On a sheet of clean paper draw two horizontal lines,
labeling one X, and the other Y.
Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.

The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking.

What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.

That sign develops the real line via the balance of two rays such that
- 1 + 1 = 0
is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
- 1 + 1 * 1 = 0
has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
Unopened, untampered with, and yet perfectly preserved.

On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> On a sheet of clean paper draw two horizontal lines,
> labeling one X, and the other Y.
> Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
>
> The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking..
>
> What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.
>
> That sign develops the real line via the balance of two rays such that
> - 1 + 1 = 0
> is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
> - 1 + 1 * 1 = 0
> has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
> Unopened, untampered with, and yet perfectly preserved.

I understand that I will have to refine my argument. I will have to attempt variations. At the same time, we understand that the orthogonal vector representation works pretty good. Yet the argument on fundamental status has to be false, simply in hindsight of the polysign criterion. Firstly, and this is probably the most difficult part, the separation of the Cartesian product of set theory (X,Y) as RxR versus the (x,y) plane with its additional requirements which do include the set theory. Immediately the topic of orthogonality and independence as confused concepts has to occur.

As an aside to this there are some pretty options which have not been discussed much. Understanding that the ray is more fundamental than the line; the line being composed of two rays; will help and leads to some strange space works that have some convincing detail. Simply draw two rays on a piece of paper with a matched origin and an angle of say 30 degrees between them. Any position within that sector can be resolved as vector positions along each ray. Let's populate it with some positions: (1,2), (1,3), (1,4), (2,2), (2,3), (2,4). Now folding these two rays and their angle we see simply that the two dimensional sector is variable in quality yet should still retain all of its character, other than the refinement of our tools to actually draw the thing. There is good reason that we do not choose to make such a representation down at a five degree angle, say. The thickness of the pencil lead starts to matter and points that would be readily resolved at thirty degrees are much more difficult to resolve at five. Yet mathematically there is no problem. We could entertain the sector at an angle of 0.001 degrees. What is so convincing about this construction? The idea that general dimensional space could unfold from naught is present. It is a peculiar space. Simply unfolding another ray gets us a 3D sector presuming that we are not locked into the plane; that these rays are in some arbitrary high dimensional space for instance, though this description disqualifies them as fundamental. Great care must be taken when claiming to construct a space. The purpose here is certainly not to rest upon any Cartesian construction, and so the language 'arbitrary high dimensional space' has to be challenged above, and yet for the novice this language makes accessible the concept particularly for the Cartesian thinker, and this pretty well covers the human population in modernity.

The sector discussion can go quite a ways, but for the moment let's go back to the two ray case, and let's carry on by raising the angle. Admittedly we do this operation on a planar surface; on a piece of paper with a pencil. No doubt these limitations are factors. Regardless we sweep the angle out to ninety degrees. Nothing in particular happens just yet, so we keep going.. We still are able to maintain a representation of the sector though it is stretching out to quite a long thing all positions are accurately maintained. Well it has to be pointed out that the positions are gradually coming toward the rays and at 170 degrees things are flattening out all over again.. Then just as they gradually come to 180 degrees the two dimensional space collapses to a single dimensional real line. At this position we see that
( 1, 1 ) = 0 ; ( 2, 2 ) = 0 ; ( a, a ) = 0 .
and these exactly opposed rays establish what is known as the 'real' line. There is no mistake here, and the sign established which ray is meant. Thus we can leave the ordered pair form and engage the signed form:
- 1 + 1 = 0 ; - 2 + 2 = 0 ; - a + a = 0 .
Of course a value such as (1,3) evaluates as -1+3=+2 in the balanced form.. Yet this is not the end of the story. Something did sort of go 'snap!' here into a fully unfolded form. Rather a lot of philosophy can be engaged at this point already in terms of challenging the fundamental status of the real number. Indeed should we bring physics into the fold we'd have a pretty big bang with just three rays barely even getting started in their separation, yet still unfolding at some arbitrarily small angle. Edge effects aside, plopping in a 14 billion light year or 45 billion light year sphere in the sector is merely a scaling problem. Of course this is fundamental mathematics so to expect full congruence at such an early stage is naive. Still, it is pretty good.

Coming back again to the fully unfolded form in three rays we find that they will settle into a planar arrangement. The maximum spread between three rays will always be 120 degrees, no matter what the dimension of the system, and again this language is compromised but to think general dimensionally is ultimately where we are going. Securing this statement does seem challenging, but let's remember that in the general dimensional Cartesian systems there are but ninety degrees between orthogonal components. From polysign the constraint is more directly built simply by assigning each ray a sign and extending the two signed form to the three-signed form:
- a + a * a = 0
and now the plane is fully built. As two rays did carry two dimensional information yet folded out to a singular dimension, three rays are capable of carrying the information of a volume until they are folded out, at which point they become planar. These simple mechanics can be worked out by an intelligent child. Just the same as that child attempts to reflect this information onto their Cartesian trained parent of teacher they will meet with stiff resistance. Not many are able to break out of the Cartesain straightjacket. They are now known as the two-signed morons, or tsms in short. So where should you place all the brilliant men of mathematics who covered the subject so supremely, yet they overlooked these simple options? Here lays the greatest promise of polysign. We are engaged in a progression and there is more to go.

Possibly returning to the folding sector model is wise, and the gimmickry of sign is false, as Descartes noted; as some to this day find distaste in the subject. Yet the three-signed form yields the complex plane and it does so out of the same rule set as the two-signed numbers used. Certainly the real number as fundamental is well disproven here if you managed to work through this chain of reasoning. The ray is fundamental.

The topic here is to challenge the Cartesian product and its meaning, and the confusion that has ensued. Two-signed morons run the show so little can be done in this lifetime.

On Friday, June 24, 2022 at 8:11:27 AM UTC-4, Timothy Golden wrote:
> On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> > On a sheet of clean paper draw two horizontal lines,
> > labeling one X, and the other Y.
> > Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
> >
> > The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking.
> >
> > What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.
> >
> > That sign develops the real line via the balance of two rays such that
> > - 1 + 1 = 0
> > is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
> > - 1 + 1 * 1 = 0
> > has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
> > Unopened, untampered with, and yet perfectly preserved.
> I understand that I will have to refine my argument. I will have to attempt variations. At the same time, we understand that the orthogonal vector representation works pretty good. Yet the argument on fundamental status has to be false, simply in hindsight of the polysign criterion. Firstly, and this is probably the most difficult part, the separation of the Cartesian product of set theory (X,Y) as RxR versus the (x,y) plane with its additional requirements which do include the set theory. Immediately the topic of orthogonality and independence as confused concepts has to occur.
>
> As an aside to this there are some pretty options which have not been discussed much. Understanding that the ray is more fundamental than the line; the line being composed of two rays; will help and leads to some strange space works that have some convincing detail. Simply draw two rays on a piece of paper with a matched origin and an angle of say 30 degrees between them.. Any position within that sector can be resolved as vector positions along each ray. Let's populate it with some positions: (1,2), (1,3), (1,4), (2,2), (2,3), (2,4). Now folding these two rays and their angle we see simply that the two dimensional sector is variable in quality yet should still retain all of its character, other than the refinement of our tools to actually draw the thing. There is good reason that we do not choose to make such a representation down at a five degree angle, say. The thickness of the pencil lead starts to matter and points that would be readily resolved at thirty degrees are much more difficult to resolve at five. Yet mathematically there is no problem. We could entertain the sector at an angle of 0.001 degrees. What is so convincing about this construction? The idea that general dimensional space could unfold from naught is present. It is a peculiar space. Simply unfolding another ray gets us a 3D sector presuming that we are not locked into the plane; that these rays are in some arbitrary high dimensional space for instance, though this description disqualifies them as fundamental. Great care must be taken when claiming to construct a space. The purpose here is certainly not to rest upon any Cartesian construction, and so the language 'arbitrary high dimensional space' has to be challenged above, and yet for the novice this language makes accessible the concept particularly for the Cartesian thinker, and this pretty well covers the human population in modernity.
>
> The sector discussion can go quite a ways, but for the moment let's go back to the two ray case, and let's carry on by raising the angle. Admittedly we do this operation on a planar surface; on a piece of paper with a pencil. No doubt these limitations are factors. Regardless we sweep the angle out to ninety degrees. Nothing in particular happens just yet, so we keep going. We still are able to maintain a representation of the sector though it is stretching out to quite a long thing all positions are accurately maintained. Well it has to be pointed out that the positions are gradually coming toward the rays and at 170 degrees things are flattening out all over again. Then just as they gradually come to 180 degrees the two dimensional space collapses to a single dimensional real line. At this position we see that
> ( 1, 1 ) = 0 ; ( 2, 2 ) = 0 ; ( a, a ) = 0 .
> and these exactly opposed rays establish what is known as the 'real' line.. There is no mistake here, and the sign established which ray is meant. Thus we can leave the ordered pair form and engage the signed form:
> - 1 + 1 = 0 ; - 2 + 2 = 0 ; - a + a = 0 .
> Of course a value such as (1,3) evaluates as -1+3=+2 in the balanced form. Yet this is not the end of the story. Something did sort of go 'snap!' here into a fully unfolded form. Rather a lot of philosophy can be engaged at this point already in terms of challenging the fundamental status of the real number. Indeed should we bring physics into the fold we'd have a pretty big bang with just three rays barely even getting started in their separation, yet still unfolding at some arbitrarily small angle. Edge effects aside, plopping in a 14 billion light year or 45 billion light year sphere in the sector is merely a scaling problem. Of course this is fundamental mathematics so to expect full congruence at such an early stage is naive. Still, it is pretty good.
>
> Coming back again to the fully unfolded form in three rays we find that they will settle into a planar arrangement. The maximum spread between three rays will always be 120 degrees, no matter what the dimension of the system, and again this language is compromised but to think general dimensionally is ultimately where we are going. Securing this statement does seem challenging, but let's remember that in the general dimensional Cartesian systems there are but ninety degrees between orthogonal components. From polysign the constraint is more directly built simply by assigning each ray a sign and extending the two signed form to the three-signed form:
> - a + a * a = 0
> and now the plane is fully built. As two rays did carry two dimensional information yet folded out to a singular dimension, three rays are capable of carrying the information of a volume until they are folded out, at which point they become planar. These simple mechanics can be worked out by an intelligent child. Just the same as that child attempts to reflect this information onto their Cartesian trained parent of teacher they will meet with stiff resistance. Not many are able to break out of the Cartesain straightjacket. They are now known as the two-signed morons, or tsms in short. So where should you place all the brilliant men of mathematics who covered the subject so supremely, yet they overlooked these simple options? Here lays the greatest promise of polysign. We are engaged in a progression and there is more to go.
>
> Possibly returning to the folding sector model is wise, and the gimmickry of sign is false, as Descartes noted; as some to this day find distaste in the subject. Yet the three-signed form yields the complex plane and it does so out of the same rule set as the two-signed numbers used. Certainly the real number as fundamental is well disproven here if you managed to work through this chain of reasoning. The ray is fundamental.

