Relative to: a relational equality

[Gem]

Originally Posted by SemperVI

I enjoyed reading your thoughts on this and found it particularly compelling. As a software architect and object modeler I work in these abstract concepts in the course of a days work. I found much of what you said to be very accurate from a software design perspective. Anyway, I thought I would recommend you consider researching relational object modeling, particularly entity-attribute-value modeling as it may provide you additional context toward your understanding. Likewise, perhaps you may find value in this basic computer science concept as it pertains to the abstract "thing".

Father of all Object Models

• Everything is an ENTITY
• Every ENTITY is an instance of a TYPE OF ENTITY
• Every ENTITY can have a relationship with any other ENTITY, including itself.
• Every ENTITY will have ROLE in a relationship.
• Every ROLE is an instance of a TYPE OF ROLE which is a TYPE OF ENTITY.
• Every ENTITY has one or more ATTRIBUTES.
• Every ATTRIBUTE is an instance of a TYPE OF ATTRIBUTE which is a TYPE OF ENTITY

The elegance of this model allows you to define and describe not just the entity/thing but also the abstract nature of the relationships between entities in all normal forms (e.g. First Normal Form aka 1NF, 2NF, 3NF and 5NF) as well as hierarchical.

Thanks for the post

Awesome. I love that conceptual framework. I can't say I grasp it well at all, though. Will certainly read a little on it. Thanks.

In dot theory the entities are non dimensional and have 'imaginary gravity'. Of course, there is no gravity in any dot alone; 'gravity' is an artifact of dots affecting each other. I'm not sure how a dot has a relationship with itself, though.

This would suggest that the entity has one type and one attribute (though the attribute is an artifice of its role)? .... It just clicked... it's three defined qualities which are contained within 'itself'. Am I comprehending this somewhat?

The entire theory actually includes no dots and one dot prior to the 2 dot scenario, but I figured the 0 and 1 dot weren't required in the logic process - but 0 and 1 are like the nuts and bolts in computing, ay?

If you know anything on quantum computing, that might be really interesting in this context!

[r6r6]

Gem---I have no disagreement at all with your geometry. It's correct. It's entirely rational to view dot theory in terms of its lines of relationship.

I'm glad your finally showing some reational, logical common sense in regards to your equal relations actually involing lines--of-relationship, that, we can state as imaginary just as you like to state an imaginary atttractive force between dots.

I do ignore other arrangements of dots because the geometry in dot theory expresses the concept of equal relation. I find shapes that are not equalateral still produce relationships where there are no lines of relationship that intersect the space.

3 dots of an irregular triangle do no intersect 2D plane space between them.

3 dots or 3 same size circles = Gems specific/partiulear equalateral triangle ergo equal distance lines-of-relationship and this triangle is a just one subset of greater cosmological set of triangles in general,

3 dots or 3 irregular size circles = one or more lines-of-relationship that are not equal to the others and these triangles is the larger set within a greater cosmological set of triangles in general.

Exactly. Its a specific rule (not a rule set because there is only one rule).

Good, I'm glad your recognize that your single set rule of equal relation dots, that, are inherently attracted each other, to be close as possible, is specific Gem rule, within a greater set of cosmological rules regarding 3 dots/points/nodes/junctions/knucles/corners triangles, and 4 dots and 4 dot/point tetrahedra.

Other arrangements of dots require the presumption of a prior space.

All dot arrangement of dots/points/nodes/junctions/corner/joints require space ergo a distance being involved between;

here at dot A and,
there at dot B, and dot C, D, E etc...............

The rule is that dots be places in closest possible relation.

Close mean that they indvidual things and do not occupy the same position/location in space. Your scenario is no differrent than using same size coins, circles etc.........Same resultants

in the case of two dots, distance is irrelevant because there is only one distance. This is a single relation.

No it is not totally relevant because distance is involve inherently and evidence of the existence of some non-specified distance being involved, is in your rule, that, the dots be as close as possible.

Once you use the word close, then distance is involved tho not a specific distance. The opposite of close is far away and both of these concepts involve distance as space, and true of any 2 or more dot scenarios, not just Gems dot scenario.

I'm not sure you recognize these facts yet.

As dot theory expands on need keep in mind that the geometry articulates a single relation, that being equal relation.

There exist equal distance relation between 2 dots irrespective of their distance/space from each other. That is why your Gems rule is not totally valid in regards to only 2 dot scenarios.

2 dots are equal in relation irrespective of distance/space between them, i..e how close they are to each other is irrelevant to their having equal relationship to each other.

With the imaginary gravity thought experiment we see that the relation is like a field that acts on all dots equally.

Imaginary gravity inherently opens the door to imaginary lines-of-relationship between 2 or more dots. Geometry is inherent to all dot/point/node/joint/corner/knucle scenarios.

We can say 2 dot and not include any ideas of gravity, or line-of-site, ergo line-of-relationship but it seems rediculously pointless to do so and that is probably why you introduced your imaginary gravity.

