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when this lecture will be discussing the decimal
place value system so its origin how it has
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been used in the indian mathematical and astronomical
text not necessarily mathematical astronomical
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so that discussion about this decimal place
value system as technology even philosophical
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literature so i will be giving certain citations
from the commentary of also wherein he draw
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sinologist from this and then
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tries to project a certain philosophical view
point which he wants to project a normally
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ahh we do not have opportunity to learn so
what is origin of a certain system so because
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the history of science is never a part of
our educational curriculum anyway so we will
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try to find out so this one of the most fundamental
discoveries and it has been fairly will recognise
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that indians where the discoveries of this
decimal place value system the earliest concrete
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reference so in terms of the representation
has to be paste from some of these are inscriptions
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so we have this brahmi and kharosthi etc at
the earliest evidence can be traced even philosophical
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literature as i was mentioning after the introduction
and the reference circum of philosophical
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as well as mathematical literature will move
on to describe three different representations
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which have been used by indian astronomers
to refer to numbers aryabhatan system katapatadi
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system and bhutasamkhya system so these are
3 different representation
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which have been employed to represent huge
numbers which occur in the astronomical works
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so the sequence in which i have ordered them
does not necessarily represent the sequence
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in which these they they were used in the
society but it is for certain different convenience
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i have used the this ordering here so bhutasankhya
seems to be the most earlier thing and based
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on the evidences that are available in literature
this seems to be the earliest so katapayadi
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when is not very sure as to when it was ahh
discovered but certainly has a employee and
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wherein the longitude are represented in some
sentences particularly in the occasion of
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what is called upakarma so this is also rendered
as per the various other rendering which is
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done and so on anyway so these are all different
representation which have been employed by
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people and we will show certain charts so
wherein the vowels and consonants
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so how are the numbers assigned to these vowels
in different representations and then we will
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have a few example so this is the outline
of the present talk on decimal place value
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system as i was mentioning so many of us do
not force the question when did we start counting
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what are the different systems of counting
or what are the different ways of representing
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numbers so we have one way of representing
script is different but even the
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way of representation normally two things
are known that is what i learnt so one is
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this the so-called arabic notation and rather
is roman notation so this are the 2 things
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which are generally thought so we are so familiar
that we do not even ask this question that
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whether they could be other representation
and when did this way of using notation started
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obviously we will be initially using words
to represent number so after all ahh notation
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comes much
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later whatever be the discipline so initially
the language so we have the word to represent
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a particular number 2 3 10 100 and so on and
then comes in the notation so we will briefly
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see how did this particular way of representing
started in the course of our lecture so as
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i as mentioning obviously pretty old but how
old so the as i was coating yesterday so this
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so where the number 3 3 9 as mean represented
in word numerous ok so we have word 300 and
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so on talking about the ingenuity of the decimal
place value system
