Indian Genius: ‘Decimal’ and ‘Place Value’ – Used in Math and Language, Both!

By: Shreepal Singh

Sanskrit is an ancient language – really very ancient one. It is regarded as the mother of all the so-called ‘Family of Indo-European languages’. Which are these European and Indian languages today?

Almost all the languages of Europe are included in this family. All these languages have some surviving traces of their Mother Language – Sanskrit or Proto (the original) Sanskrit– still available in them. The abysmally low amount of these traces available in these languages indicate that none of the European languages could preserve their mother language as its body part.

But it is not so with the Indian part of this family. Which are the languages of the Indian part of this family? Almost all the modern Indian languages are included in this family. While the European languages have these little traces in some of their words only in the form of phonetic similarity with Sanskrit words, in the case of Indian languages it is not so.

In the Indian languages still a large number of words are used in their either pure or impure Sanskrit forms. Apparently these Indian languages are the descendants of the Sanskrit, founded on Sanskrit roots with some distortion. However, there is one exception in this descent: None of these Indian languages uses the Sanskrit grammar. In the resemblance of derivative words, Hindi language is the most notable and widely spoken in India.

‘Decimal’ and ‘Place Value’ in Numbers:

Let us first consider the application of the concepts of ‘Decimal’ and ‘Place Value’ in mathematics since ages – since the very origin of Sanskrit language itself, which is shrouded in the mist of past. We all use the system of ‘Decimal’ in our day today life, without realizing the genius of ancient Indians who invented this system.

We know ‘decimal’, an English word, is derived from the Sanskrit word ‘Dashamlav’ (दशम् लव), where दशम is ‘Ten’ and लव is ‘Positioning or Placement’. दशम लव is the system of ten. Decimal system in mathematics is the incremental gradation of anything from 1 through 9, with an additional number as 0 (Zero). What is the purpose and intent of this incremental gradation? For example, what is the meaning of 1 and 2? It simply means that whatever quantum 1 holds, twice of that quantum is held by 2. Likewise, it goes on increasing always in relation to 1, up to 9 in count. Plainly, numbers 2 through 9 is a comparison with 1. It is a relation of 2 through 9 with 1. Conceptually, number 1 may have in it an amount, a quantity.  Whatever this amount or quantity may be, is immaterial. Numbers 2 through 9 are only a comparison with what number 1 holds. It is a relation, where 1 is the unit.

In Sanskrit language, the scheme of ‘Decimal’ deals with ‘relationship’ only and, incidentally, the scheme therein of alphabets coupled with sounds deals with ‘things’ only. So far as this material world – ney, universe – is concerned, from the human perspective it is only a bundle of things and their relations. Beyond this, there is nothing here. Sanskrit language is so perfect an instrument in the hands of humans that it takes care of their concern of things and these things’ relations with one another. In fact, Sanskrit is the embodiment of human speech and mathametical numbers!

In decimal system, one can go on increasing this gradation comparing 1 with any number up to the infinity and still it will be only a relation with 1 of all those individual numbers up to infinity.  But if you want to record this relationship by using some signs – or numerical script – up to any significantly high number, let alone up to infinity, you would be forced to invent a very large number of symbols in that script – or, at least, using the symbol of 1 as many times as you want to count. We know the difficulty of writing numbers by Romans numerals, which we still use for a few special purposes. It is a crude method of writing numerals. It needs a large number of symbols or, alternatively, large amount of space to put a few numerals!

We all know it.

To circumvent this difficulty, India invented a device ages ago, not only the relational concept of 1 with 2 through 9 but also an additional symbol of 0 (Zero). This 0 also is nothing but again a relation with 1. The purpose and intent of 0 is to compare it with 1. This comparison states that whatever amount or quantity (of anything) this 1 contains in it, this amount or quantity is absent in 0. It is simply a relation of 1 with 0. In the decimal system invented by the genius of ancient Indians, the only material number is 1. Rest of the numbers – up to infinity – are only the individual comparison – relation – with 1. This number 1 is the only definable entity, which could be anything, and all the rest of the numbers are relational with this number 1. You can compare this 1 with any number up to infinity.  The number 1 is a unit.

