Archive for the ‘sanskrit’ Category

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Śulbasūtras are collection of sanskrit works from the vedic period which supplements kalpa as appendices. kalpa is one of the six veda-angas which deals with procedures to perform vedic rituals. Śulbasūtras provide as the source of ancient Indian mathematics in the area of geometry developed during the vedic period.

The mathematics in the vedic period should not be confused with the 20th century work titled “Vedic Mathematics” by former Shankaracharya of Puri, the late Jagadguru Swami Shri Bharati Krishna Tirthaji Maharaj. Tirthaji’s “Vedic Mathematics” is neither vedic nor mathematics of any significant importance except for some alternate methods in arithmetics and elementary algebra. The title of the work is actually a misleading one, and people without understanding the facts propagate it as something from ancient Indian epistemology. The claim that the sanskrit aphorisms mentioned in his text were from the appendix (parishishta) of Atharva-Veda is controversial, and so far, no versions of Atharva-Veda contained such aphorisms. Since the book was published posthumously, we are not sure whether the author or the editor is to be blamed for such a misleading book title. For a more detailed discussion about this topic, please refer to the article titled “Myths and reality : On ‘Vedic mathematics’ ” by S.G. Dani, a renowned mathematician at Tata Institute of Fundamental Research, India.

The importance of mathematics were indeed well cherished in ancient Indian mathematical works, and the Jyothisha-Vedanga (attributed with Rig-Veda) glorifies mathematics as follows:

yatha shikha mayurānam nāgānām maṇayo yatḥa |
taḍvad vedāṅga shāstrāṅām gañitham mūrdhin stḥitḥam ||

“Like the crest of the peacock, like the gem in the hood of the king cobra, so is mathematics the top-head of all branches of science/knowledge”.

The geometry in Śulbasūtras particularly laid out details for the design and construction of fire altars for vedic rituals. The vast corpus of works developed in Śulbasūtras are mainly attributed to Baudhāyana, Mānava, Āpastamba and Kātyāyana. The oldest being developed by Baudhāyana during 800 BCE, and the youngest by Kātyāyana during 200 BCE.

One of the most significant work which gained popularity among contemporary mathematician is the statement about hypotenuse theorem (which is currently called as Pythagoras Theorem) contained in Baudhāyana Śulbasūtras which belongs to Taittiriya branch of the Krishna Yajur-Veda.  Though, Baudhāyana did not wrote proof to his theorem, he laid out the sūtra as follows:

dīrgha chaturasrasya akṣaṇayā rajjuḥ pārśvamānī tiryagmānī cha
yat pṛthagbhūte kurutah tat ubhayāṅ karoti. (Chapter 1, sutra 12)

A rope stretched along the diagonal of a rectangle makes a squared length which is made by the squared lengths of the horizontal and vertical sides of the rectangle together.

Other important concepts contained in Śulbasūtras are as follows:
1) Pythagorean triples.
2) Formula to find square roots.
3) Finding a circle whose area is same as a square.
4) Diagonals of rectangle bisecting each other.
5) Diagonals of rhombus bisecting at right angles.
6) Areas associated with squares, rectangles and rhombus.
7) Methodology to handle fractions.

Further reading:
http://www.math.cornell.edu/~dwh/papers/sulba/sulba.html
http://www-history.mcs.st-and.ac.uk/Projects/Pearce/Chapters/Ch4_2.html

The negative energy which manifests within an individual, and consequently, a negative energy within the society is basically due to the imbalance of human mind. This imbalance of mind eventually leads to sufferings. Every life is an integral part of the divine, and is capable of rising to experience the bliss. This capability is dormant with some, and with others they are active, or more conducive to be activated quickly. To bring the mind to a balance towards activating the bliss, the following 13 impurities of mind should be controlled which are the root cause of suffering:

1) Ragam: desire to indulge in recreational sexual activities rather than for procreation.
2) Dvesham: to take revenge on those who disturbed us or inflicted pain.
3) Kamam: desires or passion for materialistic pleasure.
4) Krodham: anger, or restlessness due to unfulfilled desire.
5) Lobham: unwillingness to give or share with others.
6) Moham: blind towards distinguishing good and bad while satisfying the desire.
7) Madham: arrogance in achieving the desire based on wealth and power.
8) Maatsaryam: envy/jealousy upon the success/achievement of others.
9) Irshya: thoughts about why do I experience this sorrow and not others.
10) Asuya: indignation at the merits or goodness of another.
11) Dambham: pretending to do good things for publicity/popularity (hypocritical/deceitful).
12) Darpam: pride in believing that no one else can match with one’s quality or skill.
13) Ahamkaram: impudent or insolent behavior.

Even if any one of the above impurity dominates the mind, we end-up driving ourselves to inauspicious circumstances eventually. We should learn to eradicate any impurity arising in our mind at its beginning stage itself. Then, we will be able to put ourselves in auspicious circumstances to experience the divine bliss.

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Consistent indulgence in ignorance (māyā) by humans over several of previous births makes him strongly associated with the accumulated/consequent subtle impressions (samskaras) and tendencies (vasanas) which hinders from listening to the voice of God. The pursuit of spiritual path to know the purpose of life appears contrary to human nature, and his conscious mind is always agitated. The humongous effort to make the conscious mind stable is to start with controlling one’s lust/passion/desire (kāmam) and anger (krodham). Adopting a yogic lifestyle makes it easier to achieve stable mind.

“The beginning of saintliness is killing of egoism or Ahamkara. The end of saintliness is Eternal Life. The key to saintliness is humility and self mortification. The light of saintliness is silent meditation. The garb of saintliness is virtue and tolerance, not the Gerua cloth alone.”  – Sivananda

Once the conscious mind is stable, the superconscious mind will start to manifest which is the faculty for pure intellect, reasoning and intuition towards realizing the truth. Then, in silent meditation, it will be possible to hear the voice of God. This inner voice which is very divine, pure and clear will guide us in the spiritual path to know the purpose of life. Meditation is a beautiful way to connect with God and enjoy the bliss of divinity. Finish up the daily meditation with this shloka (from Śivamānasapūjā) :-

Ātmā tvaṁ girijā matiḥ sahacarāḥ prāṇāḥ śarīraṁ gṛhaṁ
pūjā te viṣayopabhogaracanā nidrā samādhisthitiḥ|
Sañcāraḥ padayoḥ pradakṣiṇavidhiḥ stotrāṇi sarvā giro
yad-yat-karma karomi tat-tad-akhilaṁ śambho tavārādhanam||

“Thou (Lord Shiva) art Atma; Buddhi is Thy consort, Parvathi (who is born of mountain); the Pranas are Thy attendants; this body is Thy house; the action of sensual enjoyment is Thy worship; deep sleep is the establishment of Samadhi; walking by my feet is the perambulation around Thee; all my speeches are Thy praise; whatever actions I perform, are all Thy worship; Oh Shambhu!”

Further reading:
1) Śivamānasapūjā
2) Yoga in Daily Life – by Sri Swami Sivananda

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Classical puranams are 18 in numbers, divided into three equivalence classes, namely sattvika puranam, rajasika puranam, and tamasika puranam consisting of 6 puranas each. Varaha puranam contained in sattvika classification is correlated with one of the innumerable avatharams of Lord Vishnu, namely the varaha avataram. Avatarams are manifestation of Supreme Lord as earthly life form. Out of innumerable avatarams, ten of them are commonly worshiped together (principal avatarams), which is termed as dashavatharams which encompass various life forms.

The final take home message, or concluding remark of a particular scripture present as a verse within that scripture is referred to as charama slokam. Such a final remark present in varaha puranam is called as varaha charama shlokam. There are two more important charma shlokams, namely,  rama charama shlokam contained in Ramayanam, and krishna charama slokam contained in Bagavad Gita (or equivalently, Mahabharatham).

