What are symbols and why are symbols meaningful to me? One answer might be “the self is not physical, it is symbolic”—Becker.

Mathematics is, I think, a useful means to start an effort for comprehending the nature of symbols.

Mathematical concepts are referred to by symbols, both written and audible. Eighty-five or quatre-vingt-cinq references the same concept as does 85. Common mathematical symbols such as 0, 1,

*i*,

*pi*and

*e*are meaningful because we have become familiar with the concepts that they symbolize when we have studied mathematics in school. Our schools and colleges are interested primarily in helping us use these symbols as an algorithmic means for solving mathematical problems.

I am a retired engineer and I worked constantly for four years in college learning how to

**do**math. Doing math is very important to engineers, understanding math is of little consequence to an engineer’s job performance. I suspect most engineers would be somewhat dumbfounded if they were to be asked ‘do your understand mathematics’.

The degree of meaning that these symbols hold for each of us is dependent upon the relationship we have with the concept. Almost all of us will find that the symbols 1, 2, 3, and 4 are meaningful even before we go to school. Those who have studied math in grade school and high school will find that the other symbols mentioned have a meaning of some dimension.

L&N, Lakoff and Nunez, co-authors of “Where Mathematics Comes From”, tell us that “to comprehend a mathematical symbol is to associate it with a concept—something meaningful in human cognition that is ultimately grounded in experience and created via neural mechanisms.”

At birth an infant has a minimal innate arithmetic ability. This ability to add and subtract small numbers is called subitizing. (I am speaking of a cardinal number—a number that specifies how many objects there are in a collection, don’t confuse this with numeral—a symbol). Many animals display this subitizing ability.

In addition to subitizing the child, while playing with objects, develops other cognitive capacities such as grouping, ordering, pairing, memory, exhaustion-detection, cardinal-number assignment, and independent order.

When a child goes to school the teacher depends upon all of these past experiences as prerequisites for a child to readily comprehend arithmetic.

It is our experience in the world that eventually gives symbols significance. As we get older we travel far from these original experiences that give our world of symbols their meaning. We are constantly adding new worldly experiences to augment this meaning we attach to symbols. I suspect that if we could examine closely one of our concepts of a particular symbol we would find that concept to be as complex and convoluted as is our DNA. If we could trace the historical sequences of the structuring of a particular concept it might be as instructive as is a similar examination of our DNA.

Concepts, i.e. symbols, i.e. abstract ideas, are like a gigantic chemical molecule that continues to grow in size and in complexity as we pass through life.

**The symbol gains grounding from our experiences but the concept also has a great deal that result from our imagination. I think we might say that a symbol is an abstract idea created by experience and imagination, which becomes a significant meaning in our life.**

If such is the case can you comprehend why some people might ‘go bananas’ when the flag is burned?