What is the shape of the universe? @Philosophy
|dw:1321529745807:dw|
universe is flat
Roughly, we believe the universe looks like a three-dimensional sphere. A 1-d sphere is a circle, \( \{ (x,y) \ | x^2 + y^2 = a^2 \} \). We normally think of this as embedded in 2-dimsional space, like the Cartesian plane. But you can also think of it as a geometric object in itself not sitting in any bigger space. A 2-d sphere is what we think of as a sphere normally, the shape of a globe, \( \{ (x,y,z) \ | x^2 + y^2 + z^2 = a^2 \} \). Again, this equation thinks of a globe as sitting in our normal conception of 3-d space, which we also think of as flat. But you can also think of the 2-d sphere as a geometric object by itself. A 3-d sphere is the next version of this. If you'd like to read about this further, there is a short, elementary book with lots of fun diagrams that you might find helpful: http://www.amazon.com/Geometry-Relativity-Fourth-Dimension-Rudolf/dp/0486234002/ref=sr_1_fkmr0_1?ie=UTF8&qid=1321533353&sr=8-1-fkmr0
UNIVERSE HAS 11 DIMENSIONS
In a string-theoretic construction, there is a model of the universe with 11-dimensionals. But one is time and 7 are tightly wound dimensions that are never visible to the naked eye. If your question is what is the overall shape of the universe, the three-sphere answer I gave still stands. If you're interested in the string theory model, a very accessible book is http://www.amazon.com/Elegant-Universe-Superstrings-Dimensions-Ultimate/dp/0375708111/ref=sr_1_1?ie=UTF8&qid=1321539531&sr=8-1 (You'll notice the title of this book refers explicitly to the idea of 'hidden dimensions'!)
thanks alot james for these references, i will check them out as sooon as my life permits me to do so. btw ppl say that in the fourth dimension it is possible to view the sphere from all the direction at the same time, isnt it @m@z1ng
i think the universe reforms to fit all of the beings and ideas inside of it. just my thoughts, no science involved.
Join our real-time social learning platform and learn together with your friends!