Zero-start and one-start

We can count numbers in two manners. Either by relating start of a-unit (number zero onwards) or by relating physical a- units (in which end of a-unit is counted as '1'). Hor line ____ is a-unit! A line has a start to it, a length to it and a state to it (liner, curve, or a combination of both. Let us analyse a straight line alone). A straight line can be divided into several 'equal parts' and 'each part' can be regarded a-unit. Further, each merged "number-unit" comprises 'a number' and 'a-unit'. For example a"9 cm" is "a number-unit 9" and "a length unit" cm. Nine number units are shown below graphically!

0......1......2......3......4......5......6......7......8...zero-start

____ ____ ____ ____ ____ ____ ____ ____ ____ --->9 a-units

....1......2......3.......4......5......6......7......8......9... ---> 'Usual count' relates each unit in 'one to one position' (one-start).

Obviously it is one unit more than a digital count!

You can extend above logic to zero start 2D square matrix positions, which relates y and x ordinates and each of these have merged properties of pair-numbers. These area-units are bound by a vertical unit-y and an equal horizontal unit-x in a 2D square matrix. In a 2D matrix there are several merged 'yx' units!

You can also extend this logic to zero-start 3D cube-matrix positions, which relates z, y and x ordinates. It relates 3D-properties of "merged 3-digit numbers". Each 'cube unit' is bound by three equal 'square area-units' yz, yx and zx!

Vedic manner relates "before-units count" (either linear, or area or a cube unit), which gives us a precise 'digital number sense'. A start-unit has 'no before unit of it' and said condition 'no' is zero. Second unit has obviously 'one' unit before it. Third unit has 'two' before-units so on! This is principle of using 'zero-start number count', which is much older than 'Vedic period' in India!

However, users have consistently preferred physical 'one to one' count (one-start) , which is also explained in above graph. A Verbal explanation of these facts will confuse an ordinary user of counts. So both are concurrently explained (graphically)! Obviously a difference of one-unit exists in between a zero-start and a one-start, which is ekdhika (one more than...) explained in Vedic Mathematics. More manners to relate 'ekadhika' exist, which also applies to all Vedic sutras!

Vedic Mathematics used 'zero-start number counts' and people preferred 'one-start'!

A concerned "paradox" did exist ever since ancient Indian Mathematics grew as a public utility knowledge, which continues even now! A great possibility to apply numbers (by relating positive numbers alone) had disappeared along with Vedic Mathematics, which is now re-emerging!

A Vedic sutra "ekadhikena" (one more than...) reveals these facts in a book published by followers of shree Jagadguru Sankaracarya (1884-1960) . Some mathematicians openly claim that 'contents of "Vedic Methematics" are not-scientific'. "Truth will emerge victor". Let us wait!

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Vedic-matrix in a nutshell _1 November 4, 2007 (Author: kkr)

Vedic-matrix is an experience that has great relevance to a Vedic number application!

It relates a 2-Dimensional square-matrix (having ‘equal-number rows and columns’ that are “merged a-units” (either 0…9, or 00…99, or 000…999 or a higher order). Similar 3-Dimensional matrix application too had emerged in ancient India. Together with “linear digital numbers” said 2D and 3D ‘matrix-position-linked computing had grown as a foundation of ancient Indian Mathematics, which Vedic Mathematics followed as it is!

‘Number’ and ‘language’ relate a principle that “number is a condition”. A number added to a sentence fixes a condition/meaning, whereas, number is before-unit condition! While zero is ‘before-unit’-condition of a start-unit; 1, 2, 3 …etc are ‘before-units’ conditions of (next higher 2, 3, 4 …etc)! Obviously Vedic-sutra ekadhikena purvena (one more than previous one) correctly indicates a meaning of ‘before units’-conditions”.

Number-adding-grammar (singular, dual and plural) of Sanskrit is far more ancient than Vedas. Said grammar had helped ancient Indians to use language with bare minimum flaws” It further helped them to make a very simple number theory (linking to zero)!

Ancient Indians applied “simplest number applying principles” for day to day use of it. They primarily used human-memory to achieve it. “Visual computing” (by looking at 2D matrix) is a part of it. Meaning of Vedic-sutras and 6 computing-signs together reveal it!

