Vedas are infinities. Vedic roots of Zero.and Calculus

अनन्ता वै वेदाः = Vedas are infinities
-Arun Kumar Upadhyay 
(1) Origin-This has been stated in a story of Taittirīya Brāhmaŋa (3/10/11)-Bharadvāja spent 3 lives withBrahmacharya  to study Vedas by grace of Indra. At end, he became very old and bed-ridden. Then Indra asked what he would do if offered a fourth life of 100 years. He stated that he will complete his study of Vedas. Indra showed him 3 mountains as form of 3 vedas and took fistful of dust from each-telling that Bharadvāja had got knowledge equal to that.
भरद्वाजो ह वै त्रिभिरायुर्भिर्ब्रह्मचर्य्यमुवास । तं ह जीर्णि स्थविरं शयानं इन्द्र उपब्रज्य उवाच । भरद्वाज ! यत्ते चतुर्थमायुर्दद्यां, किमेनेन कुर्य्या इति ? ब्रह्मचर्य्यमेवैनेन चरेयमिति होवाच । तं ह त्रीन् गिरिरूपानविज्ञातानिव दर्शयाञ्चकार । तेषां हैकैकस्मान्मुष्टिमाददे । स होवाच, भरद्वाजेत्यमन्त्र्य । वेदा वा एते । “अनन्ता वै वेदाः” । एतद्वा एतैस्त्रिभिरायुर्भिरन्ववोचथाः । अथ त इतरदनूक्तमेव । (तैत्तिरीय ब्राह्मण ३/१०/११)
Here, it has been stated- अनन्ता वै वेदाः = Vedas are infinities. It is not told in singular that Veda is infinity. Plural form means that there are at least 3 types of infinities, 2 types would have made it dvivachana.
(2) Zero and Infinity-Firstly, we may see definition of infinity. In calculus or analysis, infinity is defined as the limit of 1/x when x tends to zero. This is dependent on zero, which is defined in same manner-it is limit of 1/x when x tends to infinity. 1/x tends to zero means that its value can be made smaller than any small number ε which can be imagined. Similarly, tends to infinity means that its value can be made larger than any large number G which can be imagined. Both definitions are stated in single sentence-
अणोरणीयान् महतो महीयान्आत्मास्य जन्तोर्निहितो गुहायाम्।
तमक्रतुः पश्यति वीतशोकोधातुप्रसादान् महिमानमात्मनः॥
(कठोपनिषद् //२०श्वेताश्वतर उपनिषद् /२०)
(Brahma) is smaller than the smallest and greater than the greatest. It is ātmā of this being (jantu) and enclosed in a cave. That form is akratu = detached from action, or a person detached from work and sorrow can see the mahimā of Brahma, by His grace.
There are many lines indicating Brahma as smaller than the smallest or śūnya-
अणिष्ठे वाङ्गेऽङ्गे समानयति। (मैत्रयणी उपनिषद् /)
अणीयान् ह्यतर्क्यमणु प्राणात्। (कठोपनिषत् //)
अणीयान् ब्रीहेर्वा यवाद्वा। (छान्दोग्य उपनिषद् /१४/)
अणु कोटर विस्तीर्णे त्रैलोक्यं  जगद्भवेत्। (तेजविन्दु उपनिषद् /८७)
अणोरणीयानहमेव तद्वत्। (कैवल्य उपनिषद्२०)
अणोरणीयांसमनुस्मरेद्यं (गीता /)
अणोरप्यणवं ध्यात्वा। (मैत्रायणी उपनिषद् /३८)
Līlāvatī of Bhāskarāchārya-2 gives rules for division by zero which are equivalent to notion of limit in calculus-
योगे खं क्षेपसमं वर्गादौ खं भाजितो राशिः। खहरः स्यात् खगुणः खं खगुणश्चिन्त्यश्च शेषविधौ॥
शून्ये गुणके जाते खं हारश्चेत् पुनस्तदा राशिः। अविकृत एव ज्ञेयस्तथैव खेनोनितश्च युतः॥
Reverse limits of zero and infinity are explained in his another book-Bījagaṇita-
अस्मिन् विकारः खहरे  राशावपि प्रविष्टेष्वपि निःसृतेषु।
बहुष्वपि स्याल्लयसृष्टिकालेऽनन्तेऽच्युते भूतगणेषु यद्वत्॥
 
