Saturday, 13 October 2018

Laplace and Fourier Transformations

Integration by Parts and Partial Differentiation.
--
This refers to the above link.
The above discourse is in Hindi, the subject elaborated therein is about the Manifestation and dissolution of the Existence with reference to the individual,, with reference to the collective as well as to the Causal (कारण) .
With reference to an individual, the collective, and the Causal, this at once is though a three-level process, with reference to the अद्वैत-सिद्धान्त / advaita siddhānta this applies to the Totality - समष्टि / samaṣṭi and व्यष्टि / vyaṣṭi  as well.
That is; how this whole exercise is an excellent model for me for studying this Knowledge Supreme
(ब्रह्म-विद्या).
This could also be a good example how we transform the subject of study into the expected goal first through Integration by Parts and then by Partial Differentiation of the same.
First I would like to explain a few key-words :
सृष्टि : Manifestation,
और प्रलय - and  Dissolution
उत्पत्ति - Creation,
और विनाश - Destruction.
तेजस् अंश (वीर्य) - cognate > सज्ञाति  semen (सं उपसर्ग)
ब्रह्मा - हिरण्यगर्भ - वैदिक आ-ब्रह्म -- ब्रह्मा ...brahmā.
श्रीमन्नारायण - श्रीमत् नारायण -- श्री = शक्ति, लक्षण, लक्ष्मी
नृ -- नर -- नारायण -- नृसिंह (नारायण का सिंहरूप अवतार)
नृ से अनेक शब्दों की व्युत्पत्ति दृष्टव्य है (मेरे अन्य ब्लॉग्स एवं पोस्ट्स में विस्तार से उल्लेख है)
सृष्टि और प्रलय का अर्थ उत्पत्ति और विनाश से भिन्न है।
जो आधिभौतिक स्तर पर रचना और विनाश जान पड़ता है वह आधिदैविक स्तर पर एक मध्य-क्रम की अवस्था है और कारण (Causal) के स्तर पर Manifestation और Dissolution है,
किंतु चैतन्य-परब्रह्म के अद्वैत के स्तर पर वह इन तीनों से परे सच्चिदानंद तत्व है जो अव्याख्येय है।
जहत् लक्षणा -- जहल्लक्षणा -- Partial Differentiation,
अजहत् लक्षणा -- अजहल्लक्षणा -- Integration by Parts.
सर्वजीव-घनात्मक ब्रह्मा -- sarva jīva ghanātmaka ब्रह्मा ...brahmā. -- The Compact form of Totality at 3 above-mentioned levels is  हिरण्यगर्भ / hiraṇyagarbha .
Is That which Manifests as आधिदैविक / ādhidaivika
श्रीमत्-नारायण / śrīmat-nārāyaṇa
-- श्रीमन्नारायण / śrīmannārāyaṇa
-- नारा / nārā -- is water that flows through नृ -- nṛ, or  श्रीमत्-नारायण / śrīmat-nārāyaṇa
-- श्रीमन्नारायण / śrīmannārāyaṇa,
When Manifestation (and not Creation) takes place.
This happening has again 3 points of reference as the individual, the collective-cosmic and the Causal (Cosmic as well as beyond too).
--
ब्रह्मा ...brahmā. The Consciousness as essence and substance, expresses itself in the 3 forms; namely -- The God, the world and the individual soul.The three are a single composite expression of
श्रीमन्नारायण / śrīmannārāyaṇa, which is seen by us.
--
The  हिरण्यगर्भ / hiraṇyagarbha aspect of ब्रह्मा ...brahmā that is also manifest as वेद / Veda ... शब्द-ब्रह्म / śabda-brahma is the reservoir of ब्रह्म-विद्या / brahma-vidyā and one who is fit for attaining this knowledge-body is the First वर्ण / varṇa  / ब्राह्मण / brāhmaṇa.
The four वर्ण / varṇa that originated from the हिरण्यगर्भ / hiraṇyagarbha aspect of  ब्रह्मा ...brahmā  respectively are
ब्राह्मण / brāhmaṇa ,
क्षत्रिय / kṣatriya,
वैश्य / vaiśya, and
शूद्र / śūdra, --respectively.
The four classes वर्ण / varṇa are the four pillars upon which stands the --
 धर्म / dharma or the  सनातन-धर्म / sanātana-dharma.
This धर्म / dharma or the  सनातन-धर्म / sanātana-dharma is not same as 'Religion' / 'faith' which is but the name of some tradition, -followed because one has born in certain society.
The tradition could be धर्म / dharma, अधर्म / adharma, विधर्म / vidharma, स्वधर्म / swadharma or even   परधर्म, which is elaborated in two ways in the गीता / gītā in the following way :
अध्याय  2, श्लोक 31,
--
स्वधर्ममपि चावेक्ष्य न विकम्पितुमर्हसि ।
धर्म्याद्धि युद्धाच्छ्रेयोऽन्यत्क्षत्रियस्य न विद्यते ॥
--
(स्वधर्मम्-अपि च-अवेक्ष्य न विकम्पितुम्-अर्हसि ।
धर्म्यात्-हि युद्धात्-श्रेयः अन्यत् क्षत्रियस्य न विद्यते ॥)
--
भावार्थ : तुम्हारे अपने निज क्षत्रिय-धर्म की दृष्टि को ध्यान में रखते हुए भी, तुम्हें भय से व्याकुल नहीं होना चाहिए । क्योंकि क्षत्रिय के लिए धर्मानुकूल प्राप्त हुए युद्ध से बढ़कर अधिक श्रेयस्कर दूसरा कोई अवसर नहीं हो सकता ।
--
Chapter 2, śloka 31,

