Tales from the ArXiv: The Power Law OF DEATH

First I saw a researcher (Geoff West) claim that there is The Power Law of DOOM! (That's my name for it — not theirs.) At some point, I thought I had that in a blog post, but now I think it was only verbal snarky remarks and a Facebook entry. It started with a talk that he gave years at Oxford in which Geoff started off by saying that he was only going to have very modest conclusions in his seminar, but by the end of the talk, he was predicting the imminent decline of civilization.

And on the heels of The Power Law OF DOOM, we now have claims of The Power Law OF DEATH in a new arXiv paper called "Statistical study of time intervals between murders for serial killers".

In both cases (and as is common), the claims of a power law are unlikely to be justified statistically.

See also The Small-World Network OF LUST, this old blog entry, and this old blog entry.

Triumphant Return of The Power Law Shop

I'm happy to announce the triumphant return of The Power Law Shop!https://t.co/1sgZacqhhv

Just in time for #netsci2018 (@netsci2018).

We're trying to fill a universal and critical need for scale-free swag.

— Mason Porter (@masonporter) June 3, 2018

New Word Proposal: "Scientificially"

I asked a student if a paper draft of mine passes muster with her "scientificially".

It was just a typo, but I may have to adopt this as a new word for when somebody does something artificial in science.

Example usage: "Those data were estimated scientificially to follow a power law."

"Complexity: A Story of Love and 'Power Laws'"

Apparently, somebody at Oxford is supposed to take complex systems and turn it into a work of fiction (taking inspiration from Alice in Wonderland, etc.)

"Complexity: A Story of Love and 'Power Laws'"@cgershen @SimonDeDeo @TahaYasseri

— Mason Porter (@masonporter) December 16, 2015

"Infinite Moments of Incredible Delight"

I just got a spam e-mail with the title of "Infinite Moments of Incredible Delight" (or something like that), and naturally the first thing I wondered about was which was the first moment that was no longer finite. Of course, it then struck me that that would make a great title for a paper (or section thereof) involving probability theory or power laws.

An Addendum to 'Critical Truths About Power Laws'

Here is a brief addendum to the opinion paper "Critical Truths About Power Laws that I coauthored with Michael Stumpf in 2012. I wanted to post this addendum on the arXiv, but the arXiv admins wouldn't let me post it and removed my submission. I am attempting to 'set the record straight' (or at least my perspective on it) on a specific point.

Title: An Addendum to 'Critical Truths About Power Laws'

Author: Mason A. Porter



Main Text of the Article: In Ref. [3], my coauthor Michael Stumpf and I wrote that "The power law reported for allometric scaling stands out as genuinely good" and reinforced this comment in the paper's figure. We also wrote that "... few people would dispute the reality of such a relationship." I have since learned that the "power law" in allometric scaling is in fact the subject of intense debate. Please see the discussions in Refs. [1, 2] (and in references therein) for details.



You can click on the addendum to see which references I cite.

A Log-Log Plot, Anyone?

I have to admit that my first reaction to seeing this infographic about penis sizes in the animal kingdom was a strange desire to make a log-log plot. :) (Also, I am amused by the appearance of the 'Enlarge' command above the chart. Alright, my mind is safely in the gutter now.)

And now this is making me think of a possible new t-shirt design for the Power Law Shop. I think I better step away from my computer before bad things start to happen...

"Critical Truths About Power Laws"

My opinion piece about power laws has just come out in Science. I was interviewed by a reporter writing a BBC article, which is slated to come out tomorrow. As I write this, the .html version of the article seems to have occasionally (and incorrectly) used the symbol for gamma instead of that for lambda. Sigh... The .pdf version of the file has the correct symbols. (We did all of the page-proofing on the .pdf version, so I only just saw the .html version for the first time.)

Anyway, here is a bit more about the article:


Title: Critical Truths About Power Laws

Authors: Michael P. H. Stumpf and Mason A. Porter

Tagline: "Most reported power laws lack statistical support and mechanistic backing."


What should I say? How about kaboom! Anyway, many of you know that I have been ranting about this for years.

Update (2/10/12): The BBC article is delayed until early next week. Apparently there is some actual news to report.

Thermal Conductivity of SPAM

Check out Figure 2 of this article, which shows (among other things) a plot of the thermal conductivity of SPAM as a function of temperature. Nice! And it even looks like it might be a power law...

Your institution will need to have a subscription to this journal for you to see the other side of this link, but you can always e-mail me for a copy of the .pdf file if you don't otherwise have access to the paper.

(Tip of the cap to Jing Xu.)

Irony of the Day: Barabási's Publication Record Fit to Lousy Power Law

Somehow, I think that this paper was inevitable. In Fig. 2 on page 4, Albert-László Barabási's publication record is fit to a crappy power law. Unfortunately, it appears that the authors were attempting to be earnest in their efforts. (I think that this would have been a hilarious thing to do as a prank. I wish that I had thought of it!)

Seriously: Wow!

Update (8/04/11): Here is what Cosma Shalizi has to say.

Complexity

As I wrote in the first demotivational poster that I constructed, you're doing it wrong.

I amuse myself sometimes. :)

I see that my work is done here.

One of my students wrote the following text as part of an e-mail discussion about a seminar that I missed because I am in Los Angeles:

There was also a video about power-laws in the middle that induced more than a few people to look around in terror to check that you weren't there, Mason.

Apparently, I've developed a bit of a reputation. (And, clearly, this has to be the quote of the day.)

The Word is Spreading

The Power Law Shop has been covered by Nature's blog.

What a way to get into Nature... I've also heard that some Barabasi alums are tweeting about it.

