My articles on this were published in The Hindu, 3 Sep 2014, http://www.thehindu.com/opinion/op-ed/nothing-vedic-in-vedic-maths/article6373689.ece?homepage=true, and in Hindi in Jansatta, on 10 Aug 2014, http://epaper.jansatta.com/318935/Jansatta.com/Jansatta-Hindi-10082014#page/17/1 Many people have commented: (at last view, the Hindu article had 204 comments and Facebook Like/Share count was 4.5K).
Here are my responses to those comments. (A response in Hindi to Shri Atul Kothari, who is co-convenor with Dinanath Batra is given below.)
1. Abuse. After working on decolonisation for the last 4 years, and mentioning it in the above articles (see further below), it is excessively funny to find someone accusing me of being a follower of Macaulay! These people have an equally poor knowledge of Hinduism, hence they think it can only be established by chanting abuses like mantras, and there is no possibility of serious debate. (I have given what is the possibly the strongest scientific basis for Upanishadic philosophy in time beliefs, though it is not immune from Buddhist criticism.) Why could no one see, before me, the transmission of the Indian calculus to Europe and the epistemological mess that Europeans created in mathematics? According to the Nyaya Sutra, ignorance of the purva paksa disqualifies these abusers from being taken seriously. These are the very persons who claim to own Hinduism but are in reality its worst enemies, because they will allow no space for real (proven) knowledge, and insist that everyone must agree with their childish fantasies.
2. It is ancient hence it is Vedic.
2.1 What is the proof that it is ancient? Vedic mathematics actually comes from recent times in the 1960’s. Krishna Tirtha hid his real sources (possibly because they were lower-caste artisans, and acknowledging that would have worked against the acceptance of that system). How do we even know this system is Indian in origin?
2.2 Buddhism, Jainsim, and Lokayata too are ancient. (Carvaka finds mention in the Mahabharata.) Buddhism and Jainism reject the Veda as a means of knowledge. Is that Vedic knowledge? Lokayata maintained that Brahmins are hypocrites. Is that also Vedic knowledge? If not, equating ancient with Vedic is wrong. Note that Lokayata would be classified as Hindus for purposes of present-day tax laws, for example, and even according to the census.
3. It is useful for CAT etc. The purpose of education is not to pass competitive exams That is an excessively narrow vision. The real social use of mathematics is in science and engineering, where this kind of mental arithmetic is irrelevant. For the educational reform related to the decolonisation of math and science, see below.
4. Caste and Shakuntala Devi. Carpenters, for example, needed to do calculations 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 from lower castes. Why should this fact not be mentioned? On the contrary, I was just hinting that it might explain why Krishna Tirtha hid his sources. I have no proof of that: it is just a speculation, hence I gave only a hint.
As for Shakuntala Devi, I met her only once, some 40 years ago, when she gave a performance at the Indian Statistical Institute Delhi. I was initially skeptical, but was charmed by her simplicity and candor. My point in mentioning her was simply this. Since Krishna Tirtha hid his sources, how do we even know they were Indian? And, sure enough, some people have mentioned Trachtenberg (or whatever his name). Now, Shakuntala Devi is surely Indian, and she created a sensation. If the West had any inkling then of those algorithms, she would have been quickly exposed. But the fact is that no one then could replicate her performance. So, I mentioned Shakuntala Devi to hint at this possible line of argument for the Indian origin of the algorithms. Those people who jump to conclusions without any understanding should now eat their words.
5. It is a faster algorithm.
The government of India spent some 5 million USD on a project related to traditional knowledge. One of the outcomes was some unpublished papers claiming that algorithms based on Vedic math were more efficient. The draft papers that I saw in the early 90’s reported the results of very careless research. For example, for the square root algorithm, it compared with “Newton’s method” by using an initial value which was half the number. (“Newton’s” method is sensitive to the starting guess, and 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 bit shift, and worked against the efficiency of Vedic math algorithms.) 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. Some people have pointed to Dani’s paper and said that Vedic mathematics is not mathematics. That is going too far .My position is that what Dani does is not mathematics, but is pure metaphysics based on Christian theology. One can perhaps excuse the ignorance of Dinanath Batra who is only a school teacher, but one cannot excuse Dani’s ignorance for he is a highly paid researcher in the best funded research institute in India. And the only “research” he has done in the history of math over the last twenty years is to repeat this one line on Vedic math ad nauseum. So far as lack of documentary support for Vedic mathematics is concerned, that was already exposed by K. S. Shukla: Dani’s research contribution is thus only to say that it is not the same as the Christian metaphysics he does. So what? He cannot justify that way of doing mathematics. Dinanath Batra’s associate at least immediately responded to my criticism, showing that even if his beliefs are wrong, he sincerely believes them. But neither Dani nor any one else from the Tata Institute has dared to respond to my critique of formal math stated in two books Cultural Foundations of Mathematics, and Euclid and Jesus. In my article on Kosambi in the Economic and Political Weekly, I also pointed out that the work done by mathematicians at the Tata Institute is persistently worthless for the Indian people, and it is a colossal waste of money. There has been no reply to that either. This lack of response shows that these guys are shamelessly unethical, and are deliberately cheating the country. Only Westerners praise them, since these comprador elements benefit them, and colonialism was built using precisely these elements. Dani and his brand of Christian mathematics is far more poisonous than Vedic mathematics, and they are unable to justify their beliefs, and unable to respond to the criticism for the last decade. Hence, the case against them stands proven.
7. So, what is the alternative? Nobody has raised this question yet, because of some misplaced belief that mathematics is universal and 2+2 must always be 4. (Why? Computer arithmetic does not work that way, and yet it works well.)
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 who mixed up its infinite series with the theology of eternity, thereby making math difficult. I have further explained how with the help of tradition (Buddhist sunyavada, not Vedic tradition) one can make it easy. I have demonstrated this through pedagogical experiments in three countries. (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.)
From: Prof. C. K. Raju <ckr@ckraju.net>
To: Atul Kothari <atulssun@gmail.com>
Sent: Thursday, 21 August 2014 8:51 AM
Subject: Re: दिनांक 8 अगस्त 2014 के जनतसा दैनिक में आपका लेख पढ़ा।
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 केलिए “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 पडता 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
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From: Atul Kothari <atulssun@gmail.com>
To: ckr@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
Ph-011-25898023, 65794966
Mob-09868100445,
