Posted: Feb 18, 2022 11:51 am
So, I've been thinking a lot lately about intuition and how we develop it. As a result of some recent discussions, I decided to write something about where I get my intuitions from for scientific areas I simply don't have the math for.
It's no secret that I'm pretty much a dunce when it comes to mathematics. My formal education ended at rudimentary algebra, and I never had a reason to look at algebra again until I got an office job many years later and had to use a spreadsheet, at which point I had to start again.
However, and I have a good deal of experience working in a host of live and recording situations as musician, performer or engineer, and this experience has given me a very good feel for the behaviour of waves, as well as a smattering of rudimentary information theory, and almost everything I've encountered in physics, for example, has been in some way reducible to the behaviours of waves, at least intuitionally. In fact, some of the more counter-intuitive things in QM really don't feel at all counter-intuitive to me. The uncertainty principle reflects a general uncertainty in waves; a note of extremely short duration has a lot of uncertainty in its pitch. Wave interference in the double-slit experiment is what we refer to in audio as 'comb-filtering', often seen as poor studio design or mic placement, as early reflections from a surface arrive at the mic slightly out of phase, resulting in destructive interference. Noise-cancelling headphones and the removal of expletives in recordings employ the same physics. The list goes on.
Recently, I've been working a bit on filling in some of the conceptual mathematical gaps, and it's been interesting in that it's given me a map of my intuitions and why they worked. I'm still not going to be finding any exact solutions to the Schrödinger Equation, but I can see the logic of it and how it marries with my intuitions of how waves behave.
The idea of developing better intuitions and replacing what "we" think of as common sense as something a lot more common and a fuckton more sensible is pretty much where all my thought is right now, and it's fairly well understood that we explain (and develop intuitions for) things by comparing them to things we already understand. I'd be interested to see if others could point to an instance like the above, where some comparison made something click for you.
Got any?
It's no secret that I'm pretty much a dunce when it comes to mathematics. My formal education ended at rudimentary algebra, and I never had a reason to look at algebra again until I got an office job many years later and had to use a spreadsheet, at which point I had to start again.
However, and I have a good deal of experience working in a host of live and recording situations as musician, performer or engineer, and this experience has given me a very good feel for the behaviour of waves, as well as a smattering of rudimentary information theory, and almost everything I've encountered in physics, for example, has been in some way reducible to the behaviours of waves, at least intuitionally. In fact, some of the more counter-intuitive things in QM really don't feel at all counter-intuitive to me. The uncertainty principle reflects a general uncertainty in waves; a note of extremely short duration has a lot of uncertainty in its pitch. Wave interference in the double-slit experiment is what we refer to in audio as 'comb-filtering', often seen as poor studio design or mic placement, as early reflections from a surface arrive at the mic slightly out of phase, resulting in destructive interference. Noise-cancelling headphones and the removal of expletives in recordings employ the same physics. The list goes on.
Recently, I've been working a bit on filling in some of the conceptual mathematical gaps, and it's been interesting in that it's given me a map of my intuitions and why they worked. I'm still not going to be finding any exact solutions to the Schrödinger Equation, but I can see the logic of it and how it marries with my intuitions of how waves behave.
The idea of developing better intuitions and replacing what "we" think of as common sense as something a lot more common and a fuckton more sensible is pretty much where all my thought is right now, and it's fairly well understood that we explain (and develop intuitions for) things by comparing them to things we already understand. I'd be interested to see if others could point to an instance like the above, where some comparison made something click for you.
Got any?