Chandrayaan-2 :
50-50 : The Vishnu Principle
No matter how close moonlander Vikram got to making a perfect
touchdown, its chances of success were just 50-50 at every stage
"I've been telling you for 25 years!" Prof. Vijay Vishnu exclaimed. "The only chances of anything happening ever, if they aren't zero or 100 per cent, are 50-50, and nothing else! This fellow is just talking rubbish!"
My distinguished long-time friend, who is a professor emeritus in the Old Madras University, has a passion for perfect logic and is constantly disturbed by the liberties everyone tends to take with facts and figures.
We were talking -- like millions of people all over the world, perhaps -- about India's second moonshot Chandrayaan-2, which flew so flawlessly all the way across space to the South polar region of the moon carrying the lander Vikram, which seems to have tragically collapsed just a couple of kilometers above the chosen landing spot on the lunar terrain.
What made Prof. Vishnu so angry was some self-styled expert saying on Twitter that since the distance from the earth to the moon was about 400,000 kilometers, the lander had a 200,000 - to - 1 chance of getting down to the surface safely and properly, but still somehow failed at the very end of its amazing journey.
That was just an amusing joke, of course ; but the good professor had drained so much of his time and energy questioning constant distortions of the concept of probability that he wasn't able to see the humorous aspect of the comment in question.
"That's pure, unvarnished nonsense!" he declared. "You do agree with my 50-50 Principle, don't you?"
Of course I do! In fact, I know his argument by heart because I've heard it so often ; moreover, I earnestly believe in the theory myself, and can explain it with additional inputs of my own. So here we go :-
Mirror image
The Vishnu Principle states: The probability of anything happening in any given situation, if it isn't either zero or 100 per cent, is invariably 50-50, and never anything else.
All statements like “There’s a 60 % chance of success” or “The patient has a 90 % chance of surviving the operation” are logically flawed and unsustainable, but such predictions are constantly being made.
They aren’t valid even statistically, though they may seem to be so. For the figures only recall what had actually happened in a certain set of past cases, and do not really foresee what's likely to happen in the next case, or even in the next set consisting of the same number of cases.
Let us say A is an average senior citizen. Space travel is not yet a routine activity, and isn't likely to be so in the near future, so the chances of A travelling to the moon are zero.
All men and women must die sooner or later, so the chances of A passing away eventually are 100 %. But when the doctors tell A that he or she has a 90 % chance of surviving an impending heart surgery, they’re getting it all wrong. The basis for their pep talk is that in the last 1o cases (let’s say) only one patient died, and 9 survived. But the same ratio may or may not recur in the next 1o cases. Perhaps two patients will die; if that happens the doctors will start saying that the chances of survival are 85 %, since 17 patients out of 20 lived on.
And after 100 cases they may well say: “Only 20 cases went wrong, so you have an 80 % chance of survival”. Thus, a retrospective view of facts relating to a variable past period is given a statistical twist and becomes an untenable prediction of the shape of things to come.
In other words, the mirror image of a given past picture is simply projected as a future scenario!
Which side?
But just for argument’s sake, let us assume that the ratio will be the same in the next set of 1o cases as it was in the previous set of ten. Even then the question arises : will A be the one who will collapse, or someone else? Similar will be the uncertainty facing patients B to J lined up in the wait-list. For every one of them, the chances of survival in the given situation are precisely 50-50, no more and no less!
This will be true not only in the beginning, but even as the operations progress, till one of the patients dies. And, of course, if the first nine patients survive, the last one will be the one who must die ; but even that may not happen because neither the patient nor the surgeons may have the courage to go ahead with the surgery. It only shows how precarious such predictions can be.
Or consider the following statement in Wikipedia: "The estimated long-term prevalence of retinal detachment after cataract surgery is in the range of 5 to 16 per 1000 cataract operations."
Supposing you have just undergone a cataract operation ; on which side of the odds will you be? Of course, you have no idea! Which is the same thing as saying that your own (and anyone else's) chances of suffering retinal detachment after cataract surgery are 50-50, and nothing else!
Logic trap
This kind of logic trap is almost universal in the medical field, and many eminent surgeons and researchers all over the world keep falling into it constantly. Even Dr. Christiaan Barnard, the pioneering heart-transplant wizard, seems to have been no exception!
The given examples are very elementary, of course, but the same unassailable logic governs even highly complex and intricate situations arising in the affairs of all individuals, organizations and nations, not just in the medical field, but in all spheres of life -- including space research and exploration, of course.
Now let us take the specific case of Chandrayaan-2, and try to imagine how we might be arguing if we fell into a logic trap of the same kind. There were 15 crucial stages from launch to landing (launch ; 5 earth-orbit and 5 moon-orbit maneuvers for escape/capture ; orbiter-lander separation ; 2 de-orbit maneuvers ; powered descent). So we would have progressively calculated the chances of Vikram's successful landing as follows :-
Just before launch : 7 % (because something might go wrong with any one of the 15 crucial steps). Just before going into moon orbit : 11 % (9 steps to go). Just before separation : 25% (only 4 steps remain). Just before starting descent : 50 % (last step for landing).
Did I hear you screaming : "That's all very cleverly said, but it doesn't make any sense! If anything had gone wrong at any stage, there would have been no eventual landing, would there? So the odds would have been 50-50 at every stage, wouldn't they?"
Well, I didn't say that -- you did! And that's precisely what the Vishnu Principle says : The probability of anything happening in any given situation, if it isn't either zero or 100 per cent, is invariably 50-50, and never anything else.
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ISRONAUTICS
For my reflections on India's first moonshot and other recent adventures of the Indian Space Research Organization, please see the following posts :-
Bravo, ISRO! Bravo, NASA!
Destination Mars : Bravo, ISRO! Bravo, India!
India Joins Exclusive And Elusive Cryogenix Club