(3) Grades of Infinity-Cantor’s Set theory describes grades of infinity. Smallest infinity is countable. Counting of a set of objects means we arrange them in a sequence and match each with natural (= counting) numbers 1, 2, 3, 4, …… Any set having infinity numbers can be counted with natural numbers.
Thus set of all natural numbers is equal to set of all even numbers or all squares-
1,   2,   3,   4,   5,      —— up to infinity
2,   4,   6,   8,   10, ——–
Even the set of all fractions is equal to all natural numbers. It can be shown by arranging all fractions serially, so that they can be serially matched with natural numbers-
             – – — – –
           – – — – –
            – – — – –
We arrange the first row with numerator as 1 followed by denominators as 1, 2, 3, 4, … In second row numerator is 2, third row has 3 and in all rows numerators are 1, 2, 3, 4, .
From top left corner we count diagonally, up then down, up etc. Thus in sequence 1, 1/2/, 2/1, 3/1, 2/2, 1/3….., we count all fractions and it is same as infinity of natural numbers.
Cantor showed that real numbers cannot be arranged in a sequence which can be counted by natural numbers. Whatever sequence is made, we can always find a number between 0 and 1 which does not come in any sequence. Take the first number and its first digit, it can be 0 if decimal ends, take 9, otherwise take 0 in first decimal place of new number. At second place, take a digit different from second digit of that number and so on. Thus, we get a number which is not in that sequence and real numbers are definitely bigger infinity than natural numbers. Cantor further showed that, set of real numbers is equal to number of all sub-sets of natural numbers. In each subset, a number can be taken or left. So, if infinity of natural numbers is N0, then count of real numbers is N1 = . Set of all subsets of real numbers itself will be still higher infinity equal to N2 = .
(4) Indian definitions-A jain author Vīrasena in his book Vīra-dhavalā has classified infinities of 3×3 = 9 kinds-samkhyāta, asamkhyāta, ananta-each divided into 3 categories (See Tao of Jain Sciences by Lakshmi Chand Jain-Appendix-2)
  Viṣṇu sahasranāma gives many names meaning infinity-Ananta (659, 886), Anantajit (307) Anantarūpa (932), Anantaśrī (933), Anantātmā (518), Aniruddha (185, 638), Anirdeśyavapu (177, 656), Anekamūrtti (721), Apāmnidhi (323), Avyaya (13, 900), Aprameya (46), Aprameyātmā (248) Amānī ((747), Amitavikrama (516, 641), Ameyātmā (102, 179), Ambhonidhi (517), Asamkhyeya (247), Asammita (108), Nidhih Avyayah (30), Naikah (726), Naikakarmakṛt (469), Naikajah (890), Naikamāyah (302), Naikarūpah (271), Naikaśṛngah (763), Naikātmā (468), Paramātmā (11), Parameṣṭhī (419), Parardhih (389) Parigrahah (420), Paryavasthitah (931), Pūrṇah (685), Bṛhat (836), Brahma, (663, 664), Brahmavivardhanah (665), Brahmaṇya (669), Brāhmī (668) Mahat (841), Mahardhi (350), Mahākramah (671), Mahānidhi (806), Mahāmāyah (170) Mahārhah (522), Viśvam (1), Sarvah (25). In addition, many other words also may mean infinity-Sahasra (1000, infinity), Vīra (boundary, brave, Akabar = without cover or infinite in Persian).
At 2 places, Śankarāchārya has given 2 meanings of word ‘Ananta’. At serial 659, he tells-
व्यापित्वान्नित्यत्वात् सर्वात्मत्वात् देशतः कालतो वस्तुतश्चापरिच्छिन्नःअनन्तः सत्यं ज्ञानमनन्तं ब्रह्म (तैत्तिरीय उपनिषद् /इति श्रुतेः।गन्धर्वाप्सरसः सिद्धाः किन्नरोरगचारणाः। नान्तं गुणानां गच्छन्ति तेनानन्तोऽयमव्ययः। (//२४)इति विष्णुपुराण वचनाद्वा अनन्तः।
 
At 886, he tells-
नित्यत्वात् सर्वगतत्वात् देशकालपरिच्छेदाभावात् अनन्तः शेषरूपो वा।
At both places, these meanings are indicated-eternal, all pervading, soul of all, not bound by time and space, satya (truth, sameness) of three types etc. At first place, it occurs after words-Anirdeśya-vapu = indeterminable body, Viṣṇu = enclosingall, so it means infinite in time and space. At second place, it occurs with Hutabhuk, Bhoktā =consumer etc. Here, it may mean infinite consumption or work.
Asamkhyeya means not measurable with cardinal numbers.
Aprameya is numbers not defined with algebraic formula.
Ambhonidhi is collection of continuous numbers like spread of water in 3 dimensional space.
Naikah means not measurable with cardinal numbers starting with 1.
Kātyāyana śulba sūtra defines infinity as greater than any standard-(greater than any large number imagined)-
अपरिमितं प्रमाणाद् भूयः (कात्यायन शुल्ब सूत्र १/२३)
 
