# The number zero

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Thu 10 Jul, 2008 12:03 am
What does the number zero mean?:detective:

I remember somebody stating on the forum how the number zero does not mean 'nothing' but if you have 2 apples and you get rid of 2 apples you have nothing in the perception of the value of apples.

astrotheological

Sun 7 Sep, 2008 08:10 pm
@Holiday20310401,
Holiday20310401 wrote:
What does the number zero mean?:detective:

I remember somebody stating on the forum how the number zero does not mean 'nothing' but if you have 2 apples and you get rid of 2 apples you have nothing in the perception of the value of apples.

The number zero cannot be a value because it is nothing. If the cosmos for example had nothing in it how could it be considered a value.

Victor Eremita

Sun 7 Sep, 2008 08:28 pm
@astrotheological,
The number zero denotes absence. Zero apples indicates the absence of apples, which is something, no?

Holiday20310401

Sun 7 Sep, 2008 08:45 pm
@Victor Eremita,
Exactly! Can we have an equation that works with variables that aren't something.

Arjen

Mon 8 Sep, 2008 01:57 am
@Holiday20310401,
Hi Holiday,

0 is indeed 'stateless'. There are several things I want to say.

1) What is important is that we really have a 9-number system and not 10-number. The reason for this is because 0 is not a number. We have 1-9 and then the absence of a number as we start to count the decades (not sure if decades is the right english word). 0 only exists to help us realise that we are talking of a certain number of decades and no other units. The romans used to use X for ten. Twenty was XX, thirty XXX, fifty L and hundred C. In this system the 0 is not even present.

2) Fibonacci is the one who 'invented' 0. He is often called the hero of zero. He 'invented' 0 to get his sequence started. In reality one could add 1 to nothing and then 1 to 1, coming to the same results. He felt the need to introduce 0 though. I think that 0 is not needed here and the reality is that it was needed for something else; to distract us from something, or so it seems because 0 does not mean 0 at all.

3) In physics one can use 0 as the point from which actuality flows. It is a representation of an origin of sorts; perhaps potentiality. It takes the same place as 'falso' takes in logic.

4) Marko Rodin

iconoclast

Mon 8 Sep, 2008 02:04 am
@Arjen,
zero is a number. it comes after -1 and before 1. It is a greater quantity than -1 and a lesser quantity than 1. yes?

iconoclast.

Arjen

Mon 8 Sep, 2008 02:28 am
@iconoclast,
iconoclast wrote:
zero is a number. it comes after -1 and before 1. It is a greater quantity than -1 and a lesser quantity than 1. yes?

iconoclast.

No, it is something else. 1 would be, in Holiday's example 1 apple. 0 has nu suffix. It is something else; stateless. As you well know statelesness is that from which things sprout. Just like ex falso sequitur quodlibet proves in logic. Zero is the mathematical equivalent of falso.

I understand your viewpoint as well, but that has a 'bending' effect because it does not account for statelesness. It is a 'flat' world view like empiricism so loudly trumpets. What is happening is the covering up of the 'paradox' by pretending that the different 'layer' does not exist. The statelesness is pretended to be in the same 'layer' and pretended to be noting in that layer. In effect it is true, it is none-existent in that layer; nothing. Nothing has different properties than are possible in that layer though.

Hope this helps.

Khethil

Mon 8 Sep, 2008 04:37 am
@Holiday20310401,
Its a term we invented to represent "no quantity" of <whatever>. Easy stuff

iconoclast

Mon 8 Sep, 2008 05:49 am
@Khethil,
Arjen,

My explanation employs negative numbers - does this not make a difference?

The argument so far only distinguishes betwwen positive quantities and nothing, and I can see the statelessness of nothing in that respect, but where neagtive quantities are posited, does not zero become a quantity of something greater than a negative quantity of that same thing? For instance, if you begin with -2 apples and add two apples, you have zero apples, but this is something.

iconoclast.

Holiday20310401

Mon 8 Sep, 2008 01:54 pm
@iconoclast,
Yes, -1 relative to zero is equal to 1 relative to zero in terms of the difference. We use zero to define relative points.

astrotheological

Mon 8 Sep, 2008 02:16 pm
@Holiday20310401,
Zero is nothing because there isn't a value for it.

Zetetic11235

Mon 8 Sep, 2008 06:06 pm
@astrotheological,
You seem to be missing the point. Zero is at least a denotation of absence. Zero is at most somthing conceptually greater than what it is currently viewed as. It is a mathematical tool, that is evident, however it is interesting to examine its properties. There are many inequalities and equivalencies which utilize zero. There are many applications of zero, for instance in defining homogeneous systems of linear equations with non trivial solutions notation of zero is quite useful and this mathematical tool is used in any number of scientific disciplines.

I am not sure zero holds the same philosophical intrigue as say, infinity, however there could very well be more to this than I see.

astrotheological

Mon 8 Sep, 2008 06:18 pm
@Zetetic11235,
I personally think that the number zero is actually more intriguing than infinite because it can actually fit into an equation.:Glasses:

Holiday20310401

Mon 8 Sep, 2008 06:42 pm
@astrotheological,
Or maybe they are the same thing?

astrotheological

Mon 8 Sep, 2008 07:12 pm
@Holiday20310401,
Holiday20310401 wrote:
Or maybe they are the same thing?

