Welcome To NAMASTE LECTURE SERIES

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Welcome To NAMASTE LECTURE SERIES
2009
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NAMASTE
?
GARUD AT CHANGU NARAYAN TEMPLE
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NAMASTE'S NEW NEPAL MATHS CENTRE
Presents
Something Nonmathematical and Something
Mathematical
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SOMETHING NONMATHEMATICAL
AND
SOMETHING MATHEMATICAL
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AFTERNOON
DAY
GOOD
MORNING
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PART
ZERO
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NAMASTE
At a Glance
NAMASTE National Mathematical Sciences Team A
Non-profit Service Team Dedicated to MAM
Mathematics Awareness Movement Established
March 22, 2005, at the premise of NAST .
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COMMITTEE OF NAMASTE COORDINATORS

• 1. Prof. Dr. Bhadra Man Tuladhar
• Mathematician (Kathmandu University)
• 2. Prof. Dr. Ganga Shrestha
• Academician (Nepal Academy of Science and
  Technology)
• 3. Prof. Dr. Hom Nath Bhattarai,
• Vice Chancellor (Nepal Academy of Science and
  Technology)
• 4. Prof. Dr. Madan Man Shrestha,
• President, (Council for Mathematics Education)
• 5. Prof. Dr. Mrigendra Lal Singh
• President, Nepal Statistical Society
• 6. Prof. Dr. Ram Man Shreshtha
• Academician (Nepal Academy of Science and
  Technology)
• Member Secretary (Namaste)

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NAMASTE's main objectives are

• To launch a nationwide
• Mathematics Awareness Movement
• in order to convince the public in recognizing
  the need for better mathematics education for all
  children,
• To initiate a campaign for
• the recruitment, preparation, training and
  retaining teachers with strong background in
  mathematics,
• To help promote
• the development of innovative ideas, methods and
  materials in the teaching, learning and research
  in mathematics and mathematics education,
• To provide a forum for free discussion on all
  aspects of mathematics education,
• To facilitate the development of consensus among
  diverse groups with respect to possible changes,
  and
• To work for the implementation of such changes.

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NAMASTE DOCUMENTS

• Mathematics Awareness Movement (MAM)
• Advocacy Strategy
• (A Draft for Preliminary Discussion)
• Mathematics Education for Early Childhood
• Development
• (A Discussion paper)
• The Lichhavian Numerals
• and
• The Changu Narayan Inscription

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PART ONE
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W H E R E D O W E C O M E
F R O M ?
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NO MAN
AGO
LONG
LONG
NO MATHEMATICS
AND
NO COUNTING
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LONG BEFORE MAN CAME
The big bang is often explained using the image
of a two dimensional universe (surface of a
balloon) expanding in three dimensions
THEORY OF BIG BANG

The universe emerged from a tremendously dense
and hot state about 13.7 billion years ago.
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SCIENTIFIC NOTATIONS
Number Exponential Form Symbol Prefix
1,000,000,000,000 1012 T tera
1,000,000,000 109 G giga
1,000,000 106 M mega
1,000 103 k kilo
1 100
0.01 10-2 c centi
0.001 10-3 m milli
0.000001 10-6 m (Greek mu) micro
0.000000001 10-9 n nano
0.000000000001 10-12 p pico
Age of the Universe in Years

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SHAPE OF THE UNIVERSE
Angle sum gt 180 degree
Angle sum lt 180 degree,
Angle sum 180 degree,
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Closed surface like a sphere, positive curvature,
Finite in size but without a boundary, expanding
like a balloon, parallel lines eventually
convergent
Saddle-shaped surface, negative curvature,
infinite and unbounded, can expand forever,
parallel lines eventually divergent
Flat surface, zero curvature, infinite and no
boundaries, can expand and contract, parallel
lines always parallel
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ARE WE ALONE IN THE UNIVERSE?
GENERAL BELIEF
NO

