Throughout our lives, starting at the earliest times we can recollect, we hear about fairness. Playing fair, not being fair, it’s not fair, that’s fair, all are expressions in life. They’re so completely familiar we don’t even stop to think: What the heck is “fair?”

Any definition involves two parts. We have to refer to the larger set of stuff that contains the word, everything that’s similar and alike. We also have to state specifically what’s unique about the word. What one, single thing makes this thing totally different from all other things.

Fairness is a problem. What is the set of all things that are alike? We might say honesty or justice, but aren’t those two different words similar to fairness? Would fairness be contained within honesty? Suppose we have no honesty anymore; would that totally remove fairness?

On the other hand, fairness is a high-level abstraction. It’s a concept of something, intangible, and not something we perceive with our ears, nose, fingers, or eyes. We see a “set of events” and interpret them, somehow, to be fair or unfair. But does that mean that fairness is some sort of abstract concept open to general interpretation?

More often than not, we think of a fair share or a fair decision. It speaks to some sort of balance. If you invest ten times more money than someone else, a fair share is ten times more than that other person’s. As such, there’s some sort of mathematical aspect to fairness. We don’t really interpret math, equations, and numbers do we?

How about another tough one: equal. All of us learn (somehow) what the equal sign means. We learn what it means that something is the same as, more than, or less than something else. How, exactly, do we learn that?

Although it isn’t a popular discussion, human minds have certain capabilities to make a conceptual leap of cognition. We have certain abilites that allow us to observe a pattern, draw conclusions, and assign words (and meaning to those words) to our observations. Nobody can explicitly teach a child about equal, more than, or less than. All anyone can do is provide many examples. At some point the child draws a conclusion by internal cognitive process.

What’s even more interesting is that certain ages dramatically correlate with our ability to understand equality and difference. We’ve often seen how a toddler will propose that a nickel coin is “more than” a dime coin because the nickel is larger in physical size. Likewise, at a particular age, children will say a tall thin volume of liquid is “more than” a short wide volume, even when they’re measurably the same.

But let’s take a look at music. How do we know that one note is an octave above another? They’re not at all the same, but they sound “as if” they ought to be the same. How do we know when two instruments of entirely different types are playing exactly the same note? Why can we hear harmony, dissonance, and slight wrongness in tuning?

Sounds and music are vibrational frequencies. For most of known history we had no way to actually measure and demonstrate the exact frequency of a sound. Even so, for almost all that history human beings have understood mathematical multiples of a frequency. An octave is such a multiple.

Here too, we see the innate ability of the mind to understand equal to, more than, less than. We also introduce an interesting variant: Somehow, we can sense a balance of division. When something is divided in half, thirds, quarters, eighths, we can sense how closely that division is to mathematically perfect. Many people, including children, can see a difference when two halves aren’t actually equal.

Another interesting capability related to this perception of equal-ness is our perception of symmetry. That includes a sense of balance and proportion. Take a living room wall, hang a string down the middle dividing the wall into two parts. Put up a 24-inch picture on one side, and a 5-inch mirror on the other. Ask just about anyone if the two sides of the room are balanced, and they’ll say no.

I’m not familiar with any studies into this innate capability to grasp “same as,” “different,” “equal to,” “more than,” and “less than.” Yet all of these concepts are fundamental to the comprehension of mathematics. Would we say that people who can discern “equal to” create mathematics on the spur of the moment? Or would we say that mathematics exist and human beings can perceive these relationships.

Fairness is based on our innate sense of balance, set relationships, and mathematical division. We may not know how it works, why it works, whether animals can do it, or anything else about the entire process. But the fact remains that human beings, starting almost from infancy, can directly sense these relationships.

In fact, the whole concept of a “set” relies totally on our sense of relationships. A toddler can distinguish the set of all animals as distinct from the set of all trees. How? Nobody knows; it’s a mystery.

Considering that fairness, which then leads to a sense of equality, inequality, the words equitable and justice, we have a problem. How can someone state by fiat or mandate that something is fair if it isn’t? That’s like saying two halves of a pie are equal when any child can see they’re not.

The unique characteristic of fairness, different from all other mathematical relationships, is that it examines and states a relationship between effort and reward. Effort is a concept of work. Reward is a division of the product of work. Fairness is the relationship between an amount of work, the results of that work, and the *ownership* of those results.

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