Comprehending Large Numbers

When I was in 6th grade, I wrote out the number Googol ('1' followed by 100 zeroes). I cut and taped strips of paper together to be able to display it in a single long string. It was impressive at that time.

I found another impressive number today reading through John Morris's ZDNet blog overview of the 2011 Intel Annual Investor's Meeting. The focus of the blog was mostly on the announcements made about Intel's roadmap and plans to cover the mobile computing market. About halfway down the page, there is a graph and summary of the output from Intel fabs since 2000. The metric is number of transistors shipped. For 2010, Intel shipped 74.5 quintillion (fourteen zeroes). As the graphic notes, this is about 10 billion (with a 'b') transistors for each person on Earth.

To get a scale for this numberone could make the comparison of stacking 74.5 quintillion dollar bills. The U.S. debt at the time of this writing would only be 0.01879% of that amount of cash. So that may not be quite a comprehensible comparison. (But for completists out there, it would be over 5.056 million miles high, or fill a cube with edges 234.32 miles long.)

I was just given some stats on DNA the other day. I was told that a human genome has 3 billion base pairs. If each transistor held a single base pair of DNA, this would be equivalaent to being able to map over 24800 people. notes that a single human genome map would take 200 Manhattan phone books (1000 pages each) to hold it. To hold maps totalling 74.5 quintillion base pairs would take almost 5 million thousand-page phone books.

6x6 go positionFor chess and go enthusiasts, you know that the number of transistors shipped is nowhere near the total number of legal chess or go positions. However, extrapolating from the table of Legal Positions, if we could encode a board position onto a transistor, we might be able to enumerate the legal positions of a 6x6 go board with 74.5 quintillion transistors. (I think this goes more to illustrate the complexity of the simple game of go than a big number of transistors.)

One of the other points in Morris's blog was the scaling of Atom processors from 32nm to 22nm to 14 nm in the next three years. This means more transistors on the same die sizes and an increase of the total number of transistors shipped. We're going to need more comprehensible comparison models to grasp the large production numbers of transistors that lie ahead. Do you have a favorite analogy for large numbers?

What's my point? I really don't have one. I just like to boggle my mind with big numbers every once in a while. (BTW, there are only 125.5 trillion ways that Boggle dice could be configured [6 x 16!].)

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