Or maybe there can never be zero or an infinite of existence.:a-thought:

Arjen

Tue 9 Sep, 2008 06:05 am
@astrotheological,
Hi Iconoclast,

I think you need to realise that the whole of mathematics is a way that humanity uses to make a model of reality. In that none existing model we indeed see the difference between -1 and 1 being 2 units. I understand the use of the model, but one has to be very carefull of confusing the model with reality, which was the entire point. I would like you to consider these thoughts though:

1) -2 appels do not exist in reality; only in models we create
2) -2 appels + 2 appels = 0 appels; which in reality means nothing. We might consider in our thoughts that we have an empty set of apples, but in reality we see no appels and it therefore does not exist.
3) What happens in the models we create in our thoughts is that we create mirror images; the opposites of things. This is shown below:

figure1

I know this is a model as well, but it is a model which is trying to represent reality. We see that the difference between -1 and 1 on the flat index of the figure is 2; but in the model itself the difference is a 'mirror' of sorts; the state + and -. We can neatly fold the two mirror images together as shown below:

figure2

The two mirror images are simular because they exist in the same 'dimensions'; but are eachothers counterparts. As said a negative as such cannot exist in nature. In nature a negative charge always has a positive charge as its 'mirror'. We see that 0 in that sense is something else altogether than depicted in the 'flat' world-model': it has a mirror function, it is balance; source. From this source thing 'quantify in many more directions than show above though. I think it quantifies in a lot more ways than we can concieve of. Below is a picture which more accurately depicts the situation:

figure3

Reality is a lot more complicated I think because things have their mirror images. So what comes out must go in so to speak. Adding to that the thought that things quantify in all direction and in all manners I think this the below picture is a lot more accurate:

vortex

iconoclast

Tue 9 Sep, 2008 06:52 am
@Arjen,
Arjen,

Thanks for the illustrated explanation, and I admit - the philosophy of mathematics is not something I know much about at all. I ask questions merely because I want to know the answer - and then ask further questions to see if I have understood. If I appear ignorant it's because I am - at least in relation to the phil. of math.

So, is it your contention that negative quantities only exist as logical constructs? Conceptual opposites of positive values that actually exist?

I was going to say 'what about a vacuum?' - but a vacuum doesn't exist in nature does it?

Is space not a vacuum? Does space 'exist'? Is it stateless? Or is it the negative of the positive quantity that is matter?

Or is there a distinction to be made between the logical construct that is mathematics, and reality?

Ooh, I like this subject. If I can make progress in it I think I might get hooked.
Any 'entry level' reading recommendations would be most welcome.

iconoclast.

`

Arjen

Tue 9 Sep, 2008 09:03 am
@iconoclast,
Iconoclast,

It is not that you appear ignorant, it is merely that it seems that you are holding on to an idea by not looking at what is being said. It really only proves what I was saying. Allow me to demonstrate:

Quote:

So, is it your contention that negative quantities only exist as logical constructs? Conceptual opposites of positive values that actually exist?

Yes, that indeed is the point.

Quote:

I was going to say 'what about a vacuum?' - but a vacuum doesn't exist in nature does it?
Quote:

Is space not a vacuum? Does space 'exist'? Is it stateless? Or is it the negative of the positive quantity that is matter?
Quote:

Or is there a distinction to be made between the logical construct that is mathematics, and reality?

You should know that at least. Mathematics is most definately not a model of reality, nor was it intended as such. Mathematics is the language in which we often depict models of reality. Reality being something other than its model and the model being something other than the language in which it was depicted I am certain when I say that mathematics is not reality. Be mindfull of the differences between thought-objects and reality. They can be very similar, but are never the same!

Quote:

Ooh, I like this subject. If I can make progress in it I think I might get hooked.
Any 'entry level' reading recommendations would be most welcome.

I have no such book. I would suggest you start with determining methods of discerning true thoughts from other thoughts. That seems the only problem you are facing because your thoughts are not irrational or illogical in any way. The seperation between what happens in reality and what happens in thought is just a hard one to make. Every person struggles with it.

I hope this helps.

iconoclast

Tue 9 Sep, 2008 11:42 am
@Arjen,
Arjen,

Yes, my teachers suggested there was something wrong with me rather than admit the limits of thier own knowledge - not to worry. If it's anything, it's that I have no respect for the traditional borders of knowledge.

You say:
Quote:
I am certain when I say that mathematics is not reality.

It's Godel's 'Incompleteness Theorem' that suggests the distinction between mathematics and reality, is it not?

So here's the question. If mathematics is simply a logically structured language employed to model reality - how can you refute this argument:

Quote:
if you begin with -2 apples and add two apples, you have zero apples, but this is something in terms of apples.

...by saying 'in reality' there are no negative values?

Quote:
1) -2 appels do not exist in reality; only in models we create
2) -2 appels + 2 appels = 0 appels; which in reality means nothing. We might consider in our thoughts that we have an empty set of apples, but in reality we see no appels and it therefore does not exist.
3) What happens in the models we create in our thoughts is that we create mirror images; the opposites of things.

It seems it's you who has confused thought object with reality.

iconoclast.

Fairbanks

Tue 9 Sep, 2008 12:21 pm
@Holiday20310401,
Holiday20310401 wrote:
What does the number zero mean?:detective:

I remember somebody stating on the forum how the number zero does not mean 'nothing' but if you have 2 apples and you get rid of 2 apples you have nothing in the perception of the value of apples.

The 0 allows the identity relation in addition just as the 1 allows the identity relation in multiplication and e in calculus and 'pi' in trig and i or j in complex analysis. Other uses would be metaphorical.

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