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and mention of 0 so one of the famous scientist
of recent pass the french mathematician laplace
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so observes the following the ingenious method
of expressing every possible number using
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a set of ten symbols each symbol having a
place value and an absolute value ok the place
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value and absolute value emerged in india
the idea seem so simples nowadays that its
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significance and profound important is no
longer appreciated its simplest lies in the
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way it
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facilitated calculation and placed arithmetic
foremost amongst useful inventions the importance
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of this invention is more readily appreciated
when considered it was beyond the 2 greatest
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men of antiquity archimedes and apploninius
so i will not described implication of the
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last sentence but anyway there is not much
time but he is for you to founded over so
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when historian try to trace back so what would
be the origin and so on and
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so forth obviously several hypothesis will
be put forth many of the hypothesis so would
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seem to be true so that has been very nicely
heard the origin of the so called arabic numerals
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have been written about so often that every
view on the question seems possible and the
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only way of choosing between them is by personal
conviction so why does us so we go by certain
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citations and testimonies and over a period
of time took loss of memory due to one
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soon way of understating what we convey so
it quite possible that there are gaps in process
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and this caution to take place and it is essential
that 1 police several evidences to come to
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a certain conclusion and in this regard to
the interesting book so which i would recommend
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all of you to go through and this book is
by georges ifrah so the book title universal
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history of numbers so i would take a couple
of minutes to just to say how this book are
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originated so
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apparently georges ifrah is a school teacher
and he was teaching numbers so to young kids
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so one of the students asked so where did
these numbers come from so how do we understand
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where it got originated and the present day
we of the presentation this is the only representation
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and so on and so forth so ifrah could not
answer the question raised by the student
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it is a certain conviction in his own mind
and therefore he decided that the next few
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years tracing to find out evidences to answer
this question so he resigned the job apparently
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and then it is stated that this man so went
around from one place to other place and he
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was even lying on road side not having enough
resources to stay in and he that narrates
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the seriousness with which you have gone ahead
and written this book that is what has been
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stated after doing research for decades so
he finally says with reference to the origin
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we are now going to look at it is truly remarkable
method of expressing numbers which is frequently
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found on mathematical and astronomical texts
written in sanskrit added to all other evidence
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it shows us not only to prove beyond doubt
that our present numeration is of indian origin
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and indian alone so this is following on to
convey through this so beyond what ifrah has
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said so ifrah obviously is not so conversion
with some the literature we will also go 8
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o clock evidence of literature we just give
a flavour as to how different interpretations
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can be
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given for it origin i just have it photographs
here so it says see the numbers the number
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of angles see if you look at 1 so only one
angle it say 2 so only 2 angles 3 there are
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3 angles 4 and so on so this is one rather
present says so it has nothing to do angles
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it has to do the lines so if you look at this
so only one line there are 2 lines he says
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there are 3 lines 1 2 3 4 lines 5 lines as
was the different people can obviously come
