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[Consul]

People have been talking about Infinitely extended bodies on this thread. I don't think there are or can be Infinite things of any kind. You cannot even have infinite points on a line segment, which is something most people believe has got to be true. As soon as you would have Infinite points, then the distance between the points would have to be Zero and all the points on the line would collapse onto a single point. Infinite points on a line are actually an absurdity that cannot exist. All other concepts of the number of points approaching Infinity and the distance being differentially small never produce an actual Infinity of points on a line. This only approaches Infinity. Extending this we can say: An Infinite anything is an Absurdity.

A point-based continuum such as the mathematical real-number line is such that there are infinitely many points (real numbers) between any two points (real numbers), no matter how close they are; so there is no zero distance between any two of them, in the sense that there are no points (real numbers) between them.

Anyway, being zero-dimensional objects, mathematical points and physical point-particles cannot possibly touch, since touch requires surface contact; and 0D objects do not have any surfaces that could be in contact with each other. So external contact of 0D objects via surface contact is impossible, but what about internal contact via coincidence? If physical particles are point-particles, the only possible form of spatial contact between them—including collisions—is spatial coincidence, i.e. the occupation of the same point of space at the same time by two or more point-particles. This possibility presupposes that point-particles aren't "solid" in Locke's sense = "impenetrable".

What is true is that a point-based continuum cannot be constructed additively, since you cannot create a finite or infinite one-dimensional line by adding zero-dimensional points. You cannot get extension from nonextension, since 0cm + … + 0cm = 0cm.

[The Beast]

It is sensible to say that defined objects are confined to a three-dimensional cube. The term spacetime is confined to the z axis. Such metaphysical quantities of the spacetime can get smaller although, the physical objects stay the same (x,y,z). The distance of Zeno to the door gets smaller in time to a moment when the distance is contained within the object. He opens the door. There is such thing in mathematics as small infinity contain in infinity if all in one virtual category. The meaning of more dimensions is uncertainty.

[SteveKlinko]

People have been talking about Infinitely extended bodies on this thread. I don't think there are or can be Infinite things of any kind. You cannot even have infinite points on a line segment, which is something most people believe has got to be true. As soon as you would have Infinite points, then the distance between the points would have to be Zero and all the points on the line would collapse onto a single point. Infinite points on a line are actually an absurdity that cannot exist. All other concepts of the number of points approaching Infinity and the distance being differentially small never produce an actual Infinity of points on a line. This only approaches Infinity. Extending this we can say: An Infinite anything is an Absurdity.

A point-based continuum such as the mathematical real-number line is such that there are infinitely many points (real numbers) between any two points (real numbers), no matter how close they are; so there is no zero distance between any two of them, in the sense that there are no points (real numbers) between them.

Anyway, being zero-dimensional objects, mathematical points and physical point-particles cannot possibly touch, since touch requires surface contact; and 0D objects do not have any surfaces that could be in contact with each other. So external contact of 0D objects via surface contact is impossible, but what about internal contact via coincidence? If physical particles are point-particles, the only possible form of spatial contact between them—including collisions—is spatial coincidence, i.e. the occupation of the same point of space at the same time by two or more point-particles. This possibility presupposes that point-particles aren't "solid" in Locke's sense = "impenetrable".

What is true is that a point-based continuum cannot be constructed additively, since you cannot create a finite or infinite one-dimensional line by adding zero-dimensional points. You cannot get extension from nonextension, since 0cm + … + 0cm = 0cm.

So in the Limit when there is is an Infinite number of points between two Points, what is the distance between each point on the segment between the two original Points. Logically, the Distance has to be Zero if the number of points IS Infinite. Note that I said IS Infinite and not APPROACHES Infinite. To actually be Infinite is something different than something approaching Infinite. In mathematics nothing is ever Infinite, but rather things always only approach the Infinite. Infinity does not exist. This is why a Singularity in a Mathematical equation for a phenomenon of Physics always means there is something seriously wrong with the equation. Most equations have the Singularity problem at some point.

Another way to look at this is to do the usual Limit logic. Lets say we are considering the points on the segment between 0 and 1. We can place a number of points on the line segment with spacing dx. This would give us 1/dx number of points (not counting the point at Zero). As 1/dx gets larger and larger, dx must get smaller and smaller. And we can imagine this limiting process continuing with 1/dx getting larger and larger and even approaching Infinity. The truth is that 1/dx never gets to Infinity in a Limit process, rather it only approaches closer and closer. This is because dx always must have a slightly non Zero value. Everything is nice and happy with this situation until we think about making 1/dx actually be Infinity instead of just approaching Infinity. 1/dx cannot BE Infinity unless dx IS Zero. Thus the Absurdity. It is always unwise to say there is an Infinite anything when talking about Physical phenomenon. Infinity is always a Limit concept and not something that really exists.

