The Indic Mathematical Tradition 6000 BCE To ?

[Guest]

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->India’s Scientific Heritage-XXXI : Architecture
By Suresh Soni

(The book is available with Ocean Books (P) Ltd, 4/19, Asaf Ali Road, New Delhi-110 002.)

THE sphere of our architectural science has been quite comprehensive. It included town planning, buildings, temples, sculpting, fine arts and literally everything. Roads, water supply systems, public bathrooms, drains, different shapes and kinds of buildings, their directions, measurement, land—types of land, nature of materials used for constructions, etc. were contemplated upon in great details in town planning. It was also seen that these were all nature-friendly. Dams, wells, streams, rivers were also considered among water-supply systems.

How minutely and in what detail they studied such things even thousands of years ago!

Mud, bricks, lime, stone, wood, metal, gems, etc. were used for architecture. It was said that each item must be examined thoroughly and used according to its necessity, in construction. We get an idea of how scientific were the measures used to examine each item from the following example:

Sage Bhrigu says that each item used in construction should be tested as per the following criteria:

Varnalingavayovasthah parokshyam cha balabalam

Yathayogyam, yathashaktih Sanskarankarayet Sudheeh.

—(Bhrigu Samhita)

He stresses that all traditions must consider the chroma (colour), gender (property, mark) age (from time of implant till date) condition, along with its strength or weakness and the force that will be exerted on them.

Here chroma means colour. But in architecture, colour is used in accordance with its power to reflect light, e.g. white colour reflects light completely. It is, therefore, said to be an excellent colour.

In the context of construction, a number of books by sages of ancient times, are available such as:

1. Vishwakarma Vastushastra: The first thing that Vishwakarma tells us about construction is “Poorva-bhoomim parikshyet pashchat vaastu prakalpayet” that is, one must first test the land and then start construction there. Vishwakarma further says that one must not construct anything on such a land, which is very rocky, which is hilly, where there are a large number of cracks or crevices, etc.

2. Kashyap Shilp: Sage Kashyap says that a foundation should be dug till the water is seen because after that there are rocks.

3. Bhrigu Samhita: In this, Bhrigu says that before buying land, it must be tested in five different ways, i.e. appearance, colour, taste, smell and touch. He also tells how to do it.

For the construction of a building, he has given a detailed description of the walls, their thickness and the internal arrangements, etc.

The ruins of constructions carried out on the basis of this knowledge still exist even after centuries. Some examples are as follows:

Mohanjodaro (Sind)— The archeological excavations reveal the amazing construction of this wonderful city that dates back to 3000 BC. It was an extremely well-planned city whose houses, roads, etc. had all been made as per geometrical measurements. The roads found here were absolutely straight, running from east to west and from north to south. The other amazing thing is that they crossed one-another at an angle of 90 degrees.

Houses were made in the right proportions; the joints of bricks and the height of walls were equal. There were arrangements for dining room, bathroom and bed room, etc. Besides residential houses, lawns, public places for various programmes, a massive public bathroom is also found which is 11.89 metres long, 7.01 metres wide and 2.44 metres high with two streams of water feeding it. Secondly, the walls were made of something which would remain unaffected by water. Observing this, one feels that those who had built this city must have been very well versed in architectural science.

Dwarka—Dr. S.R. Rao discovered Dwarka during archeological excavations. The ancient traces or ruins that have been found there tell us that Dwarka too, was a well planned city surrounded by a wall. The buildings were made of a stone that would not corrode in sea water. One can see double-storeyed buildings, roads and water arrangements. Copper, brass and some mixed metals have also been found. The mixed metals had 34 per cent zinc. The measurements and shapes of pillars, window panes, etc. used for the buildings, were all calculated mathematically.

Lothal Port (Saurashtra)—The port at Lothal was built around 2500 BC where not just small barges, but even big ships took harbour. Because of the port, a big city had also developed here. Its construction was very similar to that of Mohanjodaro and Harappa. Roads, buildings, gardens, lawns and public buildings were all there. The cremation ground was built a little away from the city dwelling.

Lothal Port was spread 300 metres north-south and 400 metres east-west. It had a 13 metres high wall, made of mud, bricks etc. to keep floods and storms away. This port was far more developed than the Fonetian and Roman ports made later.

Varanasi— Claud Wetley has observed that India’s great architectural heritage has been neglected or disregarded. Many of the modern buildings, despite their magnificence, are unfavourable due to India’s climate, its monsoon winds, rain, water and the perpendicular rays of the sun.