On Friday, June 24, 2022 at 6:40:56 AM UTC-7, timba...@gmail.com wrote:
> On Friday, June 24, 2022 at 8:11:27 AM UTC-4, Timothy Golden wrote:
> > On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> > > On a sheet of clean paper draw two horizontal lines,
> > > labeling one X, and the other Y.
> > > Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
> > >
> > > The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking.
> > >
> > > What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.
> > >
> > > That sign develops the real line via the balance of two rays such that
> > > - 1 + 1 = 0
> > > is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
> > > - 1 + 1 * 1 = 0
> > > has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
> > > Unopened, untampered with, and yet perfectly preserved.
> > I understand that I will have to refine my argument. I will have to attempt variations. At the same time, we understand that the orthogonal vector representation works pretty good. Yet the argument on fundamental status has to be false, simply in hindsight of the polysign criterion. Firstly, and this is probably the most difficult part, the separation of the Cartesian product of set theory (X,Y) as RxR versus the (x,y) plane with its additional requirements which do include the set theory. Immediately the topic of orthogonality and independence as confused concepts has to occur.
> >
> > As an aside to this there are some pretty options which have not been discussed much. Understanding that the ray is more fundamental than the line; the line being composed of two rays; will help and leads to some strange space works that have some convincing detail. Simply draw two rays on a piece of paper with a matched origin and an angle of say 30 degrees between them. Any position within that sector can be resolved as vector positions along each ray. Let's populate it with some positions: (1,2), (1,3), (1,4), (2,2), (2,3), (2,4). Now folding these two rays and their angle we see simply that the two dimensional sector is variable in quality yet should still retain all of its character, other than the refinement of our tools to actually draw the thing. There is good reason that we do not choose to make such a representation down at a five degree angle, say. The thickness of the pencil lead starts to matter and points that would be readily resolved at thirty degrees are much more difficult to resolve at five. Yet mathematically there is no problem. We could entertain the sector at an angle of 0.001 degrees. What is so convincing about this construction? The idea that general dimensional space could unfold from naught is present. It is a peculiar space. Simply unfolding another ray gets us a 3D sector presuming that we are not locked into the plane; that these rays are in some arbitrary high dimensional space for instance, though this description disqualifies them as fundamental. Great care must be taken when claiming to construct a space. The purpose here is certainly not to rest upon any Cartesian construction, and so the language 'arbitrary high dimensional space' has to be challenged above, and yet for the novice this language makes accessible the concept particularly for the Cartesian thinker, and this pretty well covers the human population in modernity.
> >
> > The sector discussion can go quite a ways, but for the moment let's go back to the two ray case, and let's carry on by raising the angle. Admittedly we do this operation on a planar surface; on a piece of paper with a pencil. No doubt these limitations are factors. Regardless we sweep the angle out to ninety degrees. Nothing in particular happens just yet, so we keep going. We still are able to maintain a representation of the sector though it is stretching out to quite a long thing all positions are accurately maintained. Well it has to be pointed out that the positions are gradually coming toward the rays and at 170 degrees things are flattening out all over again. Then just as they gradually come to 180 degrees the two dimensional space collapses to a single dimensional real line. At this position we see that
> > ( 1, 1 ) = 0 ; ( 2, 2 ) = 0 ; ( a, a ) = 0 .
> > and these exactly opposed rays establish what is known as the 'real' line. There is no mistake here, and the sign established which ray is meant. Thus we can leave the ordered pair form and engage the signed form:
> > - 1 + 1 = 0 ; - 2 + 2 = 0 ; - a + a = 0 .
> > Of course a value such as (1,3) evaluates as -1+3=+2 in the balanced form. Yet this is not the end of the story. Something did sort of go 'snap!' here into a fully unfolded form. Rather a lot of philosophy can be engaged at this point already in terms of challenging the fundamental status of the real number. Indeed should we bring physics into the fold we'd have a pretty big bang with just three rays barely even getting started in their separation, yet still unfolding at some arbitrarily small angle. Edge effects aside, plopping in a 14 billion light year or 45 billion light year sphere in the sector is merely a scaling problem. Of course this is fundamental mathematics so to expect full congruence at such an early stage is naive. Still, it is pretty good.
> >
> > Coming back again to the fully unfolded form in three rays we find that they will settle into a planar arrangement. The maximum spread between three rays will always be 120 degrees, no matter what the dimension of the system, and again this language is compromised but to think general dimensionally is ultimately where we are going. Securing this statement does seem challenging, but let's remember that in the general dimensional Cartesian systems there are but ninety degrees between orthogonal components. From polysign the constraint is more directly built simply by assigning each ray a sign and extending the two signed form to the three-signed form:
> > - a + a * a = 0
> > and now the plane is fully built. As two rays did carry two dimensional information yet folded out to a singular dimension, three rays are capable of carrying the information of a volume until they are folded out, at which point they become planar. These simple mechanics can be worked out by an intelligent child. Just the same as that child attempts to reflect this information onto their Cartesian trained parent of teacher they will meet with stiff resistance. Not many are able to break out of the Cartesain straightjacket. They are now known as the two-signed morons, or tsms in short. So where should you place all the brilliant men of mathematics who covered the subject so supremely, yet they overlooked these simple options? Here lays the greatest promise of polysign. We are engaged in a progression and there is more to go.
> >
> > Possibly returning to the folding sector model is wise, and the gimmickry of sign is false, as Descartes noted; as some to this day find distaste in the subject. Yet the three-signed form yields the complex plane and it does so out of the same rule set as the two-signed numbers used. Certainly the real number as fundamental is well disproven here if you managed to work through this chain of reasoning. The ray is fundamental.
> To what degree if the unfolding procedure is accurate then is P1 zero dimensional only in the unfolded regime? Yes.
> P1 means that -a=0 holds. These are the one-signed numbers. Unidirectional and zero dimensional. Time.
> To what degree do the rays unfolding from naught (angle, anyway) simply contribute to the uniray (naught ray?)? Yes.
> Basically this just means that the model holds correspondence even at zero angle, though the question of how order is engaged from such ray contributions unfolding without any identity... possibly random analysis and this then would link into quantum thinking.
> It is a very minimal set of constraints so it seems that imposing more onto it would be necessary.
>
>
> At some point here as I still naturally use the term 'dimension' freely but try to cover my tracks, possibly something will unravel.
> To unravel the Cartesian assumption is enough, but really the hope is to recover something with fundamental physical correspondence.
> >
> > The topic here is to challenge the Cartesian product and its meaning, and the confusion that has ensued. Two-signed morons run the show so little can be done in this lifetime.

