Do Negatives Exist?

[emperor_of_localgroup]

I'm not sure if this topic had been discussed here in the past.

But it occurred to me negatives do not occur in nature. It is us who
place a reference point relative to which one is opposite to another.
We use negatives to describe this opposite nature of things.
In other words, there is no such thing as negative temperatures, negative times,
negative distances, negative charges, etc. They are sometimes negative because of
our choice of reference points.

What gets me more is treating atomic energy as negative, and gravitational
potentials as negative. All are positive, why are we confusing ourselves treating them as negative quantities?

Finally, it's not only time that is unidirectional, everything in the universe, IMHO, are unidirectional.

Am I wrong in my thought?

 

[MeteorWayne]

Yes you are

Sorry

 

[Shpaget]

What about protons and electrons?
They obviously have opposite charges. You can choose not to call one of them negative, but the fact is, that no matter how you put it, it will be the opposite of the other.

 

[Jerromy]

Might be a little confusing if you try to determine which end of a battery is positive and which end is double positive. There are some scales which are based in the positive direction exclusively (Kelvin having absolute 0 as the "coldest temperature possible" to our knowledge) but there are other scales of judgement (atomic polarity of valance) where some items have a natural positive excess of electrons and others have a negative void which needs to be filled by other atoms excesses.

There are many references to physics, the forum you have posted in, where representation of a negative value would have no meaningful place. Negative mass or negative velocity would be absurd, but there are plenty of examples where polarity has logical implication.

 

[Kessy]

Well, at the risk of venturing too far into philosophy (and probably annoying any math majors reading this - sorry guys. ) I'm going to share my opinions on the subject.

I've heard quite a few people be downright poetical about how amazing it is that mathematics seems to describe our universe so beautifully. My opinion is that math does that because it was designed to describe our universe. I think that math is fundamentally a system of rules for manipulating symbolic values representing various aspects of the world we experience. From a strictly logical standpoint, it's rules are somewhat arbitrary - there's no reason that one plus one *has* to equal two, but we say it does because that reflects the reality we live in. I think it's in principle entirely possible to construct a completely logical (that is, self consistent) mathematical system that does not reflect reality at all.

So when it comes to the question of negatives, what you have to remember is that a negative, like all mathematical concepts is a symbol, and the question you have to answer is what does the symbol represent? Sometimes it does represent position relative to an arbitrary point of reference. Sometimes it represents an inherent oppositeness to something, such as with electric charge. Sometimes it represents a reversal of direction. (Yes, Jeremy, there is such a thing as negative velocity - it just means velocity in the direction opposite of what you've defined as positive.) And I'm sure it can represent many other things in other situations.

 

[origin]

there's no reason that one plus one *has* to equal two, but we say it does because that reflects the reality we live in.

Huh??? I would say the fact that it reflects reality is pretty damn good reason to say 1 + 1 = 2

 

[darkmatter4brains]

there's no reason that one plus one *has* to equal two, but we say it does because that reflects the reality we live in.

Huh??? I would say the fact that it reflects reality is pretty damn good reason to say 1 + 1 = 2

I still remember when I was sitting in the physics club room at my college one day, a couple of guys that were double majoring in math were working some math problems on the board. They kept saying stuff like, "well, in that domain 2+2 would equal 5, but we need it to equal 7"

To this day, I still wonder what math class they were taking, or if they were just nuts :lol:

EDIT: If multiverses do exist, it is hypothesized that the laws of physics may change from Universe to the next. If so, it stands to reason that math may fundamentally change as well. Within the multiverse, perhaps 1+1 doesn't always have to equal 2.

 

[centsworth_II]

...it occurred to me negatives do not occur in nature.

I think the problem arises if you look at a negative as meaning something less than nothing rather than as something the opposite of something else.

But if you have trouble dealing with negative numbers used to describe nature, imaginary numbers must give you a real fit! :lol:

 

[ramparts]

Of course negatives are described relative to a reference point - and that reference point is zero, a very qualitative and real thing. The example of charge is a good one.

If you'd like, I suppose you could abolish all negatives by taking as your reference point negative infinity, but the math would be impossible to work out, so you wouldn't have the most useful physics

 

[centsworth_II]

A proton has a charge of +1 and an electron has a charge of -1. This does not mean that the electron has less than zero of some force that the proton has. It means the electron has a force with different properties that counter balances the proton's electric force.

This is easily illustrated by the fact that the electron's having a charge of -1 is only a convention* and does not indicate that the electron has less than zero of some force. The discoverers of the electron could just has easily have said the electron's charge is +1 and the proton's is -1. All the math would have worked out just fine.