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up with
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different hypothesis it is just for the fake
just i want to show this slide there is nothing
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more to read here so finally ifrah says that
most of the presentation that find that all
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scientific location and therefore we need
to trace back and not to rely on these types
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of information so having coated from dozens
of works so both from islamic astronomer as
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well as european scholars see finally come
to the conclusion as they was seeing before
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that is
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origin this coat from the bishop in 7 century
also founds certain evidence that the science
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of the indians including the subtle discoveries
in astronomy discoveries that are more ingenious
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than those of greeks and the babylonians and
of their valuable methods of calculation which
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surpass description i mean he has been in
high price of what has been done here which
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he describe as done by means of 9 science
in fact this facility is a lot so that is
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what we need to understand from this quotation
so the kind of facilitation that it offers
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in the present in this as we will see from
the astronomical work so if one where to make
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a simple comparison i mean the way this roman
script so one has to write at the addition
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subtraction the kind of dislocation multiplication
all the offer that is something which is ahh
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really amazing and that is why even the class
5 please with the reference to the
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advent of this decimal place value system
this also in his work he says we have decided
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to explain indian calculating techniques using
the 9 characters and to show how because our
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simplicity and conciseness capable so these
characters are capable of expressing any number
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so be there all in high place of this decimal
place value system so think of multiplication
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which is representing so in roman and if you
had represent something like
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particular 20000 or something which is 1000
that so it is all extremely confused ok so
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the evidence in the form of inscriptions is
the 3rd century bc you have something like
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this this is the kind of representation that
finds in the rock edicts of ashoka so as i
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then proceed further there are buddhist inscription
so about 3 4 so second century bc so we have
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this representation and we proceed further
and in short so it seems to
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have started something like this and today
view this but almost taken about 18 centuries
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for the numeral notation which we use today
so starting from brahmi to modern so the modern
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is estimated around ahh ahh 15 century 16
century when the printing started so up we
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have different scripts in different languages
that is a different thing but the place value
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thing is a different things so with reference
to 0 as number and how it is represented
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so it is too difficult to precisely fix but
we find places of it in the panini's work
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on grammar as well as pingala from sutra so
we have so this was the word also represents
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certain understanding of what this physical
world is with reference to do this the philosopher's
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this word is does not necessarily represent
the number 0 when it is used in philosophical
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basis
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but in this chandahsutra there is nothing
to do with the philosophical implications
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but it is use as a marker now i give a couple
of quotations from commentaries on patanjali
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yoga sutra and so this form a very very concrete
evidence is a certain line ok so which you
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draw so he says if it is placed in so obviously
a certain place value 100 if you just shifted
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so it represent 10 so the same so it has a
certain place value it has a certain value
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to represent a number so both of them and
this is more graphic portrayal to
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convey a certain philosophy shankara says
we call him a boy we call husband will call
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directory we call him grandfather whatever
