आधुनिक समाजमें वेद का प्रासङ्गिकता

आधुनिक समाजमें वेद का प्रासङ्गिकता

जगन्नाथ पुरी के गोवर्द्धनपीठ के पूर्व शङ्कराचार्य भारतीकृष्ण तीर्थ महास्वामी से एक विदेशी व्यक्ति ने प्रश्न किया “पृथ्वी पर हिन्दुओँ का संख्या अल्प है । उनमें से सब आपको नहिँ मानते । तो आप कैसे अपनेको जगद्गुरु कहलाते हैँ” । उत्तरमें उन्होने कहा “जगद्गुरु का अर्थ यह नहिँ कि मैं जगत् का गुरु हुँ । परन्तु जगत् में कहिँ भी कोइ भी व्यक्ति यदि आध्यात्मिक मार्गमें प्रगति के लिये मेरा सहायता चाहता हो, तो मैं उसका मार्गदर्शन करने के लिये वाध्य हुँ । यही मेरा जगद्गुरुत्व है ।” अपनेको प्रासङ्गिक वनाने का यह एक प्रकृष्ट उदाहरण है ।

वेदके प्रासङ्गिकता पर विचार करने से पूर्व, वेद क्या है, यह जानना चाहिये । ऋक्, यजुः, साम, अथर्व नामसे प्रसिद्ध चार पुस्तकें वेदशास्त्र है । यह वेद नहिँ है । वेद सामान्य है । वेदशास्त्र विशेष है । सामान्य, ज्ञान तथा मुक्ति का विषय है – प्रतिसञ्चर मार्ग है । विशेष, विज्ञान तथा सृष्टि का विषय है - सञ्चर मार्ग है । सत्ता महासामान्य है । इसीलिये ज्ञानको एक एवं अखण्ड कहा जाता है । अनेक से एक के प्रति गमन ज्ञान है । एक से अनेक के प्रति गमन विज्ञान है । “सर्व खल्विदं ब्रह्म” मुक्तिरूप ज्ञान मार्ग है । “ब्रह्मैवेदं सर्वम्” सृष्टिरूप विज्ञान मार्ग है । ज्ञान विज्ञान के विना अधुरा है । विज्ञान ज्ञान के विना अधुरा है । दोनों के समन्वय से ब्रह्म का पूर्ण ज्ञान होता है । इसीलिये मुण्डकोपनिषद् 3-2-6 में कहागया -

वेदान्तविज्ञानसुनिश्चितार्थाः सन्यासयोगाद्यतयः शुद्धसत्त्वाः ।

ते ब्रह्मलोकेषु परान्तकाले परामृताः परिमुच्यन्ति सर्वे ।

यहाँ वेदान्तविज्ञान कहागया है – वेदान्तज्ञान नहिँ । ईशोपनिषद् भी उद्घोषणा करते हैं कि –

अन्यदेवाहुर्विद्ययाऽन्यदाहुरविद्यया । इति शुश्रुम धीराणां ये नस्तद्विचचक्षिरे ।।

यही गीताका मूल उपदेश है । इसीलिये भगवानने गीता 7-2 में कहा है कि –

ज्ञानं तेऽहं सविज्ञानमिदं वक्ष्याम्यशेषतः । यज्ज्ञात्वा नेह भूयोऽन्यज्ज्ञातव्यमवशिष्यते ।।

ब्रह्मके ज्ञानविज्ञानात्मक होनेसे भारतके मुनि-ऋषि दोनों के उपासक थे । तभी देश उन्नत था । परवर्ति समयमें सायण से लेकर अन्य व्याख्याताओं ने विज्ञानका उपेक्षा कर केवल स्तुति तथा देवपुजन का सहायता से ज्ञान का अनुसरण किया । वह लोग भुलगये कि यज् धातुका अर्थ केवल देवपूजन नहिँ, परन्तु “सङ्गतिकरण” भी है । “अग्निमीळे” में “ईळे” शव्द का अर्थ विकृत करके “ईडे” नहिँ करना चाहिये । सदागतिशाल तथा सवको प्रेरित करनेवाले अग्नि के लिये “ईळे” का अर्थ “इलँ प्रेर॑णे” धातुसे करना चाहिये । यह केवल विज्ञानभाष्यमें सम्भव है ।  “अग्निषोमात्मक जगत्” श्रुतिवाक्यमें “अग्निषोम” शव्द अग्नि ओर घी नहिँ है । यज्ञका अर्थ केवल अग्निमें घी डालना नहिँ, प्रकृतिके नियमों का विकल्प वनाकर इच्छित वस्तुका प्राप्त करना भी है । तभी तो श्रुति कहती है कि “यद्देवाः अकुर्वन् तत् करवाम” । तभी तो भारतीकृष्ण तीर्थ महास्वामीने वैदिक गणित का प्रचार प्रसार किया ।

ज्ञान का आलम्बन विज्ञान है । तभी तो गीता 7-2 में कहागया है कि “ज्ञानं तेऽहं सविज्ञानमिदं वक्षाम्यशेषतः”। जब से हमारे देशमें विज्ञानका तिरस्कार करके केवल ज्ञान का अनुसरण होने लगा, तभी से हमारा अधःपतन आरम्भ हो गया । न हम ज्ञान का पराकाष्ठा दिखा पाये न विज्ञानका लाभ उठापाये । विज्ञानके लिये हम पाश्चात्य जगतके प्रति निर्भरशील है । उधर पाश्चात्यजगत विज्ञानका अन्धानुसरण करके आज मानसिक अवसाद से ग्रस्त होकर पूर्व कि दिशामें देख रहा है । इसीलिये बृहदारण्यक उपनिषद 4-3-32में कहा गया है कि –

“सलिल एको द्रष्टाऽद्वैतो भवत्येष ब्रह्मलोकः .... एषास्य परमा गतिरेषास्य परमा सम्पदेषोस्य परमो लोक एषोस्य परम आनन्द एतस्यैवाऽऽनन्दस्यान्यानि भूतानि मात्रामुपजीवन्ति ।“ ज्ञान तथा विज्ञानके अद्वैत – द्वन्दराहित्य - हि अभ्युदय का कारण है ।

