Thinking Straight About Curved Space

[Philosophy Now]

Raymond Tallis rules out a distorting physics metaphor.

https://philosophynow.org/issues/108/Th ... rved_Space

[HexHammer]

The standard of articles on this site are always tragically low, but this is unusually low, this is pure mad ramblings!

Please delete it, to avoid embarrassing yourself further.

[RickLewis]

You might prefer this?

http://www.beano.com

[marjoram_blues]

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. From Pythagoras onwards we have been prone to the illusion that our ways of geometrising space capture space itself – perhaps even believing that the mathematical logic of pure quantities is somehow ‘out there’. 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
...
Physics, and the technology based on it (and indeed our civilisation), has flourished by being prepared to set aside the common sense that tells us that the earth must be flat otherwise people will fall off it, that a small object will always fall slower than a big one, and that the state of rest and motion in a straight line are fundamentally different. But we should not conclude from this that the mathematical portrait of the world is the last word on what is really there, or that everyday experience of lived space is in some profound sense defective or even wrong.
....
We should recognise that the notion of ‘curved space’ is less legitimate than that of ‘social space’, however useful the former might be for the development of mathematical physics. And we should not be pressured into thinking that the space of daily life, which is neither Euclidean nor non-Euclidean, is somehow not the real thing.
© Prof. Raymond Tallis 2015
Raymond Tallis’s latest book is Summers of Discontent: The Purpose of the Arts Today with Julian Spalding (Wilmington Square). His website is raymondtallis.com.

As a non-physicist, who can't even imagine 'Curved Space' or the concept of it, I had intended to steer clear of this article.
However, as a Tallis fan...

First question - is it true that this concept attempts to 'reinsert phenomenal appearances into abstraction', after reducing them to numerical values.
Next - who is likely to conclude that 'everyday experience of lived space is in some profound sense defective or even wrong'? I certainly don't think that the mathematical model is the 'last word on what is really there'. Why would anyone ?

Physicists do their thing. Other folk do theirs. It is perfectly compatible to understand and realise the worth and legitimacy of both physics space and social space. Where is this 'pressure' to think that everyday space is not real ? I'm not feeling it. Perhaps in academic wonderland...

This reminds me of the reduction of the eliminative materialist v 'common-sense' folk psychology argument.
Everyday experience or common-sense does not rule out accepting neuro-scientific or cognitive developments.

http://plato.stanford.edu/entries/mater ... fVirFolPsy

[marjoram_blues]

You might prefer this?

http://www.beano.com

Gotta love Denise the Menace
and Minnie the Minx

[SpeakerToAnimals]

" I certainly don't think that the mathematical model is the 'last word on what is really there'. Why would anyone ?"

Physicists like me do.

Tallis, is frankly talking nonsense when it comes to the supposed origins of curvature in ideas of space. And his basic ignorance is exposed, I'm afraid, by his misuse of the term 'topology' when what he actually meant was geometry.

I'll discuss 'social space' when someone can provide me with a meaningful definition of the term.................

As my first foray into 'Philosophy Now', tempted by the 'What is curved space' line on the cover, frankly I seem to have wasted £3.75 is this article is at all typical of the usual standard................................

[attofishpi]

I was drawn into this area with "What Is The Nature Of Reality?" only to find there is no sub-topic with that description.

Nevertheless, on 'time'. Time only exists as a measurement of events. We can quantify a second by a measurement of a number of known events that will occur within such a period.
In a true moment of time, there are no events. There is nothing moving, not an electron spinning, a photon emitting. TIME reversed EMIT.

As to the true nature of reality? = Panentheism.
Did we evolve into an super efficient system aeons ago due to increasing entropy? real_IT_Y?

homophones:- wait=time weight=akin to mass
People at church attend 'mass'


Beyond Reasonable Doubt?
http://www.androcies.com

[Scott Mayers]

I agree that curved space may be problematic to follow by many. I can completely understand it but simply disagree that it is necessary. Also, while the non-Euclidean geometries can be initiated with its own postulates, as long as one can be 'translated' in terms of the Euclidean geometry, these then reduce to just a reconstruction based on perspective and do not discount one over the other.

I also disagree with the general disapproval by this author as I've been writing on this site elsewhere with regards to whether we can trust math/logic to provide accountability to originate reality. Practical reality ALSO has to accept those things we interpret through the practical acceptance of the logic we use. If this is not trusted prior to measuring reality, then any practice that uses logic/math lacks as much justification than the Scientologist who uses an E-meter to defend their philosophy. And to me, this type of thinking is even more irrational.