[JackDaydream]

People have been talking about Infinitely extended bodies on this thread. I don't think there are or can be Infinite things of any kind. You cannot even have infinite points on a line segment, which is something most people believe has got to be true. As soon as you would have Infinite points, then the distance between the points would have to be Zero and all the points on the line would collapse onto a single point. Infinite points on a line are actually an absurdity that cannot exist. All other concepts of the number of points approaching Infinity and the distance being differentially small never produce an actual Infinity of points on a line. This only approaches Infinity. Extending this we can say: An Infinite anything is an Absurdity.

A point-based continuum such as the mathematical real-number line is such that there are infinitely many points (real numbers) between any two points (real numbers), no matter how close they are; so there is no zero distance between any two of them, in the sense that there are no points (real numbers) between them.

Anyway, being zero-dimensional objects, mathematical points and physical point-particles cannot possibly touch, since touch requires surface contact; and 0D objects do not have any surfaces that could be in contact with each other. So external contact of 0D objects via surface contact is impossible, but what about internal contact via coincidence? If physical particles are point-particles, the only possible form of spatial contact between them—including collisions—is spatial coincidence, i.e. the occupation of the same point of space at the same time by two or more point-particles. This possibility presupposes that point-particles aren't "solid" in Locke's sense = "impenetrable".

What is true is that a point-based continuum cannot be constructed additively, since you cannot create a finite or infinite one-dimensional line by adding zero-dimensional points. You cannot get extension from nonextension, since 0cm + … + 0cm = 0cm.

So in the Limit when there is is an Infinite number of points between two Points, what is the distance between each point on the segment between the two original Points. Logically, the Distance has to be Zero if the number of points IS Infinite. Note that I said IS Infinite and not APPROACHES Infinite. To actually be Infinite is something different than something approaching Infinite. In mathematics nothing is ever Infinite, but rather things always only approach the Infinite. Infinity does not exist. This is why a Singularity in a Mathematical equation for a phenomenon of Physics always means there is something seriously wrong with the equation. Most equations have the Singularity problem at some point.

Another way to look at this is to do the usual Limit logic. Lets say we are considering the points on the segment between 0 and 1. We can place a number of points on the line segment with spacing dx. This would give us 1/dx number of points (not counting the point at Zero). As 1/dx gets larger and larger, dx must get smaller and smaller. And we can imagine this limiting process continuing with 1/dx getting larger and larger and even approaching Infinity. The truth is that 1/dx never gets to Infinity in a Limit process, rather it only approaches closer and closer. This is because dx always must have a slightly non Zero value. Everything is nice and happy with this situation until we think about making 1/dx actually be Infinity instead of just approaching Infinity. 1/dx cannot BE Infinity unless dx IS Zero. Thus the Absurdity. It is always unwise to say there is an Infinite anything when talking about Physical phenomenon. Infinity is always a Limit concept and not something that really exists.

It does seem that Infinity about the vague limits or blurry edges, especially in relation to the body and mind. With the number of cells in the body, it would not be possible to count them, especially as they are in constant process of dying and reproducing. It can also be said that the mind is infinite because in relation to the physical and within time and space it is an underlying reality which is large with no clear end, in so far as it is expansive and is, in a sense connected to the nature of eternity.

[Consul]

So in the Limit when there is is an Infinite number of points between two Points, what is the distance between each point on the segment between the two original Points. Logically, the Distance has to be Zero if the number of points IS Infinite. Note that I said IS Infinite and not APPROACHES Infinite. To actually be Infinite is something different than something approaching Infinite. In mathematics nothing is ever Infinite, but rather things always only approach the Infinite. Infinity does not exist. This is why a Singularity in a Mathematical equation for a phenomenon of Physics always means there is something seriously wrong with the equation. Most equations have the Singularity problem at some point.

The continuous line of real numbers is an abstract mathematical thing, so the concept of spatial distance isn't applicable to it. However, if physical space is a point-based continuum, then there are measurable spatial distances between space-points. But the spatial distance between two space-points which are next to each other (direct neighbors) is undefined (neither 0m nor >0m), since no two space-points in a continuum constituted by an actual infinity of space-points are next to each other (direct neighbors), in the sense that there are no space-points between them.

