Nothing Vedic in Vedic maths: response to comments

My article in The Hindu, 3 Sep 2014, received 214 comments and 4.3k Facebook Likes.
Hindu article thumbnail

Here are my responses. (A separate response in Hindi to Dinanath Batra’s associate’s comments on my Jansatta article in Hindi of 10 Aug 2014 is given below.)

  1. Abuse. Some people have turned abusive and chanted abuses like mantras! Funnily, their abuses are always the same, no matter what the critique! After working on decolonisation for the last 4 years, and mentioning the use of Indian ganita in the above articles, it is excessively funny to be accused of being a follower of Macaulay! Pathetic. These abusers have an equally pathetic knowledge of Hinduism, and hence are its worst enemies, not its owners, as they claim, for they confuse the fakes for the real stuff. (Incidentally, I have also given what is possibly the strongest possible scientific basis for Upanishadic philosophy, relating it to scientific and refutable notions of time,[1] but it is beyond even their leaders.) Anyway, such ignorance of the purva paksa (the critique) permanently disqualifies these abusers from being taken seriously, according to the Nyaya sutra.
  2. It is ancient hence it is Vedic.
    1. Wrong! Ancient does not mean Vedic. Buddhism, Jainism, and Lokayata are also ancient, but all reject the Veda as a means of knowledge. Lokayata said that Brahmins are hypocrites. Is that also Vedic knowledge!? If not, the claim “vedic = ancient” is just a second lie invented to “save” the first (claim of “Vedic” math). A third lie is now needed to “save” the second one! (Note that Lokayata are Hindus on present-day tax laws, or the Indian census.)
    2. Besides, how do we know it is ancient? What is the pramana? Our source (Krishna Tirtha) is recent. He hid his real sources, obviously for a good reason. If they were really ancient, why did no one else mention them in so many thousands of years? How do we even know this system is Indian in origin?
    3. The article pointed out that the usual algorithms are Indian in origin (unknown to Krishna Tirtha and his followers), and based on the place value system which can be traced to the Veda. They are definitely Vedic. Why abandon the real Vedic for the fake Vedic?
  3. It is useful for CAT etc.It is a very narrow and colonial vision of education that imagines that education is intended only to pass competitive exams The real social use of mathematics is on the frontiers of science and technology, where the mental arithmetic of “Vedic” math is irrelevant.
  4. Caste and Shakuntala Devi.Carpenters calculated in their head, as opposed to astronomers or traders who could sit in one place and write things down. It is a fact that artisans were exclusively from lower castes. Why suppress this fact? It might explain why Krishna Tirtha hid his sources.

    I met Shakuntala Devi only once, and was charmed by her simplicity and candor. She created a sensation, and if anyone in the West had any inkling then of the algorithms she used, they would have quickly pointed them out. But no one then could replicate her performance. So, Shakuntala Devi’s case gives a possible line of argument for the Indian origin of the algorithms.

  5. It is a faster algorithm. Again no proof. The government of India spent some 5 million USD on a project related to traditional knowledge. The outcome was mostly some unpublished papers, some of which claimed that algorithms based on Vedic math were more efficient. The papers I saw in the 90’s reported shoddy research. [2] Therefore, at the moment, the best one can say is that Krishna Tirtha’s methods give more convenient algorithms for mental arithmetic.
  6. Vedic mathematics is not mathematics? Someone refers to Dani’s paper and states that Vedic mathematics is not mathematics. Now, that is going too far. In fact, what Dani does is neither mathematics nor secular. Hence my petition to teach religiously neutral mathematics. [3]

    Who decides what is mathematics? Dani will point to his Western masters as the sole decision makers. But why should we accept that? It is wrong to follow a seer blindly, but it is much worse to follow the West blindly: look at what happened to the Australian aborigine, or the north American Indian, or the Africans who trusted them. Decolonisation means we must be critical of the West and address our own practical interests. [4]

    Mathematics must deliver practical value, as in the Indian traditions of ganita. Dani’s math fails the test of practical value, and the entire math school of the Tata Institute contributed nil practical value to the Indian people even over 50 years. [5]

    The practical value of math still comes from its traditional core of ganita or hisab, or practical calculation, and any practical application requires calculation.The absence of practical value comes from the coating of metaphysics that this mathematics acquired in the West, and its focus on metaphysical proof instead of practical calculation. TIFR math school blindly imitates that.

