May
28, 2017 Sunday
Bedtime
Story
Levels of Abstraction
Lingering
a little bit longer on abstraction, I would like to emphasize that abstraction
is a mental process that is very commonly used by us apes.
It
is a technique to generalize or simplify something specific by leaving out the
concrete, specific details.
The
abstraction can have different levels.
Douglas
Hofstadter in his most unusual and difficult masterpiece ‘Gödel, Escher, Bach: An
Eternal Golden Braid’ (1979) illustrates six levels of abstraction in something
as banal as a newspaper.
Level
1: A publication
Level
2: A Newspaper
Level
3: The San Francisco Chronicle
Level
4: The May 18 edition of The San Francisco Chronicle
Level
5: My copy of the May 18 edition of The San Francisco Chronicle
Level
6: My copy of the May 18 edition of The San Francisco Chronicle as it was when I
first picked it up (as contrasted with my copy a few days later: in my fireplace,
burning)
The
higher up you go, the more the abstraction.
So
abstraction is inherent in most of our thought process (the book attempts to
explain how cognition emerges from single neurons using concepts from computer
science and mathematics such as self-reference and recursion); the only
difference is that mathematics requires abstraction of a degree so intense that
is lacking in average apes.
Having
said all that, I can’t help but expect you to be overwhelmed with a deluge of
nihilism leading to complete renunciation of mathematics.
That
is but natural; Most of us will make for pathetic mathematicians.
Yet,
there is hope – just a tiny bit – but it is there.
No
one can stops us from enjoying and reading on mathematics, which is
meta-mathematics.
Lack
of ability to do any meaningful and original mathematics does not imply that
one cannot savor the beauty of mathematics and knowing about those rare few
apes who CAN do original mathematics.
But
even that takes immense effort.
Before
I go into the meat of Gödel’s brilliant theorems, I wish to share with you
something what mon ami shared with me.
That
is - ‘How to Read Mathematics’.
We
shall discuss this essay before indulging ourselves further with Gödel.
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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