tagged: , , ,

## Will Google Reach a Googol Searches?!?!?

Posted by in Best Of, Just For Fun, Musings

For those of you who don’t know, the name Google was originally derived from the number Googol.  Originally coined in 1938 by a 9 year old, the number is 10^100, or 1 followed by 100 zeros.  In order to visual how LARGE of a number this is, here it is in print.

10, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000

So obviously this number is astronomically huge, but it got me to thinking.  Since Google has so many search queries everyday, how long until Google reaches a Googol searches?  Let’s do some math to determine the answer.

The Math

First, we need to determine the current rate of searches.  I’ve seen rough estimates ranging from 200 million to 3 billion queries per day.  I’ll choose 3 billion/day.  That in itself is a massive number, and so I thought we will reach a Googol in no time. (I’ll also assume the rate will be constant throughout the life of Google.)

Back to the math, take 10100/(3 x 109) =  3.33333333 × 1090.

Now 3.33333333 × 1090 divided by 365 days/year yields 9.13242009 × 1087 years!!!  Essentially we are NEVER going to reach a Googol.  To put it in perspective, our universe is 14 billion years old, that means we would have to go 6.52315721 × 1077 times the age of the UNIVERSE to reach a Googol.  For lack a better term, this number is HUGE!

So in short, WE WILL NOT REACH A GOOGOL.  (I imagine humanity, and the sun and the earth, will have died off LONG before then.)

More Complicated Math

Now I explicitly stated I made an overly simplistic assumption about the rate of searches per day.  I’ll change the math slightly now and assume that the number of Google searches will continue to grow everyday.  For mathematical ease, let’s say they will DOUBLE every single day.  (Reminds me of the elementary school exercise about doubling pennies everyday for a month!) I understand it is impossible to sustain such numbers indefinitely, but it will provide an interesting exercise nonetheless. Back to the math.

(2d) x (3 x 109) = 10100,  (where d = # of days)

(2d) = 3.3333333 x 1090

Log2 (2d) = Log2 (3.3333333 x 1090)

d x (Log2 (2)) = Log2 (3.3333333 x 1090)

d (1) = Log2 (3.3333333 x 1090) = 300.7 days ~ 301 days

So in just under a year, we will reach a Googol.  But let’s be honest, that rate of growth is unrealistic.

Even More Complicated yet SLIGHTLY More Realistic Math

Now let’s say search growth increases by 1% everyday, how long until we reach a Google.

(1.01d) x (3 x 109) = 10100,  (where d = # of days)

(1.01d) = 3.3333333 x 1090

Log1.01 (1.01d) = Log1.01 (3.3333333 x 1090)

d x (Log1.01 (1.01) = Lg1 (3.3333333 x 1090)

d (1) = Log1.01 (3.3333333 x 1090) = 20,948 days = 57 YEARS

That means by 2058, we will have finally reached a Googol!!!

Conclusion

In summary, it is gonna take a LONG time to reach a Googol, and it really depends on rate of acceleration of the Google searches.  I hope you enjoyed my little nerd-out session.  I urge you to go Google as much as possible, so that MAYBE, in our lifetime, we can celebrate Google’s Googol Day together.