‘Iterating Grace’: Ex post factoid, Part I

If you arrived here from the link in Charley Locke’s December 6th Wired article, I encourage you to begin with Part II instead. Really. Stop. Koons will be much more gratified if you read about the book in Part II (and links therein) than about boring Twitter analytics, which is what you will get if you continue below. Really. Go to Part II.

OK, I warned you. No deadly vicunas below, only boring stuff about Twitter traffic.

During the two months following my late-June post, Is ‘Iterating Grace’ re-iterating ‘Milwaukee’?, I continued to check Twitter almost daily for mention of the phrase “iterating grace” or the hashtag #iteratinggrace. I was watching for the unlikely — new substantive comments about, or credit-taking for, the mysterious early-June appearance of a small book in the tech-media circles of San Francisco. You can read much more fact and speculation about the book and its creators at the link above; this post is narrowly focused on some technical details of the resulting traffic on Twitter.

The earliest four posts using the exact title/phrase “iterating grace” (henceforth “IG”) or the hashtag, appeared on June 3, including at least one from a recipient of the book, Doree Shafrir (@doree). This was followed by a tweet from a puzzled Alexis Madrigal, editor-in-chief of Fusion, who soon received his own copy of IG, dropped off on his front porch. He wrote about it on June 8 and posted this on Twitter (sans title or hashtag):

As Madrigal, Dan Raile on PandoDaily, and others wrote and tweeted about IG, I tracked the micro-storm and posted a graph of the traffic two weeks later:

As the graph shows, there was no additional activity for four days (June 4-7). Then Madrigal’s first two posts (M) on Fusion triggered re-tweets on June 8 and 9, with a clear drop-off on June 10. There was a modest rebound with Dan Raile’s post (R) on June 11, then a long tail to the right, perturbed only by a post by Liam O’Brien (O’B) at Melville House Books in Brooklyn and a third one by Alexis Madrigal.

There are a couple of unconventional aspects of the graph. The horizontal (X) axis has tick marks every 2.5 days; and the vertical (Y) axis extends to negative values. Both of these are “features” of the beta version of the fabulous online graphing tool, MyCurveFit. The Gaussian (bell-shaped) curve is to provide a visual frame of reference, not to suggest any necessary reason why this kind of multi-author composite of several stimulus+response (tweet+re-tweet) events should necessarily follow a normal distribution. Having said which, it’s actually a pretty good fit, as indicated by the correlation coefficient (of some unspecified form), R2=0.8217.

Just so there is no mistake, this is truly a micro-storm. Maybe even a nano- or pico-storm, to use prefixes indicating ever smaller values. The total number of tweets over those first three weeks was a bit less than 350. I also saw many individual conversations and threads among Madrigal, Raile, other tech journalists, technologists, and investors. Some of these were initiated or joined by self-identified recipients of the mysterious book. My impression, admittedly without doing any counting, is that this involved fewer than 100 individuals and at most a few hundred tweets. By any measure, IG was a small event, of continuing note only to those who “experienced” it or reported on it. Plus a couple of academic hangers-on, namely, Teddy Roland (@teddyroland) and me.

Hangers-on do one thing. They hang on. So I kept checking Twitter through the end of June, into early July. Then on July 9 there was a big spike, with almost 400 tweets for the day, more than the cumulative number since June 3.


The cause was easy to identify: the overwhelming majority of them were pointing directly or indirectly to a post by Ara Rodríguez (@AraRodriquezT), Este cuento anónimo tiene en jaque a medio Silicon Valley, at the Madrid-based technology site Hipertextual. With the considerable assistance of Google Translate, I can say that her post is an excellent distillation of the essentials of the situation, apparently based on her reading of the online text of IG and reference to Alexis Madrigal’s first post. It certainly offers nothing new, but it opened the door to a Spanish-language audience that would otherwise not have heard the story.

As for the magnitude of the Twitter spike, that is presumably at least a partial reflection of the respective followings of the sources (as of early July): @Hipertextual, 338K; @ThisIsFusion, 177K; and @PandoDaily, 80K.

What I found most interesting, however, and the whole reason for writing this blog post, is that Rodríguez’s article suggested the possibility of a rare event, a perfectly-controlled experiment. Here was an audience “isolated” by language, so when they were presented with her story, their response — their tweets and re-tweets — could be attributed solely to that single stimulus. In contrast to the multi-author composite of stimulus+response events for the various English-language posts, the Hipertextual story provides a simple example of information diffusion.

There is a fairly rich research literature on the lifetimes of various types of online information (see a few representative sources at the end of this post). This work has documented that information from YouTube tends to “last longer” than that from Facebook, Twitter, and general web links. There is also subject-matter variation, with sports pages not surprisingly lasting the least time compared to business news, entertainment pages, and so on. In all cases the metric for “lasting” is a half-life, a unit indicating the interval of time necessary for a link, page, or tweet, respectively, to receive half of the clicks, views, or re-tweets that will ever happen to it. (The calculation of these half-lives is based on looking back at traffic data after a sufficiently long period has passed such that, for all practical purposes, no one is any longer paying attention. If you want some homework, it’s pretty easy to show that after 7 half-lives less than 1% of the original value will remain. HINT: residue after N half-lives = (0.5)N.)

For bloggers, tweeters, videographers, and the like, the results can be depressing. The half-lives that come out of these studies are brief, usually measured in a few hours: 7.4 hr for YouTube, 3.4 for pages, 3.2 for Facebook, and 2.8 for Twitter, according to a 2011 study at Bitly. The best of these studies are done by aggregating hundreds of millions of tweets and at least tens of millions of news articles or blog posts. So, while your mileage may vary, the odds are that 99% of the people who will ever re-tweet your 140 characters of wisdom will do so in less than a day after you click the Tweet button.

What is different here about Ara Rodríguez’s article in Hipertextual and its resulting Twitter stream is that there is no aggregation. This is a single, “pure” event followed by a cascade of “repeating” messages. And yet the result is exactly the same as for the aggregate studies, as this graph shows (no red dot, for example on day 5, means no tweets on that day):


There are only two things that you need to notice. Firstly, the correlation coefficient (in the box headed “Goodness Measures”) is simply R2 =1. This says that an exponential curve, which is the generic mathematics that describes a half-life decay, is a perfect fit to the data points for tweets in the 12 days including and following her article. Even if it’s not truly perfect, even if it were merely 0.99999 or 0.9999, we’re still in the rarefied company of people who confirm Higgs bosons for a living. Said differently, this is indeed a simple information diffusion or decay problem.

Secondly, notice in the “Coefficients” box the value of c = 0.197. This is in fact the half-life, and its units are days (the same as the X-axis). So the half-life of the tweets following her article is 0.197 days = 4.83 hours, right in the middle of the values quoted above from the Bitly researchers.

And there things should stand. As I write this on September 19, we are more than 100 days past those first tweets on June 3. That means that some 500 half-lives have elapsed. By any reasonable take on these metrics, and for that matter any more general expectations, that should be the end of it. No more re-tweets of anything, presumably no more tweets period, and no more Iterating Grace.

But what if that is not the end of it? Part II examines the question, what happens if those expectations aren’t true? In particular, what if there is more Iterating Grace?

Here are a few recent sources from the literature on information diffusion:
• Castillo et al., 2013, Characterizing the lifecycle of online news stories using social media reactions;
• Higham et al., 2014, Anticipating activity in social media spikes;
• Huberman, 2013, Social computing and the attention economy; and
• Yang and Leskovic, 2010, Modeling information diffusion in implicit networks.

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