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- Thread starter Mohd Abdullah
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Mark44

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There is a difference between physical reality and the mathematical or geometric objects we use to model reality.Hi, as we know all objects must be three dimensional. If there is two dimensional "object" or "shape" in the universe, "it" will not look different from space or nothing as "it" is neither thick nor thin. Mathematicians calling "it" as a "surface" but "it" have zero thickness, isn't it a contradiction to call that which has no thickness as a surface?

No. By your same logic, a line in space is an abstract geometric entity that extends infinitely far in two directions, and has zero thickness and zero width, but it's not the same as "nothing." Similarly, a point has zero width, zero length, and zero depth, but it is also not the same as "nothing."Mohd Abdullah said:Not to mention that two dimensional plane is extended infinitely inplying that "it" don't have shape. So, if "it" extended infinitely and have zero thickness "it" is just the same as nothing

Surfaces, including planes, lines, curves, and points are all mathematical abstractions that we use to help us understand physical reality. But so what?Mohd Abdullah said:(that which has no shape) and "it" can only be assumed to "exist" in abstraction only. Any thoughts?

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isn't it a contradiction to call that which has no thickness as a surface?

No, it is the definition of a surface in the sense under consideration. That is part of what a surface is.

So, if "it" extended infinitely and have zero thickness "it" is just the same as nothing (that which has no shape) and "it" can only be assumed to "exist" in abstraction only. Any thoughts?

Not all surfaces extend to infinity. For example, a spherical shell is a surface. But even if all surfaces "extended to infinity" that would not show that they are the same thing as nothing. "Nothing" has

- #4

anorlunda

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it" is just the same as nothing (that which has no shape) and "it" can only be assumed to "exist" in abstraction only.

I'm a sailor. I live on the surface of the sea. Believe me, it really exists.

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But if you're stuck on atoms having thickness, can you imagine a 2-D plane of electrons? Or some smaller thing that effectively has no size?

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There is a difference between physical reality and the mathematical or geometric objects we use to model reality.

No. By your same logic, a line in space is an abstract geometric entity that extends infinitely far in two directions, and has zero thickness and zero width, but it's not the same as "nothing." Similarly, a point has zero width, zero length, and zero depth, but it is also not the same as "nothing."

Surfaces, including planes, lines, curves, and points are all mathematical abstractions that we use to help us understand physical reality. But so what?

What distinguish them from nothing if assuming there are 1D lines and 2D planes in existence? Can you explain how and why?

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No, it is the definition of a surface in the sense under consideration. That is part of what a surface is.

Not all surfaces extend to infinity. For example, a spherical shell is a surface. But even if all surfaces "extended to infinity" that would not show that they are the same thing as nothing. "Nothing" hasproperties, but a surfacenohave properties. Therefore a surface is not the same thing as "nothing."does

In mathematics, perhaps we can say a 2D plane have properties but assuming if there is a real 2D plane in existence. What exactly distinguish a "surface" that is neither thick nor thin and infinitely extended in all directions from nothing such as space?

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But if you're stuck on atoms having thickness, can you imagine a 2-D plane of electrons? Or some smaller thing that effectively has no size?

If atoms themselves are 3D then 2D plane is impossible in existence.

What are exactly the differences between 2D plane, 0D point and space or nothing in reality?

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In mathematics, perhaps we can say a 2D plane have properties

Exactly. You asked if there was a contradiction. The answer to that question is no, because we are talking about definitions when we are talking about mathematics.

but assuming if there is a real 2D plane in existence.

That is a different question. I am inclined to think there are no real examples of 2D plane

- #10

nasu

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You are confusing the mathematical definitions with the physical concepts, as mentioned.

All mathematical objects are abstractions and they don't "exist" the same way real objects "exist".

It does not mean that abstract concepts are "nothing".

The number 1000 does not "exist" as a physical object but is it "nothing"?

What we call 2D and 1D objects in physics is not the same as the abstract notions of planes and lines in mathematics.

There is no point to argue about them.

The "surface" of a solid, as studied by "surface science" is a completely different object than the mathematical notion of surface.

Same as a ball is not a mathematical sphere even though we may use the math concept to model the real object.

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Exactly. You asked if there was a contradiction. The answer to that question is no, because we are talking about definitions when we are talking about mathematics.

That is a different question. I am inclined to think there are no real examples of 2D planethingsbeyonditems of convention. We talk about such items as the orbital plane of our planet or the plane containing the equator (or the equator itself), but they don't exist as tangible things out in the real world.

That's my point. In reality or existence, real 2d "shape" or "object" is impossible. Thus, if there is a 2d or 0d "shape" or "object" in reality "it" will not look different from nothing. Real objects and concrete shapes (not abstract) are necessarily 3D.

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You are confusing the mathematical definitions with the physical concepts, as mentioned.

