Yeah, I've covered this topic before... But I thought I'd have another go at it...

The premise I'm suggesting is that there is no negative one, and hence no negative anything!

The use of the '-' sign is simply a shortcut.

It simplifies the processing equations, and concepts, but...

...I believe it creates a small misunderstanding...

I shall explain...

Basically with negatives, we're either talking about opposites in cognition, or things that involve the opposite direction...

Black has white...

Up has down...

Wealth has debt...

Hot has cold...

Protons have electrons...

Mountains have canyons...

Just to name a few...

Let's introduce a concept you may be familiar with, either from Physics or Maths (or elsewhere), but for those who don't know, I'll explain it simply...

There are two categories used in looking at entity's qualities, 'scalar' components and 'vector' components.

Scalar implies the magnitude of something.

Vector implies the direction. Typically when you speak of vectors, they also have magnitude, but this is simply it's scalar component.

So I'm travelling from point A to point B. A is 20km West of B.

So the scalar component of the travel is 20km.

The vector component is A is West of B, or B is East of A.

When we talk about negatives we usually use the '-' (minus) sign.

eg. It's -4 degrees outside, or I have -$20 in my bank account, or 1 – 4 = -3.

The first example, negative temperature is a bit easy to reduce to relative comparison. I'll explain.

Some may be familiar with two different ways of expressing temperatures (Fahrenheit, 'F' and Celsius, 'C'

, and some may be familiar with a third (Kelvin, 'K'

.

32 degrees F, is equal to 0 degrees C and 273.15 K...

0 degrees F, is equal to -17.8 degrees C and 255.37 K...

-40 degrees F, is equal to -40 degrees C and 233.15 K ...

So as you can see, one heat is expressed all in non-negative numbers, the next two are split between representations at least one using a negative and another positive.

Is hot truly opposite of cold?

Numerically no...

Heat has no real direction, no directional opposite...

Qualitatively yes, on many counts... But not all, it's scalar value, and it's direction.

The second example is easy... Money...

'Can I have five minus-dollar bills for minus-five-dollar bill?'

Can I have -$20 in my account?

Or, does this just mean I owe the bank money? (rather than they owe me money when I have a positive balance).

Clearly, the scalar amount has nothing to do with negativity. The money is theoretically travelling from the bank to me, rather than from me to the bank (the bank is giving me money, as such).

The third example is a tricky one. We have all done calculations like that in school. Sometimes a hundred or more times over. When you first learnt subtraction what did they say?

Something like 'You have three apples, and you take away two... How many do you have left?' Of, course here makes sense, one apple.

Consider the example given further above...

'You have one banana and you take away four bananas... How many do you have left?'

Where on Earth will you get the other three bananas from?

You can pretty much apply this kind of reasoning to every negative you see out there...

Some tricky ones I've found are, camera film negatives and battery positives and negatives.

The camera film, shows that when you block out light exposing film during development you get a lack of light, which shows up darker colours.

Consider a house with no windows, no light gets in.

Consider another house with lots of windows, lots of light can get in.

Is the no-window house the negative of the window-house?

Batteries polarities are simply based on the flow of electrons. They like to go towards, i.e. from one place to another due to the microscopic makeup of the body.

It really gets back to going from A to B, in regards to the East/West part rather than the 20km.

So scalars can't truly be positive, you can't have negative one of something.

And, vectors simply describe the direction of travel mostly...

How can you have negative one?

The implications here, if the theory stands up, have two immediate forms:-

Perhaps we should only be taught about negatives in the 'correct' context.

Certain studies, like 'Complex numbers' in maths are relatively worthless in regards to the true applications.

What's your view on the subject?

Another apology here for the length of the post...