Category Archives: ideas

How Much Data Can Flow Through the Internet?

How much data flows through the series of tubes that make up the Internet?

Bernard Marr gives an answer that applied for 2019 in the following under two minute video:

Now, bonus question! How much does all the data that can flow through the Internet's tubes weigh?

That's a harder question to answer, but it didn't stop TopTrending from running the numbers in the following six and half minute video:

The thing to keep in mind in these numbers is that the Internet is about moving information, not storing it. 6.75 ounces is the physical weight of all the electrons that represent the estimated physical capacity of the amount of data that can flow through the internet as we know it today in a year. It also doesn't consider how that data might be moved in the future to get around those physical constraints.

But for now, that figure is also a little over one dry ounce more than the estimated weight of all the particles of SARS-CoV-2 coronavirus in the world.

Meanwhile, on Mars…

Having covered the state of Earth's economy yesterday, we have a unique opportunity to extend our planetary scale analysis to Mars, whose economy is starting to register signs of life after what many scientists believe is a 600 million year recession.

There is, after all, now signs of activity on the Martian surface. The following footage of some of that activity was recorded on 18 February 2021:

With the arrival of NASA's Perseverance rover, we estimate Mars' GDP to now be greater than $0, which is where Mars' economy had been stuck since the Mars Opportunity rover ceased operation in 2019, and which has been Mars' average GDP for millennia.

Although the Perseverance mission itself cost more than $2.4 billion, which does not include an additional $300 million for landing and operating a rover on the surface of Mars. Nearly all of these costs are properly counted toward Earth's GDP however, where nearly all of the mission's activity has occurred to date.

With an active mission on its surface, Mars' GDP is no longer at $0, but is now greater than $0.

Economic development plans are in the works for Mars, which may become the first planetary economy to run entirely on cryptocurrency.

The Perseverance rover will collect samples that will someday be exported to Earth, making the mission the one of the first to begin developing interplanetary trade within the solar system.

Update 25 February 2021: A panorama of Perseverance's view from the Jezero Crater (HT: Michael Wade)

How much do you suppose Mars' first produced exports will be worth?

Replacing Zipf’s Law in Modeling Growth of Cities

Movers in Brooklyn - Photo by Handiwork NYC via Unsplash:

Writing in 1996, future Nobel prize-winning economist Paul Krugman confronted the mystery of urban hierarchy:

The size distribution of cities in the United States is startlingly well described by a simpler power law: the number of cities whose population exceeds S is proportional to 1/S. This simple regularity is puzzling; even more puzzling is the fact that it has apparently remained true for at least the past century. Standard models of urban systems offer no explanation of the power law. A random growth model proposed by Herbert Simon 40 years ago is the best try to date — but while it can explain a power law, it cannot reproduce one with the right exponent. At this point we are in the frustrating position of having a striking empirical regularity with no good theory to account for it.

The "simpler power law" to which Krugman refers is Zipf's Law, which was originally developed to describe a power law relationship that was found to exist between the rank of a word and how often it appears in use in language. A similar pattern was observed in the ranking and relative size of cities by population in the U.S., which was described by Xavier Gabaix in a much-cited 1999 paper.

But that exercise was largely based on comparing the relative ranks and populations of cities at a given snapshot in time. Does a similar pattern hold as cities evolve over time?

The answer to that question is "sort of, but not really". If Zipf's Law worked reliably, it could be use to accurately forecast the growth of population in cities over time. It can in a limited sense, but only to the extent that the growth over time is steady and not subject to chaotic conditions.

That's where a new study by physicists Vincent Verbavatz and Marc Barthelemy makes a potentially significant advance in modeling the growth of cities over time. Here's the abstract from their paper (boldface emphasis ours):

The science of cities seeks to understand and explain regularities observed in the world’s major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most fundamental problem is to understand the hierarchical organization of city population and the statistical occurrence of megacities. This was first thought to be described by a universal principle known as Zipf’s law; however, the validity of this model has been challenged by recent empirical studies. A theoretical model must also be able to explain the relatively frequent rises and falls of cities and civilizations, but despite many attempts these fundamental questions have not yet been satisfactorily answered. Here we introduce a stochastic equation for modelling population growth in cities, constructed from an empirical analysis of recent datasets (for Canada, France, the UK and the USA). This model reveals how rare, but large, interurban migratory shocks dominate city growth. This equation predicts a complex shape for the distribution of city populations and shows that, owing to finite-time effects, Zipf’s law does not hold in general, implying a more complex organization of cities. It also predicts the existence of multiple temporal variations in the city hierarchy, in agreement with observations. Our result underlines the importance of rare events in the evolution of complex systems and, at a more practical level, in urban planning.

Verbavatz and Barthelemy find changes in migration flows to be especially significant in their new formulation, where they find a Lévy stable law provides a much better fit with empirical data from France, Canada, the United Kingdom, and the United States. The following figure from the paper illustrates these differences with results that would be expected from Gaussian-based models of growth (based on normal distributions of migration flows):

Verbavatz and Barthelemy (2020), Extended Figure 4 - Migration Flow Analysis

They also note that the Zipf-Gabaix-Gibrat model is not capable of accounting for scenarios where a city's population rank might significantly change within a short period of time. By contrast, their new model can accommodate these kinds of rapid transitions with reasonable accuracy, predicting how a city's population might change in response to shock changes in migration flows.

That's significant because 2020 is providing several potential case studies for the Verbavatz-Barthelemy model, in the form of the rapid out-migrations of people and businesses from cities experiencing break downs in public order as a result of their implementation of progressive political policies, such as New York, San Francisco, and Portland. These are examples of the kinds of turbulent shocks that Zipf's Law cannot handle but which the new general model for population growth in cities would appear to be well suited.