it is so depending up on the relation that
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you want to associate with another individual
it is describe by different terms similarly
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he says the same line so depending upon where
it is placed by shankar as an example to convey
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something else in philosophy but the point
is so we have a very very concrete
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evidence by shankar science so it has gained
and such a understanding in the society that
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examples are something which should be known
for everybody so the way did you not going
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to be certain example to convey something
else which is more perform ok the explicit
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use of decimal place value system obviously
is found in the mathematical and astronomical
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literature so the earliest text that is available
for us today is aryabhatiya or
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aryabhata so this was composed in 499 degree
so the degree of sophistication with which
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aryabhata have been able to handle is something
which is quite amazing he has introduced his
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own way of representing numbers obviously
it is a decimal place value that will be very
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very evident not only from the representation
of numbers but also some the procedures which
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aryabhatta has described to obtain square
root cube root etc so the algorithms which
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will be
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discuss later we will make it extremely clear
to you as to how they have been able to use
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this place value system in order to do lot
of mathematical computation in fact quite
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ingenious and sophisticated that a single
syllable can represent a number order of magnitude
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10 to the power of 16 this is quite convenient
to represent huge numbers but the same time
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this extremely difficult to pronounce as you
will see ahh with a few examples which i will
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show
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little later for instance this 4320000 years
is represent by by aryabhatta represent this
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particular number and what aryabhatta has
done is so he has chosen the vowels to represent
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the place value so we have a system of representing
vowels and ingenuity lies in aryabhatta making
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use of the vowels to in other words i mean
he has thought of vocalise to the place value
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i would say so vowels are essential for pronouncing
consonants
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and there is a will teach we do not say so
what are essential for pronouncing consonants
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and aryabhatta has smartly using these vowels
to pack a certain place value to that and
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the consonant will the person the number so
for those who are not familiar with vowels
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so i just thought i will just display this
chart so
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so this is all had a longer one so that is
how sutra also
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so this refers to panini so give the set of
vowels so in aryabhatta
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systems once we reach with a certain function
had tagged to that so will be multiplying
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that consonant by 10 to the power of 16 so
aryabhatta has further classified the consonant
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into 2 books so this start to help in understanding
this kind of classification so the matrix
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that you see here so this 5/5 so 25 he calls
them as varga letters so varga and the term
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has also the meaning of square so the operation
of square squaring so this is also
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referred to as varga so but as far as this
is concerned this set 5*5 i mean this 25 may
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be it is in this sense is called vargs it
falls into a certain class ok so then we have
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i do not think is employed by aryabhatta but
up to this certainly so he has associated
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certain numbers to all this consonants and
the place values will be decided by the vowels
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ok so this is extremely important because
when a string is given to decide for one has
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to have a very clear
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understanding whether this false in so when
we place these consonants with the vowels
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so we will classify depending upon whether
it is has to be placed under so if you make
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a mistake will be multiplying it by a power