Finite non-expanding universe
?
With about 200 billion stars in our own Milky Way
galaxy and some 50 billion other similar
galaxies in the universe, it's hardly likely that
our 'Sun' star is the only star that supports an
Earth-like planet on which an intelligent life
form has evolved.
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WE COME FROM
MILKY WAY
Our Galaxy
200000000000
STARS
Age 13,600 800 million years
Hundreds of Thousands of Stars
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B L A C K H O L E
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T H E S O L A R S Y S T E M
Sun Mercury Venus Ea
rth Mars Jupiter
Saturn Uranus Neptune
Pluto (?)
Distance between
the Earth and the Sun 149598000 km
Age 4.560 million years

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SOLAR SYSTEM
Distance between
the Earth and the Sun 149598000 km
Born 4,560 million years ago
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SOLAR SYSTEM
Rotation and Revolution of the Earth
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Born 4.5 billion
years ago
Rotating Earth
EARTH
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TECHTONIC MOVEMENT
LAURASIA
GONDAWANALAND
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TECHTONIC MOVEMENT
OR
CONTINENTS FORMATION
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THE WORLD

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ANCIENT CIVILIZATIONS
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WORLD CIVILIZATIONS
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INDUS CIVILIZATION
NEPAL
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Nepal The land where a well developed
number system existed as early as the beginning
of the first millennium CE.

WE COME FROM
107 AD
NEPAL
Maligaon Inscription
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• PART TWO

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What Do We Know About Our Ancient Numbers ?
?
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BRAMHI SCRIPTINASHOKA STAMBHA INSCRIPTION (249
BCE)LUMBINI, NEPAL
THE BEST KNOWN AND THE EARLIEST OF THE KIND
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Number Words In The Brahmi Script
InscriptionOfAshoka Stambha (249 BCE),Lumbini
No Numerals

• Brahmi Script Devanagari
  Script
• jL
  
• 
  c7-efluo_

read as
read as
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Brahmi Numerals

• The best known Brahmi numerals used around 1st
  Century CE.

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Some Numerals In Some Other Ancient Inscriptions

• First Phase
• Numerals for 4, 6, 50 and 200
• No numeral for 5 but for 50
• Second Phase
• Numerals for 1, 2, 4, 6, 7, 9, 10, 20, 80, 100,
  200, 300, 400, 700 1,000 4,000 6,000 10,000
  20,000.
• No Numeral for 3 but for 300
• Third Phase
• Numerals for 3, 5, 8, 40, 70, , 70,000.

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Hypotheses About The Origin of Brahmi Numerals

• The Brahmi numerals came from the Indus valley
  culture of around 2000 BC.
• The Brahmi numerals came from Aramaean numerals.
• The Brahmi numerals came from the Karoshthi
  alphabet.
• The Brahmi numerals came from the Brahmi
  alphabet.
• The Brahmi numerals came from an earlier
  alphabetic numeral system, possibly due to
  Panini.
• The Brahmi numerals came from Egypt.

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Something MoreAbout Brahmi Numerals

• The symbols for numerals from the Central Asia
  region of the Arabian Empire are virtually
  identical to those in Brahmi.
• Brahmi is also known as Asoka, the script in
  which the famous Asokan edicts were incised in
  the second century BC.
• The Brahmi script is the progenitor of all or
  most of the scripts of India, as well as most
  scripts of Southeast Asia.
• The Brahmi numeral system is the ancestor of the
  Hindu-Arabic numerals, which are now used
  world-wide.

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EPIGRAPHY VERSUS VEDIC MATHEMATICS

• Total lack of Brahmi and Kharoshthi inscriptions
  of the time before 500 BCE
• Much of the mathematics contained within the
  Vedas is said to be contained in works called
  Vedangas.
• Vedic Period Time before 8000 /1900/ BCE etc.
• Vedangas period 1900 1000 BCE.
• Sulvasutras Period 800 - 200 BCE.
• Origin of Brahmi script Around 3rd century BCE
• No knowledge of existence of any written script
  during the Ved- Vedangas period.
• Numerical calculation based on numerals(?) during
  the so-called early Vedic period highly unlikely.

