The Vedic Ganitas are based on a set of 9 symbols or Labels. The facility of this system of labels has transformed the Astrological methods around the world! Yet it itself is misunderstood or approached mistakenly.
Euler gave great thought to the principles that underlie the Ganitas, and presents them as a Algebra of 9 symbols by hich one could fractalise the experience of reality. He then generalised it into the theory of Equivalence Classes, or Clock arithmetics, orCofactor sets or groups or rings or modulo arithmetics.
All these distinguished Ames describe one process: how I formally measure the space around me using a Metron and keep it "real", that is on a humanly comprehensible scale.
Many of us do not get the chance to think about measurement in this way, as we just get on with our daily lives. But someone in every empire had to be responsible for weights and measures! Every human transaction from accounting at the empirical level through commercial transactions , out into artistic and architectural endeavours of all kinds depends on this system of weights and measures established within an empire. Euler had that responsibility in he holy roman Empire in the East, and of course had to think about such things.
The Vedic astrologers were in exactly the same position, and the Ganitas encoded the official system of weights and measurements established for the building of the temples and shrines. These important weights and measures for the temples were also adopted by the Maharajahs and rulers of the Brahmin Caste to order and build the caste system like a temple. These temples and considerations were to model the astrological apprehension of the harmonious order in the Universe. As bove so below.
There is some evidence that the nine labels or symbols were developed from a larger set of symbols, and refined to 9 , but I do not want to go into that here and now. It is sufficient to note that the 9 symbols are a product of sophisticated thought and experience as well as divine or astrological revelation, and ruling Caste approval.
We come from Shunya and we return to Shunya. All is Shunya, and hunya is the completion of everything, the perfection of all things.
This is a very esoteric and mystical sounding set of statements regarding Shunya, but in fact they are a highly pragmatic set of propositions and tautologies on which to base a system of weights and measures.
You may be familiar with my aphorism: Shunya is everything. If you dig deeper you will find that I have explored Shunya from as many sources as I can, and am always interested to learn more. Shunya however does not mean everything, but then neither does it mean nothing or zero. The Sanskrit shows that it develops from the meaning of full or swollen. Only later in Astrological circles does it come to denote the entire heavens!. The notion of perfection or Prajna-paramita comes to be allied an d associated with it and eventually interchanged by it in yogic circles. It symbol appears to be the closed loop. However the finger mudras indicate a possibility of 2 lineal representations one looking like o or 0, the other like 9. Thus the symbol 9 has always had a close association with the symbol 0 and consequently one meaning: FULL.
Fullness is interesting, for it is the end of one thing in a process and the signal to begin another stage in a process. Thus we understand at one level how all things come from Shunya and return to Shunya. We see how this is completion and we apprehend the link to perfection.
This symbol for Shunya when called zero or nine takes on a different mening according to the culture that uses it, but it has always been a mistake made by translators of the Brahmin Vedas and the summaries the Upanihads to confuse the symbol as a numeral. Numerals are symbols or labels which adjectively ad or adverbial lay sequence or order Metrons. These sequences and or orders are in fact song or dance responses to Metron arrangements or to the arrangement of Metrons. Thus the process is truly artistic and cultural and dynamic and capable of expressing or communicating 3 dimensional arrangements, seances and orders as information. This combinatorial song and dance is called Gematria or Combinatorics. They are Astrological techniques and methods of recording and distinguishing observations .
These songs or hymns, along with the dances record astrological information nd observation and data. Very much like the dance performed by bees when they return to the hive to give information about what the outside environment is like. The behaviour of meet and greet found in all animate systems performs the same function.
The hymns , the songs and the dances, the whole culture preserves astrological information and it presents it on earth. Thus Gematria becomes confused with geometry or linked to Geo Metria, the skill of land measuring using similar and sometimes identical tools for measurement.
Brahmagupta was a fuddybduddy for this reason. By ignoring the Bahmat traditions nd cultures and succumbing to Hellenism, Indians were turning their backs on centuries of recorded data, the Akashic records encoded in song nd dance within the cultures of the caste systems of India. Every Indian had his place and transmitted an important part of the knowledge within Bahmat. That wisdom was distributed among the people's and cultures, not centralised in books and Libraries. Libraries and accumulations of writing we're a Hellenistic cultural paradigm. The Sanskrit was too holy to write mundanities in. In any case too many books is a waste of time and effort. The monasteries kept a few sacred texts, but otherwise each person was encultured, skilled for their place and role in the caste system , and their relationship and responsibilities to their neighbours.
