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

**©M HEMADRI**

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