Stone chairs, thick walls, windows slanting towards the floors so that there was free circulation of air, inner courtyards, basements and the construction of a terrace-shaped thatched roof were all prevalent according to India’s traditional architecture. All these things were taken into consideration for the convenience of the community and better health. Varanasi has been accepted or acknowledged as the first organised city of the world. Prof. Bhim Chandra Chatterjee, scholar of hydro-power engineering in ancient India, writes that four generations of Ayodhya’s rulers had devoted their lives to bring the river Ganga from the Himalayas, but finally, the great Bhagirath succeeded. The flow of the Ganga was redirected towards the Bay of Bengal. <b>At Varanasi, it seems to turn towards the north and branches out into two—Varun and Asi, both fed by the Ganga, as they are derived from it.</b> At places where the intensity of water is very high, the excess water can be made to flow out. There is no other example to show such a brilliant way of preventing floods.

http://www.organiser.org/dynamic/modules.p...pid=210&page=15
<!--QuoteEnd--><!--QuoteEEnd-->

There are records to suggest that both the branches of Ganga around Varanasi - Assi-gang and Varun-gang were very much alive and healthy till the medieval times, even down till after British period. Now, thanks to all the water diversions, it is lost.

Sri Tulsidas records:

||samvat solah-sai-asi, <b>assi-gang</b> ke teer
shraavaN shukla saptamee, tulasi tyajat shareer||

{Year is samvat 1680, date is 7th of the shukla paksha of the shraavaN month. On the banks of assi-ganga, Tulasi is leaving (his) body.}

[Guest]

<b>'Indian craftsmen, artisans used nanotech 2000 yrs ago' </b>

Visakhapatnam (PTI): Indian craftsmen and artisans used nanotechnology extensively about 2000 years ago to make weapons and long lasting cave paintings, a Nobel laureate of Chemistry said here.


However, the craftsmen were completely unaware that they were practising carbon nano-techniques that are the most sought after in the current age.

Citing examples of the famous Damascus blades used in the famous sword of Tipu Sultan and Ajanta Paintings, Nobel laureate Robert Curl Jr. said studies have found existence of carbon nano particles in both.

On the sword scientists found carbon nanotubes, cylindrical arrangements of carbon atoms first discovered in 1991 and now made in laboratories all over the world.

"Our ancestors have been unwittingly using the technology for over 2,000 years and carbon nano for about 500 years. Carbon nanotechnology is much older than carbon nanoscience," Curl said at the ongoing 95th Indian Science Congress here.

The 74-year-old scientist from the US shared the 1996 Nobel Prize for Chemistry with Richard Smalley and Harold Kroto for the discovery of the carbon cage compounds, known as fullerenes.

Indian craftsmen used unique smelting techniques to manufacture the Damascus blades which led to nanotisation giving them a unique long-lasting edge.

They had the technology to make wootz steel, a 'high-grade' steel that was highly prized and much sought after across several regions of the world over nearly two millennia.

Wootz also had a high percentage of carbon, which was introduced by incorporating wood and other organic matter during fabrication.

India, for ages, was a leading exporter of this steel which was used to make Persian daggers which were quite popular in Europe centuries ago.

The technique to manufacture wootz declined steadily and has not been in use since the 17th century, Curl said.

http://www.hinduonnet.com/thehindu/holnus/...00801061523.htm

[Bodhi]

about the above report posted by k.ram (which is more important).

This event Indian Science Congress at Vizag was inaugurated a couple of days back by PM, in presence of CM YSR, and Kapil Sibal. These folks must be feeling embarrassed by hearing such stuff from this nobel laureate. In their own speeches, when the congressi morons touched upon the science history briefly, for them it started with Pandit-ji opening up the IIT-s.

In the speech of YSR, he saw no merit in mentioning anything beyond the Nehru family. Pandit ji did that and Indira ji this, Rajiv ji the other, and now Manmohan ji will do the rest. (Does not matter that no body in family has seen a graduate degree in long time) He even ignored the contributions of Sri LB Shastri like the green revolution.

[Guest]

<b>Scientists, pundits converge on Vedic science</b>
ASHOK B SHARMA
http://www.financialexpress.com/news/Scien...cience/258338/2

Posted online: Sunday , January 06, 2008 at 2024 hrs IST

Visakhapatnam, January 6: Scientists and pundits were of the view that essence of scientific truth in ancient Vedic and post-vedic Sanskrit literature was still relevant in modern times. Particularly the prescriptions of life style away from today's consumerism and deep insight into reality can be of help to the society.

The vacuum state described in quantum physics can be compared to the Brahman of Hindu metaphysics.

This was for the first time in the history of the Indian Science Congress that vedic science got recognition and two successive plenary sessions were held on the issue on Sunday. The plenary session on Vedic Science was chaired by the Chancellor of the Tirupati-based Rashtriya Sanskrit University, VR Panchamukhi. The other plenary session on `Brahman of Physics: Interface Between Physics and Vedanta was chaired by SS Rama Rao Pappu of Miami University, US.

An exclusive exhibition was arranged to display scientific insight of Vedic rishi and scholars.

