All tools have their advantages and disadvantages and for all tools there are times when they are appropriate and times when they are not.  Formal tools are no exception to this and systems of numbers are examples of such formal tools.  Thus there will be occasions where using a number to represent something is helpful and times where it is not.  To use a tool well one needs to understand that tool and, in particular, when it may be inadvisable to use it and what its weaknesses are.

However we are in an age that it obsessed by numbers.  Governments spend large amounts of money training its citizens in how to use numbers and their declarative abstractions (graphs, algebra etc.)  We are surrounded by numbers every day in: the news, whether forecasts, our speedometers and our bank balance.  We are used to using numbers in loose, almost “conversational” ways – as with such concepts as the rate of inflation and our own “IQ”. Numbers have become so famliar that we no more worry about when and why we use them than we do about natural language.  We have lost the warning bells in our head that remind us that we may be using numbers inappropriately.  They have entered (and sometimes dominate) our language of thought.  Computers have exasperbated this trend by making numbers very much easier to store/manipulate/communicate and more seductive by making possible attractive pictures and animations of their patterns.  More subtley, when thought of as calculating machines that can play games with us and simulate the detail of physical systems, they suggest that everything comes down to numbers.

For this reason it is second nature for us to use numbers in our social simulations and we frequently do so without considering the consequences of this choice.  This paper is simply a reminder about numbers: a call to remember that they are just another (formal) tool; it recaps some of the conditions which indicate when a number is applicable and when it might be misleading; it looks at some of the dangers and pitfalls of using numbers; it considers some examples of the use of numbers; and it points out that we now have some viable alternatives to numbers that are not any less formal but which may be often preferable.

So, to be absolutely clear, I am not against numbers per se, merely against their thoughless and inappropriate use.  Numbers are undeniably extremely useful for many purposes, including as language of thought – just not for every purpose and in every domain.  Also, to be absolutely clear, I do not think there is any system of representation that is superior to the others – including: logic; programs; natural language or neural networks – but that different representations will be more useful (and less misleading) in different circumstances and for different purposes.  Some of my best friends are numbers.