किसी व्यक्ति, वस्तु अथवा भावके प्रति ध्यानदेना अथवा अभिमुख होना प्रसङ्ग है । यह आभिमुख्य किसी व्यक्ति, वस्तु अथवा भावमें अन्वित होकर यावत्कालस्थायी होना उसकी प्रासङ्गिकता है । उससे उस व्यक्ति, वस्तु अथवा भावके प्रति सङ्ग जात होता है । सङ्ग से यथाक्रमे काम, क्रोध, सम्मोह, स्मृतिविभ्रम, आदि का उदय होता है (गीता – 2/62-63)। इसीलिये हमारा आभिमुख्य वदलता रहता है । साथ ही उस व्यक्ति, वस्तु अथवा भावके प्रासङ्गिकता भी वदलता रहता है ।

आधुनिक समाजमें भौतिकविलास सुखभोग नामसे प्रमुख आकर्षणका केन्द्र वना हुआ है । परन्तु यह सुखभोग क्या है? एक का अन्यके उदरमें प्रवेश करना भोग है । इससे जात मनोभावको सुख अथवा दुःख कहते हैं । इसीलिये सुख-दुःख-साक्षात्कार को भोग कहते हैं । परन्तु यह सुख-दुःख है क्या? ख अर्थात् शुन्यमें अध्यारोपित सु भावना को सुख तथा दुः भावना को दुःख कहते हैं । वास्तवमें सुख-दुःख जैसा कुछ होता ही नहिँ । केवल भोग ही होता है । भोग का सम्बन्ध विषय तथा जीव से है, जो क्षर तथा अक्षर से सम्बन्धित है । सुख-दुःख परष्पर विरोधी है । जहाँ सुख हो वहाँ दुःख नहिँ रह सकता । परन्तु हम सवमें यह द्वन्द भाव देखते हैं । यह अज्ञानके कारण होता है । यदि हम उनके स्वरूपको पहचान पायेंगे, तो उसी ज्ञानसे हम द्वन्दरहित अव्यय की प्रति दृष्टि देंगे तथा द्वन्द भावके प्रति उदासीन हो जायेंगे ।

कौटिल्य नीतिसूत्र के अनुसार -

“सुखस्य मूलं धर्मः ॥२॥ धर्मस्य मूलमर्थः ॥३॥“

इसीलिये आजकल अर्थको धर्म और काम के लिये साधन मानते हैं । परन्तु यह भ्रमात्मक है ।

पुरुषार्थभूत धर्म और काम के लिये अर्थ साधन नहीं हो सकता कारण कामनाको पुरुषार्थ नहीं कह सकते । भ्रम से ही उसके फल को सुख माना जाता है । विषयसम्बन्ध रूप कामनामक पुरुषार्थ अर्थ से संभव होता है । परन्तु उस कामसुखसे विशेष क्या होता है? यदि नारीसंभोग से भिन्न अन्य सुख को भी कामसुख माने, तो भी यह तर्क व्यर्थ है । भ्रम से अतिरिक्त उसमें भी कोई सुख नहीं है । जैसे एक श्रमिक थका हुआ हो और उस पर कोई पैर से ठोकर मारे तो उसे शरीरमर्दनका सुख मिलता है । ऐसे ही भोगेच्छा से आर्त मूर्ख सम्भोग से समझता है कि सुख मिलगया ! यदि यह सुख है, तो भी उसमें अर्थ साधन नहिँ है । जिनके पास कोई अर्थ नहिँ ऐसे श्वान आदि भी वह सुख पाते देखे जाते हैं । पुरुषको जैसे नारी अच्छा लगती है वैसे श्वान को श्वानॊ भी अच्छा लगती है । इसी प्रकार पुष्प-चन्दन आदि के भोग से हुआ सुख भी अर्थहेतुक नहीं है । अर्थशुन्य भ्रमर, कोकिल आदि भी सुगन्ध आघ्राण करते हैं । वह भी स्वादिष्ट रस पान करते हैं । संगीत श्रवण का सुख अर्थ पर निर्भर नहिँ करता । सुन्दर रूप देखकर सुख लेने के लिये भी अर्थ नहिँ चाहिये क्योंकि लोक में निर्धन पुरुष भी सभा आदि में वारनारीयोँ को देख लेते हैं और अन्य युवतियों को भी वे निःसंकोच देख पाते हैं । कोमलस्पर्श पाने के लिये भी अर्थ जरूरी नहीं है । मख्खी आदि जन्तु भी अत्यन्त कोमल पदार्थ स्पर्श कर लेते हैं। वे तो उन सुन्दरीयों के भी मुखों का स्पर्श कर लेते हैं जिन्हें अन्य धनीक भी देख नहीं सकते । जिसके पास हर तरह का पार्यप्त अर्थ है वह भी अर्थ से सारा ही विषयसुख नहीँ पा सकता परन्तु कुछ सुख तो निर्धन भी पा ही लेता है । इस प्रकार अर्थ कामसुख का साधन नहीं ।

परलोक में सुख देने वाला धर्म भी केवल अर्थ से होता ही हो यह संसार में नियमित रूप से देखा नहीं जाता । प्राचीन मुनि-ऋषि जो हमेशा भूख से कमजोर रहते थे और ऐसे निर्धन बहुत से गृहस्थ स्वर्ग गये हैं तथा बहुत धनीक भी प्रायः प्रमादी होने से, नरक गये हैं, जा रहे हैं और जाते रहेंगे । इसलिये स्वर्ग अर्थ से ही मिलता हो यह बात नहीं । अर्थ के बिना अग्निष्टोम आदि यज्ञ सम्पन्न नहीं किये जा सकते । परन्तु उनका फल जो स्वर्ग, वह तो अर्थ के बिना भी मिल सकता है, क्योंकि स्वर्ग दिलाने वाले अनेक प्रकार के साधन हैं । इस तरह अर्थ ही धर्म का निश्चित उपाय हो, यह मान नहीं सकते ।

कुछ लोग अर्थ को मोक्ष के प्राप्तिके हेतु इसीलिये कहते हैं कि उससे यागादि किये जाते हैं । जब यागादि ही मोक्षप्रद नहीं हैं, तो अर्थ मोक्षोपाय नहीं हो सकता ! ज्ञानमात्र से प्राप्य अमरता के लिये ये अग्निष्टोमादि किसी भी प्रकार से साधन नहीं हैं । यह केवल स्वर्ग दिला सकते हैं । अतः तप इत्यादि के समान ही हैं । इसलिये अर्थ के कारण अग्निष्टोम आदि भले ही हों , अमरता अथवा मोक्षोपाय का वह कारण नहिँ हो सकते।

