Relative to: a relational equality

[Gem]

The quality of a thing is defined by the way in which it is distinct from other things, which on the whole means, any one thing is defined by all other things.

What then is one thing? Is that where no relation with an other exists? No, not exactly. Things themselves only exist in relationship, which was succinctly expressed by physicist, Feynman, as, 'all mass is interaction'.

From here we have to dispense with notions of there being things, and frame this query in terms of relations. The relation itself and the related things are singular as a function. Not sequential in a timely sense, yet consequential in simultaniety.

There is no element of time in this paradigm, and the explanatory symbolism used below represents the singular relation. It is only broken into components so as to explain the theoretical philosophy.

This is where I began the philosophy I call 'dot theory'. The fundamental premise of this philosophy is the mind has formal limitations, and can not cognise form where the relation between things is equal (this wil be elaborated on below). The simplest example of this is, if there we two things called A and B. Inevitably, A relates to B in the exact same way as B relates to A (I use dots to represent this). This makes A indistinguishable from B due to what I call an 'equal relation':



The next step is dots in an equalateral triangle shape with A,B and C representing those dots.



I think the easiest way to imagine this is to imagine the corner points have a force like gravity that acts upon the other points. This symbolises the relation one dot (corner) has with the others. We can see that A,B and C's 'gravity' affect each other equally, and therefore this is an 'equal relation', just as relation between any two is an equal relation. Since things are relational, this trio representation is not in fact different from the relation between two I initially described. It's more a like two possibilities within a single equal relation. Actually, it's more like two inevitabilities of an equal relation.

The same applies to a 4 part relation - or the tetrahedral relation - which again entails 4 dots that equally affect each other (with their imaginary gravity).



So, when we ask, 'what is one thing?' We have no material to define such, but we have inevitablities of an equal relation. The last of these suggests the inevitability of volumous space (albeit it formless in its emptiness).

Remember, these images are mere representations of what I call 'equal relation', which is not a shape at all - but space is entailed in it.

In my 5th paragraph I mentioned the minds formal limitation, and at this stage that limitation arises again, because one can not place any more dots (corners) in a way that they will affect each other equally. Five dots will have an 'unequal relation'. See images:



or alternatively:



As you can see, 5 dots (corners) can't possibly be placed in a way where our imaginary gravity affects all dots equally (the same distance from all others), and thus we have 2 different relations - and since things are relational - we have more than one thing.

[r6r6]

Putting aside some dictionary definitions of the word 'thing', we can place the word 'thing' into two, or perhaps three, primary cosmic catagories:

1) thing as a metaphysical-1, concept i.e. mind/intellect, and concepts do not occupy space. Ex a metaphysical-1 concept of space irrespective of whether or not,
...1a) that space is non-occupied and has no dynamic qualities, or,
....2a) an occupied space that has dynamic qualities.

both are still concepts, and the concepts are used as metaphysical-1 communication tools.

2) 'thing' as that which occupies space ergo has dynamic qualities being expressed.

To define a 3D, volumetric space, that is systemically enclosed, we know the minimal set of things to define that 3D volumetric space are all associated with the tetra{4}hedron.

To define a 2D area space, that is systemically enclosed, we know the minimal set of things to define that 2D area, are associated with a tri{3}angle.

Ive been purporting for some years now, and in this forum, that, the minimal solid thing, can be no less than a subdivided triangle, defined by the tetrahedrons 4 vertexes{ nodal event/conjunctions.

To clarify, when a tetrahedron inside-outs itself, via one of its vertexes on a trajectory that takes it through one of its opposite openings, the is place where are all four vertexes in the same 2D triangular plane.

[Gem]

Originally Posted by r6r6r

Putting aside some dictionary definitions of the word 'thing', we can place the word 'thing' into two, or perhaps three, primary cosmic catagories:

Well, my philosophy is pretty much the definition of 'a thing' as relational, and it explains the relational possibilities of a thing. The geometric representations are all referring to that one thing. If the relation is five ways (relation between 5 dots) we then inevitably have two things (2 different relations), which are represented by the 5 sided pyramid and the hexahedron I depicted.