On Friday, June 24, 2022 at 12:22:20 PM UTC-4, Ross A. Finlayson wrote:
> On Friday, June 24, 2022 at 6:40:56 AM UTC-7, timba...@gmail.com wrote:
> > On Friday, June 24, 2022 at 8:11:27 AM UTC-4, Timothy Golden wrote:
> > > On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> > > > On a sheet of clean paper draw two horizontal lines,
> > > > labeling one X, and the other Y.
> > > > Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
> > > >
> > > > The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking.
> > > >
> > > > What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.
> > > >
> > > > That sign develops the real line via the balance of two rays such that
> > > > - 1 + 1 = 0
> > > > is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
> > > > - 1 + 1 * 1 = 0
> > > > has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
> > > > Unopened, untampered with, and yet perfectly preserved.
> > > I understand that I will have to refine my argument. I will have to attempt variations. At the same time, we understand that the orthogonal vector representation works pretty good. Yet the argument on fundamental status has to be false, simply in hindsight of the polysign criterion. Firstly, and this is probably the most difficult part, the separation of the Cartesian product of set theory (X,Y) as RxR versus the (x,y) plane with its additional requirements which do include the set theory. Immediately the topic of orthogonality and independence as confused concepts has to occur.
> > >
> > > As an aside to this there are some pretty options which have not been discussed much. Understanding that the ray is more fundamental than the line; the line being composed of two rays; will help and leads to some strange space works that have some convincing detail. Simply draw two rays on a piece of paper with a matched origin and an angle of say 30 degrees between them. Any position within that sector can be resolved as vector positions along each ray. Let's populate it with some positions: (1,2), (1,3), (1,4), (2,2), (2,3), (2,4). Now folding these two rays and their angle we see simply that the two dimensional sector is variable in quality yet should still retain all of its character, other than the refinement of our tools to actually draw the thing. There is good reason that we do not choose to make such a representation down at a five degree angle, say. The thickness of the pencil lead starts to matter and points that would be readily resolved at thirty degrees are much more difficult to resolve at five. Yet mathematically there is no problem. We could entertain the sector at an angle of 0.001 degrees. What is so convincing about this construction? The idea that general dimensional space could unfold from naught is present. It is a peculiar space. Simply unfolding another ray gets us a 3D sector presuming that we are not locked into the plane; that these rays are in some arbitrary high dimensional space for instance, though this description disqualifies them as fundamental. Great care must be taken when claiming to construct a space. The purpose here is certainly not to rest upon any Cartesian construction, and so the language 'arbitrary high dimensional space' has to be challenged above, and yet for the novice this language makes accessible the concept particularly for the Cartesian thinker, and this pretty well covers the human population in modernity.
> > >
> > > The sector discussion can go quite a ways, but for the moment let's go back to the two ray case, and let's carry on by raising the angle. Admittedly we do this operation on a planar surface; on a piece of paper with a pencil. No doubt these limitations are factors. Regardless we sweep the angle out to ninety degrees. Nothing in particular happens just yet, so we keep going. We still are able to maintain a representation of the sector though it is stretching out to quite a long thing all positions are accurately maintained. Well it has to be pointed out that the positions are gradually coming toward the rays and at 170 degrees things are flattening out all over again. Then just as they gradually come to 180 degrees the two dimensional space collapses to a single dimensional real line. At this position we see that
> > > ( 1, 1 ) = 0 ; ( 2, 2 ) = 0 ; ( a, a ) = 0 .
> > > and these exactly opposed rays establish what is known as the 'real' line. There is no mistake here, and the sign established which ray is meant.. Thus we can leave the ordered pair form and engage the signed form:
> > > - 1 + 1 = 0 ; - 2 + 2 = 0 ; - a + a = 0 .
> > > Of course a value such as (1,3) evaluates as -1+3=+2 in the balanced form. Yet this is not the end of the story. Something did sort of go 'snap!' here into a fully unfolded form. Rather a lot of philosophy can be engaged at this point already in terms of challenging the fundamental status of the real number. Indeed should we bring physics into the fold we'd have a pretty big bang with just three rays barely even getting started in their separation, yet still unfolding at some arbitrarily small angle. Edge effects aside, plopping in a 14 billion light year or 45 billion light year sphere in the sector is merely a scaling problem. Of course this is fundamental mathematics so to expect full congruence at such an early stage is naive. Still, it is pretty good.
> > >
> > > Coming back again to the fully unfolded form in three rays we find that they will settle into a planar arrangement. The maximum spread between three rays will always be 120 degrees, no matter what the dimension of the system, and again this language is compromised but to think general dimensionally is ultimately where we are going. Securing this statement does seem challenging, but let's remember that in the general dimensional Cartesian systems there are but ninety degrees between orthogonal components. From polysign the constraint is more directly built simply by assigning each ray a sign and extending the two signed form to the three-signed form:
> > > - a + a * a = 0
> > > and now the plane is fully built. As two rays did carry two dimensional information yet folded out to a singular dimension, three rays are capable of carrying the information of a volume until they are folded out, at which point they become planar. These simple mechanics can be worked out by an intelligent child. Just the same as that child attempts to reflect this information onto their Cartesian trained parent of teacher they will meet with stiff resistance. Not many are able to break out of the Cartesain straightjacket. They are now known as the two-signed morons, or tsms in short. So where should you place all the brilliant men of mathematics who covered the subject so supremely, yet they overlooked these simple options? Here lays the greatest promise of polysign. We are engaged in a progression and there is more to go.
> > >
> > > Possibly returning to the folding sector model is wise, and the gimmickry of sign is false, as Descartes noted; as some to this day find distaste in the subject. Yet the three-signed form yields the complex plane and it does so out of the same rule set as the two-signed numbers used. Certainly the real number as fundamental is well disproven here if you managed to work through this chain of reasoning. The ray is fundamental.
> > To what degree if the unfolding procedure is accurate then is P1 zero dimensional only in the unfolded regime? Yes.
> > P1 means that -a=0 holds. These are the one-signed numbers. Unidirectional and zero dimensional. Time.
> > To what degree do the rays unfolding from naught (angle, anyway) simply contribute to the uniray (naught ray?)? Yes.
> > Basically this just means that the model holds correspondence even at zero angle, though the question of how order is engaged from such ray contributions unfolding without any identity... possibly random analysis and this then would link into quantum thinking.
> > It is a very minimal set of constraints so it seems that imposing more onto it would be necessary.
> >
> >
> > At some point here as I still naturally use the term 'dimension' freely but try to cover my tracks, possibly something will unravel.
> > To unravel the Cartesian assumption is enough, but really the hope is to recover something with fundamental physical correspondence.
> > >
> > > The topic here is to challenge the Cartesian product and its meaning, and the confusion that has ensued. Two-signed morons run the show so little can be done in this lifetime.
> Angles, ....

On Saturday, June 25, 2022 at 1:09:29 PM UTC-4, timba...@gmail.com wrote:
> On Friday, June 24, 2022 at 12:22:20 PM UTC-4, Ross A. Finlayson wrote:
> > On Friday, June 24, 2022 at 6:40:56 AM UTC-7, timba...@gmail.com wrote:
> > > On Friday, June 24, 2022 at 8:11:27 AM UTC-4, Timothy Golden wrote:
> > > > On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> > > > > On a sheet of clean paper draw two horizontal lines,
> > > > > labeling one X, and the other Y.
> > > > > Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
> > > > >
> > > > > The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking.
> > > > >
> > > > > What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.
> > > > >
> > > > > That sign develops the real line via the balance of two rays such that
> > > > > - 1 + 1 = 0
> > > > > is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
> > > > > - 1 + 1 * 1 = 0
> > > > > has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
> > > > > Unopened, untampered with, and yet perfectly preserved.
> > > > I understand that I will have to refine my argument. I will have to attempt variations. At the same time, we understand that the orthogonal vector representation works pretty good. Yet the argument on fundamental status has to be false, simply in hindsight of the polysign criterion. Firstly, and this is probably the most difficult part, the separation of the Cartesian product of set theory (X,Y) as RxR versus the (x,y) plane with its additional requirements which do include the set theory. Immediately the topic of orthogonality and independence as confused concepts has to occur.
> > > >
> > > > As an aside to this there are some pretty options which have not been discussed much. Understanding that the ray is more fundamental than the line; the line being composed of two rays; will help and leads to some strange space works that have some convincing detail. Simply draw two rays on a piece of paper with a matched origin and an angle of say 30 degrees between them. Any position within that sector can be resolved as vector positions along each ray. Let's populate it with some positions: (1,2), (1,3), (1,4), (2,2), (2,3), (2,4). Now folding these two rays and their angle we see simply that the two dimensional sector is variable in quality yet should still retain all of its character, other than the refinement of our tools to actually draw the thing. There is good reason that we do not choose to make such a representation down at a five degree angle, say. The thickness of the pencil lead starts to matter and points that would be readily resolved at thirty degrees are much more difficult to resolve at five. Yet mathematically there is no problem. We could entertain the sector at an angle of 0.001 degrees. What is so convincing about this construction? The idea that general dimensional space could unfold from naught is present. It is a peculiar space. Simply unfolding another ray gets us a 3D sector presuming that we are not locked into the plane; that these rays are in some arbitrary high dimensional space for instance, though this description disqualifies them as fundamental. Great care must be taken when claiming to construct a space. The purpose here is certainly not to rest upon any Cartesian construction, and so the language 'arbitrary high dimensional space' has to be challenged above, and yet for the novice this language makes accessible the concept particularly for the Cartesian thinker, and this pretty well covers the human population in modernity.
> > > >
> > > > The sector discussion can go quite a ways, but for the moment let's go back to the two ray case, and let's carry on by raising the angle. Admittedly we do this operation on a planar surface; on a piece of paper with a pencil. No doubt these limitations are factors. Regardless we sweep the angle out to ninety degrees. Nothing in particular happens just yet, so we keep going. We still are able to maintain a representation of the sector though it is stretching out to quite a long thing all positions are accurately maintained. Well it has to be pointed out that the positions are gradually coming toward the rays and at 170 degrees things are flattening out all over again. Then just as they gradually come to 180 degrees the two dimensional space collapses to a single dimensional real line. At this position we see that
> > > > ( 1, 1 ) = 0 ; ( 2, 2 ) = 0 ; ( a, a ) = 0 .
> > > > and these exactly opposed rays establish what is known as the 'real' line. There is no mistake here, and the sign established which ray is meant. Thus we can leave the ordered pair form and engage the signed form:
> > > > - 1 + 1 = 0 ; - 2 + 2 = 0 ; - a + a = 0 .
> > > > Of course a value such as (1,3) evaluates as -1+3=+2 in the balanced form. Yet this is not the end of the story. Something did sort of go 'snap!' here into a fully unfolded form. Rather a lot of philosophy can be engaged at this point already in terms of challenging the fundamental status of the real number. Indeed should we bring physics into the fold we'd have a pretty big bang with just three rays barely even getting started in their separation, yet still unfolding at some arbitrarily small angle. Edge effects aside, plopping in a 14 billion light year or 45 billion light year sphere in the sector is merely a scaling problem. Of course this is fundamental mathematics so to expect full congruence at such an early stage is naive. Still, it is pretty good.
> > > >
> > > > Coming back again to the fully unfolded form in three rays we find that they will settle into a planar arrangement. The maximum spread between three rays will always be 120 degrees, no matter what the dimension of the system, and again this language is compromised but to think general dimensionally is ultimately where we are going. Securing this statement does seem challenging, but let's remember that in the general dimensional Cartesian systems there are but ninety degrees between orthogonal components. From polysign the constraint is more directly built simply by assigning each ray a sign and extending the two signed form to the three-signed form:
> > > > - a + a * a = 0
> > > > and now the plane is fully built. As two rays did carry two dimensional information yet folded out to a singular dimension, three rays are capable of carrying the information of a volume until they are folded out, at which point they become planar. These simple mechanics can be worked out by an intelligent child. Just the same as that child attempts to reflect this information onto their Cartesian trained parent of teacher they will meet with stiff resistance. Not many are able to break out of the Cartesain straightjacket. They are now known as the two-signed morons, or tsms in short. So where should you place all the brilliant men of mathematics who covered the subject so supremely, yet they overlooked these simple options? Here lays the greatest promise of polysign. We are engaged in a progression and there is more to go.
> > > >
> > > > Possibly returning to the folding sector model is wise, and the gimmickry of sign is false, as Descartes noted; as some to this day find distaste in the subject. Yet the three-signed form yields the complex plane and it does so out of the same rule set as the two-signed numbers used. Certainly the real number as fundamental is well disproven here if you managed to work through this chain of reasoning. The ray is fundamental.
> > > To what degree if the unfolding procedure is accurate then is P1 zero dimensional only in the unfolded regime? Yes.
> > > P1 means that -a=0 holds. These are the one-signed numbers. Unidirectional and zero dimensional. Time.
> > > To what degree do the rays unfolding from naught (angle, anyway) simply contribute to the uniray (naught ray?)? Yes.
> > > Basically this just means that the model holds correspondence even at zero angle, though the question of how order is engaged from such ray contributions unfolding without any identity... possibly random analysis and this then would link into quantum thinking.
> > > It is a very minimal set of constraints so it seems that imposing more onto it would be necessary.
> > >
> > >
> > > At some point here as I still naturally use the term 'dimension' freely but try to cover my tracks, possibly something will unravel.
> > > To unravel the Cartesian assumption is enough, but really the hope is to recover something with fundamental physical correspondence.
> > > >
> > > > The topic here is to challenge the Cartesian product and its meaning, and the confusion that has ensued. Two-signed morons run the show so little can be done in this lifetime.
> > Angles, ....
> And breaking with the real number as fundamental.
>
> The Cartesian product is misused elsewhere as well. For instance in ring theory two operations are formalized: the sum and the product. Yet in the formalization as binary operators the functional analysis calls on these humble operators suddenly to work SxS to S. Since when is summation a two dimensional operation? And the product certainly is trickier. Staying with the simple arithmetic product the same failing occurs. Why is it so difficult to simply state that a,b, and c in S will suffice?
> a + b = c
> Well, now we have posed an operator and yet where is the operation actually even defined? Perhaps this is why they call it 'ring theory', as if a theory must be left incomplete at the bottom. Upon choosing S obviously the instruction on how to add values goes directly back to what was taught in grade school. As to what was gained in the supposed generalization: now you are free to confuse commutative systems with non-commutative systems. Nize.
>
> The notion that the sum and product are fundamental operations is good. Yet leveling them completely is not necessarily sensible. After all the product derives from the sum ultimately. Within ring theory this now disappears, and further a challenge to the field axioms never occurs. Division and subtraction as non-fundamental in status due to the fact that their definitions can be had as inverse operators is never processed. Well, if it were the rational number would come under scrutiny to a curious young mind. Thence the lack of closure of that very rational value, and its supposed birth of the continuum. All a farce? Pretty well, yes. Secondary forms of unity are better descriptors of the continuum. This is the direct meaning of the decimal point. It indicates where unity lays in an otherwise natural value. So you see the continuum as natural valued in nature, though with some augmented structure, can be taken as an accurate stance. Breaking the back of the real value I had done in sign decades ago, and in magnitude more recently. Again, the ray as fundamental can lead the way through the quagmire. The ray is not the line.