Introducing "The Power Law Shop"

My snarky power law memorabilia is spreading (maybe even virally eventually?), and thanks to a discussion this morning with Aaron Clauset and Michelle Girvan, I have now set up The Power Law Shop on CafePress.

For some reason, the graphics are way too small right now, but I'll fix that later. I will also add some appropriate 'log-log' plots later as well.

But anyway, at least I now have the website up as a placeholder. I'll improve the products later. (I really ought to pay attention to the talk now...)

Update: Cosma Shalizi expressed things particularly well in his blog entry about my new shop. His blog doesn't allow comments (as far as I can tell), but I have to say that this isn't the only funny thing to come out of the SAMSI workshop---my collaborator Peter Mucha had an awesome joke slide about the Zachary Karate Club network, which people had already been making fun of ever since the first day of the workshop. (We'll see if it shows up in any of today's talks.) It's also worth mentioning that things are working pretty fast with the store, as a few of us have had a parallel e-mail conversation---continuing the live conversation just before today's talks started---during the last couple of talks. I really love the internet sometimes. :)

Update 2: Our motto is: All "power laws", all the time! (Also, thanks to Aaron Clauset for providing some of the graphics that I have used for the shop.) If you're interested in community detection, you can also order t-shirts with a Zachary Karate Club network theme.

Update 3: Here is Aaron's Clauset's link to The Power Law Shop.

Repeal Power Laws!

You don't believe me? Just take a look at this sign from the G20 summit in Pittsburgh that Aaron Clauset shows in a blog entry.

Math and the City

Here is a guest article by Steve Strogatz that appears in the New York Times. Strogatz is guest-blogging for Olivia Judson in the next three weeks. The first article is called "Math in the City" and it discusses Zipf's Law and the work by Geoff West and collaborators. (However, unlike West in his seminar yesterday, Strogatz does not discuss what I have come to call The Power Law OF DOOM.)

(Tip of the hat to Hilary Ockendon.)

Tales from the ArXiv: Steroids and Power Laws edition

Here is the abstract of a paper that just got posted on the arxiv:

\\
arXiv:0804.0061
Date: Tue, 1 Apr 2008 03:59:08 GMT (41kb)

Title: Statistical evidence consistent with performance-enhancing drugs in
professional baseball
Authors: Alexander Petersen, Woo-Sung Jung, and H. Eugene Stanley
Categories: physics.pop-ph physics.soc-ph
Comments: 9 pages, 4 figures
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
\\
Statistical analysis is a major aspect of baseball, from player averages to
historical benchmarks and records. Much of baseball fanfare is based around
players exceeding the norm, some in a single game and others over a long
career. Career statistics serve as a metric for classifying players and
establishing their historical legacy. However, the concept of records and
benchmarks assumes that that level of competition in baseball is stationary in
time. Here we show that power-law probability density functions, a hallmark of
many complex systems that are driven by competition, govern career longevity in
baseball. We also find universal power laws in the distributions of all major
performance metrics for pitchers and batters. The use of performance-enhancing
drugs has a dark history, emerging as a problem for both amateur and
professional sports. We find statistical evidence of performance enhancement in
the analysis of home runs hit by players in the last 25 years. This is
consistent with the findings of the Mitchell Report [1], a two-year
investigation into the use of illegal steroids in major league baseball, which
revealed that over 5 percent of major league baseball players tested positive
for performance-enhancing drugs in an anonymous 2003 survey.
\\ ( http://arxiv.org/abs/0804.0061 , 41kb)

Tales from the arXiv: food evolution edition

Here's the abstract of a paper that just showed up on the arXiv today:

\\
arXiv:0802.4393
Date: Fri, 29 Feb 2008 14:16:37 GMT (323kb)

Title: The Nonequilibrium Nature of Culinary Evolution
Authors: Osame Kinouchi, Rosa W. Diez-Garcia, Adriano J. Holanda, Pedro
Zambianchi and Antonio C. Roque
Categories: physics.soc-ph
Comments: 15 pages, 5 figures, 1 table, submitted to Physical Review E
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
\\
Food is an essential part of civilization, with a scope that ranges from the
biological to the economic and cultural levels. Here we study the statistics of
ingredients and recipes taken from Brazilian, British, French, and Medieval
cookbooks. We find universal distributions with scale invariant behavior. We
propose a copy-mutate process to model culinary evolution that fits very well
our empirical data. We find a cultural founder effect produced by the
nonequilibrium dynamics of the model. Both the invariant and idiosyncratic
aspects of culture are accounted by our model, which may have applications in
other kinds of evolutionary processes.
\\ ( http://arxiv.org/abs/0802.4393 , 323kb)


Insert a rant about power laws here.

Power Laws

I'm quick to rant and mock when it comes to power laws. Many of you have heard me do this before on multiple occasions. (Just search for 'power laws' in this blog and you'll see what I mean...)

Anyway, Aaron Clauset has just written a review with Mark Newman and Cosma Shalizi about getting power laws from empirical data. I don't know Cosma (though I know of Cosma), but I have tremendous respect for Mark and Aaron has both people and scientists. (Actually, Aaron has commented on this blog once or twice.)

The real reason I'm including the link is not the new article but rather the fantastic poem in Aaron's blog post. Go take a look at it.

Best "power law" EVER!

If you ever want an example of the misuse and abuse of "power laws," then look no further.

For a good laugh, check out the beauty on the bottom of page 10 of this document, which was produced by a consulting group that I'm never going to hire.

There are 5 data points (count 'em), and they "fit" (though I hesitate to use the word for 5 data points) a sinusoid (in log-log coordinates) much better than a line segment.

If you ever find a better example of what not to do, let me know...

Garbage like this is what causes me to rant about power laws so often, even though they can be useful on occasion.