You flunk on moral grounds if you propose not to cure anybody.
Any attempt to cure as many people as possible gets a B. To get an A, you must do the arithmetic and see that it is possible to cure almost everybody for a while.
Clearly the gift is finite. The doctor will eventually die, and his patients will face disease again as they will anyway when they reach seventy. This is no reason not to get the maximum benefit.
It turns out that he can cure everyone in the world whose disease or injury can be diagnosed in time to bring him to the doctor. The solution is technological.
Approximately 60,000,000 people under seventy die each year, i.e. two people die each second. We build a machine that can move 12 people per second past him on each of ten moving belts. A mechanism should be provided to stop the motion of the finger of the patient momentarily so that it touches the doctor rather than brushes his skin.
On the basis of the arithmetic the doctor need only spend 1/60 th of his time curing people, i.e. 24 minutes per day.
In order to reduce transportation costs it might be desirable to build a number of machines in different regions of the world and for the doctor to make trips to these machines, say once a month, to get the slow diseases, and to fly the emergency cases to wherever he happens to be.
It would not be very difficult for the doctor to get this solution adopted given a reasonable degree of persuasiveness either on his own part or on the part of some former patients he could recruit to help him. Doctors are often skeptical, but we have postulated a miracle that would convince almost all of them. Politicians are often shortsighted and bureaucrats bumbling, but what would be required in this case is simple enough so that they could do it. It is not possible to predict whether any important opposition to the use of the gift would develop. If so, it might be necessary to protect the doctor from assassination and the equipment from sabotage, and even then, there would be some risk of disaster.
I have not postulated any mental or physical side effects but it would be necessary to watch for them as well as for possible adverse social side effects.
The use of this gift would contribute to the population problem but not so much as one might think. In the U.S. 4,000,000 people are born each year but less than 1,000,000 under 70 die each year and most of these are past the child-bearing age. Elimination of death under 70 would require for stabilising the population that couples limit themselves to an average of say 2.1 children rather than the 2.2 children that might be allowable otherwise.
In countries with larger death rates of young people the population effect would be larger, but ordinary medicine is already having a similar effect.
Some people find the above solution repulsive because it involves a big machine with moving belts which would probably be noisy. Maybe they don't like a technological solution to what has been conceived as a moral problem.
Other people think that a law of nature is surely being violated - namely, a law that says that any apparently worthwhile innovation involving technology surely must have harmful side effects at least equal in magnitude to the apparent benefit.
There remains, however, the literary problem. Namely, imagine that the above analysis is correct and that the problem would be solved. Imagine further that the doctor, while posessing the gift of healing, is not a super-organizer or super-hero of any sort. How could one make literature of such a situation. The pessimistic and paranoid fantasies of the previous section make much better literature at least by present literary standards.
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