[nix]

In his article “thinking straight about curved space. Phil.Now 108 june /july 2015 p51-2” Tallis has misunderstood several points:

The curved trajectories of free falling objects mentioned are not the source of curved spacetime; these trajectories occur in Newtonian mechanics in which space is strictly Euclidean (flat)!

To embed the 2-D earth surface in euclidean 3-D space misses the point of the physicists analogy. All flat (2-D) maps of the earth’s surface (Mercator projection, Peter’s projection, etc) are attempts to use 2-D Euclidean space to represent something which is a non-euclidean 2-D space. They all distort the distances, or angles, between points on earth’s surface, so are not fully faithful representations of reality. (Just as Euclidean 3-D space cannot faithfully represent a non Euclidean 3-D space. We would have to embed it into 4-D space to use Euclidean geometry).

We can discover the earth’s curvature from intrinsic measurements (i.e. we do not have to leave the 2 dimensional surface to measure its curvature nor do we have to visualize it as embedded in three dimensions to deduce that it is curved.) The statement that “the least we should ask of something said to be curved is that it should have edges, surfaces, and parts that look or feel curved” is nonsense.

Riemann showed that 3-D curved space was possible and it’s curvature could be measured from within the three dimensions ; then the distances between points are not given by Euclidean geometry (pythagorus’ theorem is not obeyed). This is in direct analogy with the earth’s surface for 2 dimensions.

Einstein showed that gravity forces us to use non Euclidean geometry to describe spacetime. His simplest example imagined a flat circular disc floating in empty space. With circumference,C, diameter, D, for all circles C/D = pias predicted by Euclidean geometry (flat spacetime). Now spin the disc at constant angular velocity about an axis perpendicular to the disc passing through the center ,O. If the disc spins fast enough the edge will approach the speed of light. It will then be Lorenz contracted (C’< C) but the diameter D will not, so now C’/D < pi, a non euclidean geometry. An observer at O is not accelerated but his twin at the edge, E, experiences an acceleration proportional to the radial distance from O. From the point of view of the twins they could be standing on a stationary disc subject to a varying gravitational field, from zero at O, to a maximum at E (equivalence principle). If identical clocks and meter rulers are placed at O and E, O would say that the clock of E is running at a slower rate (time dilation) and that E’s meter stick is shorter than his own (length contraction) and would attribute this to E being in a high gravitational field (experimentally observed as: gravitational red shift, and time delays in GPS clocks ).
The presence of Gravity implies curved spacetime. (The full general theory of relativity identifies gravity as curved spacetime.)

Q: If space is curved why does Euclidean geometry describe our familiar world here on earth?

A: In the disc-world example above, the size of the Lorenz contraction of the circumference depends on how fast the disc is spinning- faster spin means greater acceleration of E, which means higher gravitational field at E. So for weak gravitational fields C’/D ~ pi ie Euclidean geometry is a good approximation and Newtonian gravity is applicable. But as gravity increases spacetime ‘curves’ more and more (becomes more and more non Euclidean) and Newtonian gravity becomes a poor approximation to reality. The corrections to the Newtonian predictions of trajectories of falling bodies are tiny even for objects the size of planets and the sun, but they were detected. Corrections become essential for massive objects like neutron stars and black holes.

[nix]

Q: How much more massive would the earth have to be to give noticeable effects due to curved spacetime?

A: Consider a disk with radius equal to the earth’s radius (R= 6.38 x 10^6 m). Let it spin at a rate so that a point on the edge,E, has speed v = f.c (0<f<1 and c= 3 x 10^8 m/s) Let the circumference C shrink by say 1% due to Lorenz contraction so that the geometry is noticeably not quite Euclidean. Then

C’/C = (1- f^ 2)^1/2 = 0.99 therefore f^ 2 = 0.02.

The acceleration, g, which E feels due to the spin is

g = v^2/R = f^ 2.c^2 /R = 0.02 x 9 x 10^16 / (6.38 x 10^6) ~ 3 x 10^8 m/s^2. (Compare that to the acceleration of gravity at the earth’s surface ge = 9.81 m/s^2 =MG/R^2.)

