***Sanskrit Number Words Handling in Formulas Demo Calculator Example*** ---- This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Aside from your courtesy, your wiki MONIKER and date as a signature and minimal good faith of any internet post are the rules of this TCL-WIKI. Its very hard to reply reasonably without some background of the correspondent on his WIKI bio page. Thanks, [gold] 12Dec2018 ---- <> ---- **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. %| translitered Sanskrit conversion, concept for sine table of Brahmagupta, 629 CE| | |% %|Arabic numerals|translitered Sanskrit, right to left| string reverse, mirror image,left to right|% &|2594 |dvi panca nava catur| rutac avan acnap ivd|& &|2719 |dvi sapta eka nava |avan ake atpas ivd |& &|2832| dvi asta tri dvi|ivd irt atsa ivd |& &|3270| tri dvi sapta sunya| aynus atpas ivd irt |& &|Note: Brahmagupta included poetic words, not listed here in this conceptual study.|& ---- ---- '''Comments Section''' Please place any comments here, Thanks. ---- ***References:*** * FromOne to Zero, the History of Numbers. George Ifrah * [http://weblogs.asp.net/ssadasivuni/archive/2004/04/02/106237.aspx%|%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 [http://www.wilbourhall.org/pdfs/BSS_VOL_I.pdf] * Mathematics and Mathematical Astronomy Website [http://www.wilbourhall.org/index.html#BSS] * Story of Indian Zero, [http://weblogs.asp.net/ssadasivuni/archive/2004/04/02/106237.aspx%|%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, ยท 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 *** <> ---- Please place any comments here with your wiki MONIKER and date, Thanks.[gold]12Dec2018 ---- <> Numerical Analysis | Toys | Calculator | Mathematics| Example| Toys and Games | Games | Application | GUI ---- <> Development | Concept| Algorithm | Human Language