Visual-computing becomes simplest when it is related to 2D square-matrix positions. Simple row(y) and column(x) merging as a ‘y x’ number carries y and x virtues into an ‘yx’-merged-number! ‘Z, y and x’ 3D-cube matrix positions/numbers also depicts similar virtues! Both 2D and 3D matrix are regarded a Vedic-matrix, which manner grew earlier to a Vedic- period! Being merged reading of z, y and x (as plus numbers) it is simplest!

Zero-start 2-Dimensional square matrix has equal ‘y and x’ units. Zero-start 3-Dimensional cube matrix has equal z, y and x units. Said equality of z, y and x units is very important! Vedic-matrix helps us to mentally relate 2D or 3D matrix position numbers (in a unique number). A natural ‘before unit/units’-count of a matrix position is either ‘a merged 2D-row-column (RC) or merged 3D-layer-row-column (LRC)’- number!

Vedic ‘before unit/units’-count is different from usual “digital-number counts” (used in computers). “Numbers less than zero” are not ‘part of Vedic-number relating’! Further, Vedic-matrix-2D is source to six basic computing signs -, +, -:-, x, = and ‘square root’. Logic of ‘computing signs’ concurrently interlinks both Vedic-matrix and Vedic-sutras!

Instead of “a usual one to one digital-number-count” (used in computers); VEDIC MATHEMATICS relates ‘before unit/units’-count, which are a-unit less than usual digital number counts. In other words usual count is “one-unit more than previous one” (Vedic sutra ‘ekadhikena purvena’), meaningfully reveal that! A merged ‘y x’ number or ‘z y x’ number is a usual Vedic merged-number. You may search merged “row and column” number applications by a ‘Yahoo’ or ‘Google’-search (“Vedic matrix’)! Salient features of Vedic matrix you will find there, which is summarized by…
1) Basically ‘before unit/units’-count are before-units of (a-unit step increasing digital positions) that had carried zero to usual “number applications” well before ‘Vedas’ were compiled! Said manner related 2D square matrix positions (as before square-units) and 3D cube-matrix positions (as before cube-units)!

2) Digital numbers are used in computers. We can easily grasp ‘digital’ / ‘whole-number-step’ or as ‘before-units count’ when it is applied as 2D-square-matrix position!

3) Before-units count does not relate “numbers less than zero”! Infinite positive numbers are applied by linking to either Vedic matrix 0...9 or 00...99 or 000...999 or a higher order, which is a great ‘endless number relating’!

4) It is difficult to do usual computing together with numbers less than zero. (‘Minus numbers’ is not part of Vedic mathematics). Minus numbers is an obvious need of Cartesian co-ordinate system! Said minus-numbers have made usual number application very complex and scope of number application also increased very much! Both are not helpful to ordinary users of computing. There is no chance that ancient Indians could have used a complex minus number relating we use today!

5) Essentially a fear of mathematics begins from minus-number relating, which is not essential 'to apply numbers'! Combined ‘plus and minus’ number relating (to computing) unsettles human minds! A consistent use of “plus numbers alone” gives ‘a zero-based instant-number-sense’, which is inner strength of “Vedic matrix and Vedic Mathematics”

6) We can relate computing either by linking to a 2D-square or a 3D-cube-matrix. It is a very important aspect. However before-unit counts are to be used as matrix positions!

7) Concurrent relating of "computing-signs and Vedic-sutras" to actual computing is an evidence that “Vedic matrix did exist in ancient India”!

8) Vedic matrix (that relates before-unit positions) had disappeared some four thousand years ago! Vedic matrix (language) was resourceful enough to teach usual computing-sense to its users. Thereby matrices became less useful. Computing signs still carry matrix-sense, which is a greater wonder!

9) Computation possibilities are huge. A small part of it is public-awareness! Vedic-mathematics could literally reverse this trend! If we disregard “before-units"- count (by a not-scientific-sense we have attached to it), we are missing an opportunity to outwit computers! Great virtues of Vedic-‘2D-square and 3D-cube’ matrixes show us right path!

Most important feature of a Vedic matrix 0…9, or 00…99, or 000…999 or a higher order is that a unique computing-manner becomes a reality by relating either linear digital number positions, or digital 2-D square matrix positions, or digital 3-D cube matrix positions! ‘Z, y or x’ zero is before-unit count, which help us to use it as source number! Zero is “affect of ‘before-unit/units’-count” that eliminates “need to use” numbers less than zero, (which helps all users of computing forever). It is greatest utility of a-zero!

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