आत्मा की परमानन्दरूपता अन्वय-व्यतिरेक से भी समझा जा सकता है ।  जहाँ आत्मा का सम्बन्ध है वहाँ प्रियता अवश्य होता है। जहाँ आत्मसम्बन्ध नहीं वहाँ प्रियता भी नहीं होती । एक-अपर के शरीरों के प्रति जो अत्यन्त प्रेम है वह किसी भी प्रकार से अन्य के उपकार के लिये नहीं है । परन्तु अपने ही उपकार के लिये है । स्त्री अपनी प्रयोजन के लिये पति से प्रेम करती है । पतिको अपनी प्रयोजन के लिये पत्नी प्रिया होती है । अपने लिये सुख चाहती नारी कामाग्नि के सन्ताप से और अन्न वस्त्र आदि पाने के लिये पति से प्रेम करती है । पति यदि पत्नी के प्रतिकूल हो, तो प्रेम नहीं हो पाता । सामान्य अनुकूलता रखने पर भी यदि पति किसी अन्य नारी में आसक्त हो तो पत्नी को वह किसी अवस्था में प्रिया नहीं होती । अथवा अन्य किसी व्यसन में उसका ध्यान लगा रहता हो, तो भी पत्नी को वह प्रिय नहीं होता । इसी प्रकार पति जो पत्नी से प्रेम करता है वह इसीलिये कि वह कामुक होता है और उसे भोजन आदि सहज भावसे मिल जाता है । यदि ऐसा न हो तो पत्नी उसे कभी प्रिय नहीं होती । जो पत्नी सुरतादि में अपने पति के प्रतिकूल रहे उस पर किसी तरह प्रेम रखने वाला पति संसार में देखा नहीं जाता । अतः यह आत्मा ही प्रिय है । स्त्री-पुरुषों को सदा सर्वाधिक प्रिय यह स्वप्रकाश सदानन्द आत्मा ही है ।

जैसे पति-पत्नी, वैसे ही पुत्र, धन, गवादि, ब्राह्मण-क्षत्रिय आदि जातियाँ, भूः आदि लोक, देवता, वेद, चर-अचर प्राणी - यह जो सारा ही जगत् है वह सब तभी प्रिय होते है जब अपने को सुख देते हों । जो अपने को सुख न दे, वह कभी प्रिय नहीं होता । कदाचित् जो कोइ प्रतिकूल व्यक्ति पर भी प्रेम करता है, तो वह मोहवश ऐसा करता है । वहाँ भी यदि उस प्रेम से स्वयं को संतोष मिलता हो, तभी प्रेम रहता है । पुत्र आदि जो प्रिय रूप से सब को अनुभव में आते है वे भी प्रतिकूल हो जायें तो प्रिय नहीं रहते । अतः वे अपने लिये ही प्रिय होते हैं । शुकदेव जी कहते हैं: जो समस्त कार्योँ को छोड़ कर सम्यक् प्रकार से शराणागतवत्सल भगवान् की शरण में प्राप्त होता है । वह देवऋण, ऋषिऋण, कुटुम्बी जन और पितृऋण - इन किसी का भी सेवक और ऋणी नहीं रहता । (श्रीमद्भागवत 11/5/41)

योगास्त्रयं मया प्रोक्ता नृणां श्रेयो विधत्सया । ज्ञानं कर्म च भक्तिश्च नोपायोऽन्योऽस्ति कुत्रचित् ॥ (श्रीमद्भागवत)

मनुष्य के कल्याण के लिये ज्ञानयोग, कर्मयोग और भक्तियोग - इन तीनों उपायों ही है । इनके अतिरिक्त, मोक्ष प्राप्ति का और कोई उपाय नहीं है । शरणागति मार्ग में इन तीनों के तात्पर्य स्वतः आ जाते हैं । अतः मुमुक्षु का इस एक ही जन्म में कल्याण हो जाता है , यथा – 

भक्तिः परेषानुभवो विरक्तिरन्यत्र चैष त्रिक एककालः ।

प्रपद्ममानस्य यथाऽश्नतः स्युस्तुष्टिः पुष्टिः क्षदपायोऽनुघासम् ॥

इत्यच्युताध्रिं भजतोऽनुवृत्त्या भक्तिर्विरक्तिर्भगवत्प्रबोधः ।

भवन्ति वै भागवतस्य राजंस्ततः परां शान्तिमुपैति साक्षात् ॥

भगवान् के शरणागतों के हृदय में भगवान् की भक्ति , उनके परात्पर स्वरूप का अनुभवात्मक ज्ञान और अन्य वस्तुओं से वैराग्य ये ती तीनों एक ही समय में अर्थात् साथ - साथ उत्पन्न होते हैं । जिस प्रकार भोजन करने वाले को उसके प्रत्येक ग्रास अर्थात् कौर के साथ - साथ ही तुष्टि , पुष्टि और क्षुधा निवृत्ति तीनों हो जाती है , उसी प्रकार हे राजन् ! भगवान् श्री अच्युत के चरण कमल का निरन्तर भजन करते करते भक्त को भक्ति , विरक्ति अर्थात कर्मयोग का फल और भगवान् के स्वरूप की स्फूर्ति अर्थात् अपरोक्ष ज्ञान ये तीनों अवश्य प्राप्त होती है और फिर वह अर्थात् मुमुक्षु साक्षात् परम शान्ति का अनुभव करने लगता है यह कवि मुनीश्वर ने राजा जनक से कहा है ।

देव, ऋषि तथा पितृ – इन तीनों के मूल परमात्मा ही हैं । अतः उन्हीं की शरण होने से मुमुक्षु सभी से उऋण हो जाता है । यथा तरोर्मूलनिषेचनेन तृप्यन्ति तत्स्कन्धभुजोपशाखाः ।

प्राणोपहाराच्च यथेन्द्रियाणां तथैव सर्वाहणमच्युतेज्या ॥ { श्रीमद्भागवत पुराण 4 / 31 / 14 }