(5) Vedic usage-Tulasīdāsa starts mangalācharaṇa of Rāmacharita-mānasa with-वर्णानामर्थसङ्घानां रसानां छन्दसामपि।मङ्गलानां  कर्त्तारौ वन्दे वाणी विनायकौ॥
 
Here, collection of letters, syllables is countable with natural numbers. Their meanings are more and partly abstract-they too are countable. Bhāva or rasa is not countable. Countable perception of world is Gaṇeśa (where Gaṇana or counting can be done). Abstract concept is Rasa-vatī or Sarasvatī. It is similar to 2 broad divisions of noun in English grammar-countable and abstract. Countable is further divided into proper, common, collective nouns. In mathematics, it is discrete or continuous theory. These are equivalent to set of natural and real numbers. In 1981, I had given example of analog and digital computers to explain this concept to Prof Abdul Salam of Pakistan who had come after getting Nobel prize and was my guest for 2 days. He was very happy with the description and made a remark in some journal that controller of Digital computer (Gaṇeśa) should be called a mouse (his vehicle). That name has become popular now.
Reverting to original context of Taittirīya brāhmaṇa, the three infinities are-
Ṛg veda (collection of forms = mūrtti)- Natural number infinity.
Yajurveda (motion, creation)-Real number
Sāmaveda (field of influence = mahimā) =Transcendental numbers.
Atharva veda (Brahma, reference) = Indeterminate.
ऋग्भ्यो जातां सर्वशो मूर्त्तिमाहुःसर्वा गतिर्याजुषी हैव शश्वत्।
सर्वं तेजं सामरूप्यं  शश्वत्सर्वं हेदं ब्रह्मणा हैव सृष्टम्॥ (तैत्तिरीय ब्राह्मण /१२//)
Īśāvāsyopaniṣad also hints at triple infinities-
 पर्यगात् शुक्रं अकायं अव्रणं अस्नाविरं शुद्धं अपापविद्धम्।
कविर्मनीषी परिभूः स्वयम्भूः याथातथ्यतो अर्थान् व्यदधात् शाश्वतीभ्यः समाभ्यः॥८॥
 
This explains 2 complementary aspects of world-Vāk and Artha. In physical world creation from abstract is by creating a boundary or cover (paryagāt), body, internal and external links, defects (gradients of density etc), separation (pāpaviddha). Abstract thought in mind remains there up to 3 stages of vāk-Parā, PaśyantI, madhyamā. When it is expressed out by speech or writing it is broken into letters, syllables, words, clause, sentence and paragraphs logically linked internally and externally and separated by comma, full stop etc. When transformation from abstract internal thought is exact, the creation (kāvya) becomes eternal. There is a similar verse about start of kāvya by Vālmīki.
Collection of letters, words, sentences in speech or writings= natural number set.
Meanings linking internal (paśyantī) and external steps of vāk = real number set.
Parā vāk = Transcendental number.
वेद में ४ प्रकार के अनन्तों की चर्चा है- (१) वेदों के ३ अनन्त-भरद्वाजो ह वै त्रिभिरायुर्भिर्ब्रह्मचर्य्यमुवास । तं ह जीर्णि स्थविरं शयानं इन्द्र उपब्रज्य उवाच । भरद्वाज ! यत्ते चतुर्थमायुर्दद्यांकिमेनेन कुर्य्या इति ? ब्रह्मचर्य्यमेवैनेन चरेयमिति होवाच । तं ह त्रीन् गिरिरूपानविज्ञातानिव दर्शयाञ्चकार । तेषां हैकैकस्मान्मुष्टिमाददे । स होवाचभरद्वाजेत्यमन्त्र्य । वेदा वा एते । अनन्ता वै वेदाः” । एतद्वा एतैस्त्रिभिरायुर्भिरन्ववोचथाः । अथ त इतरदनूक्तमेव । (तैत्तिरीय ब्राह्मण ३/१०/११)
यहां वेद और अनन्त दोनों बहुवचन हैं अतः २ से अधिक हैं। अनन्त की परिभाषा आधुनिक बीज गणित और कैलकुलस (कलन) में है कि यह किसी भी बड़ी संख्या से बड़ा है। इसके विपरीत बीजगणित में किसी संख्या से उसी को घटाने से शून्य होता है। किन्तु कैलकुलस की परिभाषा है कि यह किसी भी छोटी संख्या से छोटा है। कैलकुलस की दोनों परिभाषायें उपनिषद् में हैं-
 
