Three mathematical notes on Rajiv Malhotra's lecture at IIT Mumbai

April 20
3 mathematical notes on your lecture at Mumbai
Harsha shares three critical notes on a recent lecture by Rajiv Malhotra at IIT Bombay:
1. When you say, that the digits of pi were calculated using adhyatmic vidya. But, if you actually look at how the Kerala school did it, they do it by using the Taylor series for the sin and cos function. This is an impressive achievement, and predates the European school, by a couple of centuries. Adhyatmic vidya is itself much more important. But in this case, we shouldn't conflate the two.

2. On your comment on the speed of light, I think it is very important for you to say in your speech that this is speculative. Even Subash Kak, the original researcher does not definitively state this in his article. He presents some evidence, but leaves it to the reader at the end. Personally, I think there is nowhere near adequate evidence..

3. On vedic maths, it is important to note that what is presented is not special by today's standards. Most of the calculation rules would be considered elementary today. On the other hand, if there was evidence that these were in
the vedas, it would be interesting. But the  Shankaracharya's verses do not refer to the Vedas. Here is Prof Dani's take on it, who also makes these points.

4. As a strategy, mentioning these more speculative things in your speeches, isn't helpful to your cause. For someone who is not an expert, it would be just as impressive to mention the more established contributions which haven't been popularized (like the Taylor infinite series for sin an cos anticipating calculus) as mentioning the not more shaky claims.

... Already, the field is inundated with a lot of claims like proof of Goldbach conjecture (an open problem even today) using Vedic mathematics.

Also, someone one who is not sympathetic to your project would disproportionately emphasize these weaker claims. See this for instance, Rajnath Singh isn't correct, but Mr. Bal is chosing a particularly weak opponent, someone who cant accurately portray the known contributions...."
Rajiv comment: 
1) I agree with him on the value of pi calculated as a series - but I disagree with him that it should be called "Taylor" series. Agreed that we cannot show any DIRECT role for adhyatma-vidya in this. However, the practice of sadhana was part of the training, and hence at least indirectly part of the methodology of discovery.

2) Regarding the speed of light, I must disagree with him. Unlike value of pi which can be calculated strictly theoretically without use of measuring instruments, the velocity of light is not a theoretical derivation. Yet (and
this is the point I wanted to make), there is no evidence of measuring instruments available to get such a value in those times. So how did they "guess" such a value? My thesis is given in pages 221-234 of BD. Sanskrit mantra
theory is based on integral unity that can be "seen" (not in the normal sense of the word) in the rishi-state. A few examples are given in that chapter of BD where ancient texts indicate physical properties of objects that are remarkably accurate, but there is no evidence of physical measurement being carried out. Had the rishi discoverers used lab instruments, they would be writing about them
and teaching it to students. But they never mention what we today consider to be instruments. Except one instrument - the mind in higher state of consciousness.
So it is my "speculation" that velocity of light was an example of such discoveries. It might surprise many of you that modern Western neuroscience is now (re)discovering many facts about the mind using advanced yogis and tibetan buddhist meditators. This is going to be the subject of some volumes I have been working on that I hope to complete. The use of adhyatma-vidya as methodology of
discovery is not to be dismissed just because it does not fit the criteria of "science" as known today.

3) On Vedic maths: I do not think of the math being promoted as something directly based on vedas. But the man who promoted it starting a century ago claimed that he was "inspired" by vedas. So it could be an indirect influence of vedas. Similarly, the great modern mathematician Srinivasa Ramanujan attributed
his genius discoveries to Goddess Lakshmi, who he insisted had brought these breakthroughs to him in visions. His biographers failed to pursue this aspect
adequately, presumably out of fear of being branded as unscientific. But how does one explain such a scientific mind making a claim that seems so unscientific? I would not dismiss it out of hand. Modern science knows very
little about the mind, especially the potentials beyond "normal" states.

On the general point of not mixing more credible claims with less credible ones, I am in full agreement. I judge each context based on the audience and what would motivate them... I would like this to be the first place in India where serious scientists take up R&D on adhyatma-vidya. Why let western institutes have a monopoly on researching our tradition's methodologies?]

Narayana comments:
"...This is with reference to Rajivji's third point, regarding 'being inspired' by the Vedas. The discovery of Benzene ring by visualising the structure in a dream. Not only that but Kekule was believed to have come up with the tetravalent nature of carbon by visualising it in a dream. Western 'scientists' and their Indian acolytes (whom Rajivji refers to as ideological sepoys) dismiss visions of Indian sages and Vedic science but readily believe such 'stories'
when put out by, well, 'Western scientists'!

Rajiv comment: yes. Thats what Uturn is.

Ashok asks:
"...the 18th chaupai of Sri Hanumaan Chalisa, where the distance of the Sun from the Earth has been described clearly. Yug (12000) Sahastra (1000) yogan (8 miles) par bhanu. Comes to 96,000,000 miles, which I understand is reasonably close. Of course the earth's orbit is elliptical, so the distance will vary during different parts of the year..." 

Partha responds:
"...Sant Tulsidas whom many of us consider a reincarnation of Valmiki, lived in the 16th century, by which time information about the Sun's distance from the earth could be claimed to have been communicated worldwide, from wherever it was first learnt by whatever means. That the Sant wrote his Ram Charit Manas entirely without biblio-aids and that he practically visualized whatever he wrote should be used as an important rider, when we talk of this scientifically near-accurate astronomical data being given by him in his Hanuman Chalisa. He has also used units from olden times (Yojana, Yug etc)..."

Come adds:
"..There are references to the Sun-Earth distance in other Indian scriptures, going back to the Vedas, at least according to ancient commentators. Some scientists including Rupert Sheldrake have shown that there are other methods to acquire knowledge about nature than the modern "scientific method", ..."

Rajiv comment: Rupert Sheldrake is a prominent UTurner and should not be cited as reference for saying things he has appropriated. We must stop acknowledging as source the person(s) who stole ideas and covered up. 

tvikhanas notes:
"...To add to Rajivji's point, a staggering and undeniable example of adhyatmic influence on science is Panini's grammar. The core of this grammar "Shiva sutras" is named so because it was revealed to Panini by Shiva himself. People have remarked how wonderful the grammar is and it keeps revealing amazing new facets when examined from modern viewpoints. A researcher recently found that
the certain choices made in constructing Shiva Sutras when cast as optimization problems turn out to be the best possible solutions (A Mathematical Analysis of Panini's Shivasutras by Wiebke Petersen).

If this seems some how less remarkable, then say a proof of Fermat's Last Theorem from 1500 BC, it's because we have also internalized western view that "linguistics" is an inferior and less fundamental science compared to maths or physics along with many other ill-founded ideas. Indian tradition in fact considers Vyakarana far more important than equivalents of mathematics, metallurgy etc which perhaps explains its survival against impossible odds.

As a side note, western view towards linguistics is also evolving, mainly due to study of Sanskrit and also due to advent of computers. It is interesting to note that technical study of Sanskrit grammar is picking up again in the West. There are "mathematical linguists" like Petersen quoted above, along with Computer Scientists like Gerard Huet who have initiated major projects on parsing Sanskrit. I recently learned that there is a whole area of assigning formal semantics to natural languages in which Gerard Huet with his Sanskrit project is an important member...." 

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