Physicists say that long time ago,the universe was so small..it was smaller than a basketball...we could put the universe in your pocket....it was smaller than an electron....some people call it a singularity of infinite gravity..Now, that's silly.There is no such thing as infinite gravity.It just means that we use the... word singularity to hide our ignorance..We don't know what the hell the singularity is...

Einstein and his gravity..

Albert Einstein (March 1879 to April 1955)

Einstein first discovered the actual geometrization of gravity, first by recognizing that gravity is indistinguishable from a uniformly accelerating inertial frame. From this finding Einstein recognized that light would appear to bend if viewed from a uniformly accelerating frame. Finally, with a little more math that I have involved, Einstein predicted that since the uniformly accelerating frame was equatable to gravity, that gravity would therefore bend light, which was corroborated by taking the apparent positions of stars about the sun during a solar eclipse to make the stars visible over the glare.

Once this experiment corroborated Einsteins theory, many other similar experiments were created, such as the Pound-Rebka experiment in 1959 at Harvard University. Though the first experiment was one that all people could grasp, the Pound-Rebka experiment proved more complicated. This experiment was to test the hypothesis that time slows down in a higher gravitational field. To set up the experiment scientists at Harvard University set up an experiment to calculate the redshift of gamma ray by having a loudspeaker with iron 57 at the top floor of their building and a receiving portion at the bottom which is depicted in the diagram below

The result of this experiment corroborated Einstein’s theory further with an accuracy of 10% which was later increased to 1%.

To respond to the question of if the reality of space-time matters to non-physicists, I would have to say no. Just as there is no reason for every person to know how their computer works, there is no reason they should know the ins and outs of the warping of space-time, especially when the difference in time on earth from its lowest point to its highest point is in the order of a few nano-seconds over the average lifetime of a human.