But how does one record these relational numbers in a script? Here again ancient India excelled in its genius. Its genius invented another use of 0, in addition to its (zero’s) use as a relation with 1. This 0 was utilized to denote a specific place to these numbers 2 through 9. For example, number 2 is not only a relational quantum, that is, 2 is not always twice in amount or value of 1. In relational value, number 2 is always twice the value of number 1 but by assigning a definite place to this 2 in the script with respect to other numbers used there, this 2 changes its value. Depending upon the place assigned to this 2 in a sum, this 2 may be increased or decreased in its relational value with 1. It is not all. This ‘increase’ or ‘decrease’ in the value of 2 depending its place in the whole sum is again ‘ten-fold’. By the use of ‘0’ this ‘2’ could be increased or decreased ìn its value ten-fold at the each use of ‘0’ – in any number of steps that one may like – upto infinity.

The particular place assigned to ‘a digit’ in a sum with the aid of ‘0 digit’ is itself a value, which is again a relation with 1. In this scheme of ‘decimal’ system, the only material concepts are: ‘1’ (i.e., a unit to be compared with by any number up to infinity, which is only a relation); ‘0’ as a device (i.e. a device to assign a digit any place in the sum, which again is a relation – increasing or decreasing the value of that digit); and, ‘0’ as a relation (i.e. holding a negative value of 1, which is again a relation with 1). Indeed, it an amazing invention made by the Indian genius!

‘Decimal’ and ‘Place Value’ in Sanskrit Language:

Another wonder of the genius of ancient India is the utilizing these concepts of decimal and place value in the Sanskrit language.

Sanskrit language is written in Devanagari script. In the matters of the descent from the Sanskrit language and the popularity in modern India, Hindi language inherits the legacy of Sanskrit. Hindi is spoken by millions of people in India. Hindi, like Sanskrit, is too written in the Devanagari script. Hindi is recognized as the national language of India by the Indian Constitution. Let us consider Sanskrit and how this language utilizes the concepts of ‘decimal’ and ‘place value’ in its alphabets. While considering these aspects of Sanskrit language, to highlight these specialties, the author will compare the position of English language in this respect.

Sanskrit alphabets have classes and categories. The classes are: क च ट त प and the alphabets of conjunct-ed voice. The categories of the former class of alphabets are: Soft, Hard and Swift. The Soft category, and followed by the Hard category, of these classes of alphabets are:

Soft: क Hard: ख

Soft: ग Hard: घ  (Next note of sound in musical ascendance of क and ग ): ङ
Soft: च Hard: छ
Soft: ज Hard: झ (Next note of sound in musical ascendance of च and ज ): ञ
Soft: ट Hard: ठ
Soft: ड Hard: ढ  (Next note of sound in musical ascendance of ट and ड ): ण
Soft: त Hard: थ
Soft: द Hard: ध
Soft: प Hard: फ

Soft: ब Hard: भ

The Swift category of alphabets is made by making them ‘Half’ for sounding them swift when written in conjunction with the next following alphabet, like this: ग्वाल, कथ्था, मक्खन, चमच्च, क्लास, ख्याल, पत्थर; This is the way of Sanskrit to make the sound of an alphabet Swift. But it is made possible by writing an alphabet ‘half’ and then reading it in ‘conjunction’ with the next following alphabet. But if there is an alphabet that needs to sound swift but not in conjunction with any other alphabet but independently, how do you do it? For this ‘halant’ symbol is used, like क् ; ह् ; etc. This making a ‘half’ of one alphabet is a novel invention of Sanskrit language, which is not found in any other language, and serves to control the speed – swift or slow – of the sound of the alphabet concerned. For example, there is phonetic difference among words कलास, कालास and  क्लास in Sanskrit but in English you can write and sound ‘class’ but cannot accurately write and sound कलास and कालास words. English is handicapped in this matter.

The class of alphabets of the conjuncted voice are: क्ष ॠ त्र ज्ञ श्र and they respectively pronounced as in:  क्षत्रप ॠषि त्राटक ज्ञानी श्रीमान .