अर्थात् जैसे जड़ के सींचने से वृक्ष के अंग एवं प्राण के तृप्त होने से इन्दियां सचेत होती है , वैसे ही श्रीहऱि का पूजन करने से सभी का पूजन हो जाता है , क्योंकि भगवान् ही सबके आत्मा हैं । अतः उन्हें आत्मा सर्म्पण कर तृप्त करने पर सबकी तृप्ति हो जाती है।

अतः हमें मोक्ष मार्गके साथ साथ विज्ञानमार्ग को भी अपनाना चाहिये । तथा पाश्चात्य जगतको भी मोक्ष मार्गके उपदेश करते रहना चाहिये । वेदके जो स्तुति तथा आशिष है, वह विज्ञानमूलक है । बृहद्देवता में इनका अर्थ करते हुये शौनक महर्षि ने कहा –

स्तुतिस्तु नाम्ना रूपेण कर्मणा बान्धवेन च । स्वर्गायुर्धनपुत्रादैर् अर्थैराशीस्तु कथ्यते । ...

स्तुवद्भिर्वा ब्रुवद्भिर्वा ऋषिभिस्तत्त्वदर्शिभिः । भवत्युभयमेवोक्तम् उभयं ह्यर्थतः समम् ।।

यहाँ नाम्ना रूपेण कर्मणा बान्धवेन से Classification and nomenclature, physical characteristics, chemical properties and interactive potential विवक्षित है । अतः वेद विज्ञानमूलक है ।

REDUCTIONIST MAXIM.

REDUCTIONIST MAXIM.

On my post on the maxim of the six blind men and the elephant, a friend has raised some important questions. Here is my reply to him.

How did the blind persons really touched different parts of ONE AND THE SAME elephant? In one variant of the story, they were not physically blind, but were boasting of their great knowledge. Hence to expose their vanity, the king took the blind folded to a hard curtain with a small aperture. An elephant was paced in the other side of the curtain and only one of its body parts were placed near the aperture, so that the blind folded persons could touch only one part of the same elephant.  In other variants, the blind persons were guided to only one part of the same elephant. In any case, this is trivial, because it is not physically impossible. Hence we should concentrate on the other major issue.

Before answering the question, it would be necessary to differentiate between knowledge and science. Branching out from a common source (saamaanya) to different constituent parts (vishesha) to know the truth about that segment, is called Science (Vaisheshika). Here the segment is a derivative of the common source – hence must follow the rule of causality, i.e., the specialties must have been derived from the commonality under specific circumstances and conditions. The opposite – moving from the mix of general and special characteristics of each segment and synthesizing them towards the commonality in everything (Yoga) - is knowledge. Hence we use terms like physical sciences, chemical sciences, biological sciences, etc. for the same body. But we do not use such terms for knowledge (though we use terms like knowledge of physical sciences, it does not contradict the earlier statement, as knowledge is a collective of ALL sciences).

When we encounter divergent doctrines and points of view, we usually do NOT know whether they really relate to the same topic or whether they are mutually compatible and can be harmonized from the perspective of a *Higher Truth* or not. That is why require a competent Guru – a qualified guide to properly navigate us through the labyrinths of confusion. Otherwise, though technically the ergodic monkey typing at random may be able to produce a great novel after infinite trials, such chances are ruled out during our short life span.

When ANY person makes ANY statement, it is not a random occurrence. It is backed by a certain chain of thought and command based on his 1) natural instinct based on his DNA (indriyaartha sannikarshaat), 2) past experiences involving similar or related events (abhyaasaat), 3) socio-cultural upbringing (abhimaanaat), 4) accidental encounter that revive forgotten memories (pratyabhijnaat). These are called Preeti Sootram or the theory of attachment. These conditions are unique to each individual. Hence each perception is unique. This makes different persons perceiving the same object or event differently. But can we say any of these wrong? Suppose one uses a colored eye-piece or someone, who is color blind. Can we say his/her vision as wrong? Under those conditions, he/she is right. However, when we deal with the material word, such blurred vision does not produce the expected result. Hence it is wrong. Because proof is defined as that which produces invariant and expected results of the same object or events under similar conditions irrespective of place and time of occurrence. Hence if we go by proof, which only leads to knowledge, such vision or description is wrong in the ultimate analysis. But if we go by science, such visions are expected under those circumstances. To that extent, they are not wrong. This second vision is called Avidyaa. Though the term has other meanings, here it implies ultimate ignorance. For this reason, “ALL theories are fragments of the same (alleged) Truth”.

There may be mistaken or erroneous conjectures and theories from the universal point of view, but for a specific person in a specific context, it is not wrong. This is what Ted Howard calls “a model of a model of a model of a model of reality”. We cannot ignore that because the person’s behavior depends on that perception and it may affect us.

Now, the all-important question:  “how are we to winnow the wheat from the chaff -- how are we to separate the RIGHT theories from the WRONG ones and to preserve only the former, while remorselessly discarding the latter”? The Vedas and Upanishads have given elaborate commentaries on this under the Ashwattha Vidyaa or the theory of the inverted Ficus religiosa or sacred fig tree – also called Bodhi tree - a species of fig native to the Indian subcontinent and Indochina. The tree is called Ashwattha, which literally means that which goes on evolving and expanding. The tree is pictured as inverted: with its roots at the top against its normal position. A tree evolves from its seeds to roots and two leaves. The root forms its base – here the universe. The two leaves represent matter and energy. It evolves to the trunk, the branches, the sub-branches, ultimately the leaves, flowers and fruits. Two birds are pictured to be sitting on the tree: one eating the fruits and the other observing it. These two are the physical and the conscious aspects of the universe. It is a big analysis and I can discuss it at some other time.

To Mirovan:

1. a) I purposefully used the word Guru and mot teacher. Etymologically, the word Guru means an expert on a subject, who teaches selected disciples with a purpose of putting the knowledge to its best use. Hence by the word "guru", I am referring to ANY sort of expert, including of the scientific type, provided he is not a reductionist. By this I mean, a Guru must have total knowledge of the related fields also, while he may excel in a particular branch. For example, there is one Mundaka Upanishad, which begins with a question “What is that knowledge by knowing which we can have knowledge about everything”? The answer has been given by classifying knowledge into two categories: i) knowledge about the material universe and ii) knowledge about Consciousness. Then it switches on to discuss causality. Unfortunately, none of the commentaries available understood this and have given wrong interpretations. But the traditional scholars (I learnt it from my father 50 years ego), give a scientific interpretation, which I had written on different occasions. Vedic causality has 13 divisions. It contains four: those related to the beginning of creation. It is a greater science than modern science has achieved till date. From the above, it is clear that ALL branches of knowledge are covered by the Guru.

