Trigger & TL/DR warning: This post is wonky, long and highly speculative. I did not find any research papers that draw the conclusions I postulate here. So, this probably is way out on a limb.
CONTEXT
Universal movement
Lévy walk (left), Brownian
motion or walk (right)
However, when one gets to the scale of a galaxy, galaxy cluster or larger structures, ordered but random motion imposed by gravity and the expansion of the universe negates Lévy walk constraints. Well, at least that's what the boffins say. However, even with structures bigger than galaxy clusters, there's this bit of ambiguity: Although huge web-like structures in the universe suggest some form of Lévy walk-like behavior, the movement within these structures is more akin to a coordinated flow rather than the random, superdiffusive motion of Lévy walks.
An example for humans is taking a walk in the park or elsewhere with a hard, flat surface to walk on. Most steps are fairly uniform, but occasionally there is a longer step in the walk. The longer step happens occasionally and unpredictably, sometimes a couple are bunched together. That is Lévy walking.
Bacterial Brownian motion
bacteria moves when a water molecule bumps into a cell
Bacterial motility (swimming) toward
food (the sugar crystal) is not Brownian motion
but nonetheless is a form of Lévy walking
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A recent STD article reported that subatomic particles from colliding atomic nuclei in atom smashers move in a Lévy walk manner:
Particles in high-energy nuclear collisions move in a way that follows a pattern known as Lévy walks, a motion found across many scientific fields.
Named after mathematician Paul Lévy [in his 1937 paper describing the phenomenon], Lévy walks (or, in some cases, Lévy flights) describe a type of random movement seen in nature and various scientific processes. This pattern appears in diverse phenomena, from how predators search for food to economic fluctuations, microbiology, chemical reactions, and even climate dynamics.
Lévy walking in hadronic scattering studied via femtoscopy
(femtosecond-scale study of the space-time structure of nuclear collisions)
The authors of the Nature research paper write:
The process of Lévy walk, i.e., movement patterns described by heavy-tailed random walks, plays a role in various phenomena, from chemical and microbiological systems through marine predators to climate change. .... In high-energy collisions of heavy nuclei, the strongly interacting Quark Gluon Plasma is created, which, similarly to the early Universe, undergoes a rapid expansion and transition back to hadronic matter. In the subsequent expanding hadron gas, particles interact until kinetic freeze-out, when their momenta stop changing, and they freely transition toward the detectors. Measuring spatial freeze-out distributions is a crucial tool in understanding the dynamics of the created matter and the interactions among its constituents.
Heavy tail vs Gaussian tail (exponential decay)
A Gaussian tail walk is a random walk where the step lengths follow a Gaussian (normal) distribution. This means that the probability of taking a step of a certain length decreases exponentially as the step length increases. The Gaussian distribution is symmetric around its mean, implying that positive and negative steps are equally likely.
A heavy tail walk such as a Lévy walk is characterized by step lengths that follow a heavy-tailed distribution, where the probability of taking a very long step is higher than in a Gaussian distribution. The tails of heavy-tailed distributions decay slower than exponentially, meaning that extreme events (very long steps) occur more frequently than expected under a Gaussian distribution. Some heavy-tailed distributions have infinite variance or even infinite mean, leading to a higher likelihood of extreme events, e.g., bouts of extremism politics.
To test for the presence of Lévy walks biologists and ecologists partition telemetry data into sequences of ‘steps’ (bouts of near-unidirectional travel) and ‘turns’ or ‘stops’ that break directional persistence. If the step lengths are Gaussian distributed then the most commonly occurring steps will make the dominant contribution to the overall movement pattern. But this is not the case for Lévy walks. A defining hallmark of a Lévy walk is step-length distribution with a ‘heavy’ tail that decays more slowly than a Gaussian distribution. In a Lévy walk, the longest step dominates at least for a while, dwarfing the contributions from other steps in the movement pattern.
Linkage to politics: Real or illusion? Maybe real
Never having heard of Lévy walking before I checked it out to see what it is. Being interesting in coming up with a grand unified theory of politics, I checked to see if Lévy walking is relevant to politics. Turns out, it arguably is relevant. Maybe.
For living things, Lévy walking is believed to be the most efficient way to search space and time to find what is needed, e.g., resources such as food and water, a mating partner or room for social change. For some humans, that seems to include an overpowering need to find wealth and/or power.
T cells in the body search for cancer cells by Lévy walking. Sharks look for food hunt the same way. Climate change happens the same way. From what I can tell humans influence climate and that influence can follow a Lévy walk pattern. That strikes me as a rationale to argue that humans truly are playing Russian Roulette with the climate and environment. In politics, one can envision political change as humans collectively searching for the best outcomes. We get a big change (a long step), e.g., Obamacare, often followed by lots of ripples (short steps), states implementing the new law.
The bottom line: In my not quite novice opinion, i.e., possibly wrong, bouts of extremism in politics are inevitable. We cannot avoid it. I therefore conclude that extremism such as djt and MAGA are unpredictable and rare, but nonetheless inevitable in human history and evolution. As far as I can tell, this observation provides no specific way to make it go away or block it. But if you look closely at the first image posted at the top, notice that sometimes long steps are clustered somewhat due to the heavy tail. That implies to me that there really could be a major backlash against the authoritarianism, cruelty and corruption that dominates the long step of djt and MAGAism.
How likely is a major backlash? I do not know. After thinking about politics from a Lévy walk point of view for a while, my intuition is that a backlash (a long step) is more possible than I thought before. But I just don't have a feel for how much more possible. Also, that assumes that a backlash amounts to a long step in a Lévy walk. Short step backlash would probably be insufficient to restore something akin to the pre-djt and MAGA situation.
Reality check
Q: Can humans searching for the best solution for the human condition, e.g., democracy, authoritarianism, honesty, dishonesty, rationality or irrationality, be seen as a form of Levy walking?A: Yes, humans searching for the best solution for the human condition, such as democracy, authoritarianism, honesty, dishonesty, rationality, or irrationality, can indeed be seen as a form of Lévy walking. Here's how this analogy applies:
Short Steps and Frequent Adjustments: Incremental Changes: Much like the short steps in a Lévy walk, human societies often make incremental changes to their political, social, and economic systems. These adjustments can be seen in policy reforms, shifts in public opinion, or changes in leadership, reflecting the frequent, small steps of a Lévy walk.Long Steps and Significant Shifts: Major Political Reforms: Occasionally, there are significant shifts in political systems or ideologies, representing the long steps in a Lévy walk. Examples include the transition from authoritarianism to democracy, the rise of social movements, or the adoption of new economic models.Fractal Patterns and Complexity: Fractal Nature of Political Discourse: The fractal pattern of Lévy walks, where the movement looks similar at different scales, can be seen in the complexity of political discourse. Political debates, policy discussions, and public opinion often exhibit self-similarity, where the same themes and arguments recur at different levels of detail.
Oh yeah, forgot about the fractal pattern thingy. A Lévy walk fractal pattern is a random movement pattern with a heavy-tailed distribution of step lengths. It amounts to a self-similar fractal structure where the pattern appears similar at different scales. Thus when one zooms in on any part of the walk, one sees a similar pattern of short bursts interspersed with occasional long jumps. Boffins believe that kind of movement is ideal for efficient searching in complex environments. This pattern is often observed in animal foraging behavior. Presumably it applies to politics too (humans foraging for whatever drives them).
Lévy flight is a special class of movement characterized by many small steps punctuated by longer relocations. As the patterns show little invariance over a range of different scales, the processes associated with these movements are closely linked with fractal geometry.