In addition to these divisions, this language creates fine nuance to the sound of र by adding it as a sound or ‘Matra’ above, below or with an alphabet, like this: वर्तमान, पृथ्वी, प्रयोग, वृक्ष, कर्म, प्रथम;

The genius of ancient Indians, who crafted Sanskrit language, lies, firstly, in the fact that there is a certain relation of frequency (or pitch) of sound contained in each alphabet of these classes and its categories to the next following alphabet. For example, a) क has frequency or pitch relationship with ख b) क has again a relation with ग c) By finding the pitch relation with क and ग one can assess the pitch of the last alphabet of this class, that is, ङ . The same holds true for all the other classes and categories, viz.: च छ, ज झ  and ञ; ट ठ, ड ढ and ण; त थ, द ध; प फ, ब भ;

Incidentally, this property of phonetically two classes of Sanskrit alphabets can be exploited in computer compilation program by assigning one extra digit to the Soft class or Hard class.

In English language, there is no knowledge of such difference of the ‘Soft’, ‘Hard’ and ‘Swift’ categories of its alphabets. Also, in English there is no awareness of the ascendance of the musical notes in the sequence of its alphabets. For example, a, b, c, d, e, f etc. have neither pitch connection and difference nor any sense of ascendance of sound. In this language, these alphabets look unconnected, at random and crude in sound.

In fact, all the fine nuiences of different sounds written in Sanskrit alphabets cannot be accurately written in English language. For example, b of English is ब of Sanskrit; but English has no alphabet भ of Sanskrit (which is Sanskrit’s ‘Hard’ category of ‘ब ‘). English has to somehow make do this deficiency by joining b and h like ‘bh’. Or, t of English is ट  of Sanskrit but English has no alphabet ठ of Sanskrit (which is Sanskrit’s ‘Hard’ category of ‘ट’) and English has to somehow make do this deficiency by joining t and h like: ‘th’ etc. But unfortunately for English, if ठ of Sanskrit is written as ‘th’, then there is no way of writing Sanskrit’s थ (Hard of  त), as it would again be written in English as ‘th’. In fact, English’s ‘th’ is neither ‘ठ’ nor ‘थ’ of Sanskrit. Likewise, there is no sense of difference of ‘sound nuance’ in English language of Sanskrit alphabets: ख, घ, ङ, छ, झ, ञ, ढ, ण, ध, श, ष, स, अः, अं, अः, ऋ, क्ष, ज्ञ, त्र, श्र, ॠ etc.  and absolutely no way to accurately write them.

In Sanskrit language, there is a difference in pronouncing पृथ्वी, प्रयोग and कर्म, in all of which र (or R) is used, but English cannot make out this fine difference of the pitch of sound.

In addition to these alphabets of Sanskrit, this language has ‘Short’ and ‘Long’ sounds or vowels.

The ‘Short’ sounding vowels are: अ इ उ ए ओ अं

The ‘Long’ counterpart of these ‘Long’ vowels are: आ ई ऊ ऐ औ अः

These ‘Short’ and ‘Long’ sounding vowels can be used in two ways: Firstly, as independent alphabets. Secondly, for giving a particular sound to ‘Soft’ and ‘Hard’ alphabets.

However, the sound of अ by default is already integrated with each of the alphabets. Thus, for example, ट is  ट +  अ;  ल is ल + अ; etc. This addition of  अ  to every alphabet by default gives them the stability and depth of sound and provides a word made out of these alphabets a sonorous or musical tone. To add the tonal effect of ’emphasis’ to an alphabet, the sound of vowel  अः is put to the front of an alphabet, like चः कः नः; etc.

The genius of ancient Indians, while crafting Sanskrit, lies, secondly, in the fact that all the sound vowels available in Devanagari script are added by utilizing the space available above, below, back and front of these alphabets while hanging with their head from the top of limiting straight line. In Sanskrit, alphabets are not written by putting them one after another in a row, as is done in English. For utilizing the available space above, below, back and front of an alphabet, alphabets in Devanagari script are written like ‘hanging down at their head’ from a top straight line. Every alphabet, as a rule, has to be written below this line. The space above this line is reserved for adding a ‘Sound’ or ‘Matra’ to the alphabet hanging just at that point below the line.

