The First Dimension Is Not Logical

Discussion in 'Pseudoscience Archive' started by impaJah, Mar 24, 2012.

  1. impaJah Registered Senior Member

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    What is commonly accepted as "the first dimension" is a logical impossibility - and before you jump on me with the retort of "we know it doesn't exist in the real world, it is a useful theoretical concept" - I want to say that I am not arguing that it doesn't exist in the real world. That we can all agree on I'm sure. What I'm arguing is that it doesn't even exist in the theoretical world!

    In essence the theory of the first dimension attempts to differentiate something which is indivisible. In other words it's giving two names to the same thing in a different form.

    Let me explain.

    A one-dimensional object is described as having only length with no width or depth. But length can only be created by stacking objects of width on top of each other. And this can just as easily be looked at the opposite way, that width can only be created by setting objects of length next to each other. And though it is obvious to point out, the designation of any object's length or width is interchangeable. It is only convention that we associate length with vertical and width with horizontal.

    To fix this logical impossibility all we would have to do is define a point as "infinitely small" instead of "undefined". And from there define a theoretical length's width as "made up of string of an infinite amount of infinitely small points in succession".

    From this new defining of the dimensions we see that they are all inextricably connected to one another and are only permutations of the same essence. So there are no truly discrete dimensions, for every dimension must have at least an infinitely small kernel of all of the other dimensions in order to be a sound theoretical concept.
     
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  3. AlphaNumeric Fully ionized Registered Senior Member

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    You need to learn about continuums and uncountability in analysis. You don't seem to understand what the Reals are.
     
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  5. impaJah Registered Senior Member

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    Thanks for the suggestions. How do the "Reals" relate to my post? Do they show a contradiction?

    Thanks for the response!
     
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  7. AlphaNumeric Fully ionized Registered Senior Member

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    The Reals are the set of numbers people are familiar with. They form a continuum which has length but each element in the set is a point, which has no size at all. It's only because of particular properties that they have a total length which is non-zero.

    For instance, consider the Rationals, numbers of the form a/b for a,b whole numbers (and b non-zero). Between any two rationals there's always a rational, in fact infinitely many, yet if you sum up the total length they take up in the Reals (since all rationals are real but not all reals are rational) then you get zero, unlike the Reals.

    Furthermore there is no notion of 'next to' in a continuum, unlike for integers. The integers next to 2 are 1 and 3 but there is no Real next to 2, because, as I just said, given any 2 different Reals there's always infinitely many Reals between them. For example, consider 2 again. What's the number next to 2? 2.1? Obviously not because 2.01 is between 2 and 2.1. Is it 2.01 then? No, 2.001 is between them. So on and so on. To prove it in general you use the properties of the Reals, that if a,b are in the Reals then so is their average (a+b)/2 and if a<b then we have a < (a+b)/2 < b , so there's no real next to a.

    Talking about width and height when considering the length of sets of points is irrelevant, so your bringing it up is pointless. In fact all of your conclusions about whether the notion of building a construct with non-zero length from things of zero length is possible within mathematics/theory are false. The Reals are a contradiction of your claims. Your arguments are poorly constructed and show you haven't really made any attempt to find out about or understand this stuff. It's pretty basic mathematics, getting yourself an introductory (ie 1st year undergrad) book on analysis will help to fill in the gaps in your understanding.

    And this 'the first dimension' thing you keep referring to is a labelling of your own construction. No one in maths or physics uses such a phrase in the manner you are. You're tilting at windmills.
     

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