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If you are really serious about this question then you would also consider what mathematicians have to say about "space". Unfortunately, this is pretty much the
by mathgenius 9y ago
If you are really serious about this question then you would also consider what mathematicians have to say about "space". Unfortunately, this is pretty much the whole of mathematics, but I think special attention should be given to the duality between geometry and algebra. This stuff goes back to Descarte. For example, you can consider the points equidistant from a specific point, which gives a circle. Or you can consider the algebraic expression X^2+Y^2=1. Both of these viewpoints are in a sense, two sides of the same coin. What is that coin? Deep answers can be found when you start doing funky things like change your definition of numbers, to say, a finite field. Even just having two numbers 0 and 1 is quite interesting to consider. What is the corresponding geometry? Or, more confusing still, let's drop the requirement that xy = yx (commutativity). Now what are the non-commutative geometries on the other side of the coin?
Considering the wide variety of these apparently fanciful ideas that have made their way into theoretical physics fills me with wonder. I wonder if the authors of the article mention any of this stuff in their book.
- westoncb 9y agoControversial, I know—but I wonder how deep that connection actually is... 'the points equidistant from a specific point' and 'X^2+Y^2=1' are both descriptions that we know how to parse and and evaluate into the same thing. Don't get me wrong, I do think it's a super interesting property of the systems of description we formulate that it's possible to talk about the same things with different abstractions (which happens a lot in math: https://en.wikipedia.org/wiki/Duality_(mathematics) https://en.wikipedia.org/wiki/Duality_(mathematics)), even with very high degrees of precision—but I have a hard time seeing how this could be a property of space rather than of human conceptual structure/language.
- posterboy 9y agoThe last bit can be said about anything. It might be relevant if the notion is intrinsically motivated by an instinctive search for closed forms. "Space" being emptiness would be isomorphic (dual) to many experiences of limits. In contrast, mystifying the unknown might inspire curiosity at best, reserving free space in the back of the mind, or philosophic arguments at infinitum at worst. The article is somewhere in the middle with its talk around gravitational waves and einsteinian curvature of space, without directly mentioning them.
- RUTHLESS_RUFUS 9y agoThe humblest of nicknames!
- kefka 9y agoI like the better question: "What is a measurement?" What does the measurement actually entail? If a computer reads the contents, does that mean the computer is entwined with it? What does our consciousness do to the measurement? What does the double-slit experiment show if only computers read its result? Does the result compare when we observe it? Crazier yet, do different human observers see the same results? Has this even been tested?
- tim333 9y agoA good talk along those lines is Feynman on algebra http://www.feynmanlectures.caltech.edu/I_22.html http://www.feynmanlectures.caltech.edu/I_22.html He starts from numbers 1,2,3 etc and gets to eiθ=cosθ+isinθ which he has as 'This, then, is the unification of algebra and geometry' I've always wondered if you could go further and deduce our spacetime in a similar manner.