THIS POST IS CONTINUED FROM PART 73, BELOW-
All branches of mathematics are well represented in the Vedas, Aranyakas, Brahminical literature, Upanishads, Panini's Ashtadhyayi and Yaska's Nirukto.
It goes on to prove that most solutions that can be arrived through Algebra, Geometry and Trigonometry have Sanskrit roots. Thus, what the world knows as Pythagoras' Theorem existed in the Sulba Sutras
Sulba Sutras include first 'use' of irrational numbers, quadratic equations of the form a x2 = c and ax2 + bx = c, unarguable evidence of the use of Pythagoras theorem and Pythagorean triples, predating Pythagoras by thousands of years and evidence of a number of geometrical proofs.
Vedic geometry, though non-axiomatic in character, is provable and indeed proof is implicit in several constructions prescribed in the Sulba-sutras.
The method for calculating square roots can be found in some Sutras, the method involves repeated application of the formula: sqrtA = sqrt(a2 + r) = a + r/2a, r
India used irrational numbers for the first time on this planet. In mathematics, the irrational numbers are all the real numbers, which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.
When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning they share no "measure" in common, which would allow to express their respective lengths as integer multiples of the arbitrarily short length of this "measure". Irrational numbers may also be dealt with via non-terminating continued fractions.
The Shulba Sutras are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction
Samhita-patha is a continuous recitation of Sanskrit words bound by the phonetic rules of euphonic combination;
Pada-patha is a recitation marked by a conscious pause after every word, and after any special grammatical codes embedded inside the text; this method suppresses euphonic combination and restores each word in its original intended form;
Krama-patha is a step-by-step recitation where euphonically-combined words are paired successively and sequentially and then recited; for example, a hymn "word1 word2 word3 word4...", would be recited as "word1word2 word2word3 word3word4 ...."; this method to verify accuracy is credited to Vedic sages Gargya and Sakalya in the Hindu tradition and mentioned by the ancient Sanskrit grammarian Panini (dated to pre-Buddhism period);
Krama-patha modified i the same step-by-step recitation as above, but without euphonic-combinations (or free form of each word); this method to verify accuracy is credited to Vedic sages Babhravya and Galava in the Hindu tradition, and is also mentioned by the ancient Sanskrit grammarian Panini;
Jata-pāṭha, dhvaja-pāṭha and ghana-pāṭha are methods of recitation of a text and its oral transmission
These extraordinary retention techniques guaranteed an accurate Śruti, fixed across the generations, not just in terms of unaltered word order but also in terms of sound. That these methods have been effective, is testified to by the preservation of the most ancient Indian religious text, the Ṛigveda .
The Vedic Chant is the oldest form of psalmody known. Very strict and EXTREMELY complex methods of instruction have made it possible to preserve the ritual chant unchanged, despite thousands of years of wars, conquests and social upheavals.
The Rig Veda is chanted on 3 notes, the Yajur Veda on up to 5 notes and the Sāma Veda on 7 notes.
The Sāma is the only chant that is considered really musical per se and as such is considered to be inferior to the other two Vedas.
Because of it's 'worldly' and less mathematically precise, it is often forbidden in certain rituals. It is also prescribed that if the Sāma Veda is heard while the other two are being recited then the recitation should stop immediately and only continue after the Sāma has terminated.
According to the Taittiriya Upaṇiṣad — śikṣā-vaḷḷi there are 6 main factors that need to be taken into
1. Varṇaḥ — pronunciation
Correct pronunciation of the letters of the alphabet.
Differentiation between short and long vowels.
Sandhi — Anusvara (ṁ) changes according to the letter that follows it.
When followed by ṁ changes to
ka kha ga gha ṅa ṅ
ca cha ja jha ña ñ
ṭa ṭha ḍa ḍha ṇa ṇ
ta tha da dha na n
pa pha ba bha ma m
Any vowel ṁ
sa ṣa śa ha ya ra guṁ
samyukta akṣara (combined letter) gg
Visarga (ḥ) also changes
When followed by sa, ṣa, śa, the visarga changes into those letters.
When followed by a p it changes into pha
2. Svaraḥ — notes
The sāma veda uses 7 musical notes.
Chanting of the ṛk, yajur and atharvana veda is done using 3 notes only.
Udātta — the raised note indicated in the text by a vertical stroke over the letter. (a̍)
Anudātta — the lowered note indicated by a line under the letter. (a̱)
Svarita — the neutral drone which is not indicated in the text (a)
Nigādha — a deviant note which is based on the udātta and is like a double udātta
with the second being slight raised above the first. In the kṛṣṇa yajur veda it is usually
marked by double perpendicular stokes above the letter.
