May
27, 2017 Saturday
Bedtime
Story
The Qualities of a Mathematical Mind
As
I was saying, the problem of taking up a bedtime story as complicated as
Gödel’s incompleteness theorems is my own lack of any decent mathematical
training.
But
the second reason is even more important.
Gödel’s
paper is seriously grueling, back-breaking and mentally exhausting requiring
mastery of 46 preliminary definitions and many basic propositions before the
main results are reached.
Serious
mathematics requires high mental abstractions and formal logic perhaps even
more so.
I
am not educated enough or perhaps to put it more correctly, not dedicated
enough to go into that kind of depth and understanding of abstract mathematics
involved here.
In
mathematics, abstraction involves extracting and isolating the underlying
essence of a concept, removing its connection from any real world physical
constructs and then generalizing it to other related or even non-related
phenomena.
The
hard fact and blunt truth is that highly abstract concepts are cognitively very
challenging to grasp.
Conceptual
assimilation of such high level of abstractions requires a certain level of
mathematical maturity.
Mathematical
maturity is a mixture of mathematical experience - which can be acquired
through conventional education - and insight that is generally genetic (either
you have it or you don’t).
Mathematical
maturity demands following traits from the risen ape:
[1]
Fearlessness in the face of symbols; ability to read and understand
mathematical notations
[2]
Capacity to generalize from a specific example to a broad concept
[3]
Capacity to handle increasingly abstract ideas
[4]
Capacity to shift to learning by rote to learning through understanding
[5]
Ability to link a geometrical representation with an analytical representation
[6]
Ability to convert verbal problem into a mathematical one
[7]
Ability to recognize mathematical patterns
[8]
Ability to move back and forth between geometry and analysis
[9]
Ability to draw a line between what you know and what you do not
[10]
Ability to teach yourself
[11]
And of course, ability to remain focused
Yes,
no one said mathematics is easy.
Bertrand
Russell in 1931 wrote that the words of ordinary language are not sufficiently
abstract.
What
he was meaning to say is no matter what the level of abstraction found in
ordinary language may be, it is nothing in comparison to the depth encountered
in mathematics and mathematical logic.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
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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