Panchamukhi spoke about the essence of social science like economics, law, political science found in ancient texts. PV Arunachalam from Triupati highlighted the simple formulae of calculation in Vedic mathematics developed by the former Puri Shankaracharya, Swami Bharatiya Krishna Tirth from Atharva Veda mantras. However, VLS Bhimasankaram of Osmania University was of the view that the scientific knowledge contained in many Sanskrit texts cannot to termed as Vedic as these literatures were written in post-Vedic periods.

The keynote speaker of the second plenary session, ECG Sudarshan of the University of Texas said; "Physics deals with existence and change. As per quantum physics, an observer is an active agent in the process of change, while as per Adwaita Vedanta philosophy, he can be the presiding intelligence ie the Brahman of Physics." Sudarshan who is a professor in Physics is also reputed for discussing the relevance of Adwaita Vedanta philosophy in the West. He had been awarded Padma Vibhushan.

P Venugopal Rao from the US-based Emory University said: "the vacuum state described in quantum physics is nothing but Brahman of Hindu metaphysics." SS Rama Rao Pappu of US-based Miami University said; "Newtonian physics is similar to the Hindu Sankhya philosophy."

BD Nageswar Rao of Indiana University said: "the biological molecules cannot be explained without the help of bio-physics. In physics there are four force fields – ultimate substratum – namely gravitational field, electromagnetic field, weak interaction field and strong interaction field. Attempts are being made to find out whether electromagnetic and weak interaction fields are one. Ultimately we have to find out the ultimate substratum of existence."

DVGLN Rao of the University of Massachusetts said: "Aham Brahamasi concept of Hindu metaphysics can hold the key in finding out the source of existence." Lalitha Rao of the same university said, "the universe is a super hologram and we are infinitely inter-connected." She quoted a verse from Isavashya Upanishad which explains in the context the mathematical dictum – "infinity minus infinity is infinity"S Pendyala from the State University of New York said that Arya Bhatt in around 5 th century discovered that planets orbit around the sun in elliptical pathways. He also mentioned about mathematical works of Bhaskaracharya and Lilavati.

[Capt M Kumar]

<!--emo&:ind--><img src='style_emoticons/<#EMO_DIR#>/india.gif' border='0' style='vertical-align:middle' alt='india.gif' /><!--endemo-->
Solve complex math in a minute, the Vedic way

Madhusree Chatterjee
New Delhi, May 8, 2008

It was invented in India, but Vedic mathematics is more popular abroad, says expert Pradeep Kumar who has authored more than 75 books on the subject. He believes it could banish the fear that creeps into the minds of millions of children at the mention of math.

The world of Vedic maths, says Kumar, is mental - doing away with finger counting, carrying over digits, manual calculations and electronic computations.

Kumar, a mechanical engineer and an alumnus from the Indian Institute of Management (IIM)-Bangalore, heads the institute, Magical Methods in Delhi, which works with several schools in the Gulf and Southeast Asian countries to promote Vedic math.

"On an average, I conduct 30 workshops in schools across Asia, Europe and Canada every year. At this moment, I have three projects with schools in Hong Kong, Singapore and Bangkok," Kumar told IANS in an interview. He has 57 centres and more than 100 trained Vedic math teachers on his rolls.

Vedic math, as contained in the Atharva Veda, the last of the four Vedas, is on a revival path after several thousand years. Schools in various Asian nations, Europe and America are falling back on ancient Indian scriptures to crack complex number games that make up present-day mathematics.

But Kumar says it is more popular abroad than in India. "It is recognised by the National Council of Education Research and Training but is yet to become part of the scholastic curriculum in the country," he said.

This when mathematics is a weak link for millions of schoolchildren across India. The subject seems either too dry or as being loaded with numbers.

"The premise is simple. Break down complex numbers into their components of 10s or 100s and calculate mentally. For example, when 38 is added to 46 in conventional math, we carry over one and add it to the top-most digit in the column representing 10 (in the Indian decimal system). The result is 84.

"But in Vedic math, we break down the number into its decimal components. First, we add 30 and 40, the sum of which is 70. And then add 8 and 6, which is 14. The zero stays and one adds strength to the cardinal number in the bigger decimal column. Hence, 7 becomes 8. The end result is 84," Kumar explained, citing an example.

The mathematician has designed several puzzles and intelligent mind games for first-timers in Vedic classrooms.

The games like the Tower of Hanoi, Magic Square, Frogs and Toad and Double Game are based on reasoning and logic. "They improve concentration and reasoning abilities as they initiate rookies into the subject. It does not burden the mind and benefits children psychologically," says Kumar.

Vedic math, interpreted in the modern context in 1965 by seer Bharati Krisna Thirthaji Maharaja in his book "Vedic Mathematics", has 16 "sutras" (formulas) and 13 sub-sutras (smaller theorems) to solve the entire gamut of mathematical problems mentally in less than one-tenth of the time taken to solve them through conventional methods.

In a live demonstration, Kumar added two sets of 24-digit numbers down to its last decimal point in less than five seconds, without a word. "It comes with practice," he said.

