Map Projection. (Never knew they had such mathematical sophistication in the 16th century!)
Because the Earth is - sort of - a sphere, any attempt to project its surface onto a plane inevitably leads to distortion of some metric. Mercator projection is great for navigation because every straight line is an arc of a great circle, but it distorts the sizes of land masses as you move toward the poles. That's why there's not just one kind of projection - different maps for different apps.
One of the longstanding questions in linguistics is: why are there different grammars? For example, every possible ordering of subject, verb and object can be found in at least one language. Claims for universal grammar get pretty abstract.
Well, here's my two cents on it: because your mind is round, you can't always say what you mean.
Your neurons form a three dimensional network. Propositions/knowledge/ideas are tiny subnets of this network. Language is a great human invention, but with the significant exception of sign language, it involves a lossy projection of a three dimensional structure onto a one-dimensional medium.
And just as in the case of map projections, no matter how you do it, something is going to get distorted - some kind of information is going to be lost. This is why we have things like anaphora - for example, pronouns - that allow us to refer to the same "thing" in several different "places". In our minds, that thing is in one "place".
There's a dynamic tension in syntax between what's easy to generate and what's easy to understand. The syntax of any one language at any one time represents a dynamic equilibrium - tradeoffs in different dimensions. Syntax mutates and responds to a changing sociocultural environment because the relative perceived costs of different projective distortions change.
The same essential pattern applies to phonology - at any one time a language has a repertoire of phonemes that represent selection within two "competing" multidimensional spaces: the variety of sounds we can distinguish with our ears
(the domain of acoustic phonetics) and the variety of sounds we can make with our mouths
(the domain of articulatory phonetics). The tradeoffs are in terms of difficulty of distinguishing sounds vs. difficulty of generating them. And what determines those tradeoffs would have to be factors outside of language, as exemplified in various explanations of the the Great Vowel Shift.
When I first studied classical Greek, it amazed me that the people who spoke it apparently believed that it was so hard to pronounce a vowel followed by a 'b' sound that they had to put an 'm' between them, but the initial sequence 'pt' (as in "pterodactyl") was no trouble at all.
I'm sure this has all been said before, and I've oversimplified and overgeneralized up the wazoo, but it's a revelation to me, and I hope it will help me in my quest to ... uh ... do... whatever it is I'm trying to do....
[All illustrations are from Wikipedia]
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