Binomial Triangle Computer Binary System By Pingala Hinduism

Recently there was a News item that a Scientist has stated that Mythology is to be differntiated from Science and the attempt of the Government to include ‘Pseudo Science’ into Indian Education System.


He was speaking on ‘IIsc debunked Vimanas Theory.


He also observed that ‘the people who say that Hinduism/Vedas have said this before, why do they not say this before the facts are discovered by Science?What they say as facts from the Vedas can not be verified by experiment now”(the  quote is not verbatim, i shall get it shortly).


I shall be posting a rebuttal to this shortly.


Be that as it may, let me reproduce something from the Vedic Period on Binomial System and Binary system, that is used for Modern Computing.


Ancient Indians used Mathematics extensively and relied on it so heavily that Indian Logic, Philosophy,Hindu Rituals and the Sanskrit Language have strong Mathematical base.


Meters, called Chandas are used in Prayers, literary works have a strict Mathematical base.


Pingala, younger brother of Panini, the Sanskrit grammarian, has devised Chanda Shastra that deals with these Meters.


He  is dated to 2 BC, may be earlier.


Another Legend has it that he is the younger brother of Patanjali, who wrote the Yoga Sutra.


This assigns Pinagala to 4 BC.


Each number in the triangle is the sum of the ...
Each number in the triangle is the sum of the two directly above it. (Photo credit: Wikipedia)



The Chandaḥśāstra presents the first known description of a binary numeral system in connection with the systematic enumeration of meters with fixed patterns of short and long syllables.The discussion of the combinatorics of meter corresponds to the binomial theorem. Halāyudha’s commentary includes a presentation of the Pascal’s triangle(called meruprastāra). Pingala’s work also contains the Fibonacci numbers, called mātrāmeru.


Use of zero is sometimes mistakenly ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, while Pingala used short and long syllables. As Pingala’s system ranks binary patterns starting at one (four short syllables—binary “0000”—is the first pattern), the nth pattern corresponds to the binary representation of n-1, written backwards. Positional use of zero dates from later centuries and would have been known to Halāyudha but not to Pingala.




Formation of Binomial Triangle.Pingala Triangle.



The Importance given to 2 by Pingala: Pingala in his rules to Sanskrit prosody has given undue importance to the number 2. Typically, he lays down that, Any power of two throughout divisible by two is equal to two raised to the power of two representing the number of twos the first power is divisible by two�, i.e, 216 = 224, 232 = 225, 264 = 226 and so on (VIII.407).




In grouping heavies and lights, Pingala adopts a unique method.




If we take Heavy = H and Light = L, for two syllables, we get the combination, as follows:




  1. 1H
  2. 1L




There are two combinations.




For 3 syllables, we get,




  1. 3 H
  2. 2H, 1L
  3. 1H, 2L.
  4. 3L.




There are  four combinations.




For 4 syllables, we get,




  1. 4H
  2. 3H, 1L
  3. 2H, 2L
  4. 1H, 3L
  5. 4L.




There are eight combinations.




For 5 syllables, we get,




  1. 5H
  2. 4H, 1L
  3. 3H, 2L.
  4. 2H, 3L
  5. 1H, 4L
  6. 5L




There are sixteen combinations.




Thus, this is the formation of Binomial Numbers, Triangle and Series. They are explained as follows:




(a + b)o = 1

(a + b)1 = a + b

(a + b)2 = a2 + 2ab + b2

(a + b)3 = a3 + 3a2b + 3ab2 + b3

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

(a + b)5 = a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5

(a + b)= a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + b6



1  1

1   2   1

1  3    3   1

1   4   6   4   1

1 10  5   5  10  5  1

1   6  15  20   15    6   1

(a + b)n   = an + [n!/1!(n-1)!] a(n-1) b + [n(n-1)/2!(n-2)!] an(n-1) b2 + [n(n-1)(n-2)/3!(n-3)!] an(n-1)(n-2) b3 + [n(n-1)(n-2)(n-3)/4!(n-4)!] an(n-1)(n-2)(n-3) b4 +��+ bn




This has been explained in the context of prosody and similar exposition has been made in Vedic literature about the chanting of mantras with time scale. However, the mathematical significance has to be noted here. This Binomial triangle can rightly be called Pingala Triangle and the series Pingala series. Indian mathematicians have identified the series and arranged the numbers in the form of a pyramid, which they called asMeruprasthana and depicted as follows:




1     1

1     2     1

1    3     3    1

1   4    6    4     1

1    5    10   10  5    1

1   6    15   20   15    6   1

1   7    21    35    35   21    7    1

1   8    28   56    70   56   28   8    1

1   9    36   84   126   126   84   36   9   1

1  10   45   120  210  252  210  120  45  10   1

1  11  55  165  330  462  462  330  165  55   11  1

1   12   66  220  495  792   924  792   495  220  66  12   1






























The basis of writing numbers can be easily explained:




1. Write one in the first square. 1
2. Draw two squares below, write 1 , 1 1 1
3. Draw three squares, write 1, 1 in the first and last squares. 1 2 1


Add the adjacent numbers of the above row and write intermediate numbers i.e, 1+1=2.


4. 1, 1+2=3, 3+1=3, 1 1 3 3 1
 5. 1, 1+3=4, 3+3=6, 3+1+4, 1 1 4 6 4 1




Like, this, the squares can be continued with added numbers. The following Pingala Triangle is formed for 12 layers and it is mentioned as Meru Prasthana in the literature.










































Binary system explained.


0 0 0 0 numerical value = 1
1 0 0 0 numerical value = 2
0 1 0 0 numerical value = 3
1 1 0 0 numerical value = 4
0 0 1 0 numerical value = 5
1 0 1 0 numerical value = 6
0 1 1 0 numerical value = 7
1 1 1 0 numerical value = 8
0 0 0 1 numerical value = 9
1 0 0 1 numerical value = 10
0 1 0 1 numerical value = 11
1 1 0 1 numerical value = 12
0 0 1 1 numerical value = 13
1 0 1 1 numerical value = 14
0 1 1 1 numerical value = 15
1 1 1 1 numerical value = 16

Other numbers have also been assigned zero and one combinations likewise.

Pingala’s system of binary numbers starts with number one (and not zero). The numerical value is obtained by adding one to the sum of place values. In this system, the place value increases to the right, as against the modern notation in which it increases towards the left.

The procedure of Pingala system is as follows:

Divide the number by 2. If divisible write 1, otherwise write 0.
If first division yields 1 as remainder, add 1 and divide again by 2. If fully divisible, write 1, otherwise write 0 to the right of first 1.
If first division yields 0 as remainder that is, it is fully divisible, add 1 to the remaining number and divide by 2. If divisible, write 1, otherwise write 0 to the right of first 0.
This procedure is continued until 0 as final remainder is obtained.
Example to understand Pingala System of Binary Numbers :

Find Binary equivalent of 122 in Pingala System :

Divide 122 by 2. Divisible, so write 1 and remainder is 61. 1
Divide 61 by 2. Not Divisible and remainder is 30. So write 0 right to 1. 10
Add 1 to 61 and divide by 2 = 31.
Divide 31 by 2. Not Divisible and remainder is 16. So write 0 to the right. 100
Divide 16 by 2. Divisible and remainder is 8. So write 1 to right. 1001
Divide 8 by 2. Divisible and remainder is 4. So write 1 to right. 10011
Divide 4 by 2. Divisible and remainder is 2. So write 1 to right. 100111
Divide 2 by 2. Divisible. So place 1 to right. 1001111
Now we have 122 equivalent to 1001111.

Verify this by place value system : 1×1 + 0×2 + 0×4 + 1×8 + 1×16 + 1×32 + 1×64 = 64+32+16+8+1 = 121
By adding 1(which we added while dividing 61) to 121 = 122, which is our desired number.
In Pingala system, 122 can be written as 1001111.

Though this system is not exact equivalent of today’s binary system used, it is very much similar with its place value system having 20, 20, 21, 22, 22, 23, 24, 25, 26 etc used to multiple binary numbers sequence and obtain equivalent decimal number.

Reference : Chandaḥśāstra (8.24-25) describes above method of obtaining binary equivalent of any decimal number in detail.
These were used 1600 years before westerners/arabs copied binary system from India through trade and invasion.