It's still fine to see it in terms of lines of relationship, but that doesn't enable the mind to visualise the field like quality of equal relation or the quality of affect dots have in relation to each other.

See my above. Any dots/points/node/corners/yippions/knucles that do not have a line-of-relationship relationship or pointless and a line-less.

That being said, lines of relationship are indeed still highly relevant to the conceptualisation, particularly in showing the 2,3 or 4 dot arrangements have no lines of relation that intersect space, even when arranged as shapes that are not equalateral.

Well good, I'm glad youve finally come around the rational, logical common sense of dots involving lines-of-relationship even if that line is a line of space/distance.

Spherical packing is also a relevant way of visualising dot theory, but on has to keep in mind that dots are non dimensional entities.

1) Dots/points/vertexes,
2) lines/chords/trajectories,
3) openings/surfaces/planes and,
4) angles, were dealing with are all conceptual entities.

However, there is two ways of approaching these 4 sets;

1) dots as a thing . can be no less than a 2D plane . ergo a short line __ _ _ . . . . .

2) dots as a thing can be no less than a 3D volume that has[
4 vertexes/nodes/corners/junctions/crossings,
6 lines of relationship, and,
12 surface angles

The location of dot/point in space can only be assigned when there at least 3 other dots of relationship.

2 dots are necessarily in equal relation because there is but one relation between them.

Yes, and your Gems rule regarding closeness is irrelevant irrespective of the distance/space between 2 dots/points/nodes.

Exactly. The rule is specific to dot theory.

Yes dot theory is cosmolgical in scope. Gems dot rule is narrow limited set of dots involving only,

1) 2 dots,
2) 3 dots in equlateral rleationships, and,
3) 4 dots in equalateral relationships.

I think you have progressed in your recognition of your dot rule being involving a small subset of greater cosmological dot theory or rules, or whatever label we want to apply to them.

r6

[Gem]

Originally Posted by r6r6r

I'm glad your finally showing some reational, logical common sense in regards to your equal relations actually involing lines--of-relationship, that, we can state as imaginary just as you like to state an imaginary atttractive force between dots.

3 dots of an irregular triangle do no intersect 2D plane space between them.

3 dots or 3 same size circles = Gems specific/partiulear equalateral triangle ergo equal distance lines-of-relationship and this triangle is a just one subset of greater cosmological set of triangles in general,

3 dots or 3 irregular size circles = one or more lines-of-relationship that are not equal to the others and these triangles is the larger set within a greater cosmological set of triangles in general.

Good, I'm glad your recognize that your single set rule of equal relation dots, that, are inherently attracted each other, to be close as possible, is specific Gem rule, within a greater set of cosmological rules regarding 3 dots/points/nodes/junctions/knucles/corners triangles, and 4 dots and 4 dot/point tetrahedra.

All dot arrangement of dots/points/nodes/junctions/corner/joints require space ergo a distance being involved between;

here at dot A and,
there at dot B, and dot C, D, E etc...............

Close mean that they indvidual things and do not occupy the same position/location in space. Your scenario is no differrent than using same size coins, circles etc.........Same resultants.

Yep the notion of dots being in a 'place' is correct. The place they are in is only in relation to other dots. One dot alone doesn't assume a place. We could say 'it's anywhere'. We simply say its the origin. When we have two dots, either could be considered the origin and both dots only assume place with respect to the other. Thus we say 'they're not in the same place'. There is no definable distance between them. They may be infinitely far or infinitesimally close, or they could both be anywhere, but since they relate, all we can really say is, they are equally origin and they aren't in the same place. They are necessarily in equal relation because there is but one relationship.

No it is not totally relevant because distance is involve inherently and evidence of the existence of some non-specified distance being involved, is in your rule, that, the dots be as close as possible.

Correction: 'arranged in the closest possible relationship'. It needn't be distance. They might gods that love each other equally for all I care, but distances are easiest to visualise so I use that in the model.

Once you use the word close, then distance is involved tho not a specific distance. The opposite of close is far away and both of these concepts involve distance as space, and true of any 2 or more dot scenarios, not just Gems dot scenario.

Dot theory is Gem's scenario.

I'm not sure you recognize these facts yet.

Of course, you're explaining baby geometry. It's simple.

There exist equal distance relation between 2 dots irrespective of their distance/space from each other. That is why your Gems rule is not totally valid in regards to only 2 dot scenarios.

2 dots necessarily relate equally because there is only one relation.

2 dots are equal in relation irrespective of distance/space between them, i..e how close they are to each other is irrelevant to their having equal relationship to each other.

Exactly.

Imaginary gravity inherently opens the door to imaginary lines-of-relationship between 2 or more dots. Geometry is inherent to all dot/point/node/joint/corner/knucle scenarios.

