On Jan 29, 2014, at 4:47 PM, Neighbor <email@example.com> wrote:
> So, the point is only something that we imagine on a line that helps us to divide the length of the line, and so as to name the extremities of line we imagine them as points
That?s much better. Keep thinking about points and what they are and what they aren?t. It takes a particular discipline of the mind to give these imagined notions their own rightful substance without embellishing them with the multitude of real and physical properties we (as physical beings) are so accustomed to. As you get better at it, you pick up common strategies. One such strategy, probably the most useful strategy, is to readily recognize that when you are facing a dilemma in mathematics, the dilemma is always your own doing, because mathematics has no dilemmas. You then think inward, reflect and refactor what you were originally thinking. That is why mathematics is so useful. It is a naturally true reference like no other that trains your mind to sort things out, even non mathematical things. But keep in mind that you live in a very non-mathematical world and most people will not understand this ability. Even supposed mathematical people. Sometimes they have the abili! ty but take for granted and are unable to explain it. And other times, while they think they have the ability, what they actually have is only an appreciation for the ability. It?s like music. You can have a conversation with someone about Chopin and then realize that you are talking about playing Chopin while the other party is only talking about Chopin. One has an appreciation for playing Chopin, to repeat the entire experience, while the other has only an appreciation for Chopin. These are very different experiences.