1) thing as a metaphysical-1, concept i.e. mind/intellect, and concepts do not occupy space. Ex a metaphysical-1 concept of space irrespective of whether or not,
...1a) that space is non-occupied and has no dynamic qualities, or,
....2a) an occupied space that has dynamic qualities.

both are still concepts, and the concepts are used as metaphysical-1 communication tools.

2) 'thing' as that which occupies space ergo has dynamic qualities being expressed.

I expressed those dymamic qualities in the geometric representations.

To define a 3D, volumetric space, that is systemically enclosed, we know the minimal set of things to define that 3D volumetric space are all associated with the tetra{4}hedron.

I also expressed that.

To define a 2D area space, that is systemically enclosed, we know the minimal set of things to define that 2D area, are associated with a tri{3}angle.

Ive been purporting for some years now, and in this forum, that, the minimal solid thing, can be no less than a subdivided triangle, defined by the tetrahedrons 4 vertexes{ nodal event/conjunctions.

Yep I just philosophised how one thing is an equal relation, which can be expressed as relation between 2,3 or 4 dots. The latter relation being volumous space as we experience it (albeit empty).

To clarify, when a tetrahedron inside-outs itself, via one of its vertexes on a trajectory that takes it through one of its opposite openings, the is place where are all four vertexes in the same 2D triangular plane.

[r6r6]

First to clarify one of my previous staetments;

..."when a tetrahedron inside-outs itself, via one of its vertexes on a trajectory, that, takes it through one of its opposite openings, there is aplace where are all four vertexes in the same 2D triangular plane, and this is the minimal 2D solid, because the interior of triangle now has body as defined by the central vertex and 3 lines-of-relationship."...

Gem--Well, my philosophy is pretty much the definition of 'a thing' as relational, and it explains the relational possibilities of a thing.

I found your explanation to be lacking some clarity if not also a more comprehensive set of considerations/involvments.

"relational" = 'concerning the way in which two or more people or things are connected.' Got that in a google search


So your dot .Ais a thing and your dot .B. is a thing and there exists a line-of-relationship between them so the relational has three aspects, or three things.

We can define that relational as Line AB or Line C with a two terminal end points { or times } A and B, ergo A C B


Any expression, of non-metaphyiscal-1 dot .,at minimum, is a 2D area. imho. And here again, I go back to the minimal 2D area, that has a body, is the specific subdivided triangle I posted.

So the minimal 2D, subidivided dot, has;
... three perimeter vertexes{ nodal event/conjunction? }
....one central, or interior vertex { nodal event/conjunction? }
...3 external angles,
....9 internal angles.

The geometric representations are all referring to that one thing.

And each thing has three or more aspects;

A C B in your two conceptual dots that may be expressed as 2D areas,
and either a set of dots, or one dot expressed as a line of dots labeld C.

However, to be clear, any 2D dot is actually a line. Lines are composed of dots, but in actuality, a the expression of a 2D dot can also be said to be a 2D line-of-relationship.

I say this becase both, at mininum or 2D areas. What we may say about the what makes a 2D dot differrent from a 2D line, is that a 2D line has and extended legnth or width, than does a dot Ex.

dot .
line ____________

If the relation is five ways (relation between 5 dots) we then inevitably have two things (2 different relations), which are represented by the 5 sided pyramid and the hexahedron I depicted.

Or 5 lines-of-relationship, that, could be expressed as a 2D pentagon aka polygon, that encloses a 2D space.

Or 5 lines-of-relationship that are share one end as a common dot or vertex, or nodal event/conjunction{?} that could label as central A and the other 5 terminal end points/dots we could label as A2, A2, A,3, A4 and A5.

I expressed those dymamic qualities in the geometric representations.

Yes you did. I thought they lack some definitional clarification.

Yep I just philosophised how one thing is an equal relation, which can be expressed as relation between 2,3 or 4 dots.

Sure an equalteral triangle is equal set of angles, equal set of length of lines-of-relationship, equal number of corners/viewpoints.

The latter relation being volumous space as we experience it (albeit empty).

Sure a regular tetra{4}hedron has many equal aspects, as does an octahedron, a cube, an icosahedron, and a pentagonal dodecahedron, i.e. all of those are regular symmetrical polyhedra.

