How can something be located in space but not occupy any space?

[Sophrosyne]

Before anybody thinks that I am being difficult or argumentative, I am not.

Just having a conversation about the seeming implications of an article that I read.

If you want to know about my personal experience with the kind of problems being discussed:

I remember being taught that the definition of a circle is the set of all points in a plane that are a give distance from a given point. Points, I was taught, have no dimensions, no thickness, etc. Yet, I was then taught a certain mathematical formula to determine the area of a circle. Well...

First, the circle, by definition, has no dimensions or thickness, so how can it have an area? More importantly, the forumla given makes calculations of space that is, by definition, not part of the circle.

If by "the area of a circle" it was really meant "the area encompassed by a circle", that distinction should have been--and should be--made clear with language.

Is that being nitpicky? No, it is being the critical thinker often called a philosopher.

circles have 2 dimensions, but we equate 3 dimensions as existence (4 if you want to include time).

 

[LOVEthroughINTELLECT]

Who said it was a "part" of space? It is more like a postal address, just a pointer to a location. In other words you really cannot see it because it doesn't take up space required to be seen. If you were to go to an address you would see something at the location but the number (address) would not exist (physically) without someone actually putting up something with the number on it.

But nobody feels the need to point out that a postal address has no dimensions, no thickness, etc. Euclidean points, as I understand them, are defined as having no dimensions, no thickness, etc.

A postal address, by the way, does take up space. I will make up a postal address to demonstrate this: 100 North Euclidean Confusion Street. In this case, the graphics used to produce that address take up space. I know very little about the physics of sound, but I think that it is safe to say that if a person utters aloud "100 North Euclidean Confusion Street" that the result is space somehow being occupied by that address.

It sounds like people are saying that a point is a location and is not necessarily a part of space. Well, if it is not a part of space then what is it a part of?

Furthermore, how can a location in something--whatever that something is--not be a part of it? What if I told you that a location in Indiana is not a part of Indiana? That would not make any sense, would it?

 

[Sophrosyne]

But nobody feels the need to point out that a postal address has no dimensions, no thickness, etc. Euclidean points, as I understand them, are defined as having no dimensions, no thickness, etc.

A postal address, by the way, does take up space. I will make up a postal address to demonstrate this: 100 North Euclidean Confusion Street. In this case, the graphics used to produce that address take up space. I know very little about the physics of sound, but I think that it is safe to say that if a person utters aloud "100 North Euclidean Confusion Street" that the result is space somehow being occupied by that address.

It sounds like people are saying that a point is a location and is not necessarily a part of space. Well, if it is not a part of space then what is it a part of?

Furthermore, how can a location in something--whatever that something is--not be a part of it? What if I told you that a location in Indiana is not a part of Indiana? That would not make any sense, would it?

Think of an address in your head, is it less of an address in your mind than it is on a piece of paper or a 100 foot tall sign? The address is the SAME regardless of how you display it, it doesn't change therefore an address that exists in your mind doesn't physically exist in your mind like it does on paper or on a billboard. If you take a point and represent it as a dot and take a microscope you could then measure the area of the 2 dimensional circle and say that point exists in 3 dimensions because you can see it but if you imagine the same point without the dot on the paper to represent it as the location of the paper there it still gives you the same spot. The spot doesn't change that you are referencing only the way you represent it via physical cues or numerical coordinates. You want to take something that in your mind can be referenced just fine and force it to exist with a physical form so as to satisfy yourself. Assigning a physical construct to an idea doesn't change the original idea by doing so and the original idea still stands while the physical construct is not the idea itself but instead a representation of the idea in the end.

 

[r035198x]

LTI, can I borrow my dad's shotgun and shoot you in the head with it?That way you won't be taking up space to ask about space.

 

[LOVEthroughINTELLECT]

Think of an address in your head, is it less of an address in your mind than it is on a piece of paper or a 100 foot tall sign? The address is the SAME regardless of how you display it, it doesn't change therefore an address that exists in your mind doesn't physically exist in your mind like it does on paper or on a billboard...

An address in a person's mind takes up space in his/her brain. Neurological material that could be occupied by something else is occupied by that address.

If you take a point and represent it as a dot and take a microscope...

A dot would be a dot, not a point. If something, such as a dot on a piece of paper, has dimensions, thickness, etc. then by definition it is not a point.

you could then measure the area of the 2 dimensional circle and say that point exists in 3 dimensions because you can see it...

Again, by definition that would not be a point.

but if you imagine the same point without the dot on the paper to represent it as the location of the paper there it still gives you the same spot...

A dot on a piece of paper contains several locations, not one.