[GE Morton]

The continuous line of real numbers is an abstract mathematical thing, so the concept of spatial distance isn't applicable to it. However, if physical space is a point-based continuum, then there are measurable spatial distances between space-points. But the spatial distance between two space-points which are next to each other (direct neighbors) is undefined (neither 0m nor >0m), since no two space-points in a continuum constituted by an actual infinity of space-points are next to each other (direct neighbors), in the sense that there are no space-points between them.

"Space point" is a contradiction in terms.

[SteveKlinko]

People have been talking about Infinitely extended bodies on this thread. I don't think there are or can be Infinite things of any kind. You cannot even have infinite points on a line segment, which is something most people believe has got to be true. As soon as you would have Infinite points, then the distance between the points would have to be Zero and all the points on the line would collapse onto a single point. Infinite points on a line are actually an absurdity that cannot exist. All other concepts of the number of points approaching Infinity and the distance being differentially small never produce an actual Infinity of points on a line. This only approaches Infinity. Extending this we can say: An Infinite anything is an Absurdity.

A point-based continuum such as the mathematical real-number line is such that there are infinitely many points (real numbers) between any two points (real numbers), no matter how close they are; so there is no zero distance between any two of them, in the sense that there are no points (real numbers) between them.

Anyway, being zero-dimensional objects, mathematical points and physical point-particles cannot possibly touch, since touch requires surface contact; and 0D objects do not have any surfaces that could be in contact with each other. So external contact of 0D objects via surface contact is impossible, but what about internal contact via coincidence? If physical particles are point-particles, the only possible form of spatial contact between them—including collisions—is spatial coincidence, i.e. the occupation of the same point of space at the same time by two or more point-particles. This possibility presupposes that point-particles aren't "solid" in Locke's sense = "impenetrable".

What is true is that a point-based continuum cannot be constructed additively, since you cannot create a finite or infinite one-dimensional line by adding zero-dimensional points. You cannot get extension from nonextension, since 0cm + … + 0cm = 0cm.

So in the Limit when there is is an Infinite number of points between two Points, what is the distance between each point on the segment between the two original Points. Logically, the Distance has to be Zero if the number of points IS Infinite. Note that I said IS Infinite and not APPROACHES Infinite. To actually be Infinite is something different than something approaching Infinite. In mathematics nothing is ever Infinite, but rather things always only approach the Infinite. Infinity does not exist. This is why a Singularity in a Mathematical equation for a phenomenon of Physics always means there is something seriously wrong with the equation. Most equations have the Singularity problem at some point.

Another way to look at this is to do the usual Limit logic. Lets say we are considering the points on the segment between 0 and 1. We can place a number of points on the line segment with spacing dx. This would give us 1/dx number of points (not counting the point at Zero). As 1/dx gets larger and larger, dx must get smaller and smaller. And we can imagine this limiting process continuing with 1/dx getting larger and larger and even approaching Infinity. The truth is that 1/dx never gets to Infinity in a Limit process, rather it only approaches closer and closer. This is because dx always must have a slightly non Zero value. Everything is nice and happy with this situation until we think about making 1/dx actually be Infinity instead of just approaching Infinity. 1/dx cannot BE Infinity unless dx IS Zero. Thus the Absurdity. It is always unwise to say there is an Infinite anything when talking about Physical phenomenon. Infinity is always a Limit concept and not something that really exists.

It does seem that Infinity about the vague limits or blurry edges, especially in relation to the body and mind. With the number of cells in the body, it would not be possible to count them, especially as they are in constant process of dying and reproducing. It can also be said that the mind is infinite because in relation to the physical and within time and space it is an underlying reality which is large with no clear end, in so far as it is expansive and is, in a sense connected to the nature of eternity.

Hmmm. I'm going to have to ponder this a little more before I can say anything about it.

[SteveKlinko]

So in the Limit when there is is an Infinite number of points between two Points, what is the distance between each point on the segment between the two original Points. Logically, the Distance has to be Zero if the number of points IS Infinite. Note that I said IS Infinite and not APPROACHES Infinite. To actually be Infinite is something different than something approaching Infinite. In mathematics nothing is ever Infinite, but rather things always only approach the Infinite. Infinity does not exist. This is why a Singularity in a Mathematical equation for a phenomenon of Physics always means there is something seriously wrong with the equation. Most equations have the Singularity problem at some point.