of 10 which will go wrong so in he assign
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values 1-25 so on so we come to 25 so 1-25
is associated with the consonant which forms
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so with reference to
so it goes from 30 to 100 (refer time:
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23:06) so as i said is quite novel and ingenious
in a way aryabhatta system can be thought
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of as the the vowels as i said are used for
denoting place value but since we have classified
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the consonants into two groups varga and avarga
and man can associate as an power of 10 with
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the varga and another with our avarga in fact
he has described his system by means of a
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but all that you need to remember is so every
vowel so as we move from so it goes as 10
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to the power of 2 in this sense it can be
called as 10 decimal system so
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here i would also like to show a chart wherein
some error in fact i offered this course on
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mathematics in india to our student at iit
i thought something and then for the student
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send me send me a mail so looking at something
in the web and then said so there is he seems
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to be discrepancy between what you said and
what is there in the web so i said there is
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an error there so i thought i will just show
this to you also to see that so this year
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is not committed ok
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so we have to be very careful when we take
materials from the web so the error is the
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following so stopped this and therefore there
will be serious error in deciphering the number
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ahh when we take this stop to be the ok so
let us see a couple of examples so cute root
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so this is a very important number and that
is why i decided that we should stop with
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this example so what is to be done before
getting into this table so you
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please say look at
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this word so aryabhatta says so here we use
so term varga in 2 senses when he uses the
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00:25:46,849 --> 00:25:56,929
compound it refers to the varga letters but
when he uses the word separately so it means
200
00:25:56,929 --> 00:26:07,909
you have to place it in the we mean 10 to
the power 0 10 to the power of 2 10 to the
201
00:26:07,909 --> 00:26:18,700
power of 4 and so on so here whenever you
are given a string so when you find a varga
202
00:26:18,700 --> 00:26:27,220
letter so then we place in the and if you
encounter you have to place
203
00:26:27,220 --> 00:26:33,970
in the so now it will become pretty evident
you so you have to create a certain table
204
00:26:33,970 --> 00:26:40,129
so it will be very convenient in the initial
stages for us to decide for the number for
205
00:26:40,129 --> 00:26:51,820
every vowel you have to create two places
one is so for all we have 2 for and so on
206
00:26:51,820 --> 00:27:01,340
and so forth for every vowel will create two
places and whenever we get a varga letter
207
00:27:01,340 --> 00:27:10,899
we place in the varga and encounter avaraga
consonant you play it under varga so this
208
00:27:10,899 --> 00:27:12,590
is what the essentially
209
00:27:12,590 --> 00:27:31,719
detail and if we look at the last part of
the first half of the word it says so the
210
00:27:31,719 --> 00:27:43,649
number starts ok assigning numbers to various
functions 1-25 and then he defines what represent
211
00:27:43,649 --> 00:28:00,609
so very clearly he states so if you look at
this table
212
00:28:00,609 --> 00:28:09,989
so put together so whatever be the value that
is the value which is assign ok so that is
213
00:28:09,989 --> 00:28:19,899
what it means so this incidentally will give
you a flavour of how aryabhatta has written
214
00:28:19,899 --> 00:28:21,789
his work so that is this
215
00:28:21,789 --> 00:28:28,239
style of composition in those days and the
entire aryabhatta is just 108 versus so which
216
00:28:28,239 --> 00:28:36,120
deals with all mathematics all astronomy and
so which will be just take in a4 sheet ok
217
00:28:36,120 --> 00:28:49,859
so that is how it is this and so this is what
it is basically refers to vowels arranges
218
00:28:49,859 --> 00:29:13,929
student want means so so now we look into
this example 3 vowels and 3 consonants that
219
00:29:13,929 --> 00:29:31,389
define here and vowels are 2 vowels and 3
consonants so is the second thing ok third
220
00:29:31,389 --> 00:29:32,389
so the
221
00:29:32,389 --> 00:29:52,139
value of is 2 and we find also there so that
has the value 4 and we find
222
00:29:52,139 --> 00:30:01,660
now when we try to arrange it here so since
does not have a vowels on its own so when
223
00:30:01,660 --> 00:30:09,409
you have this kind of a combination so then
the vowel that is tagged to the consonant
224
00:30:09,409 --> 00:30:15,950
with succeeding it so will be the vowel which
is tagged with this previous consonant with
225
00:30:15,950 --> 00:30:36,279
vowel also so this is the annotation
and place this in varga place set below varga
226
00:30:36,279 --> 00:30:37,279
fine then
227
00:30:37,279 --> 00:30:47,889
we move on to the next syllable so the next
