- July 24, 2007
- 4 comments
Humans are linear thinkers. We have trouble grasping exponential growth, as Ray Kurzweil eloquently points out.
Google PageRank is such an exponential function. It is log-transformed to make the numbers small and friendly, just like the Richter scale. In both PageRank and earthquakes, a 7 is much larger than a 6. An 8 is much much larger than a 7. And a 9… well, you get the idea. Because PR scores are log scaled, because they’re small and easily grasped, because they fit on the fingers on two hands, it is too easy to lose the sense of their exponentiality.
Search Engine Land started a new column in May called Search Illustrated, which presents concepts in search marketing graphically. The May 8th post, Search Illustrated: Google PageRank Explained, offers this cool representation of PageRank as a mighty mountain.
Note the big red blowup section. On the full mountain, this red zone occupies just the smallest bottom smidge on the bottom left of the full mountain.
PR 0 through 7, represented in the blowup section, only takes you up to tree line. 8 is just above treeline. 9 is alpine, but still far below the snow line. And the elusive 10 is the summit — supplemental oxygen clearly needed.
While the mountain is an inexact visual metaphor, it does give a strong sense of the non-linear nature of PageRank.
Cool graph, SEL!
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That is a pretty sweet picture. I always thought page rank was exponential but I didn’t think there was that much difference. Thanks for pointing that out to me.
What should be noted is that the amount of low-PR pages is probably a lot larger than this image would suggest.
Excellent point, Johann. It is so hard to display exponential trends in a comprehensible way. If the mountain was really to scale, it would be so wide at the base it would look like a huge flat pancake with a really thin tall sharp needle coming up from the middle, or something like that. And if you take logs, the data fit nicely, but our brains are inherently linear in their perspective, and most people can’t get a true sense of scale after data have been logged. Elliance’s graph is more a metaphor than an accurate presentation, but even as metaphor, I think the image is quite cool and a good teaching tool. Thanks for the comment!
I love that image. Shows you pretty much how much work you have to do to “scale the mountain”