We now use zero and one (0 and 1) in representing binary numbers, but it is not known if the concept of zero was known to Pingala— as a number without value and as a positional location.Pingala’s work also contains the Fibonacci number, called mātrāmeru, and now known as the Gopala–Hemachandra number. Pingala also knew the special case of the binomial theorem for the index 2, i.e. for (a + b) 2, as did his Greek contemporary Euclid..


This article is based on the research work of Dr.K.V.Ramakrishna Rao and material from the site’s Link provided second at the end of the Post.


Cell Division under New Microscope Video

One of the mysteries of Life is the division of Cells.

Viewing it under Microscope is an experience.

Now a New Microscope has been developed an it can provide interesting 3 D viewing.

The microscope uses a technique called lattice light-sheet microscopy, which involves scanning a cell with ultra-thin sheets of light. This process allows scientists to collect high-resolution images while minimizing light damage to the cells. The research was described in a paper published online in the journal Science on Oct. 24.

“There are many cells you could look at forever in 3D,” Dr. Eric Betzig, a physicist, inventor, and engineer at the institute who developed the microscope, said in a written statement. “We know what the microscope can offer in terms of the imaging, but I think there are a lot of applications we haven’t even thought of yet.”

Watch the Video.

News Source.

Scientists Admit Fake Study Papers

Often I come across ‘scientific studies’ claiming outrageous and down right ridiculous statements on many disciplines,including social sciences.


One would claim that a woman’s sexual references can be predicted by her nail polish colors!


And the father of all this is Sigmund Freud, who blamed everything under the Sun for one’s behavior,especially one’s parents.


If you are aggressive, it is because of gregarious parents:if you are timid, it is because of retiring parents.


If you are a pervert, your parents are responsible.


But never You, for your actions or for what you are!


So much for these ‘Scientific studies!’


I have posted some articles on this.


Now read more news on this.

Scientist admits faking Study.jpg
Scientist admits faking Study.


preliminary investigative report issued on Monday by Tilburg University has concluded that dozens of research papers authored and co-authored by Stapel contain fabricated data.

“We have some 30 papers in peer-reviewed journals where we are actually sure that they are fake, and there are more to come,” says Pim Levelt, chair of the committee that investigated Stapel’s work. If all of these papers are withdrawn, Stapel’s will become one of the worst cases of scientific misconduct in history.

Stapel is the researcher behind a number of eye-catching studies which, prima facie, seem to offer provocative insights into human nature. His research topics range from the effects of beauty product ads on consumer self-esteem, to how urban decay (like littered streets) promote stereotyping and discrimination — the latter being a study we reported on here at io9.

Whether these studies are included in the 30+ papers known to contain fraudulent data remains to be seen. Tilburg University has yet to provide a list of which studies contain fudged results, though Stapel’s paper on the tie between urban decay and discrimination, published in April in the journal Science, has already been flagged with an expression of concern by the journal’s publishers.

Stapel is believed to have acted alone, deceiving colleagues, collaborators, and even PhD candidates for years by providing them with fictitious data. Given Stapel’s prominence within the field of social psychology, (not to mention the sheer volume of publications already identified as tainted), it’s safe to say that the effects of his outing will be far-reaching…..

otably, none of these mention anything about science, fact-finding, or statements about converging upon truth. (Note, in the past I’ve gone so far as to suggest that even the process of citing specific papers is biased and flawed, and that we would be better off giving aggregate citations of whole swathes of the literature.)

The second article takes almost an entirely economic, cost-benefit perspective of peer-review again focused on publishing results in journals. Only toward the end does the author directly address peer-review’s purpose in science by saying:

…[T]he most important question is how accurately the peer review system predicts the longer-term judgments of the scientific community… A tentative answer to this last question is suggested by a pilot study carried out by my former colleagues atNature Neuroscience, who examined the assessments produced by Faculty of 1000 (F1000), a website that seeks to identify and rank interesting papers based on the votes of handpicked expert ‘faculty members’. For a sample of 2,500 neuroscience papers listed on F1000, there was a strong correlation between the paper’s F1000 factor and the impact factor of the journal in which it appeared. This finding, albeit preliminary, should give pause to anyone who believes that the current peer review system is fundamentally flawed or that a more distributed method of assessment would give different results.