On Saturday, June 25, 2022 at 7:10:07 PM UTC-4, Dan joyce wrote:
> On Saturday, June 25, 2022 at 1:09:29 PM UTC-4, timba...@gmail.com wrote:
> > On Friday, June 24, 2022 at 12:22:20 PM UTC-4, Ross A. Finlayson wrote:
> > > On Friday, June 24, 2022 at 6:40:56 AM UTC-7, timba...@gmail.com wrote:
> > > > On Friday, June 24, 2022 at 8:11:27 AM UTC-4, Timothy Golden wrote:
> > > > > On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> > > > > > On a sheet of clean paper draw two horizontal lines,
> > > > > > labeling one X, and the other Y.
> > > > > > Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
> > > > > >
> > > > > > The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking.
> > > > > >
> > > > > > What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.
> > > > > >
> > > > > > That sign develops the real line via the balance of two rays such that
> > > > > > - 1 + 1 = 0
> > > > > > is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
> > > > > > - 1 + 1 * 1 = 0
> > > > > > has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
> > > > > > Unopened, untampered with, and yet perfectly preserved.
> > > > > I understand that I will have to refine my argument. I will have to attempt variations. At the same time, we understand that the orthogonal vector representation works pretty good. Yet the argument on fundamental status has to be false, simply in hindsight of the polysign criterion. Firstly, and this is probably the most difficult part, the separation of the Cartesian product of set theory (X,Y) as RxR versus the (x,y) plane with its additional requirements which do include the set theory. Immediately the topic of orthogonality and independence as confused concepts has to occur.
> > > > >
> > > > > As an aside to this there are some pretty options which have not been discussed much. Understanding that the ray is more fundamental than the line; the line being composed of two rays; will help and leads to some strange space works that have some convincing detail. Simply draw two rays on a piece of paper with a matched origin and an angle of say 30 degrees between them. Any position within that sector can be resolved as vector positions along each ray. Let's populate it with some positions: (1,2), (1,3), (1,4), (2,2), (2,3), (2,4). Now folding these two rays and their angle we see simply that the two dimensional sector is variable in quality yet should still retain all of its character, other than the refinement of our tools to actually draw the thing. There is good reason that we do not choose to make such a representation down at a five degree angle, say. The thickness of the pencil lead starts to matter and points that would be readily resolved at thirty degrees are much more difficult to resolve at five. Yet mathematically there is no problem. We could entertain the sector at an angle of 0.001 degrees. What is so convincing about this construction? The idea that general dimensional space could unfold from naught is present. It is a peculiar space. Simply unfolding another ray gets us a 3D sector presuming that we are not locked into the plane; that these rays are in some arbitrary high dimensional space for instance, though this description disqualifies them as fundamental. Great care must be taken when claiming to construct a space. The purpose here is certainly not to rest upon any Cartesian construction, and so the language 'arbitrary high dimensional space' has to be challenged above, and yet for the novice this language makes accessible the concept particularly for the Cartesian thinker, and this pretty well covers the human population in modernity.
> > > > >
> > > > > The sector discussion can go quite a ways, but for the moment let's go back to the two ray case, and let's carry on by raising the angle. Admittedly we do this operation on a planar surface; on a piece of paper with a pencil. No doubt these limitations are factors. Regardless we sweep the angle out to ninety degrees. Nothing in particular happens just yet, so we keep going. We still are able to maintain a representation of the sector though it is stretching out to quite a long thing all positions are accurately maintained. Well it has to be pointed out that the positions are gradually coming toward the rays and at 170 degrees things are flattening out all over again. Then just as they gradually come to 180 degrees the two dimensional space collapses to a single dimensional real line. At this position we see that
> > > > > ( 1, 1 ) = 0 ; ( 2, 2 ) = 0 ; ( a, a ) = 0 .
> > > > > and these exactly opposed rays establish what is known as the 'real' line. There is no mistake here, and the sign established which ray is meant. Thus we can leave the ordered pair form and engage the signed form:
> > > > > - 1 + 1 = 0 ; - 2 + 2 = 0 ; - a + a = 0 .
> > > > > Of course a value such as (1,3) evaluates as -1+3=+2 in the balanced form. Yet this is not the end of the story. Something did sort of go 'snap!' here into a fully unfolded form. Rather a lot of philosophy can be engaged at this point already in terms of challenging the fundamental status of the real number. Indeed should we bring physics into the fold we'd have a pretty big bang with just three rays barely even getting started in their separation, yet still unfolding at some arbitrarily small angle. Edge effects aside, plopping in a 14 billion light year or 45 billion light year sphere in the sector is merely a scaling problem. Of course this is fundamental mathematics so to expect full congruence at such an early stage is naive. Still, it is pretty good.
> > > > >
> > > > > Coming back again to the fully unfolded form in three rays we find that they will settle into a planar arrangement. The maximum spread between three rays will always be 120 degrees, no matter what the dimension of the system, and again this language is compromised but to think general dimensionally is ultimately where we are going. Securing this statement does seem challenging, but let's remember that in the general dimensional Cartesian systems there are but ninety degrees between orthogonal components. From polysign the constraint is more directly built simply by assigning each ray a sign and extending the two signed form to the three-signed form:
> > > > > - a + a * a = 0
> > > > > and now the plane is fully built. As two rays did carry two dimensional information yet folded out to a singular dimension, three rays are capable of carrying the information of a volume until they are folded out, at which point they become planar. These simple mechanics can be worked out by an intelligent child. Just the same as that child attempts to reflect this information onto their Cartesian trained parent of teacher they will meet with stiff resistance. Not many are able to break out of the Cartesain straightjacket. They are now known as the two-signed morons, or tsms in short.. So where should you place all the brilliant men of mathematics who covered the subject so supremely, yet they overlooked these simple options? Here lays the greatest promise of polysign. We are engaged in a progression and there is more to go.
> > > > >
> > > > > Possibly returning to the folding sector model is wise, and the gimmickry of sign is false, as Descartes noted; as some to this day find distaste in the subject. Yet the three-signed form yields the complex plane and it does so out of the same rule set as the two-signed numbers used. Certainly the real number as fundamental is well disproven here if you managed to work through this chain of reasoning. The ray is fundamental.
> > > > To what degree if the unfolding procedure is accurate then is P1 zero dimensional only in the unfolded regime? Yes.
> > > > P1 means that -a=0 holds. These are the one-signed numbers. Unidirectional and zero dimensional. Time.
> > > > To what degree do the rays unfolding from naught (angle, anyway) simply contribute to the uniray (naught ray?)? Yes.
> > > > Basically this just means that the model holds correspondence even at zero angle, though the question of how order is engaged from such ray contributions unfolding without any identity... possibly random analysis and this then would link into quantum thinking.
> > > > It is a very minimal set of constraints so it seems that imposing more onto it would be necessary.
> > > >
> > > >
> > > > At some point here as I still naturally use the term 'dimension' freely but try to cover my tracks, possibly something will unravel.
> > > > To unravel the Cartesian assumption is enough, but really the hope is to recover something with fundamental physical correspondence.
> > > > >
> > > > > The topic here is to challenge the Cartesian product and its meaning, and the confusion that has ensued. Two-signed morons run the show so little can be done in this lifetime.
> > > Angles, ....
> > And breaking with the real number as fundamental.
> >
> > The Cartesian product is misused elsewhere as well. For instance in ring theory two operations are formalized: the sum and the product. Yet in the formalization as binary operators the functional analysis calls on these humble operators suddenly to work SxS to S. Since when is summation a two dimensional operation? And the product certainly is trickier. Staying with the simple arithmetic product the same failing occurs. Why is it so difficult to simply state that a,b, and c in S will suffice?
> > a + b = c
> > Well, now we have posed an operator and yet where is the operation actually even defined? Perhaps this is why they call it 'ring theory', as if a theory must be left incomplete at the bottom. Upon choosing S obviously the instruction on how to add values goes directly back to what was taught in grade school. As to what was gained in the supposed generalization: now you are free to confuse commutative systems with non-commutative systems. Nize..
> >
> > The notion that the sum and product are fundamental operations is good. Yet leveling them completely is not necessarily sensible. After all the product derives from the sum ultimately. Within ring theory this now disappears, and further a challenge to the field axioms never occurs. Division and subtraction as non-fundamental in status due to the fact that their definitions can be had as inverse operators is never processed. Well, if it were the rational number would come under scrutiny to a curious young mind. Thence the lack of closure of that very rational value, and its supposed birth of the continuum. All a farce? Pretty well, yes. Secondary forms of unity are better descriptors of the continuum. This is the direct meaning of the decimal point. It indicates where unity lays in an otherwise natural value. So you see the continuum as natural valued in nature, though with some augmented structure, can be taken as an accurate stance. Breaking the back of the real value I had done in sign decades ago, and in magnitude more recently.. Again, the ray as fundamental can lead the way through the quagmire. The ray is not the line.
> So what you are proposing is that the Cartesian coordinate system is not valid?
> Maybe I am not interpreting your message right.
>
> Dan

