The recent discussions about Techmeme’s introduction of a leaderboard (for example here, here, here) and ways to manipulate it in such a way that you’re on top (here an here) have triggered some thoughts.

It seems to me that most of the mathematics in these rankings is about “who has the biggest…”. This, of course, being an important measure for advertisement revenues and ego. but as an unwanted side effect, it also helps the blogging sphere to become a bounded sterile surrounding, like a vacuum. Once a few sites have become sufficiently big enough it will lead to 2 unwanted things:

- New blogs, no matter how hard they try will not succeed in becoming read by others, as their importance is diminished by the bigger ones. Robert Scoble wrote about that earlier in his post Techmeme lists heralds death of blogging
- Everyone links to the same sites, bringing the same “scoops” making the blogosphere more and more predictable and immune to new or creative thoughts (same blah blah right?)

So the question becomes, isn’t there a way to come up with a metric that will benefit every blogger, as well as preventing the blogosphere to become inert and boring?

A disclosure here is in order, *anything written below is done so without any serious knowledge or expertise in blog ranking, or mathematics for that matter.*

I have written earlier about the work of Jonathan Harris, who has done some amazing work on tracking the emotions of millions of people, and sorting the news that is relevant today in a very different way. Particularly his universe project has some interesting aspects that use a totally different paradigm from current web browsing to present information. He organises information as the stars in the sky, and allows you to make any news item be the center of the universe showing you the important things revolving around that item. See the picture below for an example.

So, what if we take this idea of stars and constellations and use the metrics involved there to determine the importance of blogs. And, what if we can determine the importance of blogs in relation to other blogs as well? In other words, can we calculate the attraction between for example my blog and TechCrunch? Well, the obvious solution to this problem is supplied by Sir Isaac Newton using his 3 laws of motion and his law of universal gravitation.

So bear with me, I am by no means a brilliant mathematician or Search expert.

Newtons Universal law of gravitation states that

“Every object in the Universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to their masses and inversely proportional to the square of the separation between the two objects”.

F_{g} = G (m_{1} m_{2}) /r^{2 }

F_{g }is the gravitational force, G is the universal gravitational constant, m_{1} and m_{2} are the masses of the bodies, and r is the separation between the two objects.

We need to define the mass and radius of a blog and the distance between two blogs in order to make this work.

So lets calculate the mass of a blog as the sum of all posts in the blog * the pagerank of each blogpost. If you write lots of posts with high pagerank, you have a lot of mass.

But what about the radius of your blog, in other words, is there a way to measure how far out your blog extends to the blogosphere? Keep in mind we are talking about attraction right?

The best kind of attraction to me is the one that is bidirectional. In other words if two blogs attract each other there is value created between them. If one blog is getting lots of attraction but not giving any it is narcistic! If a blog is linking the hell out of other blogs but never gets back any interest it is probably not very attractive to its readers.

Given all this we define the radius of a blog to be 1/ the number of shared links with other blogs or in a formula:

∑^{1-n} 1 / # shared links

where n stands for the number of blogs that link to a blog or the blog itself links to. Since I only look at blogs that link to me (or me to them) we won’t get a division by zero issue here (phew).

We also need to look at the separation between 2 blogs. In order to do that we need the center of mass between the two blogs. Lets assume that the separation between 2 blogs is the sum of the two radii of the two blogs divided by the number of their shared links. In plain words. Each blog extends itself into the blogosphere by its radius (number of shared links with other blogs). But the distance between 2 blogs is inversely related to the links they share together. If I don’t link to another blog then our distance is infinitely large. But the more we link to each other, the closer we get (attraction right!).

So the distance between two blogs then becomes:

(∑^{1-n} (1 / # shared links of blog 1) + ∑^{1-m} (1 / # shared links of blog 2)) / The number of links that blog 1 and 2 share

In case of no link share the distance is ∞

Still with me?

So now we have everything in place to calculate the attraction between my blog and any other blog. Newton’s law of universal gravitation then becomes the universal law of blog attraction:

Any blog in the blogosphere attracts every other blog with a force directed along the lines of centers fro the two blogs that is proportional to the product of their masses (number of posts * pagerank) and inversely proportional to the square of the distance (shared links) between them

F_{g} = G ((# posts blog 1 * pagerank each post blog 1) * (# posts blog 1 * pagerank each post blog 1)) /( (∑^{1-n} (1 / # shared links of blog 1) + ∑^{1-m} (1 / # shared links of blog 2)) / The number of links that blog 1 and 2 share)2

And, for the narcistic bloggers amongst us (aren’t we all a bit), the weight of my blog compared to another is calculated in this way. Using Newton’s second law of motion (f = m*a) we can also calculate the acceleration due to attraction at any blogs surface.

So, lets summarize what we have just written in complex math (well to me anyways :-))

The narcistic way of ranking (who has the biggest..) seems less valuable to me than being able to see which blogs attract me and I am attracted to. Newton’s universal law of gravitation, which calculates the attraction between two objects seems perfect to tweak into a blog attraction formula. The fun part about it is that in order to reach a high attraction value to my readers, I better link to them often and hope that they will do the same to me. this might turn into a 2 way spamming system to improve attraction, but I am inclined to believe that mutual attraction will be defined by true value. Or in other words, if I write valuable stuff in my blog and my readers enjoy reading it, it will lead to value creation between us as my readers start writing to me in their blogs.

Now, lets see if readers find this post interesting enough to become attracted to my blog. You know what to do. And if you like me, and I like you, well, who knows what will happen…

Anyone care to comment on the absurdity of it, or implement this :-)

There you have it: QED.

Written 7 days ago, far more interesting ideas than 10 x Scoble, diverse content etc bla bla, and what do you get? A stochastic german comment and a dysfunctional – not dis – system.

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