# The number zero

Arjen

Tue 9 Sep, 2008 01:31 pm
@iconoclast,
Hi Iconoclast,
iconoclast wrote:

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.

However in this discussion you seem to be quoting from the rulebook. It is I who is going against everything in the books.

Quote:

It's Godel's 'Incompleteness Theorem' that suggests the distinction between mathematics and reality, is it not?
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So here's the question. If mathematics is simply a logically structured language employed to model reality - how can you refute this argument:

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

The argment I was making was supported by your own reasoning. That is what I used to show that the thought is not equal to reality.

Quote:

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

iconoclast.

No Iconoclast, I have not. Might I ask why you always seem to be arguing 'again' something instead of trying to work out what would work?

iconoclast

Wed 10 Sep, 2008 03:32 am
@Arjen,
Arjen,

Well, as I say, I don't really know what the rule book says on this subject - I'm very much shooting from the hip as a means to explore the question. Until shown otherwise I'm defending the hypothesis I offered on the first page:

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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?

You disagreed:

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No, it is something else. 1 would be, in Holiday's example 1 apple. 0 has nu suffix. It is something else; stateless.

While entertaining this notion, I began to test it:

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

You then gave you illustrated explanation for which I thanked you; but saw a potential problem in your statement:

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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:

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

To which you replied:

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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:
if you begin with -2 apples and add two apples, you have zero apples, but this is something in terms of apples. how can you refute this argument...by saying 'in reality' there are no negative values?

And still, so far as I'm concerned, you're saying that maths is a language used to model reality, but then showing the statelesness of zero with reference to reality:

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.

So, what I'm asking is - how do you appeal to two different standards of verification. If it's a language with no necessary relation to reality, you cannot establish the status of a symbol within the logical framework with reference to that which is outside the logical framework.

iconoclast.

p.s. Please stop imparting emotional motives to my questions. Please stop giving me advice about what I should be mindful of, and what I must realize is... It comes across as condescesion, and frankly, until you clear up the illogic of your own position you seem little qualified to condescend to me.

Arjen

Wed 10 Sep, 2008 08:48 am
@iconoclast,
In my opinion it is true that the scientific model(s) has as its goal to form a thought-object of reality as accurately as possible. The scientific model uses mathemathics as its language. In that sense we should, to ensure the accuracy of the model, compare the model with reality...or what we know of it. Not that we cannot deviate from it in the model, but we should be aware of the differences.

Physics and chemistry are examples of models of reality. In these sciences it is clear that a negative numer or 0 do not actually exists as such in reality. The negative charge of an object for instance signals the presence of certain particles which we have predicated as having a negative charge. We sometimes say that an object is -3 or something. In reality this denotes something else. But when we start to calculate things with this knowledge we use the -3 in a much more 'real' manner. We pretend, in the language of the model that -3 really is -3. In the same sense 0 exists, while 0 denotes something else entirely.

Another example might be that after every chant Christians exclaim 'Amen'. This 'Amen' is a modern form of the name 'Amon'. So, while Christians everywhere think to be paying respect to the one 'God', they are calling towards the sun God Amon. The difference is very real, and although it does not matter to the Christians in question because they have a different intent I think it of great importance to realise what it denotes.

iconoclast

Wed 10 Sep, 2008 05:15 pm
@Arjen,
Arjen,

Okay then. I know that thought objects and reality can never completely coincide, but this is not the issue. This is something you assume I don't understand - but you are projecting your own confusion onto me.

Your proof of the statelesness of zero has become more prossaic than ever before. 'It's like when Christians say Amen.' No, it's not.

To put this in the simplest possible terms, if you want to establish the statelesness of zero - it must be done with reference to the logic of the mathematical language. You again make the mistake of appealling to that which lies outside the language - a mistake i have been attempting to point out to you.

If I were to go about proving your argument I would show that zero, when added to a positive number has a result equal to the positive number. When added to a negative number, similarly the result is equal to the negative value. When divided or multiplied by itself the result is zero. When divided or mutiplied by a positive or negative number the result is zero.

This would be considered a mathematical proof of the statelesness of zero - for it is drawn from the logical structure of the language itself, not from outside it. Apples, Christians, physics and chemistry are all outside.

iconoclast.

