January 30, 2017 Monday
Bedtime Story
Mathematics, Logic and Mathematical Logic
These two books, (namely the Tractatus and The Introduction to
Mathematical Philosophy) and their deep study by Moritz Schlick and his group
had a profound impact on the mind of Gödel and aroused in him a great interest
in mathematical logic.
Though both mathematics and logic go back centuries earlier, mathematical
logic is a fairly new branch of mathematics, its ideas germinating somewhere in
mid 1800s.
We very well know that mathematics is generally about numbers.
What is lesser known is that mathematics involves ever increasing
abstractions.
A 1998 paper published by Laurent Cohen and others in Trends
Neuroscience points out that there is evidence to suggests that animals,
infants and adult human apes have in them biologically determined,
domain-specific representation of both number and elementary arithmetic
operations.
Neuroscientists study brains using either images of it such as functional
MRI or by noting down loss of specific functions in brains that patients
present with area-specific lesions.
In us human apes the area that is associated with knowledge of
numbers and “number sense” is very specific.
This area is bilateral reflecting its survival importance suggesting
an evolutionary safeguard for damage or injuries to brain that may occur
unilaterally.
The mathematics area lies in the parietal association cortex or
the intraparietal cortex.
There is a strong correlation of its presence even in non-verbal
organisms and thus its evolutionary mechanism of origins stands out loud and
clear.
Moreover, the studies show that this biological and evolutionary
endowment is rather limited to very specific purposes suited primarily for survival
and mating.
The ability to discriminate
between two numbers increases as the numerical distance between them does.
For example, it is far easy
for organisms to differentiate 5 from 10 than 2.5559 from 2.6.
Moreover, for the same
numerical distance, the ability to identify numbers worsen as their numerical
size piles up.
Example being that it is
rather simple for most animals to discriminate 5 from 6 bur rather cumbersome
in differentiating 1,246,456,789,345 from 1,246,456,789,344.
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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