The Vedic math expert, who used the technique to solve his mathematical problems in his IIM entrance test (CAT), has designed modules for students trying to crack the IIT and IIM as well as bank jobs and IAS examinations.

[Husky]

<!--QuoteBegin-Capt M Kumar+May 8 2008, 12:45 PM-->QUOTE(Capt M Kumar @ May 8 2008, 12:45 PM)<!--QuoteEBegin--> Solve complex math in a minute, the Vedic way 
[...]
"But in Vedic math, we break down the number into its decimal components. First, we add 30 and 40, the sum of which is 70. And then add 8 and 6, which is 14. The zero stays and one adds strength to the cardinal number in the bigger decimal column. Hence, 7 becomes 8. The end result is 84," Kumar explained, citing an example.[right][snapback]81357[/snapback][/right]<!--QuoteEnd--><!--QuoteEEnd-->That's how I do it. It <i>so</i> explains why many kids in western primary school found addition of two digit numbers (or more) harder. Let's not kid anyone here: I'm not good at maths - beyond first year uni-level at any rate - it's just that they found it harder.

Ooooh, implication of the above: I reinvented the wheel! Does this mean I am clever? <!--emo&:clapping--><img src='style_emoticons/<#EMO_DIR#>/clap.gif' border='0' style='vertical-align:middle' alt='clap.gif' /><!--endemo--> :all-hopeful Or maybe it's just the way our Hindu minds do maths. For subtraction I used my own odd technique: 84-78 would be the opposite of the last two digits subtracted in the opposite direction. That just sounded confusing. An example then: rather than 4-8, do the simpler 8-4 = 4. Now take the 'opposite with respect to 10': opposite of 4 w.r.t 10 = 6.
It takes long to explain but it's easy in my head. When I was young, I found this easier than doing ?4-?8 = '14'-8 = 6.

[Hauma Hamiddha]

The so called "vedic mathematics" is almost a hoax. It has nothing to do with the Atharva Veda as is commonly claimed. The sutras were a recent production of a Shankaracharya of one of the Mathas. "Vedic arithmetic" is vastly exaggerated in terms of their ability to produce quick numerations - a waste of time.

[Capt M Kumar]

<!--emo&--><img src='style_emoticons/<#EMO_DIR#>/sad.gif' border='0' style='vertical-align:middle' alt='sad.gif' /><!--endemo-->
<span style='font-size:14pt;line-height:100%'><span style='font-family:Impact'>The world of Vedic maths, says Kumar, is mental </span></span>-
<span style='font-family:Arial'>doing away with finger counting, carrying over digits, manual calculations and electronic computations.</span>

As far as, I am concerned, doing mental math also known as visual math, makes me faster than any other gadget known to mankind;
so, it rather saves me time and money!

[Bharatvarsh]

Can anyone who has had studied in the vernacular in India tell me if they used the right names when teaching maths, like Pingala Triangle instead of Pascal's Triangle etc.

[Husky]

<!--QuoteBegin-Husky+May 8 2008, 04:47 PM-->QUOTE(Husky @ May 8 2008, 04:47 PM)<!--QuoteEBegin--><!--QuoteBegin-Capt M Kumar+May 8 2008, 12:45 PM--><div class='quotetop'>QUOTE(Capt M Kumar @ May 8 2008, 12:45 PM)<!--QuoteEBegin--> Solve complex math in a minute, the Vedic way
[...][right][snapback]81357[/snapback][/right]<!--QuoteEnd--><!--QuoteEEnd-->[...]
Ooooh, implication of the above: I reinvented the wheel! Does this mean I am clever? <!--emo&:clapping--><img src='style_emoticons/<#EMO_DIR#>/clap.gif' border='0' style='vertical-align:middle' alt='clap.gif' /><!--endemo--> :all-hopeful[right][snapback]81361[/snapback][/right]
<!--QuoteEnd--></div><!--QuoteEEnd--><!--QuoteBegin-Hauma Hamiddha+May 8 2008, 11:42 PM-->QUOTE(Hauma Hamiddha @ May 8 2008, 11:42 PM)<!--QuoteEBegin-->The so called "vedic mathematics" is almost a hoax. It has nothing to do with the Atharva Veda as is commonly claimed. The sutras were a recent production of a Shankaracharya of one of the Mathas. "Vedic arithmetic" is vastly exaggerated in terms of their ability to produce quick numerations - a waste of time.
[right][snapback]81373[/snapback][/right]<!--QuoteEnd--><!--QuoteEEnd-->So I'm back to being not clever? Knew it was too good to be true. Oh well, easy come easy go.

[Guest]

OK..probably not the correct thread to insert this news item, but since the news pertains to Maths, I thought it would be OK. [Mods: - please feel free to shift it to another thread if necessary.]


