The Sanskrit verse for the value of pi
hindufocus.wordpress.com
hindufocus.wordpress.com
There are many alternate views on the origin of this verse itself. The one I find most believable, is that this is a fairly recent fabrication [1]. There is nothing to suggest that we had this level of accuracy that far back. For instance, how was this arrived at? Methods? None. But much later, _in the 5th century AD_, Aryabatta used a simpler expansion for which we actually have some evidence.
Just like most other religious texts, the Vedas don't stand up to modern science and rigor. You'll see plenty of revivalist material on the web; many here in India hold it in high regard. In my view, its lasting significance has been the role in dividing India into castes. From the priests to the serfs, a system that continues to hurt even today.
[1]: http://vedicmathmyth.quora.com/The-misconceptions-of-the-poe...
The Quora blog you linked has issues with terminologies and timelines of this specific "Vedic Mathematics" book - such as calling these mental calculation techniques and tricks as Vedic even though there are no references to them in Vedas[2]. This is more of a political matter ;) And, it's already pointed out in the article linked by OP[3]. I'm quoting it here:
It must be pointed out that these sutras given by Tirtha Maharaja are created by the author himself, as stated in the introduction to his book, "Vedic Mathematics" (published posthumously) and are therefore not actually Vedic.
These mathematical sutras are Vedic only in the sense that they are inspired by the Vedas in the mind of one dedicated to the Vedas. Thus the title "Vedic Mathematics" is not correct.
[0]http://en.wikipedia.org/wiki/Katapayadi_system
[1]http://en.wikipedia.org/wiki/Vedic_Mathematics_%28book%29
[2]http://en.wikipedia.org/wiki/Bharati_Krishna_Tirthaji#Mathem...
[3]http://www.vedicsciences.net/articles/vedic-mathematics.html
/dividing india into castes by religion/ -- This is completely humans fault. What Bhagavadgita explained were the variety of things people do to get tired/frustrated in this place and get enlightened. Look at the meaning of division without the caste mirror. You see the same set of things happening everywhere in the world. a) People who are good at protecting others b) People who are good at taking care of the mess created by others c) people who are good at providing things to others c) People who are good at understanding things and sharing the knowledge with society. At some point, this whole thing got misunderstood, misinterpreted and exploited for ones selfishness. We are paying the price now. But, the same things explained still holds true everywhere in the world.
Yes, that's what modern science refers to, the thought processes we use to determine what's true. Going back a while, Aristotle "reasoned" that women had less teeth than men. Such reasoning isn't accepted these days. The same science is what rejects most other religious texts - it does not stand up to current requirements of reason.
Here is a difference i have observed between science/religion. In religion, we try to reject things rather than try to find true meaning (via thought process or practice). Which is really difficult in this time as "i can go buy pizza in 5 mins" kinda mindset.
One more way we use reasoning is "if i didn't experience (via the senses) it doesn't exist". It takes time, really long time for the people (in tech terminology scientists, in religion terminology saints) to understand the universe and give us peace. Both religion/science are true. Religion talks about things which can't be experienced by our senses, but gain peace. While Science talks about the other, where the gain seem to be human advancement (to where ?). This may sound confusing at beginning, as it was to me. But, if we go through the same struggle of finding the truth, we will get it.
The way we approach and do science has evolved drastically ( http://en.wikipedia.org/wiki/History_of_scientific_method ). For example empirical falsifiability which is one of the primary tenant of modern science is less than 100 years old, but forms an essential part on how we do science now a days.
Parent comment's point being; while we may be trying to understand the same principle/phenomena, not only the data available to thinkers that time was very sparse compared to the present; but also the level of rigour applied was of significantly lower standards. While there might be scattered scientific truth in the vedas ( or any other religious document) ; it is insolent to believe that it is good reference manual for scientific knowledge.
The amount of data accessible to the people in the past is a lot more when compared to current. Thats why there able to explain things that can't be experienced by our senses. To share such things in the current time, the "can be verified by our senses by a independent vendor ?" rule rejects. So, very few people experience them and bring it down to such a level that every human gets benefited from it.
