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:
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".
(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 .........
My health is a function of (related to, depends 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.