Thus, for example, the sound of इ  is added to the alphabet क by going above the limiting line – just above this क – to make it look like, कि or to add another sound of उ by going just below the limiting line, like: कु

All the sounds are added to the alphabet: like प – प पा पि पी पु पू पं पो पौ पे पै; like त – त ता ति ती तु तू तं तो तौ ते तै; etc.

The advantage of this scheme is that, in Sanskrit language employing Devanagari script, one can write and pronounce any alphabet, word or sentence of any language of the world with the mathematical accuracy. But the reverse of this not true. There is perhaps no language in the world, except the Sanskrit language, that can accurately write and pronounce all the possible sounds of alphabets, words or sentences so accurately.

For example, in Sanskrit one can accurately write and pronounce: रावण; तट; तत् सत;  त्रोटक; षौडष; सिहं, शीस, सीसा, शशिकला etc. But in English there is no way to accurately write or pronounce these words. In English these words would be written like this: Ravana, tat, tat sat, trotak, shodash, singh, sheesh, seesa, shashikala, which in Sanskrit would be read as रावणा, टट, टरोटक, शोडाश, सिघं, शीश, सीसा, शाशिकाला etc. (which words have meanings different from their original Sanskrit counterparts!)

Sanskrit language is mathematically accurate and precise in its scheme of the arrangement of these alphabets. This accuracy and precision of the Sanskrit’s scheme of arranging alphabets contributed to the discovery of the Periodic Table of Elements by Mendeleev. In making his discovery of the Periodic Table of Elements Mendeleev was inspired by the arrangement of alphabets in Sanskrit.

Sanskrit Language is Music:

Sanskrit is a music producing language. It has everything to do with ‘दशम लव’ or the number 10. In this language there are only 10 alphabets each in its two categories, viz, soft and hard. The alphabets in soft category, as stated above, are  क ग च ज ट ड त द प and ब. Each one of these 10 alphabets in Soft category has its equivalent in the Hard category, thus adding 10 more alphabets. These 10 hard counterparts of their Soft cousin are: ख घ छ झ ठ ढ थ ध फ and भ.

Now, there are 10 more alphabets that have no Soft or Hard categories. These are:  न म य र ल व श ष स and ह. Thus, in all there are 10 basic alphabets in the Soft category plus 10 as their counter part in the Hard category and 10 more alphabets without category. In all they become 30 in number.

Apart from these alphabets, as stated above, Sanskrit language has 5 vowels of Short sound and 5 vowels of Long sound: अ इ उ ए ओ (of the Short sound); आ ई ऊ ऐ औ (of the Long sound). Apart from these, there are 2 more sounds or vowels, which have no Short and Long forms, viz.: अं अः . When these Short or Long sounds are added to the Soft or the Hard alphabets, they produce a peculiarly accentuated kind of sound for every Sanskrit word. In addition to the joining of these sounds to Soft and Hard alphabets, these sound are also used as independent alphabets.

The tone, nuance and sound vibration of every alphabet and word of the Sanskrit language is so precise that learning and speaking this language is the best speech therapy.

The wonderful thing that one finds in this language is that, when spoken, these notes of sounds embedded in Sanskrit words and sentences produce a rhythmic sound or music, apart from the meaning that these words – producing such music – convey.

What is a musical sound? A strongly regular waveform of any sound is a musical sound. The pitch of a sound is determined by the frequency of the vibration of that sound.

If one is able to recite the Sanskrit prose or poem accurately, it is a music. Now, music creates a positive impact on human mind. The musical impact of Sanskrit speaking nourishes the human brain and enhances its memory retention power.

Sample of Sanskrit speaking:

Sample 1:

Sample 2:

Sample 3:

Sample 4:

It has been found that if Sanskrit text – prose or poem in Slokas – is spoken regularly by a person for a sufficiently long period, it produces a change in the biological structure of the brain of that person. A neuroscience researcher conducting experiment on the effect of Sanskrit speaking on the human brain has found that regular Sanskrit speaking enhances one’s memory and the concerned part of the human brain is biologically changes its shape by increasing its area.

This research paper is published in the Scientific American HERE.

Also have a look at this article on this subject HERE.

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