This is going to test HN's tolerance for myths and pseudo-science, but then it's a Sunday. "It has a self-contained master-key for extending the evaluation to any number of decimal places." is not going to convince many people here.
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.
The verse 'gopi bhagya' basically follows Katapayadi system[0]. Earliest known usage of Katapayadi system was in 683 AD. That verse is from a 1965 book called "Vedic Mathematics" by Bharati Krishna Tirtha Maharaja[1].
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.
/Just like most other religious texts, the Vedas don't stand up to modern science and rigor/ -- There is no such thing as modern science. Its the same universe that existed billions of years ago and with our "thought process" we are able to understand it better (compared to what was written in the past) and are calling it modern now. Go forward 100 years and look back at current science. What is it called as now ?
/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.
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.
As i see, the current science is more rigorous because people are producing lot of crap. So, we made it to be like "if it can't be verified/repeatable its not science". But do we really know for sure ? How many discoveries are being overridden by new discoveries coming from future ?
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.
> As i see, the current science is more rigorous because people are producing lot of crap
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!
> science says that we are confident Higgs Boson exists ( 5-sigma).
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.
It vastly depends on the actual science which standard of proof is accepted.
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.
Falsification and Incompleteness are two different things. Since we reason about physicals system using the language of mathematics/logic; it has be based on certain axiom which cannot be proved or disproved ( Godel's incompleteness theorem ). Though this renders certain statements inside physical theorem non-provable ; it certainly does translate to every claim made by a proposed theory. Further many aspects of physicals systems can be disproven experimentally. ( It is still in active debate if Mathematics should treated as science per se : http://en.wikipedia.org/wiki/Mathematics#Mathematics_as_scie... )
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.
I think we're largely making the same point : that science is largely based on a utilitarian definition of truth. A somewhat more direct way to state that is that scientific truth is simply
"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.
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.
"thought process" is what distinguishes humans from others in terms of deciding whats right/wrong, (finding the truth) its not just science.
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.
> "It has a self-contained master-key for extending the evaluation to any number of decimal places."
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.
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...