syllable is is 4 and it has to be placed below
228
00:30:47,889 --> 00:30:59,710
so because the vowel tagged with so this actually
represents 4 zeros followed here so 4320000
229
00:30:59,710 --> 00:31:10,700
so this is the representation which has been
given by aryabhatta aryabhatta give reprehensive
230
00:31:10,700 --> 00:31:25,440
numbers so we will see one more example so
that is why i said it has an advantage of
231
00:31:25,440 --> 00:31:29,019
representing huge numbers in very short form
but it is bit
232
00:31:29,019 --> 00:31:43,679
difficult to read so here we again notice
that there are several vowels which have been
233
00:31:43,679 --> 00:32:02,950
employed in this string
we have so
234
00:32:02,950 --> 00:32:33,629
if you look at this table
235
00:32:33,629 --> 00:32:47,549
so this
236
00:32:47,549 --> 00:32:56,450
basically represents the number of revolutions
made by moon so in fact to give you the significance
237
00:32:56,450 --> 00:33:02,190
of this number so this gives the number of
revolutions made by the sun in a large period
238
00:33:02,190 --> 00:33:07,950
which is called so under this representation
the number of revolutions of sun and this
239
00:33:07,950 --> 00:33:08,950
represents
240
00:33:08,950 --> 00:33:15,929
the number of revolutions made by the moon
in the same period of 4320000 years so this
241
00:33:15,929 --> 00:33:24,309
are strings which have been provided by aryabhatta
in order to tell you the number of revolutions
242
00:33:24,309 --> 00:33:37,299
made by the planets in a large period called
and one more example
243
00:33:37,299 --> 00:34:09,679
so here
244
00:34:09,679 --> 00:34:19,690
we have without vowel and the following vowel
is and therefore represent 4 and represent
245
00:34:19,690 --> 00:34:30,800
6 ok these things it is very very difficult
to pronounce but these all basically the
246
00:34:30,800 --> 00:34:36,640
revolution numbers which has been stated by
aryabhatta much more interesting thing is
247
00:34:36,640 --> 00:34:43,530
so aryabhatta actually present the entire
time table in numbers so you may remember
248
00:34:43,530 --> 00:34:47,880
that in school days you would have referred
to sin table class cable one page to page
249
00:34:47,880 --> 00:35:03,770
all that will be there but this man has presented
in simple words so this is how the so all
250
00:35:03,770 --> 00:35:13,590
these basically represent this values of sin
difference in fact we say sin table so the
251
00:35:13,590 --> 00:35:19,490
quadrant is divided into 24 parts will see
later as to how indian astronomers and mathematicians
252
00:35:19,490 --> 00:35:26,870
have found very efficient ways of computing
ahh accurate sin values for a certain period
253
00:35:26,870 --> 00:35:33,300
of time so this aryabhatta what he has done
is he has basically presented this sin table
254
00:35:33,300 --> 00:35:58,240
in one words because it is tagged with e so
you have two 25 25 so this two 25 basically
255
00:35:58,240 --> 00:36:04,720
represents the sin so sin theta suppose theta
is 3 degree and 45 minutes so sin theta
256
00:36:04,720 --> 00:36:11,840
is theta you know right so it is presented
in minutes and therefore so 225 so if you
257
00:36:11,840 --> 00:36:18,490
take 3 degree 25 minutes if you represent
in minutes 225 so sin theta is theta so what
258
00:36:18,490 --> 00:36:25,760
is the kind of thing so what has increases
the next value of 225 it chose so it will
259
00:36:25,760 --> 00:36:31,730
reduce will keep on reducing so basically
what aryabhatta has given is sin table in
260
00:36:31,730 --> 00:36:38,470
the form of differences suppose you want to
find out the sign of 10 degrees so you have
261
00:36:38,470 --> 00:36:40,260
to add this+this
262
00:36:40,260 --> 00:36:48,060
and then you had use some interpellation to
get the value so how this has represented
263
00:36:48,060 --> 00:36:57,510
ok now we move on the other system called
which is called kattapayadi system so the
264
00:36:57,510 --> 00:37:10,840
name kattapayadi stems from the fact that
in this system so all of them represent 1
265
00:37:10,840 --> 00:37:20,790
see if you look at this table so below so
we have representation from 1-0 so here also
266
00:37:20,790 --> 00:37:30,980
it is mapping of consonant to a certain number
but since we have 25 of them so in kattapayadi
267
00:37:30,980 --> 00:37:31,980
what has been
268
00:37:31,980 --> 00:38:05,550
done is and so on and so
aryabhatta not assign the value to and that
269
00:38:05,550 --> 00:38:12,760
represents number 9 ahh here there is no classification
as varga and avarga that you have many to
270
00:38:12,760 --> 00:38:18,040
one mapping or other one to many mapping so
if you want to represent number 1 you can
271
00:38:18,040 --> 00:38:24,380
choose any of the 4 here ok so 2 you can choose
many of the 4 and so on so this is what basically
272
00:38:24,380 --> 00:38:30,740
katapayadi system is all about what has been
done here has been beautifully
273
00:38:30,740 --> 00:38:50,780
ahh summarised in one single words by so the
entire systems has been captured in this
274
00:38:50,780 --> 00:39:09,730
so it says then
275
00:39:09,730 --> 00:39:28,230
it comes to a conjunct form of a syllable
then how do you decide to here in aryabhatta
276
00:39:28,230 --> 00:39:33,480
system since the vowel was used to tag the
place value so we have problem here it is
277
00:39:33,480 --> 00:39:38,960
not that way so you find the string and you
keep on it always start from so the least
278
00:39:38,960 --> 00:39:45,230
the place value and then you proceed to the
higher so when you have a certain string fun
279
00:39:45,230 --> 00:39:58,870
instances you look at this so in fact a famous
work ends with string represent this number
280
00:39:58,870 --> 00:40:18,590
so when you look at the definition which has
been provided in this so it says actually
281
00:40:18,590 --> 00:40:32,830
represents consonant ok so means any vowel
tagged to the consonant once should not considered
282
00:40:32,830 --> 00:40:42,950
