The Language of Mathematics (35): why 2 negatives make a positive

http://www.chycho.com/?q=node/1762

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.

The Language of Mathematics: Table of Contents
http://www.chycho.com/?q=math_Table_Contents

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[ofschorchedpumpkins]

What you said about math being like languge using a double negative, blew my fucking mind.

[chychochycho]

Good, because it blew my mind when i realized it as well.

Peace.

[rccaulfield]

Sorry for going back to this but if the fundamentals aren't right in my head i can't respect the applied areas- What observations led to this operation being formed then? For example in terms of debt if you owe 3 dollars to someone(thats -3) and owe 3 other people 3 dollars, then isn't your debt 9 dollars(-9) not plus 9 i mean they would owe you 3 each in that case? I'm not talking about adding up your debt here. I'm talking about multiplying your debt by 3 debts? Robert Robert

[chychochycho]

Sure, 3 times -3 would be -9.

Don't let this confuse you, just treat it as you would in English, a double negative is positive. 

[Kevo216666]

I'm pretty sure you can prove anything when you substitute one concept for another. You're either a brilliant or this is bullshit. I'm not sure.

[chychochycho]

Well, it is just an inherent property of the language, and yes, you are correct, you can prove anything this way. This video is not for people who are well versed in the language of math, it's for people who are having a hard time with it.

The simplest answer to this question is given at 1:47 into the video. Just like the English language, where a double negative makes a positive, so it is with math. It's really that simple... the rest of the video is a song and a dance.

[kingofdice66]

@Kevo216666 i assure you this is bullshit and has nothing to do with math, that's not a mathematical proof, this is very confusing

[thetableswillturn]

Single and couple here represents x and x^2 so when you take x multiply by another x you get x^2 You've just replaced x and x^2 with single and couple in order to fit your example but the overall is example is different to what is actually happening when 2 negatives are multiplied together.

[thetableswillturn]

2 ex singles can be thought of as -x^2 that's true, but, couple and single are diferent things. You may think i've misconstrued something here but i haven't. Example -3 x (-3) is really equal to -3 on a number line but it's absolute value is a positive 9 (+9) because what's really happening is it goes from 0 to -3 then back to 0 then back to -3, but has moved 9 places. This is what MUST really be meant by - x - = + Which is therefore an incomplete explanation. Should be - x - = + absolute value

[thetableswillturn]

Absolute value is different from representation

[hazloasi]

3 OF 3 While standing there you can be facing left or right or you can move forward or backwards. Lets define that facing right is positive and moving forward is also positive, while facing left is negative and moving backwards is also negative. If I tell you TO place yourself at the zero mark, face left, and move backwards 3 steps. What will happen? You will end up 3 units to the right, two negative actions resulting in a positive. Hope it helps!