The Math of Work Space – All Nature is based on math – so why not us?

I ended my old life as SVP HR at CIBC – one of Canada’s largest banks. The organization was one of the things I thought about a lot. In traditional HR there is no model for structure other than dogma based on span of control that is itself based on nothing. Over the last 20 years I have been looking for the math that must underpin optimally organized work units – here is some of what I found.

Many of us are starting to see that there is math that underpins human community – The Dunbar Number and related math that defines the hierarchies of trust are gaining credence as being “real“.

I think that they should be: for surely all else in Nature that is about relationships has math? Light, Gravity, Water and Heat etc. So why would there not be Math that supports how Human Relationships work?

I was re-reading my favourite text the other day – Christopher Alexander’s Pattern Language – and I was stunned, but not surprised, to learn that not only do we humans have a gradient of Trust governed by math but that there are limits in the physical space as well beyond which, we fall out of community. Naturally these limits are hardly known, least of all by architects and maybe hardly at all by any of us who wish to design a physical space that promotes a healthy human community.

Alexander brings up this topic in the section on Small Public Squares (Pattern 61). He asks why so many public squares are dead space?

Here is the Space Magic Number #1 – 70.

  • We cannot make out another face much over 70 feet away
  • We cannot hear another person properly over 70 feet away

Any space that exceeds this – Piazza San Marco and Trafalgar are exceptions because they are a nexus in a large city and get filled to the right density – feels un social.

So here is Space Magic Number #2 – 300

  • Any space with more than 300 square feet per person will feel “deserted”
  • So a space with a diameter of 100 feet needs 33 people in it to feel ok
  • So a space with a diameter of 35 feet needs only 4
  • A space with 60 feet needs only 12
  • It’s hard to get 33 or more people into a public space at any one time – it is much easier to get 4

I wonder – do these numbers then tie into what we know about group satisfaction – (Chris Allen)


My bet is that there must be a link between these two sets of numbers.

Forming the best groups in the best spaces will surely have an impact on the power of these groups. This then raises another question. Might getting the group size and the group space optimized have an impact on group power?

Do these numbers have any connection with Adoption?


Might knowing more about ideal groups and ideal spaces address the question that we all have – How can I optimize my power in the world?

Our model until now has been to use money as a substitute for social power.

Are we close now to seeing the Social Power Model? I think so.

In my follow up post to this, I will share a Fractal Model of how we have found social adoption to work in a university setting. If this is Fractal, then the social design we see in a University should match all fields of social groupings.

We may be getting close.