We can say 2 dot and not include any ideas of gravity, or line-of-site, ergo line-of-relationship but it seems rediculously pointless to do so and that is probably why you introduced your imaginary gravity.

Line of relationship is fine, and line of sight is even better (though where we have 3 or 4 dots 'sight' isn't linear, but encompasses the space. It's also a good thought experiment to imagine you are a dot looking at other the dots. I've played around with that one as well.

I explained, 'imaginary gravity' is used for 3 basic reasons.: 1) it holds the dots in closest possible relation; 2) one can visualise the mutual effect dots have on each other; and 3) where more than 2 dots are concerned there is a field like force which isn't only linear, but also pervades the resulting space.

See my above. Any dots/points/node/corners/yippions/knucles that do not have a line-of-relationship relationship or pointless and a line-less.

Well good, I'm glad youve finally come around the rational, logical common sense of dots involving lines-of-relationship even if that line is a line of space/distance.

Sight or 'sees' becomes a spacial 'field of vision', if you will, where more than 2 dots are used. We could say the dots have 'imaginary sight' and have a similar conception to 'imaginary gravity'.

1) Dots/points/vertexes,
2) lines/chords/trajectories,
3) openings/surfaces/planes and,
4) angles, were dealing with are all conceptual entities.

However, there is two ways of approaching these 4 sets;

1) dots as a thing . can be no less than a 2D plane . ergo a short line

PLEASE LOOK UP THE MATHEMATICAL DEFINITION OF A POINT!

2) dots as a thing can be no less than a 3D volume that has
4 vertexes/nodes/corners/junctions/crossings,
6 lines of relationship, and,
12 surface angles

The location of dot/point in space can only be assigned when there at least 3 other dots of relationship.

Not exactly.

First we go back to one dot, which is 'anywhere'
we then put another dot, which is equally 'anywhere', but not in the same 'place'.
we throw in the third, and it's not in the same place as the others, and could equally be the origin.
or we have four separately place dots, any of which could be the origin. It doesn't matter which is considered the origin, so any or them could be 'anywhere' provided they aren't in the same 'place'.

This 'anywhere other than the same place rule', which applies to them all equally, actually founds them in 'equal relation'. Since equal relation also stipulates the dimensional aspect of their arrangement, space itself is derived through the relationship. We then see how space itself is dimensional as a discretly quantised unit - yet completely formless.

From there, the fifth dot can't be 'anywhere' per se, because it is dimensional constrained to take a different relational place to the original four. We can now say that 2 different distance are required. Required.

Required implies that dots can no longer be 'anywhere'.

You have to understand, this is a strictly relational model. You don't get to place the dots yourself. They assume 'place' themselves in relation to the others.

Yes, and your Gems rule regarding closeness is irrelevant irrespective of the distance/space between 2 dots/points/nodes.

Gem's axiomic rule is only applied for sake of easy visualisation. There are actually no dots or shapes. These are mere representations used for conveyance.

Yes dot theory is cosmolgical in scope. Gems dot rule is narrow limited set of dots involving only,

You say I'm limited whereas you can't get past euclidean geometry. That's really quite ironic.

1) 2 dots,
2) 3 dots in equlateral rleationships, and,
3) 4 dots in equalateral relationships.

I think you have progressed in your recognition of your dot rule being involving a small subset of greater cosmological dot theory or rules, or whatever label we want to apply to them.

r6

I assure you, Dot Theory is well and beyond the baby steps of euclidean geometry; it reaches into utterly abstract conceptions. You don't seem to understand the underpinning abstractions.

For me, I don't need the dots and shapes because I think in abstraction. I only formulate the concept with a little story about a few dots for the sake of communicating the idea. You can't understand the idea because you are thinking about the shapes.

I didn't have any idea that similar conceptual devices applied to computing and data, so that was pretty surprising to me. I only progressed by trying to understand that.

[r6r6]

Gem--- There is no definable distance between them.

YOur in error. I repeat, dots close or far inherently infers/implies a distance of space. YOu dont seem to grasp this fact.

They may be infinitely far or infinitesimally close, or they could both be anywhere,

Your in error here again. Your statement illogical, irrational and not common sense i.e. close and far are words that inherently infer a finite distance.

There is no such reality as infinitely close to each other or infinitely far from each other. Many people do not really grasp the meaning of infinite, so your not alone. imho.

Distance is inherently finite ergo we can say the dots are close or far relative to some specific finite distance.

Close and far are words involved with relativity.

Infinite is a word that does not relate because it is beyond relationship ergo beyond existence. It exists only as non-relative concept and as macro-infinite non-occupied space.

but since they relate, all we can really say is, they are equally origin and they aren't in the same place. They are necessarily in equal relation because there is but one relationship.

Yes the two are in a finite relationship ergo line-of-relationship.

Infinity is beyond relationship. Two finite halves are equal also. This is the two radii of two same size coins or circles.