svadharmamapi cāvekṣya 
na vikampitumarhasi |
dharmyāddhi yuddhācchreyo
:'nyatkṣatriyasya na vidyate ||
--
(svadharmam-api ca-avekṣya 
na vikampitum-arhasi |
dharmyāt-hi yuddhāt-śreyaḥ 
anyat kṣatriyasya na vidyate ||)
--
Meaning :
Even if you look from the perspective of your own way of 'dharma', you need not get perturbed. Because, such a war for a noble cause, (that has been imposed upon you) is in perfect harmony with your own path of 'dharma'.
-- 
And as in :
अध्याय 3, श्लोक 35, 
--
श्रेयान्स्वधर्मो विगुणः परधर्मात्स्वनुष्ठितात् ।
स्वधर्मे निधनं श्रेयः परधर्मो भयावहः ॥
--
(श्रेयान्-स्वधर्मः विगुणः परधर्मात्-स्वनुष्ठितात् ।
स्वधर्मे निधनं श्रेयः परधर्मः भयावहः ॥
--
भावार्थ :
अच्छी प्रकार से  आचरण में लाये हुए दूसरे के धर्म से, अपने अल्प या विपरीत गुणवाले धर्म का आचरण उत्तम है, क्योंकि जहाँ एक ओर अपने धर्म का आचरण करते हुए मृत्यु को प्राप्त हो जाना भी कल्याणप्रद होता है, वहीं दूसरे के धर्म का आचरण भय का ही कारण होता है ।
--
Chapter 3, śloka 35, 

śreyānsvadharmo viguṇaḥ 
paradharmātsvanuṣṭhitāt |
svadharme nidhanaṃ śreyaḥ
paradharmo bhayāvahaḥ ||
--
(śreyān-svadharmaḥ viguṇaḥ 
paradharmāt-svanuṣṭhitāt |
svadharme nidhanaṃ śreyaḥ
paradharmaḥ  bhayāvahaḥ ||
--
Meaning :
Though has not merits, it is far better to follow one's own way of 'dharma', than to follow and act upon the duties of another's 'dharma'. Even the death while pursuing own 'dharma', results in the ultimate good, where-as practicing another's 'dharma' is just horrific.
--
Though  श्रीकृष्ण / śrīkṛṣṇa and अर्जुन / Arjuna क्षात्रधर्म / kṣātradharma both followed the  सनातन-धर्म / sanātana-dharma, ब्राह्मणधर्म / brāhmaṇadharma was विधर्म / vidharma for both as no-one of them was born in a ब्राह्मण / brāhmaṇa  lineage by वर्ण / varṇa or Social class.
The link talks of वर्ण-संकरत्वं / varṇa-saṃkaratvaṃ, the cross-breeding in different वर्ण / varṇa or Social classes. 
Interestingly, अर्जुन / Arjuna tooexpressed his suspicion by this logic :
अध्याय 1, श्लोक 43,

