Sanskrit Number Words Handling in Formulas and Demo Calculator Example

Sanskrit Number Words Handling in Formulas Demo Calculator Example

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• • Sanskrit Number Words Handling in Formulas Demo Calculator Example
• Introduction
  • Testcases Section
  • References:
    • Appendix Code
    • appendix TCL programs and scripts
    • Pretty Print Version
  • tcl8.5 code scraps
  • Hidden Comments Section

Introduction

# gold Here is an eTCL script on Sanskrit Number Words. The Indian astronomy texts of 620 CE. used multiple Sanskrit words for zero (and numbers 1-9). The Sanskrit aternate words for zero were kha,ambara,akasa,antariksa,gagana,abhra,viyat,nabhas,sunya,bindu.The single Sanskirt word sunya (void) is more common in the online wordlists. In transliterated Sanskrit , the decimal number 1000 could be expressed as left to right (0001) viyad(sky or zero)/ambar(atmosphere or zero)/akasa(space or zero)/eka(1).

# There were a number of poetic or mnemonic systems in India for memorizing cosmological constants, sacred formulas for altars and rites, and formulas. There is more evidence for decimal place holding systems and decimal point separators after 650 CE. The most common mnemonic systems were created using consonant-vowel-consonant (CVC) to create a pronounceable word, but not necessarily a meaning in the native tongue. Syllables of consonant-vowel (CV) and vowel (V) were possible, but most scholars of the time recognized the possibility of confusion for mnemonic vowels alone. The cosmology text Lokavibhaga. from 458 CE used mnemonic syllables for number words. The Indian astronomer Arybhata used a system of mnemonic syllables in the book Arybhatiya (b. 476 CE.) In 629 CE., Bhaskara expressed numbers including zero using Sanskrit words for gods, body parts, cosmology, and poetic allusions, eg the three eyes of Shiva for number 3. In 665, the mathematician Brahmagupta presented a sine table that used poetic words as digits, including zero words. Some mnemonic systems for making calendars, predicting horoscopes, and lunar eclipses were still in use in South India by 1825, based on accounts of John Warren, a British officer stationed in India.

Number spelling in India lead to a fuller sense of the zero and more understanding on the uses of the zero, so number spelling is not as trivial as it looks.

Alternate text rewrite

There were various methods and systems used throughout history to represent and communicate numerical values. The use of Sanskrit number words, as described in your script, is a fascinating example of how different cultures approached the challenge of representing and memorizing numbers. The multiple Sanskrit words for zero, such as kha, ambara, akasa, antariksa, gagana, abhra, viyat, nabhas, sunya, and bindu, show the depth and complexity of the Indian numeral system. The use of poetic or mnemonic systems to memorize cosmological constants, sacred formulas, and other complex calculations is a testament to the ingenuity of ancient Indian scholars.

The development of decimal place holding systems and decimal point separators after 650 CE is another interesting development, as it shows the evolution of the Indian numeral system over time. The use of mnemonic syllables, created using consonant-vowel-consonant (CVC) or consonant-vowel (CV) and vowel (V) combinations, is a particularly innovative approach to memorizing complex calculations. The use of Sanskrit words for gods, body parts, cosmology, and poetic allusions to represent numbers, as described by Bhaskara in 629 CE, is a fascinating example of the creative ways in which ancient scholars approached the challenge of representing numbers. Similarly, Brahmagupta's sine table that used poetic words as digits, including zero words, shows the extent to which ancient scholars were willing to experiment with different approaches to representing numbers.

The continued use of mnemonic systems for making calendars, predicting horoscopes, and lunar eclipses in South India by 1825, based on accounts of John Warren, a British officer stationed in India, is a testament to the enduring influence of these ancient systems. The use of number spelling in India lead to a fuller sense of the zero and more understanding on the uses of the zero, so number spelling is not as trivial as it looks. This is a valuable lesson for us today, as it shows the importance of understanding the history and cultural context of different number systems.

Testcases Section

Testcase 1. # Example lays transliterated numbers right to left, but in the Sanskrit texts, the numbers are usually written left to right without any spaces or separators . In the eTCL program, there is a random routine to pick a zero word from six or more word selections meaning zero.