The division between religion/science is very small, when both are approached using similar thought-process. Its just that some rules reject others. As human we need to approach and find truth for oneself without being biased.
Good, grief. No!!! It is a way of managing uncertainty and saying something with a precision that is available at a given point of time.
> How many discoveries are being overridden by new discoveries coming from future ?
This is beauty/and USP of science. Every scientific proof is always open for scrutiny and revision in light of new data or discovery ( tenants of falsifiability kick in here). That is, it tries hard NOT to be dogmatic by being provisional. For example, science says that we are confident Higgs Boson exists "accounting for one-in-a-million chance on the contrary" ( 5-sigma).
Let me flip your argument on the converse; success rate at which we could make ground breaking theories [ like evolution, theory of relativity , uncertainty principle ] ( which is standing the test of time for extended period of time) using the scientific method is sheer staggering and amazing. The methodology has accelerated our progress and understanding by leaps and bounds which no alternate system has managed to do so, so far!
> The amount of data accessible to the people in the past is a lot more when compared to current.
I lost you completely here. Can you please elaborate and the rest of the paragraph. ( My belief: If you take 20 random guesses; one of them turned out to be true; it is more likely to be a coincidence than a mystical insight. If on the contrary, the Monte Carlo filter I routinely simulate might just be the most insightfully entity I have encountered ).
> The division between religion/science is very small
Epistemologically they are apples and oranges! Falsifiability is not applicable to religion nor is it is provisional and routinely advocates absolute (and imho dogmatic) reasoning!
Agreed, Science comes from our experience/understanding of things around us by our senses. Try to explain the above Higgs Boson to a blind person who has never seen anything in their life. As long as science explains stuff that can be experienced by the senses, everybody else with similar senses get them.
> Epistemologically they are apples and oranges!
Its all in our thought process. Everything came from our thinking/undertsanding of things around us. It just happened to be that we are closer to prove somethings easily vs others.
> ... using the scientific method is sheer staggering and amazing > The amount of data accessible to the people in the past is a lot more when compared to current.
Appreciated the hardwork done by all these determined people. How did only few people have access to such knowledge ? In order to find the truth we should not be biased. The reason why people in the older generations might not have shared such knowledge is to prevent mis-use of it, for better of mankind. While we take pride in such innovations.
For maths, with a 5-sigma result you can maybe get a mention in the "curiosa" section if it's weird enough. It is certainly not considered a valid mathematical result.
For biology, a 1 sigma result is considered pretty good. And due to experimental restrictions, this is actually more strict than medicine requires.
Many science disciplines work with known-wrong theories. Civil engineering for example, works with pre-Newtonian mechanics (not even "turtle mechanics" : in the best simulations a building stands on ground, which stands on a plate which is magically suspended in a "downward" gravity field, not on a planet).
The idea of "this is the standard of proof for 'science'" is a nice one, but it doesn't exist in any reasonable sense. Only the utilitarian definition sticks : we have 100 standards of proof, and if the theory works (or gets enough money if your cynical) we'll find the standard of proof that allows us to call it science.
Furthermore, there are several inconsistencies in the science underpinning, for example, the Higgs boson discovery. We do not actually have rigorous proofs for constructing even natural numbers by the standards of first-order logic. And second order logic has paradoxes that stand unresolved (there is a lot of research to find something "more flexible" than first-order logic, but stricter than second-order that works, but this research has been going on for more than a century and there are no really good candidates, only really bad ones like the famous failure of the Choice axiom)
The standard model doesn't even contain gravity, so if you're being pedantic you could drop a pen from your desk and claim, correctly, that you've just falsified the entire standard model, or at least proven it's incompleteness.
Less pedantically in the physics itself there is the massive open question. The Higgs field only causes inertia, not gravity. Yet the measure of interaction with the Higgs field of any object we've ever measured matches exactly the value we've got for that same object's gravitic interactions. Does anyone believe this to be a coincidence ? Major open hole there.
