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Mathematics (06/22/2020)

Mathematics is a language for describing reality, and like any language, one is not limited in what they can express through it. One may be suprised to find that there are no "problems" within mathematics, only questions and statements. When viewed in this manner, equations become like lines of poetry. The more they correspond to something meaningful, the more emotionally evocative they might be perceived.

It is unfortunate that the only emotions evoked by mathematics for many is a sense of displeasure or apathy. This is understandable. When one is forced to study something without being given reasons as to why, or it is presented in a language that one cannot easily follow, how can they ever learn to enjoy it? Let's try a different way of learning for a moment...

We can often rearrange the words in a statement to say the same thing in a slightly different way. For example, we could say:

"The dog and cat eat food in the morning."
or
"In the morning, the dog and cat eat food."

The overall meaning of the statement has not changed, and thanks to grammar, the message is clearly conveyed in either instance.

Now, if an equation is a statement, then the "nouns" and "verbs" of this statement would be the numbers and mathematical operations (like addition, subtraction, multiplication, division, and so on). We can also rearrange equations without changing their general meaning. For example:

2 + 3 = 5
3 + 2 = 5
5 - 3 = 2
5 - 2 = 3

This is essentially what "Algebra" is! It is a set of grammar-like rules that helps us to rearrange equations while keeping their meaning consistent. Again, not a problem in sight. But why would we want to do this?

Putting a familar statement into different words can sometimes help us to find new meanings or to communicate something more subtle. Are we emphasizing the fact that it is the dog and cat that are doing the eating, or the fact that they both eat in the morning?

Some music:
Glass Hammer - So Close, So Far

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