I am not a physicist, but I bet that the language of physics could map countless atoms occupying countless locations on a single dot on a piece of paper.

The spot doesn't change that you are referencing only the way you represent it via physical cues or numerical coordinates...

Okay, so we use something that has dimensions to refer to something that by definition does not have dimensions. That does not address the question of how the something that has no dimensions can be located in space while not occupying any space.

Numerical coordinates bring up another problem. Numerical coordinates show the distances between something and two or more other things. But if any of those things does not have any dimensions how can there be any quantity between them and other things?

You want to take something that in your mind can be referenced just fine and force it to exist with a physical form so as to satisfy yourself. Assigning a physical construct to an idea doesn't change the original idea by doing so and the original idea still stands while the physical construct is not the idea itself but instead a representation of the idea in the end...

But we don't just create a physical-world reference to an idea. We take what you seem to be conceding is a metaphysical entity and from it make scientific conclusions about physical entities.

It is, it seems, using logical extensions of the metaphysical to make conclusions about the properties, structure, behavior, etc. of the physical.

 

[Sophrosyne]

An address in a person's mind takes up space in his/her brain. Neurological material that could be occupied by something else is occupied by that address.

does it? I thought it was about nerve connections not space itself. If things took up space in your brain when you learned too much it would explode unless your brain is empty.

A dot would be a dot, not a point. If something, such as a dot on a piece of paper, has dimensions, thickness, etc. then by definition it is not a point.

yes, but people represent a point in geometry using a dot.

A dot on a piece of paper contains several locations, not one.

if the dot was representing a point it would have two dimensional location numbers (x,y) on the paper.

Okay, so we use something that has dimensions to refer to something that by definition does not have dimensions. That does not address the question of how the something that has no dimensions can be located in space while not occupying any space.

you again are trying to take one type of something and apply it to another type of something. A location is where you can have something not where something necessarily is.

Numerical coordinates bring up another problem. Numerical coordinates show the distances between something and two or more other things. But if any of those things does not have any dimensions how can there be any quantity between them and other things?

Distance is distance, one only uses objects to put "bookends" on a distance for reference. If I said mile... you would have an idea how far that is without two objects one to measure a distance between. I could put a point on each end of the mile or a car on each end and you would equally say both miles are the same distance.

But we don't just create a physical-world reference to an idea. We take what you seem to be conceding is a metaphysical entity and from it make scientific conclusions about physical entities.

It is, it seems, using logical extensions of the metaphysical to make conclusions about the properties, structure, behavior, etc. of the physical.

Some ideas work well with a direct physical world translation, while others only approach something akin to a metaphysical entity. In some cases the logic of scientific principles such as mathematics and physics create a 1:1 relationship with reality such that even through representations are not actual they can be applied to the actual to both understand and predict reality in use. One can put two dots on a map (points) and then go to where those points represent on the map and travel the distance between the two points and measure it and get close to distance in reality and in the map representation.

 

[Sojourner1]

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Thread has been moved at the request of the OP.


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[Nanopants]

What if you have a meter stick, with infinitesimal points marked at every tenth part, and between every mark you have ten more infinitesimal points marked in the same way, ad infinitum.

How much space would be occupied by all of the points marked inclusively?

Is it the entire length of the meter stick, or zero?

 

[acropolis]

I think Cantor Dust is relevant to this discussion.

 

[Sophrosyne]

What if you have a meter stick, with infinitesimal points marked at every tenth part, and between every mark you have ten more infinitesimal points marked in the same way, ad infinitum.

How much space would be occupied by all of the points marked inclusively?

Is it the entire length of the meter stick, or zero?

Points don't occupy space, that is the issue here as points just are locations and not the space itself. If points occupy space then something there that has a "point" attached to it would occupy more space than it did before the point was there and it doesn't.

 

[quatona]

Euclidean points, the foundation of all of geometry, by definition have no dimensions, no thickness, etc. You know, stuff that you were taught the first day of 10th-grade geometry. Yet, by definition they are located in space--we use them to describe and measure space. Therefore, we have something that is supposedly part of space but does not occupy any space.

I may be wrong but I have always thought of them as conceptual tools rather than of objects.

 

[Sophrosyne]

I may be wrong but I have always thought of them as conceptual tools rather than of objects.

You are correct, they don't exist in the physical realm as we know of because if a point had a finite volume to occupy space then you could use a formula for volume to calculate it. The formulas regarding volume require perhaps an infinite amount of points (lines) surrounding the volume encompassed and mathematically speaking the points do not add to the volume either nor take up any more space to show the volume there is therefore by elimination they don't have volume so cannot occupy space.