The udātta changes into a nigādha in the following situations:—
• When a mantra ends in a long udātta
• When a mantra ends in a anusvara which carries the udātta
• When the udātta is followed by a samyuktākṣara (combined letter such as kṣ, stha, tv,
3. Mātra — duration
ardha — half — when a word ends in a halanta.
hrasva — short (the short vowels a, i, u, ṛ & ḥ )
dīrgha — long (ā, ī, ū, e, ai o & au — sometimes indicated by the digit 2 after the letter in a
pluta — extra long — indicated by the digit 3 after the syllable
4. Balam — emphasis
Alpa prāṇa — soft — these are all the regular vowels and consonants.
Mahā prāṇa — hard — these are all the aspirated consonants also ṣa and ha.
5. Sāma — continuity
One must ensure a continuity and smooth flow of the chanting.
6. Santānaḥ — punctuation
One must pause at the appropriate places - commonly indicated by (|)
In addition a slight pause is required:—
After chanting OM
When a word ends in a vowel and is followed by a vowel.
When a visarga (ḥ) is followed by kṣa
All the Vedic texts as well as in two Brāhmaṇas — Taittiriya [and its Araṇyaka] and the
Śatapatha Brāhmaṇa [including the Bṛhadaraṇyaka Upaṇiṣad] are marked with the accent
The Vedic chant is based upon these accents or svaras and consists of basically 3 notes; The
chief tone is the Udātta [raised] the other two being the Svarita [drone] and the Anudātta
There are 4 different methods of marking the svaras in the texts. In the Rik, Yajur and
Atharva Vedas and the Taittiriya Saṃhita & Brāhmana the svarita is not marked at all
because it is the middle pitch.
The preceding anudātta is marked by a horizontal stroke below the syllable, and the
following udātta is marked by a perpendicular stroke above the syllable, two perpendicular
strokes together mean that there is an elongated double raised sound -nigādha.
In some texts
the udātta is marked by a crescent above the syllable, when this is done then the elongated
double sound is marked by a singular perpendicular line.
The place of the principle accent the svarita is governed by grammatical rules. A udātta
always follows an svarita and is called the 'enclitic udātta’. When an svarita is lost due to an
euphonic combination [sandhi] of the vowel into the corresponding semi-vowel e.g. kva =
kua then the udātta is called the 'independent udātta.
When an independent udātta is placed immediately before an svarita then it is accompanied
by the numeral 1 if the vowel is short and by the numeral 3 if the vowel is long; the numeral
itself being marked with both the udātta and the anudātta.
In the Sāma Veda the figures 1, 2, & 3 are written above the accented syllable to mark the
svarita, udātta, & anudātta respectively.
When there are 2 successive svarita then the second is not marked but the following udāttas
has a 2r written above. The independent udātta is also marked with a 2r, and the preceding
anudātta is marked with a 3k.
A peculiar feature of the Vedic chant is that the anusvara changes to a GUṀ before the
following letters; a, ha, sa, sa, & r.
Example; saṁhita = saguṁhita
padaṃ sadā = padaguṁ sadā
Vedic recitation has assumed two distinct forms that evolved to preserve its immutable
character:— Prākṛti and Vikṛti with sub-forms.
The pāda pāṭhaḥ forms the basis of a number of special recitations known as 'vikriti' or
'crooked' recitations. The text is recited backwards or forwards or the successive words are
chanted in specific combinations.
These were originally designed to prevent the student froṁ
forgetting even one letter of the text, however through the ages these mnemonic techniques
became an end in themselves.
1. Saṃhita pāṭhaḥ — continuous recitation
2. Pāda pāṭhaḥ — word for word recitation — 1/2/3/4/5
1 2 3 4 5 6 7 8
ī̱śā vā̱sya̍m i̱daṁ sarva̱ṃ yat kiñca jaga̍tyā̱ṃ jaga̍t
3. Krama pāṭhaḥ — words recited in pairs — 1 2 / 2 3 / 3 4 / 5 6 / 7 8 /.......
1 + 2 2 + 3 3 + 4 4 + 5 5 + 6
ī̱śā vā̱sya̍m vā̱sya̍m i̱daṁ i̱daguṁ sarva̱ṃ sarva̱ṃ yat yat kiñca
In the Prākṛti form the words do not change their sequence
There are 8 traditional vikriti combinations which are;
jaṭā; 1 2 2 1 1 2 / 2 3 3 2 2 3 / 3 4 4 3 3 4 / 4 5 5 4 4 5 / .........
mālā; 1 2 / 2 1 / 1 2 / 2 3 / 3 2 / 2 3 / 3 4 / 4 3 / 3 4 / ........