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Numerals in Ancient Nepal
MALIGAON INSCRIPTION
Read as samvat a7 gri- pa 7 d(i)va pka
maha-ra-jasya jaya varm(m)a(nah) and
translated by Kashinath Tamot and Ian Alsop
(In) the (Shaka) year 107 (AD 185), (on) the 4th
(lunar) day of the 7th fortnight of the summer
(season), of the great King Jaya Varman
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WHY DO WE FOCUS ON THE NUMBERS
?
in the Maligaon inscription
in the Changu Narayan inscription

• Earliest of the available number-symbols.
• Concrete evidences of the knowledge of the
  concept of number and the existence of numerals
  and a well-developed number system in Nepal at a
  time (around 2nd century CE) when a civilization
  like Greek civilization worked with very
  primitive or alphabetic numerals
• Beginning of the recorded history of ancient
  Nepal

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Lichhavian Number 1 to 99
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Lichhavian NumbersandMajor Number Systems
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Table I(A)
Table I(B)
Numbers Brahmi Chinese Lichhavian Tocharian
100
200
300
400
500
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Something About Lichhavian Number System

• Lichhavian numerals for 1, 2 and 3 consist of
  vertically placed 1, 2 and 3 horizontal strokes
  like the Chinese 14th century BCE numerals,
  Brahmi numerals of the 1st century CE and
  Tocharian numerals of the 5th century CE.
• The Lichhavian numerals for 1, 2, 3, 40, 80 and
  90 look somewhat similar to the corresponding
  Brahmi numerals.
• There is a striking resemblance between the
  Lichhavian and Tocharian numerals for, 1, 2, 3,
  20, 30, 80 and 90 just like many Tocharian
  albhabet.
• Several other Tocharian numbers appear to be some
  kind of variants of the Lichhavian numbers.
• Each of the three systems uses separate symbols
  for the numbers, 1, 4, 5, 6, 7, 8, 9, 10, 20, 30,
  40, 50, 60, 70, 80, 90, 100, 1000, .

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Something About Lichhavian Number System

• Compound numbers like 11, 12, , 21, 22, , 91,
  92, are represented by juxtaposing unit symbols
  without ligature.
• Hundred symbol is represented by different
  symbols and is often used with and without
  ligature .
• Non-uniformity in the process of forming hundreds
  using hundred symbol and other unit symbols.
• Several variants of numerals are found during a
  period of several centuries.

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Something About Lichhavian Number System

• Each of the three systems uses separate symbols
  for the numbers, 1, 4, 5, 6, 7, 8, 9, 10, 20, 30,
  40, 50, 60, 70, 80, 90, 100, 1000,
• Compound numbers like 11, 12, , 21, 22, , 91,
  92, are represented by juxtaposing unit symbols
  without ligature.
• Hundred symbol is represented by different
  symbols and is often used with and without
  ligature .
• Non-uniformity in the process of forming hundreds
  using hundred symbol and other unit symbols.
• Several variants of numerals are found during a
  period of several centuries.
• Available Lichhavian numbers are lesser than
  1000.
• No reported number lies between 100 and 109, 201
  and 209, , 900 and 909. Numbers for 101, 102, ,
  109, 201, 202, , 209, , 901, 902, , 909 are
  missing

.
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Something About Lichhavian Number System

• Arithmetic of Lichhavian is not known
• Formation of two and three indicate vertical
  addition, while formation of 11, 12, , indicate
  horizontal addition in the expanded form a kind
  of horizontal addition.
• Lichhavian system is additive
• Lichhavian system is a decimal system.
• Liichhavian system is multiplicative
• numeral for 4 attached to symbol for 100 by a
  ligature stands for 400 to be read as 4 times
  1 hundred
• numeral for 5 attached to symbol for 100 by a
  ligature stands for 500 to be read as 5 times
  1 hundred
• numeral for 6 attached to symbol for 100 by a
  ligature stands for 600 to be read as 6 times
  1 hundred,
• Existence of some kind of arithmetic in
  Tocharian number system may provide some clue in
  this direction.

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Something About Lichhavian Number System

• Lichhavian numbers like
• 
  462
• is to be read as
• 4 times hundred or 4 hundreds and 1 sixty
  and 2 ones
• or, 4(100) 1(60) 2(1) 4?100 1 ?
  60 2 ? 1
• and 469
  
  
• is to be read as
• 4 times hundred or 4 hundreds and 1 sixty
  and 1 nine
• or, 4(100) 1(60) 1(9) 4?100 1 ?
  60 1 ? 9.