<!--QuoteBegin-->QUOTE<!--QuoteEBegin--><b>Indian teacher in maths big league</b>

 
Original research in mathematics is rare in India but a schoolteacher inspired by the legendary Srinivasa Ramanujam has won accolades for extending two complex theorems of geometry by his sheer grit and genius.

Shri Ram Gupta's contribution is now being appreciated not only by NCERT, HRD ministry and Limca Book of Records but also by the American Mathematical Society.

Otherwise, Gupta, 59, had been happily teaching at a Kendriya Vidyalaya in Jhansi for over three decades. The teacher's works on Menelaus' theorem and cyclic polygons theorem have led to their extension to bring about approximate generalizations. A theorem is good when its applicability is universal and he always felt there was something amiss in both postulates.

"For 10 years or so, I'd think about these theorems day and night. I felt there was something amiss. This doubt prompted me to keep exploring. I was successful in generalizing them for higher geometric shapes," Gupta told TOI after he had made a presentation of his second theorem at NCERT on Tuesday.

Submitted to the American Mathematical Society on July 24 last year, the work was acknowledged by it as "extension" of Menelaus' and cyclic quadrilateral theorems. The citation by Limca Book says that Gupta "developed original theorems and registered them with the ministry of HRD on April 12, 2005".

For his second theorem, the teacher even coined a new phrase — "interior alternate angles" — in place of "apposite angles" because by using interior alternate angles, the theorem has been proved and generalized for any even-sided cyclic polygon.

Gupta was interested in the study of Menelaus' theorem (named after the Greek mathematician) from the beginning and he was intrigued by the fact that the nature of all rectilinear figures was approximately the same. This led him to develop his postulate. Rectilinear figures refer to triangles and other geometric shapes containing any number of sides. The second theorem, however, came to Gupta more as "random thought" about the symmetric nature of cyclic hexagons (a geometric figure with six sides).

In mathematical parlance, the work done by Gupta can be classified as a major achievement because of their "generalization strength", a crucial aspect of establishing a postulate. His work, which can be used by architects in planning projects, is also the first ever copyright in geometry.

"Mathematical research is languishing in India. Most young people now go for job-oriented courses and basic science suffers. I wish more attention was paid to basic research. This would also help establish the hidden Indian talent on the international stage," Gupta said. 

http://publication.samachar.com/pub_arti...id=2048243<!--QuoteEnd--><!--QuoteEEnd-->

[Bharatvarsh]

Good to see contribution by an Indian, we used to be one of the leading nations in maths, now our contributions have become negligible, part of it has to do with the Indian education system and lack of recognition of giftedness, most of the mathematicians and scientists of note in the last century had to go to US for their research (Khorana, Chandrasekhar etc), until this changes I don't expect any overnight miracles.

[G.Subramaniam]

I am thinking of getting vedic math
there are several books , DVDs can anyone give recommendations

[Pandyan]

<!--QuoteBegin-G.Subramaniam+Jun 5 2008, 08:39 PM-->QUOTE(G.Subramaniam @ Jun 5 2008, 08:39 PM)<!--QuoteEBegin-->I am thinking of getting vedic math
there are several books , DVDs can anyone give recommendations
[right][snapback]82402[/snapback][/right]
<!--QuoteEnd--><!--QuoteEEnd-->

G.Sub, an earlier post from Hauma.

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->The so called "vedic mathematics" is almost a hoax. It has nothing to do with the Atharva Veda as is commonly claimed. The sutras were a recent production of a Shankaracharya of one of the Mathas. "Vedic arithmetic" is vastly exaggerated in terms of their ability to produce quick numerations - a waste of time.<!--QuoteEnd--><!--QuoteEEnd-->

[Bodhi]

<!--QuoteBegin-Bharatvarsh+May 9 2008, 07:04 AM-->QUOTE(Bharatvarsh @ May 9 2008, 07:04 AM)<!--QuoteEBegin-->Can anyone who has had studied in the vernacular in India tell me if they used the right names when teaching maths, like Pingala Triangle instead of Pascal's Triangle etc.
[right][snapback]81403[/snapback][/right]
<!--QuoteEnd--><!--QuoteEEnd-->

BhV, I don't know about other boards, but UP board teaches the mathematical terms in accordance to Indic names. (at least they used to do when I studied. probably they still do). The series, theorems, etc are given Indic names like bodhAyana-prameya for Pythagorean Theorem, srIdharAchArya-samIkaraNa for quadratic equation etc. Terms especially in calculus, algebra and statistics, were skt-based hindi, and very easy to relate to. Learning maths in Hindi was very effective, and I think same should be true for other vernaculars too. Trouble comes when student prepares for JEE etc. in JEE, hindi paper used to be so difficult to even understand the questions. This is more so for physics and chemistry.