On Sunday, June 26, 2022 at 9:27:31 AM UTC-4, Timothy Golden wrote:
> On Saturday, June 25, 2022 at 7:10:07 PM UTC-4, Dan joyce wrote:
> > On Saturday, June 25, 2022 at 1:09:29 PM UTC-4, timba...@gmail.com wrote:
> > > On Friday, June 24, 2022 at 12:22:20 PM UTC-4, Ross A. Finlayson wrote:
> > > > On Friday, June 24, 2022 at 6:40:56 AM UTC-7, timba...@gmail.com wrote:
> > > > > On Friday, June 24, 2022 at 8:11:27 AM UTC-4, Timothy Golden wrote:
> > > > > > On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> > > > > > > On a sheet of clean paper draw two horizontal lines,
> > > > > > > labeling one X, and the other Y.
> > > > > > > Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
> > > > > > >
> > > > > > > The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking.
> > > > > > >
> > > > > > > What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.
> > > > > > >
> > > > > > > That sign develops the real line via the balance of two rays such that
> > > > > > > - 1 + 1 = 0
> > > > > > > is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
> > > > > > > - 1 + 1 * 1 = 0
> > > > > > > has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
> > > > > > > Unopened, untampered with, and yet perfectly preserved.
> > > > > > I understand that I will have to refine my argument. I will have to attempt variations. At the same time, we understand that the orthogonal vector representation works pretty good. Yet the argument on fundamental status has to be false, simply in hindsight of the polysign criterion. Firstly, and this is probably the most difficult part, the separation of the Cartesian product of set theory (X,Y) as RxR versus the (x,y) plane with its additional requirements which do include the set theory. Immediately the topic of orthogonality and independence as confused concepts has to occur.
> > > > > >
> > > > > > As an aside to this there are some pretty options which have not been discussed much. Understanding that the ray is more fundamental than the line; the line being composed of two rays; will help and leads to some strange space works that have some convincing detail. Simply draw two rays on a piece of paper with a matched origin and an angle of say 30 degrees between them. Any position within that sector can be resolved as vector positions along each ray. Let's populate it with some positions: (1,2), (1,3), (1,4), (2,2), (2,3), (2,4). Now folding these two rays and their angle we see simply that the two dimensional sector is variable in quality yet should still retain all of its character, other than the refinement of our tools to actually draw the thing. There is good reason that we do not choose to make such a representation down at a five degree angle, say. The thickness of the pencil lead starts to matter and points that would be readily resolved at thirty degrees are much more difficult to resolve at five. Yet mathematically there is no problem. We could entertain the sector at an angle of 0.001 degrees. What is so convincing about this construction? The idea that general dimensional space could unfold from naught is present. It is a peculiar space. Simply unfolding another ray gets us a 3D sector presuming that we are not locked into the plane; that these rays are in some arbitrary high dimensional space for instance, though this description disqualifies them as fundamental. Great care must be taken when claiming to construct a space. The purpose here is certainly not to rest upon any Cartesian construction, and so the language 'arbitrary high dimensional space' has to be challenged above, and yet for the novice this language makes accessible the concept particularly for the Cartesian thinker, and this pretty well covers the human population in modernity.
> > > > > >
> > > > > > The sector discussion can go quite a ways, but for the moment let's go back to the two ray case, and let's carry on by raising the angle. Admittedly we do this operation on a planar surface; on a piece of paper with a pencil. No doubt these limitations are factors. Regardless we sweep the angle out to ninety degrees. Nothing in particular happens just yet, so we keep going. We still are able to maintain a representation of the sector though it is stretching out to quite a long thing all positions are accurately maintained. Well it has to be pointed out that the positions are gradually coming toward the rays and at 170 degrees things are flattening out all over again. Then just as they gradually come to 180 degrees the two dimensional space collapses to a single dimensional real line. At this position we see that
> > > > > > ( 1, 1 ) = 0 ; ( 2, 2 ) = 0 ; ( a, a ) = 0 .
> > > > > > and these exactly opposed rays establish what is known as the 'real' line. There is no mistake here, and the sign established which ray is meant. Thus we can leave the ordered pair form and engage the signed form:
> > > > > > - 1 + 1 = 0 ; - 2 + 2 = 0 ; - a + a = 0 .
> > > > > > Of course a value such as (1,3) evaluates as -1+3=+2 in the balanced form. Yet this is not the end of the story. Something did sort of go 'snap!' here into a fully unfolded form. Rather a lot of philosophy can be engaged at this point already in terms of challenging the fundamental status of the real number. Indeed should we bring physics into the fold we'd have a pretty big bang with just three rays barely even getting started in their separation, yet still unfolding at some arbitrarily small angle. Edge effects aside, plopping in a 14 billion light year or 45 billion light year sphere in the sector is merely a scaling problem. Of course this is fundamental mathematics so to expect full congruence at such an early stage is naive. Still, it is pretty good.
> > > > > >
> > > > > > Coming back again to the fully unfolded form in three rays we find that they will settle into a planar arrangement. The maximum spread between three rays will always be 120 degrees, no matter what the dimension of the system, and again this language is compromised but to think general dimensionally is ultimately where we are going. Securing this statement does seem challenging, but let's remember that in the general dimensional Cartesian systems there are but ninety degrees between orthogonal components. From polysign the constraint is more directly built simply by assigning each ray a sign and extending the two signed form to the three-signed form:
> > > > > > - a + a * a = 0
> > > > > > and now the plane is fully built. As two rays did carry two dimensional information yet folded out to a singular dimension, three rays are capable of carrying the information of a volume until they are folded out, at which point they become planar. These simple mechanics can be worked out by an intelligent child. Just the same as that child attempts to reflect this information onto their Cartesian trained parent of teacher they will meet with stiff resistance. Not many are able to break out of the Cartesain straightjacket. They are now known as the two-signed morons, or tsms in short. So where should you place all the brilliant men of mathematics who covered the subject so supremely, yet they overlooked these simple options? Here lays the greatest promise of polysign. We are engaged in a progression and there is more to go.
> > > > > >
> > > > > > Possibly returning to the folding sector model is wise, and the gimmickry of sign is false, as Descartes noted; as some to this day find distaste in the subject. Yet the three-signed form yields the complex plane and it does so out of the same rule set as the two-signed numbers used. Certainly the real number as fundamental is well disproven here if you managed to work through this chain of reasoning. The ray is fundamental.
> > > > > To what degree if the unfolding procedure is accurate then is P1 zero dimensional only in the unfolded regime? Yes.
> > > > > P1 means that -a=0 holds. These are the one-signed numbers. Unidirectional and zero dimensional. Time.
> > > > > To what degree do the rays unfolding from naught (angle, anyway) simply contribute to the uniray (naught ray?)? Yes.
> > > > > Basically this just means that the model holds correspondence even at zero angle, though the question of how order is engaged from such ray contributions unfolding without any identity... possibly random analysis and this then would link into quantum thinking.
> > > > > It is a very minimal set of constraints so it seems that imposing more onto it would be necessary.
> > > > >
> > > > >
> > > > > At some point here as I still naturally use the term 'dimension' freely but try to cover my tracks, possibly something will unravel.
> > > > > To unravel the Cartesian assumption is enough, but really the hope is to recover something with fundamental physical correspondence.
> > > > > >
> > > > > > The topic here is to challenge the Cartesian product and its meaning, and the confusion that has ensued. Two-signed morons run the show so little can be done in this lifetime.
> > > > Angles, ....
> > > And breaking with the real number as fundamental.
> > >
> > > The Cartesian product is misused elsewhere as well. For instance in ring theory two operations are formalized: the sum and the product. Yet in the formalization as binary operators the functional analysis calls on these humble operators suddenly to work SxS to S. Since when is summation a two dimensional operation? And the product certainly is trickier. Staying with the simple arithmetic product the same failing occurs. Why is it so difficult to simply state that a,b, and c in S will suffice?
> > > a + b = c
> > > Well, now we have posed an operator and yet where is the operation actually even defined? Perhaps this is why they call it 'ring theory', as if a theory must be left incomplete at the bottom. Upon choosing S obviously the instruction on how to add values goes directly back to what was taught in grade school. As to what was gained in the supposed generalization: now you are free to confuse commutative systems with non-commutative systems. Nize.
> > >
> > > The notion that the sum and product are fundamental operations is good. Yet leveling them completely is not necessarily sensible. After all the product derives from the sum ultimately. Within ring theory this now disappears, and further a challenge to the field axioms never occurs. Division and subtraction as non-fundamental in status due to the fact that their definitions can be had as inverse operators is never processed. Well, if it were the rational number would come under scrutiny to a curious young mind. Thence the lack of closure of that very rational value, and its supposed birth of the continuum. All a farce? Pretty well, yes. Secondary forms of unity are better descriptors of the continuum. This is the direct meaning of the decimal point. It indicates where unity lays in an otherwise natural value. So you see the continuum as natural valued in nature, though with some augmented structure, can be taken as an accurate stance. Breaking the back of the real value I had done in sign decades ago, and in magnitude more recently. Again, the ray as fundamental can lead the way through the quagmire. The ray is not the line.
> > So what you are proposing is that the Cartesian coordinate system is not valid?
> > Maybe I am not interpreting your message right.
> >
> > Dan
> The Cartesian product of RxR is not a fundamental construction of the plane. Yet most think of it this way. Clearly the geometry of the real line is well established by the fact that:
> - a + a = 0, or more simply:
> - 1.0 + 1.0 = 0
> These directions -1 and +1 are exactly opposed. Draw two rays in opposite directions, labeling one '-' and the other '+'. Trace the path -1 , +1. This means we travel one in the minus direction and one in the plus direction, and we wind up back at zero. Thus the two-signed system is the real line. Now progressing to the three-signed system we'll have:
> - 1.0 + 1.0 * 1.0 = 0
> and this three ray system does in fact require the plane. These are rays at 120 degrees from one another. The three balance. Symmetry has gone three-fold. The geometric requirement of the plane is present here in three rays rather than the four of the Cartesian product. So you see the tie from algebra to geometry can be had through sign. In hindsight I am in a position to challenge the Cartesian system of thought. This includes challenging the real number as fundamental. It is not. The critique of the Cartesian coordinate system does follow out of this. RxR is but two copies of the real line.. There is no connection between the two. Opting to connect them at zero is a restriction in their independence. Opting to insist on a ninety degree angle and calling these things independent coordinates is problematic and has been habituated by humanity. Orthogonality and independence are not the same thing. Yet every time a Cartesian product is taken it is as if this is the case.
>
> Worst of all the very operators addition and product are now treated as binary operations which map SxS to S. To state that the Cartesian system of thought is badly contaminated is readily established by careful analysis. As to who dipped their hands in where and pulled on what: in this case I believe it is a commitment to functional analysis as if functional analysis were primitive. I assure you that the sum is far more primitive. https://en.wikipedia.org/wiki/Binary_operation
> Also the sum as n-ary by this account will have a sum of four values being in RxRxRxR, which it is not.
>
> I think that possibly another way to attack the Cartesian product is to ask whether two copies of the same set are the same set? This seems to be exactly as the mathematicians would have it. Were the sets of differing types then the product as a free-standing preservation of the two types as natural is readily formed. For instance those two-signed (P2) and three-signed (P3) numbers will not interoperate. Each is in their own domain and the meaning of their signs is unique to that domain. In this way a natural progression like:
> P1 P2 P3 P4 ...
> is a free-standing product that does not even require the formality of the Cartesian product. Lo and behold the unidirectional P1 looks like time, and forms of emergent spacetime ensue due to a breakpoint in the product behavior:
> P1 P2 P3 | P4 P5 P6 ...
>
>
> Staying on the point of set copies gets us into the ordered pair and triple as (x,y) and (x,y,z) say, where these are all real valued. The notion that x and y should not interoperate is present, yet the fact that they can and do is as well present. For instance upon laying down some constraint as:
> y = 3 x x + 2 x - 4
> we've obviously broken the law on their independence. Does this help explain how the binary operators are defined? Clearly they can only remain independent for so long. Yet by definition RxR is an unconditional form of independence isn't it? As such any equality as written above is invalid. Wow! You could almost think I was joking here. Honestly I've never been here before and I will certainly remain open to falsification. This usenet environment tends to yield very poor quality analysis. Still as an uncensored medium I respect it.
>
> I guess we've bumped again into functional analysis. Perhaps this latter analysis will come around and tie up the whole loop properly. Operator theory is in this loop. If anything I am in search of new operators; ones that emerge from polysign without all of this baggage. Still the falsification remains a point of interest and the more we can eat into standing theory the more the two-signed morons will have to yield. Their accumulation is nearly as corrupt as capitalism is in this day. Can we really even call the American form capitalism? I didn't realize militarism would be such a large part of it. Meanwhile, try to sell some goods on the street and you'll probably be prosecuted.
> It would be less relevant if there were less government paid mathematicians. The security of the bomb makers is well established. For the rest of us there will be no welfare state. So we try at least to practice self sufficiency. It is good. Catch the trickle down to pay the taxes to build the bombs? Boy, do I feel secure... not(z).
>
> It's interesting that as I falsify the polynomial and that style of functional analysis I am left asking what do i have in the polysign form?
> Certainly it looks quite different.