While the pen falling from a desk do point out to the incompleteness ( non-Godel sense) of the standard model, which is widely accepted ( http://home.web.cern.ch/about/physics/standard-model : last paragraph ), it does not falsify it. Science is full of open holes, and no one knows ( my bet is against) that it will be completely patched up; but it is the best form of reasoning we have in understanding things, and its ongoing goal is to seek explanations that with the least amount of uncertainty possible.
"What works for me"
And nothing more.
I do disagree on one point though. The standard model doesn't just "lack" gravity. It describes a world without gravity. Therefore that gravity exists must mean that the standard model is wrong. It describes a universe that is most certainly not the one we live in. I therefore find it hard to describe that theory as true. It is more akin to "currently the best-known least-wrong theory". Even best-known has to be in there since, for example, relativity theory was known long before Einstein got his ball rolling, and Newton's equation was known before the apple fell. So we do likely know about better theories than the standard model, we just currently have no way to distinguish them from either the standard model, or (more likely) the better theories are just failing to get enough attention from well-publicized physicists. Of course, when you don't know exactly which theories are in fact better, their existence doesn't matter.
Well, at least if someone would actually say what the freaking "master key" is, it might be intellectually delightful even if historically BS. ... but I can't find any description of what this "master key" is.
Anyway, the source the linked article cites is
http://www.vedicsciences.net/articles/vedic-mathematics.html
which notes
It must be pointed out that these sutras given by Tirtha Maharaja are created by the author himself, as stated in the introduction to his book, "Vedic Mathematics" (published posthumously) and are therefore not actually Vedic.
These mathematical sutras are Vedic only in the sense that they are inspired by the Vedas in the mind of one dedicated to the Vedas. Thus the title "Vedic Mathematics" is not correct.Inscribe a circle within a square. Choose random points within the square. As the number of points approaches infinity, the number of points that fall within the circle divided by the total number of points, times four, is pi. http://mathfaculty.fullerton.edu/mathews//n2003/montecarlopi...
Memorizing something like the first 8 digits of pi is enough to calculate the circumference of the Earth to within a few inches, iirc. (My memory is bad, so it's probably 8 +/- 2 digits.)
The quadrillionth bit of pi is zero. http://www.daemonology.net/papers/
And keeping in spirit with the post, here's a pi chant: http://pi.ytmnd.com/
I'm Indian myself and I've done quite a bit of study on this topic.Vedic mathematics is rooted in ignorance and a disregard for proofs. It's pretty much a way for nationalists (which intensified after the british conquest) to appease and make a billion people feel good about their history. In short, it's pretty much bullshit. What Ramanujan did was math, not this hindutva propaganda crap. Next thing you know, you'll start hearing about astrology and how it's a Vedic science.
Nearly all of his findings were without proof, so what are you trying to imply here?
And about astrology, they did know about the Arundhati twin star system, so they did know something. While you are at it, blow your minds and lookup the fact that they gave a measurement of speed of light in Mahabharata.
It's not about nationalism. No offense, I don't know you but you kind of sound like all those Indians who just have to look down on everything Indian.
None taken. Personally, I believe that if you're vehemently "proud" of your country and heritage, you havent accomplished much else in life thus far. I don't look down upon Indians, only worried that pseudoscience like this is a dent to credibility and only belittles and overshawdows the great work that's being done today/will be done in the future
As for early scriptures, suppose after 5000 years if the current civilization is no more and the future generations get hold of a book with no mathematical proofs but astounding facts which clearly state the technological advancements of our time, they should just call it "pseudoscience". Yeah, right.
Personally I believe that if somehow you are proud of only the things YOU have done, you have got way too many problems of your own to take care of.
The fact that you couldn't google a simple fact says a lot about your "achievements/accomplishments" too. Here you go http://alishekh.blogspot.in/2009/05/speed-of-light-in-rig-ve...
It's pretty simple Sanskrit, it's not even riddled, it's plain Sanskrit. If you understand even a little Sanskrit (I do) the translation will make sense. Of course you could trust the author of the article too for having done a good job in translating and explaining. And just so you know that guy who has written this seems to be a Muslim, so zero benefit in advancing the said "propaganda".
