Number system flawed?

Originally posted by Alcra
That reminds me of a joke I saw somewhere (might have been here at RHP).

Two men, one of which happens to be a mathematician, are sitting in a park, watching a house across the road. At some point, someone enters the house, and a few minutes later, two people leave. Says the mathematician, "If another person should now enter the house, it will be empty."

LOL, I like that one! Gets a rec.

Originally posted by nickhawker
Give me an example of a negative number existing in reality then...

What do you mean by "in reality", exactly? Something you can pick up in your hands? Sorry, probably can't do it, at least off the top of my head.

But in order to MEASURE physical qualities, negative numbers are essential. Unless I'm experiencing imaginary temperatures in the middle of winter...

And last time I checked, the Dead Sea's altitude wasn't imaginary either.

The point being that negative numbers connote DIRECTION from the zero point. 40C and -40C are both forty degrees centigrade away from 0, but I'm pretty darn sure you can detect the difference in direction.

Originally posted by orfeo
What do you mean by "in reality", exactly? Something you can pick up in your hands? Sorry, probably can't do it, at least off the top of my head.

But in order to MEASURE physical qualities, negative numbers are essential. Unless I'm experiencing imaginary temperatures in the middle of winter...

And last time I checked, the Dead Sea's altitude wasn ...[text shortened]... entigrade away from 0, but I'm pretty darn sure you can detect the difference in direction.

Thats what i'm mean when i say they don't exist. Take the dead sea,

Its "altitude" is say -100m. That is true. But what you mean is it is 100m below your zero level. You haven't got a negative length, thats nonsense, but you have a length of 100m under your defined zero. Your using the negative sign to represent this as a number that you can then do maths with. We are used to seeing this and so automatically visualise then negative as meaning below or opposite to positive.

Now, with "i" things are no different at all, but we arn't used to "seeing" i as we can a negative number, so it feels weird.

The dead sea is -100m above sea level.

Originally posted by nickhawker
Thats what i'm mean when i say they don't exist. Take the dead sea,

Its "altitude" is say -100m. That is true. But what you mean is it is 100m below your zero level. You haven't got a negative length, thats nonsense, but you have a length of 100m under your defined zero. Your using the negative sign to represent this as a number that you can then ...[text shortened]... rent at all, but we arn't used to "seeing" i as we can a negative number, so it feels weird.n

So, does that mean that you take for real the 'substraction' (as in 'take away' an amount) but not the 'shortage'. Is the eight pawn, after it has been taken away by your opponent real only because it was taken away? Has your opponent a material advantage, but you have no material disadvantage?

Next step is that you don't accept zero ('0'😉 as real. Brings us back a few thousand years ....

Originally posted by nickhawker
Thats what i'm mean when i say they don't exist. Take the dead sea,

Its "altitude" is say -100m. That is true. But what you mean is it is 100m below your zero level. You haven't got a negative length, thats nonsense, but you have ...[text shortened]... ed to "seeing" i as we can a negative number, so it feels weird.

Alright then, is "three" real? When was the last time you held "three" in your hand? Not three objects, but the actual thing that the word "three" describes?

No? Didn't think so. So why do you say "three" is more real than "minus three"?

"100 metres" is merely a measurement, it's not 'real'. We decided what a metre was, and we decided what "100" meant. None of it is real.

"100 metres down" is another measurement, with more information, both distance and direction.

🙂 A meter is 1/299792453.684314 light seconds 🙂

Originally posted by orfeo
Alright then, is "three" real? When was the last time you held "three" in your hand? Not three objects, but the actual thing that the word "three" describes?

No? Didn't think so. So why do you say "three" is more real than "minus three"?

"100 metres" is merely a measurement, it's not 'real'. We decided what a metre was, and we decided ...[text shortened]...
"100 metres down" is another measurement, with more information, both distance and direction.

So, your point is that "100 metres" is not an absolute physical quantity, and metres are an imaginary system that is used to try and quantify the distance between two physical points. Basically, you are saying that metres arn't physically "real" but are a tool used to write down a physical property in a quantitive manner. They are a tool to allow us to perform mathmatical operations such as addition.

Are you sure you arn't on my side in this debate? Cos, thats my point.

Originally posted by nickhawker
Give me an example of a negative number existing in reality then...

The charge on an electron?

The force exerted by two electrons on each other?

The net saving of the US government?