The hymns, dances and the mudras thus carry information about Shunya and how accounting was done. The symbol 9/0 is not nine or zero but Shunya, the mudra means complete or finished or perfected.. This particular mudra seems to have travelled to the romance countries where it still holds the meaning of culinary excellence.
Shunya therefor can e placed nowhere. Of all the western Astrologers Euler appears to be the one who understood Shunya best. His work on equivalence classes draws together Euclids algorithm for fractalising space and the Indian system of ciphers and thus generalises the whole issue into modulo arithmetics and modulo algebras, called p-adic algebras.
It is Napier who introduces both the logarithm of sines and the p-adic number system called base 10 which was a version of the Indian Vedic system based on the Ganitas sutras. The breakout difference was in the misunderstanding of Shunya. Shunya appears twice in the base ten system, once as 0 and again as 9 . When written on a circle the two meld, and confusion is introduced as to whether one should use 0 to 8 or 1 to 9. Let's clear that up combinatorially.
Shunya like Selah in the Psalms in the Tanakh is a procedural symbol, not a numeral. Just as Selah directs the hymnist to "be like a rock" Shunya directs the hymnodist to "stop and start anew; this one is full"
As a symbol shunya may be placed before after, above or below or even around the numeral that denotes completion or fulness. Only Euler appears to have recogised this fluidity of use, and its relation to the euclidean algorithm as the remainder theorem/ property.
Because of Napier and others the symbol called a cypher came to be used as a placeholder, only eventually acquiring is numeral status and number value of zero.
Combinatorially there is no concept of "nothing" in fact nothing is a onsense term when used in this numerical way. Hamilton in introducing the symbol in his development of a science of Pure time makes several pertinent remarks as to what it is and how it is to be used. Unfortunately these remarks are usually left out when passing it off as a number rather than a a symbol. Even to call it a numeral is misleading.thus the numerals can be any marks other than shunya as long as they have an attributed order and sequence against which real objects may be variously compared or matched, either as a quantity of magnitude(a measurement) or a count of quantities of magnitudes(whole objects).
This wonderfuly algebraic definition is lost on those who through training have comd to believe numbers are something ontological rather than adjectial or advebial descriptions of ontological objects.
In the alphanumerical system we inherited from the greeks numerals could be single letters or special names å for example as a number would be called en in greek The quality of wholeness of magnitude was called monas because it distinguished itself from a group but its name was en and its symbol å. Thus we never start with Shunya or the symbol for shunya or the symbol picked out by the shunya symbol. We always start at the beginning of any sequence used in this way and that is with an å or a 1 symbol.
The vedic 9 is therfore shunya. The decimal system has taken it as nine and used another symbol for shunya as zero, but apart from that notational conundrum the vedic system transfers as intact.
Writing 10 as the number, that is combination of numerals that succeeds shunya is using displacement to count graphically. The actual system relies not on graphic displacement but a sequence of Mudras or finger gestures or arrangements. These mudras meant that the typical student or commercial trader could combine counts of metrons very rapidly and very naturally. Foreigners thought that the practitioners were doing the combinations in their heads, and dismissed the Mudras, missing the significance of the systems. Today Vedic maths is being taught in the west as the facility it gives to the mental ability to calculate and the confidence in arithmetic is unsurpassed. Mental arithmetic or counting on your fingers is a natural and self affirming thing to do. It quickly leads to amazing confidence and computational ability.
The displacement method of writing the Vedic system has become standard scientific and mathematical and economic way of combining weights and measure, that is all sorts of metrons, but historically cultures have clung on to fractions and other non decimal systems of weights and measures and this has led to complications in students understanding and developing confidence. Nevertheless if the imperial office of wights and measures set out a system of accounting subjects had to comply! thus a lot of what is "mathematically" interesting is reduced to rote learning. Euler established the ultimate system of weights and measures through his equivalence classes, thus making it a straight forward task to lay out a system of weights and measures in their fractal divisions. The reduction to a simple decimal system was resisted on cultural grounds, not ease of use grounds.
Some find switching culturally more confusing than switching mathematically, because everyone around them is at odds with them. Britain since 1976 has been decimal, but the imperial system is still entrenched in some preschool childrens consciousness because their parents have not changed over, nor their parents before them.
The mudras and Shunya seem miraculous to many who calling it casting out 9 are impressed at how the symbols flow and combine with the !0 system! This is clearly a misunderstanding of the terms. The system is the same, just written using a displacement notation, thus the decimal system is the Vedic system but presented graphically. Also the way the numeral combine even in extended notation is a feature of the combining of the modulus, that is the largest quantity of magnitude distinguishable by the system, the fullness quality of the metron as it scales.
