Oct 20, 2012

Ritual Mathematics




By Marsigit

In Javanese society all aspect of daily life or activities can be viewed as underpine from religious perspectives. It is not surprising that, for example, in a certain village, the people in one week get invitation to come to ritual activities for more than seven.


Some of the important activities are the celebration of the 'fifth' and the 'thirty fifth' baby birthday, the ritual feast to mark some one's death in the 'seventh day', 'forthyth day', 'a hundreth day' and 'a thousanth day'. The problem is the people, specifically the man who are responsible of carrying out the ritual meal, should exactly decide that the death has long been whether seven days, forthy days, one hundreth days, or one thousand days. They do it well and they learn it for generations. The people, who are concerned about it, sometimes involves in the dialog informally to justify whether the counting the numbers of tha days is right or wrong. Most of them are relatively correct. They just use simple formula which is ussualy spoken and not ever written, e.g. 'nomosarmo', 'norosarmo', nonemsarmo', etc.

They use three kinds of numbers system at the same time : 10 based numbers system, 7 based numbers system and 5 based numbers system, in the frame work of position system. Position system for numbers was found by Indian and Javanese people knew it before the Europen because it directly was brought by Indian to Indonesia. They use Numbers System Basis 10 when they should decide the duration of time; 35 days, 40 days, 100 days and 1000 days. They use Numbers System Basis 7 (Week system) when they use the name orderly of the days : Sunday, Monday, Tuesday, Wednesday, Thuersday, Friday and Saturday.

They use Numbers System Basis 5 (Dino Pasaran system) when Javanese people have been using system 'Dino Pasaran' for along time before Western system of callendar came to Indonesia. In this system there are only five days orderly in a cycle of period of time called 'Pasar'. Those are 'Legi', 'Pahing', 'Pon', 'Wage', 'Kliwon'. One day in this system is equals to one day in Week system, that is 24 hours.

Thus one Dino Pasaran has five days, two Dino Pasaran has 10 days, three Dino Pasaran has 15 days, etc.
Mathematically, for all of the system numbers, the notation of numbers 'm' can be written as polynomial from 'b' such as follows : m = a0 bn-1 + a1 bn-2 + a2 bn-3 + ... + an-1 b + an where, b is any numbers greater than 1, and a is the basis. According to this formula, we can write any number at any system using the same pattern i.e. for basis 10, basis 7 and basis 5. In Basis 10 we have the numbers : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. In Basis 7 we have the numbers : 0, 1, 2, 3, 4, 5, 6

We can match the name of the day with those numbers orderly : 0 = Sunday 1 = Monday; 2 = Tuesday; 3 = Wednesday; 4 = Thuersday; 5 = Friday and 6 = Saturday. In Basis 5 we have the numbers : 0, 1, 2, 3, 4. We can match the name of the day in Dino Pasaran with those numbers orderly : 0 = Legi, 1 = Pahing, 2 = Pon, 3 = Wage, 4 = Kliwon. How can we write 35 of Basis 10 into Basis 7 ? The following is the formula 3510 = 5 x 71 + 0 x 70 = 507. How can we write 100 of Basis 10 into Basis 7 ? The formula is 10010 = 2 x 72 + 0 x 71 + 2 x 70 = 2027. How can we write 1000 of Basis 10 into Basis 7 ? The formula is 100010 = 2 x 73 + 6 x 72 + 2 x 71 + 6 x 70 = 26267

How can we write 35 of Basis 10 into Basis 5? The following is the formula 3510 = 7 x 51 + 0 x 50 = 705. How can we write 100 of Basis 10 into Basis 5? Thai is 10010 = 4 x 52 + 0 x 51 + 0 x 50 = 4005 How can we write 1000 of Basis 10 into Basis 5 ? That is 100010 = 1 x 54 + 3 x 53 + 0 x 52 + 0 x 51 + 0 x 50 = 130005

Javanese people always have two unseparated name for the day. For example : Sunda Legi, Sunday Kliwon, Monday Wage, Friday Pahing, Saturday Kliwon, Saturday Pon, etc. It is clear that the numbers of combinations is 35 names. If this day is Monday Pahing then the duration up to on the next Monday Pahing is 7 x 5 = 35 days. Thus when somebody wish to celebrate the 35 th of his son's birthday he just waiting for the next day with the same name. It is easy and he need not to do with mathematics at all in his mind. Forthyth days ritual feast to mark some one's death by transforming 4010 = 557 and 4010 = 805. Numbers 55 is ended by 5; it mean that 'the fourty days duration of time' will begin on the day i and ended on the day 5 th of Week System.