Correction: 'arranged in the closest possible relationship'. It needn't be distance. They might gods that love each other equally for all I care, but distances are easiest to visualise so I use that in the model.

Closet or closet, far or farthest are words inherently involving relationships of distance of space or distance of dimension.

Yes we can model any finite existence. We cannot model infinity.
You not the only one who does not really grasp what the words infinite, infinity, infinitely mean/infer/imply/suggest.

Dot theory is Gem's scenario.

No, Gem dot theory is subet rule of greater cosmological set of 2, 3, 4 dots or more. You aparrently do not understand what a hierarchy is. Your Gems dot theory is at the bottom of top-to-bottom cosmic dot theory sets.

Cosmic Dot Theories
...1) all dots
...2) Gems 2, 3, and 4 dot theory.

Your rule needs to be altered to better reflect the 2 dot qualities Ive mention in last reply to you.

Of course, you're explaining baby geometry. It's simple.

Yeah but Ive added a lot of clarification to your thoughts to make clear the differrences between your limited set of dots with Gems equal relation rule that includes closenes, that, does not apply to 2 dots having equal relation.

So I think your beginning to recognize some simple stuff that Ive seen no evidence that you or others understood before. Including myself, because in reviewing these ideas we discover new viewpoints that either never had, or had forgotten.

2 dots necessarily relate equally because there is only one relation.

We can have two equal dots as 2D circles or imaginary 2D coins, and each circle or imaginary coin has a radius. These two radii are equal too each other irrespective of how far apart, or how close the centers of the two circles or imaginary coins are.

One relation is two equal radii of two 2D, same size circles or imaginary coins.

Exactly.

YEah but you dont yet acknowledge that your Gem rule states that only 2 dots are close as possible, ergo closeness is irrelevant to equal relation.

Ive made clear that closness is not neccessary for equal relations with only 2 dots and maybe even 3 dots. Your Gem rule on close-as-possible needs to be altered.

Line of relationship is fine, and line of sight is even better (though where we have 3 or 4 dots 'sight' isn't linear, but encompasses the space. It's also a good thought experiment to imagine you are a dot looking at other the dots. I've played around with that one as well.

Yeah Ive had line-of-relationship from the very beginning yet you tended to fight that idea for many posts. Again, you finally appear to recognize the significance of any dot theory only having relevance if there is line-of-relationship, whether, as gravity, photons, string, tomatoe paster whatever.

I explained, 'imaginary gravity' is used for 3 basic reasons.: 1) it holds the dots in closest possible relation;

And Ive told you from beginning that inherently infers/implies 3 lines-of-realtionship

2) one can visualise the mutual effect dots have on each other;

Only because as humans we have visualized, touched, smelled, or heard two three or more things in relationship to each other. Without any of those senses we could not know what a dot is much less what I triangle is.

and 3) where more than 2 dots are concerned there is a field like force which isn't only linear, but also pervades the resulting space.

Well now your entering a differrent subject by introducing the word "field" for the first time in all of these posts. That complicates the matter becuase like any word or set of words, there has to be common agreement of defined meanging or there can be no clear communication.

Sight or 'sees' becomes a spacial 'field of vision', if you will, where more than 2 dots are used. We could say the dots have 'imaginary sight' and have a similar conception to 'imaginary gravity'.

YOu can say whatever you want. When I say see im referencing human sight ergo very narrow spectrum of light visible to the human eye as photons.

Of course photons occur at all frequencies of EM spectrum but that uncessarily complicates the subject where disscussing

Not exactly.

Yes to get a fix/location on something we need three lines-of-relationship. Its called triangulation.

First we go back to one dot, which is 'anywhere'
we then put another dot, which is equally 'anywhere', but not in the same 'place'.

The 2 dots have a finite distance between them and that is significant to any dot scenario.

we throw in the third, and it's not in the same place as the others, and could equally be the origin.

3 lines-of-relationship ergo 3 finite distances between 3 dots/points

or we have four separately place dots, any of which could be the origin.

4 lines-of-relationship ergo, as Ive mentioned previously, there is a quantum leap from 3 lines too 6 lines-of-relationship,

and from only 3 surface angles to 12 surface angles,

and from 1 triangle to 4 triangles.

It doesn't matter which is considered the origin, so any or them could be 'anywhere' provided they aren't in the same 'place'.

Location can only be determined via triangulation. Each dots/points can only be located/position as related to the other three. It is called triangulation,i.e. to get a fix on single something( dot ) it takes three other lines-of-relationship

This 'anywhere other than the same place rule', which applies to them all equally, actually founds them in 'equal relation'. Since equal relation also stipulates the dimensional aspect of their arrangement, space itself is derived through the relationship. We then see how space itself is dimensional as a discretly quantised unit - yet completely formless.

3 dots are not formless. Form is shape ergo pattern ergo geometry.

Form boards are used to create the form, shape, pattern, geometry.