They define a enclosure of space ergo the seperate a conceptually infinite "U"niverse or finite Universe, into two parts;

1) all the space inside the polyhedron, and,

2) all the space outside of the polyhedron, with this latter being the background by which we observe the defininig, lines-of-relationship.

r6

[Gem]

Originally Posted by r6r6r

First to clarify one of my previous staetments;

..."when a tetrahedron inside-outs itself, via one of its vertexes on a trajectory, that, takes it through one of its opposite openings, there is aplace where are all four vertexes in the same 2D triangular plane, and this is the minimal 2D solid, because the interior of triangle now has body as defined by the central vertex and 3 lines-of-relationship."...




I found your explanation to be lacking some clarity if not also a more comprehensive set of considerations/involvments.

"relational" = 'concerning the way in which two or more people or things are connected.' Got that in a google search

good enough definition.

So your dot .Ais a thing and your dot .B. is a thing and there exists a line-of-relationship between them so the relational has three aspects, or three things.

We can define that relational as Line AB or Line C with a two terminal end points { or times } A and B, ergo A C B

There is no A or B in fact, only the equal relation, so I just use the A and B dots as a representation.

Any expression, of non-metaphyiscal-1 dot .,at minimum, is a 2D area. imho. And here again, I go back to the minimal 2D area, that has a body, is the specific subdivided triangle I posted.

So the minimal 2D, subidivided dot, has;
... three perimeter vertexes{ nodal event/conjunction? }
....one central, or interior vertex { nodal event/conjunction? }
...3 external angles,
....9 internal angles.

You're getting caught up in the representation but that representation is only an explanation of the concept. It needn't be dots or lines at all. Another representation would be as good.

And each thing has three or more aspects

One thing has one aspect. Equal relation. But the philosophy shows how equal relation has different possibilities.

A C B in your two conceptual dots that may be expressed as 2D areas,
and either a set of dots, or one dot expressed as a line of dots labeld C.

However, to be clear, any 2D dot is actually a line. Lines are composed of dots, but in actuality, a the expression of a 2D dot can also be said to be a 2D line-of-relationship.

The dot represents a zero dimensional entity.

I say this becase both, at mininum or 2D areas. What we may say about the what makes a 2D dot differrent from a 2D line, is that a 2D line has and extended legnth or width, than does a dot Ex.

dot .
line ____________





Or 5 lines-of-relationship, that, could be expressed as a 2D pentagon aka polygon, that encloses a 2D space.

Or 5 lines-of-relationship that are share one end as a common dot or vertex, or nodal event/conjunction{?} that could label as central A and the other 5 terminal end points/dots we could label as A2, A2, A,3, A4 and A5.




Yes you did. I thought they lack some definitional clarification.



Sure an equalteral triangle is equal set of angles, equal set of length of lines-of-relationship, equal number of corners/viewpoints.

It expressing the equal relation, so it is equalateral.

Sure a regular tetra{4}hedron has many equal aspects, as does an octahedron, a cube, an icosahedron, and a pentagonal dodecahedron, i.e. all of those are regular symmetrical polyhedra.

The tet can express equal relation but the cube can not because there are three different distances between a cubes vertices. (Dots would be at vertices.)



Where more that 4 dots exist there can not be an equal relation.

They define a enclosure of space ergo the seperate a conceptually infinite "U"niverse or finite Universe, into two parts;

1) all the space inside the polyhedron, and,

2) all the space outside of the polyhedron, with this latter being the background by which we observe the defininig, lines-of-relationship.

r6

Not exactly, the inside and outside is an act of distinction (see George Spencer Brown) - the equal relation is not. The shapes I used only represent the equal relation concept. The 4 dot relation just shows that space is an inevitable facet of equal relation.

[r6r6]

"relational" = 'concerning the way in which two or more people or things are connected.' Got that in a google search

Gem-good enough definition.

Yes it covers your A and B.

There is no A or B in fact, only the equal relation, so I just use the A and B dots as a representation.

The problem removing A and B doing that is that you then have no visual expression to aid you in whatever definition/meaning your trying to apply to your word "relational".
So basically, if you do away with A and B your left with the google definition I offered, and agree with.

So were back todefining what a 'thing' is. How we define a 'thing' and that leads to using words like dot, A dot B, line-of-relationship etc.....

And some of the words I added to disscussion, ex angle, 2D area is the mininmal expression of a dot and a dot is really just a short line.

