18 Jul '18 04:25>2 edits
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The post that was quoted here has been removedAnd in our universe, if standard cosmology holds up, we can only theoretically make a physical circle the size of our universe and no bigger which would say there would be no such thing in our universe as an infinite sized circle since our universe is thought to be something like 50 billion light years across and so about 160 billion light years 'around' if you can even say that. So any infinite circle would forever only exist on paper.
Originally posted by @sonhouseOur universe is but one bubble, in a bathtub filled with bubbles.
And in our universe, if standard cosmology holds up, we can only theoretically make a physical circle the size of our universe and no bigger which would say there would be no such thing in our universe as an infinite sized circle since our universe is thought to be something like 50 billion light years across and so about 160 billion light years 'around' if you can even say that. So any infinite circle would forever only exist on paper.
Originally posted by @wolfe63In another thread vivify (I think) made a statement along the lines that science is not a matter of opinion. I disagreed and claimed that his statement may be true in mathematics, where one can make conclusions from axioms, but not in science where interpretation of experimental results, and for that matter the reality of the ontology of theories, is a matter of opinion. Duchess pointed out that the veracity of the continuum hypothesis is undecidable based on the standard axioms in set theory, in other words, even in mathematics there are statements that are a matter of opinion. I was aware of the problem with my post when I was making it, being aware of Godel's incompleteness theorem, but wanted to keep it simple, and didn't bother replying because her interjection only served to strengthen my basic point. To cut to the chase, that the continuum hypothesis can neither be proven or disproven from ZFC set theory is a somewhat obscure fact which a complete fraud is relatively unlikely to be aware of. Her proofs in the two threads under discussion (root two and Maths Olympiad) are standard, but it is possible to reinvent the wheel. The problem is that it is difficult to be completely original on these forums as we'd be getting into Millennium Prize territory - care to work out a set of axioms for Quantum Field Theory and show that Yang-Mills theories exist?
Joe Shmo makes a valid observation.
Show your work Duchess64.
Originally posted by @deepthoughtI don't buy it. I know nothing of the continuum hypothesis, yet If I were reading your post about it and you mentioned it by name as simple google search of "continuum hyptho..." and google literally suggest "continuum hypothesis undecidable". from which I can skim through the text and pull the statement from Wolfram
In another thread vivify (I think) made a statement along the lines that science is not a matter of opinion. I disagreed and claimed that his statement may be true in mathematics, where one can make conclusions from axioms, but not in science where interpretation of experimental results, and for that matter the reality of the ontology of theories, is a ...[text shortened]... re to work out a set of axioms for Quantum Field Theory and show that Yang-Mills theories exist?