Hello!

You have asked a very interesting question. What is the highest known numerical value? Do you mean "What is the biggest number?" I could try to write it out for you, but there would be a problem: you could just write "+ 1" at the end of whatever I had written, and the number would be bigger.

You might also be interested to know the largest number with an english name. We call 10¹⁰⁰, or ten multiplied by itself 100 times, or a 1 with 100 zeroes behind it, a googol, which is where the internet search company Google borrowed its name from. We can also write 10^googol, or 1 with a googol zeroes behind it. This is called a googolplex, and to my knowledge it is the largest number with an english name. Of course, a googleplex can't be the largest numerical value, since i could just say "+ 1" after it, or say "a googol googolplexes" or something like that... it has the same problem discussed above.

Maybe you're more scientifically oriented, and want to know the highest numerical value of some thing. It is estimated that the human body contains around 100 trillion (100,000,000,000,000) cells. Still greater, the Avogadro number, the number of carbon-12 atoms in 12 grams of unbound carbon-12 in its ground state, is about 6.02*10²³ (602,000,000,000,000,000,000,000). The number of atoms in the known universe is estimated to be on the order of 10⁸⁰. So already we can see that naming big numbers is getting to be somewhat ridiculous, since there aren't even a googol atoms in the entire universe!

Scott Aaronson, a computer scientist, has written an informative and entertaining article about just this problem. It's fairly long, but it really covers quite a bit of the historical discussion concerning the "biggest number". You can find it by clicking here:

http://www.scottaaronson.com/writings/bignumbers.html

I hope you found this to be informative.

Gabe