January 03, 2017 Tuesday
Bedtime Story
Hilbert's Paradox of the Grand Hotel
The poles and the center can be tackled like the famous Hilbert’s
Paradox of the Grand Hotel or Hilbert’s Hotel.
Hilbert introduced this thought experiment of the Grand Hotel in a
lecture that he delivered in 1924.
George Gamow the great cosmologist popularized this idea in his
book:
One Two Three… Infinity: Facts and Speculations of Science (published
in 1947).
This paradox is a classic example of a veridical paradox (as opposed
to falsidical paradox).
The veridical comes from the Latin veridicus which is derived from
two Latin words:
Verus, meaning “true” and dicere, meaning “to say”.
A veridical paradox states something that sounds very absurd yet
the result is provably true.
In contrast, a falsidical paradox is one that produces a result
that not merely appears counter-intuitive or false but as a matter of fact, is
false.
The classical example of a falsidical paradox are all the nine
paradoxes proposed by Zeno such as the Achilles and the tortoise or the Arrow
paradox.
In the first, Zeno proposes that the in a race, the quickest
runner can never overtake the slowest as there are infinite number of points to
be covered between the quickest and the slowest.
In the second, he proposes that the flying arrow will never reach
its target since at every instant of time it is stationary.
Though it is obvious that Zeno’s paradoxes are not genuine it was
not easy to disprove the argument made by Zeno for a long time.
It was only in the 1800s when Weierstrass and Cauchy (Cauchy was
prolific with 800 high quality research papers and 5 whole books) gave a
rigorous definition of calculus and logic using epsilon-delta that the
mathematics of infinities came under control.
And Zeno’s paradoxes proven to be falsidical.
Hilbert proposed his paradox as follows.
Consider a hypothetical hotel with countably infinite number of
rooms, all of which are occupied.
Would it be possible to add any new guest in it where the
pigeonhole principle ought to come into effect.
What on earth is this pigeonhole principle?
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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