śikhā; 1 2 2 1 1 2 3 / 2 3 3 2 2 3 4 / 3 4 4 3 3 4 5 / 4 5 5 4 4 5 6 / ..........
rekhā; 1 2 / 2 1 / 1 2 / 2 3 4 / 4 3 2 / 2 3 / 3 4 5 6 / 6 5 3 4 / 3 4 / 4 5 6 7 8 / 8 7 6 5 4 /
4 5 / 5 6 7 8 9 10 / 10 9 8 7 6 5 / 5 6 / ......
dhvaja; 1 2 / 99 100 / 2 3 / 98 99 / 3 4 / 97 98 / 4 5 / 97 98 / 5 6 / 96 97 / ....... 97 98 / 3
4 / 98 99 / 2 3 / 99 100 / 1 2 .
daṇḍa; 1 2 / 2 1 / 1 2 / 2 3 / 3 2 1 / 1 2 / 2 3 / 3 4 / 4 3 2 1 / 1 2 / 2 3 / 3 4 / 4 5 / 5 4 3 2
ratha; 1 2 / 5 6 / 2 1 / 6 5 / 1 2 / 5 6 / 2 3 / 6 7 / 3 2 1 / 7 6 5 / 1 2 / 5 6 / 2 3 / 6 7 / 3 4
/ 7 8 / 4 3 2 1 / 8 7 6 5 /.....
ghana;1 2 2 1 1 2 3 3 2 1 1 2 3 / 2 3 3 2 2 3 4 4 3 2 2 3 4 / 3 4 4 3 3 4 5 5 4 3 3 4 5 / ........
In the Nambudiri tradition the Rik Veda belongs entirely to the Vāskala recension
Rhyme is not used in the Rig-veda.
The metres are regulated by the number of syllables — akṣaras — in the stanza (ṛk), which consists generally of 3 or four Pādas, measures, divisions, or quarter verses, with a distinctly marked interval at the end of the second Pāda, and so forming two semi-stanzas of varying length.
The most common metres consist of 8, 9, 10, 11, 12, syllables (akṣaras) is each pāda these are known as anuṣṭubh, bṛhati, paṅkti, triṣṭup, jagati.
The anuṣtubh is the prevailing form of metre in the Dharma-sastras, the Mahabharata, the Ramayana, and all the Puranas.
The Pādas of a stanza are generally of equal length and of more or less corresponding prosodial quantities: but sometimes two or more kinds of metre are employed in one stanza, and then the Pādas vary in quantity and length.
A pathin is a scholar who has mastered the pathas. Thus, a ghanapaathin has learnt the chanting of the scripture up to the advanced stage of ghana.
The Ghanapatha or the "Bell" mode of chanting is so called because the words are repeated back and forth in a bell shape.
The sonority natural to Vedic chanting is enhanced in Ghana. In Jatapatha, the words are braided together, so to speak, and recited back and forth.
The samhita, pada and krama pathas can be described as the natural recitation styles or prakrutipathas. The remaining 8 modes of chanting are classified as complex recitation styles or Vikrutipathas as they involve reversing of the word order.
The backward chanting of words does not alter the meanings in the Vedic (Sanskrit) language.
PANINI LIVED IN 5500 BC
Pāṇini created the Ashtadhyayi, a sutra-style treatise on Sanskrit grammar,. His 3,959 verses on linguistics, syntax and semantics in "eight chapters" is the foundational text of the Vyākaraṇa branch of the Vedanga
Patanjali 5000BC made a bhasya ( commentary ) on Panini’s aphoristic text called Mahabhasya
Panini's analysis of noun compounds still forms the basis of modern linguistic theories of compounding in Indian languages.
Panini was kicked forward in time by BASTARD white historians and Tamil Christian converts to make the world believe that Sanskrit is a recent language . They said , sutra 2.1.70 of Panini, which mentions kumara-sramana means a BUDDHIST NUN –and hence he lived after Buddha was born
WHEN THE WHITE INVADER CAME TO INDIA BUDDHISM WAS DEAD .. JEW ROTHSCHILD REVIVED IT USING HIS STOOGES LIKE BR AMBEDKAR
The BASTARD white historian created several such FAKE proofs-- that the word yavanānī (in 4.1.49, means "Greek woman" and hence he must have lived after Alexander the Great conquered India -- the truth is Alexander the Great and wife Roxanna was on his knees before King Porus begging for his own life
According to the memoirs of 7th-century Chinese scholar Xuanzang, there was a town called So-lo-tu-lo on River Indus, where Rishi Panini was born, and he composed Chingming-lun (Sanskrit: Vyakarana)
SO NOW WE INDIANS HAVE TO LEARN OF OUR OWN HISTORY FROM SLIT EYED , YELLOW SKINNED CHINESE ?
Some BASTARD white historians wrote that Panini was killed by a lion a per Panchatantra. Well Panchatantra was written in 3000 BC .
