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Brahman
Of the nature of Sat (Existence), Chit (Consciousness) and Ananda (Bliss), Brahman is the absolute non-dual reality. There is nothing apart from Brahman here. Whatever exists is only an illusion of names and forms in Brahman. Thus we all are Brahman only.
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Ishwara
Synonym for Brahman or the ultimate reality. As the word denotes controller, Ishwara is considered as Brahman associated with Maya or the illusory power that causes names and forms.
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Maya
That which doesn't ultimately exist but seems to exist empirically. That which is beyond logic and intellect. The cause of names and forms (or creation in short). Illusory power of Ishwara (who is Brahman associated with this power).
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Jagat
The illusion of names and forms (naama roopa) in Brahman. Seemingly exists, temporary, sorrowful and ultimately unreal.
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Avidya
Ignorance of one's own nature of Brahman. Not much of a difference between Avidya and Maya. Avidya is anirvachaneeya like Maya - that which cannot be spoken about as either real or unreal.
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Aavarana
One of the two powers of avidya. This is the veiling power which veils the reality from being apprehended. Put in Chinmaya's beautiful terminology, aavarana is non-apprehension.
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Vikshepa
The second power of avidya which is the projecting power. This projects duality into the non-dual entity which hasn't been apprehended. Put in Chinmaya's word, vikshepa is mis-apprehension.
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Adhyaasa
Superimposition of the reality on the unreality and vice-versa. Eg: snake being superimposed on the rope. In Vedanta, adhyaasa is superimposition of the Self on the not-Self (considering the not-Self of body-mind-intellect to be real) and of the not-Self on the Self (considering the not-Self of body-mind-intellect to be "I"). Adhyaasa is the cause of all our sorrows and sufferings in the world - in Sankara's words, adhyaasa is anartha hetu (cause of anartha or miseries). Sankara's introductory commentary to the Brahma Sutras where he explains the need and necessity of learning Brahma Sutras is titled Adhyaasa bhashya because of the detailed analysis of adhyaasa.
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Jeeva
Jeeva is the reflection of Consciousness in the intellect which gets associated and attached to the body-mind-intellect complex. Is equivalent of ahamkaara or Ego. We generally consider ourselves as the jeeva whereas we are the Original Consciousness of Atman which is realized when the jeeva is purified (purification means removal of the intellect which in turn would merge the reflection in the intellect into the original).
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Avyaktha
Unmanifested state of Brahman associated with Maya prior to getting manifested. Equivalent of the deep sleep state wherein we are merged into the Self in a state of unmanifested existence which then leads to manifestation of dream and waking worlds.
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Mahat
Known as Mahat Tattva, Vishwa Manas, Mukhya Prana and Brahma. Mahat is the first manifestation from Brahman when associated with the power of Maya.
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Pancha Tanmaatras
The five primal essence of sound, touch, sight, taste and smell.
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Pancha Mahabhootas
The five primal elements of Ether (sound), Air (touch), Fire (sight), Water (taste) and Earth (smell).
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Panchikarana
The process of quantuplication wherein each of the fiver primal elements gets split into two halves. Each half again gets split into 4. Each 1/8th gets added/married to other elements. Thus Ether will end up with 1/2 ether, 1/8 air, 1/8 fire, 1/8 water and 1/8 earth. Similarly with Air, Fire, Water and Earth.
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Antah karana
The inner equipments which is split into 4 based on the activity performed - doubting mind, determining intellect, storing chitta and associating ahamkaara.
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Manas
Doubting faculty of the antah karana which enters into sankalpa and vikalpa (doubts and imaginations). When a person is coming towards Rama, Rama thinks "Is this my friend Krishna?" - this is mind functioning.
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Buddhi
The determining faculty of the antah karana. In the above example, Rama determines that "this is my friend Krishna" which is the intellect functioning.
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Chitta
The store-house of antah karana wherein thoughts in the form of people, things and knowledge are stored for future reference and recollection.
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Ahamkaara
The associating faculty of antah karana which associates and attaches itself to things and people in the form of "I" and "mine".
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Bahih karana
External equipments which consists of the pancha jnaana indriyas, pancha karma indriyas and the pancha pranas.
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Pancha Jnaana Indriyas
Five sense organs of perception which include ears (sound), skin (touch), eyes (sight), tongue (taste) and nose (smell). The physical parts that we see aren't the indriyas but just the openings through which the indriyas function. This is clearly known through a person having physical eyes but still not able to see things.