The continuous line of real numbers is an abstract mathematical thing, so the concept of spatial distance isn't applicable to it. However, if physical space is a point-based continuum, then there are measurable spatial distances between space-points. But the spatial distance between two space-points which are next to each other (direct neighbors) is undefined (neither 0m nor >0m), since no two space-points in a continuum constituted by an actual infinity of space-points are next to each other (direct neighbors), in the sense that there are no space-points between them.

Logically, it seems to me that If two points are not on top of each other then there is distance between them. If two points are direct neighbors then they much touch each other. The only way they can touch each other is if they are on top of each other. I assume we are talking about the normal definition of a point where the point has Zero dimension.

[Consul]

"Space point" is a contradiction in terms.

It would be if "space-point" meant "spatially extended point", but that's not its meaning. A space-point is a spatially unextended element of a space which is a point-based continuum.

[Consul]

A space-point is a spatially unextended element of a space which is a point-based continuum.

You can also have space-points in a space which is point-based and noncontinuous/discrete, such that every volume of space contains only a finite number of space-points.

[SteveKlinko]

Mathematical Points and Dimensional Points

A Mathematical Point has identically zero diameter and has no dimensional properties. It is simply a location in Space. Also, if you let dx be the differential distance between the Points on a line then you can make dx as small as you like and the Points will never touch. Only when dx is identically zero do the Points touch each other, but they also all collapse onto a single Point. This means you can not arrange Points next to each other in a line configuration where they touch each other.

An n-dimensional Observer will naturally think of a Point as something that has n-dimensional characteristics. A 2D Observer thinks of a Point as a tiny Circle, a 3D Observer thinks it's a tiny Sphere, and a 4D Observer thinks it's a tiny Hyper Sphere. We will call this tiny object a Dimensional Point and if the dimension is specified we use the term nD Point. An nD Point is just the set of all Points in nD Space that are equidistant from a central Point with a differential Radius (dR). A 2D Point is an Empty Circle of Points, a 3D Point is an Empty Sphere of Points, and a 4D Point is an Empty Hyper Sphere of Points. A Full nD Point can be defined as an nD Point including all internal Points, so a Full 2D Point is a Full Circle, a Full 3D Point is a Full Sphere, and A Full 4D Point is a Full Hyper Sphere. The definition of an nD Point can also be used to define a 1D Point which is an Empty or Full Line and the 0D Point which is the same as a Point.

The real utility of nD Points is that two or more nD Points can touch. Since the surfaces of nD Points are made out of Points, we can define two nD Points as touching when a Point from one is at the same location in space as a Point from the other one. Multiple nD Points can be arranged like Points to form Lines and Planes, but unlike Points the nD Points can touch. Also, an nD Point has surface structure that can visually be seen to rotate, whereas a Point cannot visually rotate.

An nD Point can be thought of as the smallest Object that can exist while retaining the n-dimensional characteristics of the Space. For 2D Space a Point is not an existent Object. It is a Mathematical concept. It has no existence or extension into any dimension. The basic Object in 2D Space is the 2D Point because it has extension in 2 dimensions. A 2D Point has a differential Area whereas a Point has identically zero Area. However a 2D Point has no real existence in 3D Space because there is no extension into 3D Space. A 2D Point has identically zero Volume. When we work in 3D Space we will need to use 3D Points, which have extension into all 3 dimensions and have a differential Volume. Similarly, a 3D Point will not have any real existence in 4D Space because there is no extension into 4D Space and the Hyper Volume is identically zero. We will need to use 4D Points when working in 4D Space. Also note that a higher Dimensional Point can not fully exist in a lower dimensional Space. Only a cross section of the higher Dimensional Point can exist in the lower dimensional Space.

Since an nD Point is a representation of the smallest thing in nD Space that retains the dimensionality characteristics of the nD Space it would not be physically compatible, for example, to consider a 2D Point in 3D Space. A 2D Point only has extension and existence in two dimensions and would make no sense in 3D Space. You could not construct 3D Objects in 3D Space with 2D Points. A 3D Observer would naturally think that a Point has some dR radius all the way around in any angular direction, but the 2D Point has dR radius only within the plane of the 2D Point Circle and has identically zero radius in all other directions. A 2D Point is Flat in 3D Space. The 2D Point would need to be replaced with a 3D Point. The dimensionality of the nD Point must be the same as the dimension of the Space. We cannot just take a 2D Point out of 2D Space and see how it behaves in 3D Space. A 3D Point is needed.

