An equation for Mobility

Mobility in a space is the ease and freedom to move within it.

Starting with equal mobility

Take two people looking to move in a space. They’re wearing different coloured jumpers (because it would be so awkward if the both ended up wearing the same jumper that day!). For the two people of equal ability in a space, their mobility y is equal:

y = y’
y is the mobility of the person wearing an orange jumper
y’ is the mobility of the person wearing a blue jumper

Blue jumpers get priority

Now, the authority of the space says:

People in blue jumpers now have priority over everyone else. People in orange jumpers should make sure that they’re visible, keep safe and Share The Space. If the people in blue jumpers Don’t See You it might cause some harm to you so be careful.

As a person with a blue jumper, my priority (p’) means I have increased mobility! But alas, the mobility of the person with the orange jumper (y) is down to a fraction of what it was:

y = y’ / p’
p’ is the effect of priority given to the person with mobility y’

One tonne machinery enters the mix

Now the authority of the space says:

People in blue jumpers are now also licensed to operate one tonne machinery in this space (when they are not, they must wear orange jumpers). People in orange jumpers can press a button if they would like to continue on their journey. However, they must wait as we wouldn’t want Traffic to build up for the people in blue jumpers. If there is no button provided, then people in orange jumpers should walk into the space where the machinery is being operated, and Be Seen, because you never know!

Nice one! Now as the person with a blue jumper operating machinery, my mobility has increased again! Due to the laws of physics, with my machinery with a nice bit of mass (m) and an impressive bit of acceleration (a), my mobility will be multiplied! That’s because I now have the ability to kill the person with the orange jumper, so their natural tendencies will be to keep themselves alive. I can assume priority even where I don’t have it, thus multiplying my mobility:

y = y’ / p’ma
Where m is the mass of the vehicle that the person now has with mobility y’ and priority p’. a is its acceleration.

The mass and acceleration of the vehicle, combined with the social contract of agreed priority, effectively reduce the mobility of y to a tiny value, relative to the person with mobility y’. Unfortunately for the person in the orange jumper, their mobility is at a tiny fraction of what it was.

First change: priority

What can we do to help person with mobility y? We could separate the spaces, so that the two people never have to cross paths. But that’s not practical usually for a species confined to the surface of their planet.

The authority of the space says:

People in orange jumpers and people in blue jumpers now have equal priority. It doesn’t matter if you’re in a vehicle or not, you get to go ahead when you want to and others will give way. Junctions will allow the same number of people through in every direction in a given time period, regardless of colour of jumper.

So let’s introduce an equal priority given to the person in an orange jumper:

y = y’p/p’ma
Where p and p’ is the equal priority bestowed upon both people. This is a model, it does not reflect current reality.

Even with equal priority, the mobility of the person in an orange jumper is a fraction of what it was, due to the ability of the mass and acceleration of the other’s machinery to kill them.

Real change: Mobility plans for new tactics

The authority of the space says:

Enough! The mobility of people in blue jumpers is costing too much to others. We all have the right to safe mobility without fear of death, and without priority bestowed to you based on what jumper you chose to wear today. We will redesign points of interaction to give equal priority. We will take engineering, design, social and legal measures to ensure equal priority.

Unfortunately for the person with mobility y’ their mobility is being decreased. But it’s still a large multiple of the mobility with mobility y. so there’s not much reason to worry.

The effect of these measures, or tactics, are introduced to increase increase the mobility of the person with the orange jumper:

y = y’pt/p’ma
Where t are engineering, design, social and legal tactics deployed.

The answer to mobility therefore lies in increasing the priority of p, and implementing tactics. t But those tactics must be so big that they can counter the weight of the laws of physics.

Small change doesn’t help mobility, it must be BIG

The thing about the tactics t is that they need to be BIG! The tactics t need to have the same effect on mobility as the mass times acceleration of the machinery. A parklet here, a widened footpath there, this is simply not enough to effectively balance mobility. The approach must therefore be over-arching, consistent and brave. It needs to feel unreasonable, because normality is unreasonable, and needs a big change to increase mobility.


Thanks to Paul Fitz for making me think about this:

My understanding of his point was that the views on mobility needs to be balanced, yet this didn’t add up for me. If the person with mobility y’ is calling for balance, it’s missing the point of how big tactics t need to be.

I’m not claiming for this to be mathematically true, because I don’t have enough experience in maths to achieve that. In fact, I assume that I’ve made a mistake with the operations and how to represent relations. Contact me with feedback if you see flaws in my assumptions and algebra. Or leave a comment on the tweet.

As you can read from my narrative, I am also biased in favour of increasing y.