May
18, 2017 Thursday
Bedtime
Story
Numbers are like Nested Russian Dolls (Matryoshka)
At
this point I wish to share with you (once again), an excerpt from the book Prime
Obsession.
I
want you to understand how mathematicians view numbers.
An
average dude on the street or even an apparently very smart person sitting in
an office is quite ignorant about it, something as basic as numbers.
Derbyshire
writing on the Riemann hypothesis first had to explain to his readers what
complex numbers are.
In
the framing of Riemann hypothesis, the complex numbers are as fundamental as is
the zeta function 𝜁
I
can and could have written it in my own language but I like Derbyshire style
and want to share it with you.
It
is not an easy task to write mathematics that can be a pleasure to read.
So
here it goes:
“To
get a balance view of complex numbers, you really need to understand how a
modern mathematician thinks of numbers in general.
I’m
going to try to give an account of this, including complex numbers in my
account.
Don’t
worry too much about what they are right now; I’ll go into detail a bit later.
I
include the complex numbers in these next few paragraphs for the sake of
completeness.
So
how does a modern mathematician sees numbers?
As
hollow letters, that’s how.
As ℕ, ℤ, ℚ, ℝ
I
have been trying to think of a good, memorably daft, mnemonic for keeping these
letters in mind but have so far been unable to come up with anything better
than “Nine Zulu Queens Ruled China”.
Perhaps
I’m getting ahead of things a bit.
Here’s
an alternative answer to the question.
Mathematicians
think of numbers as a set of nested Russian dolls.
[1]
Innermost doll: The natural numbers 1, 2, 3, 4,…
[2]
Next doll: The integers. That is, the natural numbers together with zero and
the negative whole numbers (for example, -12)
[3]
Next doll: The rational numbers. That is, the integers together will all
positive and negative fractions (for example, numbers like 3/2, - 1/917635).
[4]
Next doll: The real numbers. That is, the rational numbers along with the
irrational numbers like √2
[5]
Outermost dolls: The complex numbers.”
I
shall continue a bit more of direct quotations from this wonderful book as
nowhere else have I encountered numbers being illustrated in such an
enthralling manner.
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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