Gem's axiomic rule is only applied for sake of easy visualisation. There are actually no dots or shapes. These are mere representations used for conveyance.

Without experience of all of these then the info about them could not even be communicated or understood.

To teach a child what triangle or square shape is, then they have to see it, feel it, hear three seperate events in three locations or smell three in three locations.

You say I'm limited whereas you can't get past euclidean geometry. That's really quite ironic.

Now your taking offense. Yes your Gems rule needs to be altered and its scope is very limited and a the bottom of a top-to-bottom dot scenario heirarchy. That should not be surprising to you, as Gems rule-- that needs to be altered ---only deals with 2, 3 and 4 dots.

3 and 4 dots are also dealt with in the greated dot theory, becuase Gems therory stops at 4 dots/points. These are the fact you have offered adn Ive addressed with additional information to make clear for all readers the differrences in your Gem rule of dots and the all other dot theories that are related to 99.99999999999999 of Universe.

I assure you, Dot Theory is well and beyond the baby steps of euclidean geometry; it reaches into utterly abstract conceptions. You don't seem to understand the underpinning abstractions.

No, there not beyond 2, 3 and 4 dot scenarios based on Gems rule, and that rule needs to altered becuase Ive made clear several times now, that your closeness rule is irrelevant to 2 dots, and now I think your close as possible rule is irrelevant to 3 dots and maybe even 4.

Here is hoe believe you should alter Gems Rule, it should not be about how close-- ergo your close as possible --but rather, that there all equal distance from each other.

Ive not seen evidence that you really grasp that key change in your Gems Rule, to better reflect truth/fact/.

For me, I don't need the dots and shapes because I think in abstraction.
I only formulate the concept with a little story about a few dots for the sake of communicating the idea. You can't understand the idea because you are thinking about the shapes.

YOu can say I dont understand, but I think your in error to do so. I not only understand, Ive gone further in elaboating upon, what all is involved with your Gems dot theory and how Gems Rule needs to be altered to better reflect the truth/facts of your dot scenarios.


I think if you can avoid taking offense, then you can better address recognizing the error in your Gems Rule and that all of my information has been given to for all of us to better grasp the truth of dot theory and specifically 2, 3 and 4 dots, whether as regular/symmetrical ergo equalateral relationships or irregular non-equal relationships.

r6

[SemperVI]

Originally Posted by Gem

I'm not sure how a dot has a relationship with itself, though.

Hmmm - Perhaps it can't from a dot theory perspective on the surface, but I am not yet willing to concede the assertion that in dot theory an entity can't be related to itself specifically because of what you addressed below.

When you describe the dot in a 2D or 3D plane - I don't see the dot as a singular entity - it is far more complex than a basic building block for lack of a better term. This dot has properties that are intrinsic to the existence of the dot it self.

From an object model perspective, an entities relationship with itself is implicitly understood through inheritance and polymorphism.

Explanation: As previously established -- every ENTITY is an instance of a TYPE OF ENTITY. If the "dot" we are speaking of is viewed as an entity - then this dot has a super entity that the dot inherits from that defines the dot's origin like dot "A". Taking this further - if the said dot is in a 3 dimensional plane - then this dot would need to have exactly 3 attributes to define the X,Y,Z coordinates (aka attribute > attribute type > entity type > entity) required to exist in the 3 dimensional plane. This inheritance is precisely how the relationship with itself is established. Each instance of inheritance is just another building block to define the requirements in order for the dot to exist in the plane it is designed for.

Originally Posted by Gem

This would suggest that the entity has one type and one attribute (though the attribute is an artifice of its role)? .... It just clicked... it's three defined qualities which are contained within 'itself'. Am I comprehending this somewhat?

I think so in the sense that when you reverse engineer the properties and definition of the dot (which I think is what we are doing here) - you are breaking it down to its most common abstract element or entity! ...and yes - when you break it down to the most abstract element in computing you are looking at a boolean or binary entity. (true/false, on/off, exists/does not exist (null/void). To me, I see no reason why this would not apply in dot theory but I have little understanding of it so....

Originally Posted by Gem

The entire theory actually includes no dots and one dot prior to the 2 dot scenario, but I figured the 0 and 1 dot weren't required in the logic process - but 0 and 1 are like the nuts and bolts in computing, ay?

I'm not sure I followed you here except to say that once a dot is defined. The same dot entity used to to define the origin and the X,Y plane of point "A" in a 2D plane can be used to define an instance of the entity of point "B". This combined with the relationship between these two points is also an "entity" that describes the space between point "A" and point "B". All three of these complex entities combined can also be viewed/defined as a singular entity. This is where polymophism comes into play

Originally Posted by Gem

If you know anything on quantum computing, that might be really interesting in this context!

I don't know anything about quantum computing; however - in thinking about how object modeling and dot theory may be related - I could not help but wonder how quantum entanglement applied, particularly as it pertained to an entity being related to itself. This is probably best left in the realm of spooky action at a distance:-)

Hope I was able to further clarify myself and I did not muddy the waters of the discussion you wanted to have about dot theory. Again to me it seems very similar to computing, interesting post!