Of course you could have a system where instead of using negative numbers, you can say things like there is a 'nega-charge' of 1 on an electron, and a 'posi-charge' of 1 on a proton. But how does one combine 'posi-charge' and 'nega-charge'? Isn't it actually the case that a proton has 4/3 posi-charge and 1/3 nega-charge when you look at the quarks? Are posi- and nega-charge fundamentally different phenomena, or is one simply the reverse of the other? If the latter, I think you'd have a very strange sense of what is intuitive if you didn't start using negative numbers.

Originally posted by nickhawker
So, your point is that "100 metres" is not an absolute physical quantity, and metres are an imaginary system that is used to try and quantify the distance between two physical points. Basically, you are saying that metres arn't physically "real" but are a tool used to write down a physical property in a quantitive manner. They are a tool to allow us ...[text shortened]... ons such as addition.

Are you sure you arn't on my side in this debate? Cos, thats my point.

Your point, I thought, was that negative numbers are somehow less real than positive ones. I am saying they are equally "unreal".

Originally posted by Acolyte
The charge on an electron?

The force exerted by two electrons on each other?

...[text shortened]... If the latter, I think you'd have a very strange sense of what is intuitive if you didn't start using negative numbers.

But thats exactly his point. An electron doesn't have less than zero charge; it merely has a charge that is opposite in direction (well, it has a vector that represents the charge opposite in direction) to that of a proton. To say something has less than zero charge in the sense that a non-mathematical interpretation would imply is ludicrous; either something has charge or it doesn't.You could just as easily say an electron has a charge of one, a proton of three and define 2 as the point of no overall charge, but as you pointed out, this would be silly. Negativity is a mathematical concept, it doesn't make sense in the 'real' world.

Negative numbers argument:

I have four sheep. I sell you nine, on back order. I then buy 6 sheep, which are delivered today. I then send you your five. I now have 1 shoop ( 🙂 could not resist that, sorry!)


At one stage, I had 4 sheep, then 10, then 1. On "the books", I had 4, then -5, then 1.

Originally posted by corp1131
But thats exactly his point. An electron doesn't have less than zero..[text shortened].. doesn't make sense in the 'real' world.

Having had a think about it, I am going to change my position a little. For vector quantities (ones with both magnitude and direction) such as force, charge, velocity, displacement etc., my previous stance holds. The negative sign in this instance merely infers the direction and cannot be grasped in the real world, as it depends completely on where the zero level is defined. A displacement above sea level of -100m simply means a distance of 100m in the other direction, you cannot measure this negative number, only infer its negativity from the frame of reference. For a scalar quantity (one with magnitude but no direction) such as money, number of sheep etc., negativity has slightly more meaning in the real world; in that you define it as 'owing' something to someone. Whether this counts as a real negative number is up for debate. Personally I think in reality if you have -£100 in the bank, you in fact have zero in the bank and also owe money to them, which they conveniently represent by being a minus amount. You cannot hold this amount though, you cant go look at it in the bank, it is simply a convinient tool.

I suppose this is kind of off topic now the thread has gone in the direction which it has, but I found it strange that there are infact more irrational numbers than rational numbers that exist, for example, if you were to examine every number between 1 and 2 there would be more irrational numbers than rational ones.

I'm not great at maths (currently doing AS Maths) but I found this interesting, what do other people think? ... or is it just something thats obvious 😕

Originally posted by corp1131
Having had a think about it, I am going to change my position a little. For vector quantities (ones with both magnitude and direction) such as force, charge, velocity, displacement etc., my previous stance holds. The negative sign in thi ...[text shortened]... ou cant go look at it in the bank, it is simply a convinient tool.

If you mean vector in a mathematical sense, direction isn't a particularly intuitive concept either. Two non-zero vectors are said to be parallel if one is a multiple of the other (including negative multiples). Otherwise, they are not parallel, but that's all you can say about their relative directions. On the other hand, saying that one vector is minus another immediately makes sense: it means if you add them together, you get the zero vector. If anything, direction is a more advanced idea than negativity.

You seem to be over-generalising about the meaning of vectors depending on 'where the zero level is defined': while some vector quantities are only defined up to a constant, all the ones you mention do not have this limitation: it makes perfect sense to talk of zero force, or zero displacement, without recourse to units of measurement. What is the case is that many statements about vector spaces, such as magnitude, occur in the context of a specific inner product, which roughly translates to the overall 'shape' of space-time, but that's not the same.

BTW, I wouldn't describe charge as a vector quantity, as in a physics context 'vectors' are 'space-time vectors'. AFAIK charge has no association with spatial-temporal direction.