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• COLLECTION
• CLASSIFICATION
• COMPREHENSION
• MANIPULATION
• MANIFESTATION
• MYSTIFICATION

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MALIGAON INSCRIPTION
Saka 107 (185 AD) or Saka 207 (285 AD)
CHANGU NARAYAN INSCRIPTION
Interpreted by as
Saka 386
Babu Ram (Nepali) 464 AD
Bhagwan Lal (Indian) 329 AD
Levi (French) 496 AD
Flit (British) 705 AD
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SEQUENCIAL GAP AND INCONSISTENCY
One unit symbol attached to the symbol
is being interpreted as 200
Two unit symbols attached to the symbol
is being interpreted as 300
One five unit symbol attached to the symbol
is being interpreted as 500
LIGATURE
One six unit symbol attached to the symbol
is being interpreted as 600
NOT REPORTED SO FAR
Three unit symbols attached to the symbol
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MANIPULATION, MANIFESTATION, MYSTIFICATION
One four unit symbol attached to the symbol
is being interpreted as 400
Two unit symbols attached to the symbol
is being interpreted as 500 also
One five unit symbol attached to the symbol
is being interpreted as 500 also
How to justify such ambiguous interpretations?
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One Possible Solution

• Adopt a uniform system in which the hundred
  symbol attached to one of the first nine numbers
  is considered as the next hundred e.g.,
• as 200
• as 300
• as 500
  
• as 600
• as 700
• 1000 would look like

What is the symbol for 400 ? Naturally, it must
look something like
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Best Solution

• Adopt an internationally accepted uniform system
  in which the hundred symbol attached to one of
  the first nine numbers is interpreted as the
  same hundred as the attached unit number e.g.,
• as 100
• as 200
• as 400
  
• as 500
• as 600
• 1000 would have a new symbol

What is the symbol for 300 ? Naturally, it must
look something like
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CRITICAL ISSUES ?

• The interpretation of the number-symbol
• in the number
• as 100 and as 200 by the epigraphers.
• The interpretation of the number
• in the Changu Narayan inscription as
• the number 386.

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CRITICAL ISSUES ?

• The unfortunate interpretation of the same symbol
• both as the number 300 as well as the number
  500 by the same experts in a large number of
  inscription (as can be seen from the earlier
  slides).
• The hesitation of a great section of epigraphers
  and ancient history of Nepal in rectifying their
  old interpretation of the number on the basis of
  a logical reason and the procedure followed by
  many ancient civilizations in forming such
  numbers.

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WHAT IS TO BE DONE?

• Since Changu Narayan Inscription is considered
  as the starting point for interpolating and
  extrapolating the ancient history and hence that
  of the whole history of Nepal, the date
• inscribed in the inscription and read even today
  as the number 386 needs a careful reexamination
  on the basis of various facts pointed so far.
• We must first of all decide

Whether the Lichhavian number
stands for

a) both 386 and 586 or, b) 386 only but not
for 586 or, c) 586 only but not for 386 or,
d) 286 ?
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WHAT IS TO BE DONE?

• Since the number of kings and the average
  period of the rule of known and unknown kings
  vary from expert to expert, the same process of
  interpolation and extrapolation of available
  information yield totally unacceptable imaginary
  inferences. This is further aggravated by
  interpretations of the Samvat 386 such as
• 329 AD by Bhagwan Indrajit
• 464 AD by Babu Ram Acharya
• 496 AD by Levi
• 705 AD by Flit.
• In such a situation, we have to decide
• Whether we have to change these dates, at
  least, to
• 229 AD, 364 AD, 396 AD and 605 AD ?

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WHAT IS TO BE DONE?

• Collection of information, classification and
  comprehension become meaningless at a time when
  manifestation of unreasonable manipulation takes
  place in the form of obvious mystification as can
  be seen from the following table

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HUNDREDS IN ANCIENT CIVILIZATIONS
Hindu-Arabic Babylonian Chinese Egyptian Greek Roman Nepali
100 200 300 400 500 600
A B
A B
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THANKS