[Gem]

Originally Posted by r6r6r

YOur in error. I repeat, dots close or far inherently infers/implies a distance of space. YOu dont seem to grasp this fact.
Your in error here again. Your statement illogical, irrational and not common sense i.e. close and far are words that inherently infer a finite distance.

There is no such reality as infinitely close to each other or infinitely far from each other. Many people do not really grasp the meaning of infinite, so your not alone. imho.

I know the whole history of infinity and have read a bit on fractal geometry/chaos theory.

Distance is inherently finite ergo we can say the dots are close or far relative to some specific finite.

Close and far are words involved with relativity.

Infinite is a word that does not relate because it is beyond relationship ergo beyond existence. It exists only as non-relative concept and as macro-infinite non-occupied space.

Yes the two are in a finite relationship ergo line-of-relationship.

Infinity is beyond relationship. Two finite halves are equal also. This is the two radii of two same size coins or circles.


Closet or closet, far or farthest are words inherently involving relationships of distance of space or distance of dimension.

Closet? Tee hee.

Yes we can model any finite existence. We cannot model infinity.
You not the only one who does not really grasp what the words infinite, infinity, infinitely mean/infer/imply/suggest.

I've read quite a lot about infinity, but I'm no mathematician.

No, Gem dot theory is subet rule of greater cosmological set of 2, 3, 4 dots or more. You aparrently do not understand what a hierarchy is. Your Gems dot theory is at the bottom of top-to-bottom cosmic dot theory sets.

Cosmic Dot Theories
...1) all dots
...2) Gems 2, 3, and 4 dot theory.

Your rule needs to be altered to better reflect the 2 dot qualities Ive mention in last reply to you.

Would you say to Cantor that his rule of taking out the middle third of a line is limited subset of the cosmological set and then tell him he has to expand?

I don't need set theory (hierarchy) for this theory.

Yeah but Ive added a lot of clarification to your thoughts to make clear the differrences between your limited set of dots with Gems equal relation rule that includes closenes, that, does not apply to 2 dots having equal relation.

Inevitably, A relates to B in the exact same way as B relates to A.

I think your beginning to recognize some simple stuff that Ive seen no evidence that you or others understood before. Including myself, because in reviewing these ideas we discover new viewpoints that either never had, or had forgotten.[/quote]
Frankly, Your geometry on this thread is like grade school level and I haven't learned anything. My learning has been trying different ways to explain the theory. So far we're still talking about grade school geometry.

We can have two equal dots as 2D circles or imaginary 2D coins, and each circle or imaginary coin has a radius. These two radii are equal too each other irrespective of how far apart, or how close the centers of the two circles or imaginary coins are.

DOTS ARE NON DIMENSIONAL

One relation is two equal radii of two 2D, same size circles or imaginary coins.


YEah but you dont yet acknowledge that your Gem rule states that only 2 dots are close as possible, ergo closeness is irrelevant to equal relation.

In 'closest possible relation'. Distance isn't a necessary representation for that, but its easiest to visualise. Just visualise gravitational attraction and its dead easy.

Ive made clear that closness is not neccessary for equal relations with only 2 dots and maybe even 3 dots. Your Gem rule on close-as-possible needs to be altered.

Exactly, any single distance value applied to the dots is equal relation.

Yeah Ive had line-of-relationship from the very beginning yet you tended to fight that idea for many posts. Again, you finally appear to recognize the significance of any dot theory only having relevance if there is line-of-relationship, whether, as gravity, photons, string, tomatoe paster whatever.

Sure It doesn't worry me, the relation can be anything, it doesn't matter. 'imaginary gravity' is used for specific reasons I have explained.

And Ive told you from beginning that inherently infers/implies 3 lines-of-realtionship

Like duh.

Only because as humans we have visualized, touched, smelled, or heard two three or more things in relationship to each other. Without any of those senses we could not know what a dot is much less what I triangle is.

Relation is very specific as an operation.

Well now your entering a differrent subject by introducing the word "field" for the first time in all of these posts. That complicates the matter becuase like any word or set of words, there has to be common agreement of defined meanging or there can be no clear communication. [/quote]
I've been talking about the same subject all along, and we can just simply visualise how an imaginary gravity permeates throughout the space.

YOu can say whatever you want. When I say see im referencing human sight ergo very narrow spectrum of light visible to the human eye as photons.

Of course photons occur at all frequencies of EM spectrum but that uncessarily complicates the subject where disscussing

Ok forget sight then, lines of relationship is fine, but visualising an imaginary gravity is optimum I think.

Yes to get a fix/location on something we need three lines-of-relationship. Its called triangulation. The 2 dots have a finite distance between them and that is significant to any dot scenario.


