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Joe McCarthy

Having recently read "The Power of Pull", I can see how the ideas in this 2007 post (which I discovered via a tweet today) influenced many of the ideas presented there.

This is a very interesting analysis - and labeling - of the Paretian World (though I'm wondering how that might best be pronounced ... more like "Parisian" or "paration"). The terms "fat tails" and "extreme clusters" are also good takeaways.

The emphasis on increasing interdependence and interconnection is well taken, and helps explain why it seems increasingly challenging to make sense of [Gaussian-based] statistics reported on a variety of phenomena.

I particularly like your insights about surface events, distraction, diversion and complexity in a Paretian world, which helps explain why, at a time when we've never had so much direct access to original sources of information, more and more people seem to simply skim the surface (e.g., retweeting links to articles with provocative titles without taking the time to actually read them).

For what it's worth, I reviewed some related ideas in a blog post of my own in 2010 on power laws and pyramids: participation, gratification and distraction in social media, synthesizing some insights from Ross Mayfield, Josh Bernoff, Christopher Allen and Charles Cooley.

Ryan McCormack


Thanks very much for the thought-provoking post. It makes me even more excited to read your book, which I coincidentally ordered last night!

Practitioners in social media, and people interested in social media metrics, would do well to read your post and ponder its implications. In particular, the quest for a simple (single) metric for "influence" seems like a Gaussian way of thinking (and probably a fool's errand).


ERP/MRP II needs a fundamental rethink. SAP, Oracle, Infor, ERP et al are designed to push a hierarchal plan. In a world of extremes systems now need to pull in demand and produce results without generating reams of redundant accounting and lead time exceptions.


John, I *really* enjoyed this post, and I will equally enjoy re-reading it along with the amazing conversation /posts you generated.
I am in the midst of a strategic and intellectual exercise that is Paretian/Gaussian in nature, around what we used to call the "Black Swan Event."
We are looking for big changes that while unexpected, impact an entire ecosystem and change the rules forever-even generating revisionist history or assumptions. We (perhaps arrogantly) want to be a trigger of one of those Black Swan events, or at least be among the first to see one happening and thus maneuver ourselves to take optimum advantage of it. You know, jump into the dry river bed before the storm, and all that. But Black Swan events no longer occur (as in the past) in isolation or outside of the system. So they're not so easy to see, or even interpret. There is an argument that they only occur in the concert of multiple (and non-collaborating) actors in a system. In fact, we expect that they will occur in-sync and as a part of the *Omniscient* or organic changes of a system... Meaning that we can no longer "try" to make one happen. Kind of like the folly of "purposefully designing" a viral video or a new genre of popular music.
So while dramatic and perhaps cataclysmic or creatively destructive, they will still likely come from within or adjacent to one of our ecosystem spheres... because *everything* is now "connected" as never before.
Yet we don't have a way to map those connections because they form and are broken and form back so easily and dynamically.
The idea is that these *connections* are less expensive, and that as a result, things occur *and* morph/extend in near-real-time across the "real-time Web" (which has become a buzzword around here).
So in a business sense, and in a sociological context we see these "ripples" of an event repeated, and then creating additional concentric ripple-waves of their own, it often becomes one big chaotic hair-ball to interpret cause-and-effect. No matter how good your math is.
Borrowing another metaphor, it is also seeming to become more like the Schrödinger's Cat/Copenhagen shift of perspective. In an advertising condition, discrete outcomes are measured but not *known* until later, as there are secondary-dependent actions and outcomes that define the "success" of the ad transaction. Is the cat dead or alive? Is the ad successful or not? Depends on when you look, and if you look. And how you look.
We see connections that are accidental, incidental and unintentional actually impacting and changing the nature of the ecosystem. Gmail goes down because someone forgot to update a server. Twitter fails because of the usage shift, realtime communications shift to this discussion. People create alternative communications conduits (like a living organism creates new blood vessels to the heart when others get clogged up), and thus the system is permanently altered. Or is it? Sorry about the trivial and banal example with Gmail and Twitter.
But the point I'm struggling with, and which excites me about your post, and the subsequent brilliant discussion (others' not mine) is that we have apparently underestimated the evolutionary or quantum shifts happening faster due to connections and realtime feedback cycles being shortened.
We are looking at ordinary consumer and advertiser behavior around ads and the social graph. Simply by *introducing* a set of ad control feedback (passive and active) mechanisms we see that *other* incidental and accidental connections and feedback results begin to change the entire nature of the interaction, especially scattered in these infinite, concentric wavelets or droplets. So we see wonderful chaos that we now get to sort out in a Paretian/Gaussian shift to figure out if there is any cause-and-effect (or meaning) or if it is munging up (another technical term) because the very nature of the mass activity is shifting organically... as in Copenhagen.
In the end, we won't know until we know, and then if it is a Black Swan, we'll likely back-into a justification of the shift (as writers of history) and use the luxury of hindsight as our "proof." I think we'd like to figure out how to get 5% better than that and see if we can trend-spot something this big and get in front of it. Gaussian/Paretian, Schrödinger's cat/Copenhagen
Ok enough. This is fun, but it's hurting my brain on a sunny California Autumn afternoon to be inside and thinking so hard.
Keep up the great conversation! I'll try to keep up.
Matt Weeks


One piece of nitpicking: We have never been in a Gaussian world, where anything involving human social systems was concerned.

Adam Marsh

Great post! One issue to be careful with, however, is distinguishing between ranked data and probability density functions (PDFs). Ranked data is by definition always decreasing, and so of course can never be a bell curve or Gaussian. In some cases, ranked data can match a power law, in which case the corresponding PDF is also a power law. However, if the ranked data has a "long tail" but doesn't really fit a power law, the corresponding PDF can in fact be an exact Gaussian! More on this here and here.

