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Can you show me a pure 1D or 2D object? A line and a plane have a thickness. A pure 1 D line is one with no width. But if its width is zero, it doesn't exist. Similarly, a 2D plane is perfectly 2D only if its thickness is 0 which makes the plane vanish.

So are all objects in the universe 3D? What's so special about the number 3? Isn't there a chance that everything is 3D because we can perceive only upto 3D?

So thinking in the same way (even if I cant imagine it in a physical form in my mind), are there really an object which is purely 3D? There should be a dimension which should go to zero to make it really 3D (like line and plane) which should make the object doesn't exist in the first place. So, can't I extend this argument and say that an object doesn't really have a dimension?

I don't know if I make any sense. I don't know how to phrase what's in my mind correctly(tried my best) and I don't even know if it's a Mathematical question or Philosophical question (don't know what tags to put on the question!). NB: I posted it first on Mathematics and they told me it's better suited on Physics.

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  • $\begingroup$ All mathematical abstractions are "pure", and in that sense, unphysical (for example, is there a "pure" sphere anywhere in the physical world?). So it seems to me that your question is really about the relationship between the clean and abstract world of mathematics and the messy, living world we experience and deal practically with when doing physics. This is an age-old classic philosophical question. $\endgroup$
    – Stéphane Rollandin
    Commented Jul 24, 2020 at 14:13
  • $\begingroup$ In physics, we may calculate vector components of motion in one or two dimensions, but the moving objects have mass and thickness. $\endgroup$
    – R.W. Bird
    Commented Jul 24, 2020 at 14:29
  • $\begingroup$ Related, but for 0-dimensional objects physics.stackexchange.com/q/66733/226902 and 1-dimensional objects physics.stackexchange.com/q/812384/226902 $\endgroup$
    – Quillo
    Commented Apr 30 at 12:16

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Well, it's quite "obvious" that all the real objects around us are 3D.

But if we dig into the matter structure we find atoms which consist of elementary particles. Is electron actually 3D? If it is made of some continuous substance - then what these parts of electron consist of? (By the way, as far as I know there is nothing found that can be interpreted as "inner part of electron") And if the electron is not made of some continuous substance is it possible to say it is 3D?

Even though the world around us looks like 3D, it is very possible that actually it is quite thin "sheet" or "tube" in, let's say, 4D or 5D. And may be if we dig deep enough we will find these dimensions.

So, I can't give an example of "pure" 1D, 2D or 3D object. Or any other "pure" object. Bottomline of my answer is, that it doesn't matter.

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Re.

A line and a plane have a thickness. A pure 1 D line is one with no width. But if its width is zero, it doesn't exist. Similary, a 2D plane is perfectly 2D only if its thickness is 0 which makes the plane vanish.

Note that in a 1D space the term (and variable) 'width' does not exist, and similarly for the term 'thickness' in a 2D space. You are measuring things in 1D and 2D spaces with a 3D measuring instrument--which can not exist in 1D or 2D spaces.

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What you are saying is that the 3D-volume of these objects is zero, and yes, you could generalize this to higher dimensions. However, this does not mean that the object is non-existent.

On the other hand it is true that real-life object, even when scientists talk about 1D or 2D materials, are in fact 3-dimensional. This is not so hard to understand, since everything is made out of atoms that have a 3-dimensional spatial structure.

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