On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> On a sheet of clean paper draw two horizontal lines,
> labeling one X, and the other Y.
> Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
>

The generalization of sign demands the plane at P3, just as it demanded the line at P2. Onward and upward we see P4 as the rays emanating from the center of a tetrahedron out to its vertices. You can delete the frame of the tet. Just four balanced rays exist, each with their own sign -,+,*,# so that the number of strokes needed to draw the sign indicates what can be interpreted as a modulo four component within what ordinarily is known as 3D space, though this modulo four concept acts through the product. As a vector space you needn't even worry about that. Just the fact of the balance suffices:
- 1.0 + 1.0 * 1.0 # 1.0 = 0 .
As much as this law is an algebra it is a law of rendering as well. It is a law of the geometry of P4. Indeed should we render a value such as:
- 2.3 + 3.4 * 4.5 # 5.6
it will land in exactly the same position as:
+ 1.1 * 2.2 # 3.3
and simply the -2.3 + 2.3 * 2.3 # 2.3 portion not only goes to zero by the algebra, but it goes to zero by the act of vector rendering. Possibly I should not even use this word 'vector' but in its additive sense it is correct.. The ray as fundamental has to be engaged here too though. But the vector is somewhat a ray concept, so all is well. Possibly I have not dwelt here long enough.

The inverse that was once known back in P2 as -a is no longer present. In P3 it became -z+z. In P4 it becomes -z+z*z. How's that? Simply put:
P2 : - z + z = 0 .
P3 : - z + z * z = 0 .
P4 : - z + z * z # z = 0 .
Yes: the law of balance works generally. Strangest of all there is a little brother P1:
P1 : - z = 0
and yet P1 can take a value, such as -1.2345. That which is unidirectional is zero dimensional in its geometry by the demands of polysign! The exact correspondence to time is evident.

Why wouldn't one get straight over to the physics here? Mimicing the text books, if they've got an f(t) that matters, f() being real valued... and suddenly we are on the plane? All of these steps are dubious now. The notion of a ray as time, geometrically extended ,may be suitable, but it will have to be pointed out that it's gone superdimensional, or some such. This is somewhat the case of every piece of paper in a stack: they may each represent the plane, but they exist in a superspace that allows for the stacking. If we have failed to qualify reality carefully, and based upon the ambiguities that I've exposed I do see this as a real possibility, then obviously all of physics and some of philosophy will be suffering in consequence. To some this is not a bother for the field of mathematics. There is an intersection, whereby the three sisters separated; each going their own way for need of space and to raise their own without interference from one another. That they interfered at all would obviously cause the quagmire of the separation. To some that divorce was invalid; it never occurred at all. Yet the tension remains. It is not a matter of three knowledgeable sisters, but instead a matter of their guess work going wrong. They could not live with each other no different that we in this day find out that Russiagating Americans cannot live with their counterparts who saw through the lies. Upon doubling down and now tripling down to the point of living at the edge of nuclear catastrophy; the cold war reignited to a pitch that needn't have ever occurred other than for the convenience of one political party, and a deep state that saw the destruction of the other political party that once was their strong hold. As to who must stand down: it is a large quantity of the status quo power structure. So many media organizations as to be overwhelming should the deletion actually occur. Live with them and their lies? I don't think so. Here we stand at a provable neo-fascist turning point, they with their blindfolds secured above their masks and their left arms raised on command.