    However, the metaphysics underlying formal math is not universal; it is not even religiously neutral. My book Euclid and Jesus exposes its basis in false history and crooked Christian theology. Teaching Christian metaphysics through math today is decidedly poisonous, especially because few have any inkling of this insidious  indoctrination into a supposedly “universal” metaphysics. Mathematics is not universal, e.g. present-day mathematics differs from Indian ganita in rejecting empirical proofs. In Cultural Foundations of Mathematics, I set out a different philosophy of math, well adapted to mathematics done on a computer.

    At least there must be a debate on whether to blindly imitate the Western philosophy of math, and whether that is even secular. Now, Dinanath Batra’s associate, Atul Kothari, at least immediately responded to my criticism (see below), showing that even if his beliefs are wrong, he sincerely believes them. But Dani and his colleagues from the Tata Institute have avoided debating my critique of formal math, and that shows that they are insincere and unethical, and know that any debate will quickly expose them. They do care for practical benefits but only at the personal level: a TIFR professor Nitin Nitsure justified formal math by saying “they” are willing to pay for it! Westerners naturally praise the TIFR math school, since these comprador elements benefit the West: colonialism was built with the help of a fifth column of people who sold out. But we must insist on our practical benefit.

  7. So, what is the alternative? So how exactly do we achieve that? Through decolonised math based on Indian traditions, of ganita and hisab, as stated in the article. Europe got most of its math from India and their leading intellects  repeatedly got confused by it, like Gerbert. Descartes raised some foolish arguments against the infinite series of the Indian calculus, and Newton’s physics failed just because he misunderstood the calculus. [6] The European misunderstanding of math and the consequent intrusion of metaphysics has made math difficult: [7] one cannot even explain why 2+2=4 without reference to Peano’s axioms and Western notions of infinity.

    This misunderstanding was globalised by colonialism; nevertheless it is NOT universal. We can reject it and revert to the traditional ganita or hisab. This avoids the Western obsession with metaphysical proof and focuses on practical calculation. That also makes math easy. I have demonstrated this through pedagogical experiments, involving 8 groups of students in 5 universities, in 3 countries, by teaching calculus in five days [8]

    Governments all over the world (and not in India alone), especially in former colonies, need to take up a critical review of math and how the practical uses of math can be separated from the superimposed Christian metaphysics. Especially, secular countries like India are obliged to do so, as I have argued in my petition to teach religiously neutral mathematics.

Improving the understanding of mathematics, improves statistics and science
which depend on it.

For the case of probability and statistics I have explained the change (in the context of the Rgveda, Mahabharata, and quantum mechanics) in my article on probability in ancient
India. [9]

For the case of physics, I have explained the change in the appendix to Cultural Foundations of Mathematics and in my other articles [10] and talks, [11] as also articles on physics and physics education. [12}


1 C. K. Raju, “Atman Quasi-Recurrence and paticca samuppada”,
in Self, Science and Society, Theoretical and Historical Perspectives,
ed. D. P. Chattopadhyaya, and A. K. Sengupta, PHISPC, New Delhi,
2005, pp. 196-206.
http://ckraju.net/papers/Atman-quasi-recurrence-and-paticca-samuppada.pdf.

2 For example, for the square root algorithm, a paper compared Vedic math with “Newton’s method”. For “Newton’s method” the starting guess used was half the number. Now, it is well known that “Newton’s” method is sensitive to the starting guess. They could very well have used half the exponent. Since the computer anyway converts to the mantissa exponent representation, this would have involved just one additional bit shift, but would have worked against the claim of superiority of Vedic math algorithms.

3 “Petition to teach religiously neutral mathematics”, http://ckraju.net/blog/?p=94.
Also, http://www.ipetitions.com/petition/teach-religiously-neutral-mathematics

4 Specifically, it is necessary to refute another common caricature that my critique is blindly anti-West. See, C. K. Raju, “Be critical: choose what is best”, The Sun, Malaysia, 29 Aug 2011, p. 16. Clip posted at http://ckraju.net/press/2011/the-Sun-29-Aug-2011-p16-clipping-ckr-response.gif

5 “Kosambi the mathematician” Special article, Economic and Political Weekly 44 (20) May16–22 (2009) pp. 33–45. http://ckraju.net/papers/Kosambi-EPW.pdf.