In the following Animation two Empty nD Points will be constructed on the y-Axis, which is the Hyper Axis for a 2D Point World. A 2D Point is first constructed at the origin and then another one 1 Diameter away in the positive direction on the y-Axis. We use Empty nD Points because we are mostly interested in the surface behavior of these Objects. The 3D Reference shows the actual placement and the Axis Shared area shows what a 2D Observer would see. A 3D Observer sees that the two 2D Points are not touching. In fact they can not touch no matter how close you bring them. They can only touch when they are at the same location because a 2D Point has zero extension in the direction of the y-Axis. A 2D Point is Flat in 3D Space. Circles are added to form two 3D Points. The 3D Points can now touch. The 3D Points touch at a single Point as indicated. The 2D Observer can not directly see the touching 3D Points that make up the Line but must interpret what is depicted in the Axis Sharing area. The 2D Observer sees the component Circles of the 3D Points displayed across the x-Axis. The 2D Observer imagines that each component Circle is in a separate parallel layer of 2D Space somewhere. The Axis Sharing area depicts a kind of sideways rendition of the actual 3D Space because as you go Up or Down in 3D Space you go Right or Left in the Axis Sharing Area.

https://www.theintermind.com/ExploringT ... nYAxis.gif

[JackDaydream]

Reading the various posts on the thread I am wondering to what extent mind fits into space and time. The body is in 3D reality; but this is where it becomes complex, especially how does mind and body fit into dimensions; especially the division between mind and matter, of which both 'body' and 'mind' are aspects. It can also be asked, to what extent is body equated with matter and to what extent is mind physical or non-physical?

[The Beast]

“This, which exist always existed”
Instead of a point of diameter zero I might consider an evolved manifold somewhere in a grid of unknown dimensions and properties. This manifold or point in a grid grew its volume creating an energy diverticulum, long periods of transformations and the Big Bang. Two tangents to the diverticulum/Universe and perpendicular to each other are virtually the axis x,y. the intersection of x,y or (0,0) is the intersection some point before the neutrino escape. As the Universe grew the axis (virtually) moved as well to accommodated the cartesian (x,y,z) the units of are manifolds that might or not be containing the quantum foam. At (1,1,1) a plane is also formed which is also the basis of a Universal grid. This grid of manifolds might contain or not the foam to facilitate the formation of stars. The grid is not in a fixed position and might drag and push planes due to the gravity of big bodies. It is possible that the z axis might have suffered adjustments in its geometry and planes might share the same coordinate if virtual. Although, the unit is the manifold for practical purposes we might say that the z axis is a vector called the spacetime continuum and is around 14 billions light years. As to the Nature of the Universe, I ponder: is it like bubble gum stretching out from a starting point or like a Universal plane evolving in each z plane? Our place in the universe is an evolved life manifold (x,y,z,..n)

[Consul]

A Mathematical Point has identically zero diameter and has no dimensional properties.

As far as I know, strictly speaking, there's a distinction between being zero-dimensional (point-sized) and being adimensional or dimensionless, i.e. lacking a defined dimension. For example, if abstract objects such as sets and linguistic types exist (e.g. the letter-type <a>), then they are adimensional rather than zero-dimensional.

The real utility of nD Points is that two or more nD Points can touch. Since the surfaces of nD Points are made out of Points, we can define two nD Points as touching when a Point from one is at the same location in space as a Point from the other one.

Right. Generally, direct contact between 2D or 3D objects can be defined in terms of coincidence (colocation) of (parts of) their lower-dimensional boundaries. Circles and spheres are in direct contact when two of their respective boundary-points coincide; and squares and cubes are in direct contact when two of their respective 0D, 1D, or 2D boundaries coincide (partially at least in the case of line or surface contact).

Multiple nD Points can be arranged like Points to form Lines and Planes, but unlike Points the nD Points can touch. Also, an nD Point has surface structure that can visually be seen to rotate, whereas a Point cannot visually rotate.

A point qua 0D object cannot rotate at all!

[Consul]

It can also be asked, to what extent is body equated with matter…

In my understanding, "immaterial body" is a contradiction in terms. The idea of "spiritual bodies" that we find in spiritualist and occultist literature makes no sense unless "spiritual" is read as "made of a special form of matter (unknown to natural science)". For the truly nonphysical souls/spirits of academic philosophy/theology (Cartesian souls), which are bodiless and consist of no (material) stuff at all, are different from the paraphysical souls/spirits/ghosts of folk mythology, which are not really bodiless but merely consist of some alien, exotic, "fine"/"thin"/"transparent"/"ethereal"/"airy"/"gassy" stuff, as opposed to the familiar, "coarse"/"hard"/"solid"/"thick" stuff of which ordinary material objects are composed.