Lord Vishnu took an avataram as a wild boar (varaham) emerging from the nostril of Lord Brahma. The mission of this manifestation was to rescue the mother earth (bhuma-devi) which was immersed in the primordial ocean (pralaya-samudram) by a demon Hiranyaksha. The primordial ocean, or the pralaya-samudram is a highly viscous (jelly like) matter present in cosmos. Upon rescuing bhuma-devi from this pralaya-samudram, there occurred a series of question-answer conversation which is later compiled by Vyasa as varaha puranam.

It is understood that during the time of death, what people think in mind also influences the next birth. Bhuma-devi points out to varaha about the difficulty of being devotional and think of Lord during these last moment, and prayed to show mercy to all her children (we humans) and provide a solution to avoid this last moment dilemmas. Then, varaha promised to Bhuma-devi that instead of humans thinking about Lord during the last moment, He himself will think about them during their last moments if they accepted Him with all devotions when they were perfectly healthy both physically and mentally (also known as sharanagathi). This promise is summarised as varaha charama slokam:

sthithE manasi susvasthE sarIrE sathi yO nara:
dhAthusAmyE sthithE smarthA visvarUpam cha maamajam
tathastham mriyamANam thu kAshtA paashaNa sannibham
aham smarAmi madh bhaktham nayAmi paramAm gathim

If a person who while having mind and body in good shape with all the natural elements in fine fettle, thinks of me as the birth-less one, when such a person reaches the time of death lying insentient like a log of wood or stone and becomes unable to think, I will remember that person at that time and take him to the highest state.

Further reading:
http://www.ramanuja.org/sv/bhakti/archives/jul98/0166.html

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Chitta-shuddhi can be loosely understood as preparing and purifying the mind to reside in the self.  An individual who has attained chitta-shuddhi finds it easy to comprehend God knowledge. The core here is mind itself, and the effort here is to calm the mind from disturbances (chitta-vritti).

Chandhogya upanishad ordains “annamayam hi saumya manah apomayah pranah tejomayi vag iti; bhuya eva ma bhagavan vijnapayatv iti; tatha saumya, iti hovaca” [1].  The nature of food that we eat manifests as nature of our mind. Food that we consume falls under three general categories: sattvic, rajasic and tamasic.

When we eat food belonging to sattvic category, our mind will be at peace and very much conducive towards spiritual learning. Food belonging to rajasic category keeps mind agitated and drags us through all sorts of materialistic disturbances. Tamasic food keeps mind very dull and make people behave stupidly.

For life to sustain, it is impossible to abstain from bringing harm to another life form one way or the other. In Srimad Bhagavatham [2], it is described as follows: ahastāni sahastānām apadāni catuṣ-padām phalgūni tatra mahatāṁ jīvo jīvasya jīvanam [1.13.47].  Here the fact  “jīvo jīvasya jīvanam” specifically points that stronger life forms will depend on weaker life forms. But, we as humans possessing the strongest intellect can make choices to minimize the harm to other life forms.

Chandhogya upanishad ordians further [3] as “ahara-suddhau sattva-suddhih, sattva-suddhau dhruva- smritih, smritilambhe sarvagranthinam vipramokshah” which means “By the purity of food, follows the purification of the inner nature; on the purity of the inner nature, the memory becomes firm; and on the strengthening of memory follows the loosening of all ties, and the wise get liberation thereby

Adi Shankaracharya emphasizes that food for us is not only the stuffs that we eat, but anything which reaches mind through sense organs are also our food. So, to attain chitta-shuddhi, it is not only essential to have control over the food that we eat is of sattvic nature, but also the stuffs we see, hear, perceive through touch and smell be also of sattvic and pure nature so that our mind will get enveloped with pure thoughts, and make it easier to realize God.

References
[1] http://www.swami-krishnananda.org/chhand/ch_2c.html
[2] http://www.vedabase.com/en/sb/1/13/47
[3] http://sivanandaonline.org/public_html/?cmd=displaysection&section_id=860