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Originally posted by lucifershammerAll mathematical constructs are encompassed in this Universe, aren't they? Frame of reference are created to measure SOMETHING, are they not? What something is outside of the Universe?
Frames of reference don't "exist" in the same way as objects do - they are coordinate systems for measurement; i.e. they are mathematical constructs.
Originally posted by lucifershammerThe word "unique" was used because the article was discussing the expansion of the Universe. The Universe appears to us to be expanding in all directions, so it looks like we're the center. However as the article explains, this appearance is true for every location in the Universe. The idea of a non unique center of a physical object is, of course, a contradiction in terms.
LOL!
A frame of reference is not some kind of physical object that can be "encompassed" by the Universe - it is (basically) a coordinate system that one uses for measurements.
You've still not answered why your source said "no unique center" rather than "no center" (as you're claiming). Do you really not see a difference?
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Originally posted by no1marauderNot at all. Systems of objects in curved spaces can have more than one centre. For instance, the centre of a circle is the point on the space that is equidistant from all points on the circle. In a Euclidean space, of course, this centre is unique. If you had a curved space, that needn't be so. So, if you had a Riemann space, the circle in question would have two centres - the two poles.
The word "unique" was used because the article was discussing the expansion of the Universe. The Universe appears to us to be expanding in all directions, so it looks like we're the center. However as the article explains, this appearance is true for every location in the Universe. The idea of a non unique center of a physical object is, of course, a contradiction in terms.
The reason the Universe does not have a unique centre is precisely that it is not Euclidean. If it did, then it would indeed have a preferred centre of mass (since the matter in the Universe is not infinite).
Originally posted by no1marauderMathematical constructs don't exist as, for instance, the stapler on my desk does. Some mathematical constructs (like number) may be instantiated in the physical universe, but the constructs themselves are abstract conceptions.
Name one that isn't. And after you do, it will be.
Originally posted by lucifershammerI suggest you read the article rather than giving your flawed conclusions on what the authors meant. Saying every point is the center of an object is nonsense. Saying every point can be considered the center of the universe is similarly nonsense.
Not at all. Systems of objects in curved spaces can have more than one centre. For instance, the centre of a circle is the point on the space that is equidistant from all points on the circle. In a Euclidean space, of course, this centre is unique. If you had a curved space, that needn't be so. So, if you had a Riemann space, the circle in question wo ...[text shortened]... ould indeed have a preferred centre of mass (since the matter in the Universe is not infinite).
Originally posted by lucifershammerNonetheless, they exist. What is a thought but the manifestation of the firing of synapses and neurons? What is a stapler but atoms organized in a specific matter? You need to study the Tao.
Mathematical constructs don't exist as, for instance, the stapler on my desk does. Some mathematical constructs (like number) may be instantiated in the physical universe, but the constructs themselves are abstract conceptions.
Originally posted by no1maraudermarauder: "What is a thought but the manifestation of the firing of synapses and neurons?"
Nonetheless, they exist. What is a thought but the manifestation of the firing of synapses and neurons? What is a stapler but atoms organized in a specific matter? You need to study the Tao.
That's Maraudian thought you're talking about ....... 😀
Originally posted by lucifershammerWhat you demonstrated clearly is that anything any RCC apologist writes in an attempt to smear Galileo, you'll believe. It was established in that thread that Brahe's theory was never accepted by any significant part of the scientific community (even the website established by ancestors of Brahe conceded this unfortunate, for you, fact). By the mid 1600's at the latest, polycentrism was dead among the educated though still officially a heresy in the RCC's view.
That's utter BS. I demonstrated clearly in the other thread that the scientific evidence favoured Brahe's theory over Galileo's. You're the one spewing lies now.