Sometimes i do not learn math for the skill or for educate even not for a mathematics things. I just step my foot right to the class. I don't get what it mean, i don't get what it about, but i feel some sense of happy and its just pass me by.
This is when my first class of Geometry. I build my intuitive even its wrong, n i do not care bout that. First, Euclidesan geometric. I love to think it like a mapping our own style of thinking. I do not find an euclidean object on any room, but it's in my mind. When i walk in to my mind, i don't even know where to start or where its should end. Its like a swimming on God will. As euclidean want, if i put an 8, so add one on that and i got 9. I can put any one on any numbers i like. I don't know where to start n where to end. Even when you tell me a cube and it will be figured in my mind right cube. Right mean its real cube with the properties they should be. So intuitively i say that euclidean was on my mind.
When i start to belief on Euclidean, i figure out that its not real at all, since my first time heard bout Lobachevsky's works. I realize that in my visual space, everything is curved. I saw a cubical object, but it curved. I walk in an highway but its curved. When something move outward us, their spatial properties decrease in curve. As when we walk to some object, they will increase its spatial properties. Its real and the things is exist as Lobachevsky say.
I feel i'm on the end of journey, but its not true. I realize that in our perfect world, euclidean, we could predict and models what happen to the 'real'. When i think its complete on Euclid and Lobachevsky, Riemann bring other new world. As like I heard someone says, 'when you become clever enough, your limit is no more than an illusion." Yes, i think if i draw a line on a planar object, they will length in space for unlimited being. But I realize that it may exist other room, other space, other geometric being that if i drew a line, i will meet its tail exactly on the starting point. Yup, I imagine how earth can be the real models of what Riemann brings. Its like we walk to outer space, watch and learn about where we are in exist.
Its crazy even i haven't learn it all yet. Its just my imagination say that time over time. Now when i realize it, i think maybe we could say that the space, is not just an image. It will be more easy if we describe it on an object-properties-method view, or on an analysis based on Tensor. I don't know where will i stop to realize, but its a nice trip n fantasy. May be you can teach me well on what really they are, right before my imagination goes wild.
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