What separates curved space from Euclidean space is not an abstract 'curved path' representation it's the fact there are several different directions you can travel that take you from A->B. Picture someone standing on the North Pole, if they walk a strait line then any direction leads to the South Pole. As to curved space, there are multiple orbits that all lead back to your starting point but that's not really what people think of as curved space.
This author has serious cases of both my-intuitions-trump-your-predictive-models and lack-of-joy-in-the-merely-real.
> The most obvious assault on space is analogous to that which time has had to suffer: reduction to a pure quantity. Space is translated into points, lines, surfaces, and volumes; to dimensions or quantitative parameters x y, z. Places – habitats – are stripped down to decimal places. Much is lost in consequence.
It's really ironic when people use written examples to complain about symbolic representations being inadequate.
My viewpoint is directly opposite to the author's here; their modus tollens is my modus ponens. Because points and lines and formulas can be used to predict things in the real world, they are clearly not lacking-of-the-original-essence w.r.t. what they represent. Math is not a muted version of reality lacking the core substance, it is unreasonably effective [2].
> The putative curvature of non-Euclidean space is intrinsic: it is present at every level above that of an infinitesimally small spatial point. So resistance to the idea of curved space does not arise from a superficial misunderstanding that can be cured with the help of a simple analogy. Rather, it is resistance to the odd idea that emptiness can have any topology, curved or straight.
The author seems to be assuming that the lack of any topology is equivalent to flat space, i.e. Euclidean topology. Why would that be the case? They have no actual grounds for expecting space to "default to" the L2-norm. Why wouldn't it default to the much simpler L1-norm (i.e. taxicab geometry [3]), or just a disconnected set of points with no distance relationship between them at all?
> The unintelligible idea of ‘curved space’ is the product of misidentifying a system of representation with that which is represented. This habit has a long history. [...] However, the immense power of mathematical physics – which requires abstracting from phenomenal reality and the reduction of experienced and experienceable reality to mere parameters to which numerical values are assigned – does not justify uncritically accepting concepts such as ‘curved space’ that attempt to re-insert phenomenal appearances into its abstractions.
Curved space is a concept so well defined that you can explain it to a computer. It is the opposite of unintelligible.
The reason we think it's a good model of actual reality, thus justifying the statement "space is curved", is that it makes new, different, and confirmed predictions. If you think it's so easy to come up with an interpretation of general relativity that doesn't involve mixing space and time, why don't you learn it and try to do that? (Fun fact: it's easy to do in special relativity; just pick a preferred rest frame [4].)
Prof. Tallis has constructed a critique of something he clearly isn't willing to understand: his example of a straight line connecting two points on the earth's surface through means of a tunnel is simply the invention of an extra dimension, a simple concept that even a superficially educated but curious layperson (like me) would recognize.
He creates a bizarre straw man equivalency between 'social space' and curved mathematical space based apparently solely on the fact that they're both labeled by the same word, then kind of axiomatically assigns legitimacy to the former over the latter without any explanation. The whole thing is bizarre in the extreme.
I think Tallis is thinking at the level of the words and the analogies. But the thing is, what the physicists really believe are the equations. (Hat tip to C. S. Lewis, from whom I stole that observation.) Tallis is expecting the physicists to talk in the same way (using the same tools of communication) that philosophers do, and they don't, so Tallis misses the point.
Oh I agree. And if you're right, it's a pretty thumping indictment of Prof. Tallis, don't you think? On what basis does he form that expectation? If a man is so conscious of language and meaning that he feels confident dissecting a long-established tool of physics on the grounds of semantics, and he simultaneously ignores the existence of jargon, culture, and context in another field, then I think it's hard to take him seriously at all.
(Sorry if that sentence was hard to parse; this horrid article infected me.)
That may be a bit strong. There are interesting fundamental links in some of the replies here. He is wrong, but it's educational to understand exactly how he is wrong.
I find this funny, because from thinking about the idea of empty space having topology, I went down a path of thinking that given light curves only slightly in the gravitational fields, density variations and scales that we happen to inhabit, and also that we use it as our major sense, reality just happens to look reasonably Euclidean most of the time.
However there are still a few acres missing due to gravity from the earth's surface, and other measurable discrepancies around, so while generally we can observe triangles behaving nicely and stuff, the strength of the concepts of space behaving nicely and straight lines existing is partly an accident of location and biology.
Forget about empty space and light, by far the most significant curvature in human experience is the curavature of the Earth's surface You only need to travel by boat or air (and maybe automobile), or set up some mirrors to bounce light around the Earth (for example: radio), to gain an appreciation of that curvature. But travelling on foot, the curvature is not really noticeable.
