Saturday, March 17, 2007

2am Accepts Thinking Blogger Award and Passes on Others

Updated on 3/17/2007 at 11:19 p.m. to include a complete trace of the meme to my site.

Updated again on 3/18/2007 at 12:35 p.m. to make some corrections to the meme propagation calculation.

Earlier this week, I received word from the author of the Have the T-Shirt blog that she had bestowed upon me a Thinking Blogger Award.

A recipient may present this meme-based award to five other bloggers whose postings have made the recipient think.

I would like to thank the author of Have the T-Shirt for including me in her list. I derive a sense of fulfillment in knowing that the content of this space has managed to challenge or inspire others as they deal with the big questions of their own lives.

I also would like to thank the bloggers onto whom I will pass this award, for I don't believe I would have been able to dig as deeply into my own issues without having read their postings or comments that they left in this space.

Finally, I would like to thank the readers who don't have blogs but leave challenging and insightful comments here. You keep this from degenerating into a circus of self pity and renew in me the resolve to persevere.

And now the envelope please...

2amsomewhere's Thinking Blogger Award Choices

Getting an honorable mention is Fear the Wrath of the Drunken Housewife. I chose not to give the Drunken Housewife an actual award because she is not that fond of chained communication, and I consider myself quite fortunate in getting her to participate (without propagation) with the last one that I tagged her.

Feel free to visit these quality blogs.

Mandatory Meme Participation Language

Should you choose to participate in this meme, please make sure you pass this list of rules to the blogs you are tagging.

  1. If, and only if, you get tagged, write a post with links to five blogs that make you think.

  2. Link to this post so that people can easily find the exact origin of the meme.

  3. Optional: Proudly display the Thinking Blogger Award with a link to the post that you wrote (available in silver or gold version).

A Little Bit of Meme Mathematics

High school level math text books that deal with logarithms usually feature a word problem on the propagation of chain letters. Blog memes function the same way. If the person starting the meme gives the award to five recipients, and each recipient complies, and the process keeps repeating, the number of awards for each round will increase exponentially (5^i, where i = the number of rounds of awards).

A question one might ask is: Assuming that every recipient participates and succeeds in getting five additional recipients to participate in kind, how many iterations would it take for the entire blogosphere to have such an award? To answer the question, we need an estimate on the size of the blogosphere and a formula for computing exponential sums. To get the former, I'll use a blogger's critique of the Technorati estimate made in August 2006. The latter can be found as a MathWorld encyclopedia entry. A little massaging gives the formula:

The left hand side of the formula is what we're trying to compute, and the right hand side is much easier to calculate. We can then equate the right hand side with our estimate of the blogosphere, which we call a.

The goal then becomes to solve this equation for M, which can be done with some algebraic manipulation.

Setting r = 5, a = estimate of 1.6 million bloggers, and solving for M, we get a value of M = 8.74. That means it would take about 9 rounds.

For those of you who think that this is algebraic hocus pocus, I've included a small C program that computes the sum using the brute force formula.

int main(int argc, char* argv[])
int i;
const double memeChildren = 5.0;
const double blogosphereSize = 1.6e+6;
double runningProduct = 1;
double runningSum = 0;

for (i = 1; runningProduct < blogosphereSize; ++i)
runningProduct *= memeChildren;
runningSum += runningProduct;
printf("round %d:, number of recipients: %e\n", i, runningSum);
return 0;

And here is its output:

round 1:, number of recipients: 5.000000e+000
round 2:, number of recipients: 3.000000e+001
round 3:, number of recipients: 1.550000e+002
round 4:, number of recipients: 7.800000e+002
round 5:, number of recipients: 3.905000e+003
round 6:, number of recipients: 1.953000e+004
round 7:, number of recipients: 9.765500e+004
round 8:, number of recipients: 4.882800e+005
round 9:, number of recipients: 2.441405e+006

The "e+nnn" in the recipient count is to be read as "times ten to the nnnth power.

So how many generations did it take for me to get awarded? I managed to walk the entire chain of posts back to the originator, and here they are in reverse order, from leaf to root.

  1. Have the T-shirt


  3. Iced Mocha

  4. Daily Piglet

  5. Ghost Stories

  6. My Grimm Reality


  8. The Fifth Column

  9. Original Man

  10. A Work of Art: Raising Our Exceptional Son

  11. The Journey

  12. Under the Mad Hat

  13. Bub andPie

  14. So Fast Away: Journal of a Joyful, Grateful, Manic Melancholic

  15. Life, the Ongoing Education

  16. CaliforniaTeacherGuy

  17. History Is Elementary

  18. another history blog

  19. Primordial Blog

  20. Sandwalk

  21. Greg Laden

  22. The Thinking Blog

Wow! 22 levels of award recipients separate me from the originating blog. That's more than double the best case estimate of 9 levels that I back-of-the-enveloped out in the original version of this post. It's interesting to look at the domains of interest for each blog. Along the way, one passes through a thicket of parenthood blogs, and as you get closer to the root, the focus shifts to education and science.

We all may be connected in more ways than we know. Paradoxically, that lack of awareness might be both a shame and a source of sanity, depending on where those connections lead.
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