Nowadays it is very obvious for us to write a large number , whether it is the distance of Earth from Sun in centimeters or the age of our universe, by simply setting enough number of zeros in the right side of some figure and most surprisingly by doing this we may easily write down the number which is greater than the total number of atoms of the universe that is identically 300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 or in a shorter notation 3x1074. But this method was not known to the people of the ancient time. In fact this it was invented less than two thousand years ago by some unknown Indian Mathematician. Now in the next few minutes, I am going to talk about how was the world of writing numbers before this great discovery.
Now let me tell you some facts about the 'Khoikhoi' (a group of Khoisan people native to southwestern Africa. The Dutch settlers called them Hottentots). They don't have in their vocabulary the names for numbers larger than three. They used to describe any number, larger than three, as "many". If you ask them how many fingers they have they will say 'many'. Coming back to the process of writing large numbers, ancient Egyptians used many different symbols to write a number as an example if you wish to write 8732 in their way you may write it as
whereas in Rome, it was accustomed to use alphabets to write numbers. 8732 can be written as
MMMMMMMMDCCXXXII , which is known to us as roman numbers and still have some use in some particular places. In the both above mentioned cases it is very tedious work to write a large number like one billion. Even if you wish to write one million in these way you will need to use more than two or three pages and more than few hours.
The great scientist Archimedes was the first person to show that actually it is possible to write big numbers and the method was quite similar to the way large numbers are written in modern science. He begins with the largest number that found in the ancient Greek arithmetic: 'a myriad' or ten thousands. Then he introduced 'a myriad myriad' that is ' an Octade' or a units of second class, which is equal to a hundred million then 'octade octades' or a unit of third class ( a ten million billion) etc. I know this is a little bit confusing but please keep patience.
To revive and make the discussion more interesting let me tell you one another story. we all know the game of chess and some of us also know that chess was invented in India by Sissa Ben Dahir. For inventing and presenting this game to King shirham of India, king asks Sissa Ben to claim something large as a gift. Clever Sissa Ben desire to have one wheat grain to put in the first box of the chessboard then 2 grains to put in the second box and 4 grains to put in the third one and 8 grains in the fourth box and so for the next each box. Listening to this the king was happy because he thought this gift would not cost him a lot.
Now let's calculate how much grains actually need to cover all the 64 boxes in the way mentioned by Sissa Ben. It will be a geometric progression (G.P) series like this: total no of grains = 1+2+4+8+16+32+64+..........................+(64th term )
= 1+21 +22+23+24+25+26+ ..................................+263 = 18446744073709551615 (approximately ) which is equal to the total wheat production of the world for more than one thousand years.
** In Archimedes's notation the calculation should be like this
In the above discussion, we have faced some really large numbers like the amount of wheat claimed by Sissa Ben. Still, you can deal with this numbers if enough time permits. But there exist some numbers which are really infinite. you can't write them no matter how long and how hard you work.
I'll talk about infinite numbers latter in my post.For this post I thoroughly followed One Two Three Infinity by Gamow George
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