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I dunno if reality is based on perception. Commonly held beliefs are. The earth being flat was the commonly held belief, but now we think we know better.
We, of course, define what flat is, and since that isn't necessarily the reality, maybe the earth is flat, just not abiding by our definition.
I don't think absolute truth is attainable, because we are not all-knowing. No all-knowing being would limit his knowledge on a subject, because he'd know that that probably isn't a goood thing for society. If we were, we'd know everything already. I firmly believe there are limits to our knowledge. If you believe in strictly science, and calculate how fast nerve responses travel, etc, it would be mathematically impossible to know everything.
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And here I thought we define things by what they do, their purpose etc.
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We define them by what we observe them to do or what we observe their purpose to be.
I have a friend that says anything's possible within the realm of possiblity but that we shouldn't entertain most of those because they aren't very probable, and that's true, but that's part of the reason I think absolute truth isn't attainable.
For example, I don't think the Earth is flat because of all the observations we can make. But maybe it's a great illusion. Should I seriously entertain that notion? No. But who knows...
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A spere is a manifold which by definition means yes, it is locally flat. That's why people thought the earth was planar for so long, it's euclidean in very small neighborhoods of any point. The same thing would happen if the earth were any shape deformable into a spere (and of course, smooth).
In a way the same thing would happen if the earth was shaped like a torus, though we would be aware of the "hole".
Really thats all you can tell about manifolds if your stuck on one, how many holes it has.
Fundamental groups.
MMMMMM..... Algebraic Topology.
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You're crazier than me ;p
No, it's cool to see someone else in mathematics.
