December 14, 2018 Friday
Bedtime Story
Depth of Understanding
Last night we were discussing the Argentinean
mathematician and computer scientist Chaitin and his take on understanding.
He makes an argument for data compression
to be equivalent to understanding.
Being a mathematician he asks us to
consider the real number 0.333… which he points out is made up enormously large
number of data not for the reason that it is infinite but that it requires an
understanding of five concepts of mathematics.
These five concepts are the zero, the
decimal system, number line which has number 3, the infinity and finally
infinities of 3s.
Most apes chose to convert it into a simple
fraction one-third (this is what I do whenever I get an ape-child to teach
which is not very often but since both my nursing staff have one each I do get opportunities
to interact with them from time to time at my leisure).
It is interesting to watch the difficulties
an ape-child faces in grasping the conceptual basis of mathematics that they
are taught to perform mechanically.
Now the beauty of the fraction 1/3 is that
in understanding it one would have to know just two mathematical concepts of
the number line and the division.
The second one, i.e. 1/3 is a compressed
version of the first, i.e. 0.333… and thus data compression can be seen as
understanding.
While Chaitin is obviously looking at the
subject of understanding from the point of view of computer scientist and
machine learning using smart algorithms the psychologists have an even more
interesting take on this subject.
While they agree that understanding is
ubiquitous to many life forms and humans of all sorts and ages, when it comes
to humans there is a qualitative difference of understanding that varies from
individual to individual and from time to time.
Understanding anything is a continuous
range that is “measured” in terms of depth which varies from shallow to deep.
The assessment of the depth of
understanding of a subject is often done through different examinations which
are definitely not full proof.
We shall return to the subject of
assessment of understanding in human apes a bit later.
Mon Ami never ceases to express the view
that a person who is really interested in his subject or who loves to do what he
does will have an understanding whose depth would be hard to fathom for average
apes.
Most of us average apes get easily satiated
with a nominal understanding of our subject of profession that allows us to
stay functional and useful to the society which is turn renders us the means of
earning livelihood.
That much understanding is often relatively
shallow as is evident by our universal fear of examinations that to a large
extent test our understanding of what we profess to be expert in.
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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