अणोरणीयान् महतो महीयान्आत्मास्य जन्तोर्निहितो गुहायाम्।
तमक्रतुः पश्यति वीतशोकोधातुप्रसादान् महिमानमात्मनः॥
(कठोपनिषद् १//२०श्वेताश्वतर उपनिषद् ३/२०)
कैण्टर की सेट थिओरी (१८८०में अनन्तों की २ श्रेणियों की व्याख्या हैएक वह जो गिना जा सके। १,,,….. आदि संख्याओं का क्रम भी अनन्त है। इन संख्यामों से सभी वस्तुओं को ११ कर मिलाया जा सके तो यह प्रथम प्रकार का अनन्त है। भिन्न संख्यायें भी इससे एक विधि द्वारा गिनी जा सकती हैं। पर कुछ संख्यायें ऐसी हैं जो इससे नहीं गिनी जा सकती हैंजैसे ० और १ के बीच की सभी संख्या या किसी रेखा खण्ड के विन्दुओं की संख्या। यह बड़ा अनन्त है जिसको २ के अनन्त घात से सूचित किया जाता है। एक अन्य अनन्त भी हो सकता हैजो २ के दूसरे अनन्त घात के बराबर होगा। ऋग्वेद मूर्त्ति रूप हैवह गिना जासकता हैप्रथम प्रकार का अनन्त जो १,,, …. क्रम के बराबर है। यजुर्वेद का क्रिया या गति रूप अनन्त वही है जो विन्दु की गति से बने रेखा में होगायह दूसरा अनन्त है। साम उसकी महिमा तीसरा अनन्त है।
 