Satyendra Nath Bose, Max Perutz, Linus Pauling, or Hideki Yukawa can be considered in this category to a limited extent, because they were reductionists – they specialized in some branch, but did not have the same mastery in related branches.

b) Most ancient texts describe about how to select a competent Guru. Here personal integrity and depth of knowledge (to clear doubts on any subject) are given maximum weightage.

2. The word Bodhi, made famous because Buddha attained knowledge under such a tree, does not reflect the sense of Ashwattha, which literally means that which goes on evolving and expanding. But this expansion is not continuous expansion. Its spatial expansion stops after sometime due to scientific reasons I have discussed on different occasions. But its time evolution does not cease. The reason why the tree is pictured as inverted has been explained while discussing the difference between science and knowledge. Knowledge tends towards unification. When our eyes see a flower, it creates a blurred image of color only in our brain. Our sense of touch describes us its form. Sense of taste describes its radiance (freshness). Sense of smell describes its fragrance. Our sense of hearing describes its spatial arrangement in layers (sound is a longitudinal wave, also called compression wave). When all these sensations are mixed in our brain and compared with our memory, we “know” that it is a flower. But science is limited knowledge about something. Hence if we study color, texture or smell etc. those will be science. Since science is a part, it flows from the whole. Since the universe is perceived by us as parts, it is science. But the source of this science is one knowledge from which it flows. Thus, the tree is pictured as inverted. Because it depicts the creation and time evolution of the universe from one source. Its branches and other parts describe different sciences. A standing tree would imply growth of the original source. But an inverted tree implies parts emanating from one source, which together grows to form the whole. This is a vast subject and unless someone is an expert in Quantum physics, it will be very difficult to understand its meaning. Even then it uses a science much higher than modern science.

The two birds are one representing living bodies and the other representing Consciousness. We may have knowledge about different subjects, but the universal content of all knowledge is of the form: “I know……..(about this)”. Secondly, knowledge is the result of measurement (or perception, which is the same as measurement). We compare something with a standard unit scale up or down to know the result. Hence, the result of measurement always returns scalar quantities (2kg or 5 kg, where kg is a pre-known unit that is in our memory). As long as the measurement process goes on, our mind rests with it due to inertia. Like inertia of motion is destroyed due to friction or application of another force, the inertia of mind, i.e. thought, is destroyed due to getting the object of desire (praapti), or intense pain, which diverts our mind, or knowledge about the object. The moment we “know”, our mind rests – no action. The knowledge is posted in our memory. Hence knowledge implies cessation of action. This is called the observer of quantum physics and explains “collapse”. For this reason, the other bird is described as only observing.

REASONABLE EFFECTIVENESS OF MATHEMATICS

REASONABLE EFFECTIVENESS OF MATHEMATICS

INTRODUCTORY

The validity of a mathematical statement is judged by its logical consistency. The validity of a physical statement is judged by its correspondence to reality. We collect too much data and without judging properly reject most (like at LHC). If we re-envision classical and quantum observations as macroscopic overlap of quantum effects, we may solve most problems. The physics community blindly accepts rigid, linear ideas about the nature of space, time, dimension, etc. These theories provide conceptual convenience and attractive simplicity for pattern analysis, but at the cost of ignoring equally-plausible alternative interpretations of observed phenomena that could possibly have explained the universe better. Modern theories do not give a precise definition of the technical terms used, but give an operational definition that can be manipulated according to convenience. Wigner¹ defined mathematics as the science of skillful operations with concepts and rules invented just for this purpose. This is too open-ended. What is skillful operation? What are the concepts and Rules? Who invented them? What is the purpose? Do all concepts and rules have to be mathematical? Wigner says: The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible, but leaves out what is permissible and what is not; leaving scope for manipulation.

Relations between material objects must be expressed in a language compatible with the way in which objects in the real world actually interact - through the transmission/reception of mass/energy/information. Every object is a summation of the same fundamental stuff (quarks, leptons, etc) in varying orders. Events are energy rearranging fundamental particles. The space-time location makes intervals in both space and time dependent on where we measure them from. This implies space-time is related to the origin of the coordinates of the observer’s frame of reference. Measurement is carried out at here-now – thus, time variant (since now is the fleeting interface between past and future). Its quantitative description is mathematics – it describes the changing physical phenomena when the number or arrangement of any of the constituent parameters is changed. The changes are expressed as the result of measurement after comparison with a scaling constant (standard unit). These are always pure numbers, i.e., scalar quantities, because measurement is only the operation of scaling up or down the unit for an appropriate number of times. The results of measurement, which are time invariant, are frozen even though the object measured continues to evolve in time. Your 10 year old photo is not you.

Mathematics is the ordered accumulation and reduction in numbers of the same class (linear or vector) or partially similar class (non-linear or set) of objects. Number is one of the properties of all substances by which we differentiate between similars. If there is nothing similar at here-now, the number associated with the object is one. If there are similars, the number is many. Our sense organs and measuring instruments are capable of measuring only one at a time. Thus, many is a collection of successive one’s. Based on the sequence of perception of such one’s, many can be 2, 3, 4….n. In a fraction, the denominator represents the one’s, out of which some (numerator) are taken. Zero is the absence of something at here-now that is known to exist elsewhere (otherwise we will not perceive its absence at all).

Burrowing from M. Polanyi, Wigner says¹: The principal point …. is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity. Wigner admits not only the incompleteness of mathematics but also its manipulation according to the aesthetic sense of the operator. He gives the example of complex numbers and burrowing from Hilbert², admits: Certainly, nothing in our experience suggests the introduction of these quantities. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius. A reverse self-fulfilling effect!

Negative numbers are related to mutually exclusive objects or events of a coupled system. For example, position (fixed coordinates) and momentum (mobile coordinates) are mutually exclusive. In two accelerating frames of reference, one who gains has positive value corresponding to the negative value of the other. Since one is without similars, it does not change the value in any operation except linear addition and subtraction (becoming many or zero). Thus, squaring or square-root of 1 is 1 (these involve field). Since negative numbers belong to mutually exclusive couplets and not exclusive one’s, complex numbers are neither physically nor mathematically valid. No computer algorithm is possible using complex numbers.