[G.Subramaniam]

<!--QuoteBegin-Pandyan+Jun 6 2008, 07:59 AM-->QUOTE(Pandyan @ Jun 6 2008, 07:59 AM)<!--QuoteEBegin--><!--QuoteBegin-G.Subramaniam+Jun 5 2008, 08:39 PM--><div class='quotetop'>QUOTE(G.Subramaniam @ Jun 5 2008, 08:39 PM)<!--QuoteEBegin-->I am thinking of getting vedic math
there are several books , DVDs can anyone give recommendations
[right][snapback]82402[/snapback][/right]
<!--QuoteEnd--><!--QuoteEEnd-->

G.Sub, an earlier post from Hauma.

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->The so called "vedic mathematics" is almost a hoax. It has nothing to do with the Atharva Veda as is commonly claimed. The sutras were a recent production of a Shankaracharya of one of the Mathas. "Vedic arithmetic" is vastly exaggerated in terms of their ability to produce quick numerations - a waste of time.<!--QuoteEnd--><!--QuoteEEnd-->
[right][snapback]82406[/snapback][/right]
<!--QuoteEnd--></div><!--QuoteEEnd-->

Actually I purchased some of these books yesterday and I can vouch for their effectiveness

They use algebra to simplify arithmetic

We learn basic arithmetic in grade 1 or 2
and algebra in grade 8

But we remain stuck with the grade 2 methods for arithmetic instead of moving onto grade 8 methods

I was already fairly good at mental math, and yet, these speeded me up
10X

These books are cheap, for $20, you can get a set by Dalton
Some of these books you can buy used at Amazon for $5

[dhu]

Contributions to Physics from Ancient India

Dr. B. N. Narahari Achar

Although contributions to Mathematics and Astronomy from ancient India are acknowledged, even if grudgingly, contributions to Physics per se are not even mentioned in books on History of Physics. This paper will survey the contributions regarding topics, which are generally considered to be in the domain of Physics. We will examine concepts of space, time, motion, velocity, momentum, action at a distance, rotation, sound etc. We will even present typical example problems in kinematics from a popular text of the 10th century CE. You will be surprised to find Newtonís first law of motion there. Some people even consider the law of gravitation to have been found. Judge for yourself.

[Husky]

http://www.ivarta.com/columns/OL_051210.htm
<!--QuoteBegin-->QUOTE<!--QuoteEBegin--><b>Does no one remember the Hindu contribution to Mathematics?</b>

Whenever I read about the great “Arabic” contribution to Mathematics and Science (often in an apologetic tone of “how could these great people come to such a pass?”) the thing that really upsets me is the complete omission of any reference to the Hindu contribution to mathematics and numbers.

Slightly more than a year ago (Aug ’04), in an article in the Sunday Times www.michaelportillo.co.uk/articles/...press/islam.htm, Michael Portillo, eminent Conservative party leader in the UK and a one-time aspirant to the leadership of the Tory Party, wrote that, “Islam brought back to the West knowledge of architecture, mathematics and astronomy that had been lost during the Dark Ages.”

In response, I wrote, 

“…The phrase “brought back” is at best, condescending and at worse, historically inaccurate.

For this knowledge, which Arab traders brought to Europe (typified in the Arabic numeral system - itself a misnomer, since the Arabs did not invent it but merely acted as the purveyors of this knowledge) was not Islamic or Arabic. In fact much of this knowledge was originally derived from ancient Vedic literature from India and passed through Arab traders and conquests to Middle East and eventually reaching Europe.

To quote from Carl B. Boyer in his "History of Mathematics", “...Mohammed ibn-Musa al-Khwarizmi, ..., who died sometime before 850, wrote more than a half dozen astronomical and mathematical works, of which the earliest were probably based on the Sindhind derived from India. Besides ... [he] wrote two books on arithmetic and algebra which played very important roles in the history of mathematics. ... In this work, based presumably on an Arabic translation of Brahmagupta, al-Khwarizmi gave so full an account of the Hindu numerals that he probably is responsible for the widespread but false impression that our system of numeration is Arabic in origin. ... [pages 227-228]...”.

In a translation of Alberuni ‘s “Indica”, a seminal work of this period (c.1030 AD), Edward Sachau, writes this in his introduction, “Many Arab authors took up the subjects communicated to them by the Hindus and worked them out in original compositions , commentaries and extracts. A favourite subject of theirs was Indian mathematics..." etc.  

Needless to say, the letter never got published.

Then, more recently, while reading the “The World is Flat”, by Thomas L. Friedman www.thomaslfriedman.com/worldisflat.htm, I came across this text in Chapter 11, "The Unflat World" (Pg 405), "As Nayan Chanda, the editor of YaleGlobal Online pointed out to me, it was the Arab-Muslim world that gave birth to algebra and algorithms, terms both derived form Arabic words. In other words, noted Chanda, "The entire modern information revolution, which is built to a large degree on algorithms, can trace its roots all the way back to Arab-Muslim civilization and the great learning centres of Baghdad and Alexandria," which first introduced these concepts, then transferred them to Europe through Muslim Spain.