3 lines-of-relationship ergo 3 finite distances between 3 dots/points


4 lines-of-relationship ergo, as Ive mentioned previously, there is a quantum leap from 3 lines too 6 lines-of-relationship,

and from only 3 surface angles to 12 surface angles,

and from 1 triangle to 4 triangles.

Location can only be determined via triangulation. Each dots/points can only be located/position as related to the other three. It is called triangulation,i.e. to get a fix on single something( dot ) it takes three other lines-of-relationship

3 dots are not formless. Form is shape ergo pattern ergo geometry.

Form boards are used to create the form, shape, pattern, geometry.


Without experience of all of these then the info about them could not even be communicated or understood.

To teach a child what triangle or square shape is, then they have to see it, feel it, hear three seperate events in three locations or smell three in three locations.[/quote]

Im not trying to teach geometry. I merely use it as representation.

Now your taking offense. Yes your Gems rule needs to be altered and its scope is very limited and a the bottom of a top-to-bottom dot scenario heirarchy. That should not be surprising to you, as Gems rule-- that needs to be altered ---only deals with 2, 3 and 4 dots.

The rule is dots in closest possible relation. Up to 4 dots that's equal relation. More than 4 dots can't be equally related. Dot theory applies to any number of dots.

3 and 4 dots are also dealt with in the greated dot theory, becuase Gems therory stops at 4 dots/points. These are the fact you have offered adn Ive addressed with additional information to make clear for all readers the differrences in your Gem rule of dots and the all other dot theories that are related to 99.99999999999999 of Universe.

No, there not beyond 2, 3 and 4 dot scenarios based on Gems rule, and that rule needs to altered becuase Ive made clear several times now, that your closeness rule is irrelevant to 2 dots, and now I think your close as possible rule is irrelevant to 3 dots and maybe even 4.

Equal relation is abstract, but distance can be applied as a value.

Here is hoe believe you should alter Gems Rule, it should not be about how close-- ergo your close as possible --but rather, that there all equal distance from each other.

Equal distance form each other is closest possible relation.

Ive not seen evidence that you really grasp that key change in your Gems Rule, to better reflect truth/fact/.

On the contrary, you don't have a grasp on the abstraction, and are stuck in baby geometry.

YOu can say I dont understand, but I think your in error to do so. I not only understand, Ive gone further in elaboating upon, what all is involved with your Gems dot theory and how Gems Rule needs to be altered to better reflect the truth/facts of your dot scenarios.

I guess you could say that about any geometric theory. Could say the same to cantor's line rule or Kosh's snowflake rule. These guys wewn't talking about the geometry itself, they were using geometry to discuss infinity and/or fractal dimensions and unbounded values in finite spaces and so on.

I think if you can avoid taking offense, then you can better address recognizing the error in your Gems Rule and that all of my information has been given to for all of us to better grasp the truth of dot theory and specifically 2, 3 and 4 dots, whether as regular/symmetrical ergo equalateral relationships or irregular non-equal relationships.

r6

There is no error in the rule. The rule is arbitrary.

[Gem]

Originally Posted by SemperVI

Hmmm - Perhaps it can't from a dot theory perspective on the surface, but I am not yet willing to concede the assertion that in dot theory an entity can't be related to itself specifically because of what you addressed below.

I did think about how dots relate to themselves, and I think understand how they do, but they only relate to themselves in the presence of other dots. We should probably say that one dot in isolation has no definitive quality, and is entirely arbitrary as an entity, which is to say, it has no inevitable quality due to relation. 2 dots retain their arbitrary defintion of course, but are also 'non-arbitrarily' or necessarily defined by their relationship. We say something like A is to B as B is to A. At this piont the dots start to relate to themselves, or more accurately, begin to behave according to the dimensions of the relation.

When you describe the dot in a 2D or 3D plane - I don't see the dot as a singular entity - it is far more complex than a basic building block for lack of a better term. This dot has properties that are intrinsic to the existence of the dot it self.

Exactly. When we get to the three dot, the relation with others changes and thus so too does that dots dimensional relation with itself - or a vertex is not separate from the plane. At the four dot level the dot become 'placed' in 3D, so to speak.

If you take a dot's dimensional relation with itself to be relevant, and I think it is because that definition isn't actually arbitrary, but stipulated in accordance to relativity; then a dot is perhaps quasi-dimensional rather than Non-dimensional, in which case - it has a very particular, and peculiar, relation with itself.

From an object model perspective, an entities relationship with itself is implicitly understood through inheritance and polymorphism.

Ok because this 'inter-dimensional dot' could be said to be polymorphic.

Explanation: As previously established -- every ENTITY is an instance of a TYPE OF ENTITY. If the "dot" we are speaking of is viewed as an entity - then this dot has a super entity that the dot inherits from that defines the dot's origin like dot "A". Taking this further - if the said dot is in a 3 dimensional plane - then this dot would need to have exactly 3 attributes to define the X,Y,Z coordinates (aka attribute > attribute type > entity type > entity) required to exist in the 3 dimensional plane. This inheritance is precisely how the relationship with itself is established. Each instance of inheritance is just another building block to define the requirements in order for the dot to exist in the plane it is designed for.

