Onmatu- General Math Learning Article
Probability and the future
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The theory of probability and mathematical statistics became today an important and even indispensable part in our lives.
The economy and insurances use largely probabilistic laws. Every
science that is based on measurements is inevitably interested in this
branch of the theory of probabilities known as "the theory of errors".
In the last analysis, physical world was found to be of probabilistic
nature. Some of the fundamental aspects of biology are also
probabilistic. Any call on experience, using selection processes,
depends, for its interpretation, on the statistical theory. Many of the
judgments and decisions that we all have to take daily are based on a
weighing, conscious or intuitive - and for sure more intuitive -
of probabilities. Even the courage, like Socrate said, is the knowing
the reason of fear or hope and therefore depend(s) of the probabilistic
estimations of the risks implied in our fears and hopes.
However, despite its importance, those who fall within the responsibility of education issues have not yet recognized as it should the universal significance of the theory of probability and mathematical statistic. Without a doubt, the mathematicians will get in the coming years deeper, stronger and more general results in every of these domains. It seems very likely that all areas of social sciences, as they will be more solidly grounded, will use increasingly more the theory of the probabilities. The question of legal judgments have been examined by the probabilistic people since the time of publication of the anonymous article, "A calculation of confidence in the testimony of people" which appeared in England in 1699 in a number of the magazine "Philosophical transactions". With little more than a century later, the Frenchman Condorcet wrote an essay called "The essay on probabilistic analysis applications to taking multiple decisions".
There was an article that illustrates how interesting and important are the applications of the theory of the probabilities in the functioning of a democratic system.
If you don't feel weird to end this at somewhat humorous note, let's consider the following problem: "If A, B, C and D tell each the truth (independently) just in one case from three and if A say that B deny that C declares that D is a liar , then what is the probability that D to tell the truth?". This problem, which is called "the truth of the four liars" is not too complicated. Sir Arthur Eddington used it in a book that he wrote in 1935, but he gave a solution back then which subsequently confessed that it was not correct. For this problem to have rational sense, we have to give some additional information. The solution of Eddington, of 25/71, is valid only if we add a condition that is a little ridiculous. With the additions that seem most reasonable, the solution is 13/41. You can make a probabilistic thinking exercise for this problem.
We do hope that this scientific progress will accompany the progress in education that elements of the probability theory will be included in the high school programs and the extremely interesting results of this one will replace outmoded various mathematical methods, of purely historical interest that are still in use. We do must hope also that secondary schools will have better care for those wishing to study physical sciences, biological, medical or social, to know the foundations of the theory of probability and mathematical statistics - disciplines that have proved their worth and have matured fully. Thank you.