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Understanding 1+1=2

May 29, 2015

All a senior manager really needs to know, I sometimes say to grab attention, is to understand the following:

1+1 = 2

The simplest arithmetical equation. Surely this is totally obvious. But there is, I am told, a Sufi saying along the lines of:

Because you understand ‘1’ you think you understand ‘2’ because 1+1=2. But first you have to understand ‘+’.

In other words, knowing about the components of a system is not enough – you need to know about the nature of the interactions between them. Within a systems thinking context, with its focus on components, interactions and boundaries, this is obvious. But in general discourse, it is too easy to accumulate facts without understanding the linkages that lead to wisdom. This can be the cause, for instance, of a lot of mid-thesis angst, where a doctoral student has completed the collection of evidence, thinking the job is mostly done, but then needs to put it all together and work out what it all means. The evidence may have disproved the initial hypothesis, but does not speak for itself in suggesting a new one. The instances do not necessarily tell us about the patterns or connections.

Similarly, in investigations or evaluations of what is going on in organisations, or in society, learning about several individual instances of success or failure is not enough. Case study analysis is in itself a significant discipline in trying to extract commonalities, differences and themes from individual cases. But this type of analysis does not go to synthesising the meaning.

There is a further dimension to this: we also need to understand =. There are at least two possibilities for the meaning of =. One is that of definition, the other of calculation. We could define 2 as the sum of 1 and 1. Or, more interestingly, we can take 2 as an independent construct, and try to show that 1+1 is formally identical to 2. In mathematical terms, this is not straightforward. gives a 53-line proof, and refers to Russell and Whitehead taking about 360 pages in Principia Mathematica to reach this conclusion. Part of the reason for the length of the proof is that they do need to consider the formal meaning of =.

In the organisational analogue, we need to understand how and  how reliably the components and the interaction (the various 1’s and the +) lead to the final result. Does = mean always leads to?  Usually leads to? Leads to in certain defined conditions? For example, let’s say that we understand what is going on in the various divisions of a company. We also understand the interactions between them – the informal and formal communications, the hierarchies, the controls and whether these are working or not. That is, in itself, a tall order for senior management – to get across the 1’s and the +. But the manner in which this assemblage leads to overall company success or failure is often not clear, and the point of intervention to fix any problems is likewise often hidden.

So if you really understand 1+1=2, you’ve got it made.

© Numerical Advantage 2015


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