September
05, 2017 Tuesday
Bedtime
Story
Early Mathematics was Whimsical and Capricious
Very
early in the history of mathematics, several statements were considered true
simply because they seemed intuitively right or worse self-evident.
I
mean just imagine 5000 years ago if a person of authority would make a claim
such as “Air is weightless” or “Air is colorless”, who would think about
countering those claims.
After
all, these pronouncements seem to be intuitively self-evident.
It
was the same with the primitive arithmetical or mathematical statements.
If
someone would have said that “Numbers can only be positive”, then it would seem
very natural to accept that as a self-evident truth since in real life there
are no negative apples or hens.
Most
of early mathematical statements were built either this way or derived
eventually starting from such self-evident “truthful” sentences.
There
was hardly any austere definition or formal criteria for selecting such
intuitive evidence.
So
if most people deemed a statement to be collectively intuitive and agreed upon
it, then it would be deemed to be intuitively true.
We
all know how hopeless the relationship is between human intuition and reality.
Such
was the case with geometry in the civilizations of Fertile Crescent and may be
our ancestors in Africa.
All
geometry that had this type of foundation can be called pre-Euclidean geometry.
Yet
there was hope as there were wise men even then who realized the cataclysmic
perils of this method and understood the complete absence of objectivity in
this technique.
From
then onwards, the axiomatic method showed a change of direction wherein great
emphasis was made to reduce or minimize dependency on such intuitive evidence.
Rules
in mathematics began to be more Spartan and demand was raised that every
sentence that would be deemed true would have to be proved.
Obviously
such a lofty ideal is virtually impossible to realize as any student of
mathematics would affirm.
In
actual mathematics, one true sentence is derived from another true sentence
which in turn from yet another and so it continues.
As
it is evident, this type of reasoning will lead either to the problem of
infinite regress or to a vicious cycle if one true sentence ends up back to
some original true sentence.
Thus
the entire exercise has to be discontinued somewhere.
Mathematicians
of the past saw the difficulties of the deductive system and decided to come at
an understanding that was not exactly close to the ideal they had decided upon
but wasn’t as dismal as the primitive method of intuitive truths.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night mon ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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