Heuristic: "What responsibility could a newborn have for what some person did in another life?": Our souls are eternal. The newborn's soul is not new, it lived in a previous existence and so now it suffers. That is not so say that we should not try and assuage that suffering because the judgement of souls is for G-D alone.
I see. From my perspective, it's difficult for me to imagine what this "soul," devoid of all personality, memory, and awareness, could possibly be. The formation of individual identity seems so completely dependent on particular neurological development, guided and shaped by genes and environment, that I don't see a role for a "soul" anywhere, much less how this soul could be considered culpable for acts committed when it was part of another personality.
Second, what does mathematics have to do with this? What is the equation?
Since the human population expands geometrically, I have trouble figuring out where all these extra souls could come from.
"Heuristic does NOT see proof that G-D cares...": I did not peg you as a Deist. Go figure. Spinoza would have smiled. However, proof is all around you.
Primo Levi, a reknowned atheist survived Auschwitz. In his writings he spoke of a very popular view amongst Survivors (including a couple of my own now avowedly secular relatives). He asks how any G-D would allow such suffering.
G-D created everything. HE gave us all we need to survive, all we need to be happy. At that point it became our responsibility to manage and utilise that which HE had given. He does not trouble HIMself over our second-to-second affairs. HE can and does intervene when need be, but only rarely...
If you have a child, you pamper the child, give him all that he needs...The child grows up always whining, hitting others, ruining his room, spitting at you, what do YOU do? You still love him but you realise that the more you do the worse he will get. From there on in you wait for him to realise the error of his ways, and you wait patiently.
An atrium waters itself, might be a way to try and visualise it, albeit in a very basic way.
If you believe that all the evil which befalls another is deserved, then I suppose the problem of evil becomes less of a problem. But... I think there remains a thorny problem. Here it is.
I am able to do evil to another. To do evil to another is to visit harm upon he who does not deserve it. But then, if I am able to do evil upon another, then another can and does suffer that which he does not deserve. And if I am free to do great evil to another, then another can suffer great evil which he does not deserve.
If I am NOT able to do evil to another, then I have never, and cannot, commit evil, and thus deserve no punishment or suffering.
So in either logical case, we have a universe in which God permits individuals who do not deserve great suffering, to nonetheless fall victim to it.
It's a logical possibility that there is some place or way by which God compensates those who have suffered unjustly. But if so, that is a part of the universe of which I am not aware. The observed universe does not seem to embody any moral law, much less enforce it.