The Aṣṭādhyāyī is the central part of Pāṇini's grammar and is extremely compact without sacrificing completeness
Dimitri Mendeleyeev wrote that he could NOT have made his Periodic table of elements without Panini’s grammar and Sanskrit’s 54 alphabets
SANSKRIT is the oldest language in the world , with the most immense vocabulary, clear speech, perfect pronunciation, accurate expression and politeness. Malayalam ( my mother tongue ) is the second oldest again with 54 alphabets.
High Literature Malayalam is more or less Sanskrit.
You can read MALAYALAM both ways.. King Solomon's ( hero of the Jews and son of David ) seal ( 900 BC) , photos given in Madame Blavatsky's book is in Malayalam script.
Since Panini wrote the adaptable Sankrit grammar 7500 years ago, there has been NO changes, it is that perfect-- the work of a genius!!
Rig veda was written down in 5000 BC in Sanskrit. Sanskrit has a construct like geometry in cymatics and can be digitalised. Sanskrit has no meanings by connotations and hence cannot age.
It has perfect morphology that leaves no room for error. NASA had declared that sanskrit is the only unambiguous spoken language on the planet.
Its alphabets are impeccably arranged. There are no proper nouns in Sanskrit. Every single Sanskrit word has a meaning built into the word itself.
The principles of sound harmonics working precisely and consistently through the entire language, from the basic four sounds through thousands of words and their variations. The way words unfold from their seed forms is amazing.
The mathematical precision throughout the language and give it its extraordinary power . There is a direct link between the sound and signs,it is phonetic. The writing of Sanskrit language is based on the sound of the spoken form. Sanskrit has no spelling, nor there are any silent letters .
There is logic in its sound system, and a natural continuity in its word-making as well as sentence-making. Sanskrit sentence structure is flexible--to hell with syntax. The order of words in a sentence does not matter.
Sanskrit has three genders (masculine, feminine, and neuter), three numbers (singular, dual, and plural), and eight cases (nominative, accusative, instrumental, dative, ablative, genitive, locative, and vocative), although only in the singular of the most common declension does a noun show different forms for each case.
Adjectives are inflected to agree with nouns. Verbs are inflected for tense, mode, voice, number, and person.
There is a vibration or resonance in the sounds of Sanskrit and hence is the choice language for mantras.( CYMATICS )
To hell with the ridiculous English spelling bee contest -- a wart counting competition would be better. Only stupid languages have spelling.
ramah ramau ramaah -Nominative
ramam ramau raman -Accusative
ramena ramabhyam ramaihi - Instrumental
ramaya ramabhyam ramebhyah -Dative
ramat ramabhyam ramabhyah - Ablative
ramasya ramyoh ramanam- Genitive
rame ramyoho rameshu -Locative
he ram! he ramau! he ramaah!
Sanskrit grammar has extensive grammatical tenses. There are ten tenses: one form for the present tense, three forms for the past tense and two forms for the future tense.
There is also imperative mood, potential mood, benedictive mood (called asheerling, which is used for indicating a blessing), and conditional. Each tense has three separate words for each of the three grammatical persons (first person, second person and third person), and it further distinguishes if it’s referring to one, two, or more than two people (called eakvachan, dvivachan and bahuvachan).
There are three categories of the verbs called atmanepadi, parasmaipadi and ubhaipadi. These forms indicate whether the outcome of the action is related to the doer or the other person or both. In this way there are ninety forms of one single verb.
Sanskrit words are formed of a root word called dhatu. For instance: kri root word means ‘to do,’ gam root word means ‘to go.’ So, there are ninety forms of each of these verbs like, karoti, kurutah, kurvanti, and gachchati, gachchatah, gachchanti etc. There are ready-made single words for all kinds of uses and situations.
There are words for all the three genders and each word has twenty-one forms of its own which covers every situation. Then there is a very elaborate and precise system of composing, phrasing, making a sentence, joining two words and coining any number of words according to the need.
Sanskrit grammar has the capacity for creating any number of new words for a new situation or concept or thing.
The morphology of word formation is unique and of its own kind where a word is formed from a tiny seed root (called dhatu) in a precise grammatical order which has been the same since the very beginning.
Any number of desired words could be created through its root words and the prefix and suffix system as detailed in the Ashtadhyayi of Panini.
Furthermore, 90 forms of each verb and 21 forms of each noun or pronoun could be formed that could be used in any situation. Its vowels are the actual ‘voice pattern’ of the sound and consonants are only the ‘form’ of the ‘voice pattern’ of the sound.
So a consonant alone cannot be pronounced as it is only a ‘form’ of the ‘voice pattern’ until it is attached to a vowel. Thus, a vowel, which itself is a ‘voice pattern,’ can be pronounced alone (like,) or it can be modulated by adding a consonant to it (like,).
