Start with what you know and build on it by using known theorems/axioms while keeping track of whether you are getting closer to what you want to prove, and then finally, when you have achieved your destined equation mentioned in the question paper, you end your answer with a concluding statement --LEFT HAND SIDE (L.H.S.) = RIGHT HAND SIDE (R.H.S.), HENCE PROVED!
What makes that final statement so special? Why do the examiners insist on you writing it? If you skip the final statement, should you be given any marks? Alternately, if you simply wrote the final statement as your answer without really proving the equation, should you be given any marks?
If you ask me, both are vital -- the proving steps, as well as the final statement.
NOTE: I am talking of Prove-That questions which you are solving on your own, and not the ones which you learnt by heart the previous night or the ones which you copied from your neighbor in the exam hall.
Let me take you backwards to the point history when a genius by the name of Archimedes got into his bath tub with a perplexing look on his face. This wasn't the first time he was having his bath. Then why did he have to yell out "Eureka" in the midst of his washings, and run to the Royal Palace, unshaven, naked, with his towel-carrying maidservant trying to nab him from behind?!! The steps for the proof (the principle of buoyancy) were there in the bath tub earlier too. Moreover, they were also there in all other bath tubs, not just in Archimedes'. So, what was missing in the proof? It was the "Eureka!" -- the conclusion that 'I have realized it!' And it took an Archimedes to blurt it out, and thus reveal the proof in all it's nakedness for the world to see and admire!
That same "Eureka", the "I got it!" proclamation you have to state in your answer paper in a more dignified form with the statement: "L.H.S. = R.H.S., HENCE PROVED!"
If you don't, then how would the examiner know that you realize that the steps you have written in sequence are actually proving the equation mentioned in the question paper? You can very well write all the right steps in the proof, but still not know that those form the proof! Is it not? If that's the case, then is your answer worthy of any mark?
Let me ask you a question:
What comes first -- your proof, or you realizing that you have proved it?Take your time and first understand the question. Re-read, if that brings any clarity.
Proving a proposition (or, even disproving it!) is quite logical in approach. But the final step, that "YOU HAVE REALIZED IT" is anything but logical. You can't logically conclude the final statement. You just have to know it! Both the logical and the illogical happen together, in a flash (in Archimedes' case, it was a splash)!
When the mind is standstill, and you are in the present moment, in the NOW, the truth reveals itself!! The veil of ignorance is taken off and the light of knowledge dawns upon you. You are enlightened!
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For the sidebar;
I remember playing a trick on the examiner during one of my Engineering semesters. It was a prove-that type of question on a mathematical equation involving vectors. I started the proof with known statement(s), and after deriving about 3-4 pages of new equations one after another, I had still not reached the unproven equation from the question paper. I knew that I was fairly close. The time, however, was not on my side. At that moment, an idea struck me! I went back to the start of my answer and numbered some of the equations in my proof at random. At the end, I left some space to fill in later through a backtracking process and then entered the most cherished statement in the proof: "L.H.S. = R.H.S., HENCE PROVED!" Then a step above that I wrote the to-be-proved equation. On top of that I wrote another equation which one can easily derive to be same as the to-be-proved equation by rearranging the terms on L.H.S. and R.H.S. Then, the clincher -- link up the flow from the top and the flow from the bottom by the phrase: "From equations 6, 12 and 25, we get--". And thus a charlatan was born!
8 comments:
My cousin's guru once told him "All knowledge is possible in ignorance". My cousin pondered over the meaning of the statment, and had a eureka effect when he was driving his bike! He said all his questions disappeared since then.
That my friend, is driving to conclusion!
Well, that's a good advice from your cousin's guru. I am sure it was meant to mean that you drop all that you have read or learnt from the books or other fellow creatures... and be "innocent" (not same as "ignorant")... and in your "innocence", you will awaken to the All-Knowing Unknowable!
What makes you so sure what he really meant?
wotever i answer, it wouldnt lead you anywhere... so forget about getting any answer and increasing your understanding... just be innocent and perceive the world inside-out!
The reason I asked was bcos... On one hand you are saying be innocent and open, but on the other hand you are saying "I am sure...". When you are sure about something, you leave no room for the truth to enter, because you are already full.
So there are two contradictory statements within one statement.
I guess this is what he meant by "All knowledge is possible in ignorance". A statement can be both true and false at the same time depending on the beleif system of one perceiving the statement. So the statement can be proved one way or another, based on the assumption of the proof. And since any assumption can be made in ignorance, "all knowledge is possible in ignorance" [Q.E.D]
"When you are sure about something, you leave no room for the truth to enter, because you are already full" is true, and I am sure of it!:)
Excellent point!!
But still, is it not better to leave things open so that your readers may have the same pleasure of discovering the truth on their own?
Otherwise some will blindly agree to what ur saying and think "If prabhuji is sure, then it must be correct. Cos he is usually right". And that statement although true will make no vital difference to them, because it doesnt make them inquire.
Forget the readers, Is it ever a good thing to come to conclusions, even if it is about not coming to conclusions? Why not have an open door policy about everything including closing the door....wait a minute...that means you are right in coming to a conclusion, because it never not okay to not be okay.....okay I quit
The problem with the mind is that it tries to find logic in everything! I am sure, which I can't justify by mind's logic, that a contradictory statement has the key to make the mind either fight for it's survival, or come to a standstill! You have a choice here, and it's your free-will!!
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