Infinity is like one: without similars. But whereas the dimensions of one are fully perceptible, the dimensions of infinity are not perceptible. There cannot be negative infinity to positive infinity through zero, as it will show one beginning or end of infinity at the zero point, which is non-existent at here-now. No mathematics is possible with infinity, as all operations involving it will have undefined dimensions – thus indistinguishable from each other. History shows that whenever infinity appears in any theoretical model, it points to some fundamentally different and novel phenomena. In aerodynamics formulas, as the velocity approached the velocity of sound in the medium where the aircraft moved, the resistance of the medium returned infinite figure. It was believed that supersonic motion is impossible. But when supersonic motion became obvious, the formulas were reviewed. It was noted that they described resistance only in a continuous medium without abrupt jumps in density and pressure. However, transition from subsonic to supersonic motion involves a shock wave in front of the body, leading to abrupt jumps in density and pressure. When these factors were taken into account, the infinity vanished.

The so-called irrational numbers are also perceived as the nearest fraction of integers. Otherwise, we cannot use them in programming. We may be as precise as we want to fix the value of a number tending to zero, but it will never be zero, as that will make it non-existent at here-now making the operation impossible. Similarly, a number tending to infinity will never become infinite, as the result of all such operations become indistinguishable from each other. Like energy, infinities coexist. Only, space, time, coordinates and consciousness are infinite.

Language is the transposition of information to another system’s CPU or mind by signals or sounds using energy (self communication is perception). The transposition may relate to a fixed object/information. It can be used in different domains and different contexts or require modifications in prescribed manner depending upon the context. Since mathematics follows these rules, it is also a language. Mathematics explains only how much one quantity, whether scalar or vector; accumulate or reduce linearly or non-linearly in interactions involving similar or partly similar quantities and not what, why, when, where, or with whom about the objects. These are subject matters of physics. The interactions are chemistry. There is no equation for Observer. The enchanting smile on the lips of the beloved is not the same as geometry of mouth or curvature of lips. Thus, mathematics is not the sole language of Nature.

MATHEMATICAL PHYSICS

            Because of logical consistency, mathematics is always deterministic. Look at the structure of any equation. The initial condition or parameters are represented by the left hand side. The equality sign describes the special conditions to be met to start any interaction: be it at macro level or micro level. Given the initial conditions, the right hand side describes the theorized outcome of the interaction. We are free to vary the parameters of the left hand side. That is our freewill (though our choices or degrees of freedom may be variously limited). Once the initial parameters are set; (math can’t predict this), the right hand side (final outcome), varies correspondingly. This predetermined outcome is mathematics. The equality signs - the special conditions (like temperature threshold to start a chemical reaction), are also predetermined. But it is not defined in a logically consistent way (why that temperature?) – hence not mathematical.

            Some say; mathematics, because of its inbuilt logic, writes itself - one can start writing things down without knowing exactly what they are, and the language makes suggestions to proceed. This is the ergodic monkey phenomenon, where a monkey plays with the key-board randomly and the outcome is a master piece of a novel. Though theoretically it is possible as a chance, it does not happen in reality. Others say: Master enough of the basics; and you rapidly enter what sports players call ‘the zone’. Suddenly it gets much easier. You are propelled along. This is the 100^th monkey phenomenon of Sheldrake - notion that new skills are learnt with increasing ease as greater quantities of a population acquire them. There is no proof to justify this view beyond chance and functional ease due to repeated use.

            Wigner says¹: applied mathematics is not so much the master of the function: it is merely serving as a tool. Others say; using mathematics, we can build abstract models without the restrictions imposed by the physical world. This leads to the incompleteness issues, which exploit problems arising out of unnatural mathematics. We see something when the radiation emitted by it interacts with our eyes. We touch the mass that radiates light. Thus we do not touch what we see (radiation) and see what we touch (mass). Nature prohibits reductionism. Whole is a sum of its parts and more. Water is more than 2H and O. A triangle is more than three straight lines. This is natural number theory.  5 has independent perceptual value than 5 ones.  If we can purchase a car in € 5k, with € 1k, we can purchase 1/5 of a car. This may look mathematically valid, but 1/5 of a car is an undecidable proposition. Hilbert’s problem whether mathematics is complete (every statement in the language of number theory can be either proved or disproved) and Gödel’s negative solution arise out of such unnatural mathematics. Brute force approach is similarly unnatural, though sometimes it may succeed by chance.

            Wigner is right when he talks about¹ the succession of layers of laws of nature, each layer containing more general and more encompassing laws than the previous one and its discovery constituting a deeper penetration into the structure of the universe than the layers recognized before. This is the principle that both macrocosm and microcosm replicate each other. As the Minutes of the American Mathematical Society for October, 2005 reported, the theory of dynamical systems used to plan trajectories of spacecrafts and those of transition states of chemical reactions share the same set of mathematics. Wigner is also right that all these laws of nature contain … only a small part of our knowledge of the inanimate world. But he misses the point when he says: All the laws of nature are conditional statements which permit a prediction of some future events on the basis of the knowledge of the present, except that some aspects of the present state of the world…are irrelevant from the point of view of the prediction. In fact, it is most relevant as the probabilistic laws of Nature. The conditional statements show interdependence of all systems in the cosmos. Our sense organs and measuring devices have limited capacity, so that it measures limited aspects in limited intervals. Since time evolution is not uniform, but conditional on interactions, we do not see each step from the flapping of the wings of the butterfly till it turns into tempest elsewhere. The creation is highly ordered and there is no randomness or chaos. We fault Nature to hide our inability to know.