Panini’s grammar describes algorithms to be applied to them for the generation of well-formed words. It is highly systematised and technical. Inherent in its approach are the concepts of the phoneme, the morpheme and the root.
His rules have a reputation for perfection – that is, they tersely describe Sanskrit morphology unambiguously and completely.
A consequence of his grammar's focus on brevity is its highly unintuitive structure, reminiscent of modern notations such as the "Backus–Naur form". His sophisticated logical rules and technique have been widely influential in ancient and modern linguistics. In the Aṣṭādhyāyī, language is observed in a manner that has no parallel.
IF AT ALL ETHICAL NLP CAN BE MADE—IT CAN ONLY BE IN SANSKRIT –NOT STUPID ENGLISH
Pāṇini's grammar, defines the linguistic expression and a classic that set the standard for Sanskrit language. Pāṇini made use of a technical metalanguage consisting of a syntax, morphology and lexicon.
This metalanguage is organised according to a series of meta-rules, some of which are explicitly stated while others can be deduced
I LEARNT SANSKRIT IN SCHOOL FROM CLASS 6 TO CLASS 9 – BECAUSE MY MOTHER TONGUE IS MALAYALAM IS WAS A PIECE OF CAKE
Pāṇini's Ashtadhyayi has three associated texts.
The Shiva Sutras are a brief but highly organised list of phonemes.
The Dhatupatha is a lexical list of verbal roots sorted by present class.
The Ganapatha is a lexical list of nominal stems grouped by common properties.
The Shiva Sutras describe a phonemic notational system in the fourteen initial lines preceding the Ashtadhyayi. The notational system introduces different clusters of phonemes that serve special roles in the morphology of Sanskrit, and are referred to throughout the text.
Each cluster, called a pratyāhara ends with a dummy sound called an anubandha (the so-called IT index), which acts as a symbolic referent for the list. Within the main text, these clusters, referred through the anubandhas, are related to various grammatical functions.
The Dhatupatha is a lexicon of Sanskrit verbal roots subservient to the Ashtadhyayi. It is organised by the ten present classes of Sanskrit, i.e. the roots are grouped by the form of their stem in the present tense.
The ten present classes of Sanskrit are:---
bhū-ādayaḥ (root-full grade thematic presents)
ad-ādayaḥ (root presents)
juhoti-ādayaḥ (reduplicated presents)
div-ādayaḥ (ya thematic presents)
su-ādayaḥ (nu presents)
tud-ādayaḥ (root-zero grade thematic presents)
rudh-ādayaḥ (n-infix presents)
tan-ādayaḥ (no presents)
krī-ādayaḥ (ni presents)
cur-ādayaḥ (aya presents, causatives)
The small number of class 8 verbs are a secondary group derived from class 5 roots, and class 10 is a special case, in that any verb can form class 10 presents, then assuming causative meaning.
The roots specifically listed as belonging to class 10 are those for which any other form has fallen out of use (causative deponents, so to speak).
The Ganapatha (gaṇapāṭha) is a list of groups of primitive nominal stems used by the Ashtadhyayi.
After Pāṇini, the Mahābhāṣya ("great commentary") of Patañjali on the Ashtadhyayi is one of the three most famous works in Sanskrit grammar.
It was with Patañjali that Indian linguistic science reached its definite form. The system thus established is extremely detailed as to shiksha (phonology, including accent) and vyakarana (morphology).
Syntax is scarcely touched, but nirukta (etymology) is discussed, and these etymologies naturally lead to semantic explanations. People interpret his work to be a defence of Pāṇini, whose Sūtras are elaborated meaningfully.
Nirukta covers etymology, and is the study concerned with correct interpretation of Sanskrit words in the Vedas
Nirukta, means "uttered, pronounced, explained, expressed, defined, loud". It also refers to the etymological interpretation of a word, also the name of such works.
Don't memorize, seek the meaning
What has been taken [from the teacher's mouth] but not understood,
is uttered by mere [memory] recitation,
it never flares up, like dry firewood without fire.
Many a one, [although] seeing, do not see Speech,
many a one, [although] hearing, do not hear Her,
and many a one, She spreads out [Her] body, like a wife desiring her husband.
The meaning of Speech, is its fruit and flower.
— Yaska, Nirukta 1.18-1.20
Words are created around object-agent, according to Yaska, to express external or internal reality perceived by man, and are one of six modifications of Kriya (action) and Bhava (dynamic being), namely being born, existing, changing, increasing, decreasing and perishing.
