Gregg,

Yes, I heard the Penrose's talk with Weinstein. Non-Euclidean geometry 
(Riemannian sphere) indeed has been a great knife to cut many an apple. 
Relativity led to creation of various transformations because as the 
frames of references & medium of communication (space) change calculations.

Figure one and two are trajectories of submarines travelling from same 
point A to B in the ocean.
*Question - */Which of the two figures is more likely to take lesser 
time to travel would the submarine be travelling at constant speed in 
both cases./

Those who answered Figure 1 are wrong. Because for someone floating on 
the ocean Figure 1 seems straight. But for someone far in space or sky, 
Figure two is straight, quite like a straight line joining two points on 
a circle is always shorter than the circumferential arc.

Similarly, London, Paris & Moscow actually form a right angled triangle 
on earth but Pythagoras theorem does not hold true for them. While the 
earth's surface is Riemannian, our local space is Euclidean. Therefore, 
we need to make adjustments. Quite similarly, the curvature of space 
changes with its average density. Light moves in a straight line, but 
straight for an observer inside curved space is curved for an observer 
far away, where the curvature does not exist. So that which is straight 
for one inside, is curved for one outside the impact of mass.

The time for a laser signal propagating in a laid straight cable will be 
more than that needed for a laser signal propagating straight in air. So 
for our frame of reference we need to make transformations to calculate 
the correct time taken by light when it passes in proximity to large 
stars or blackholes.

In context of my writings - it meant that representations allow for 
simplification and resolution of problems. The curved space is real, its 
transformation on a complex plane, helps us calculate time taken to 
travel through it from point of view of our non-curved space. So the 
curvature is real, its transformation is a mathematical representation 
for precision of calculation.

There are numerous non-spherical representational geometries. As an 
example two parallel lines on a hyperbolic planes (Thermal Plant 
condensers if your have seen them) never meet (like parallel lines) but 
the distance between them is not constant.

TY
DL



On 11/23/2020 8:41 PM, Henriques, Gregg - henriqgx wrote:
>
> Thank you, Deepak.
>
> Lots here, but let me home in on something you wrote, given your 
> background in physics:
>
> “Quite like a sphere is a representation of a complex plane. The 
> Complex plane does not exist, it is a mathematical abstraction for 
> representing a sphere (mathematically) on a Descartes plane. It is 
> very important to underline that the capability of an abstraction to 
> solve certain physical problem does not make the abstraction real. It 
> is just an information-manipulative, discovered reason for a physical 
> truth for which a real reason is not found or is not easy to be found 
> and in some rare cases a real reason might not exist (this happens in 
> case of informational truths, which have no physical existence at all).”
>
> One such representation is the Riemann Sphere:
>
> I am curious if you have an opinion about why we need the complex 
> number plane is necessary for the scientific mapping of the real. 
> Indeed, as this podcast between Eric Weinstein and Roger Penrose note 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__www.youtube.com_watch-3Fv-3Dmg93Dm-2DvYc8-26t-3D200s&d=DwIDaQ&c=eLbWYnpnzycBCgmb7vCI4uqNEB9RSjOdn_5nBEmmeq0&r=HPo1IXYDhKClogP-UOpybo6Cfxxz-jIYBgjO2gOz4-A&m=WvUYN0wHkTjJhxKQzdJ-riX__W7350A5cuCt3EWXoik&s=QYtqakqhcwh3ge-mSHt1r256b8oQtVON_S5lLQ5ilH8&e= >, it seems to be a 
> feature of both quantum mechanics and general relativity, as opposed 
> to classical mechanics. Below is a quote from Niels Bohr on this point 
> that many folks found at least somewhat mysterious:
>
> Love to get your take on this.
>
> Best,
> Gregg
>
> PS Please try to remember to put TOK in the subject headers for folks 
> to classify their emails easier.
>
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