|View single post by kurtwaters|
|Posted: Mon Apr 15th, 2013 03:31 am||
On a side note - let's have a test of imagination. Try and make a verbal description of how would you imagine a place with fractional value of number of dimensions. Let's say, instead of mainstream 3 dimensions let it be 3.14 dimensions.
My first thought was do you mean the three familiar dimensions plus another .14 dimension or a small bit added to the 3 familiar dimensions. I chose the latter.
If I may, can I suggest a couple of known conceptions that may add some more perspective to this task of imagining you decided to undertake? Feel free not to read them if you want to do this completely on your own. I'll make the text white so you won't accidentally read it if you don't want to. You're probably familiar with 4-dimensional imaginary hypercube (aka tesseract). It's kind of a common conception, there are even videos of 2D and 3D 'shadows' of tesseract as a computer model. I think observing the way it behaves both mathematically and in terms of theoretical physics can be a decent starting point for this imagination challenge. Another good conception is geometry. Most common Euclid's geometry bases on the fact that sum on triangle angles is always 180 degrees. But there are approaches that challenge this premise. Riemann and Lobachevsky went opposite ways on this and ended up having planes looking like sphere and distinct saddle-like form respectively. I get the impression that you think that you can imagine 3.14 dimensions more accurately than you already did. Thus I'm not going to give my take on it yet to not influence your effort. Please tell me if(when) you'd like me to do it.
I came upon your puzzle late at night, wrote my initial reaction in this e-mail and then went to bed. As I lie awake waiting for sleep to come I began to realize problems. How does one actually define a dimension? A line can only be 2, right? A point always 0, no? Then I fell asleep.