Dismayed, I wrote the following email to Nayan:

“May I respectfully point out that is not historically accurate and continuing research is providing evidence that the roots of the so-called Arab contribution to Mathematics and Science were further east in the lands of India and in the works of Indian mathematicians and scholars from several centuries ago.”

“I hope that you will re-consider your views in the light of these excerpts and a significant body of research that is now publicly available on this subject. I would be more than happy to provide more details if you wish.”

No acknowledgement was expected and none was received. I wanted to copy Thomas Friedman on it but could not find his contact details on his website – the only email address was that of his literary agent and PR agency.

This apparently widespread misunderstanding and ignorance - about the Hindu contribution to the number system and sciences - prompted me to dig deeper. Here is what I found:

From an online research piece on Al-Khwarizmi and his work (by Shawn Overbay, Jimmy Schorer, and Heather Conger) http://www.ms.uky.edu/~carl/ma330/projec...hwa21.html 

“ Al-Khwarizmi wrote numerous books that played important roles in arithematic and algebra. In his work, De numero indorum (Concerning the Hindu Art of Reckoning), it was based presumably on an Arabic translation of Brahmagupta where he gave a full account of the Hindu numerals which was the first to expound the system with its digits 0,1,2,3,....,9 and decimal place value which was a fairly recent arrival from India. Because of this book with the Latin translations made a false inquiry that our system of numeration is arabic in origin. The new notation came to be known as that of al-Khwarizmi, or more carelessly, algorismi; ultimately the scheme of numeration making use of the Hindu numerals came to be called simply algorism or algorithm, a word that, originally derived from the name al-Khwarizmi, now means, more generally, any peculiar rule of procedure or operation. 

Interestingly, as the article notes, “The Hindu numerals like much new mathematics were not welcomed by all. In 1299 there was a law in the commercial center of Florence forbidding their use; to this day this law is respected when we write the amount on a check in longhand (ernie.bgsu.edu).”

From a very well-researched online article, “Numbers: Their History and Meaning” http://home.c2i.net/greaker/comenius/9899/...rals/india.html

“It is now universally accepted that our decimal numbers derive from forms, which were invented in India and transmitted via Arab culture to Europe, undergoing a number of changes on the way. We also know that several different ways of writing numbers evolved in India before it became possible for existing decimal numerals to be marred with the place-value principle of the Babylonians to give birth to the system which eventually became the one which we use today.

Because of lack of authentic records, very little is known of the development of ancient Hindu mathematics. The earliest history is preserved in the 5000-year-old ruins of a city at Mohenjo Daro, located Northeast of present-day Karachi in Pakistan. Evidence of wide streets, brick dwellings an apartment houses with tiled bathrooms, covered city drains, and community swimming pools indicates a civilisation as advanced as that found anywhere else in the ancient Orient.



These early peoples had systems of writing, counting, weighing, and measuring, and they dug canals for irrigation. All this required basic mathematics and engineering.

And later in the article, “The special interest of the Indian system is that it is the earliest form of the one, which we use today. Two and three were represented by repetitions of the horizontal stroke for one. There were distinct symbols for four to nine and also for ten and multiples of ten up to ninety, and for hundred and thousand.”



and further “…Knowledge of the Hindu system spread through the Arab world, reaching the Arabs of the West in Spain before the end of the tenth century. The earliest European manuscript, which came from the Hindu numerals were modified in north-Spain from the year 976.” And finally an important point for those who maintain that the concept of zero was also evident in some other civilisations: “Only the Hindus within the context of Indo-European civilisations have consistently used zero.”

Fortunately, online encyclopaedias came across as less biased and more open in acknowledging the true source of the “Arabic” number system. For example, from MSN Encarta http://encarta.msn.com/encyclopedia_761578...athematics.html 

“The system of numbers that we use today, with each number having an absolute value and a place value (units, tens, hundreds, and so forth) originated in India. Mathematicians in India also were the first to recognize zero as both an integer and a placeholder. When the Indian numeration system was developed is not known, but digits similar to the Arabic numerals used today have been found in a Hindu temple built about 250 bc. 

In the 5th century Hindu mathematician and astronomer Aryabhata studied many of the same problems as Diophantus but went beyond the Greek mathematician in his use of fractions as opposed to whole numbers to solve indeterminate equations (equations that have no unique solutions). Aryabhata also figured the value of “P” (pi)  accurately to eight places, thus coming closer to its value than any other mathematician of ancient times. In astronomy, he proposed that Earth orbited the sun and correctly explained eclipses of the Sun and Moon. 

The earliest known use of negative numbers in mathematics was by Hindu mathematician Brahmagupta about ad 630. He presented rules for them in terms of fortunes (positive numbers) and debts (negative numbers).