so why is he stating this so if a vowel occurs
on its own without a consonant activate then
283
00:40:42,950 --> 00:40:49,160
it represents a number but if it is tagged
along with so only consonant
284
00:40:49,160 --> 00:41:01,810
has to be considered so that is what
means that which is close to so for instance
285
00:41:01,810 --> 00:41:13,140
in this string which has been given here is
a vowel so all vowels where present number
286
00:41:13,140 --> 00:41:23,470
0 so so if you look at the definition so is
a certain pneumonic which has been used to
287
00:41:23,470 --> 00:41:34,250
refer to all the vowels so it has to prove
panini sutra which is used to refer to all
288
00:41:34,250 --> 00:41:48,620
the vowels similarly in fact if you look at
the maheshwara sutras something which is used
289
00:41:48,620 --> 00:42:08,440
to refer to all the consonants so we can see
this example
290
00:42:08,440 --> 00:42:10,900
consonant so what to do is you drop
291
00:42:10,900 --> 00:42:20,201
and you take the consonant which immediately
preceded the vowel so it can be a ahh consonant
292
00:42:20,201 --> 00:42:26,540
2 consonants and 3 consonant fed with all
those cases the one which immediately proceed
293
00:42:26,540 --> 00:42:41,330
to vowel has to be considered has to be counted
and therefore you count only what
294
00:42:41,330 --> 00:42:49,090
is drop only is taken so basically it is represent
number 1 7 1 2 2 1 0 commentator as said this
295
00:42:49,090 --> 00:42:55,480
actually represents the date on which this
work got completed so this is the another
296
00:42:55,480 --> 00:43:02,580
way of coding in fact there are several examples
like this also
297
00:43:02,580 --> 00:43:12,110
it starts with the it represents date and
appears in the last verses text and determiners
298
00:43:12,110 --> 00:43:18,280
this number if you see this the difference
is only 5 days apparently this person nilakantha
299
00:43:18,280 --> 00:43:25,090
has composed the commentator say this entire
work something about 430 verses and all in
300
00:43:25,090 --> 00:43:33,640
just 5 days so this all exam quickly i will
also mention about this bhutasankhya in bhutasankhya
301
00:43:33,640 --> 00:43:39,940
system as the term itself gives an idiom so
bhuta is something which is
302
00:43:39,940 --> 00:43:49,480
existing so sankhya is number so you choose
a certain elements in nature so for instance
303
00:43:49,480 --> 00:43:57,580
eye when you say eyes so they represent 2
ok so when you say fingers it represent 10
304
00:43:57,580 --> 00:44:07,560
when you say veda it represents 4 so based
on the familiarity so with the bhutas bhutas
305
00:44:07,560 --> 00:44:14,760
not necessarily the physical elements we could
be physical element it could be certain mythological
306
00:44:14,760 --> 00:44:19,170
think it could be referring to some literature
which is quite common so for instance when
307
00:44:19,170 --> 00:44:32,450
they say
308
00:44:32,450 --> 00:44:42,350
so
moon the moon associated with the earth so
309
00:44:42,350 --> 00:44:45,180
they all represent number 1 so any synonym
310
00:44:45,180 --> 00:44:56,120
of earth to represent 1 of moon will the present
so then for representing 0 the use space looks
311
00:44:56,120 --> 00:45:02,450
like a shadow empty in the sense so space
is used to represent number 0 any synonym
312
00:45:02,450 --> 00:45:15,640
of is 0 so as i said eyes ears jaws knees
hands finger system hands is 2 so sometimes
313
00:45:15,640 --> 00:45:30,250
they use there are 14 manmantras and therefore
represents 14 ok and rama ayodhya rama balarama
314
00:45:30,250 --> 00:45:40,700
parasurama so it represents 3 so guna when
they used all this things so this is
315
00:45:40,700 --> 00:45:49,250
how the bhutasankhya system is when they use
month there are 12 month so one interesting
316
00:45:49,250 --> 00:46:01,770
example is maathavas value of pi so what i
thought just used herr so so you look from
317
00:46:01,770 --> 00:46:12,560
here so basically represent so therefore it
is 33 so it has to do with the description
318
00:46:12,560 --> 00:46:26,000
found in puranas and
319
00:46:26,000 --> 00:46:42,850
is 2 then and we
320
00:46:42,850 --> 00:47:03,420
have 3 here 3 also represents 3 represents
333 consecutively ok 3 and then we have
321
00:47:03,420 --> 00:47:23,050
and
so this first line basically
322
00:47:23,050 --> 00:47:33,380
represents this number and the denominator
is represent this actually gives you the value
323
00:47:33,380 --> 00:47:39,600
of pi which is correct to 11 decimal places
will discuss later so these are all few other
324
00:47:39,600 --> 00:47:57,610
examples so so to conclude so aryabhatta system
though quite ingenious is a bit difficult
325
00:47:57,610 --> 00:48:04,110
to use that systems to represent because it
is too difficult to pronounce and therefore
326
00:48:04,110 --> 00:48:10,910
not many people in fact we do not know of
any aryabhatta using his system to represent
327
00:48:10,910 --> 00:48:18,050
the number so it is very profound in its own
way as far as is familiar with the
328
00:48:18,050 --> 00:48:25,660
saturn system it is in fact it is very convenient
to use both system for composition so which
329
00:48:25,660 --> 00:48:31,370
is also see if you are familiar with certain
terms it is quite convenient to read and therefore
330
00:48:31,370 --> 00:48:35,910
mostly astronomers have resorted to system
in fact that seems to have been the most deadliest
331
00:48:35,910 --> 00:48:44,610
system but then aryabhatta device own and
had own format and in fact as i told you something
332
00:48:44,610 --> 00:48:48,200
else and it also represent the number in fact
the entire system of
333
00:48:48,200 --> 00:49:00,990
astronomy is based on this when you decode
it gives you if anything conclusively so all
334
00:49:00,990 --> 00:49:07,880
these proved the facility with which people
have been using decimal place value system
335
00:49:07,880 --> 00:49:08,910
so with this we conclude here thank you