The Largest Numbers in the World

Date: 11/21/2005 at 17:02:39
From: Rose
Subject: The largest number in the world.

When I was in 8th grade my math teacher said duodecillion was the 
largest number of anything in the world that is measurable.  Can you 
tell me what that "thing" is that measures a duodecillion?  What's the
biggest number we know of or use?  Thank you.  

Date: 11/22/2005 at 11:34:52
From: Doctor Minter
Subject: Re: The largest number in the world.

Hello Rose!

The number duodecillion represents 10^39.  I must concede that this 
number is large beyond imagination.  

I believe that the current estimate for the number of electrons in the
known universe is 10^88 (a.k.a. ten-thousand quattuordecillion), which
considerably outshadows the relatively miniscule duodecillion.  You
could square duodecillion, and not be at 10^88.  

10^88 is the largest number that measures something "tangible," as in
"represents a physical value," that I have come across in my studies
as a physicist.

To fully answer your question, we must try to define the word
"measurable."  If by measureable, we mean "able to make a direct 
measurement," then measureable values are considerably small.

Obviously, no one went out one fine summer day and counted all of the 
electrons in the universe.  This value was deduced by using the 
knowledge of the properties of the elements and compounds that exist 
in our universe, and their abundance.  This definition of measureable 
would be "able to estimate using known facts."  This opens up a larger
window to use numbers that apply to large values that are indirectly
measureable.

In the strange realm of quantum mechanics, physicists deal with 
probabilities (not observations or measurements) that certain events 
occur.  The largest (calculated) number that I have ever seen in this 
field is 10^(10^30), which deals with the probability (or should I say
"improbability" in this case) of something called "quantum tunneling"
on the macroscopic level.  An example of quantum tunneling is that you
could technically walk through a wall if all of the empty space in
your molecular structure were temporarily lined up with all of the
empty space in the wall's molecular structure, but this is an
exceedingly improbable event.

Let me make an attempt to describe 10^(10^30).  If a person wanted to 
write out this number without using scientific notation, and this 
person wrote at a rate of one digit per second, it would take that 
person about 3 x 10^22 (that's thirty billion trillion years) just to 
WRITE the number, and the piece of paper used would not fit in our 
entire known universe.  This number is written as a one, followed by 
10^30, or one million trillion trillion, zeroes.  Wow.

Now think of how large one trillion is (one trillion dollar bills 
stacked up would be twice as high as Mount Everest, Earth's highest 
point, and one trillion dollar bills laid end-to-end at the equator 
would circle the planet nearly 3,000 times), and how EASY it is to 
write: 1,000,000,000,000.  This should suggest that the task of 
WRITING the number is a very feeble indication as to it's size.  Apply
this concept to the number 10^(10^30), and the idea is truly 
mind-boggling.

All in all, don't expect to walk through a wall anytime soon!

The largest named number that uses the "-illion" suffix that I am 
aware of is simply called "centillion."  In the American System, it 
is 10^303.  I have also seen it written as 10^600, but I'm not sure 
what "system" that uses.  Perhaps the SI (Standard International) 
system, but that is a guess, not a fact.

For the grand finale, the number googol-plex is THE largest-valued, 
named number that your loving Math Doctor has come across in his 27 
years on this planet.  I believe that some people have heard of this 
number, but cannot begin to comprehend its magnitude.  It is written 
as 10^(10^100).  A googol is 10^100, which is very large.  A googol-
plex is a one followed by a googol of zeroes, which is unimaginably, 
ridiculously, incomprehensibly huge.  I'm getting light-headed just 
thinking about it.

I hope that this has been interesting, if nothing else.  Please feel 
free to write again if you need further assistance, or if you have 
any other questions.  Thanks for using Dr. Math!

- Doctor Minter, The Math Forum
  http://mathforum.org/dr.math/