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> My fried claimed that it's impossible to think logically (btw. etymology of word logic is "word" or "what is spoken") without verbally running the the words and sentences in your head.

In this case, would numbers represent “words” in the language of mathematics? When I was younger and sharper, I used to see products of numbers physically manifest in my mind. This is a form of logic, but it also required an “alphabet” of sorts.

As an aside, I once saw an interview with a mathematical genius of sorts who stated that he associated numbers with colors. He saw the product of two numbers as a third color. Again, logic without traditional language.




Mathematical proof did not originate with number, but geometry.




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