Arjen

Wed 10 Sep, 2008 06:53 pm
@iconoclast,

Holiday20310401

Wed 10 Sep, 2008 08:37 pm
@Arjen,
Ok Arjen. I have my own view on your idea of zero.

You are saying that zero is stateless right? How does that actually differ from Iconocast's? Zero has no magnitude, and no direction. Bear with me here.

You say that under the 'wrong' model, adding 2 apples and three pears to zero gives two apples? And in reality, obviously, you get both 2 apples and 3 pears.

Apples and pears are subjectively of magnitude, and direction is undefined, but based on the potential given it still will have a set path of value.

Zero is not a quantity because it can't imply direction or magnitude, and I think all of us can agree that zero as a relative point is invented. We can give it no other value because a one dimensional position implies that. But what other model allows for Euclidean vectors.

Or perhaps zero is a formlation that allows for euclidean math to be possible, providing the relative statelessness that Arjen implies. And of a statelessness implies value in that property, restricting zero to the kind of symmetries we see in mathematical systems today. But is zero needed for patterning? fractals? 1 1 2 3 5 8 13 21? Is it relative within patterns, and systems?

iconoclast

Thu 11 Sep, 2008 03:18 am
@Holiday20310401,
Arjen,

In mathematical logic:

2a+0a+3p=(2a+3p)

not 2a.

In reality it makes a rather nice crumble.

There goes the model!

Why do you keep saying things like:
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I can see this is not going to sink in.

...when it's you getting the lesson in elementary logical proofs.

More 'keep in mind' and 'what you have to remember is'

Pretentious twit.

iconoclast.

Arjen

Thu 11 Sep, 2008 07:18 am
@iconoclast,
Holiday,

What I have been saying is that the model in itself is something else than reality. If in the model something has a certain value we think (hope?) that it has the same value in reality. In that sense that 0 Iconoclast is speaking about and the 0 I am speaking about are two different 0's. That is what I have been trying to show by holding the results of the model up to reality. One might call the differences between the two 0's ontological differences. The importance of this has to do with paradoxes which was my first reason of replying. I had hoped to get to that stadium.

The document I have been preparing is done by the way. I am letting it cool down a day or two and am then going to re-read it to see if it is understandable and if I have forgotten anything that needs to be in it.

Iconoclast,

I am trying to help you. I had hoped to get past the stadium of namecalling so we can examine this situation. You seem to be focussed on just your own opinion. That is fine by me, but that makes the discussion moot. That is why I said that it was not going to sink in. I'd best invest my time in something else.

Before I go I would like to show how much you are missing of what I am saying:

1) I was using the apples and pears as an example. I said that if the model does not take pears into account, thenif something outside the ontological layer is present, then the model cannot give an accurate reflection of it; like with 0.

A thought to consider is that by deviding by 0 all outcomes become possible. The reason for that is the ex falso sequitur quodlibet principle.

2) Please realise that mathematics and logic are two different things. Allthough mathematics is derived from a quantification of logic it, in no way, is logical. Logic concerns the workings of our mind while mathematics concerns the language of the scientific model we use to mirror our observations. All such scientific models are therefore derived by logic, but are in no way logic themselves.

3) Logical proofs say nothing whatsoever about what is true or not. It is merely a formalisation of thought to deduce if the reasoning is correct. A correct reasoning will give an incorrect outcome if the variables inserted are incorrect.

4) At no point in my life have I ever pretended to be something I am not (apart from the time I thought I was Napoleon offcourse). The reason you feel patronised is because I am looking at what you are doing and I can see how it fits in the grander model. I was trying to show you how you can step out of that and stop making circulatory arguments. I can understand that that makes you feel uncomfortable, but if I cannot point to where I see you taking a wrong turn, then where is the conversation? Where is the discussion? That was the reason why I tried leaving the discussion before. I am sorry that I did not conclude so soner, but I thought we'd be able to discuss things in all seriousness.

5) The discussion is now, to me, over. I am sorry I made you feel bad, but you are going to have to be able to deal with people pointing you towards something you have missed, even if they are insensitive towards you. I am a brute and I know it. I do mean well though. I hope that we can discuss things in a civilised manner in the future.

Arjen

Holiday20310401

Thu 11 Sep, 2008 03:14 pm
@Arjen,
I hardly think this is over.