6 For the point that Newtonian physics failed because of a conceptual defect about the notion of time, and had no clear way to measure time, see C. K. Raju, Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994. For the point that Newton took a step backward in making time metaphysical, see “Time: What is it that it can be measured?”, Science&Education 15(6) (2006) pp. 537–551,  http://ckraju.net/papers/ckr_pendu_1_paper.pdf. For the alternative theory of gravity that results from the correction of Newton’s error, see C. K. Raju, “Retarded gravitation theory”, in: Waldyr Rodrigues et al. (ed.), Sixth International School on Field Theory and Gravitation, American Institute of Physics, New York, 2012, pp. 260–276.
http://ckraju.net/papers/retarded_gravitation_theory-rio.pdf.

7 In Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE,Pearson Longman, 2007, I pointed out that calculus was foolishly misunderstood by Europeans because they mixed up its infinite series with the Christian theology of eternity.

8 For a partial report, see, C. K. Raju, “Teaching mathematics with a different philosophy. 1:Formal mathematics as biased metaphysics.” , Science and Culture 77 (2011) (7-8) pp. 274–79. http://www.scienceandculture-isna.org/July-aug- 011/03%20C%20K%20Raju.pdf. “Teaching mathematics with a different philosophy. 2: Calculus without limits.” Science and Culture 77(2011) (7-8) pp. 280-86  http://www.scienceandculture-isna.org/July-aug-2011/04%20C%20K%20Raju2.pdf

9 C. K. Raju, “Probability in Ancient India”, chp. 37 in Handbook of the Philosophy of Science, vol 7. Philosophy of Statistics, ed. Prasanta S. Bandyopadhyay and Malcolm R. Forster. General Editors: Dov M. Gabbay, Paul Thagard and John Woods. Elsevier, 2011, pp. 1175-1196. http://ckraju.net/papers/Probability-in-Ancient-India.pdf.

10 e.g. C. K. Raju, “Decolonising math and science”. In Decolonizing our Universities, Claude Alvares and Shad Faruqi ed., Citizens International and
University Sains Malaysia, Penang, 2012, chp. 13, pp. 162-195.  http://ckraju.net/papers/decolonisation-paper.pdf.  Video is first 34 minutes of the one at http://vimeo.com/26506961.

11 E.g. Tehran talk http://ckraju.net/papers/presentations/decolonizing-mathematics.pdf. See also, http://ckraju.net/blog/?p=98.

12 E.g. See above books and article, and C. K. Raju, “Functional differential equations. 1: A new paradigm in physics”, Physics Education (India), 29(3), July-Sep 2013, Article
1. http://physedu.in/uploads/publication/11/200/29.3.1FDEs-in-physics-part-1.pdf, and “Functional differential equations. 2: The classical hydrogen atom”, Physics Education (India), 29(3), July-Sep 2013, Article 2. http://physedu.in/uploads/publication/11/201/29.3.2FDEs-in-physics-part-2.pdf.


