Figuring out the largest numbers ever used

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

08 April 2007

In 1910, Lord Ernest Rutherford instructed his students, Ernest Marsden, to bombard a very thin sheet of gold (a fraction of a millimetre in thickness) with positively charged particles from a radioactive source. The idea was to find out how they would be deflected by the film.

Marsden found that most of the particle passed through the gold film un-affected but a very small fraction – about one out of every 8,000 – was reflected backwards. That seemingly tiny number puzzled Rutherford – to him it appeared too large!

He therefore embarked on a theoretical investigation to find out the actual fraction expected to be reflected backwards based on the prevailing atomic model of the time. The result of his analysis was that the probability of a particle bouncing back from the gold film was about one in the 10 to the power of 3,5000!

By any standards, a number with 3,500 zeroes is a very large. It is the numeral one followed by 3,500 zeroes! That makes the fraction extremely small. It is no wonder that Rutherford considered the one in 8,000 particles is to be too many. This is, in fact, the experimental result that led Rutherford to think up a new atomic model based the motion of planets around the sun…and it is till taught in school today, but that’s another story.

For me, one followed by 3,500 zeroes is the largest number that I have ever encountered in real mathematical application. But that doesn’t make it the largest number I have ever seen. The calculator in Microsoft Windows computer programme can write numbers with about 100,000 zeroes – I bet you didn’t know that!

Now last week, I invited readers to tell me the largest number they can imagine. Surprisingly, many people restricted themselves to money and therefore they came up with relatively small values, like “billion-billion shillings”. That has only 18 zeroes.

However winner must be John Chege’s “billion-billion raised to the power of a billion-billion”. That works to be the number with 18 billion-billion zeroes. Chege says, “It is not necessary to think of figure bigger than this because I believe it can take care of all the atoms in the universe”

That is correct are correct; there are actually “only” ten raised to the power 80 atoms in the whole universe. That is much smaller than Chege’s number. However, some mathematical proofs can yield numbers that are greater than any countable objects – for example, Rutherford’s one followed by 3,500 zeroes.

A while ago, the largest named number used to be the googol, that is, one followed by 100 zeroes. This is actually where www.google.com adopted its name from. But then some geek came up with a “googolplex” which a googol zeroes. Now, is this greater than Chege’s number? I leave you to find out.