Q: Is there a real life example where two negatives make a positive?

Physicist: Although the laws of the universe are very absolute, the equations and terms we use are generally easy to rewrite and rephrase.  For example: it seems natural to describe the motion of a ball in terms of its altitude.  In this case gravity is negative (it decreases altitude).  But if instead you describe the motion of the ball in terms of “distance fallen”, then gravity becomes positive.

The classic example of the “arbitrarity of sign” is Ben Franklin’s horrifying mistake.  At the time that he was working it was impossible to tell where charge came from (in terms of electrons and protons), so he arbitrarily chose negative to be what we now know is the charge on electrons, and positive to be the charge on protons.  It makes no difference to the physical laws, which only care that the charges are different.  But it is annoying to electrical engineers who are haunted by the fact that “current”, which is defined as the flow of positive charge, actually points in the opposite direction in which the electrons move.

The point is this: I can’t think of any example of putting together two negative things and getting a positive thing, that couldn’t equally well be thought of as putting together to negative things and getting another negative thing.  For example: the force between two negative charges is repulsive.  So if you want to define “apart” as positive then two negatives (charges) makes a positive (force).  But if you define “together” as positive then two negatives make a negative.

Feynman summed up the general feeling in physics toward sign error (flipping positive/negative) when he said “If the sign is wrong, change it.”  So if, after lengthy calculation, you find that the moon is  – 238857 miles away, don’t stress about it.

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7 Responses to Q: Is there a real life example where two negatives make a positive?

  1. The Uncertain One says:

    I can think of two examples.

    Alice knew that there were 50 apples in the basket on the table, but now it looks like there are fewer apples. What happened?

    Alice asked Mary. Mary said that Bob said that he would give three apples from the basket to each of his friends in the neighborhood. “How many friends does Bob have in the neighborhood?,” Alice asked. “Nine,” Mary replied.

    “So there must be 50 + ( -3 x 9 ) = 23 apples in the basket”, thought Alice. In this calculation, the “3” is negative because every time Bob gave apples to a friend, there were 3 LESS apples in the basket.

    A little later, Bob came by and clarified that, of the nine friends invited, only five actually came.

    How can Alice know how many apples are in the basket, now that she has the correct information?

    Well, she can start from scratch and re-calculate:

    There must be 50 + ( -3 x 5 ) = 35 apples in the

    Or she can trace her steps back from the previous calculation:

    I had calculated that there were 23 apples, based on
    false data, but later on I knew that the basket had
    3 LESS apples, four LESS times, so there must be
    23 + ( -3 x -4 ) = 35 apples in the basket, right

    The other example goes like this…

    I’m on the road, halfway between the city and the beach. I’m driving towards the beach, which is positive for me, because I love surfing.

    As I stop the car, I can think of two ways of going back to the city, which is negative for me because I hate pollution.

    One way is to change gears so that my car moves back, instead of forward. This way, I would drive in reverse all the way back to the city, which is a negative.

    Another way is to turn the car around and drive forward. Since the front of the car is aimed at the city, driving forward would now get me back, which is a negative.

    The first action would give me a negative and the second action would also give me a negative. What if I applied both? What would happen?

    I was driving towards the beach and I stopped the car. Now I turn it around, towards the city, but I change gears because I don’t want to drive forward. I want to drive back because that would give me a positive!

    I tried to explain this to the officer, but he insisted on giving me a ticket and a warning.

  2. Killian says:

    Think of a video displaying an object in motion. Say the object is going 5 mph.

    Then if you fast-forward the video speed 2x, it will appear to be going 10 mph.

    If you rewind it (which can be thought of as fast-forwarding it (-1)x), it will appear to be going -5 mph.

    Now take another video, of an object going backwards at 5 mph, so its speed can be described as -5 mph.

    Then if you rewind that, you get an object going forward at 5 mph. -5*-1 = 5.

  3. sandeej says:

    It just plain and simple is a created piece of fabrication to force a theory to work. Another case of number manipulation. It’s actually even worse than that because it was created to make someone’s idea work.

    Many people can accept it because they are told that, but NObody, ever has been able to give me a real logical and correct theory to prove it. And it continues to be forced down the throats of every math student.

    Just doesn’t! I asked my professor today, hoping she could finally give me the answer…her face went totally blank. She didn’t have an answer. She finally told me that it is just one of those things that you just do…

  4. Stan says:



    Two negatives make a possitive and it is not a fabrication, but logical. If two possitive make a possitive, then two negative shold also make possitive. Fabrication is if two possitive or two negative make a negative (i for example).

    About the real life example – there are actually no negatives in the real life. Things could be negative only compared to something else (or another their state).

  5. The Observer says:

    Somebody annoys me (Negative), I sock him/her in the sensitive bits (Negative) : I feel better about myself and they feel like crap physically. (Positive) That’s math for ya!

  6. Strategies of war says:

    The enemy (-) of (*) my enemy (-) is my friend (+).
    The friend (+) of (*) my enemy (-) is my enemy (-).
    The enemy (-) of (*) my friend (+) is my enemy (-).
    The friend (+) of (*) my friend (+) is my friend (+).

  7. Nagarajan says:

    Hydrogen is flammable gas as well as oxygen.
    But when they both combine together they become water which is an extinguisher.
    So consider, these two items having a negative property becomes a positive property when united

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