You're getting caught up in the representation but that representation is only an explanation of the concept. It needn't be dots or lines at all. Another representation would be as good.

As I originally concept of a metaphysical-1 dot cannot be expressed with less than 2D area.

The minimal area is a 2D triangle and it has;

..3 angles,
..3 lines-of-relationship,
..3 corners/vertices connecting only two lines,

and similar too--- tho not exact --it divides infinite "U"niverse and finite Universe into two parts;

...all the space inside and all the space outside of the triangle.

One thing has one aspect. Equal relation. But the philosophy shows how equal relation has different possibilities.

Well relation = relationship and that is at minimal is composed of three aspects, that I presented to you previously. A C B

A terminal end point/dot or whatever you want to call it

B terminal end point/dot that is 180 degrees diametric at other end of the,

C line-of-relationship.

The dot represents a zero dimensional entity.

That is what I refer to as a metaphysical-1 ergo conceptual dot, or point.

It expressing the equal relation, so it is equalateral.

All polyhedra all symmetrically equal in their a respective set of;
... interior angle,
...surface angle and,
.... exterior angle

A as beginning point/dot of line-of-relationship C, is not equal to B, if we consider that A comes before B in the actualy creation of a line-of-relatonship, between beginning A and ending point B.

And again, any metaphysical-1, i.e. conceptual line-of-relationship, actually expressed, can be no less than 2D area i.e. a expressed line, at mininimum is just a long dot.

gem-The tet can express equal relation but the cube can not because there are three different distances between a cubes vertices. (Dots would be at vertices.)

True, insofar as, the tetrahedrons design does not allow for lines-of-relationship between the vertices across the volumetric interior i.e. the tetrahedron does not have allow for diametric diameters between vertices ergo those 6 lines-of-relationships are chords.

Whereas the cube and other three regular polyhedra I mentioned previously do allow for volumetrically diametric lines-of-relationship.

r6



Where more that 4 dots exist there can not be an equal relation.


Not exactly, the inside and outside is an act of distinction (see George Spencer Brown) - the equal relation is not. The shapes I used only represent the equal relation concept. The 4 dot relation just shows that space is an inevitable facet of equal relation.[/quote]

[Riboflavin]

There is no such thing as equality. It doesn't actually exist precisely because everything is defined by it's relativity.

What you're also describing is a holographic universe in which there are only two dimensions with the third dimension being holographic. This is also part of the basis of my belief in "Predeterminism".

In sacred geometry, the very act of creating random points will have the result of creating inevitable geometric shapes no matter what you do. There literally is no way to create a non-relative series of anything.

[Gem]

Originally Posted by Riboflavin

There is no such thing as equality. It doesn't actually exist precisely because everything is defined by it's relativity.

The philosophy is the query: What is a thing?

It agrees that a thing is relative on the basis of Feynman's statement, "all mass is interaction". This presupposes that a thing, while being singular in itself, is discrete due it requiring relational components.

This philosophy uses dots to show how one relates to the other, and the thought experiment is to imagine each dot has a gravity-like force. Using that representation it is easy to envisage the affect that one dot has on another, that affect constituting their relation.

Of course, 2 dots affect each other equally. This philosophy goes on to demonstrate other relations between dots that have the same equal interaction.

What you're also describing is a holographic universe in which there are only two dimensions with the third dimension being holographic. This is also part of the basis of my belief in "Predeterminism".

Since this philosophy is framed as singular thing being an equal realtion, and both the 2D form of three dots and the 3D form of four dots both constitute equal relations, this can indeed be related to holographic principles. This philosophy supposes that the 2,3 and 4 dot relations are the one and same equal relation where there is but one effect.

In sacred geometry, the very act of creating random points will have the result of creating inevitable geometric shapes no matter what you do. There literally is no way to create a non-relative series of anything.

Exactly, a thing is a relation, which is the hypothesis of this philosophy. I'm just showing how there a few different possibilities that constitute a single relation (where each component affects all other equally).

[Gem]

Originally Posted by r6r6r

"relational" = 'concerning the way in which two or more people or things are connected.' Got that in a google search



Yes it covers your A and B.

It covers all the representation I describes.

The problem removing A and B doing that is that you then have no visual expression to aid you in whatever definition/meaning your trying to apply to your word "relational".
So basically, if you do away with A and B your left with the google definition I offered, and agree with.

