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Comment: Re:How to discover aliens in one almost easy step (Score 1) 343 343

Good point, but sadly faster than light communication allows messages to be sent back in time (due to special relativity). So once we invent FTL communication were going to be more worried about some severe problems with causality than about aliens many light years away.

Comment: Re:Summary of the Poincare conjecture is inaccurat (Score 1) 117 117

Excuse me for replying to my own post. I should also mention that Poincaré's conjecture was not about 'a method for determining whether a three-dimensional manifold is a spherical'. It is simply the question of whether there are non-spheres in 3d which have all loops contractible (for a more accurate description, see the parent). The question about methods/algorithms for determining whether or not something is a 3-sphere is in itself very interesting though.

Comment: Summary of the Poincare conjecture is inaccurate (Score 2, Informative) 117 117

As someone who's job involves research into geometry and topology, I would like to point out that the summary is wrong in a couple of places. The Poincare conjecture states (in simple terms) that:

Any closed smooth three dimensional space ('manifold') without boundary where all loops can be contracted to a point is 'homeomorphic' (essentially the same as) the three dimensional sphere (that is, the unit sphere in 4 dimensions).

The words "homologous" and "boundless" have little/nothing to do with it.

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