How High Can You Count? — Some Historical Tales of BIG Numbers!
Counting number is one of the fundamental skills that acts like the backbone of the modern world. It’s almost impossible to survive without number. It has such deep penetration into society that even Illitrates at least know how to count.
Engineers, Scientists, Economists, Doctors, Farmers, Vendors, Merchants, You name the profession and numbers are there. Even last surviving Tribes have their own way to count. It’s the most secular stuff that everyone knows irrespective of the governments, Religion, sect, gender!
But, do you know people have always been in a race to find the biggest number. You may be thinking today that it is such a bizarre question! Counting is neverending and is infinite! There no such thing as a big number!
But people didn’t have this wisdom centuries ago, and were always searching for the bigger numbers!
Here are such tales from the history
Two Hungarian aristocrats decided to play a game in which the winner will be the one who calls the largest number.
“Well,” said one of them, “you name your number first.”
After a few minutes of hard mental work the second aristocrat finally named the largest number he could think of.
“Three,” he said.
Now it was the turn of the first one to do the thuiking, but after a quarter of an hour he finally gave up.
“You’ve won,” he agreed.
Of course these two Hungarian aristocrats do not represent a very high degree of intelligence and this story is probably just a malicious slander, but such a conversation might actually have taken place if the two men had been, not Hungarians, but Hottentots which is an African tribe.
African explorers say that many Hottentot tribes do not have in their vocabulary the names for numbers larger than three. Ask a native down there how many sons he has or how many enemies he has slain, and if the number is more than three he will answer “many.”
Thus in the Hottentot country in the art of counting fierce warriors would be beaten by any child of kindergarten age who could boast the ability to count up to ten!
Nowadays we are quite accustomed to the idea that we can write as big a number as we please whether it is to represent war expenditures in cents, or stellar distances in inches by simply setting down a sufficient number of zeros on the right side of some figure. You can put in zeros until your hand gets tired, and before you know it you will have a number larger than even the total number of atoms in the universe, 2 which, incidentally, is
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.
3*10⁷⁴
But this “arithmetic-made-easy” system was not known in ancient times. In fact it was invented less than two thousand years ago by some unknown Indian mathematician.
Ancient Egyptians used to write numbers by using a special symbol for each of what we now call decimal units, and repeating this symbol as many times as there were units. For example the number 8732 was as:
If you were to write in roman numbers,
MMMMMMMMDCCXXXII
There were no symbols for higher decimal units because their needs did not exceed even more than few thousands. It would be embarrassing if told to write “One Million”.
You would write 1000 M’s! to represent 1 million! Hours of hard work!
For the ancients, very large numbers such as those of the stars in the sky, the fish in the sea, or grains of sand on the beach were “incalculable” just as for a Hottentot “five” is incalculable, and becomes simply “many”!
It took the great brain of Archimedes, to show that it is possible to write really big numbers. In his treatise The Psammites, or Sand Reckoner, Archimedes says:
“There are some who think that the number of sand grains is infinite in multitude; all the grains of sand which may be found in all the regions of the Earth, whether inhabited or uninhabited.
Again there are some who, without regarding the number as infinite, believe that no number can be named which is great enough to exceed that which would designate the number of the grains of sand on Earth.
But I will try to show that there are bigger numbers, some exceed not only the number of grains of sand which would make a mass equal in size to the Earth, but even equal to a mass the size of the Universe!.”
Archimedes proposed a way to write very large numbers which is very similar in modern science.
He began with the largest number that existed in ancient Greek arithmetic: a “myriad” or ten thousand.
Then he introduced a new number, “a myriad myriad” (a hundred million), which he called “an octade” or a “unit of the second class.” “Octade octades” (or ten million billions) is called a “unit of the third class,” “octade, octade, octades” a “unit of the fourth class” etc.
To calculate the number representing the grains of sand necessary to fill up the entire universe, Archimedes had to know how big the universe was.
In his time it was believed that the universe was enclosed by a crystal sphere to which the fixed stars were attached, and a famous astronomer, estimated the distance from the earth to the periphery of that celestial sphere about 1,000,000,000 miles.
Comparing the size of that sphere with the size of a grain of sand, Archimedes completed a series of calculations that would give a highschool boy nightmares, and finally arrived at this conclusion:
“It is evident that the number of grains of sand that could be contained in a space as large as that bounded by the stellar sphere as estimated by Aristarchus, is not greater than one thousand myriads of units of the eighth class.”
Archimedes’ estimate of the radius of the universe was rather less than that of modern scientists. The distance of one billion miles reaches only slightly beyond the planet Saturn of our solar system.
The universe has now been explored with telescopes to the distance of 5,000,000,000,000,000,000,000 miles( 5.4×10²³ miles), so that the number of sand grains necessary to fill up all the visible universe would be over: 10¹⁰⁰ (that is, 1 and 100 zeros)!
I also have another interesting story but this article already got pretty Big!
So I will continue it in my next post!
If you read this story, you will surely like the next one! It has got some great morals and learnings also!
I am quite new on medium, and there are no “Bell Icons” here like youtube so that you will get my notification! So If you are aware what to do here, DO that! So that you don’t miss the next story!
Thank you!
