## Friday, 30 March 2018

### Ergodicity and its application to organisational management

It is extremely interesting the link between human biology, mathematics and management.

It is often true that poor performers continue to perform poorly – for instance most hospitals with a high standardised mortality rate continue to have it for very long times, difficult to shift. In case of human body, obese people often continue to be obese. This phenomenon is true for average performers and for high performers as well.

In the human body, this phenomenon is called homeostasis.

Mathematical explanation of performance can partly be understood by the law of large numbers. According to this law, if initial seemingly random results are observed over a longer period of time, they converge to the expected average results i.e. it "guarantees" stable long-term results for the averages of some random events

Often what looks like an improvement or worsening of performance if observed over a period of time essentially reverts to the mean, which means over a period of time performance remains unchanged; this phenomenon is explained by the normal distribution of most random events.

Well, that is how nature works. We can accept that if our organisation (or our health) is a top performing one and so mostly it will stay top performing over longer period of time. What if our organisation was a poor performer; the chances are it will continue to perform poorly; that would not be acceptable for a variety of reasons, especially if our organisation is in the business of healthcare. So when an organisation wants to become better, it embraces change in the hope that change will lead to an improvement. Often this change takes the form and language of transformation, reorganisation, change and other optimism inducing terms.

Here is when the concept of ergodicity becomes useful in leadership and management.

ERGODICITY

Ergodicity is the concept which states that:

·      The time average is the same as the space average
·      A system is Ergodic when the time average is the same as the space average

As an example suppose you’re trying to figure out the most popular park in London is. One method (time average) is to follow one person over a long period of time and see which parks he visits. Alternatively you can obtain a snapshot (spacial/statistical) average by seeing how many people are in a given park at a given point in time. The degree to which the time average equals the spatial average is called ergodicity and when the time and space average are the same then it is ergodic.

Concepts of Ergodicity applied to Organisational Management

Applying this to organisational management:

1)    If you take the whole organisation average on any given day vs whole organisation average over period of time (say 3 months) – if they are the same, then organisation is erogodic

2)  If you take the average of one department on a given day and the average of the whole organisation on the that given day – if they are the same, then organisation could arguably be ergodic but may not be truly so by definition.

3)    If you take the best of one department on a given day vs the best of the whole organisation on on that given day – if they are the same, then the organisation could, arguably, be erogodic but may not be truly by definition.

The three conditions provided above can be simplified into one to arrive at a fourth condition to demonstrate that a system is ergodic (note that conditions 2 & 3 are independent of time and hence alone are not sufficient to prove that a system is ergodic):

4) If you take the whole organisation average on any given day vs the average of one department over a period of time (say 3 months) – if they are the same, then the organisation is erogodic

·      This essentially could mean that a process even if random is or could be, stable
·      This is why organisations do plenty of activity, calling it transformation, change programmes, etc but yet do not improve as it is the nature of systems to show ergodicity.
·      It is okay for good performing organisations that are high performing to be ergodic.

That is very well, but what should organisations do to enable a higher level of performance and results irrespective of whether they are high performing or poor performing organisations do to improve?

Ergodic Transformation

Here is the example from wikipedia

·      if the set is a quantity of hot oatmeal in a bowl, and if a spoon of syrup is dropped into the bowl, then iterations of the inverse of an ergodic transformation of the oatmeal will not allow the syrup to remain in a local subregion of the oatmeal, but will distribute the syrup evenly throughout. At the same time, these iterations will not compress or dilate any portion of the oatmeal: they preserve the measure that is density.

·      Ergodic transformation does a thorough job of ‘stirring’ the system without disturbing the fundamental nature of the system (due to the inverse of ergodic transformation seen in oatmeal example above)

·      This becomes a Measure Preserving Transformation – which means though there has been an addition (in the oatmeal + syrup example) the system remains ergodic (space average = time average)

Ergodic Transformation applied to organisational management

This is good for systems that are already high performing and want to become even higher performing.
For systems and organisations that are poorly performing a measure preserving transformation is of no use; hence the ergodicity of the system must be broken to see if better results can be obtained.

Ergodicity breaking

·      Spontaneous symmetry breaking: This is what wikipedia says “Is a spontaneous process It is a spontaneous process by which a system in a symmetrical state ends up in an asymmetrical state. It thus describes systems where the equations of motion or the Lagrangian obey certain symmetries, but the lowest-energy solutions do not exhibit that symmetry.”

Spontaneous Symmetry Breaking applied to organisational management

My lay application of this to organisational management is that when organisational symmetry breaks spontaneously though the overall organisation would be stable the processes and people within the organisations have changed so much that there could be significant improvement (there may be significant worsening as well, which is what the organisation has to monitor and prevent)

·      Explicit symmetry breaking (https://en.wikipedia.org/wiki/Explicit_symmetry_breaking) : This is what wikipedia states “this term is used in situations where these symmetry-breaking terms are small, so that the symmetry is approximately respected by the theory”

Explicit Symmetry Breaking applied to organisational management

·      By demanding explicit transformation we seem to end up (at least according to mathematical, physics theories) with changes that are very apparent, visible, but it does not transform the whole system. There is obviously cautiousness resulting only in very small changes, subject to resistance, these changes are planned, defined and delivered – yet the organisation does not change

Do we need to have spontaneous symmetry breaking when managing organisations?

·      Not always

·      If you have a high performing stable system you may not want this (you may want explicit symmetry breaking or measure preserving transformation so that you can get improvement without making the system unstable, improvement without the trauma of conventional transformation)

·      Yes – if you have a poor performing organisation you want spontaneous symmetry breaking so that we can have improvement with transformation – there is risk of asymmetry which may be beneficial (explicit symmetry breaking may actually be harmful by ensuring status quo while putting out an image/impression of change/improvement)

In summary

Ergodicity could be a useful principle when applied to operational management. Organisations, their systems and people have their own stability irrespective of whether they are high or low performing. To improve the performance of an organisation or to transform an organisation, it may be relevant to consider whether different approaches apply to high and low performing organisations. For high performing organisations it may be relevant to consider the concept of measure preserving transformation where there can be explicit induced changes which are absorbed as a part of good process measures which are maintained as the average increases.  For poorly performing organisations, it may be relevant to consider the concept of spontaneous symmetry breaking where beneficial asymmetry within the organisation is sought out to enable transformation; this means looking for areas within the organisation where people are attempting to or doing things differently and when they are beneficial to capture and systematise them even though the changes may not be compatible to what was externally mandated or top down defined for them; in poor performing organisations demanding explicit changes which are externally mandated or defined top down may result in status quo if lucky or could result in poorer performance making the organisation worse.

PS: Any mathematician, statistician, probability expert or physicist can educate me on this topic, especially enlighten me where I am wrong, I would be very grateful.

Acknowledgement: The above writing was advised and supported by Mr B. Patel