1. In 1202 Fibonacci introduced zero to Europe. Zero was eventually understood to be a number. The resulting change in mathematics was evident by around 1350 when the harmonic series 1+1/2+1/3+… was found to be divergent.
2. The paradoxes of naive set theory around 1900 led to the development of Category Theory, which solved cardinality paradoxes by ignoring them. Category Theory is proving useful in AI development.
There are many more examples that this comment box is too small to contain.
I sent along this piece to my dear friend Fotini, who’s an accomplished quantum physicist (https://en.wikipedia.org/wiki/Fotini_Markopoulou-Kalamara). She wrote a great response but is not on Substack. She’s given me permission to share it with you directly. Is there a way to easily do this?
Two historical events to support your argument:
1. In 1202 Fibonacci introduced zero to Europe. Zero was eventually understood to be a number. The resulting change in mathematics was evident by around 1350 when the harmonic series 1+1/2+1/3+… was found to be divergent.
2. The paradoxes of naive set theory around 1900 led to the development of Category Theory, which solved cardinality paradoxes by ignoring them. Category Theory is proving useful in AI development.
There are many more examples that this comment box is too small to contain.
Math is the counting of beans. It is expression not equation that answers. Unlike the Mathematikoi.
Hello Alex,
I sent along this piece to my dear friend Fotini, who’s an accomplished quantum physicist (https://en.wikipedia.org/wiki/Fotini_Markopoulou-Kalamara). She wrote a great response but is not on Substack. She’s given me permission to share it with you directly. Is there a way to easily do this?
Alternatively it would be cool if you posted it here in comments if you like.
Perhaps she'll warm up to comments. For now, I'll send it across.
Absolutely!
Did you have ChatGPT help with some of this?
I had it generate the 3 mathematical examples and 3 mathematical techniques of compactment. For your reference, see my at-length breakdown "the sublation of mathematics", none of which touched any llm. https://docs.google.com/document/d/1arlyF6zIH2f5hlLcFoyBFNcsQqlEfxZvkZOoIDTtTeY/edit?usp=drivesdk
Sorry this one https://docs.google.com/document/d/1UU5lcrfTEoQcXrfPhJX-0XEmrcsCy_Bg-yZHXXQqFkU/edit?usp=drivesdk