Vectors from Leibniz to Einstein
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mathenchant.wordpress.com
- Related: https://mathenchant.wordpress.com/2023/06/16/what-is-a-matri...
- May I suggest adding a link to https://mathenchant.wordpress.com/feed/ somewhere more easily found than via "View Source"?
- Since you (a) mentioned a working title "... Adventures of Plus and Times" and (b) have classroom experience, do you have any opinions on the following: when overloading the "high school" arithmetic operators for ring- and lattice-like structures, is it easier for people to learn (a) overloads with traditional use (ie × ↦ meet, + ↦ xor in Electrical Engineering), (b) overloads with mnemonic stories: "product makes things larger; modulo makes things smaller", or (c) any consistent overloads, because just making the abstraction leap is much more difficult than remembering any operator assignments?
But Lee Smolin come up with an interesting interpretation:
https://www.quantamagazine.org/how-to-understand-the-univers...
I only recently learned that Einstein had three large portraits in his Berlin office: Michael Faraday, James Clerk Maxwell, and Arthur Schopenhauer. Einstein considered Schopenhauer a genius. Friends and colleagues frequently found him reading random passages of "The World as Will and Representation". He even seems to have copied Schopenhauer's hairstyle in later years. Schopenhauer was also very important to Wolfgang Pauli and Erwin Schrödinger [0].
[0] https://en.wikipedia.org/wiki/Arthur_Schopenhauer#Influence_...
In a sense, he was kind of like that poor doctor who was ridiculed by his peers for suggesting doctors need to wash their hands (and who later committed suicide because of all the bullying). Sorry, cannot recall his name at the moment.
So, it could've been admiration of determination and confidence in one's own beliefs. More so than the admiration of the beliefs themselves.
The problem was that water and soap wasn't enough. Semmelweis wanted them to wash their hands in a really nasty concoction that was bad for the skin. Lister later came up with a different nasty thing for hand washing and sterilization of equipment.
Another issue is that Semmelweis' data wasn't anywhere near as clean as later hagiographies make them out to be. They were in fact very noisy -- not because he did anything wrong but because of an epidemic that came and went.
One way is to multi-verse out of it another is to recognize the limitations of that methodology.
While in principle you get to keep your methodology in the first approach, by definition you are now also left with unobservable phenomena flirting with the platonic world.
In the same vein reflecting about the methodology also enters the realm of philosophy. But imho in a more honest way by calling out the default, construct another and get back into physics.
A lot of platonic thinking prevalent in mathematics and physics isn't overtly discussed, mostly out of convenience as one mathematician put it: in my workdays I'm a Platonist and on my weekends I can also afford to be an Intuitionist.