The Language of Mathematics (35): why 2 negatives make a positive
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I knew the following question would be the first place the next phase of The Language of Mathematics series would begin:
"Why is a negative and negative equal a positive?"
It has taken me a long time to reply to this inquiry (the email presented in it's entirety at the end of this article). The reason being is that it required quite a bit of thought since I had never encountered this question before.
After thinking about this for some time I realized that this one question defined a quintessential reason why so many people have struggled in trying to communicate in the language of mathematics.
The Language:
The quick and simple answer to why a negative and a negative makes a positive in the language of mathematics is along the same lines as to why a double negative is a positive in the English language. Let's explore this further so that we can fully understand its implications.
All languages have certain characteristics. Relationships between symbols follow certain rules in presenting information. Mathematics is like any other language, it just happens to be the core, the base language from which all other languages were born.
After doing some research I realized that this one concept has been a major Achilles' heel for many in their development of their abilities to communicate in the language of mathematics. In essence, this one concept is the reason why so many have remained illiterate in this language that has the ability to break all cultural barriers, uniting our global community (more on this later).
To Start:
A negative number does not have a negative connotation; it is just a property. The best way to look at this is to consider a "negative" as a property of a number, not an emotional attachment. Think of it as blue eyes for a person, or their gender, or hair color, or any other feature on a person, an animal or a thing. It is just an observed trait.
Once you begin to think of it this way then things should fall into place. For example, let's define a single person as a negative number, let's say --1. Let's define a married couple as a positive number, let's say +1. Then if a single person and another single person merged, they would become a married couple. Writing this in mathematical terms would be (-1) * (-1) = +1.
Keep in mind that words when translated into the language of mathematics have specific meanings. The word "and" in math is multiplication. The word "with" in general means addition. So if we say a single person came with another single person then they would make two single people: (-1) + (-1) = -2.
This is just one example where the language of mathematics is consistent with the English language. There are many more, infinitely more to be exact, even though we do not really understand the concept of infinity.
Treat Mathematics Like Any Other Language:
It is virtually impossible to learn to communicate in a specific language in one day. It is also impossible to learn a language without knowing the letters/symbols that make up the language. This means that to be able to communicate in any language you must first learn the basic concepts.
In the English language, letters are placed together creating patterns that bring meanings to strings of words. This is exactly would happens in mathematics. Numbers along with symbols are placed together creating patterns that bring meaning to what is presented. What defines the image that has been created, may it be in English or Mathematics, depends on our definition of reality and how well we understand the specific language.
The more you learn, the broader your reality will become, encompassing concepts that will help you understand previous lessons. This means that learning mathematics will take time, just like learning any other language. The amount of time required to learn this language depends on how in-depth you wish to be able to communicate with it.
So the only way to improve your skills is to use what you have learned, just like anything else. This means that doing exercises is crucial for being able to use math, or being able to understand other people when they try to convey a message with it.
Becoming literate in the language of mathematics will help you to understand concepts about our world that you would not have understood before. It has been said that "learning new languages is like sharpening the saw", so just imagine how sharp your saw would be if you learned the core language that all other languages are based on.
It is well worth the effort to learn the language of mathematics; it has the ability to greatly enhance your life.
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