I strongly disagree with his final conclusion here. A perfectly plausible explanation for this result would be that scientists rate papers in “better” journals higher because they’re published in journal perceived to be better. This would appear to be a source of bias and a major flaw of the current peer-review system. Rather than giving me pause as to whether the system is flawed, one could easily interpret that result asproof of the flaw.

The most common response that I encounter when speaking with others scientists about what they think peer-review is for, however, is some form of the following:

Peer-review improves the quality of published papers.

I’m about to get very meta here, but post-doc astronomer Sarah Kendrew recently wrote a piece in The Guardian titled, “Brian Cox is wrong: blogging your research is not a recipe for disaster”.


More than 120 computer-generated “gibberish” research papers are being removed from the archives of scientific journal publishers Springer and the Institute of Electrical and Electronic Engineers (IEEE) after a French computer scientist determined the papers were fakes.

The bogus research papers, it turns out, were created by an automated word generation program that can string random, seemingly sophisticated words together in plausible English syntax.

Scientific papers, especially those dealing with computer science and mathematics, as these fake papers were, feature reams of sophisticated jargon. Even legitimate papers can seem like gibberish to an unfamiliar reader.


Ocean Beneath Earth Hinduism Science Confirms

The description of the Universe is elaborate in Hindu Puranas.


It is the grammar of the Puranas that it must contain the description of the Evolution, Growth and Dissolution of the Universe.


All the Puranas contain this and these description appear in the beginning of the Puranas.


Though there are variations can be found in respect of some incidents relating to Hinduism, there is no difference among them in describing the Universe.


On the description of the Earth, following is the abstract.




Google Map Looks into the Sea.Image.jpg.
Google Map Looks into the Sea.Image credit.×471.jpg

The Land Mass and Seas described in the Vishnu Purana is as under.

1.Jambu Dweepa, surrounded by Salt Sea.(lavana)

2.Palaksha Dwipa, Surrounded by Sugar Cane Juice.(Ikshu)

3.Salmali Dwipa, surrounded by a Sea of Wine(Sura)

4.Kusa Dwipa, surrounded by a sea of Clarified Butter,Ghee(Sarpi)

5Krauncha Dwipa , surrounded by a sea of Curds(Durghda)

6.Pushkara is surrounded by a Sea of Fresh Water(.

This makes Five Continents, all of them surrounded by Water.’


Significance sugar cane Juice etc is unclear.


Now look at the latest study and image of the earth as it was Millions of years ago.”


Now. what Science has found now is,


A reservoir of water three times the volume of all the oceans has been discovered deep beneath the Earth’s surface. The finding could help explain where Earth’s seas came from.

The water is hidden inside a blue rock called ringwoodite that lies 700 kilometres underground in the mantle, the layer of hot rock between Earth’s surface and its core.

The huge size of the reservoir throws new light on the origin of Earth’s water. Some geologists think water arrived in comets as they struck the planet, but the new discovery supports an alternative idea that the oceans gradually oozed out of the interior of the early Earth.

“It’s good evidence the Earth’s water came from within,” says Steven Jacobsen of Northwestern University in Evanston, Illinois. The hidden water could also act as a buffer for the oceans on the surface, explaining why they have stayed the same size for millions of years.

Pinging the planet

Jacobsen’s team used 2000 seismometers to study the seismic waves generated by more than 500 earthquakes. These waves move throughout Earth’s interior, including the core, and can be detected at the surface. “They make the Earth ring like a bell for days afterwards,” says Jacobsen.


By measuring the speed of the waves at different depths, the team could figure out which types of rocks the waves were passing through. The water layer revealed itself because the waves slowed down, as it takes them longer to get through soggy rock than dry rock.

Jacobsen worked out in advance what would happen to the waves if water-containing ringwoodite was present. He grew ringwoodite in his lab, and exposed samples of it to massive pressures and temperatures matching those at 700 kilometres down.”


Mathematics Principle Of Threes Confirms Hinduism

Recent Mathematical Study of Numbers and Quantum has proved the Hinduism‘s Theory of Number Three.


Hinduism ascribes special status to Number Three.


Quantum Principle of Three.Image.jpg.
Harald Ritsch/IQOQI Efimov trimers are states of matter that theoretically come in an infinite range of sizes. Experimentalists recently observed consecutive trimers, verifying the strange theory.


