Our group, along with a few students, has been reading statistics handbook and refreshing our understanding of the basic statistics. I was given 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.

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.

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).

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.

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].