Friday, August 6, 2010
soap bubbles and humongous numbers - फेनिल-बुद्बुद
फेनिल = soap. That which foams.
बुद्बुद = bubble. This is an onomatopoeia word, based on the sound bubbles make.
The बुद्बुद is used as a metaphor for this world.
The scales that Indians have thought (and used) in numbers and time, is staggering. rAmAyaNa (रामायण) has mention of numbers upto 10^60 [yuddha kANDa, 28:33-38], that is 1 followed by 60 zeros, which is 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 to be precise. This was in connection with the size of rAma's army. Of course the number is not exact and surely an exaggeration, but the main point is that vAlmIki (वाल्मीकि) explains the NAMES of the place values in the number system upto 10^60.
100 = 1 shatam (शतं)
100,000 shatam = 10^7 = 1 koTi (कोटि)
100,000 koTi = 10^12 = 1 nIla (नील) or sha~Nku (शंकु) or sha~Nkha (शंख)
100,000 sha~Nku = 10^17 = 1 mahA-sha~Nku (महा-शंकु)
100,000 mahA-sha~Nku = 10^22 = 1 vRinda (वृन्द)
100,000 vRinda = 10^27 = 1 mahA-vRinda (महा-वृन्द)
100,000 mahA-vRinda = 10^32 = 1 padma (पद्म)
100,000 padma = 10^37 = 1 mahA-padma (महा-पद्म)
100,000 mahA-padma = 10^42 = 1 kharva (खर्व)
100,000 kharva = 10^47 = 1 mahA-kharva (महा-खर्व)
1000 mahA-kharva = 10^50 = 1 samudra (समुद्र) (yes, multiplied by 1000 and not 100,000)
100,000 samudra = 10^55 = 1 ogha (ओघ)
100,000 ogha = 10^60 = 1 mahaugha (महौघ, महा-ओघ)
How do you do that with Roman numerals?
Thinking upon this, makes you wonder that without this simple concept of place value and zero, not much science would have progressed. No calculus for sure, and no going to the moon. How do you do logarithms in Roman again? There is not enough praise for this simple but far reaching counting system.
The same was true for time scale. From a fraction of a second (nimiSha निमिष) all the way to mahAyuga (महायुग) (4,320,000 years), the scale went full range [bhAgavat-purANa].
The age of creation itself is mentioned indirectly. The Tower of Hanoi problem is originally an Indian problem. It has 64 disks of varying sizes, that need to be moved from one peg to another following certain rules. It is said that a priest sits in the temple of brahmA (ब्रह्मा), making the moves without error, and when he is done, the creation will restart. So much for 2012! Mathematically it will take 2^64 moves. If one correct move is made every second, even then the time taken comes to 585 billion years. Now that is an order of time not thought of anywhere else! Trademark Indian thought.
Except modern astronomy, which feels not only comfortable with such large numbers but would not exist in lack of them! That is why a light-year is not a measure of time, but of distance, the distance light would travel in a year (6 trillion miles, 10^16 meters). And then there is the radius of the observable universe at 46.5 x 10^9 light years = 46.5 x 10^22 kilometers = 465,000,000,000,000,000,000,000 kilometers!
To just go crazy thinking more such 'fictional' numbers, :) :) which make no sense to anyone but astronomers and those who believe in them, check out Light Year. And then, when you are all excited, read some of the purANas, they will appear more believable, even if unfathomable! LOL!
Seeing all this, our human life is what - a bubble on the surface of a fast flowing stream? That won't even be noticeable cosmically. Now, this doesn't mean one needs to go in depression :) but just that 'This too shall pass' - so have neither gloom nor pride.
In Hindi there is a beautiful couplet that goes:
pAnI kerA budabudA, asa mAnasa kI jAta |
dekhata hI chhipa jAyegA, jyo tArA parabhAta ||
(पानी केरा बुदबुदा, अस मानस की जात | देखत ही छिप जाएगा ज्यो तारा परभात ||)
i.e. water produced bubble, such is human birth. it will set in no time, like a morning star.
Enjoy before the bubble bursts!
[There is a lot more to write on this theme, but for sake of brevity, I will stop here, maybe some other time.]
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