Just one of its more obvious gems:
2000 Dhanus = 1 Gavyúti (distance to which a cow’s call or lowing can be heard) = 12000 feet
2000 Dhanus = 1 Gavyuti hmmm, they must have first calculated a Gavyuti and then just randomly equated it to 2000 dhanus. The fact that they named it after a cow's call (range approximately 12000 feet) is the proof. People named unit erlang after erlang, so <insert a bullshit correlation here>
</sarcasm>
And, why do think it's bullshit? I don't see anything wrong in the "Vedic Mathematics" book. They are a bunch of mental calculation techniques and tricks. I'd suggest to keep this propaganda propaganda to yourself.
[1]http://www.vedicsciences.net/articles/vedic-mathematics.html
... but please do cut out the "Indians did this ages ago" crap, for it is the least intellectually interesting of all things ... unless the poster backs up any such claim with proper first-hand references.
One of them is called Padhuka Sahasram, was written in less than a day in response to a challenge and contains 1008 verses in 32 chapters.
The 30th chapter called Chitra Paddathi or Picturesque Chapter (aka Matrix of Artistry) contains verses that whilst paying homage to the feet (Padhuka) of the Lord also paint elaborate patterns, such as The Knight's Tour (1).
One hint as to why "Indians did this ages ago" is of intellectual interest to "some" indians is because the middle name of the early-stage investor and long time board member of google is KaviTark.
[1] http://www.ibiblio.org/sripedia/ebooks/vdesikan/rps/chitra.h...
If he spent 24 hours non-stop writing those verses, he's have to write 7 verses every 10 minutes on the average. If it is really a "less than a day" 8 hours, he'd have to write nearly 3 verses every minute. In summary, this sounds like something that will need some serious substantiation to believe.
Those of us who come from India and have grown up with this have older uncles and others who can compose extremely mellifluous and deep meaning verses extemporaneously.
The Chitra Paddathi which comprises of 40 verses (of the 1,008) takes 7mins 37secs.
If you are so inclined you can hear it at (1) - You can follow along with the romanized english phrases with meanings at (2) and you can see it's corresponding visual artistry at (3)
(1) http://andavan.org/audio/7.CHITRA%20%20%20PADDHATHI.mp3 (2) 92, 93, 94 & 95 (10's) at http://www.ibiblio.org/sripedia/ebooks/vdesikan/rps/92.html (s/92/93 etc.) (3) http://www.ibiblio.org/sripedia/ebooks/vdesikan/rps/chitra.h...
This video shows their pronunciation: http://www.youtube.com/watch?v=y8GhoAIAtt4
This structure is same in all Indian languages.
Incidentally, I used the same technique to memorize some (fewer) digits pi in English. https://en.wikipedia.org/wiki/Mnemonic_major_system
[('go', 3, 3),
('pi', 1, 1),
('bha', 4, 4),
('gya', 'UNKNOWN', 1),
('ma', 5, 5),
('dhu', 4, 9),
('vra', 'UNKNOWN', 2),
('ta', 1, 6),
('srngi', 'UNKNOWN', 5),
('so', 5, 3),
('da', 3, 5),
('dhi', 4, 9)]
In "lorem ipsum" text, translating a->1, b->2,... you find 3141(391491322514) at position 170 onwards. And the collected works of william shakespeare (as downloaded at http://www.gutenberg.org/cache/epub/100/pg100.txt) contain the following "PI approximations" (encoded as above):
3 => 290159 occurences 31 => 116402 occurences 314 => 7913 occurences 3141 => 3970 occurences 31415 => 1650 occurences 314159 => 39 occurences 3141592 => 8 occurences 31415926 => 0 occurences
Shakespeare must have been a closet mathematical genius ! (Hmmm, I guess he lived after the discovery of Pi, ... oh well, still makes the point I guess)
Even the bible contains actual approximations to pi (for example the surprisingly accurate 22/7). It even makes sense that it does. For a lot of history the bible was effectively the only book available for a large percentage of the population (and even then, often not directly). It seems the authors knew that and included tons of relevant stuff. It contains descriptions of how "large" buildings can be built (large by medieval standards, of course). Including textual descriptions of plans for things like churches. It contains details of how to make agriculture work, when to sow, when to harvest, when to switch between grain and animals, when to ... to make land productive. We still use the 7-year land rotation rule on today's farms.
