In 2014 Australian programmer started "social experiment" - he allowed thousands of viewers on Twitch to play computer game. Thousands of people could write into common chat to decide what the player controlled character in Pokemon Red will do - will he move up or down? Will he fish in the fond or ride a bicycle? What pokemon would he catch? Having in mind online troll culture, one could not have expected much, but in 16 days the game was completed.

Recently one programmer working at Amazon entrusted Twitch viewers with his lifetime savings of 50 thousand US dollars. This project already runs for about two weeks and so far the internet did not waste his savings...

This curiosity could be viewed on StockStream Twitch channel. But you can not only watch, but also influence the trades that will be executed. This can be done during session hours of New York Stock Exchange (workdays from 15:30 to 22:00 in Lithuanian time).

Last time when we wrote about Lotka-Volterra equations, we have mentioned Verhulst's model of population dynamics, given by

\begin{equation} \mathrm{d} x = r x ( 1 – x ) \mathrm{d} t, \end{equation}

which describes temporal evolution of ecological systems with limited supply of food. The model has parameter \( r \) which controls the availability of food to the population. It would be natural to ask how the availability of food impacts the dynamics of model? Does the population converge? If so, then to which state? May be the population does not converge? How do the answers to these questions change based on model parameter? More on this and the interesting mathematics in this Numberphile video.

Imagine during your routine checkup a doctor randomly suggests you to take a test, which would tell (with 99% accuracy) if you have a rather rare disease (only 0.1% people have it). Is it worth to be curious? What would you do if you test positive? Panic? Shock? The test is 99% accurate!

Now imagine that you have 1000 people. Only one of them (0.1%) will have this disease and there is a rather significant probability that he will test positive. Likely 10 people, out of 999 healthy people, will also test positive (1%). So in the end you have 11 positive results and only 1 sick person in the group. So actually there is only 9% chance that you actually have this disease.

This "paradox" is not a mathematical paradox, nor its a mathematical trick. It is actually Bayesian trap! More on it in the following video by Veritasium.

Did you notice that maps use just but a few colors, while we have more than 200 countries here on Earth. Obviously it would not be rational to use different color per each different country. It is more convenient for our human vision, then there is as few colors as possible as then we can pick contrasting colors. Wouldn't it be interesting to know if there is some minimal number of differing colors necessary to create colored maps? More about this in this Numberphile video.

Human behavior is perplexingly complex. Why their collective behavior is so well described by rather general mathematical models using very few parameters? Why do they not need deeper insight into the human psychology or decision making? One of the simple answers - if the statistical signature is not present in the data, which is usually aggregated at least to some degree, we can do nothing about it. Namely, usually we do not observe individuals making decisions and as such we are will not be able to differentiate between different mechanisms of human decision making. There are two major mechanisms of human decision making - homophily (selecting your peers) and peer pressure (adopting your peers behavior). Mathematically there usually will be no difference between them, both mechanisms can be be described using the same Kirman's model.

In this text we will consider Bass diffusion model with heterogeneous agents (each of them having his own independent parameters). We will show that the heterogeneous model produces similar macroscopic dynamics as homogeneous model. To simplify matter even further we will use unidirectional Kirman's model.