The p adic system is a combinatorial system, but a restricted set of labels or symbols are used to distinguish the combinations of the metrons. Ultimately it is the metron that determines how quickly and easily an accounting may be done. The problem is to set up a system of weights and measures that allows for fine detail but also enables huge quantities to be quickly and conveniently accounted for. This means that a Scale of metrons has to be used, and the scales must have a simple or obvious relationship.
Such scales combinatorially are the p-adic scales or numbers systems which may be written in a plyynomial form and thus enable any quantitiy to be represented by a polynomial Procedure. This procedure is often ignored and the resultant emphasised and called a number! it is a collection of numerals which is meaningless without the underlying procedural basis.
Using this analysisi Napier was able to establish the logarithm of sines as an effective look up calculation tool, and then to develop rods that similarly speeded up calculation, all of which rely upon an understanding of the vedic system which came to full fruition in Euler's equivalence class notation and modulo arithmetics. The importance of Eulers work was that he laid down principles that enabled engineers to establish a weights and measures system for computational processors : the binary system. It is still imposed on computers today as their system of weights and measures.
The modulus is defined as the difference between two quantities. Simply it is the remainder after the smaller quantity is subtracted from the larger. It's old name was the subtrahend. Modulo is a cute word trying to capture the remainder process and it simply means divide and focus on the remainder.
So we use the term base which derives from Wallis introducing exponential notation. Napier had devised the logarithms of Sines as a table of values based on a decreasing proportion. By this I mean a ratio is set up between 2 quantities and the ratio is repeatedly applied in the fractalisation process so that each quantity is reduced. As the reduction is carried out each new or resultant part is then reduced again in the same ratio. This process is repeated iteratively as many times as desired. This whole process was named a reducing proportion by Napier and it is a fractal process devised By or found in Euclid's Stoikeioon as part of Euclids algorithm in general and the extreme and mean geometric relation in particular.
The logarithms are actually tabulated as identies and thus can be plotted on Cartesian axes, pre dating Descartes Cartesian paradigm and reminding us that despite what pedagogues say the coordinate system was used and understood far more flexibly than today. In fact Bombellis used a version of it which he explained came from the Greek Fathers. Standardisation is a helluva thing, but should not be used to obscure the facts.
Thus Wallis introduced the exponential notation in which the logarithm was identical to an exponent of some fixed term. This term symbolised a quantity and since it was a fixed quantity it became referred to as the base supporting the raised exponent. "Ex ponent" itself means coming out from the pons or "bridge", the basis that lifts and carries.
Using the divisor as a base and the remainders as moduli a notation was devised to record the combinatorial construction of the number systems as a polynomial. This is the p- adic polynomial system especially when" prime" bases are used. This notation of the systems of numbers reveals the differences between the Vedic nine label system and the western Arabic ten label system. Because the ten label system actually uses a label that does nothing this displaces the Vedic system by one place and means the Vedic system is utilised almost directly graphically ie in numerals on the page. This leads to the curious ability to read the decimal structure for the Vedic value from the Mudras, but this is not the Vedic conception but a decimal translation. Combining in nines is different to combining in tens, and it's advantage is the Mudras it enables the practitioner to hold within the arrangement of the fingers. These Mudras are thus a direct neurological stimulus to a concept of distinction in comparison. As the comparisons progress in the count the mudras cycle endlessly. This cyclical " movement" in the mudras is visibly spiral not circular. The spiral is a scaling spiral and so the combining in 9's produces a neurological computer that scales to any size always in 9's.
Of course tens do the same, as this is a logarithmic spiral, but the neorological connection through the shift patterns in the finger Mudras is lost, replaced by a static or circle system, the scale runs off the fingers immediately, only 10 Mudras are possible! Thus to show 45 on my fingers I have to flash 4 tens and hold up 5 fingers. The Vedic 45 is a cool finger mudra: 4 fingers on one hand with one finger bent( 5 x 9) and 5 fingers on the other hand! Really the Vedic mudra for 45 is just the bent 5th finger the other fingers can then be used to represent 46 to 53 with 54 being represented by the next finger bending down freeing up 9 fingers again.
Translating across into the decimal system actually slows the process down, and reflects a decimal centric bias. The Mudras are an enneagonic biased system, and computers typically run on a binary bias system. It seems clear that the Vedic system seems to be the best bias for the human neurology just as binary is the best for the electronic systems of the past. With today's sophisticated signal processors we could probably enhance the electronic systems to respond to more than 2 signals, but the diode reveals the fundamental dual contra flow of electromagnetism which must be a design constraint that should be worked with not ignored. To me this indicates that powers of 2 not 3 will be the basis of electronics. However powers of 3 due to the spiral may be the basis of tapping the power of electromagnetism.