective from Gilbert Strang’s excellent online lectures, as opposed to the abstract/axiomatic perspective we had in my college course.