            Wigner says: The physicist is interested in discovering the laws of inanimate nature…. It is, as Schrodinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. In an earlier paper³, we have shown that: uncertainty is not a law of Nature. It is the result of natural laws relating to measurement related to causality that reveal a kind of granularity at certain levels of existence. The uncertainty relation of Heisenberg was reformulated in terms of standard deviations, where the focus was exclusively on the indeterminacy of predictions, whereas the unavoidable disturbance in measurement process was ignored. A formulation of the error – disturbance uncertainty relation, taking the perturbation into account, was essential for a deeper understanding of the uncertainty principle. By directly measuring errors and disturbances in the observation of spin components, Ozawa developed a formulation: ε (q) η(p) + σ(q)η(p) + σ(p)ε(q) ≥ h/4π. Ozawa’s inequality suggests that suppression of fluctuations is not the only way to reduce error, but it can be achieved by allowing a system to have larger fluctuations. Nature Physics (doi:10.1038/nphys2194) describes a neutron-optical experiment that records the error of a spin-component measurement as well as the disturbance caused on another spin-component. The results confirm that both error and disturbance obey the new relation but violate the old one in a wide range of experimental parameters. Even when either the source of error or disturbance is held to nearly zero; the other remains finite: thus, mutually exclusive. that is said to encode the causal structure of Spacetime. Each event in Spacetime has a double-cone attached to it, where the vertex corresponds to the event itself. Time runs vertically - the upward cone opens to future of this event. The downward cone shows past. But if the light pulse radiates in all directions, it should show concentric spheres and not a double-cone. The trick is done by first taking two dimensions and time as the third dimension. But even then it will be concentric circles and not a conic section. Event horizon is the limit of our vision.

            Light Cone is a mathematical model

Not only time is cyclic, but also is unidirectional because ‘now’ is linked to future in a different way; than it is linked to the past. Space, Time and coordinates arise from our concept of sequence and interval. When it is related to objects, we call the interval space. When it is related to events, we call the interval time. When we describe inter-relationship of objects, we describe the interval by coordinates. Present and future are segments of these sequences of intervals that are strictly ordered - future always follows present. The same is not true for past, because any past event can be linked to the present bypassing the specific sequence. This proves unidirectional time. Since the intervals are infinite, space and time are an infinite continuum. We use segments of this analog reality. Thus, our description relates to here-now over a medium scale, which we tend to universalize. This gives a distorted picture.

MISSING THE WOODS FOR THE TREES

Does the structure and availability of existing mathematics shape the formulation of physical theories? Yes! Examples:

Dimension is the perception of differentiation between internal structural space and external relational space of an object. Since we observe through electromagnetic radiation, where the electric field and the magnetic field move perpendicular to each other and both move perpendicular to the direction of motion, we have three mutually perpendicular dimensions representing length, breadth, height that are invariant under mutual transformation. There are no extra large or compact or n’th dimension. The surface of a cube is not 2D, as it has no independent existence. There is no independent straight line in 1D. It is a mark on a three dimensional paper or space. The surface of a sphere is not 1D, but 3D.

Directions (axes) and sequential arrangement (coordinates) of an object are used with reference to an origin in relation to other objects. With only one object, direction is meaningless. Direction is used to:

1) Measure distance between two objects from origin by assigning + or – signs   from origin along various axes.

2) Indicate shortest distance between two objects on a curved surface like a geodesic.

3) Reflect the behavior of fundamental forces of Nature; i.e., strong interactions move towards center, part of weak interactions limits movement away from center, e.m. interaction move out from center to lower concentration, beta-decay separates a part from the center, gravitational interaction relates interaction between bodies. But often, dimension is exchanged for direction in phase space portrait and its quantum Avatar, Hilbert space. This leads to the undecidable propositions.

If we divide 20 by 5, then we take out bunches of 5 from the lot of 20. When the lot becomes empty or the remainder is zero or below 5 (divisor) so that it cannot be considered a bunch and taken away further, the number of bunches of 5 are counted. That gives the result of division as 4. In case of division by zero, we are supposed to take out bunches of zero, which is impossible as it is not at here-now of the operator. At no stage the lot becomes zero or less than zero. Thus, the operation is not complete and result of division cannot be known, just like while dividing 20 by 5, we cannot start counting the result after taking away two bunches. Conclusion: division by zero is mathematically void; hence it leaves the number unchanged. Since zero does not exist at here-now, it does not affect addition or subtraction. During multiplication by zero, one non-linear component of the quantity is extended to zero, i.e., moves away from here-now to a superposition of states. Thus, the result becomes zero for the total component, as we cannot have a Schrödinger’s undead cat in real life. In division by zero, the non-existent part is sought to be reduced from the quantity (which is an operation akin to collapse reversal in quantum mechanics), leaving the quantity unchanged. Division by zero leaves the number unchanged.

Two possibilities of measurement of a moving rod suggested by Einstein in his 1905 paper⁴ were:

(a) The observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod, in just the same way as if all three were at rest, or

(b) By means of stationary clocks set up in the stationary system and synchronizing with a clock in the moving frame, the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is the length of the rod.

The method described at (b) is misleading. We can do this only by setting up a measuring device to record the emissions from both ends of the rod at the designated time, (which is the same as taking a photograph of the moving rod) and then measure the distance between the two points on the recording device in any unit. But the picture will not give a correct reading because:

• If the length of the rod is small or velocity is small, then length contraction will not be perceptible according to the formula given by Einstein.
• If the length of the rod is big or velocity is comparable to that of light, then light from different points of the rod will take different times to reach the recording device and the picture we get will be distorted due to different Doppler shift. Thus, there is only one way of measuring the length of the rod as in (a).

The fallacy in the above description is that if one treats as if all three were at rest, one cannot measure velocity or momentum, as the object will have zero relative velocity. Einstein missed this point when in the same paper⁴, he said: Now to the origin of one of the two systems (k) let a constant velocity v be imparted in the direction of the increasing x of the other stationary system (K), and let this velocity be communicated to the axes of the co-ordinates, the relevant measuring-rod, and the clocks. But is this the velocity of k as measured from k, or is it the velocity as measured from K? K and k each have their own clocks and measuring rods, which are not treated as equivalent by Einstein. Therefore, according to his theory, they will measure the velocity of k differently. Einstein does not assign the velocity specifically to either system. Everyone missed it and got misled. His spinning disk example in GR also falls for the same reason.

On the definition of synchronization Einstein says: Let a ray of light start at the “A time” t_A from A towards B, let it at the “B time” t_B be reflected at B in the direction of A, and arrive again at A at the “A time” t’_A. In accordance with definition the two clocks synchronize if:

 t_B -  t_A = t’_A - t_B.

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:

1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.

