3 ms·

We certainly need the concept of Euclidean space in order to make sense of the phrase "warped space". Fortunately, our "everyday" space is almost Euclidean, so

We certainly need the concept of Euclidean space in order to make sense of the phrase "warped space". Fortunately, our "everyday" space is almost Euclidean, so this condition is met. If we lived in a different place in Universe, not sure what our concepts could have been. But I think same applies to just any concept we derive from our observations. E.g., we would never be able to form a notion of ice if we lived near some star. But I can't see how your statement about "real" vs "apparent" follows from here.

stareatgoats 9y ago
"Real" vs "apparent" simply follows from what we can infer from the picture, i.e. the galaxies appear to be several because of the light-warping effect of gravity, in reality they are not. Further, I don't think space (or time for that matter) are comparable to the notion of ice, but let's keep it simple for now :-)
- resource0x 9y ago
  How about this: we live in a rare oasis in the Universe where the things are more or less 'stable', and due to this, we can form more or less consistent concepts (not 100% consistent, but enough for most practical purposes). Beyond this oasis - who knows, maybe the notions of space and time themselves become fuzzy (not unlike ice, by the way - though you objected to comparison). And this view is not that far-fetched - look no further than quantum mechanics, which is an example of what happens when we cross the boundaries of the 'oasis'. We still can write formulas, but we don't understand the meaning. I personally believe that just everything we "know" - applies only in the vicinity of our habitat. Won't be surprised if all our observations about the Universe turn out to be illusions resulting from infinite warping of just everything :)
  - stareatgoats 9y ago
    yes, I actually subscribe to this view too. We are observing things at the borders of the capacity of our instruments that is so far removed from our natural habitat as humans that we may never understand much more. I don't think we should give up however, and the distinction between appearances and reality is fundamental to proceeding further IMO. To clarify, it seems to me probable that real space itself (and time for that matter) is/are exempt from such localized notions. They probably 'permeate' or 'contain' everything, have always done and will always do, regardless of location and scale. It is obviously possible that they may lose relevance at a certain scale, but that scale is nowhere near our current horizon AFAICT.
    - resource0x 9y ago
      I'm not so sure about this exemption. It's just very difficult for us to reason about it. And even formulating a counter-argument in a meaningful way requires some notions we don't have. Tangentially related: http://www.paradise.caltech.edu/cook/Workshop/Physics/QMQuestion.html http://www.paradise.caltech.edu/cook/Workshop/Physics/QMQues...

stareatgoats 9y ago

"Real" vs "apparent" simply follows from what we can infer from the picture, i.e. the galaxies appear to be several because of the light-warping effect of gravity, in reality they are not. Further, I don't think space (or time for that matter) are comparable to the notion of ice, but let's keep it simple for now :-)

resource0x 9y ago
How about this: we live in a rare oasis in the Universe where the things are more or less 'stable', and due to this, we can form more or less consistent concepts (not 100% consistent, but enough for most practical purposes). Beyond this oasis - who knows, maybe the notions of space and time themselves become fuzzy (not unlike ice, by the way - though you objected to comparison). And this view is not that far-fetched - look no further than quantum mechanics, which is an example of what happens when we cross the boundaries of the 'oasis'. We still can write formulas, but we don't understand the meaning. I personally believe that just everything we "know" - applies only in the vicinity of our habitat. Won't be surprised if all our observations about the Universe turn out to be illusions resulting from infinite warping of just everything :)
- stareatgoats 9y ago
  yes, I actually subscribe to this view too. We are observing things at the borders of the capacity of our instruments that is so far removed from our natural habitat as humans that we may never understand much more. I don't think we should give up however, and the distinction between appearances and reality is fundamental to proceeding further IMO. To clarify, it seems to me probable that real space itself (and time for that matter) is/are exempt from such localized notions. They probably 'permeate' or 'contain' everything, have always done and will always do, regardless of location and scale. It is obviously possible that they may lose relevance at a certain scale, but that scale is nowhere near our current horizon AFAICT.
  - resource0x 9y ago
    I'm not so sure about this exemption. It's just very difficult for us to reason about it. And even formulating a counter-argument in a meaningful way requires some notions we don't have. Tangentially related: http://www.paradise.caltech.edu/cook/Workshop/Physics/QMQuestion.html http://www.paradise.caltech.edu/cook/Workshop/Physics/QMQues...