In order for the earth to produce such a gravitational acceleration and begin to observe non euclidean geometry of space, it would have to have a mass ~ 3 x 10^7 (thirty million) times its present mass contained in its present size! Hence we do not notice curving of space here on earth (except in very high precision measurements which can detect tiny effects).

[nix]

I agree that curved space may be problematic to follow by many. I can completely understand it but simply disagree that it is necessary. Also, while the non-Euclidean geometries can be initiated with its own postulates, as long as one can be 'translated' in terms of the Euclidean geometry, these then reduce to just a reconstruction based on perspective and do not discount one over the other.

It is only possible to translate non Euclidean geometry in n dimensional space into a Euclidean geometry in n+1 dimensional space so we are forced to introduce a redundant coordinate to use Euclidean geometry and this is more complicated than using the non Euclidean geometry! For example in a three dimensional non Euclidean geometry (say of a very rapidly rotating flat disc with 2 space dimensions and 1 time dimension) what fourth dimension would you introduce to make the geometry Euclidean? In What 5 dimensional space would you embed 4 D spacetime to avoid non Euclidean geometry? Better to deal with the coordinates we actually have.

[Scott Mayers]

I agree that curved space may be problematic to follow by many. I can completely understand it but simply disagree that it is necessary. Also, while the non-Euclidean geometries can be initiated with its own postulates, as long as one can be 'translated' in terms of the Euclidean geometry, these then reduce to just a reconstruction based on perspective and do not discount one over the other.

It is only possible to translate non Euclidean geometry in n dimensional space into a Euclidean geometry in n+1 dimensional space so we are forced to introduce a redundant coordinate to use Euclidean geometry and this is more complicated than using the non Euclidean geometry! For example in a three dimensional non Euclidean geometry (say of a very rapidly rotating flat disc with 2 space dimensions and 1 time dimension) what fourth dimension would you introduce to make the geometry Euclidean? In What 5 dimensional space would you embed 4 D spacetime to avoid non Euclidean geometry? Better to deal with the coordinates we actually have.

The geometric interpretations as models still can be represent equivalent representations. While we are limited to how we illustrate them on paper, each new geometry only recreates a perspective logic as a tool. Yet underlying them all there is a foundation logic unique to them all. It is just more difficult for us to express them. In reality the best map coincides with the reality itself. Our models take perspective forms of this to help us focus on the details the authors of them want to convey or emphasize. But one form of logical description does not displace the other.

You ask how a 4D space could be drawn in Euclidean (paper) spaces? Just use an extended axiom in which you define the initial 3D spaces as a line (or even a point), and build on it from there. You wouldn't be able to illustrate all factors at once. But if you understand it, that is all that counts.

[Hobbes' Choice]

I was drawn into this area with "What Is The Nature Of Reality?" only to find there is no sub-topic with that description.

Nevertheless, on 'time'. Time only exists as a measurement of events. We can quantify a second by a measurement of a number of known events that will occur within such a period.
In a true moment of time, there are no events. There is nothing moving, not an electron spinning, a photon emitting. TIME reversed EMIT.

As to the true nature of reality? = Panentheism.
Did we evolve into an super efficient system aeons ago due to increasing entropy? real_IT_Y?

homophones:- wait=time weight=akin to mass
People at church attend 'mass'


Beyond Reasonable Doubt?
http://www.androcies.com

TIT is the same backwards and forwards.
People shit, but they also talk shit. which end do you use, your arse over tit?

[nix]

In reality the best map coincides with the reality itself.

I agree; that is why we need a non-Euclidean 2-D geometry to represent the 2-D surface of the world correctly, and a 4-D non-Euclidean geometry to represent 4-D spacetime when gravity is present.

[nix]

In reality the best map coincides with the reality itself.

To say the curvature of spacetime is just a perspective which could be removed by adding a dimension, is to ignore the fact that we are physical beings 'embedded' in three space and one time dimensions. What we measure with our meter sticks and clocks is the 4-D spacetime. The curvature or otherwise of this spacetime is then a question which can be determined empirically and has been by experiments such as gravitational redshifts, gravitational lensing, and the direct determinations of the rates of atomic clocks in different gravitational fields (differential aging of twins in different gravity). In the latter experiments the clocks start off together and are identical, they are then moved to locations with different gravitational fields and later are brought back together. The clock in the higher gravitational field actually ages less than the other in accordance with the general theory of relativity.