The world is an interesting place. Here are some things that are interesting!
If you take an audio signal and average every adjacent pair of samples, what do you get?
A low-pass filtered version of the signal! In other words, a signal with high frequencies muted.
Read more about filtering here.
Most physical phenomena can be modelled using partial differential equations. In general these are pretty nasty to solve. However, there's a way out!
An easy way to solve your differential equation is just to play an impulse into it. An impulse looks like this:
Then you take the output, and multiply it with any input you'd like and you'll get the output.
This only works for linear systems, but luckily many systems are linear (or almost-linear). For example, room reverb is approximately linear, so this allows you to measure the reverb and then apply the reverb to any sound you want!
There exists a notation for juggling!
Explain here
Matter is made up of (very) small parts. What we call an "object" is some pattern of those parts – but how do we define where the pattern ends? For all objects there is some fuzzy region where it's hard to tell what we're looking at.
Furthermore many of the categories of object that we define have fuzzy edges. For example, "horse" seems well defined – but are zebras a kind of horse? If not, what about a zebra-horse hybrid? What about ponies, are they a sub-type of horse? How different would a breed have to be in order to not be a horse any more?
The rather trivial solution to these problems is the realisation that, actually, the concept of an "object" is fundamentally a made-up, human distinction. It makes sense for our brains to abstract reality into discrete chunks to be processed separately, but this isn't actually representative of reality as a whole. The notion of an "object" or any sort of category is an artificial construct. So we shouldn't get too attached to them!
Incidentally, this solves the ship of Theseus riddle: the "ship of Theseus" doesn't actually physically exist.
These are books that I've enjoyed. They aren't necessarily very intellectually enriching.