All mathematical objects are abstractions and they don't "exist" the same way real objects "exist".

It does not mean that abstract concepts are "nothing".

The number 1000 does not "exist" as a physical object but is it "nothing"?

What we call 2D and 1D objects in physics is not the same as the abstract notions of planes and lines in mathematics.

There is no point to argue about them.

The "surface" of a solid, as studied by "surface science" is a completely different object than the mathematical notion of surface.

Same as a ball is not a mathematical sphere even though we may use the math concept to model the real object.

What we call as 2d or 1d "object" or "shape" in physics is too, impossible in existence. Just like the mathematical abstract notions of planes and lines. Even if 2D, 1D or 0D "shape" or "object" is possible in existence, what is the difference between them and space or nothing? All objects, real objects and concrete shape, are necessarily 3D unless someone makes an abstract "shape" in his or her mind.

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nasu

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How can be existing objects impossible?What we call as 2d or 1d "object" or "shape" in physics is too, impossible in existence.

Graphene sheets, nano-wires, quantum dots - they all exist and are very possible. It's just that associating these real structures with 2D or 1D models does not make them abstract mathematical objects.

You won't say that the 100 dollar bill in your pocket is "impossible" just because the number 100 is an abstract concept which is impossible "to exist".

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How can be existing objects impossible?

Graphene sheets, nano-wires, quantum dots - they all exist and are very possible. It's just that associating these real structures with 2D or 1D models does not make them abstract mathematical objects.

You won't say that the 100 dollar bill in your pocket is "impossible" just because the number 100 is an abstract concept which is impossible "to exist".

Graphene sheets and nanowires are actually 3D, as it is formed by atoms which are necessarily 3D and still have a very small amount of thickness. A real 2D "shape" in reality will have no any difference from nothing, as "it" is neither thick nor thin and "it" have zero thickness. Not to mention "it" will have no extended dimensions in existence. About the quantum dots, I'm not sure about "it" as "it" keep popping out from nothing and then disappear again into nothing. I think we need to define the word "exist" unambiguously.

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nasu

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So the discussion has no point. Arguing about existence or not of abstract mathematical concept is pointless. They have the same level of "existence" as all abstractions.

And there is no relevance for the existence of the objects modeled by these abstractions.

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Chestermiller

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Points, lines, surfaces and volumes - all define places … and none of them are concrete (i.e. real, and not abstract) things.

So, if your definition of a 'thing' is that it has mass and is made of stuff, then you're right, a surface is no-thing. Note, however, that in the physical universe, all things (that are made of stuff and have mass)__have__ a place, an edge (bounding surface) and a volume (but it would be untrue to say that they __are__ their place, edges or volume).

A volume, on the other hand - is just the place where stuff exists, and a surface is just the place where one thing stops and another starts (such as the surface of the ocean, as another person remarked).

A surface is clearly a place of transition - and can never be a__physical__ thing in its own right.

So, if your definition of a 'thing' is that it has mass and is made of stuff, then you're right, a surface is no-thing. Note, however, that in the physical universe, all things (that are made of stuff and have mass)

A volume, on the other hand - is just the place where stuff exists, and a surface is just the place where one thing stops and another starts (such as the surface of the ocean, as another person remarked).

A surface is clearly a place of transition - and can never be a

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In maths I can be anything.

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Points, lines, surfaces and volumes - all define places … and none of them are concrete (i.e. real, and not abstract) things.

So, if your definition of a 'thing' is that it has mass and is made of stuff, then you're right, a surface is no-thing. Note, however, that in the physical universe, all things (that are made of stuff and have mass)havea place, an edge (bounding surface) and a volume (but it would be untrue to say that theyaretheir place, edges or volume).

A volume, on the other hand - is just the place where stuff exists, and a surface is just the place where one thing stops and another starts (such as the surface of the ocean, as another person remarked).

A surface is clearly a place of transition - and can never be aphysicalthing in its own right.

I define thing, or object, as that which has shape. But it seems a 2D plane can be interpreted as an object and not as an object in mathematics. 2D plane is generally defined as having two extension or someone can call the extensions as width and length (width is just length if someone see it from another orientation) and is not thin and thick (zero thickness). This 2D plane also extend into infinity, so this definition fall within the category of nothing while if someone define 2D such as abstract shapes like triangle and square then it fall within the category of object.

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In maths I can be anything.

Sorry what do you mean by that?

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I think he meant in a humorous way that math produces results which depends on what assumption are made.Sorry what do you mean by that?

Math is not a problem, but assumptions can be.

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I can make a logically sound argument that is complete nonsense.

I can be a perfect circle in math that can't be in reality.

I can also divide by zero.

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A.T.

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Thing can mean different things.

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Which thing, some thing, any thing or every thing?

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