I remember that a friend introduced me to the "hedgehog's dilemma". Supposedly, if two people are too far apart they would be sad because they are lonely, but if they are too close they can hurt each other too. So he said that his solution would be to stay far away.

I suppose that he might be right if the hurt you can get from being too close would never be greater than the worst loneliness you can possibly get. However, if that is the case, then people would not come together to form societies; they would be more like plants, the farther apart, the better. So apparently there seems to be an optimal distance.

But where is it? I thought of this:



Apparently, you would get a graph like this when you plot



where k and p are positive constants, a > b > 0.

If you are that interested in the ideal distance, you can differentiate and work out the solution, but it would be pointless because we don't know what y, k, x, a, p, b stand for.

BUT the repulsive force probably doesn't go up forever! E.g, When two hydrogen atoms get too close, they experience Coulomb repulsion, but if they get really really close, they can attracted to each other due to residual strong force. (which is stronger than Coulomb repulsion at that distance, then the weak force would turn one of the protons into a neutron so there's no more Coulomb replusion) Then they will stay together, and nothing but a blackhole can tear them apart!

Well... I leave that to your interpretation. My point is, staying far away probably isn't the best policy.