^{[a]}diagram, as reposted below.

It looks somewhat like beads, evenly spaced on equal-length taut strings, being rotated relative to each other. Hence the thread's title. To recap, Alice, the right-most bead-string, accelerates to the right at 1g, with each bead representing a propertime step of constant value on her clock. She is however stationary in her own reference frame. The bead-strings behind her represents observers with clocks that are also accelerating so that each remain at a constant (but different) distance behind Alice.

As mentioned in the other post, no observer can achieve that at x = -1 (the left-most bead-string), because it will need infinite acceleration in order to do so. Reminiscent of the what happens at the event horizon of a black hole? Yes, exactly! But before we jump into black holes, here is the structure above in a somewhat controllable 3-D package. Just drag the pointer on the image to rotate it in a direction (I'm not sure what it does on touch-screens).

You may notice that the z-axis is now propertime and that the y-axis is now hyperspace (the 4th spatial dimension). This is more compatible with the specific 3-D package used for the image.

^{[b]}There are now 21 beads on each string (20 HSPT steps). By rotating, you can verify that all strings are of equal length and bead-spacing.

What you are viewing is curved spacetime, as viewed by an accelerating observer, or as viewed by an observer sitting on earth's surface in earth's gravitational field. It is this type of gravity that Einstein used in 1911 to predict (half of the true) deflection of light that passes close to the sun. We will get to the other half soon, but like Einstein, we first need to digest the 'gravity of the situation'.

^{[c]}

At the surface of earth (or of the sun), gravity is not particularly strong and the constant linear acceleration scenario is extremely close to the gravity scenario. If we consider earth as a (non-rotating) point source of gravity, then unless we were propped up by something, we would all have fallen to the center of earth and been crushed by the singularity that would have existed there, at distance zero - essentially experiencing 'infinite gravity' there.

Using this linear approximation of real gravity, Einstein could have predicted the full deflection of light in 1911, had he considered another (approximately) linear effect - the curvature of space (not spacetime, just space). Notice that the x-axis in the above representation is straight - it is only the rotation (or tilting, if you like) of the bead-strings that cause the HSPT structure change with distance from the singularity.

Here is an attempt to picture spatial curvature on the HSPT structure: this rotatable picture. Note that the bead strings do not start at the x-axis (where y=0), but at a position that is more and more offset in the y-direction, depending on the value of x.

^{[d]}

At the singularity (x=-1), the left-most bead-string has been shifted more than a string-length, but it is anyway out of view, inside the singularity, whatever that may mean.

Now, how would this have helped Einstein to predict the full deflection of the starlight (1.75 arc-sec)? The answer is that both the tilting (gravitational time dilation) and the shifting (curved space) of the bead-strings have equal effects on anything, including light, that moves through the HSPT structure. The curvature of space contributes the 'missing half' at the time of the 1911 prediction. The curvature of space was also needed to predict the correct perihelion for Mercury, which Einstein also calculated later, when he had the full theory.

I know this is quite a mouthful, but there is still one more 'trick' op the sleeve of the bead-string visualization - the full 2nd order representation, but that will have to stand over for another post.

Notes:

[a] Hyperspace is a term used when more than 3 spatial dimensions are considered. In order for 4-D spacetime to be curved, one must consider at least one extra spatial dimension into which the normal 4-D spacetime can be curved.

[b] I have used the 3-D graphs part of vis-4.20.0.

[c] Although this is not what I referred to above, the real "gravity of the situation" became very acute when the 1st WW broke out, just as a team of astronomers set out to measure the predicted (half-of true) deflection of light. They got captured in Russia and barely survived the ordeal, but with no results, AFAIK.

[d] The 'true' x-axis will be bent, but the 3-D utility does not support that, AFAIK.