Of course it is my hope that polysign can have some influence upon physics and philosophy. As reductionism and constructivism take to a general dimensional playing field the rules do require further investigation. Consistency of the existing work is dubious. In effect the inconsistencies somewhat build the subcults of each group. Here the strange ability of humans to sub-segregate as they self-segregate is tantamount to religion. It makes a laughing stock of them. Two-signed morons; all.

Other than Mitch, that is, who is an unsigned moron, or possibly just a presigned moron. We are all caught as colloidal conglomerates in spacetime; it's resultants. Therefor our access to the basis from which we come is not at all granted and if anything it is guaranteed to be a quagmire of guessing games out of thin air. As we seek spacetime correspondence there is now but one game in town. I think though that we await some more constructive freedom. As to where or what exactly... wave theory perhaps? Should that pesky photon be falsified? Possibly. So it takes a certain amount of energy at a certain wavelength to raise an electron so as to get some action... this is the discrete nature of the atom rather than of the photon. Put up a bunch of mirrors to concentrate the otherwise too dim waves and suddenly an image appears. On the other hand getting the atom as a stable derived structure would be a huge gain. Far beyond my abilities.

> The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking..
>
> What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.
>
> That sign develops the real line via the balance of two rays such that
> - 1 + 1 = 0
> is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
> - 1 + 1 * 1 = 0
> has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
> Unopened, untampered with, and yet perfectly preserved.

On Tuesday, June 28, 2022 at 6:51:01 AM UTC-7, timba...@gmail.com wrote:
> On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> > On a sheet of clean paper draw two horizontal lines,
> > labeling one X, and the other Y.
> > Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
> >
> The generalization of sign demands the plane at P3, just as it demanded the line at P2. Onward and upward we see P4 as the rays emanating from the center of a tetrahedron out to its vertices. You can delete the frame of the tet. Just four balanced rays exist, each with their own sign -,+,*,# so that the number of strokes needed to draw the sign indicates what can be interpreted as a modulo four component within what ordinarily is known as 3D space, though this modulo four concept acts through the product. As a vector space you needn't even worry about that. Just the fact of the balance suffices:
> - 1.0 + 1.0 * 1.0 # 1.0 = 0 .
> As much as this law is an algebra it is a law of rendering as well. It is a law of the geometry of P4. Indeed should we render a value such as:
> - 2.3 + 3.4 * 4.5 # 5.6
> it will land in exactly the same position as:
> + 1.1 * 2.2 # 3.3
> and simply the -2.3 + 2.3 * 2.3 # 2.3 portion not only goes to zero by the algebra, but it goes to zero by the act of vector rendering. Possibly I should not even use this word 'vector' but in its additive sense it is correct. The ray as fundamental has to be engaged here too though. But the vector is somewhat a ray concept, so all is well. Possibly I have not dwelt here long enough.
>
> The inverse that was once known back in P2 as -a is no longer present. In P3 it became -z+z. In P4 it becomes -z+z*z. How's that? Simply put:
> P2 : - z + z = 0 .
> P3 : - z + z * z = 0 .
> P4 : - z + z * z # z = 0 .
> Yes: the law of balance works generally. Strangest of all there is a little brother P1:
> P1 : - z = 0
> and yet P1 can take a value, such as -1.2345. That which is unidirectional is zero dimensional in its geometry by the demands of polysign! The exact correspondence to time is evident.
>
> Why wouldn't one get straight over to the physics here? Mimicing the text books, if they've got an f(t) that matters, f() being real valued... and suddenly we are on the plane? All of these steps are dubious now. The notion of a ray as time, geometrically extended ,may be suitable, but it will have to be pointed out that it's gone superdimensional, or some such. This is somewhat the case of every piece of paper in a stack: they may each represent the plane, but they exist in a superspace that allows for the stacking. If we have failed to qualify reality carefully, and based upon the ambiguities that I've exposed I do see this as a real possibility, then obviously all of physics and some of philosophy will be suffering in consequence. To some this is not a bother for the field of mathematics. There is an intersection, whereby the three sisters separated; each going their own way for need of space and to raise their own without interference from one another. That they interfered at all would obviously cause the quagmire of the separation. To some that divorce was invalid; it never occurred at all. Yet the tension remains. It is not a matter of three knowledgeable sisters, but instead a matter of their guess work going wrong. They could not live with each other no different that we in this day find out that Russiagating Americans cannot live with their counterparts who saw through the lies. Upon doubling down and now tripling down to the point of living at the edge of nuclear catastrophy; the cold war reignited to a pitch that needn't have ever occurred other than for the convenience of one political party, and a deep state that saw the destruction of the other political party that once was their strong hold. As to who must stand down: it is a large quantity of the status quo power structure. So many media organizations as to be overwhelming should the deletion actually occur. Live with them and their lies? I don't think so. Here we stand at a provable neo-fascist turning point, they with their blindfolds secured above their masks and their left arms raised on command.
>
> Of course it is my hope that polysign can have some influence upon physics and philosophy. As reductionism and constructivism take to a general dimensional playing field the rules do require further investigation. Consistency of the existing work is dubious. In effect the inconsistencies somewhat build the subcults of each group. Here the strange ability of humans to sub-segregate as they self-segregate is tantamount to religion. It makes a laughing stock of them. Two-signed morons; all.
>
> Other than Mitch, that is, who is an unsigned moron, or possibly just a presigned moron. We are all caught as colloidal conglomerates in spacetime; it's resultants. Therefor our access to the basis from which we come is not at all granted and if anything it is guaranteed to be a quagmire of guessing games out of thin air. As we seek spacetime correspondence there is now but one game in town. I think though that we await some more constructive freedom. As to where or what exactly... wave theory perhaps? Should that pesky photon be falsified? Possibly. So it takes a certain amount of energy at a certain wavelength to raise an electron so as to get some action... this is the discrete nature of the atom rather than of the photon. Put up a bunch of mirrors to concentrate the otherwise too dim waves and suddenly an image appears. On the other hand getting the atom as a stable derived structure would be a huge gain. Far beyond my abilities.
> > The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking.
> >
> > What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.
> >
> > That sign develops the real line via the balance of two rays such that
> > - 1 + 1 = 0
> > is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
> > - 1 + 1 * 1 = 0
> > has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
> > Unopened, untampered with, and yet perfectly preserved.

Oftentimes it's tried to keep things as simple as inner and outer products,
about direct products, about scalar products, vector and tensor prioducts, .....

Matrix products have that: most all MACHINE INTEGERS is "words", fixed
width register words that according to register transfer the arithmetic
logic unit processes into products. Then with fixed and combinatorial
bounds, is about that "matrix products are rectilinear". There are general
matrix products with the generalized matrix products and what results
the determinantal analysis, which is very regularly used for all sorts of linear
indicators, an example of a scalar and inner and dot product.

Linear products are mostly in the same dimensions they are from, ....

Results from carry and remainder are of course modulus products, of a sort.
(Or unitary in a lattice of the modular, for example, products in the scalar that
results residues in the unitary of a modulus.)

Suppose you try some temporary explanation with some mechanism via multisets, instead of using the cartesian product.
Or is the usage of Set Theory in the first place, the point you criticize? I m curious

