'Magic' Numbers


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20/Aug/2015

When you hear the term 'magic numbers' you might think of numerology, or numbers like three, seven, or thirteen being special. We're using 'magic' here to mean things that function below the conscious level, in your unconscious. This is all with 'Fast'/Type 1 thinking, which is something discussed in more detail, elsewhere.

A very common magic number to do with human thinking is five, plus or minus two. This seems to be the limit of the mind to 'grasp' things. If you're asked to recall a series of unconnected numbers, for example digits of a telephone number, then it can help a lot to break them into smaller groups, each of three to five digits. On a much higher level a manager can effectively manage three to seven people, the limit being how different and complex their tasks are; their 'Span of Control'.

A much less well-known number is two-and-a-half. This is the number of 'levels of abstraction' that the human mind can handle at once. For a practical example you can think about an organisation, where each level does different things, such as a level of workers, a level of managers, and a managing director. If you try and understand all of their activities at the same time you will find that either the bottom, or the top one, becomes a bit unclear.

An interesting number that comes from combining the first, pushed to its limit of seven, and the second, is fifty. You get fifty, for example in an organisational context, by having seven managers, each of which manages seven workers, and a single managing director. This is why companies which grow past a certain staff size need a major reorganisation. Their overall structure can't be grasped, and they need to be broken into smaller units, 'black boxes', the internal details of which are ignored in considering the larger structure.

From a different point of view, you might wonder why some meetings you attend work, and others don't. Part of it is to do with meeting size, and the individuals being able to keep track of the views and requirements of the other individuals there. You can have seven in a, cooperative, working group. Eight, in particular, causes problems. Beyond seven sub-groups form, and individuals appoint themselves leaders of these. Having a good facilitator can help, but if you want the best out of everyone present you either need to add a lot of structure to the meeting, or limit numbers to seven.

A related issue is class size. If there is more than twenty-five in a taught class with a single teacher things start to breakdown. One interpretation is that the teacher can't handle more than five times five relationships, twenty-five, between them and their students, at once. A solution often put forward is to have a 'teaching assistant', however the teacher (and the assistant) have to then manage a complex relationship between each other, as well as the one to their students. So, each has only left four times four 'student' relationships, giving a total of thirty-two. The two not being equal also complicates things.

A far easier number to understand is how many 'customer-facing' staff a business needs, in a single outlet, as a minimum. This is one reason that running a shop, on your own, is very difficult. The number is two-and-a-half, which covers breaks, for meals and biology, sickness, and holidays. If you want a twenty-four-hour operation then that's probably three eight-hour shifts, so six-and-three-halves. With reasonable wages, even without thinking about an 'unsocial hours' premium, this can obviously get quite expensive. The half person is generally someone doing back-office work, the rest of their time.

Going back to that wonderful subject of managing information on a personal basis, have you noticed how you need to work differently when the number of things you're working with increases? Thinking about a list, if there are up to five, maybe seven for simple items, you can grasp the list as a whole, if you're trying to check something. Up to about twenty-five you need to scan the list. For lengths of list up to about a hundred-and-twenty-five you need to have the list ordered in some way, or you will miss things. Beyond that you need sub-lists. Humans can have villages where they know everyone, and their business, up to about a magic number called Dunbar's Number; might that be related?

Numerology on Wikipedia
Span of Control on Wikipedia
Black Box on Wikipedia

Dunbar's Number on Wikipedia

(c) ROMsys Ltd, August 2015, permission given to use for non-profit making purposes

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