In this article I'm going to discuss the number a googol and a googolplex. Firstly what are they? Well a googol is 10

^{100}, that is a one followed by one hundred zeros, or the less catchy title, ten duotrigintillion. Just how big is that then? Well, there is estimated to be about 1.33×10

^{50}atoms in the entire Earth. A googol is almost 10

^{50}as much as this number. Nothing like maths to make you feel tiny and insignificant.

If you think that's large, your head may just explode when you're introduce to a googolplex. A googolplex is 10

^{googol}, that is enormous. A one followed by a googol zeros. That is so large it is almost impossible to comprehend. I'll try my best to explain just how mammothly big this number is.

Astronomer Carl Sagan estimated that writing a googolplex would be impossible, why? It would require more space than the known universe can provide. Seriously. There is only about 2.5×10

^{89}elementary particles in the known universe, so even if every particle was a digit, it would still need the observable universe to be about one hundred billion times larger.

But, if you could fit the number into the known universe it would take an unbelievable amount of time to write. If you could write 120 digits a minute, it would take around 1.51×10

^{92}years to finish (almost a googolplex years!). This amount of time is 10

^{82}times the age of the universe. So, I wouldn't really start trying to write it out. There's a high chance, that even if it was possible to write for that period of time, that the entire universe will have inevitably died.

A more nerdy way to try and explain the size of a googolplex is to look at Planck time. Planck time (which I won't go into too much detail now), is the time it takes for light to travel one Planck length in a vaccuum, which is roughly 5.4×10

^{-44}, this is unbelievably quick. A googol is larger than the estimated amount of Planck times that have past since the start of the universe (8×10

^{60}), so a googolplex is much, much larger than even the smallest measurement of time that has past since the dawn of everything.

There is however a larger number that still has a use, it is known as Graham's number. But that's a different article for a different time. I hope this post has given you a small idea into the enormity Maths can hold.

Now I really want to know about Graham's number.. maybe I'll just Googol it :)

ReplyDeleteQuote: "Well, there is estimated to be about 1.33×10^50 atoms in the entire Earth. A googol is almost twice as much as this number."

ReplyDelete"Well a googol is 10^100[...]"

You are saying that 10^100 < 2*1.33*10^50

I am nothing close to a mathematician, but that sounds pretty weird to me... Or is it maybe the english you are using that I don't understand?

But for me it is still, 10^100 >> 2*1.33*10^50

I made a grave, grave mistake here. My apologies. It is in fact 10^50 times less, this was a very early post from me so I do apologise.

DeleteI made a grave, grave mistake here. My apologies. It is in fact 10^50 times less, this was a very early post from me so I do apologise.

ReplyDeleteFor those interested, here is an explanation of what Graham's number is and why it matters: https://www.youtube.com/watch?v=XTeJ64KD5cg&feature=plcp

ReplyDelete