Comment by hshdhdhehd
3 days ago
Funny how a car manifold is also a mathematical manifold but the word seems to come from different roots.
3 days ago
Funny how a car manifold is also a mathematical manifold but the word seems to come from different roots.
I just looked it up because I was interested in their etymologies, but it seems that the words actually have the same (Old English/Germanic) root: essentially a portmanteau of "many" + "fold."
This has always caused me trouble when learning new concepts. A name for something will be given (e.g. manifold) and it sounds very much like something that I've come across before (e.g. a manifold in an engine) - and that then gets cemented in my brain as a relationship which I find extremely difficult to shake - and it makes understanding the new concept very challenging. More often than not the etymology of the term is not provided with the concept - not entirely unreasonable, but also not helpful for me personally.
It becomes a bigger problem when the etymology is actually a chain of almost arbitrary naming decisions - how far back do I go?!
On many occasions in my mathematics education I was able to figure out and use a concept based solely on its name. (e.g. Feynman path integral)
Names are important.
I thought those are ethymologically about the thin-walled containment of a volumetric interior space where said space is connected to only specific ports/holes, and is often but not necessarily mandatory intertwined with a second such containment for a second space (intake+exhaust).