Yāska defines four main categories of words:--
nāma – nouns or substantives
ākhyāta – verbs
upasarga – pre-verbs or prefixes
nipāta – particles, invariant words (perhaps prepositions)
The meaning of Vedic passages has to be understood through context, purpose stated, subject matter being discussed, what is stated, how, where and when.
Yaska, in his famous text titled Nirukta, asserts that Rigveda in the ancient tradition, can be interpreted in three ways - from the perspective of religious rites (adhiyajna), from the perspective of the deities (adhidevata), and from the perspective of the soul (adhyatman)
The fourth way to interpret the Rigveda also emerged in the ancient times, wherein the gods mentioned were viewed as symbolism for legendary individuals or narratives.
It was generally accepted that creative poets often embed and express double meanings, ellipses and novel ideas to inspire the reader.
Nirukta enables one to identify alternate embedded meanings that poets and writers may have included in old texts
tatsaviturvarenyam bhargo devasya dhimahi
Separate all compound words into their constituents and number the words:
tat savituh varenyam bhargah devasya dhimahi
1 2 3 4 5 6
In the kramapatha chant, use a text obtained by combining two neighboring words according the rules of sandhi, resulting in six words.
1+2 2+3 3+4 4+5 5+6 6+6
tatsavituh saviturvarenyam varenyambhargah bhargodevasya devasyadhimahi dhimahiti dhimahi
A Krama patha expert chants the krama-version of all the verses.
To understand its error detecting capability, divide the chant into syllables so that the syllable ends with an vowel a, i, u etc. Both the third syllable and sixth syllables are same namely vi.
Suppose we commit an error and chant the third syllable as va. According to the krama chanting, the sixth syllable should be same as the third syllable. He would pronounce it as vi, since we are assuming he will make only one error.
Then he notices that an error has taken place since va is different from vi. An error has obviously occurred, but he does not know which is correct, va or vi? There are other methods which detect these errors and also methods that show how to correct them.
The various forms of chanting are called as vikratis and there are eight of them
Ancient Math is all composed in Sanskrit, usually consisted of a section of sutras in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student.
This was followed by a second section consisting of a prose commentary (sometimes multiple commentaries by different scholars) that explained the problem in more detail and provided justification for the solution. In the prose section, the form (and therefore its memorization) was not considered so important as the ideas involved.
All mathematical works were orally transmitted until approximately 5000 BC; thereafter, they were transmitted both orally and in manuscript form
In the Kerala school of Math ( Kodungallur University ) —the oldest Math school on the planet , the series expansions for trigonometric functions (sine, cosine, and arc tangent) were taught as early as 2700 BC.
Chanakya was a Kerala Namboodiri Math professor in Taxila ( today in Pakistan )
The Bakhshali Manuscript is a mathematical manuscript written on birch bark which was found near the village of Bakhshali near Peshawar in 1881. ( today in Pakistan )
It is kept in the Bodleian Library at the University of Oxford—the content has been lifted and patented in the white man’s name
The manuscript is a compendium of rules and illustrative example. Each example is stated as a problem, the solution is described, and it is verified that the problem has been solved.
The sample problems are in verse and the commentary is in prose associated with calculations. The problems involve arithmetic, algebra and geometry, including mensuration.
The topics covered include fractions, square roots, arithmetic and geometric progressions, solutions of simple equations, simultaneous linear equations, quadratic equations and indeterminate equations of the second degree..
Near the colophone appears a broken word rtikāvati, which has been interpreted as the place Mārtikāvata mentioned by Varāhamihira as being in northwestern India (along with Takṣaśilā, Gandhāra etc.)
The manuscript is a compilation of mathematical rules and examples (in verse), and prose commentaries on these verses
Typically, a rule is given, with an example or examples, where each example is followed by a "statement" (nyāsa / sthāpanā) of the example's numerical information in tabular form, then a computation that works out the example by following the rule step-by-step while quoting it, and finally a verification to confirm that the solution satisfies the problem
There is a commentary on the gaṇita (mathematics) chapter of the Āryabhaṭīya, including the emphasis on verification. Varahamihira was a pupil of Aryabhatta of 2700 BC
The rules are algorithms and techniques for a variety of problems, such as systems of linear equations, quadratic equations, arithmetic progressions and arithmetico-geometric series, computing square roots approximately, dealing with negative numbers (profit and loss), measurement such as of the fineness of gold, etc
The dot symbol used as a zero the Bakhshali manuscript came to be called the shunya-bindu (literally, the dot of the empty place).
All of today's geometric shapes and angles were present in the way the Yajnabedis or the holy sacrificial fires were erected. Each design had a typical astronomical or cosmic meaning to it and a specific purpose for which the yajna was to be conducted.
The word 'Geo' (as in Geometry, Geography, Geology, etc.) have been derived from the Sanskrit word 'Jya'.