दोषैरेतैः कुलघ्नानां वर्णसङ्करकारकैः ।
उत्साद्यन्ते जातिधर्माः कुलधर्माश्च शाश्वताः ॥
--
(दोषैः एतैः कुलघ्नानाम् वर्णसङ्करकारकैः ।
उत्साद्यन्ते जातिधर्माः कुलधर्माः च शाश्वताः ॥)
--
भावार्थ :
कुल में वर्ण की संकरता (मिश्रण) होने पर, कुल के सदा से चलते चले आये पारंपरिक जातिधर्म एवं कुलधर्म इन वर्णसंकर कुलघातियों के दोषों के कारण अवश्य ही विनष्ट हो जाते हैं ।
--

doṣairetaiḥ kulaghnānāṃ
varṇasaṅkarakārakaiḥ |
utsādyante jātidharmāḥ
kuladharmāśca śāśvatāḥ ||
--
(doṣaiḥ etaiḥ kulaghnānām
varṇasaṅkarakārakaiḥ |
utsādyante jātidharmāḥ
kuladharmāḥ ca śāśvatāḥ ||)
--
Meaning :
Because of these evils, the mixing-up of the castes, the ritualistic, the traditional, orthodox religious customs that have been running in the family since ever, are also destroyed.
--
But as the Destiny dictated the Great war of  महाभारत / mahābhārata could not be averted for whatsoever reasons.
The essentials of the 4  आश्रम / āśrama , that form the backbone of सनातन-धर्म / sanātana-dharma, is also explained.
And here is the core point that emphasize the institutionalization of विवाह / marriage for maintaining and preserving the सनातन-धर्म / sanātana-dharma.
How an event takes place at the same moment in the 3 Realm of  Existence and is 'interpreted' at the level of  'Physical' only restricts the approach of 'Science'.
How Gandhi in His Book 'वर्ण-व्यवस्था' appreciated the way of  सनातन-धर्म / sanātana-dharma. in deciding the profession of a person according to His inclinations, attitudes and actions.
Gandhi suggested that if the cast is not defined according to 'Karma' (actions, profession, livelihood), one can not work properly in any society.
The viewpoint expressed by Sri Ramana Maharshi is also the same :
  
