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 10^{100}/(3 x 10^{9}) = **3.33333333 × 10 ^{90.}**

Now **3.33333333 × 10 ^{90 }**divided by 365 days/year yields

**9.13242009 × 10**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

^{87 }**6.52315721 × 10**times the age of the UNIVERSE to reach a Googol. For lack a better term, this number is HUGE!

^{77 }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.

(2^{d}) x (3 x 10^{9}) = 10^{100}, (where d = # of days)

(2^{d}) = 3.3333333 x 10^{90}

Log_{2} (2^{d}) = Log_{2} (3.3333333 x 10^{90})

d x (Log_{2} (2)) = Log_{2} (3.3333333 x 10^{90})

d (1) = Log_{2} (3.3333333 x 10^{90}) = **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.

(1.01^{d}) x (3 x 10^{9}) = 10^{100}, (where d = # of days)

(1.01^{d}) = 3.3333333 x 10^{90}

Log_{1.01} (1.01^{d}) = Log_{1.01} (3.3333333 x 10^{90})

d x (Log_{1.01} (1.01) = Lg1 (3.3333333 x 10^{90})

d (1) = Log_{1.01} (3.3333333 x 10^{90}) = **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.

Maybe we’ll hit a googol shortly after we’ve achieved the singularity (http://www.time.com/time/health/article/0,8599,2048138,00.html)?

There aren’t even a googol atoms in the universe, so I don’t think we will ever make it. Check out some atom math: http://www.madsci.org/posts/archives/oct98/905633072.As.r.html

These calculations ignore all the past Google searches that have ever been done. ie they assume you start counting the searches from TODAY. So the first step is to ask “how many searches has Google done so far?” and deduct that number from a googol. But it will still get you pretty close to 57 years. I love Google and I love googol.