Imagine, we are given a task to fill up as many pages as possible on word, in a given time, with the letter ‘A’. One way is to copy ‘A’ into the clip board and keep pressing Ctrl V. This is the AP(Arithmetic Progression) way. There is another way; we can copy ‘A’ and keep pressing ctrl C, Ctrl A, ctrl V in sequence. This is the GP way. Mathematics tells us that although Ctrl V appears once in three buttons, the GP method is faster. This is not obvious for a common man at the first sight. And most of the public, are insensitive to logical arguments. Nevertheless, one can convince anyone of this fact, simply by demonstrating it.
The above is an example of what I call as an operationally testable statement. However there are statements which are not operationally testable. The man on the platform, says “the train is moving”; while, the man in the train says “the platform is moving”. Usually, a common man assumes that the man on the train is wrong; he knows the ‘truth’- the train is moving. The profound realisation is that, neither of them are wrong. But there is no way to demonstrate it! This concept of relative motion is operationally un-testable. So much so, that this un-testability was responsible for the Galileo affair. (besides religious concerns)
In fact, most of the statements with profound reasoning are operationally un-testable. For instance, the counter intuitive results of cantor, like the number of points on a side of a cube, the number of points on a face and the number of points inside its volume, are all equal; it is impossible to trisect an angle using a straight edge and a compass. A common man certainly has problems with accepting it. And unfortunately, there is no operational way to convince him of this fact; i.e, a person who assumes the contrary will not be punished for being wrong. Hence it is apparent that there is no way to convince the public of these facts.
To digress a bit, I often say utilising an object is to do something with it, which cannot be done without using it :D. By that token, reasoning should be used to conceive (currently)un-testable facts. Because, operationally testable facts can be conceived even without reasoning. Hence, real utilisation of reasoning is to conceive operationally un-testable facts.
How do I convince a common man of such facts? In the first place, should one care to convince someone who is not sensitive to logic? To answer these questions, I shall consider examples from the history where the task of convincing the public has been accomplished.
The earth is not flat, but spherical, and further, it is not at rest, it is rotating and revolving. These two are among the most profound, but operationally un testable realisations. However, they are widely accepted by the public!. Let us examine how were the public convinced of these. Aristotle conceived that the earth is spherical. At that time this would have been counter intuitive and operationally un testable; So, he would have had a great trouble in convincing people about it. It is clear that he did care about convincing people about it; why else would he list down the common fallacies in logic committed by people (see ‘Aristotle’s 13 fallacies’). And the way he did it, was to impose it as a belief. This is clear from how people believed everything that Aristotle said.
Most of the public today, believe that the earth is in a complicated motion. They just believe- they don’t really know the reasoning which led to this fact!. In fact, to really go through the reasoning, one has to understand relative motion. This was the major trouble with accepting Galileo’s arguments; he was asked to prove that the earth is moving (for which he gave a wrong argument :P). And it is apparent that most of the public don’t really appreciate relative motion. So, it is clear that they have been convinced of the heliocentric theory, just by imposing it as a belief. This, is not very different from religion!. Isn’t it unjustified for an intellectual to impose a belief?
Majority of people are insensitive to logical reasoning; ie, if the result of a logical reasoning is against their intuition or religious or any other concerns, they cease to accept it. Therefore, it is impossible to propagate the picture of moving earth, through reasoning. If it was not propagated as a belief, the public would have accepted a different picture of the earth, still as a belief!. Hence it is not unjustified, to propagate a belief, if it is necessary to convince them of these facts.
It is clear that whether or not a statement gets propagated as a belief among the public doesn’t depend on whether the statement is based on a sound reasoning or not!. It depends on the ability to impose a belief among the public, of the person who conceived it. This means, almost anything can be propagated as a belief!. That is a little disturbing :D. There ought to be a fundamental difference between conceiving a statement out of rigorous logical reasoning, and claiming without a strong logical background. I guess this difference is brought out in the confidence: the confidence attained by conceiving a fact through thorough reasoning is stronger. I guess(hope :P) this difference can be utilised to beat the propagation of unsupported claims.
Finally, I come to the question I postponed to the end. Is it necessary to care about convincing others? Again let’s ask (old)people :D.Usually, mathematicians don’t care about the public; after conceiving a result, they wouldn’t worry about convincing. Kepler, who went a long way ahead of Galileo, at the same time, didn’t care to convince everyone; that is why he doesn’t have an affair attached to his name, unlike Galileo :D. Apparently, he was able to go that far simply because he didn’t care about convincing people. It is clear that Galileo and Aristotle cared about convincing people. If none of the physicists and mathematicians care about convincing others, their next generation to be physicists and mathematicians will find it hard to see the facts amidst misconceptions. Avoiding this is the only possible motivation for a physicist/mathematician to get in to the job of convincing, as far as I can see right now. This post is the longest one so far, and has crossed 1K words and so I stop here