*By convention, the charge of an electron is −1, while that of a proton is +1.... One of the foremost experts on electricity in the 18th century was Benjamin Franklin.... Arbitrarily (or for a reason that was not recorded) he identified the term "positive" with vitreous electricity and "negative" with resinous electricity. http://en.wikipedia.org/wiki/Electric_charge

 

[Kessy]

there's no reason that one plus one *has* to equal two, but we say it does because that reflects the reality we live in.

Huh??? I would say the fact that it reflects reality is pretty damn good reason to say 1 + 1 = 2

My point is that we've designed math to reflect reality, but you could, if you wanted, design a kind of math that doesn't reflect reality. Think of it like painting - you can paint images that are downright spooky in how perfectly they capture how reality looks, or you can paint something totally abstract and bizarre. It all depends on what you want to do with it.

 

[Jerromy]

I'd say Kessy hit that on the head. Math can be whatever you want it to be. Kelvin didn't like Celsius being centered on solid water, but he liked the scale. Perhaps I'll make a Payne, in which the highest possible temperature (.99999999c quark movement), is zero and everything else is colder and an exclusively negative scale.

 

[emperor_of_localgroup]

Huh??? I would say the fact that it reflects reality is pretty damn good reason to say 1 + 1 = 2
My point is that we've designed math to reflect reality, but you could, if you wanted, design a kind of math that doesn't reflect reality. Think of it like painting - you can paint images that are downright spooky in how perfectly they capture how reality looks, or you can paint something totally abstract and bizarre. It all depends on what you want to do with it.

Yes , that was my point, we use negative values for mathematical convenience, not for matching with reality. We can also say, we shaped our math not only to conform with reality but also to make computation convenient. But my question is about this convenience, some mathematicians may go too far to describe reality with the results they get from 'convenience'. Even imaginary numbers in my opinion is a convenient representation of something, but not reality. well, it may lead us to a physical reality but it's not reality. How's that possible?

We can say
1+1 = -2
But in that case we have to change all rules of arithmetics, and can be made right. We can also write
1 + 1 = *
In that case we have to redo mathematical symbols.

Another argument I have is electron charge is -e, proton charge is +e (or +p), this represents opposite nature of the same physical object. But we don't use +N for north pole of a magnet and -N for its south pole, counter clockwise rotation is not the negative of clockwise rotation in its representation, except for spins in atomic level.

I still think there may be a better way to represent gravitational potential than assigning a negative value to it.
In my conclusion, negative quantities do not exist in nature, they are here for our convenience.

 

[origin]

We can say
1+1 = -2
But in that case we have to change all rules of arithmetics, and can be made right. We can also write
1 + 1 = *
In that case we have to redo mathematical symbols.
I still think there may be a better way to represent gravitational potential than assigning a negative value to it.
In my conclusion, negative quantities do not exist in nature, they are here for our convenience.

Yes we could say 1 apple and 1 apple added together make -2 apples, then we could say that -2 apples added to 1 apple would make 3 apples or maybe -3 apples. So is 1 + 0 = -1 and what the heck is 2.

We could say that 1 + 1 = * and * + * = armadillo

We could put either of these systems into place and in about 100 years we will all be chipping flint to make weapons.

 

[origin]

To be fair there is some arbitrariness to the whole what is negative concept. You could say that positive is negative and vice versa as long as you are consistent (I beleive that is exactly what is done in the US Navy for electricity). But it is necessary to have negatives. Look at friction in calcualtions it is a negative force - if not you will find that your calculations will indicate that you will speed up when the brakes are applied.

Imaginary numbers are another odd thing but very useful. It is a tool that is used in calcuating power in AC circuits. AC was so baffling to Edison that he rectified all of the AC generated to DC, which is a much less efficient form of power transmition.

If you can come up with a new method of mathematical notation that is more effective then more power to you; but you will have to do better than 1 + 1 = iris.

 

[centsworth_II]

...In my conclusion, negative quantities do not exist in nature, they are here for our convenience.

Negative quantities do not exist in nature, but opposites do. And one half of a pair of opposites is often noted by the negative sign. The negative sign indicates an opposite, not a negative quantity.

 

[nailpounder]

Origin wrote:
We could put either of these systems into place and in about 100 years we will all be chipping flint to make weapons.[/quote]


Damn you, I spit chocolate chip cookie crumbs all over my keyboard when I read that. :lol:

 

[InnyBinny]

You are right in that one can define reference points to make any known quantity - say a velocity - that once was negative, so that is turns positive. But is it possible to define a reference point so that all possible velocities are positive? Unless you consider infinity, then no, it is not.

And infinity is a bit of a tricky issue.

But when it comes to things such as charge, which are defined as opposites, then it becomes a little clearer. Negatives are used as a mathematical construct to define opposites in physics such as charge...I think it must be said that negatives to exist in this case.

