February 17, 2018 Saturday
Bedtime Story
Bernoulli Family
It is here that Ada Lovelace goes totally
mathematical and from the mathematics develops an algorithm which if following
by the engine would enable it to come out with Bernoulli Numbers.
Before we further continue with the Note G
of hers, it behooves me to explain at least cursorily the concept of Bernoulli
numbers, as even though a lot of us would be bound to be familiar with the
Swiss surname of Bernoulli, we may have little or no knowledge of the eponymous
numbers.
The reason for some of us being familiar
with this strange name is that this name belongs to not one, but eight gifted
mathematicians of the same family albeit of different generations.
Though originally from Antwerp, Belgium, the
first known Bernoulli being a doctor (somewhere in 1560s), whose son moved to
Frankfurt.
The great grandson of the Antwerp doctor
was Jacob Bernoulli who eventually moved to Basel, Switzerland in 1620 and
finally acquired its prestigious citizenship, though I am not sure how the
process of citizenship worked out four centuries ago.
Yet, even this Bernoulli was not endowed
with any noteworthy mathematical gift.
It is only the two of the four grandsons’
of this Bernoulli who started displaying their mathematical gifts in earnest.
This first notable mathematician among
these four grandsons’ was Jacob Bernoulli who was born in 1655 and was a
contemporary of Leibniz (which naturally makes him a coeval of his rival Newton
as well) who was born few years before him in 1646 not too far away in Leipzig,
Saxony, Holy Roman Empire.
Of the four brothers, Jacob was the eldest
and the other three to follow him sequentially were Nicolaus, Johann and
Hieronymus.
Oh these three, only Johann showed an
inclination towards mathematics and was in fact spotted early on and educated
by his elder brother Jacob in mathematics.
It is the elder brother Jacob Bernoulli
after whom Bernoulli numbers are named and which were the subject of algorithm
of Ada Lovelace for the Analytical Engine.
Each mathematician Bernoulli has a tale to
tell but for now we shall stick with the first gifted one because dealing
fairly with each of them will take us away both from Menabrea and Lovelace and
as a consequence from the Analytical Engine itself.
Bear in mind that we have now moved from
the England of nineteenth century to Europe of seventeenth century where it was
indeed dark and dangerous to be born in Europe.
Nearly eleven thousand years of agricultural
revolution had flown by and soon the industrialization of the agricultural
revolution would be to begin in earnest.
Most of us modern apes who sit in our homes
and have never even once ploughed the fields have been fed with a diet of an
extremely romantic view of the agricultural revolution; as romantic as most of
our National Geographic channel viewers hold the view of nature.
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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