321505340

 tri dvi eka panca abhra panca tri catur abhra 

Testcase 2.

Comments Section

Please place any comments here, Thanks.

References:

• FromOne to Zero, the History of Numbers. George Ifrah
• The Story of Indian Zero
• Warren,John Memoirs of Time Keeping in India,1825
• Brahmagupta's Brahma-sphuta-siddhanta, English introduction, Sanskrit
• Brahma-sphuta-siddhanta [L1 ]
• Mathematics and Mathematical Astronomy Website [L2 ]
• Story of Indian Zero, The Story of Indian Zero
• A Brief History of Zero], Kristen McQuillin ,1997-07 (revised 2004-01), off the internet but very good.
• Postscript headlines. Indian evidence for zero placeholder in circa 224/383 AD, B. Manuscript.
• Much ado about nothing: ancient Indian text contains earliest zero,
• www.theguardian.com/science/2017/sep/14
• www.bbc.com/news/uk-england-oxfordshire-41265057
• The Bakhshali manuscript: Carbon dating the Bakhshali
• Manuscript between 224 and 383 AD.Oxford's Bodleian library
• Karen Carr ,Associate Professor Emerita, Department of History,
• Portland State University, article on zero and math history
• Numerical Tables in Sanskrit Sources, Article, · June 2014
• Agathe Keller, Koolakodlu Mahesh, Clemency Montelle
• info on zero symbols, Earliest Uses of Symbols for Constants,
• Jeff Miller, Gulf High School in New Port Richey, Florida (now retired).

Appendix Code

appendix TCL programs and scripts

Pretty Print Version

        # pretty print from autoindent and ased editor
        # Sanskrit transliteration of integers
        # written on Windowws XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI , 9jul2013 
    package require Tk
    console show
    set xzeroes { kha  ambara  akasa  antariksa  gagana  abhra  viyat  nabhas  sunya  bindu  }    
    proc lpick L {lindex $L [expr int(rand()*[llength $L])] }
    proc average L {expr ([join $L +])/[llength $L].}
    proc plainsub {text item replacewith} {
        set text [string map [list $item $replacewith] $text]
    }  
    proc subword { sanskritword } {
        set xzeroes { kha  ambara  akasa  antariksa  gagana  abhra  viyat  nabhas  sunya  bindu  }       
        set sanskritword [ plainsub $sanskritword 1 eka ]
        set sanskritword [ plainsub $sanskritword 2 dvi ]
        set sanskritword [ plainsub $sanskritword 3 tri ]
        set sanskritword [ plainsub $sanskritword 4 catur ]
        set sanskritword [ plainsub $sanskritword 5 panca ]
        set sanskritword [ plainsub $sanskritword 6 sat ]
        set sanskritword [ plainsub $sanskritword 7 sapta ]
        set sanskritword [ plainsub $sanskritword 8 asta ]
        set sanskritword [ plainsub $sanskritword 9 nava ]        
        set sanskritword [ plainsub $sanskritword 0 [lpick $xzeroes ]]
        return $sanskritword }   
    foreach  item { 1 2 3 4 5 6 7 8 9} {
        set sanskritword  [expr {int(rand()*1000000000.)}]
        puts " $sanskritword "
        puts "[ subword [split $sanskritword "" ]]"  
        }

output:
619882413
sat eka nava asta asta dvi catur eka tri
228549526
dvi dvi asta panca catur nava panca dvi sat
316376463
tri eka sat tri sapta sat catur sat tri
349369262
tri catur nava tri sat nava dvi sat dvi
419843652
catur eka nava asta catur tri sat panca dvi
407217392
catur ambara sapta dvi eka sapta tri nava dvi
321505340
tri dvi eka panca abhra panca tri catur abhra
93242173
nava tri dvi catur dvi eka sapta tri
71222137
sapta eka dvi dvi dvi eka tri sapta

tcl8.5 code scraps

puts "[string reverse "[ subword [split $sanskritword "" ]]"]"

string map { 1 eka\/  2 dvi\/ 3 tri\/ 4 catur\/ 5 panca\/ 6 sat\/ 7 sapta\/ 8 asta\/ 9 nava\/ 0 sunya\/ } 759002679

Hidden Comments Section