The representation is a way of describing the concept, and the concept itself is 'equal relation'.

So were back todefining what a 'thing' is. How we define a 'thing' and that leads to using words like dot, A dot B, line-of-relationship etc.....

And some of the words I added to disscussion, ex angle, 2D area is the mininmal expression of a dot and a dot is really just a short line.

"It is important to understand that a point is not a thing, but a place" (Math Open Reference). A dot represents non-dimension.

As I originally concept of a metaphysical-1 dot cannot be expressed with less than 2D area.

It is a dimensional representation, but it's used represent 0D.

The minimal area is a 2D triangle and it has;

..3 angles,
..3 lines-of-relationship,
..3 corners/vertices connecting only two lines,

and similar too--- tho not exact --it divides infinite "U"niverse and finite Universe into two parts;

...all the space inside and all the space outside of the triangle.



Well relation = relationship and that is at minimal is composed of three aspects, that I presented to you previously. A C B

Yes A,B and C being dots - or 'points' if that's preferable ( I just use 'dots' because I call this philosophy 'Dot Theory'. In this philosophy, we aren't concerned with the triangular shape per-se. The thought experiment is to imagine the dots have a gravity-like force and this makes it easy to visualise how they'd effect each other equally.

A terminal end point/dot or whatever you want to call it

B terminal end point/dot that is 180 degrees diametric at other end of the,

C line-of-relationship.



That is what I refer to as a metaphysical-1 ergo conceptual dot, or point.

A point is defined in mathematics, it has no dimension, and that definition is good enough for this philosophy.

All polyhedra all symmetrically equal in their a respective set of;
... interior angle,
...surface angle and,
.... exterior angle

Where we use more than 4 dots, any dot can't be the same distance from all other dots, thus since more than one distance inevitably exists, there can't be an equal relation (see OP).

A as beginning point/dot of line-of-relationship C, is not equal to B, if we consider that A comes before B in the actualy creation of a line-of-relatonship, between beginning A and ending point B.

There is no before in this philosophy. This philosophy shows that there are various configurations that constitute a equal relation, thus a thing in and of itself is discrete, yet has not particular shape nor size. It's more like probabalistic entity (exists in different possibilities). My use of shapes merely portrays that concept.

And again, any metaphysical-1, i.e. conceptual line-of-relationship, actually expressed, can be no less than 2D area i.e. a expressed line, at mininimum is just a long dot.

A dot used in representation has dimension, but it represents a non-dimensional entity. The representation is used to convey meaning only.

True, insofar as, the tetrahedrons design does not allow for lines-of-relationship between the vertices across the volumetric interior i.e. the tetrahedron does not have allow for diametric diameters between vertices ergo those 6 lines-of-relationships are chords.

Exactly - all dots (vertices) are the same distance from all others, therefore the relation is equal.

Whereas the cube and other three regular polyhedra I mentioned previously do allow for volumetrically diametric lines-of-relationship.

Precisely. Once you relate more than four dots, the distance of any one to all others can no longer be the same. Eg. To relate five dots, 2 distances are required. Equal relation can between 2,3 or 4 dots.

[r6r6]

Gem--Where more that 4 dots exist there can not be an equal relation.

Couldn't finish my reply earlier so now I'm back. So yes, previously I agreed that, regular tetrahedron is unique, in that its design does not allow for volumetrically diametric lines-of-relationship, because of only having 4 vertices.

I.e. we do not consider volumetric diameters, as you showed within the cube, and all other polyhedra of Universe, except the tetrahedron.

Not exactly, the inside and outside is an act of distinction (see George Spencer Brown) - the equal relation is not.

Yeah, any 2D polygon or polyhedron divides the "U"niverse or Universe into two;

...inside the polyhedron,
...outside the polyhedron.

The shapes I used only represent the equal relation concept. The 4 dot relation just shows that space is an inevitable facet of equal relation.

Your A dot is beginning and is not exactly equal to B dot ending, because A is beginning and the the B is ending. In actuality/reality that would be two differrent times and two different locations.

An irregular tetrahedron does not follow your "equal relation" concept. Not that your saying it does.

Same goes for irregular triangle not having your meeting your equal relation" criteria.

r6