Indian religious works knew Pi and it is a very old number. Even in ancient days several hand calculation were done using this formula and similar ones to calculate approximations to pi to over 500 decimal places .
The modern computers have made it much simpler. In 1910 the great Indian mathematician Ramanujan discovered a formula that in 1985 was used to compute pi to 17 million digits.
Vedic Mathematics is entirely doable in mind alone. Vedic Mathematics also starts at a basic level of numbers and gradually progressing to simple additions, subtractions, multiplications, division etc. and goes much more beyond just the basic calculations.
With Vedic Mathematics one can also solve complex geometrical theorems, algebraic problems, Calculus etc. Vedic Mathematics can be started at later ages as well without any difficulty. In deed the word 'Vedic' refers not only to actual texts but also has a literal meaning of 'knowledge'.
The formulae or sutra of Vedic Mathematics describe the way the mind naturally works and are therefore a great help in directing the student to the appropriate method of solution. By this way the learner is getting a chance of out of box thinking.
Vedic Mathematics is very unreasonably entangled with so called HEATHEN and PAGAN religious barrier.
NOT ANY MORE !
Indians are more prone to accept whatever is coming from West. Similar incident happened with “Yog”, it became only popular in India after it traveled around from the West and became “Yoga”.
There are Shlokas in classic Sanskrit literature like Védas which talk about very large numbers, particularly in powers of 10 with precise names to them.
A table follows: Table 1: Large Numbers with Names in One System Sr. No. Number Name Number Value Number as Ten Power Modern International English Name
1 Dasha 10/ 10^1 /Ten
2 Śata 100/ 10^2/ Hundred
3 Sahasra 1,000/ 10^3 /Thousand
4 Ayuta 10,000 /10^4 /Ten Thousand
5 Niyuta 100,000 /10^5/ Lakh
6 Prayuta 1,000,000 /10^6 /Ten Lakh / Million
7 Arbuda 10,000,000/ 10^7 /Crore
8 Nyarbuda 100,000,000/ 10^8 /Ten Crore
9 Samudra 1,000,000,000/ 10^9/ Hundred Crore / Billion
10 Madhya 10,000,000,000/ 10^10 /Ten Billion
11 Anta 100,000,000,000/ 10^11 /Hundred Billion
12 Parārdha 1,000,000,000,000/ 10^ 12/ Trillion
4000 YEARS LATER--THE WHITE MAN WAS COUNTING ON HIS FINGERS AND TOES
Sanskrit is classically called the divine language of Gods. Syntactically, logically, grammatically it is so perfect a language that even the Computer Scientists have never stopped praising it like anything. In fact, Sanskrit is considered as the future medium of best human-machine interface.
The Śulba sutras are one of the appendices to the great Védas
Jew Rothschild stole the technical texts BRAHMANAS ( part 2 ) and the ARANYAKAS ( part 3) of our Vedas—leaving us with SAMHITAS ( ridiculed as cowherds’s verses ) and UPANISHADS ( philosophy )
Sanskrit is rich in many mathematical features like its logic, context free grammar, in particular Boolean logic, null operator, etc.
A context-free grammar is simple and mathematically precise mechanism which gives methods by which phrases in language are built from smaller blocks, capturing the “block structure” of sentences in a natural way. It’s where formalism is applied which is base for mathematical study.
This wouldn’t have been possible without implicit and explicit knowledge and application of mathematical tools.
Amongst the four Védas, the Samvéda specially deals with music.
Nātya Śāstra further contributed to its development. Pingala is considered to be musical theorist whose Chhandas Śāstra or Chhandaḥ-sūtra is notable work on music. All these have been with concrete mathematical base.
The syllabic combinations in any musical note are purely mathematical construction. Importantly, this was fully realized by Indians in those days and mathematical techniques like modeling were induced for formation of different Rāgas
The thousands of verses in hundreds of epics couldn’t have been remembered without precise mathematical techniques for memorization which were very profoundly developed.
The Ancient rhythms in shlokas, recitations of mantras, enchanting intonations were all inherently mathematical in nature. They are today studied as smart application techniques of mathematics with modern memorization methods heavily relying on these as base.
Today it has been confirmed beyond doubt that the development and application of mathematics, that the ancient Indian culture has been involved in, was unparalleled.
IN 250 YEARS THEY CONVERTED US FROM THE RICHEST TO THE POOREST COUNTRY ON THIS PLANET
THEY BUILT RAILWAYS, ROADS , BRIDGES AND HARBOURS ONLY TO CART OFF OUR WEALTH
THE BASTARD WHITE MEN STOLE ALL OUR KNOWLEDGE, PATENTED IT IN THEIR OWN NAMES, AND CALLED US HEATHEN, PAGAN SAVAGES
ANGREZ CHALE GAYE -AULAAD KO CHODH KE .