The proof for the ex falso sequitur quodlibet principle is not conveying any truth and it deals with an ontological system that is separate from reality, so... what practical uses?

iconoclast

Thu 11 Sep, 2008 03:23 pm
@Holiday20310401,
Holiday,

Quote:
I hardly think this is over.

You're wrong as well.

iconoclast.

Fairbanks

Thu 11 Sep, 2008 05:23 pm
@Arjen,
Arjen wrote:
. . . The reason for that is the ex falso sequitur quodlibet principle . . .

Anything asserted about an empty set is true. That is, whatever is said about space aliens is true since there are none. But, a set consisting of a zero is not empty, or my database admin claims.

Zetetic11235

Thu 11 Sep, 2008 05:26 pm
@astrotheological,
astrotheological wrote:
I personally think that the number zero is actually more intriguing than infinite because it can actually fit into an equation.:Glasses:

Interesting, obviously you have never had any calculus. There are many mathematical operations which involve infinity. Remember that infinity includes the infintesimal as well as the infitely large.

Zetetic11235

Thu 11 Sep, 2008 06:18 pm
@Zetetic11235,
Iconoclast,

I beleive the example Arjen was giving was 2a+0a(3o)=2a which should have been obvious in context. Clearly in reality multiplying 0 apples by 3 oranges does not elicit a lack of oranges, however it seems like this example is missing somthing in its approach. Multiplying does not have any real connection to what is being examined. 0 apples added 3 oranges times does not make sense. If we look at the quantity of fruit and lump together apples and oranges as fruit and take 2f+0f(3f) we still get 2 pieces of fruit, but this is because we are treating object names as variables. This is not a correct application.

It is true, however, that mathematics is necessarily a subset of physical reality. I would hope that at least none of us are disputing this. I might also note that unless you are a mathematics major or possibly a graduate student in mathematics, you probably do not know or understand much if any mathematical logic. It is nothing like basic algebra, so do not refer to it as such. Mathematics at most could provide a comprehensive relational framework to reality, this is possibly false though it has not been proven to be so. Science is applied mathematics(mathematics applied to physical data through induction) with a specific investigative objective in mind. There are no proofs in science, as it is an open system, though theories are made over closed systems of data and falsifiable. Science generally attempts to find a relational structure to physical data in order that extrapolations an manipulations of physical states of affairs can be manipulated to elicit a desired result, at least that is my conception of it.

Arjen was pointing at somthing which I think is quite important, that is the state which the numbers refer to. He claimed that zero is not, in fact, somthing which can have a state. I would disagree. Zero can have any state taken as a scalar. A zero vector, for instance, does the same thing to a vector as zero does to a number. adding zero apples to two apples is in fact the same as adding zero oranges instead.

Numbers in and of themselfs are in fact, stateless. That the state of zero is inconsequential to the system makes no direct difference. It is a tool of manipulation which may or may not be appropriate. We are no longer in a purely mathematical system when we apply a state such as one apple or two cars and we must adapt to this as is needed. It is the same principle of physics being a subset of mathematics. Physics presents us with a reasonably accurate mathematical model in order that we might manipulate a state of affairs to our likeing. That the model is sucessful in applications thus far is of no consequense. No matter how many times a physical theory is justified, it is not proven true. A proof cannot be written as it would be over an open system with unknown variables.

When we consider a negative number, it is false to consider some state in which it would hold true. When we need to apply these numbers as they appear useful, for instance to note the direction of forces, then we consider the method of application. When we consider a negative force, we are considering it with respect to a positive force, and in fact the same is true of numbers. There are not really any positive values in that they cancel negatives, for this is also a mathematical construction in respect to the negative values.

A negative value is simply a value with the property to cancel some ammount of a positive value. In this we see negative two apples is nonsensical, but negative force is not, the negative simply denotes direction. In the example of the fruit, the negative denotes nothing. In order to apply a model, it must be wholly applicable, not partially. You cannot leave part of the model in mathematical space and try to apply it to somthing aside from mathematical space. Application should be held very distinctly of pure mathematics. Mathematical models do not in themselfs have states which are not mathematical in nature, that we have found a way to apply these models is inconsequential to their actual natures.

