Physics of Risk

Lecture on power-law distributions

Aleksejus Kononovicius — Tue, 24 Feb 2026 08:00:00 +0200

This year I was invited to give lecture to gifted high school students attending Nacionalinė moksleivių akademija. It was a great experience for me. I hope that my lecture was at least a bit useful and inspiring. You can find the slides here.

Immediately after the lecture I have remembered that have forgotten to make an important philosophical point, and to somewhat contradict the conclusion made by Veritasium in a recent video on power-law distributions.

In the video's thumbnail, one can see a claim that "working hard is not enough." I do agree with this point, but by the end of the video, one of the hosts (Casper) suggests that in a power-law world, it becomes "more important to be persistent than consistent". This interpretation is sound, and the emphasis on persistence seems both intuitive and motivating. That said, it is important to add a nuance to the discussion.

In environments governed by power laws, outcomes are often heavily influenced by chance and/or external factors. As a result, many considerable successes cannot be fully explained by individual qualities such as ability, persistence, or consistency alone. From this perspective, persistence may increase exposure to opportunities, while the ultimate magnitude of success remains strongly shaped by factors outside individual control. The point I am trying to make is well-presented in the Talent vs Luck model.

Similarly, the wealthiest agents in kinetic exchange models with savings are the ones with largest saving propensity. These agents are successful because they contribute to the shared pot the least, while having a chance at receiving an equal share of the pot back.

J. Blitz-Jones: Law of large numbers

Aleksejus Kononovicius — Tue, 17 Feb 2026 08:00:00 +0200

In an earlier post we have taken a moral formal look at the law of large numbers. But what about the intuition behind this law? I believe this video by Jeremy Blitz-Jones provides a great general level overview of the importance of this law.

Law of large numbers

Aleksejus Kononovicius — Tue, 10 Feb 2026 08:00:00 +0200

Our group, along with a few students, has been reading statistics handbook and refreshing our understanding of the basic statistics. I was given to cover a chapter about the central limit theorem, which reminded me that I had already given a similar presentation while being PhD student myself. While diving into the topic, I have noticed a couple things, which are usually glanced over in a typical statistics handbook. Let me share them with you. But first, let us start simple - with the law of large numbers.

A. Einstein: Why socialism?

Aleksejus Kononovicius — Tue, 27 Jan 2026 08:00:00 +0200

Did you know that Albert Einstein once wrote an essay titled "Why Socialism?" [1]. I did not either. Recently I have watched a YouTube video, which referred me to a video by Dr. Fatima in which a broader discussion about the essay, as well as about Physics in politics and problems faced by Palestinian physicists, can be found. Feel free to watch the video linked below, or go read the original essay [1].

My take away from both the video and the essay is an observation that in capitalist society, you can make money through owning stuff only if you pay laborers less than the value of their labor. To be fair, often the tools are what enables the labor. Yet without a laborer the tool is often as useless. Either way, such practice diverts the gains from the improving technology and other increases in productivity to the pockets of the select few instead of benefiting society as whole. The worst thing is that having deep pockets, enables the select few to exert influence over politics and shaping the society to their will. To break or circumvent check and balances that should exist in free society.

Additional note

After watching the video, reading the essay and discussing its contents with couple of different people, I have a few things to add. Now on the social media I get bombarded with low effort libertarian AI slop. Most of the time it is various AI-generated comics about how bad it was to live in the Soviet Union and how stupid young people are for trying to bring it back. Yes, they are dumb, if they are trying to bring Soviet Union in all its glory. Yet, Einstein advocates for a different thing - planned socialist economy with strong democratic safeguards.

Though I think that given the inherent economic complexity, the need to balance interests of many different groups, it would be extremely hard for any committee to produce an economic plan. "Distributed" computing of the free markets does help with this. So, one needs to look for a reasonable middle ground between the extreme ideas.

References

A. Einstein. Why Socialism? Monthly Review 61: 55-61. doi: 10.14452/MR-061-01-2009-05_7.

Veritasium video on power-law distributions

Aleksejus Kononovicius — Tue, 20 Jan 2026 08:00:00 +0200

In a recent video Veritasium talked about a topic close to our heart - power-law distributions! It is a neat video, which covers a lot of important models and concepts. And it also explains the implications of power-law distributions on everyday life. We invite you to watch it, and maybe revisit our posts on some of the models discussed in the video (such as The Saint Petersburg paradox, Ising model, self-organized criticality models, Barabasi-Albert model).

Boundary conditions and zealotry in the noisy voter model

Aleksejus Kononovicius — Tue, 13 Jan 2026 08:00:00 +0200

When writing our recent article [1], we (I and Rytis) had argued about the relationship between having stable voter base (zealots) and imposing boundary conditions on the noisy voter model. This post explores the subtle differences between these notions.

Overview of 2025

Aleksejus Kononovicius — Tue, 06 Jan 2026 08:00:00 +0200

Happy New Year! It is time for the traditional post about our last year's yield. And its still quite good. Though this year, I received some help from my colleague Vygintas Gontis who wrote four posts on macroeconomics and prepared one interactive app.

Fig. 1:The number of posts written in English and still available on this iteration of Physics of Risk (as of the end of 2025). The wide bars represent total number of posts for each year since 2010, while the narrower bars represent a number of posts containing an interactive app.

We have started the year with various modifications of the Colonel Blotto game. This series of posts culminated in Colonel Blotto moving to an adjacent field of sports. Next we have discussed periodic polling effects and information delay in the noisy voter model [1]. While in the autumn, we have had couple of posts on various assorted topics.

What's next? Still, I am bit overwhelmed and have no concrete plans, but occasionally I'll post something interesting.

References

A. Kononovicius, R. Astrauskas, M. Radavičius, F. Ivanauskas. Delayed interactions in the noisy voter model through the periodic polling mechanism. Physica A 652: 130062 (2024). doi: 10.1016/j.physa.2024.130062. arXiv:2403.10277 [physics.soc-ph].

Numberphile: The Game of Risk

Aleksejus Kononovicius — Tue, 30 Dec 2025 08:00:00 +0200

In this Numberphile video prof. Marcus du Sautoy talks about mathematics behind the board game he likes to play with his kids. What a better way to spend winter holidays, than playing board games? Watch the video not only to gain competitive edge, but also to see how serious mathematics (and physics) can be applied to a fun casual activity.

Accidental politicians

Aleksejus Kononovicius — Tue, 16 Dec 2025 08:00:00 +0200

Over the last few posts I have been writing about variety of research conducted by a group based in University of Catania. I have covered some of their models illustrating various often counter-intuitive effects of randomness within social systems. This time let us talk about how a certain degree of randomness could benefit our political life [1].

Is the United States' productivity advantage merely a result of the chosen measurement methodology?

Vygintas Gontis — Wed, 10 Dec 2025 13:00:00 +0200

Global economic media frequently report that U.S. productivity has been growing much faster than in Europe and other developed Western economies for many years. As an example, consider the recent publication in the Financial Times (FT). This is not journalistic exaggeration—such conclusions follow directly from the still widely used methodology of calculating real GDP and productivity, and from international comparisons based on that methodology.

The FT article clearly illustrates that Europe's economic lag behind the United States is treated as an objective reality at the highest levels of politics, and that policymakers have been searching for ways to "close this gap" for many years. We present these remarks because doubts about the magnitude of the United States’ economic advantage naturally arise from the study of international macroeconomics and economic growth theory.