ऋग्भ्यो जातां सर्वशो मूर्त्तिमाहुःसर्वा गतिर्याजुषी हैव शश्वत्।
सर्वं तेजं सामरूप्यं ह शश्वत्सर्वं हेदं ब्रह्मणा हैव सृष्टम्॥ (तैत्तिरीय ब्राह्मण ३/१२//)
दूसरा अनन्त भी २ प्रकार का हैजो गणित सूत्रों द्वारा व्यक्त हो सके वह परिमेय या प्रमेयजो उससे व्यक्त नहीं हो सके वह अप्रमेय ह। विष्णु सहस्रनाम में अनन्त के लिये ३ शब्द हैंअनन्तअसंख्येयअप्रमेय। इसके अनुसार प्रथम संख्येय अनन्त है। असंख्येय अनन्त २ प्रकार का है,प्रमेय और अप्रमेय। उसके बाद परात्पर अनन्त ब्रह्मरूप अथर्व वेद है।स ब्रह्मविद्या सर्वविद्या प्रतिष्ठा ज्येष्ठाय पुत्राय अथर्वाय प्राह-(मुण्डकोपनिषद् १//)
जैन गणितज्ञ वीरसेन (सम्भवतः हर्ष विक्रम ४५६ ई.पू.के समकालीनकी वीरधवला में इन ३ अनन्तों के मिलन से ९ अनन्तों की चर्चा है।
(वर्ण और अक्षर रूप अनन्त गिना जा सकता हैजो गणेश है। उसका अर्थ द्वितीय प्रकार का अनन्त है। उसकी महिमा या भाव तृतीय अनन्त है , जो भाव या रसरूप होने से रसवती = सरस्वती है। वर्णानामर्थसङ्घानां रसानां छन्दसामपि। मङ्गलानां च कर्त्तारौ वन्दे वाणी विनायकौ॥ (रामचरितमानसमंगलाचरण) वाक् के ४ पदों में अन्तिम वैखरी प्रथममध्यमा द्वितीयतथा पश्यन्ती तृतीय अनन्त है। परा वाणी इससे भी परे है। जो पश्यन्ती और मध्यमा के अर्थ को ठीक ज्यों का त्यों प्रकट कर सकता हैउसी की रचना शाश्वत होती है-स पर्यगात् शुक्रंअकायं अव्रणंअस्नाविरं शुद्धंअपापविद्धं कविर्मनीषी परिभूः स्वयम्भूः याथा-तथ्यतो अर्थान् व्यदधात्शाश्वतीभ्यः समाभ्यः-ईशावास्योपनिषद्८। यही रामायण में है-मा निषाद प्रतिष्ठां त्वां अगमः शाश्वती समाः। यत् क्रौञ्चमिथुनाद् एकं अवधीः काम-मोहितम्। वायु-पुराण में रावण को काम-मोहित क्रौञ्च कहा हैउस मिथुन का दूसरा मन्दोदरी काम-मोहित नहीं थी। मा= लक्ष्मी का निषाद = निवास श्रीराम हैं। उनकी प्रतिष्ठा से साहित्य शाश्वत होता है। या उपनिषद् अनुसार मा (मस्तिष्क गुहा) की वाणी को व्यक्त रूप में प्रतिष्ठा कार्ने से शाश्वत होगा। वाक्य के वर्ण विपर्यय से काव्य हैवाक्य तात्कालिक घटनाकाव्य शाश्वत है।
(३) सृष्टि के अनन्त-(क) सृष्टि का मूल पुरुष का ३ पाद थाउसका एक ही भाग  विश्व बनाने में प्रयुक्त हुआबाकी ३ भाग का प्रयोग नहीं हुआ,अतः वह ज्यायान् (भोजपुरी में जियान = बेकारअनुपयुक्त) है। ३ भाग जो बच गयेवे शेष (अनन्त) हैं। १ पाद का व्यक्त जगत् पुरुष है४ पाद मिलकर पूरुष हैं। या विराट् विश्व (व्यक्त रचनायें) पुरुषउनका अधिष्ठान या महिमा पूरुष है। ये अप्रमेय और परात्पर अनन्त हैं। पादोऽस्य विश्वा भूतानि त्रिपादस्यामृतं दिवि। एतावान् अस्य महिमा अतो ज्यायांश्च पूरुषः (पुरुष सूक्त ३,४)
(ख) स्वयम्भू मण्डल असंख्येय अनन्त हैब्रह्माण्डों का समूह संख्येय है। ब्रह्माण्ड का केन्द्र ब्लैक होल = कृष्ण हैइसी के आकर्षण से रज = लोक (ब्रह्माण्ड = जनः लोक) बने हुये हैं-आकृष्णेन रजसा वर्तमानोनिवेशयन् अमृतं मर्त्यं च(ऋग्वेद १/३५/२वाज यजु ३३/४३) तैत्तिरीय सं. (३/४/११/२) इमे वै लोका रजांसि। (यजुर्वेद ११/शतपथ ब्राह्मण  ///१८ब्रह्माण्ड केन्द्र से आकर्षित रचना अमृत (विष्णु पुराण २/७ में अकृतकऔर सूर्य आकर्षण का क्षेत्र अकृतक या मर्त्य है। बीच में सूर्य हैब्रह्माण्ड के लिये कणतथा सौरमण्डल का वामन।
(ब्रह्माण्ड के केन्द्र से निकली सर्पिल भुजा वेद का अहिर्बुध्न्य (इसका समुद्र या विरल पदार्थ बुध्न्यउसका सर्प अहिः है)। इसमें जहां सूर्य है उस क्षेत्र की मोटाई के बराबर व्यास का गोला महर्लोक है जिसके १००० तारा शेष के १००० सिर हैंजिनमें १ सिर सूर्य पर कण मात्र पृथ्वी है।
(पृथ्वी का नक्शा उत्तरी गोलार्ध में ४ भगों में बनता था जिनको भूव्पद्म का ४ पटल कहा हैभारतपूर्व में भद्राश्वपश्चिम में केतुमाल तथा विपरीत दिशा में उत्तर कुरु। दक्षिण में भी ४ पटल होंगे। गोल पृथ्वी का समतल नक्शा बनाने पर ध्रुव की तरफ नक्शा में आकार बढ़ता जाता है,जैसे ग्रीनलैण्ड भारत से छोटा है पर १५ गुणा बड़ा दीखता है। उत्तरी ध्रुव जल भाग है (आर्यभटअतः वहां कोई समस्या नहीं है। पर दक्षिणी ध्रुव पर स्थल है जिसका नक्शा इस विधि से नहीं बन सकतावह अनन्त आकार का हो जायेगा अतः अलग से नक्शा बनाना पड़ेगा। अतः इसे अनन्त (अण्टार्कटिचाकहते हैं।


S. Kalyanaraman

https://beta.groups.yahoo.com/neo/groups/IndiaArchaeology/conversations/messages/16792

Bacon, sausage and other processed meats cause cancer, World Health Organization warns

‘Sufficient evidence’ linking processed meat to colorectal cancer.

