
Thinking Straight about Curved Space - raldu
https://philosophynow.org/issues/108/Thinking_Straight_About_Curved_Space
======
AnimalMuppet
So a philosopher is going to tell the physicists that the way they're thinking
and talking about space is wrong. Priceless.

------
Retric
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.

Gravitational lensing
[https://en.wikipedia.org/wiki/Gravitational_lens](https://en.wikipedia.org/wiki/Gravitational_lens)
demonstrates that same idea of multiple paths to the same point.

[https://upload.wikimedia.org/wikipedia/commons/b/b9/HST-
Smil...](https://upload.wikimedia.org/wikipedia/commons/b/b9/HST-Smiling-
GalaxyClusterSDSS-J1038%2B4849-20150210.jpg)

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Strilanc
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].)

1:
[http://lesswrong.com/lw/or/joy_in_the_merely_real/](http://lesswrong.com/lw/or/joy_in_the_merely_real/)

2:
[https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...](https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences)

3:
[https://en.wikipedia.org/wiki/Taxicab_geometry](https://en.wikipedia.org/wiki/Taxicab_geometry)

4: [https://www.physicsforums.com/threads/what-is-the-pfs-
policy...](https://www.physicsforums.com/threads/what-is-the-pfs-policy-on-
lorentz-ether-theory-and-block-universe.772224/)

------
scrumper
What a steaming pile of unmitigated bullshit.

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.

The picture is just wonderful, however.

~~~
AnimalMuppet
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.

~~~
scrumper
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.)

------
gohrt
Flagged.

Author is a medical doctor who has written several non-academic books on
philosophy. His metaphysics has never been peer-reviewed.

~~~
scrumper
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.

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elektromekatron
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.

~~~
gohrt
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.