Ok that sounds like what I just said.

OK dimensionality is perhaps the super entity - yep dimensional or 'quasi-dimensional', so the plane is but one mode of dimension, whereas the dot exists equally and unchanged in quasi-dimensionality.

I think so in the sense that when you reverse engineer the properties and definition of the dot (which I think is what we are doing here) - you are breaking it down to its most common abstract element or entity! ...and yes - when you break it down to the most abstract element in computing you are looking at a boolean or binary entity. (true/false, on/off, exists/does not exist (null/void). To me, I see no reason why this would not apply in dot theory but I have little understanding of it so....

Yep. in the 1 and 0 scenario it's like someting/nothing and this changed with the 2 dot scenario where we call one 'beginning' hence the other is 'end' we say one is 'up' hence other is 'down' which is basic taoist duality. Dot theory sees this differentlly and not so black and white because the relation is such that there are no 'slight differences' and all 'differences' are necessarily extreme by relationship since there is only one difference defined by a single relationship.In dot theory, then, we would say something like "they are different to the exact degree that they are the same" - which is like uber-taoist! hahah.

I'm not sure I followed you here except to say that once a dot is defined. The same dot entity used to to define the origin and the X,Y plane of point "A" in a 2D plane can be used to define an instance of the entity of point "B". This combined with the relationship between these two points is also an "entity" that describes the space between point "A" and point "B". All three of these complex entities combined can also be viewed/defined as a singular entity. This is where polymophism comes into play

Dot theory doesn't presume space, so a plane is defined by 3 dots in relation. I think it's easiest to imagine this in context of the Planck scale, but 'size' is actually irrelevant - though 'quanta' is relevant. We might say it's a 3 dot quanta for simplification, but the spacial quanta is more like a simultaneous apparition of equal relation. The geometry shows how the relations define dimension and as the relation entails more entities dimension becomes a constraint until we simply can not physically place dots equidistantly from all others. The concept of distance or shape actually only arises when we require distances, which is to say, when we require more that one value of distance in order to arrange dots.

I don't know anything about quantum computing; however - in thinking about how object modeling and dot theory may be related - I could not help but wonder how quantum entanglement applied, particularly as it pertained to an entity being related to itself. This is probably best left in the realm of spooky action at a distance:-)

OK I'm glad you also brought up distance as spooky, because I was attempting to be a bit spooky is my previous paragraph (edit)

Hope I was able to further clarify myself and I did not muddy the waters of the discussion you wanted to have about dot theory. Again to me it seems very similar to computing, interesting post!

It was a good clarification and I probably muddied it with dot theory, but I've found this train of thought revealing and there is indeed a way a dot relates to itself through the super entity of its dimensional context.

[SemperVI]

Ok that sounds like what I just said.

Sorry - did not mean to patronize you. It was more of an effort to clarify the subtle yet important point that was being made for other's who might be reading the thread

Dot theory doesn't presume space, so a plane is defined by 3 dots in relation. I think it's easiest to imagine this in context of the Planck scale, but 'size' is actually irrelevant - though 'quanta' is relevant.

Ergo quantum indeterminacy... I think I understand what you're saying; for the sake of argument and clarification can dot theory - while not presuming space or size - measure this in relation to other origins?

[Gem]

Originally Posted by SemperVI

Sorry - did not mean to patronize you. It was more of an effort to clarify the subtle yet important point that was being made for other's who might be reading the thread

Nope not parotnising at all. It's been pretty meaningful, actually.

Ergo quantum indeterminacy... I think I understand what you're saying; for the sake of argument and clarification can dot theory - while not presuming space or size - measure this in relation to other origins?

We don't really have an origin in particular because in the 2,3,4 dot relations any dot could be equally origin. Only when the 5 dot relation happens does it 'make a difference' which dot is considered origin, and in that case there are only 2 'different' origins, relatively speaking.

It basically means that things are formless where equal relation exists, but have quanta. We can codify the quanta with representations, but it's fundamentally immeasurable. The representations can only 'give someone an impression'.

This gets a little bit more obscured when we consider that there is nothing in and of itself, or rather, all things are interaction. Niels Bohr expressed this by saying, there is no quantum world; there is only abstract descriptions of a quantum world.

The quantum abstractions are utterly counter intuitive, we have particles with no size that have mass, for example. The math in QM doesn't describe distinct things; it speaks of a blur of probability and uncertainty. There is a founding philosophy to QM: the observer defines a question which determines the context of the answer, but it never actually answers how the universe is - it only gives context to what we can say about nature. Bohr sums it all up by saying:

"There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature..."

[SemperVI]

Appreciate the explaination