The World Health Organization (WHO) announced on Monday that it has classified processed meat as a human carcinogen.

Red meat also was classified as a probable human carcinogen, according to the release by WHO’s International Agency for Research on Cancer (IARC).

The group cited “sufficient evidence” linking processed meat—such as bacon and sausage—to colorectal cancer, and noted associations with stomach, prostate, and pancreatic cancers. Processed meat is preserved by smoking, salting, fermenting, or by the addition of chemicals, and the category includes bacon, sausage, deli meats, and hot dogs. The red meat category includes beef, veal, pork, and lamb.

The IARC evaluates substances suspected of causing cancer in humans, and arrives at its classifications byconvening a working group of international experts to review and assess the strength and quality of the evidence—in this case, more than 800 studies. Although the meat classifications have no regulatory impact in the United States, they are likely to further intensify the already heated debate about meat-eating, which has made headlines since February, when the committee charged with updating the US Dietary Guidelines recommended that Americans should eat less meat.

It’s also possible that the classification could fuel lawsuits. Another recent IARC report, which classified the herbicide glyphosate as a probable human carcinogen, has promptedsome law firms to seek out cancer sufferers who were exposed to the chemical, to file suit on their behalf.

The American meat industry, understandably, takes strong issue with any suggestion that meat is something consumers should eat less of. The North American Meat Institute (NAMI) immediately issued a statementdeclaring the classification as defying “both common sense and dozens of studies showing no correlation between meat and cancer and other studies showing the many health benefits of balanced diets that include meat.” In fact, many of the studies NAMI references do show correlations, but describe them as “inconsistent” or “weak.”

Like much of the research on how diet affects health, the research on the link between meat and cancer has enough ambiguity that it’s possible to cherry-pick a research list that supports either position, but many reviews of research on the best-established link between meat and cancer—colorectal cancer—find, as this 2014 review published in the American Journal of Clinical Nutrition does, that there is a convincing association between meat eating and colorectal cancer. The question, though, is whether the meat eating causes the cancer, or whether meat eaters, who are different from non-meat eaters in many ways, are eating or doing other things that put them at risk.

The National Cancer Institute’s position is that the preponderance of the evidence does find a correlation between meat consumption and cancer risk, but it cites inconsistent results and confounding factors as barriers to a definitive conclusion. “The evidence is inadequate” to determine whether eating less meat would cut colorectal cancer incidence, the group says.

In an interview with Fortune, Shalene McNeill, executive director of human nutrition research for the National Cattlemen’s Beef Association, acknowledged the association between cancer and meat, but pointed to those confounding factors as the culprit: “Red meat is being consumed in the context of an unhealthy diet,” she said, and pointed out that meat-eaters are more likely to smoke and be overweight. David Klurfeld, National Program Leader for human nutrition at the USDA and a participant in the IARC process, wrote in a recent paper that meat-eaters also exercise less, drink more, and eat fewer fruits and vegetables. Controlling for these things is a tricky business, and there are undoubtedly other behaviors, not included in the data, that can’t be controlled for at all.

The IARC acknowledges the difficulty of determining causality, but their report concludes that, “the consistent associations of colorectal cancer with consumption of processed meat across studies in different populations, which make chance, bias, and confounding unlikely as explanations.” On red meat, though, “Chance, bias, and confounding could not be ruled out with the same degree of confidence.”

In light of all this, it’s not surprising that scientists do not speak with one voice on this issue. Leaning toward the IARC position is Andrew Chan, an associate professor of medicine at Harvard Medical School whose research focuses on colorectal cancer prevention. “I think the evidence is reasonably supportive of that position,” he toldFortune of the IARC classification. He acknowledged that “many studies are flawed,” but nevertheless said that if you look at the preponderance of the evidence, the IARC conclusion is “a reasonable one.” He notes that the evidence for processed meat is stronger than that for red meat.

Tamar Haspel is a journalist on the food and science beat. She writes the James Beard Award-winning Washington Post column, Unearthed, and farms oysters off Cape Cod.

https://www.google.ca/search?q=Dr.+Carson&rlz=1C1CHWA_enCA630CA630&oq=Dr.+Carson&aqs=chrome..69i57&sourceid=chrome&es_sm=93&ie=UTF-8