…The best-known Indian mathematician of the early period was Bhaskara, who lived in the 12th century. Bhaskara supplied the correct answer for division by zero as well as rules for operating with irrational numbers. Bhaskara wrote six books on mathematics, including Lilavati (The Beautiful), which summarized mathematical knowledge in India up to his time, and Karanakutuhala, translated as “Calculation of Astronomical Wonders.”

The reality is that the so-called “Arab” contribution to mathematics was substantially built on prior knowledge of the Hindus and the Greeks and while the Greek influence and origins are frequently acknowledged, the Hindu contribution is very rarely mentioned.

We need to spread awareness about this and try and establish the facts whenever an opportunity arises – unless we do that, this “history” will be lost and become so little-known and distant as to become a myth.

Talking of forgotten Indian contribution to sciences and arts, here is another example of a glaring error in a recent news story in <b>“TIME” Magazine</b> and an email I sent in response www.time.com/time/europe/magazine/a...1129488,00.html

“May I point out two inaccuracies in your recent news story on an exhibition on Arab Science in Paris titled, “Ahead of Their Time” (Time Magazine, Nov 21, ’05; Pp48-49) by Ann Morrison?

In a paragraph about the Arab’s interest in astronomy, Ann writes, “…Though the Arabs built many observatories during the Golden Age, not many survived. But viewers can see current images of two of these amazing outdoor structures in the Indian cities of Delhi and Jaipur…”

The observatories that Ann refers to in this paragraph were not built by Arabs but by the Hindu ruler Sawai Raja Jai Singh between 1724-1730 and were amongst the five that he built in Northern India (the other three were at Varanasi, Ujjain and Mathura) and are called Jantar Mantar (actually “Yantra Mantra”, yantra for instrument and mantra for formula).

The observatory in Delhi has also been depicted in a postage stamp and was the logo of the 1982 Asian Games, held in New Delhi, India.

To call them examples of Arab interest in the sciences is inaccurate and misleading.

In a later paragraph which details the interest of Arab scholars in astrology, Ann writes, “…Another manuscript illustration from 17th century India, Astrologers working on a Nativity”, shows a procession of music makers and gift bearers wending their way through palace walls toward a newborn who would grow up to be the 14th century warrior Tamerlane...”

Again, this is an example of Indian art (and Indian interest in astrology) rather than having anything to do with Arabs or Arab art. Tamerlane himself was not an Arab king but from Central Asia (as were the Mughals).

As usual, I received neither an acknowledgement nor a response. 

For those of you who would like to read more:

Here’s Alberuni on Pre-Islamic India's Science, Math, and Architecture http://www.infinityfoundation.com/mandala/...umar-v_math.htm

And an interesting article on the origin of the decimal system
answering-islam.org.uk/Science/math.html

B Shantanu<!--QuoteEnd--><!--QuoteEEnd-->(That last link, answering-islam, is a christo site.)

"This apparently widespread misunderstanding and ignorance about the Hindu contribution..." is the conclusion Shantanu draws from the eternally repeating pattern of them not taking his verifiable facts and printing retractions or at least addendums.

But he and others ought to know the real reasons TIME (famous for marking Kashmir as specifically independent from India on their map of the country) and the motivated lying by other christowestern publishers and 'researchers'/'scholars'. The idea is to negate Hindu civilisation. Why do Hindus think any real researcher or journalist or writer would purposefully avoid sharing a discovery that may negate some previous misconceptions they had and therefore not publish what they have now learnt to be the facts? Hindus need to think about why anyone would not publish truths once they learnt about it.

To assume it was all 'some sort of benign mistake' is just people's own delusion. The sooner we wake up to this, the sooner we will take our matters into our own hands and stop letting the liars lie with impunity, stop letting them try to prevent our learning/teaching our Samskritam, stop letting them try to elect/crown people in our country, stop letting them lie and lecture us about "religious freedom" and "racism" ( <!--emo&:blink:--><img src='style_emoticons/<#EMO_DIR#>/blink.gif' border='0' style='vertical-align:middle' alt='blink.gif' /><!--endemo--> what the? - don't ask. Only possessing the oxymoron known as 'christologic' will allow one to understand <i>that</i> - and does one really want to be possessed by christologic?)

[Pandyan]

It seems like most of the ancient mathematicians were Brahmin, are there examples of other castes being mathematicians?

[Husky]

<!--QuoteBegin-Pandyan+Jun 19 2008, 11:16 PM-->QUOTE(Pandyan @ Jun 19 2008, 11:16 PM)<!--QuoteEBegin-->It seems like most of the ancient mathematicians were Brahmin, are there examples of other castes being mathematicians?[right][snapback]83046[/snapback][/right]<!--QuoteEnd--><!--QuoteEEnd-->(Insert: there were also Jaina mathematicians in our history.)

Don't know the answer to your question. But just to state the obvious: any Hindu's accomplishments are <i>all</i> Hindus' accomplishments. They were meant for all Hindus.