by Milton Dawes

Simply put, mathematics is about relationships. Mathematicians have developed a language of precise relationships, illustrated through their formulas and equations. We live in a world where so far as we have observed, everything is related and everything is experienced as different. Applying “relative invariance under transformation“, (interpreted as “this is like that“), we can learn about relationships in our world by looking at mathematical relationships that seem to match the situation being explored.

For instance there is a relationship between distance traveled, time of travel, and speed of travel. Mathematics provides a relatively simple equation:

distance traveled = average speed multiplied by time of travel

In simpler mathematical terms, d = s x t.

Now you might find it important to compare this formula with an actual driving situation, where variables – including wind, road conditions, weather conditions, drivers’ psycho-physical states, etc. – create difficulties in determining, with mathematical precision, times, distances and speed. But we can get a good approximation by using the formula. Here we have a good example of the map (mathematics equations) not being identical to the driver-road-physical-situations represented.

I believe one reason that mathematics is not more generally applied has to do with a tendency to ‘think’ of mathematics only in terms of numbers, precision, quantification, and so on. We forget that mathematics is also about relationships, relatedness, relationships between relationships, interconnections, dependency (functions), changing relationships (calculus), factors that constitute relationships (variables), structure (order, relationships), asymmetric relationships (order), (graphical, numerical, and other representations (mapping), increase and decrease (addition, subtraction , multiplication, division, etc.) and so on.

In other words, in our education systems, there is not enough emphasis placed on, or not enough value given to, mathematics principles and methods, and relationships between ourselves, mathematics, and our everday situations. We could, for example, relate the numbers one and zero to existence and non-existence. One of anything indicates it exists.

General semantics involves applying the methods of science and mathematics to our everyday living. For instance, if we ‘think’ of things – anything – in terms of the “variable”, we will come to realize that like the mathematical variable that is sometimes a higher value and sometimes a lower value, we should expect things and situations to change. Sometimes this change will occur in the way we like; other times not. Sometimes more than we expect, sometimes less. Sometimes we will observe no significant change. We can expect our moods and ‘feelings’ to vary.

‘Thinking’ in terms of the variable better prepares us to anticipate and manage changes in our lives. This could reduce a great deal of stress in our lives – stress related to our forgetting that thing-processes are not constants. Family, partners, friends, work situations, health, etc., won’t stay the way we found them or the way we expect them to go. ‘Thinking’ in terms of the variable, we would expect variations in our lives, and situations to vary related to different ‘time’, ‘places’, contexts, and so on.

Again in terms of the “variable”, we can ‘think’ of words as “semantic variables”. An awareness of words as semantic variables could help us improve the ways we communicate with each other and ourselves. I would help us minimize and avoid many conflicts by recognizing that we each assign different meaning-values to what hear, read, see, and so on. In terms of spelling, words can be considered “constants”. But in terms of meanings we assign, words represent semantic variables. Words are not identical when we include a reader, a listener, an evaluator. This suggests that we ought to take responsibility for the meanings we give, the values we assign, to what we hear, or read. A word is not its meaning.

The notion of a “function” is another mathematical tool we can apply to our everyday situations. Function in mathematics has to do with “relationships between variables – how a dependent variable changes when related variables change. In a simple equation y=3x, if we change the value of x, then y changes. Y is called the dependent variable, and x the independent variable. In other words the value of y depends on the value we give to x. And in this equation, we can give x any value we choose.

In our everyday living, we do many things that are related to other things – although not as precisely as in mathematics – and we give values, assign meanings, and so on. Our whole living involves relationships. Our successes are a function of our efforts. The way others treat us is a function of how we behave towards them. Meanings, values, significance, understanding, etc., are functions of ‘time’ – more specifically information available at a ‘time’.

It is important to keep in ‘mind’ that with regards to our everyday relationships, unlike mathematical equations, precision is not the important factor-variable here. Important factors involve recognizing relationships, interconnections, and “interdependencies”. An important factor is to be aware that we assign our own individual values to what we see, hear, read, and so on. We could avoid, or better manage many conflicts, by remembering variables and functions.

When we forget that we each assign our own values, we are likely to believe and act as if what we say, believe, know, understand, etc., is identical with what is going on. In terms of the relative invariance principle, this would be like saying that in the equation y=3x, x is identical with y. When we don’t recognize that we assign values, abstract different features, and so on, we tend to relate to each other in potentially conflict-creating two valued terms of right/wrong, good/bad, etc., rather than in terms of different abstraction-selection-exclusion values.

As an exercise in getting a ‘feel’ for functions, complete the following ‘functional’ expressions – again keeping in ‘mind’ that our lives are immeasurably more complex than mathematics, so don’t forget the “etc”.

My health is a function of (related to, depends on) ……..(Include anything you believe contributes to, or is related to, your health. You can do this with any other state, activity, relationship etc.)

Satisfying personal relationships is a function of …….

Success in my job depends on ……..

Good communication involves ……….

Developing skills in applying general-semantics to my everyday living depends on ……..

Benefits I can derive from general semantics depend on ………

In a world where as far as we know everything is related, we can learn a lot about our everyday relationships by studying the approaches of a system that deals specifically with relationships. Variables and functions are only two examples of a vast number of other mathematics approaches we can apply to better understand our everyday relationships. For another example see my article An Approach to Everyday Living – A Note Regarding the Calculus.