4 July, 1935
Talk 58.
Mr. Ranganathan, I. C. S: In Srimad Bhagavad Gita there is a passage:
One’s own dharma is the best; an alien dharma is full of risks.
What is the significance of one’s own dharma?
M.: It is usually interpreted to mean the duties of the orders and of
the different castes. The physical environment must also be taken
into consideration.
D.: If varnasrama dharma be meant, such dharma prevails only
in India. On the other hand the Gita should be universally
applicable.
M.: There is varnasrama in some form or other in every land. The
significance is that one should hold on to the single Atman and not
swerve therefrom. That is the whole gist of it.
sva = one’s own, i.e., of the Self, of the Atman.
para = the other’s, i.e., of the non-self, of the anatma.
Atma Dharma is inherence in the Self. There will be no distraction
and no fear. Troubles arise only when there is a second to oneself.
If the Atman be realised to be only unitary, there is no second and
therefore no cause for fear. The man, as he is now, confounds the
anatma (non-Self) dharma with atma (the Self) dharma and suffers.
Let him know the Self and abide in it; there is an end of fear, and
there are no doubts.
Even if interpreted as varnasrama dharma the significance is only
this much. Such dharma bears fruit only when done selflessly. That
is, one must realise that he is not the doer, but that he is only a tool
of some Higher Power. Let the Higher Power do what is inevitable
and let me act only according to its dictates. The actions are not
mine. Therefore the result of the actions cannot be mine. If one
thinks and acts so, where is the trouble? Be it varnasrama dharma
or loukika dharma (worldly activities), it is immaterial. Finally, it
amounts to this:
sva = atmanah (of the Self)
para = anaatmanah (of the non-self)
Such doubts are natural. The orthodox interpretation cannot be
reconciled with the life of a modern man obliged to work for his
livelihood in different capacities.
A man from Pondy interposed: Sarva dharmaan parityajya maamekam
saranam vraja (leaving all duties surrender to me only).
Sri Bhagavan: (All) Sarva is only anaatmanah (of the non-self);
the emphasis is on ekam (only). To the man who has strong hold
of the eka (one) where are the dharmas? It means, “Be sunk in
the Self.”.
गीता / gītā tells :
अध्याय 4, श्लोक 13,

चातुर्वर्ण्यं मया सृष्टं गुणकर्मविभागशः।
तस्य कर्तारमपि मां विध्यकर्तारमव्ययम् ॥
--
(चातुर्वर्ण्यम् मया सृष्टम् गुणकर्मविभागशः ।
तस्य कर्तारं अपि माम् विद्धि अकर्तारम्-अव्ययम् ॥)
--
भावार्थ :
गुण तथा कर्म के विभाजन के अनुसार चार प्रकार की मूल प्रवृत्तियों का समूह (वर्ण्य), जिनसे समस्त भूत अनायास परिचालित होते हैं, मेरे ही द्वारा रचा गया है । उस समूह का रचनाकार (स्वरूपतः) अकर्ता तथा अव्यय मुझको ही जानो ।
--
Chapter 4, śloka 13,

cāturvarṇyaṃ mayā sṛṣṭaṃ
guṇakarmavibhāgaśaḥ|
tasya kartāramapi māṃ
vidhyakartāramavyayam ||
--
(cāturvarṇyam mayā sṛṣṭam
guṇakarmavibhāgaśaḥ |
tasya kartāraṃ api mām
viddhi akartāram-avyayam ||)
--
Meaning :
According to the innate nature and tendencies for action of man, I have created the four-fold order in this world. Even though I AM the Imperishable, and the Creator of them, know for certain I AM as such ever, the non-doer. 
--
This again affirms the fact that the सनातन-धर्म / sanātana-dharma says nothing about the Caste, but insists about the 'actions' and tendencies of man as is clear in  :
गुणकर्मविभागशः / guṇakarmavibhāgaśaḥ ,
as cited above.
A note about अश्वमेध / aśvamedha,  / गौमेध / gaumedha :
As the 'Creation' when seen as the Manifestation through an 'act' of ब्रह्मा ...brahmā, and this process is compared by the example of Horse the same performance / ritual  (यज्ञ / yajña) is called अश्वमेध / aśvamedha, and when seen as an example of 'cow', the same becomes 'गौमेध / gaumedha'.
अश्वमेध / aśvamedha implies assuming the Creation in the form of Horse.
Likewise गौमेध / gaumedha implies assuming the धर्म /'dharma' in the form of a cow.
And there is another word नरमेध / naramedha that could be interpreted as assuming the 'man' as the example of the 'Creation', but the meaning 'war' has somehow become prevalent.
The link also tells how a  ब्राह्मण / brāhmaṇa is unfit for performing an अश्वमेध / aśvamedha, and only a क्षत्रिय / kṣatriya deserves to do so. However a ब्राह्मण / brāhmaṇa can gain all the merits of this just because / if he understands the core of the process.
I wish to close this here at this point.
Enough for those who can't understand the Hindi Dialogue in the given Link.
--
  

 /

No comments:

Post a Comment