श्री अतुल कोठारी जी,
आपकी मेल मिली. अच्छा है कि आप नें सच्चाई को माना कि आप जिस गणित का प्रचार कर रहें हैं उसका वेद से कोई सम्बन्ध नहीं. कोई भी चीज महज़ प्राचीन होनें से “वैदिक” नहीं बन जाती: जैसे बौद्ध धर्म या लोकायत प्राचीन है मगर उसे “वैदिक” कहना सरासर गलत होगा. लोकायत का मानना था कि ब्राह्मण पाखंडी हैं. क्या आप इसे “वैदिक” ज्ञान मानते हैं? अगर नहीं तो आपकी परिभाषा गलत है. दूसरी तरफ जिन लोगों की वेद के प्रति आस्था है वह भी “वैदिक” शब्द के ऐसे दुरुपयोग से बहुत दुखी हैं, क्योंकि ऐसे दुरुपुयोग से वेदों की गरिमा को चोट पहुंचती है.
गणित की सामान्य विधियों का मूल तो निश्चय ही भारतीय है, और वह प्राचीन भी हैं. तो आपकी परिभाषा के अनुसार उनको भी “वैदिक” गणित कहना चाहिये. फिर उस सामान्य “वैदिक” गणित को हटाकर भारती कृष्ण तीर्थ का गणित क्यों लाना चाहते हैं? इस बिन्दु पर आप सीधा जवाब नहीं दे पाये. बल्कि आप के पास प्रमाण ही क्या है कि कृष्ण तीर्थ का गणित प्राचीन है या भारतीय मूल का है? आपका स्त्रोत तो कृष्ण तीर्थ है, जो आधुनिक है, प्राचीन नहीं. और सच्चाई तो यह है कि उसने मूल स्त्रोत को छुपाया, तो ज़रूर कोई छुपाने लायक बात होगी.
अफ़सोस है कि आप यह सब जानते हुए भी अपने राजनीतिक फायदे के लिए “वैदिक” शब्द का दुरूपयोग करने पर अड़े हैं.
अफसोस यह भी है कि आप का शिक्षा के प्रति दृष्टिकोण इतना संकुचित है कि वह प्रतिस्पर्धात्मक परीक्षाओं तक सीमित है. गणित का असली उपयोग तो विज्ञान और तकनीकि के क्षेत्र में है. यहां कृष्ण तीर्थ के गणित का रत्ती भर भी महत्व नहीं.
मैनें भारतीय परम्पराओं से जुडे गणित पर गहन शोध किया है और उस पर ५०० पन्ने की एक पुस्तक प्रकाशित की: Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE, Pearson Longman, 2007. इसमे (कलन जैसे) गणित को यूरोपियों ने मूर्खतापूर्वक जटिल कैसे बनाया इस बात का गहरा विशलेषण है. उसे परंपरा की सही समझ से आसान कैसे बनाया जा सकता है, यह समाधान भी है, जिसे मैने तीन देशों में शैक्षणिक प्रयोग कर के दर्शाया है. (C. K. Raju, “Teaching mathematics with a different philosophy. 1: Formal mathematics as biased metaphysics.” Science and Culture, 77 (2011) (7-8) pp. 274-79. http://www.scienceandculture-isna.org/July-aug-2011/03%20C%20K%20Raju.pdf. “Teaching mathematics with a different philosophy. 2: Calculus without limits.” Science and Culture, 77 (2011) (7-8) pp. 280-86. http://www.scienceandculture-isna.org/July-aug-2011/04%20C%20K%20Raju2.pdf.)
गणित का दर्शन बदलने से सांख्यिकी में क्या फरक पढता है यह बात मैने इस लेख में समझायी है वेद, महाभारत और क्वांटम मेकैनिक्स के सन्दर्भ में.
(C. K. Raju, “Probability in Ancient India”, chp. 37 in Handbook of the Philosophy of Science, vol 7. Philosophy of Statistics, ed. Prasanta S. Bandyopadhyay and Malcolm R. Forster. General Editors: Dov M. Gabbay, Paul Thagard and John Woods. Elsevier, 2011, pp. 1175-1196. http://ckraju.net/papers/Probability-in-Ancient-India.pdf.)

और गणित का दर्शन बदलने से विज्ञान कैसे बदलता है यह भी मैने समझाया है उपरोक्त पुस्तक और लेख में और मेरी दूसरी पुस्तकों, वक्तव्यों और लेखों में.
(जैसे कि C. K. Raju, “Decolonising math and science”. In Decolonizing our Universities, Claude Alvares and Shad Faruqi ed., Citizens International and University Sains Malaysia, Penang, 2012, chp. 13, pp. 162-195. http://ckraju.net/papers/decolonisation-paper.pdf. Video is first 34 minutes of the one at http://vimeo.com/26506961. एवं तेहरान में वक्तव्य http://ckraju.net/papers/presentations/decolonizing-mathematics.pdf, एवं C. K. Raju, “Functional differential equations. 1: A new paradigm in physics”, Physics Education ( India), 29(3), July-Sep 2013, Article 1. http://physedu.in/uploads/publication/11/200/29.3.1FDEs-in-physics-part-1.pdf, and “Functional differential equations. 2: The classical hydrogen atom”, Physics Education ( India), 29(3), July-Sep 2013, Article 2. http://physedu.in/uploads/publication/11/201/29.3.2FDEs-in-physics-part-2.pdf. आदि. और देखिये http://ckraju.net/blog. )

