to determine compatibility and project long-term success of a relationship. But, no matter what method we use, there is a serious catch: the timing! Do we ever get the opportunity to do any such analysis when it matters the most? That would happen to be before we get into a relationship, when we still have a fighting chance to exit the bad ones. Usually not.
. Now, imagine a spherical surface surrounding the object—two such surfaces of difference sizes are shown in . All the lines of force penetrate such a surface. The total number of lines remains the same no matter how large we choose to make the enclosing sphere, but as the sphere gets larger, the lines would get increasingly farther and farther apart. As a result, the same square bit of area on a larger and farther out surface will have fewer lines penetrating it than if it were closer, as can be seen by comparing the two spheres in . But the surface area of the sphere increases as the square of its distance, r, to the object at its center. This means that the density of the lines of force will decrease as square of the distance as we go farther out from the object. We can visualize the force as being proportional to the number density of these “lines of force” at a given distance from the source; therefore, the force must decrease as the square of the distance as well.
Figure 10.1 Lines of force are visual depiction of force fields due to gravity or electromagnetism. The force becomes stronger closer to the source, since the lines get closer together, and their spatial density increases.
. If instead of a marble there is a more massive object, the distortion will be bigger. Now, if we roll a coin around that pucker, it will revolve around the marble, just like the moon does around the earth. In the extreme case of a super heavy mass, the sheet will just be punctured and form a hole—like in those gumball vending machines in the mall or the supermarket, where an inserted coin spirals round and round and eventually falls down into the hole in the center, like in —that’s pretty much what would happen to an object shot sideways into the event horizon of a black hole. Quite literally, black holes punch a hole in space-time, referred to as a singularity.
Figure 10.3 A two-dimensional visualization of how gravity distorts space-time around it. Gravitational attraction can be understood as arising due to an object moving toward the “depressions” in the warped space-time.
Actually, this view of gravity provides a much more telling analogy of why we are attracted to certain people. They distort and morph the social space around them, and we fall into that distortion and end up in their social orbit. The stronger the attraction exuded by such a person, the deeper the well of social vortex around them, and the harder it is to pull free, and in the extreme case they can become the social equivalent of black holes puncturing a hole in the social fabric in their vicinity. Think of the popular kids in your high school; they had (or have) a lot of people in their social circle, didn’t they? Wherever they go, any party they are at, there is always a group of people around them in their warped social space.
Figure 10.4 If the gravitational distortion is very strong, it can puncture a hole in space-time called a singularity; this is what happens in black holes.
The surface area of a sphere with radius (distance of the surface to the center) of length denoted by “r” is given by the formula 4π r2, where the Greek letter π is a constant with the approximate value of 3.1415.