WHAT DO YOU THINK OF THE CUNT IN THE VIDEO BELOW?
VEDAS DEAL WITH THE LONGITUDINAL WAVE –SCALAR ENERGY INHERENT IN SOUND ENERGY
In physics, a quantity described as "scalar" only contains information about its magnitude. In contrast, a "vector" quantity contains information both about its magnitude and about its direction.
Longitudinal waves include sound waves (vibrations in pressure, particle of displacement, and particle velocity propagated in an elastic medium) and seismic P-waves (created by earthquakes and explosions).
In longitudinal waves, the displacement of the medium is parallel to the propagation of the wave.. Longitudinal waves are scalar in nature. They typically occur in a medium, as sound or shock waves, based on variances of pressure transported by way of tiny movement along the direction of propagation.
The human DNA can produce longitudinal scalar waves . Mantra is a carrier wave with potent information within it.. All partical radiation are by definition longitudinal waves or scalar waves.
Mendeleev gleaned that Panini did the phonological patterning of Sanskrit alphabet sounds as a function of their articulatory properties. So he just arranged the chemical properties of elements are a function of their atomic weights.
This is impossible unless Sanskrit is a divine language.
This is why Sanskrit mantras can reprogram human DNA. You may scoff, but even homosexuality can be cured.
Lord Siva produced 14 sound sequences from the Damaru while in the throes of his tandav. These sounds formed the foundations for later developments of all phenomes of speech, notes of music and beats of dance.
These sounds were heard by Panini while in a meditational trance and penned down as the Siva Sutras in his Ashtadhyayi. Sound was structured to provide speech.
Though speech was designed for communication among humans themselves, the maharishis also realized that it should also serve to elevate the level of human consciousness by mantras.
Vedas penned in 7000 years ago, states that cosmic creation began with sound, and thus sound is a sure spiritual tool to liberation. OM is considered as the sound of Cosmic Energy and contains all the sounds in itself.
The earth vibrates at 7.83 Hz and so does OM. The primordal vibrations of atoms and molecules is thus represented by OM. Chanting OM stimulated your Vagus nerve which releases anti-ageing neuro-trasnsmitters..
It helps regenerate your organs and cells by activating stem cells. Since life began, the Earth has been surrounding and protecting all living things with a natural frequency pulsation of 7.83 HZ—the ancient Indian 12 starnd maharishis called OM. Resonances of earth, ie, 7.83, 13.7, 19.6, 25.5, 31.4, 37.3 and 43.2 Hertz of earth. We all know 7.83 hz being the strongest of all, OM or Schumann frequency.
The human ear can discern only a very narrow band between 20 Hz to 20000 Hz. The rest in inaudible. This is why NO cosmic sound can be heard by the human ear. These cosmic sounds were heard by 12 strand DNA maharishis in their spiritual trances which broadened their sense spectrums.
"The goal which all the Vedas declare, which all austerities aim at, and which men desire when they lead the life of continence … is OM. This syllable Om is indeed Brahman. Whosoever knows this syllable obtains all that he desires. This is the best support; this is the highest support. Whosoever knows this support is adored in the world of Brahma." - Katha Upanishad I- 5000 BC
drashtur lingatvam eva ca
tan-matratvam ca nabhaso
lakshanam kavayo viduh
Srimad Bhagavatam (3.26.33)—5000 BC
"Persons who are learned and who have true knowledge define sound as that which conveys the idea of an object, indicates the presence of a speaker and constitutes the subtle form of ether."
A cosmic creative vibration (called sphota or explosion) arises between Shiva and Shakti called Nada. This Nada then gets consolidated into Shabda Brahman (differentiated sound energy), the universal cosmic resonance, symbolized by OM. From this arises cosmic intelligence that is responsible for the creation.
The Taithiriya Upanishad says that "with OM, Brahma begins creation." It means the whole creation comes out of sound
The cosmos is vibrant with a mystic melody comprising planetary chimes as well as the plaintive song of atoms, unknown to us and unheard by us.
And unheard by us is even the strident crescendo of the universal orchestration in which galaxies, stars and planets whirl around perpetually in spirals, cycles, whorls and vortices causing incessant resonance, was the incessant boom of the damaru of Lord Shiva during his frenzied tandav or cosmic dance.
This unheard, dynamic vibrato is recognized in the Vedas as the sound-vehicle of the power of Brahman permeating the cosmos as the forces of creation and destruction.
It is called the Shabda Brahman, that is the Ultimate Reality in its aspect of sound.
THIS POST IS NOW CONTINUED TO PART , 75
TO BE CONTINUED-
CAPT AJIT VADAKAYIL