Math Morals (Part 5): Lessons In Equations, Integers, Expressions and More...

Equality vs. Justice: The equal sign '=' shows that both sides of the equation must have the same value. However, we need to recognize that equality is not the same as justice. So for example, if someone has two sons, one is 15 years old and the other is 4 years old, it would be an equal division to give them the same amount to eat. But it would be unjust for the elder one to be given the same little amount as the younger one. This is because the younger one ate to his full while the elder one still remains hungry.

Expressions and Equations: Now let us take a look at the lesson we can derive from the difference between equations and expressions. Expression is a mathematical statement without any comparison. It just states a quantity. Whereas an equation compares two expressions. Therefore, the variables in an expression can take any value, but the value of the variable in an equation must be the one that satisfies the equation to keep both sides equal. Since expressions are written alone, without any comparative statement and equations are written with comparative expressions, therefore, this shows us that when we are alone, we are free to do what we like but when we are with others, we need to make compromises which limit us. So if we work on a project with others, we need to consider their ideas as well, but when we are doing a project by ourselves, we are free to do whatever we like. Another example would be that of living. If we live alone, we can make our own choices, but living with others means to make certain compromises.

Integers and Decimals: Integers are complete whole numbers while decimals contain a fractional part. The difference between integers and decimals simply shows us the beauty of complete things. So for example incomplete projects, incomplete relationships, incomplete ideas etc. all look uglier than their complete forms. Imagine if a painter left his picture half drawn and signs if off. Or imagine if someone reads only half a book. Imagine if half an apple grew on trees?

Like Terms: Combining like terms such as 2x + 2x = 2x(1+1) = 4x, shows us that in order to bring people together, commonalities should be highlighted. Common beliefs bring people together (this is the idea behind interest groups). Why would people go somewhere where they will not find anything interesting or something that intrigues them?

Simplifications: Simplifying mathematical expressions such as saying that 2 + (3^2) - (5*6) = 2+6+(-30) = -26, etc. shows us that in order to reach a simple life, we first need to work hard. It also shows us that in order to understand one concept in a simple way, we first need to learn a lot of other things (the idea of pre-requisites) and then we can easily understand that one concept.

Fractions: In fractions, the more the value of the denominator while the numerator stays the same, the lesser the value of the fraction. This shows us that the more activities we participate in, and the more groups we join, the value of what we have to offer and our productivity goes down. We can only focus on a few things at a time. We can only take on a few activities without losing much value of work. Also we may lose focus on one task by being involved in many.

These were some philosophical insights that I had to offer for now. I strongly believe that science should not be studied alone, but it should be studied alongside philosophy. Science can show us the way the universe works, but we must think about why it works the way it does in order to answer deeper questions about life.