Reading 2.6: Mathematical communication
When you looked at the title of this reading, did you experience unease? Most people shudder at the thought of dealing with anything mathematical, remembering the torturous lessons at school trying to grapple with calculus, statistics and logic. Yet most of us use mathematical communication all the time. Buying things at your local shop, planning the time it will take to do things during the day, or determining how much petrol to put into your car for a particular journey, all involve mathematical symbols, if only in your head. Another way of distinguishing the way you think and communicate is to differentiate your thoughts in terms of qualification (the way you feel about something) and quantification (measurement).
Mathematics is a wonderful way to record, analyse and communicate measurable information in an accurate and efficient way. A string of eight symbols on your watch, e.g. 18:32:57, will give you precise (to the second!) information. There is no simpler and more precise way in which to coordinate collaborative activities of people. For example, a significant proportion of my time researching Amerindian tribes was spent waiting around for people to turn up for interviews since the most accurate representation of time, without the mathematical precision of a clock, would be vague statements like 'early afternoon'. Thus, you could view mathematics as the language of simplicity, precision and zero emotional content.
But there is an additional aspect to mathematical communication than just hard-nosed precision and logic.
This additional aspect can be seen starkly within the culture of a small isolated Amerindian tribe, the Pirahã, found in the heart of the Amazon. This tribe has no words for numbers. The closest they come to quantifying their surroundings is in terms such as 'small size/amount', 'somewhat larger size/amount', and 'many'. This tribe has developed a culture totally based on the present. They have no sense of their history or future. When their hunt is abundant, they 'store their meat in the belly of their brother'. Everything is consumed immediately and nothing is built for permanence.
When a culture is founded on the principle of immediacy of experience, there is no need for numeracy. It is impossible to consume more than one thing at a time, so differentiating between 'a small amount', 'a larger amount' and 'many' is enough for survival.
Any culture planning for their long-term future requires the precision and logic of mathematics. It is not surprising that mathematics evolved in situations where the environmental conditions presented predictable seasonal scarcity (therefore requiring advanced planning for survival), while at the same time allowing for accumulation (a dry and/or cold season which prevented things from spoiling).
Thus, mathematics is most commonly used to represent amounts, and their rates of change. Most numbers you come across are associated with a unit of measurement (e.g. kilograms; miles; years; decibels; dollars; etc.) or their rates of change (units/time).