Viscosity — looking on the bright side of life!

I wish to share an analogy that illustrates two profound principles about thought in general.  This analogy will be about something called “Viscosity” —  in this article we will invent a new sense of the word “Viscosity” which corresponds with the concept which will herein be articulated.

But before explaining viscosity or the analogy, I want to briefly mention these two principles of thought, particularly thought concerning a specific topic, these are:

  1. There always exists a deeper level at which you can think about something, deeper than the way you are currently thinking about it, and;
  2. There always exists something positive about everything you are thinking about (even of course, negative things), often to be found in point #1, by thinking about it on a deeper level.

To be clear, by my point #2 I do not mean a facetious positive way of thinking about something — I mean a genuinely true and positive way of thinking about things, even things as severe and horrible as robbery, rape, and murder. However, the analogy I will draw is much less serious than those cases!

A story of aggressive drivers — the “initial thought”

Well, let’s start our story with something that I assume most people in the world hate: Aggressive drivers. Think about it seriously; when was the last time you were filled with glee when someone rudely cut in front of you, destroying your healthy following distance and making you slam on your brakes?  I think aggressive drivers who are always cutting in and out of traffic, always just trying to get one step ahead of everyone certainly frustrate most people who encounter them. Here is something quite negative, “Aggressive drivers”, because we all know they reduce safety and put peoples lives in danger. I know of no single individual who has positive feelings towards them.

Now, what I just wrote in that paragraph is what I call “Initial thought“, or the first level of thinking about a thing. Quite obviously, I am not trying to prove to everyone that aggressive drivers are GOOD. Of course they are bad and of course they are dangerous, however what I want to illustrate is that

  1. There is a deeper level at which we could think of aggressive drivers and
  2. There is something positive about them.

Now that we have concluded that aggressive drivers are negative, what is the deeper level at which we could think of them?

Fluid Flow

Such is life — sometimes we build models of things in order to better understand and manipulate them. Often we use mathematics and physics to model things or draw parallels. Herein I will describe how traffic can be modelled as fluid flow.

Think of a fluid, like water, travelling through a complex system of pipes. Now, add to it that pressure applied to that water in different directions and at different points in this pipe system. Now picture valves at different points of the system allowing the flow of water in particular directions only at specific times. The picture that you are starting to see is actually one of the models used to understand traffic flow, namely traffic behaves in many ways as a fluid, for example a group at the university of Alberta have done research modelling this mathematically.

Viscosity

One of the properties of fluids is called “Viscosity”, viscosity is defined as “Resistance of a liquid to shear forces (and hence to flow)” There is a direct relationship  between what is called “shear forces” and the ability of a liquid to flow. So what are shear forces? Perhaps it’s time to draw a simple picture.

As you can see from my simple diagram, a shear force is a force applied to an object that tends to bend it in the direction shown. If this object were malleable, after the shear force is applied it would look more like this:

 

So how does that work in liquids? Well if you can imagine in the liquids small pieces of the substance trying to push their way past each other. For example, in honey which you are pouring out at a spout of some kind, the little pieces of honey are all trying to slip past each other because of the force of your pouring them. But because honey has a high viscosity (I.E A high resistance to shear force) it struggles to come out at any rapid pace. In simpler words viscosity is the “thickness” of the fluid. Time for another crude diagram:

 

Honestly I can’t find a single diagram of something so simple online, they are all so complicated! This picture is definitely an approximation, but it illustrates the point.  The black shape is the spout of the container, the red stripes are representations (WAY too large) of “pieces” of honey (perhaps the word “fibers” would make you think of the shape I am thinking of) as they exit the container because the end is smaller than the beginning they are forced to interact with each other in a shear kind of motion, and the blue arrows represent the shear forces between these pieces. Again this scale is very poor, the scale at which this shear force happens is much smaller, but the idea is the same. Water has a much lower viscosity and thus pours out more rapidly, in simple terms because the individual “pieces” are able to flow past each other much more easily.

Viscosity in Traffic

So now how does this grand analogy come together?

Well, as something modeled as a fluid, traffic thus has fluid like properties, one of which is viscosity. In the previously cited article they said “In real traffic flow, a small viscosity is present”. If you think about cars on a road with over two lanes, you could imagine their “difficulty” of passing each other as viscosity. But you’re thinking “cars in the other lane don’t affect how I drive in my lane, they can’t slow me down or resist my movement” — correct to an extent, but still not entirely true.

Firstly, if one lane were at a standstill and your lane (next to it) were travelling very quickly, it is likely that you would slow down for safety reasons, this could be thought of as psychological viscosity. It’s true, the ways humans think affects the properties of the fluid flow based on their driving habits. Anyway, secondly and more importantly in my analogy, not all roads are straight and have two lanes! Because of traffic lights, turning intersections and expansions and contractions in the size of the road, this variable of viscosity is indeed a factor of the flow of traffic.

Now what does this have to do with aggressive drivers? You see aggressive drivers are always trying to get ahead of others and are impatient. They will cut in and out of lanes to get further, we usually think that they are selfish, of course mostly they are. However, do you realise that if everyone tried to get to their destination faster the overall flow of traffic would improve? Indeed the way that aggressive drivers cut in and out of lanes and especially overtake others more easily and quickly could be interpreted as their acting to reduce the viscosity of traffic, although that is not their intention.

Now that I have explained the principle, let me illustrate with another picture: keep in mind I drive on the left hand side of the road!

traffic

In this diagram, there is a two lane road heading upwards, I will explain what each symbol represents.

  • A) A car trying to turn right but who is waiting because of oncoming traffic
  • B) Cars behind car A, who are obstructed because of car A
  • C) Traffic lights indicating that you can go forward but not yet go left
  • D) Oncoming traffic
  • E) A car trying to turn left but who is waiting for the traffic light to indicate that it can.

The black arrows I’ve drawn represent the “flow” of traffic around these two obstacles, car A and car E, both of whom are blocking one of the two lanes but at different points.

Now imagine two scenarios:

Scenario #1 — low viscosity extreme

All B drivers drive very defensively, rather waiting behind an obstacle car than overtaking it; What will happen is cars will pile up behind car A and car E and if no one overtakes then there is no flow of traffic. This represents a scenario where the viscosity is basically 100%, meaning no shear actions / flow of traffic is allowed, this would lead to a standstill and worsen traffic with cars lining up behind the obstacles in both lanes causing a backup.

Scenario #2 — more aggressive driving, decreased viscosity

Now scenario #2, all B drivers are more aggressive and want to get past those obstacles as quickly as possible. What will happen is that both of the lanes behind car A will merge into one lane just before the point of car A and pass next to car A in the left hand lane. Then, seeing car E ahead with its indicators and the traffic light, they will then flow into the right hand lane and pass car E as well; thus merging both incoming lanes into one virtual outgoing lane, which although is not optimal (optimally both lanes flow) it is definitely faster flowing than a standstill. In this scenario the aggressiveness and impatience of the drivers represents a dramatic decrease of viscosity of the traffic, since shear forces can be imagined as the ability of cars to rapidly pass one another when they are next to each other and especially flow past blockages.

Of course, neither of these scenarios would happen exactly as described since not all drivers are on either extreme, however if more of them are more aggressively inclined in this situation the traffic would flow faster for everyone else, especially those waiting behind this situation.

Hence this faster driving behaviour actually serves to relieve traffic!

Did you ever think of it that way before?

Next time people try to cut in front of you just think….

“Viscosity”….

And work hard to see the positive in every situation!

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