If you have two convex shapes (like a circle and a rectangle) which have the same center, if you think of the center as a target, and throw darts at the target.

If you have two convex shapes (like a circle and a rectangle) which have the same center, if you think of the center as a target, and throw darts at the target. The dart will be more likely to land in the intersection of the two shapes than would be derive by multiplying the probability of landing in one and the probability of landing in the other. If you were talking about independent events, like rolling 1s on two dice, you'd get the probability of both things happening by multiplying their independent probabilitis: so 1/6 * 1/6 = 1/36 probability for snake eyes. Another example would be the correlation between weight and height. If you took the median weight and median height, and took say the 10% of the population around that height and the 10% of the population around that weight, the overlap would be more than the 1% that would be calculated by taking 10% of 10%. The GCI says that for any reasonably distributed variables, this inequality (the probability of falling around the central tendency of all variable) will be greater than the product of the probability of falling around the center for each variable taken independently.