Verbavatz, Vincent and Barthelemy, Marc. The Growth Equation of Cities. Nature, 587, 397-401(2020). [Ungated PDF document]. DOI: 10.1038/s41586-020-2900-x. 18 November 2020.

Gabaix, Xavier. Zipf's Law for Cities: An Explanation. Quarterly Journal of Economics, Volume 114, Issue 3, August 1999, pp 739-767. [Ungated PDF Document]. DOI: 10.1162/003355399556133. 1 August 1999.

Yirka, Bob. A stochastic equation for modeling population growth in cities. [PDF Document]. 20 November 2020.

Krugman, Paul. Confronting the Mystery of Urban Hierarchy. Journal of the Japanese and International Economies, Volume 10, Issue 4, pp 339-418. [Ungated PDF Preprint Document]. DOI: 10.1006/jjie.1996.0023. December 1996.

Newitz, Annalee. A mysterious law that predicts the size of the biggest cities. Gizmodo. [Online article]. 9 December 2013.

Image Credit: Photo by Handiwork NYC on Unsplash

Campbell’s Soup Presents "The Magic Shelf"

It's the day after Thanksgiving 2020, and like many Americans, we're now pondering what can we have to eat along with our turkey leftovers.

Longtime readers know we have a strong affinity for Campbell's Tomato Soup, since we've tracked the price of an iconic can of the condensed product since 1897.

That's why we were excited to discover the following 21 minute time capsule video from 1952. While it starts with an awful magic act that becomes an awfully long commercial for Campbell's Soups, it really says quite a lot about how Americans lived and ate nearly seven decades ago. Not to mention showing how Campbell's supply chain worked to get the finest ingredients to make its soups and get them to American consumers, as the company's home economist, Ann Marshall, was working to "create new ways in which soup can serve you even better".

We have to admit we were surprised by the very existence of the Chicken-Cranberry Salad featured in the film, which somehow hasn't survived into the 21st century. It seems whatever partnership existed between Campbell's and the Knox gelatin corporation at the time wasn't strong enough for this chilled concoction to endure.

But since we came for tomato soup, here's a quick overview of the suggestions Campbell's had for how to use its tomato soup in your recipes in 1953:

  • As a base for beef stew.
  • Use it just as it comes from the can as tomato sauce.
  • Pour half a can into your meat loaf as an ingredient, then heat and steam the rest of it to cover your meat loaf as a pour-on sauce.
  • Make a full-flavored spaghetti sauce from it. Or tomato cheese macaroni.
  • A "spicy, mellow-favored" cake!
  • A French salad dressing when shaken with oil, vinegar, and seasoning.
  • Combined with equal parts clam chowder and milk or water for a really hearty soup.
  • Combined with equal parts split pea soup and milk or water to create "Purée Mongole", which apparently "wins rave notices every time".

We didn't know what Purée Mongole was either, but it turns out "it was popular in the 1930s, being served in Manhattan restaurants in New York City. Mongole soup has since declined in popularity and is rarely (if ever) seen today." The New York City hotel chef who created it, Louis Diat, is better known for also creating the cold leek and potato soup known as vichyssoisse in 1917.

Speaking of which, there is a tomato-based version of vichyssoisse that looks pretty appealing. Is anyone else hungry for soup all of a sudden?

Previously on Political Calculations

Our coverage of America's most iconic soup, presented in reverse chronological order!

Rules to Follow for a Happy Thanksgiving

We hope you have a Happy Thanksgiving. To help achieve that goal, Michael Wade has crafted 10 rules to follow to help ensure your Thanksgiving experience is a happy one.

  1. Thou shalt not discuss politics at the dinner. There is next to no chance that you'll convert anyone and any hard feelings that are generated may last long after the pumpkin pie is finished. Why spoil a good meal?
  2. Thou shalt limit discussion of The Big Game. This is mainly directed at the men who choose to argue plays, records, and coaches while their wives stare longingly at the silverware. The sharp silverware.
  3. Thou shalt say nice things about every dish. Including the bizarre one with Jello and marshmallows.
  4. Thou shalt be especially kind to anyone who may feel left out. Some Thanksgiving guests are tag-alongs or, as we say in the business world, "new to the organization." Make a point of drawing them in.
  5. Thou shalt be wary of gossip. After all, do you know what they say when you leave the room? Remember the old saying: All of the brothers are valiant and all of the sisters are virtuous.
  6. Thou shalt not hog the white or dark meat. We know you're on Atkins but that's no excuse.
  7. Thou shalt think mightily before going back for seconds. Especially if that means waddling back for seconds.
  8. Thou shalt not get drunk. Strong drink improves neither your wit nor your discretion. Give everyone else a gift by remaining sober.
  9. Thou shalt be cheerful. This is not a therapy session. This is not the moment to recount all of the mistakes in your life or to get back at Uncle Bo for the wisecrack he made at your high school graduation. This is a time for Rule #10.
  10. Thou shalt be thankful. You're above ground and functioning in an extraordinary place at an extraordinary time. Many people paid a very heavy price (and I'm not talking about groceries) to give you this day. Take some time to think of them and to express gratitude to your friends and relatives. Above all, give special thanks to the divine power who blesses you in innumerable ways.

Ignore any one rule at your own risk. And if it helps, they're not just rules, they're also basic tools you can use to discover happiness in your life after your family's Thanksgiving dinner is over.

Slicing pumpkin pie beside bread at end of Thanksgiving dinner - Source: Element5 Digital via Unsplash -

Image Credit: Photo by Element5 Digital on Unsplash