What is a point? – Dialogue about Euclid’s definitions– D9

This was our first true approach to Euclid. As with everything, you must start with the beginning, and in Euclid’s Elements that is the definitions from Book I. There are 23 and for about an hour and a half we couldn’t discuss more than 7. Yes people, only seven. We spent like 45 minutes discussing the first one, what is a point? Euclid says: “A point is that which has no part”. Any guess? We had a lot of guesses but none of them persuaded everyone. It was mentally exhausting, although I must admit it was a little fun to actually think from scratch. That was because one of the “rules” is to forget everything you may think you “know” and trying to understand Euclid under his own terms. Quite a challenge, ha? You may also be questioning why are we reading Euclid when we have many modern math books that are more “updated”. Well, Euclid’s Elements are the foundations of geometry and from his work derives many of the so-called modern math. The purpose is to explore and discover the foundations that are taken for granted in the math we usually learn in school and college, and go through the process Euclid did to make the propositions of his works. It is to go through the logic process to discover nature’s properties.