The concept of relativity is valid only between two objects. Introduction of a third object brings in the concept of privileged frame of reference and all equations of relativity fall. In the above description, the clock at A is treated as a privileged frame of reference for proving synchronization of the clocks at B and C. Yet, he claims it is relative!

Russell’s paradox raises an interesting question: If S is the set of all sets which do not have themselves as a member, is S a member of itself? The general principle is that: there cannot be a set without individual elements. Collection of different objects unrelated to each other would be individual members as it does not satisfy the condition of a set. Thus a collection of objects is either a set with its elements, or individual objects that are not the elements of a set.

Example: p(x): x Ï x, is the defining property p(x) of any element x such that it does not belong to x. Many sets have this property. A library p(x) is a collection of books. But a book is not a library x Ï x. Suppose this property defines the set R ={x : x Ï x}. It must be possible to determine if RÎR or RÏR. However if RÎR; then the defining properties of R implies RÏR, which contradicts the supposition that: RÎR. Similarly, the supposition RÏR confers on R the right to be an element of R, again leading to a contradiction. The only possible conclusion is that, the property x Ï x cannot define a set. It is convenient to choose a largest set in any given context called the universal set and confine the study to the elements of such universal set only. This set may vary in different contexts, but in a given set up, the universal set should be so specified that no occasion arises ever to digress from it. Otherwise, there is every danger of colliding with paradoxes such as the Russell’s paradox. In the case of EP, we do blunder!

All objects fall in similar ways under the influence of gravity. Hence locally, it is said, the difference between an accelerated frame and an un-accelerated frame cannot be known. But these must be related to be compared as equivalent or not? In the example of a person in an elevator falling down a shaft, it is assumed that during any sufficiently small amount of time or over a sufficiently small space, the person can make no distinction between being in the falling elevator and being stationary in completely empty space, where there is no gravity. This is a wrong description – distinction of what? Unless we relate the elevator to the outside space, we cannot relate motion of the elevator to it. The moment we relate to the structures beyond the elevator, we can know the relative motion of the elevator. Inside a spaceship in deep space, objects behave like Brownian motion (unaccelerated) or like the asteroids in the asteroid belt (accelerated). Usually, they are relatively stationary within the medium unless some other force acts upon them. If the person can see the outside objects, then he can know the relative motions by comparing objects at different distances. If he cannot see the outside objects, then he will consider only his position with reference to the spaceship – stationary or floating within a frame. There is no equivalence because there is no other frame for comparison. Relativity theory needs revision.

A same logic applies to the ray of light that appears curved to the occupants of the spaceship. The light can be related to the spaceship only if we consider the bigger frame of reference containing the source of light and the spaceship. If we consider outside space as a separate frame of reference unrelated to the spaceship, the ray emitted by it cannot be considered inside it. If the passenger could observe the scene outside, he will notice this difference and know that the spaceship is moving. Otherwise, the consideration will be restricted to the rays emanating from within, which will move straight. In either case, the description is faulty. Thus, the foundation of GR - the EP - is wrong description of reality. Hence all mathematical derivatives built upon such wrong description are wrong. There is no inertial mass increase.

Einstein has used equations x²+y²+z²- (ct)² = 0 and ξ² + η² + ζ² – (cτ)² = 0 to describe the evolution of the same light pulse that the observers see. But x²+y²- (ct)² = 0 describes a circle with ct as the radius! Hence z and ζ have to be zero. It can’t be a sphere! Since (x. y. z) is a point on the circumference, moving in z direction will be tangential. It describes a cylinder and not a sphere! The geometer’s descriptions of π-sphere and the topologist’s descriptions of n-dimensional sphere are mathematically and physically void.

Einstein can describe two concentric spheres with the points (x,y,z) and (ξ, η, ζ ) on their respective circumferences. Since the second person is moving away from the origin, the second equation relates to sighting from his here-now (new origin). Assuming he sees the same sphere, he should know its origin (because he has already seen it, otherwise he will not know that it is the same light pulse). In case he takes a new measurement from his origin, according to Einstein, the reading from two frames will be different. In other words, he will either measure it independently as different or measure the same radius as the other, implying:  either:

x²+y²+z²- c²t² ≠ x’²+y’²+z’²-c² τ ²,     t ≠ τ.

Or c²t² = c² τ²   or t = τ.    This creates contradictions, which invalidates his mathematics.

LOOKING AHEAD

            Recent discovery of galactic blue-shift (Lowell Observatory Bulletin No. 58 Vol. II No. 8) and arXiv: 1402.6319 v1 [astro-ph.GA], galactic merger (Astronomy Newsletter - 18^th July, 2014) and the absence of red-shift in galactic or lesser scales should prove dark energy a myth. Energy is perceived through its interactions. If it is not interacting, it cannot be energy. Fluids are also smooth and persistent. Interpretation of M & M experiment is faulty, as light is a transverse wave, which is background invariant. Like the solar system, the universe is spinning around a galactic center. Dark energy is the universal background structure.

            Abundance of ‘Hot Jupiters’ among alien planets and protons in cosmic rays shows macro-micro relation. Separately we have shown that the internal structures of Jupiter and proton are similar.

Bare mass or bare charge is fiction. The equation e = mc² is mathematically invalid as LHS is time invariant and RHS time variant (per second). It should be written as (m) e → (mc)² which balances it to show the rate at which energy acts on mass. Energy cannot be confined in packets, but only by mass. Confined mass-energy is fermion (hence half integer spin) and unconfined mass-energy is boson (zero spin). Fluid (intermediate) behavior is integer spin.

            Result of Time dilation experiment with atomic clocks was faked. This can be verified from the original data kept at US Naval Archives. The delayed signal of GPS is due to refraction when the signal re-enters the denser atmosphere of Earth. Time dilation is relative time evolution of elements in entropy, where thermodynamic process sustains life and total disorder is annihilation of form.

           

There is a need to ponder over these issues, introspect and rewrite physics.

REFERENCES

1.      Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” in Communications in Pure and Applied Mathematics, vol. 13, No. I

2.      Abh. Math. Sem., Univ. Hamburg, 157 (1922), or Gesammelte Werke (Berlin: Springer, 1935), p. 188.

3.      “Is Reality Digital or Analogue” published by the FQXi Community on Dec. 29, 2010,

4.      “On the Electrodynamics of Moving Bodies” by Einstein.