Diagram: Path Dependency

Path Dependencydefinition/feature.php

'Path-dependent' systems are ones where the system's history matters - the present state depends upon random factors that governed system unfolding.

Related Ideas and Terms: Arrow of Time Contingency Sensitive to Initial Conditions History Matters


Inherent vs Contingent causality

Why is one academic cited more than another, one song more popular than another, or one city more populated than another? We tend to imagine that the reason must have to do with inherent differences between academics, songs or cities. While this may be the case, the dynamics of complex systems may lead one to doubt such seemingly common-sense assumptions.

We describe complex systems as being non-linear - this means that small changes in the system can have cascading large effects - think the butterfly effect - but what it also implies is that history, in a very real way matters. If we were to play out the identical system with very slight changes, the specific history of each system would play a tangible role in what we perceive to be significant or insignificant.

Think about a cat video going viral. Why this video? Why this particular cat? If on a given day 100 new cat videos are uploaded, what is to say that the one going viral is inherently cuter than the other 99 out there? Perhaps this particular cat video really is more special. But a complexity perspective might counter with the idea of path-dependency: that amongst many potentially viral cat videos, a particular one played  this potentiality out - but this is an accident of a specific historical trajectory, rather than a statement about the quality of the video itself.

Butterfly Effects:

The reason for this returns to the idea of the non-linearity of the system. Suppose we have six cat videos that are of inherently equal entertainment value. All are posted at the same time. We now roll a six sided die to determine which of these gets an initial 'like'.  This initial roll of the die now causes subsequent rolls to be slighted weighted - whatever received an initial 'like' has a fractionally larger chance of being highlighted in subsequent video feeds. Let us assume that subsequent rolls reinforce, in a non-linear manner, the first 'like'. Over time, like begets like, the rich get richer, and we see one video going viral.

If we were to play out the identical scenario in a parallel universe, with the first random toss of the dice falling differently, then an entirely different trajectory would unfold. Such is the notion of 'path-dependency'. Of course, it is normal to assume that given the choice of two pathways into an unknown future,  the path we take matters, and will change outcomes. But in complex systems this constitutes an inherent part of the dynamics, and a 'choice' is not something that one actively elects to make,  as much as something that arises due to random system fluctuations.

Another way to think about this is with regards to the concept of Phase Space. Any complex system has a broad state of potential trajectories (its phase space), and the actualization of any given trajectory is subject to historical conditions. Thus, if we want to understand the dynamics of the system, we should not only attune to the path that actually unfolded - rather we should consider the trajectories of all possible pathways. This is because the actual unfolding of any given pathway within a system is not inherently more important then all of the other pathways that did not happen to unfold.

One of the reasons that computer modeling is popular in understanding complex systems has to do with this notion of phase space and path dependency. A computer model allows us to 'explore the phase space' of a complex system: seeing if system trajectories are inherently stable and repeat themselves consistently, or if they are inherently unstable and might manifest in all kinds of different ways.

Sometimes we can imagine that a system does unfold differently in phase space, but that this unfolding tends towards particular behaviors. We then say that the system has an {{attractor}} HANDLEBAR FAIL. One of the features of complex systems is that they often have multiple attractors, and it is only by allowing the system to unfold that we are able to determine which attractor the system ultimately converges towards. It would be a mistake, however, to grant a particular attractor as being more important than another based only upon one given instance of a system of unfolding.

Another feature of path dependency is that, once a particular path is enacted, it can be very difficult to move the system away from that pathway, even if better alternatives exist.

A great example of path dependency is the battle between VHS and BETA as competing video formats. According to most analysts, BETA was the superior format, but due to factors involving path dependency, VHS was able to take over the market and squeeze out its superior competitor.

Another example is that of the QWERTY key board. While initially a solution to the problem of keys jamming when pressed too quickly on a manual keyboard, the solution actually slows down the process of typing. However, even though we have long since moved to electronic and digital keyboards where jamming is not a factor, we are 'stuck' in the attractor space that is the QWERTY system. This is partially due to the historical trajectory of the system, but also all of the reinforcing feedback that works to maintain QWERTY: once people have learnt to type on one system, it is difficult to instigate change.

An Urban example may also be instructive here: In Holland people bike as a normal mode of transport, in North America they drive. We can make arguments that there are inherent differences in North American and Dutch cultures that create these differences, but a complexity argument might propose, instead, that such differences are due to path-dependency. Perhaps any preferences that the Dutch have for biking are only random. That being said, over time, infrastructure has been created in the Netherlands that incentivizes biking (routes everywhere), and disincentives driving (many streets closed to traffic, lack of parking, inconvenient commutes). In North America, we have created infrastructure that in incentives driving: big streets, huge parking areas close to where we work, and lack of other transport alternatives. We then arrive at a situation where the dutch bike and the north-american drives. But place a North American in Holland and they will soon find themselves happily biking, and place a Dutchman in the USA and they will soon find themselves purchasing a vehicle to drive along with everyone else. Neither driving or biking is inherently 'better' in so far as the commuter is concerned (although there may be more environmental and health benefits associated with one versus the other), but the pathways each country have taken wind up mattering, and reinforcing behaviors through feedback systems.

If we are able to better understand how to break out of ill-suited path-dependency, we may be able to solve a variety of problems that seem to be 'inherent' or 'natural' choices or preferences.

some discussion here about the butterfly effect, and lorenz ... Tie this back to Sensitive to Initial Conditions

 


Photo Credit and Caption: Underwater image of fish in Moofushi Kandu, Maldives, by Bruno de Giusti (via Wikimedia Commons)

Cite this page:

Wohl, S. (2019, 13 November). Path Dependency. Retrieved from https://kapalicarsi.wittmeyer.io/definition/non-linear

Path Dependency was updated November 13th, 2019.


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