Fundamental principles of Universe is three-Creation,Sustenance and Destruction(Hiding and Benevolence,Thirodhaana and Anugraha are implied in

these three.


The Three principles of Evolution of the Universe.


Purusha, Prakriti.


Implied in this, which is not often noticed, is the ‘Sparsa Matra’, between these two.



Sparsa is loosely defied as touch.


It is more than touch,more than a touch without touching, difficult to translate the Sanskrit word.


The Purusha and Prakriti are two entities evolves only after Sparsa Matra, just the moment after touching.


So along with Purusha and Prakriti, this makes the Trinity of Principles facilitating  Evolution.


Three Gunas, Dispositions, Sathva, Raja, and Tamas.


The trinity of Hindu Pantheon, Brahma, Vishnu an Rudra.


The Three Yogas,


Jnana Yoga,


Karma Yoga,


Bhakthi Yoga.


Pranava consists of Three letters.






Three layers of Nature, Light, Fire and Darkness.


States of Being-Immanent, Transcendent and Absolute.


Periods of The Day, Morning, Noon and Evening.


Three Primary worlds Bur, Bhuvah, Suvah.


Three breaths, Poorakam(inhaling0, Rechakam(exhaling) and Kumbhakam(retention).


The triangle of female genital organ,


The Three synchronization, Thoughts, Words an Deeds.


The mark(3) worn By shaivites and Vaishnavas(three lines on the forehead.


The three strands of Upaveeda.


Three primary Stages of life, Asrama-Brahmacharya, Gruhastha and Vanaprastha-Sanyasa can be practiced in any of the three.


The importance of three is elaborately explained thus.


Now Mathematical research has proved the Principle of three.


“In 1970, Vitaly Efimov was manipulating the equations of quantum mechanics in an attempt to calculate the behavior of sets of three particles, such as the protons and neutrons that populate atomic nuclei, when he discovered a law that pertained not only to nuclear ingredients but also, under the right conditions, to any trio of particles in nature.


While most forces act between pairs, such as the north and south poles of a magnet or a planet and its sun, Efimov identified an effect that requires three components to spring into action. Together, the components form a state of matter similar toBorromean rings, an ancient symbol of three interconnected circles in which no two are directly linked. The so-called Efimov “trimer” could consist of a trio of protons, a triatomic molecule or any other set of three particles, as long as their properties were tuned to the right values. And in a surprising flourish, this hypothetical state of matter exhibited an unheard-of feature: the ability to range in size from practically infinitesimal to infinite.

“It’s a pretty wild idea,” said Randy Hulet, a physics professor at Rice University in Houston. “You get this infinite series of molecules.”

Efimov had shown that when three particles come together, a special confluence of their forces creates the Borromean rings effect: Though one is not enough, the effects of two particles can conspire to bind a third. The nesting-doll feature — called discrete scale invariance — arose from a symmetry in the equation describing the forces between three particles. If the particles satisfied the equation when spaced a certain distance apart, then the same particles spaced 22.7 times farther apart were also a solution. This number, called a “scaling factor,” emerged from the mathematics as inexplicably as pi, the ratio between a circle’s circumference and diameter.

“It’s like layers of an onion,” Hulet said. “You see molecules at one layer. Peel the layer away, and you see that there’s a molecule there 22.7 times smaller. Every time you peel away a layer, you find another molecule.”..



Rudi Grimm and his group at the University of Innsbruck in Austria managed to create an Efimov trimer for the first time in 2006, building it from a trio of cesium atoms cooled to 10-billionths of a degree above absolute zero. It was a long-awaited triumph for Efimov, who, Grimm recalled, became very emotional when he heard the news.

But the result did not decisively prove the theory.

“With just one example, it’s very difficult to tell if it’s a Russian nesting doll,” said Cheng Chin, a professor of physics at the University of Chicago who was part of Grimm’s group in 2006. The ultimate proof would be an observation of consecutive Efimov trimers, each enlarged by a factor of 22.7. “That initiated a new race” to prove the theory, Chin said.

Eight years later, the competition to observe a series of Efimov states has ended in a photo finish. “What you see is three groups, in three different countries, reporting these multiple Efimov states all within about one month,” said Chin, who led one of the groups. “It’s totally amazing.”


Quoted Text and Image Citation Credit.


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