Given that the bible clearly was meant to be a sort of "civilization in a single (if massive) book", it makes sense that intuitive descriptions for pi would be one of the things found in there. Perhaps the same is true for the vedas ?
Maybe I'm putting the horse before the cart here. The situation could be reversed as well. Assuming a religion gets of the ground at all, it's survival depends on how well it's subjects do. So it's only natural that the religions that grow huge in some way things like the (approximate) value of Pi, and stuff like making agriculture work. And like in the real world you have different flavors of survival. Building, breeding, growing and defense clearly weighed heavily on the bible, vedas and buddhist texts (all of those books, for example, heavily favor not counterattacking an enemy that comes and fights for plunder, merely to let plunder run out and let the attacker starve), whereas conquest, plundering and looting predominate, for example, the quran or the original mongol religion (those religions focus on things like plunder, remaining mobile (e.g. absurd punishments for doing things to horses), and very strict rules about not directly attacking other religions (only their power on the ground). They all have rules about recruiting new cannon fodder (ie. promises of plunder for anyone who joins the religion, making it everyone's duty to recruit new members, ...). Islam actually contains rules that bear a resemblance to a multilevel marketing scheme. If you bring new members, you get a share of their loot for a while). "Growing" religions are vulnerable when they reach a large size, because at some point the borders can't expand while the population keeps growing. "Attacking" religions have the same problem any predator population does : they can only grow by destroying other populations, never by themselves. They survive as tiny inactive pockets, every now and then blowing up exponentially only to die off just as fast soon after, leaving enormous devastation (to read about this in nature, read about the history of wildlife management, or about what happened in Australia, or for a less extreme example American national parks).
Maybe we should just look at religions as just another form of life. Not "really" alive, but certainly making a huge difference in the world. (Yes, I've read Jared Diamond's books).
If a religion did not imitate a real-world survival technique it simply wouldn't survive. So there probably have been a lot of alternate versions, just almost no surviving ones.
"Sa" means 4 different numbers in order to make it work. That's not reasonable.
Even if it does fit, it's still a hoax. Look how far shakespeare got. Do you believe that he intentionally put 8 references to 7 digit approximations in his texts ?
Without (at least) the inverse tangent expansion of pi, this number could not have been constructed. Furthermore, if it came from divine inspiration, there's a glaring omission : why doesn't it mention the irrational nature of Pi ? Otherwise even a 100 digit approximation would lead any reasonable reader to a wrong conclusion. In this case to nothing better than an Indian version of this : http://en.wikipedia.org/wiki/Indiana_Pi_Bill.
Every "real" mathematical book on Pi contains three proofs. First that it is irrational (that you can only approximate Pi, it doesn't have any finite representation), that some method of series expansion approximates Pi, and that said series converges. Without these 3 bits of data you don't know what Pi is. The actual value of Pi is almost inconsequential, and can be trivially measured using a rope and a measuring stick by a first grader to an accuracy of at least 10 digits. Alternatively you could calculate without an explicit value, like the ancient Greeks did.
Furthermore there's nothing special about this. When it comes to written references to the value of Pi, there are documents going back ~4000 years (E.g. the Rhynd papyrus). If you accept buildings that could not have been constructed without an approximation of Pi's value, then we can go back 6000 years before we really get into trouble. If you accept the reasoning that pyramids which are the "internal" pyramid of a ball shape could not have been a coincidence, knowledge of pi (which is necessary to construct such a shape) goes back nearly 10000 years.
Also, I don't have any comments about that Pi verse itself. From what I gather, it's first occurrence was in a book from 1965. So, may be it's a retro-logic based on Katapayadi system (http://en.wikipedia.org/wiki/Katapayadi_system).
In all seriousness, I've always wondered how I could learn Pi. I've seen people assimilating a word to each double digits. Then make a story out of those words.
But first you'd have to learn exactly 100 associations.
Anyone knows of another technique ?