Less than zero percent?

@Kilroy70
I remember the name now, virtual particles.

https://en.wikipedia.org/wiki/Virtual_particle

@sonhouse said
@vivify
Of course there can be either when it comes to money, you buy at 100, sell at 50, you have a minus 50% profit, or a 50% loss, take your pick.
Or you buy at 100, sell at 200, 200% gain, X2,

Right. But can you *end up* at a percentage that is less than zero? Obviously you can subtract 10 percent from a whole; but can you actually *arrive* at a total remaining percentage that equals a negative?

@vivify said
Somehow I missed this post.

So by the very definition of percentages being out of 100, the idea of a negative percentage is not possible, correct?

What about the fact that percentages can be over 100 percent? Like if business had a 200 percent increase in profits? If percentages can exceed 100 percent maybe they can be lower than zero? Unless I'm missing something you can clear up.

A percentage is just a number and can therefore have any value. Negative a million percent for example is simple -1,000,000% = -1,000,000/100 = -10,000

When you talk about chances of something happening you are in the realm of probability. In math probability ranges from 0 to 1, but that is the same as 0%-100%. So the fact that it's a percentage is irrelevant.

Try to separate in your mind the idea of percentages and the idea of the chance of something happening because those are two completely independent concepts. Any example with numbers can be converted into percents.

Let's say Sumo Sam is trying to gain weight. His weight is only 200 lbs. He eats his fatty sumo rice (or whatever it is they eat) and a month later weighs himself again. He is 190 lbs!

Sumo Sam's weight increase is -5%.

@vivify said
Right. But can you *end up* at a percentage that is less than zero? Obviously you can subtract 10 percent from a whole; but can you actually *arrive* at a total remaining percentage that equals a negative?

Depends on what you're analyzing. No, you cannot have negative 50% of a cake, but it has nothing to do with the percents. It's just you cannot have negative cake at all!

But if you're measuring something that can go negative, like altitude above sea level, then whether you measure the negative as just a number (500 meters) or a percentage (50% of a kilometer) it's still possible to be negative. -500 m above sea level is 500 m deep in the water, which is also -50% of a km above sea level, or 50% of a km down into the water.

Can you have a negative number? What is an example of a negative number? This is basically the same question you are asking. What does -3 look like? Can you have -3 pairs of shoes? No...but if a shoe store lists on it's inventory that it has changed by -3 shoes because they were sold the number has real meaning.

Thanks, ATY. I appreciate you taking the time to clear that up.

@AThousandYoung
Hey, nice poem. Eldorado.

@vivify said
Can a percentage be in the negatives, like a -5% chance of something happening? Can a percentage of a total be in the negatives?

If negative fractions exist, doesn't this imply that negative percentages also exist?

One can speak of a "-5% increase," which means a 5% decrease. But saying an event has a -5% chance of occurring has no meaning. A 0% chance of an event occurring means the event cannot occur.

@soothfast said
One can speak of a "-5% increase," which means a 5% decrease. But saying an event has a -5% chance of occurring has no meaning. A 0% chance of an event occurring means the event cannot occur.

It's exactly right, like 5 - 3 is the same as saying 5 + -3. Otherwise, ATY got it right.



But also, saying something has a -5% chance of occurring is just like saying that it has a 5% chance of NOT occurring. You're just moving the negative.

@athousandyoung said
In fact temperature cannot equal zero either.

Maybe on the Kelvin scale.

@vivify said
Somehow I missed this post.

So by the very definition of percentages being out of 100, the idea of a negative percentage is not possible, correct?

What about the fact that percentages can be over 100 percent? Like if business had a 200 percent increase in profits? If percentages can exceed 100 percent maybe they can be lower than zero? Unless I'm missing something you can clear up.

+ and - are just direction, man. They have no value, they just tell you which way to go.

@suzianne said
But also, saying something has a -5% chance of occurring is just like saying that it has a 5% chance of NOT occurring. You're just moving the negative.

That is a curious interpretation that I, as a mathematician, have never heard of. So a -100% chance of something occurring means a 100% chance of not occurring, which in turn means a 0% chance of occurring. You've inverted the entire scale, but for what purpose?

One could define negative probabilities in this way, perhaps, but the standard definition of the probability P of an event E restricts the possible values of P to between 0 and 1. Multiply by 100 to get a percentage.

@suzianne said
+ and - are just direction, man. They have no value, they just tell you which way to go.

Not surprisingly, in hindsight, there is a twig in the tree of mathematics that plays with negative probabilities, though it looks like physicists were the main driver behind it:

https://en.wikipedia.org/wiki/Negative_probability

Physicists sometimes talk about "negative mass" and "negative energy," so I guess I should have expected this.

EDIT: You can read the article and let me know if the physicists' notion of negative probability jibes with yours!

@soothfast said
That is a curious interpretation that I, as a mathematician, have never heard of. So a -100% chance of something occurring means a 100% chance of not occurring, which in turn means a 0% chance of occurring. You've inverted the entire scale, but for what purpose?

One could define negative probabilities in this way, perhaps, but the standard definition of the prob ...[text shortened]... event E restricts the possible values of P to between 0 and 1. Multiply by 100 to get a percentage.

But, see, a -100% chance of occurring and a 100% chance of not occurring is the same thing, resulting in a 0% chance of occurring.

Somehow the circle come back around on itself, to where -100% equals 0%.

But, a 50% chance of occurring is also a 50% chance of not occurring.

Perhaps I misspoke (I was always crap at math). Maybe a 5% chance of occurring equals a 95% chance of not occurring. That sounds more like it. The numbers have to equal 100, so you may be right, that -% of something occurring is nonsense.

I was trying to move beyond practical into theoretical, and it just didn't work. 🙂

@soothfast said
Not surprisingly, in hindsight, there is a twig in the tree of mathematics that plays with negative probabilities, though it looks like physicists were the main driver behind it:

https://en.wikipedia.org/wiki/Negative_probability

Physicists sometimes talk about "negative mass" and "negative energy," so I guess I should have expected this.

EDIT: You can read the article and let me know if the physicists' notion of negative probability jibes with yours!

It might work, but I lack the math knowledge to even ascertain if that's possible.

Your Wiki link is beyond my pay grade, although the idea of + versus - in the quadratic in the denominator is interesting, but that example is from physics, so slightly easier for me to begin to "get it".

@soothfast said
Not surprisingly, in hindsight, there is a twig in the tree of mathematics that plays with negative probabilities, though it looks like physicists were the main driver behind it:

https://en.wikipedia.org/wiki/Negative_probability

Though, from that page it seems that you can't have negative probabilities after all, only negative quasi-probabilities.

Remains the fact that it's not the percentage which is the problem, it's the probability. Doesn't matter if you express the probability out of 100% or out of 1.0, it can't go below zero. And on the other hand, doesn't matter if you measure growth in cm or in % of the original, it can go negative.