Thus, if now is Sunday then forty days to come will be the fifth day from Sunday that is Thuersday. Javanese people called 'five' as 'limo' or briefly 'mo'. Number 80 is ended by 0; it mean that 'the fourty days duration of time' will begin on the day of Pasar j and ended on the day j + 0 or ended on the same day. Thus If this day is Sunday Kliwon then it will be 40 days on the next Thuersday Kliwon.

If this day is Friday Legi then it will be 40 days on the next Tuesday Legi. If this day is Wednesday Pahing then it will be 40 day on the next Sunday Pahing, etc. Javanese people just called 'no mo; sar mo' that mean : no = dino = day; mo = limo = five; and sar = Pasar = Basis 5. Thus, no mo means 'the fifth day of Week System' sar mo means 'the fifth day of Pasar System'

For one hundred days ritual feast to mark some one's death as I described that :10010 = 2027 and 10010 = 4005. Number 202 is ended by 2; its mean that 'the one hundred days duration of time' will begin on the day i and ended on the day 2 th of Week System . Thus, if now is Sunday then forty days to come will be the 2 nd day from Sunday that is Monday. Javanese people called 'two' as 'loro' or briefly 'ro'. Number 400 is ended by 0; it mean that 'the fourty days duration of time' will begin on the day of Pasar j and ended on the day j + 0 or ended on the same day.

Thus If this day is Sunday Kliwon then the next 100 days will be on the next Monday Kliwon. If this day is Friday Legi then the next 100 days will be on Saturday Legi. If this day is Wednesday Pahing then the next 100 day will be on Sunday Pahing, etc. Javanese people just called 'no ro; sar mo' that mean : no = dino = day; ro = loro = dua; and sar = Pasar = Basis 5. Thus, no ro means 'the second day of Week System' sar mo means 'the fifth day of Pasar System'. One thousand days ritual feast to mark some one's death is calculated by the same way they use the formula 'no nem; sar mo' that mean 'the sixth day of Week System and the fifth day of Pasar System'

5 comments:

  1. Menarik bahwa pembahasan matematika ternyata bisa disangkutkan dengan adat lokal Jawa termasuk dalam peringatan kelahiran bayi dan juga peringatan kematian. Perhitungan matematis nampak jelas dalam penentuan hari peringatan itu sendiri. Selain itu, perhitungan primbon juga sifatnya matematis sehingga penamaan “ritual mathematics” memang sangat pas dan sesuai pula.

    Dwi Margo Yuwono
    S3 PEP A

    ReplyDelete
  2. Rospala Hanisah Yukti Sari
    16790251016
    S2 Pendidikan Matematika Kelas A Tahun 2016

    Assalamu’alaikum warohmatullahi wabarokatuh.

    Dengan elegi ini, maka kita bisa mematahkan pendapat yang mengatakan bahwa penerapan matematika itu jauh dari kehidupan. Penggunaan matematika dalam peringatan hari kematian, memperingati kelahiran bayi, penanggalan jawa, dll. tentu hal ini menarik jika disampaikan kepada siswa dan menumbuhkan keingintahuan siswa lebih lanjut terhadap matematika.

    Wassalamu’alaikum warohmatullahi wabarokatuh.

    ReplyDelete
  3. Andina Nurul Wahidah
    16701251019
    PEP-S2 Kelas B

    Memahami makna matematika secara dangkal, dapat ebrarti “perhitungan” atau ilmu hitung-menghitung. Yang dapat saya pahami dari artikel di atas, adalah bahwa ilmu matematika yang diterapkan dalam kehidupan sehari-hari. Perhitungan minggu, menggunakan “7” hari. Perhitungan hari menggunakan “24” jam, dsb. Begitulah perhitungan yang kita gunakan sehari-hari.
    Namun, makna matematika itu sendiri adalah sesuatu yang amat luas maknanya apabila kita memahaminya.

    ReplyDelete
  4. martin/RWANDA
    PPS2016PEP B
    Ritual is a science of precision. Like any proper performance or game, ritual choreographs action to the beat and bounds of time, and it manipulates symbols with rigorous rules of accounting. The calendar, the timepiece, the tokens, the altars, the counts—to mathematics and the astral sciences are owed the rigor of ritual, one might say, and to ritual, one of the very meanings of these sciences.

    ReplyDelete
  5. martin/RWANDA
    PPS2016PEP B
    Ritual is a science of precision. Like any proper performance or game, ritual choreographs action to the beat and bounds of time, and it manipulates symbols with rigorous rules of accounting. The calendar, the timepiece, the tokens, the altars, the counts—to mathematics and the astral sciences are owed the rigor of ritual, one might say, and to ritual, one of the very meanings of these sciences.

    ReplyDelete


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