But and even clearer example of negatives in nature would be production of something like negative energy, which of course suggests the reality of negative mass. An actual quantity of energy that is less than zero.

And negative mass would have pretty obvious effects - F = ma is probably the most obvious example. A force in one direction would cause an acceleration in the other - and these two vectors being in opposite directions simultaneously I think pretty much makes the natural existence of the negative pretty emphatic.

 

[Kessy]

What I'm trying to say is that all math and all numbers are symbolic in nature, even natural counting numbers. (1, 2, 3, etc) Asking if negatives exist in reality is the wrong question to be asking, the question to ask is what do they represent in reality? Sometimes when working with symbolic systems like math, or even knowledge in general, you'll get an answer that you have to stop and figure out what it represents - that's no reason to throw it out completely. All math has a certain "unreality" to it, so long as it works in correctly describing what we observe, there's no reason to try to say that some of it is less real then others.

For example, I could just as easily make a case that natural counting numbers don't exist in reality either. I mean, what is one? To take the classic example of apples, what exactly constitutes one apple? Apples come in different varieties and different sizes and different consistencies - even apples of the same type are never exactly identical. What if one apple is a little bigger then the other? Do you still have two? What if one of them has a small nick in it? For that matter, if you look at an apple microscopically, it's made of the same carbon, hydrogen, oxygen, and nitrogen as any other organic matter, such as, say, the wooden table it's sitting on. Where exactly does the apple end and the table begin? Wouldn't choosing one particular atom to make the boundary be arbitrary? And what about where the apple begins and the apple tree it came from ends?

When examined closely, the real world is seldom, if ever, as nice and clean cut as our conception of it.

On a side note, if tachyons are found to exist, they would by definition have an imaginary rest mass. So yes, Virginia, there are negative numbers.

 

[InnyBinny]

What I'm trying to say is that all math and all numbers are symbolic in nature, even natural counting numbers. (1, 2, 3, etc) Asking if negatives exist in reality is the wrong question to be asking, the question to ask is what do they represent in reality? Sometimes when working with symbolic systems like math, or even knowledge in general, you'll get an answer that you have to stop and figure out what it represents - that's no reason to throw it out completely. All math has a certain "unreality" to it, so long as it works in correctly describing what we observe, there's no reason to try to say that some of it is less real then others.

For example, I could just as easily make a case that natural counting numbers don't exist in reality either. I mean, what is one? To take the classic example of apples, what exactly constitutes one apple? Apples come in different varieties and different sizes and different consistencies - even apples of the same type are never exactly identical. What if one apple is a little bigger then the other? Do you still have two? What if one of them has a small nick in it? For that matter, if you look at an apple microscopically, it's made of the same carbon, hydrogen, oxygen, and nitrogen as any other organic matter, such as, say, the wooden table it's sitting on. Where exactly does the apple end and the table begin? Wouldn't choosing one particular atom to make the boundary be arbitrary? And what about where the apple begins and the apple tree it came from ends?

When examined closely, the real world is seldom, if ever, as nice and clean cut as our conception of it.

On a side note, if tachyons are found to exist, they would by definition have an imaginary rest mass. So yes, Virginia, there are negative numbers.

I think you're over-analysing it. We can consider different varieties of apples to be part of the 'apple' set. Then, 'grannysmith', 'braeburn' and 'fuji' would all be different elements of that set. When you say 'I have two apples', you are merely saying that you have two as yet unknown members of the 'apple' set. It doesn't matter whether they are the same or they are different. You are merely stating the fact that you have two members of that set.

The other issues you bring up are categorisation issues, not really physical or mathematical ones. Biology, English and common sense will tell you when some object can be considered as part of the 'apple' set. Where the apple ends and the table begins is really quite obvious using physical interactions between particles, but again, this is more a categorisation and not mathematical issue.

So, what is one? Well, if you were to define the pure concept of one, physical reality would be detached from the concept, as mathematics is independent of physics. I really have no idea how to word the definition for the fundamental concept of one, because I'm not a professional mathematician by any means, but I'm sure they have a pretty good one out there. I'd probably just call it the first cardinal number.

And I don't know if it is easily possible to create a mathematical world where 1 + 1 = -2 that is internally consistent with itself. Any system of mathematics that has internal consistency can be considered as having equal value as any other, but I don't think it would be very easy to define another different one very well.

 

[centsworth_II]

...something like negative energy, which of course suggests the reality of negative mass. An actual quantity of energy that is less than zero.

In this case 'less than zero' means negative as in 'opposite', not as in 'less than nothing'.

Negative energy or mass would not be energy or mass of a quantity less than nothing, it would be energy or mass with properties opposite of the those for 'normal' energy or mass.