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Pancha Karma Indriyas
The five sense organs of action which are vaak (speech), paani (hands), paada (feet), paayu (organ of excretion) and upastha (organ of procreation).
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Pancha Pranas
Though Prana or vital force that sustains life is one alone, it is split into five based on the functionality and the parts of the body where it functions. Pancha pranas are prana, apana, vyana, samana and udana.
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Sthoola Shareera
The gross body composed of the pancha bhootas.
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Sookshma Shareera
Also known as linga shareera, this is composed of 17 parts of pancha jnaana indriyas, pancha karma indriyas, pancha pranas, manas and buddhi (some places it is considered as having 18 or 19 parts depending on the addition of chitta and ahamkaara).
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Kaarana Shareera
Causal body which is the cause of the other two bodies of sookshma and sthoola. Ignorance is the kaarana shareera.
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Jagrat avastha
Waking state wherein we perceive the waking world composed of gross beings and objects.
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Svapna avastha
Dream state where we perceive a subtle world similar to the waking world but a creation of the mind.
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Sushupthi avastha
Dreamless deep sleep where we don't perceive either gross world or subtle world. This is a state having just two experiences as pronounced by us when we wake up from the state - "I slept happily" (happiness) and "I didn't know anything" (ignorance). This state is very similar to the state of liberation - difference being in ignorance resulting in unawareness of the happiness in the deep sleep state.
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Three types of karmas
The three types of karmas are sanchita, prarabdha and aagaami.
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Sanchita karma
Sanchita karma is the karma that has been stored and accumulated in the various past births. This gets converted to prarabdha karma which is enjoyed in this birth.
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Prarabdha karma
The karma that causes and sustains the current birth is prarabdha karma.
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Aagaami karma
Aagaami karma is the karma that is going to be enjoyed in the future or is accumulated in the future by our current day actions.
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Sruthi
Literally meaning that which has been heard or that which has been revealed. The Vedas are the sruthi as they are without any beginning and has been revealed to rishis during times of deep absorption. It is also called sruthi as it is learnt through oral teaching. Rishis are not mantra karthas but mantra dristas or seers of mantras which are the verses of the Vedas.
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Smrithi
Literally meaning that which has been remembered or memorized or caused out of the intellect. Smrithi is secondary source of knowledge unlike Sruthi which is the primary source. Smrithi depends on Sruthi for its authority and validity. Anything in Smrithi which contradicts Sruthi is ruled out. The most common smrithis are Bhagavad Gita, Manu Smrithi and Yajnavalkya Smrithi.
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Puranas
Pura api navam ithi puraana -- ancient but still new and fresh. Puranas are the writings of Veda Vyasa which embeds the reality in Sruthi or Upanishads through stories and glories of the Lord.
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Itihaasa
Itihaasa are historical stories or narrations about different people and places.
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Bhashya
Word by word detailed commentary on a particular work. Bhashya cannot go against the work and hence it explains the original work by relating the words in order and explaining each of the words. The most famous bhashyakara is Sankara who has written bhashyas on the prasthaana trayas of Upanishads, Gita and Brahma Sutras.
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Vyaakhya
Vyaakhya is a detailed explanation of a particular work. Unlike bhashya, vyaakhya might or might not explain each of the word in the original work but it does explain in depth the entire sloka of the work. The most famous vyaakhyakara has been Rama Tirtha of 16th century who was the advaita Guru of Madhusudana Saraswathi and who wrote vyaakhyas on Upadesa Sahasri, Vedanta Saara, Sankshepa Sareeraka and Dakshinamurthy astakam among many others.
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Tika
Tika is a gloss on a particular work. This will not explain in detail the original work nor will it deal the explanation of each word in the original work. It just gives in brief the explanation of the entire sloka. The tikakara in advaita is Ananda Giri who has written tikas on Sankara's prasthaana traya bhashyas.
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Vartika
Vartika speaks about three things -- uktha, anuktha and duruktha of a work. Uktha is whatever has been mentioned in the original work will be explained. Anuktha is explanation of things that has been missed out in the original work. Duruktha is explanation of things that has been wrongly mentioned in the original work. Unlike bhashya and other types of commentaries, Vartika can go against the original work. Vartikakara of Advaita is Sureshwaracharya who has written vartikas on Sankara's Brihadaranyaka and Taittiriya bhashya, Manasollasa on Dakshinamurthy astakam and Panchikarana Vartikam.