यह सब बातें दुनियाँ में पहली बार किसी नें कही हैं. इसलिए आपका यह कहना कि मैं विषय की गहराई में नहीं गया सरासर गलत और अत्यंत अनुचित है. इससे सिर्फ यह साबित होता है कि आप पूर्व पक्ष से बेवाकिफ हैं तो न्याय सूत्र के अनुसार आप संवाद या विवाद करने योग्य नहीं. विषय की गहराई की शायद आप को कल्पना तक नहीं. अगर पांच-दस साल तपस्या समझ कर अध्ययन करेंगे तो हो सकता है कुछ बातें आप की समझ में आ जाएँ.
आपको जानना चाहिये कि आपके नकली “वैदिक गणित” के कारण दुनियाँ में बहुत से लोग आप पर (और वेदों पर) हंसते हैं. और आपके कारण भारतीय परम्पराओं पर भी. मेरे गम्भीर प्रयासों पर भी पानी फिर जाता है. जिस देश में सत्ताधारी लेकिन अज्ञानी लोग शिक्षा नीति तय करते हैं उस देश में विद्वान कौन है इसकी सही पहचान तक नहीं, तो विद्या और वेद दोनों का विनाश निश्चित है.

चंद्रकान्त राजू

==========================================
C. K. Raju
web: http://ckraju.net

Euclid and Jesus:
How and why the church changed mathematics and Christianity across two religious wars
Draft webpage: http://ckraju.net/Euclid

From: Atul Kothari <***@gmail.com>
To: ***@ckraju.net
Sent: Thursday, 14 August 2014 1:44 PM
Subject: दिनांक 8 अगस्त 2014 के जनतसा दैनिक में आपका लेख पढ़ा।

श्री चन्द्रकान्त जी,
भारत वन्दे,
दिनांक 8 अगस्त 2014 के जनतसा दैनिक में आपका लेख पढ़ा। आपने लिखा है कि जिसको आज वैदिक गणित कहा जाता है, वह वेदों में कही नहीं है। तकनीकी दृष्टि से आपकी बात सही है। परन्तु वैदिक का अर्थ वेदों में जो है उतना ही नहीं है। भारत में जो भी प्राचीन है वह वैदिक है। क्योंकि भारत की प्राचीन संस्कृति को वैदिक संस्कृति कहा जाता है। इसका अर्थ यह कतई नहीं है कि सभी बातें वेदों में लिखी है। वेदों में आधारभूत बातें सूत्रबद्ध है।
दूसरी बात जो आपने लिखी है कि क्या? गणित से शिक्षा का भारतीयकरण हो जायेगा? देखिये शिक्षा का भारतीयकरण की संकल्पना बड़ी व्यापक और विस्तृत है। राजनैतिक चष्में से देखने वाले, लिखने वालों ने इसे अपने मन से बहुत संकुचित कर दिया है। भारतीयकरण की व्यापक संकल्पना में एक बिन्दू है प्राचीन और आधुनिकता का समन्वय। वैदिक गणित में वैदिक गणित संकल्पना प्राचीन है, परन्तु आधुनिक युग में वैदिक गणित प्रतियोगी परीक्षा में आशीर्वाद रूप हो रहा है। इस हेतु प्रतियोगी परीक्षा की तैयारी कराने वाले सारे आधुनिक क्लासिक वाले हजारो रूपया लेकर इसको सिखाते है और छात्र सिखने जाते है।
वैदिक गणित वेदों में है की नहीं? यह आपका प्रश्न हो सकता है। परन्तु छात्रों के मन से गणित का डर निकालने के लिए वैदिक गणित पर आज सबसे उत्तम गणित है। अत्यंत सरलता, आसानी से गिनती हो सकती है।
तीसरी बात आज इंगलैण्ड, जर्मनी, आस्ट्रेलिया जैसे अनेक देशों में इसका स्वागत हो रहा है। इंगलैण्ड मैं भारत से भी ज्यादा अच्दी पुस्तकें वैदिक गणित पर विलियम्सन आदि ने लिखी है। यह बात आपकी जानकारी में होगी ही। इसलिए आपसे विनम्र प्रार्थना है कि किसी भी विषय की गहराई में गये बिना राजनीतिक दृश्टि से विरोध में लेख लिखना आप जैसे विद्वान व्यक्ति के लिए उचित नहीं होगा।
मैंने कुछ अधिक लिख दिया हो या आपकी भावना को ठेस पहुंची हो तो इस हेतु क्षमा प्रार्थना।


ATUL KOTHARI
Secretary- Shiksha Sanskriti Utthan Nyas
Co-Convener- Shiksha Bachao Andolan Samiti

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