Arjen

Fri 12 Sep, 2008 02:02 am
@Zetetic11235,
To dot the I's:

1) I was saying that the scientific model could not mirror reality because it cannot take into account ontological differences.
2) Mathematics being the language of the scientific model cannot do that either. It become even worse because in pure math things like -3 are stated while they are, in that respect, none sensical. The - or + indeed shows direction of sorts; a presence of another nature.
3) These two differences make an argument for the unreliability of the scientific model.
4) In reality 0 is something else alltogether. One can see that by deviding by 0 or observing that reality quantifies in all directions from 0 in a graph.
5) 0 is taken as stateless in mathematics because it cannot handle the values it is given in the scientific model and the scientific model takes 0 as within this ontological layer because it cannot handle other ontological layers.

Hope this helps.

Zetetic11235

Fri 12 Sep, 2008 07:46 am
@Arjen,
Here are my perspectives on each of these points:
Arjen wrote:
To dot the I's:

1) I was saying that the scientific model could not mirror reality because it cannot take into account ontological differences. .

I agree; scienece operates over closed subsets of an open system, thus it cannot full encompass the ontological totality of possible experience for there are potentially unknown variables.
Arjen wrote:

2) Mathematics being the language of the scientific model cannot do that either. It become even worse because in pure math things like -3 are stated while they are, in that respect, none sensical. The - or + indeed shows direction of sorts; a presence of another nature.

They are nonsensical in an incomplete application or incorrect application but not in and of themselves an in relation to the system by which they are generated. There is a definite logical relational structure which relates them to each part of the system thus they have a sense to them and a logical form, thus they are not inherently nonsensical. Any state which is non-mathematical that is applied to a mathematical object is contingent upon the appropriate method of application to be carried out. Mathematics is a stand alone series of partially disjoint logical structures.
Arjen wrote:

3) These two differences make an argument for the unreliability of the scientific model..

Only the first, which is very similar to Karl Popper's view point of science. Check out critical rationalism if you haven't. That being said, it is certain that the scientific model is an approximation with certain limitations. It is definitely at the very least asymptotic to reality.
Arjen wrote:

4) In reality 0 is something else alltogether. One can see that by deviding by 0 or observing that reality quantifies in all directions from 0 in a graph.

I think that zero is syntactic as is infinity, and this is recognized in mathematical logic. Zero is the identity for addtion that returns the same state, it is the input for the binary operation of multiplication such that the operation returns zero.
Arjen wrote:

5) 0 is taken as stateless in mathematics because it cannot handle the values it is given in the scientific model and the scientific model takes 0 as within this ontological layer because it cannot handle other ontological layers.

0 is a syntactic object. It is a rule set. When the rule set elicits the information required, it is applied to the given data. 0 is stateless because it is not an object, but a set of parameters. 0 came about in western mathematics due to Fibbonacci, who used it to denote somthing quite simple: a null component. The exploration of zero with respect to the existing mathematical structure has show various relational properties, some of which (for instance division by zero) are asymptotic indicating a syntactic aspect to zero. 1/0 elicits infinity, which is a syntactic object; it is a rule set which prompts a non terminating series of a repetitive binary operation over a given domain. When the operation is applied once we take the result and reapply this binary operation to the initial object and the resultant of the last operation. I am not sure if this is true for say n-ary operations but I would say that it is. It is certainly a much more difficult a concept to consider.

Grimlock

Fri 12 Sep, 2008 08:03 am
@Zetetic11235,
A couple quick questions:

1) Arjen - what, if anything, does the number zero have to do with your bank account balance?

1A) Are you angry with the number zero on account of the above or are you angry with ABN AMRO?

2) Is "nothingness" actually a state of existence, or merely a useful idea, sort of like 1, 2, 27 and 5,623,890.3475563?

2A) If there is no nothingness, why should I give anymore thought to zero than I give to 27?

Arjen

Fri 12 Sep, 2008 01:09 pm
@Grimlock,

astrotheological

Fri 12 Sep, 2008 02:16 pm
@Zetetic11235,
Zetetic11235 wrote:
Interesting, obviously you have never had any calculus. There are many mathematical operations which involve infinity. Remember that infinity includes the infintesimal as well as the infitely large.

Your right but give me example of a simple calculus equation involving infinite and tell me the answer.:listening:

Zacrates

Fri 12 Sep, 2008 02:19 pm
@Grimlock,
I agree with Grimlock, and if there is nothingness, wouldn't nothing be something.

astrotheological

Fri 12 Sep, 2008 10:54 pm
@Zacrates,
that doesn't make any sense. Nothingness can't be anything at all. Hemlock in words.