To not taking your precious time I will start in second.
How is it possible that sphere can be turned inside out? I realy cant grasp that. Is that some quantum/math trick?
Geometry is quite interesting when we know that Einstein believed that we can explain all trough geometry, Poincare conjecture and that often stumble upon geometry in math where we dont excepct it, like in prime numbers etc etc.
In searching for answer I stumble to even more mysterious things. Atleast 20 mysteries which even scientists have problems to explain. Because time is factor to me I just picked up few which I try to connect although they dont have nothing with above. Or they have.(?)
a) Banach Tarski paradox said that when we cut ball into finite number of pieces then reassemble it we get two balls equal size as first ball. Interestingly Paul von Nuemann also conclude on 2D analogy. (He is interesting to me because Game theory). Anyway is hard to me to grasp that. So can we conclude that surface is some quantum trampoline thing or does it replicate or perhaps infinite?
b.)Why I think is infinite? Because we have thing called Gabriel horn where we have finite volume and infinite surface object. Obviously we have objects with infinite surface.
c) There is paradox called coastline paradox where in a sense coastline is infinite.
d) Holographic paradox say that information that can be stored in volume isnt proportional to volume but to area that bounds that volume.
Obviously surface is REALY mysterious to us. Or is it just to me.
Thanks in advance.
Edited by the L, 23 June 2013 - 05:11 PM.