I mention this because the distributions you mention as "Pareto", e.g. frequency of word use, are typically thought of as ranked data: the graph is that of words (x-axis) vs. frequency of use (y-axis), ordered from highest to lowest frequency. This of course cannot possibly be a Gaussian, since it is by definition decreasing!

This graph has a corresponding Cumulative Distribution Function (CDF): frequency of use (x-axis) vs. number of words with at least this frequency (y-axis). If this graph follows an inverse power law, then it's called a "Pareto distribution" (a Pareto distribution originally described the percentage of people owning more than x amount of wealth). However, this isn't the graph most people first associate with "frequency of word use"!

Finally, the corresponding PDF would be frequency of use (x-axis) vs. percent of words with that frequency (y-axis). Here's where you could potentially look for a Gaussian.

Rutger van Waveren

Please have a look at this:

It's a link to an interview with Nassim Taleb about his new book Black Swan.

The interview deals mainly with Gaussian truths and extreme events and the unpredictability of these events. The interview (MP3)is excellent.


As someone who prefers jumping from the saddle-point, your wonderfully written viewpoint brought me joy. But, then your perspectives usually do.

So, I can only assume that you've noticed this isn't confined to business trends. Perhaps human and universal tendancies are shifting. In the words of Gregory Bateson, "[It is] difference that makes a difference" and "Embedded and interacting systems have a capacity to select pattern from random elements."

I look forward to reading more on this topic and related communities of thought. Here's to patterns that connect!

George Albert

First, the mathematics of the two are substantively different. Gaussian law is based on the law of large numbers. Pareto made no such claim in any of his writings. In fact Pareto's work as it pertains to distribution is sui generis. Next Pareto elements are based on sharing properties while Gaussian distribution is based on common elements intrinic (maybe naturally so) in a system.


Love this blog. I am creating a course that has as its goal (in fact my whole company has this as its goal) to shift the mindset of systems engineers to more knowledge of the "Paretian" world from the Gaussian, but I didn't have those words to describe it until I read this. Gotta get my hands on the journal paper. Thanks.



I submit that we are already living in a "Paretian World". Consider the scale-free nature of the things in our daily lives (e.g., transportation hubs; web search engines; social network topologies). Most of us simply choose to ignore it because Gaussian methods support our dogmas so nicely.

Our education system (particularly in the west) thrives on reductionism that is inconsistent with a true "system of systems" view. Hence our fascination with single metrics in the most complex of situations (e.g., "enemy combatants killed"), and our preference for "silver bullet" solutions.

We also favor uniqueness in our answers, because that too favors our propensity for simple solutions. And we have a really tough time conceiving of very large numbers (q.v. Huxley's "six monkeys" strumming on typewriters that would, in a mere matter of years, randomly write all the works of Shakespeare -- when the real answer is more like 1E30 years to randomly get Hamlet).

My point: I absolutely agree with your charge to "change mindsets" and think more dynamically. As a parent of a kindergartener and a 4th grader, I try to expose my kids to as wide an array of disciplines and opinions as possible. This is perhaps the most important challenge of our time: how to raise dynamically-thinking, socially aware citizens of the world who will thrive in the connectedness that is upon us.

vr/ shane


Thanks for this concise treatment of a very intriguing property of the real world. Your readers might also enjoy the references to power-law distributions as an emerging property of dynamic systems in Eric Beinhocker's "The Origin of Wealth" (see my review at http://livepaola.wordpress.com/2007/04/21/eric-d-beinhocker-the-origin-of-wealth-a-must-read/).


Great post !! One of the things that I have seen especially with my friends doing research is that most of them love the gaussian distribution because the mathematical tools available to handle gaussian are quite well established while there are not good tools.
For ex I have seen so many glee over the fact that Fourier Transform( of a Gaussian) is again a Gaussian and this helps them build to nice illustrations and papers explained neatly in mathematical equations.

IMHO I think the problem starts from the scientists is prevalent all the way to economists & business people.

Will try to check out the two books mentioned the comment but I think the only book that I have seen which has given the pareto distribution its due in fooled by randomness by NN Taleb.


Adelino de Almeida

Extreme events are just that... regardless of the distribution used to fit them. Averages are not applicable to phenomena described by normal distributions... frankly, this argument could use a bit of Occam's Razor

Leandro Herrero

Excellent! Power law is at the core of our methodology of ‘management of change’, described in my book ‘Viral Change: the alternative to slow, painful and unsuccessful management of change in organizations’ (meetingminds, 2006) I apply that network based conceptual framework to the management of the organizational change. I can also say that it works! In many organizations I am working with, cultural and other changes become more sustainable and appear faster, precisely because we are using the power law distribution of people within the organization in terms of their influence. The power of a small set of non negotiable behaviours, spread by the small number of people in the head of the power law, generates social copying and tipping points of new routines ( cultural change, process change…) It is a contrarian view to the traditional linear, sequential, painful, expensive and mostly unsuccessful ‘change management process’. I create internal epidemics of success. Thanks for all the above thoughts which will help further building… - Leandro Herrero (www.thechalfontproject,com)

John Robb


Excellent explanation that brings clarity to an important topic.

I use some of the same type of analysis in my work on warfare. Long tail war. Dynamism pattern recognition through never ending analysis/synthesis loops (Boyd's snowmobile) vs. static snapshots to support dogma.

If you get a chance, check out my book Brave New War (it's on Amazon). I'm also going to write this up on my weblog, Global Guerrillas, in some fashion.

Thanks much for such great work.


John Robb

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