On Tuesday, June 28, 2022 at 1:12:33 PM UTC-4, Ross A. Finlayson wrote:
> On Tuesday, June 28, 2022 at 6:51:01 AM UTC-7, timba...@gmail.com wrote:
> > On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> > > On a sheet of clean paper draw two horizontal lines,
> > > labeling one X, and the other Y.
> > > Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
> > >
> > The generalization of sign demands the plane at P3, just as it demanded the line at P2. Onward and upward we see P4 as the rays emanating from the center of a tetrahedron out to its vertices. You can delete the frame of the tet. Just four balanced rays exist, each with their own sign -,+,*,# so that the number of strokes needed to draw the sign indicates what can be interpreted as a modulo four component within what ordinarily is known as 3D space, though this modulo four concept acts through the product. As a vector space you needn't even worry about that. Just the fact of the balance suffices:
> > - 1.0 + 1.0 * 1.0 # 1.0 = 0 .
> > As much as this law is an algebra it is a law of rendering as well. It is a law of the geometry of P4. Indeed should we render a value such as:
> > - 2.3 + 3.4 * 4.5 # 5.6
> > it will land in exactly the same position as:
> > + 1.1 * 2.2 # 3.3
> > and simply the -2.3 + 2.3 * 2.3 # 2.3 portion not only goes to zero by the algebra, but it goes to zero by the act of vector rendering. Possibly I should not even use this word 'vector' but in its additive sense it is correct. The ray as fundamental has to be engaged here too though. But the vector is somewhat a ray concept, so all is well. Possibly I have not dwelt here long enough.
> >
> > The inverse that was once known back in P2 as -a is no longer present. In P3 it became -z+z. In P4 it becomes -z+z*z. How's that? Simply put:
> > P2 : - z + z = 0 .
> > P3 : - z + z * z = 0 .
> > P4 : - z + z * z # z = 0 .
> > Yes: the law of balance works generally. Strangest of all there is a little brother P1:
> > P1 : - z = 0
> > and yet P1 can take a value, such as -1.2345. That which is unidirectional is zero dimensional in its geometry by the demands of polysign! The exact correspondence to time is evident.
> >
> > Why wouldn't one get straight over to the physics here? Mimicing the text books, if they've got an f(t) that matters, f() being real valued... and suddenly we are on the plane? All of these steps are dubious now. The notion of a ray as time, geometrically extended ,may be suitable, but it will have to be pointed out that it's gone superdimensional, or some such. This is somewhat the case of every piece of paper in a stack: they may each represent the plane, but they exist in a superspace that allows for the stacking.. If we have failed to qualify reality carefully, and based upon the ambiguities that I've exposed I do see this as a real possibility, then obviously all of physics and some of philosophy will be suffering in consequence. To some this is not a bother for the field of mathematics. There is an intersection, whereby the three sisters separated; each going their own way for need of space and to raise their own without interference from one another. That they interfered at all would obviously cause the quagmire of the separation. To some that divorce was invalid; it never occurred at all. Yet the tension remains. It is not a matter of three knowledgeable sisters, but instead a matter of their guess work going wrong. They could not live with each other no different that we in this day find out that Russiagating Americans cannot live with their counterparts who saw through the lies. Upon doubling down and now tripling down to the point of living at the edge of nuclear catastrophy; the cold war reignited to a pitch that needn't have ever occurred other than for the convenience of one political party, and a deep state that saw the destruction of the other political party that once was their strong hold. As to who must stand down: it is a large quantity of the status quo power structure. So many media organizations as to be overwhelming should the deletion actually occur. Live with them and their lies? I don't think so. Here we stand at a provable neo-fascist turning point, they with their blindfolds secured above their masks and their left arms raised on command.
> >
> > Of course it is my hope that polysign can have some influence upon physics and philosophy. As reductionism and constructivism take to a general dimensional playing field the rules do require further investigation. Consistency of the existing work is dubious. In effect the inconsistencies somewhat build the subcults of each group. Here the strange ability of humans to sub-segregate as they self-segregate is tantamount to religion. It makes a laughing stock of them. Two-signed morons; all.
> >
> > Other than Mitch, that is, who is an unsigned moron, or possibly just a presigned moron. We are all caught as colloidal conglomerates in spacetime; it's resultants. Therefor our access to the basis from which we come is not at all granted and if anything it is guaranteed to be a quagmire of guessing games out of thin air. As we seek spacetime correspondence there is now but one game in town. I think though that we await some more constructive freedom. As to where or what exactly... wave theory perhaps? Should that pesky photon be falsified? Possibly. So it takes a certain amount of energy at a certain wavelength to raise an electron so as to get some action... this is the discrete nature of the atom rather than of the photon. Put up a bunch of mirrors to concentrate the otherwise too dim waves and suddenly an image appears. On the other hand getting the atom as a stable derived structure would be a huge gain. Far beyond my abilities.
> > > The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking.
> > >
> > > What we have then is a system that has been engaged in by convention. Even the name "Cartesian" is a misnomer. He never used this and he never confused these two things. He did bring algebra into geometry, but his geometry was very Euclidean in nature. His usage of negative values as 'false' values is well established.
> > >
> > > That sign develops the real line via the balance of two rays such that
> > > - 1 + 1 = 0
> > > is where the geometrical integrity of the line begins. That the plane's geometrical integrity begins with:
> > > - 1 + 1 * 1 = 0
> > > has been overlooked by everyone until now afaict. This is the proper constraint that yields the plane and two dimensional thinking. Yet this term 'dimensional' has been tied to the real line as if that real line was fundamental, but it is not. So we have cracked open a rather large can with a rock here. Dipping a twig in we can get a bit of the juice out to taste it and it tastes pretty good. This can has been sitting around for four hundred years.
> > > Unopened, untampered with, and yet perfectly preserved.
> Oftentimes it's tried to keep things as simple as inner and outer products,
> about direct products, about scalar products, vector and tensor prioducts, ....
>
> Matrix products have that: most all MACHINE INTEGERS is "words", fixed
> width register words that according to register transfer the arithmetic
> logic unit processes into products. Then with fixed and combinatorial
> bounds, is about that "matrix products are rectilinear". There are general
> matrix products with the generalized matrix products and what results
> the determinantal analysis, which is very regularly used for all sorts of linear
> indicators, an example of a scalar and inner and dot product.

On Tuesday, June 28, 2022 at 6:52:55 PM UTC-4, michael Rodriguez wrote:
> Suppose you try some temporary explanation with some mechanism via multisets, instead of using the cartesian product.
> Or is the usage of Set Theory in the first place, the point you criticize? I m curious
Well polysign is so close by that it is next to impossible to keep mentioning it here on this thread.
How about an embarrassingly simple instance? Put a thermometer X on an aluminum bar.
Put a thermometer Y on a copper bar. Move this copper bar to the North Pole..
These are independent values consistent with the Cartesian product.
Nicely enough there is no problem with the trace of a graph of x,y (no matter how they are graphed) doing some loops and so forth.
Paths are present and correlations would be of interest, like during an eclipse both temperatures drop together then rise together.
Whatever geometry these thermal issues imply is it all just a farce?
As we attempt generality would it be wise to put a bunch of thermometers along a line? Spaced in a plane? Volumetrically aren't they appropriate? Why is geometry confused with set logic? I feel like the more we can open the system up the better. Actual physical space is of interest. Actual physical effects are too.

I see the muiltiset primitive but I don't think I use it much. If polysign are so great then where is electromagnetism posted in their terms?Relativity theory? Complex analysis? On and on the potential subjects go. Of course we are curious as to what P4, P5, and P6 are exactly. You have managed division and I have to confess I can barely keep up with it. I apologize for not keeping up with it in terms of getting it into the code. I've been wandering lately.
I hope you will weigh in on your own leading question on multisets.

On Tuesday, June 28, 2022 at 6:52:55 PM UTC-4, michael Rodriguez wrote:
> Suppose you try some temporary explanation with some mechanism via multisets, instead of using the cartesian product.
> Or is the usage of Set Theory in the first place, the point you criticize? I m curious

I guess I just don't see it this way, but if you do then I think it's worth trying an interpretation, even if you know it's wrong. As I go through this again I'd like:
1. a compact falsification of the Cartesian product as it applies to geometry as (x,y) coordinates, say.
2. physics; as in physical geometry; mechanics. Atoms, and everything.
3. basis: pure arithmetic, hopefully yielding 2.

That's a very rough outline and I'm trying to stay loose a bit. The multiset does seem relevant if we shift over toward information theory and redundancy. Redundancy is present in nature. At some level it is the means by which we process nature and physics. Repeatability as redundancy in time is a fundamental part of the scientific method. Challenging it could cause some quagmires. A failure to observe it when it is present would be a fine instance of an error that humans are capable of. If we've made an early distinction that doesn't actually hold then we've missed out on a generality.

Is it possible that the point is such a thing? Of course we are caught in physics with point particles as a matter of convention through the Euclidean train of thought. Pretty clearly this is how the 'di'mension comes to be accessed. You need two points to get a distance. In Euclidean geometry things like BC can have a dimension.

Polysign does portray the point differently under P1. That our optical system is involved as we observe a point on a piece of paper; visible from any angle (ideally) it seems helpful that we are out a dimension from the paper.. That the point is down another couple of dimensions: now we are getting multidimensional. If the point is zero dimensional then why does it need two dimensions to map it on the paper? Isn't it then a two dimensional point? Whether we have upcast or downcast is quite relevant, and in that we as observers of the point might be engaged in a graphic, then the point will form a ray when we fix the observer into the system with the paper and the graphite in what we believe to be a 3D space. Throwing in more observers we'll land with the simplest of math objects becoming an isotropic radiator or some such. Descartes actually was quite eloquent on such awareness. I believe he mentions a trick of the eye, and rather a lot of properties that the point is capable of.

Leaving the point and engaging instead in another form of analysis based on solid objects we get a different sense of space. It will take more than three real values to specify the objects position completely. In this way the point reduction is inadequate. Still, that very point reduction becomes useful in working out the freedoms of this solid state. Fixing just one point of the solid then all other points on the object form spheres around that initial point based on their freedom of movement. Fixing a convenient secondary position on the object we now have the object spinning freely about an axis, and then selecting another point and fixing its position involves just a bit more information. (The electron somewhat has similar features.) It turns out that all of that could be encompassed by tensor mathematics which will sort of flatten out the character of this problem. Well, possibly there lays the work that we have to do. We have to get the relative reference frame mathematics going in polysign. Switching over to the Cartesian system is not going to be acceptable. I do it plenty in my code; projections for instance as outlined above here somewhere. These need to be done through polysign.

You, Michael, have the matrix math abilities way beyond me. The division algorithm that you worked through is a tremendous piece of work.
We really do have a new basis to work from yet to rework everything verbatim does not seem authentic either. I guess it will happen over time as a series of breakthroughs. There must be something that we are missing in terms of making this progress. Of course we all suffer the Cartesian assumption and in this way we are deadlocked from the start. Euclidean thinking as well is embedded into us at an early age. That polysign could yield subtle surprises as it works its way into these areas I find believable.

Even if all that we do is to break the problem open for somebody else's brilliant solution that is far better than sitting around here bickering about infinity. Also the sector awareness is a sort of pre-polysign thing that has a nice way of unfolding space from naught. That is the sort of thing that physics is after. The human race has committed early to the two-form fully unfolded version and somewhat gone multiset with it, though I don't think that is quite the right terminology. Still, how did we get to three...
Pull it out of a hat and see if it matches. If not three maybe four, or even five will do. No, six?

On Thursday, June 23, 2022 at 10:04:21 AM UTC-4, Timothy Golden wrote:
> On a sheet of clean paper draw two horizontal lines,
> labeling one X, and the other Y.
> Now choose a position along X and label it 'a', and choose a position along Y and label it 'a'. This is consistent with the Cartesian representation of (X,Y). Indeed if you were to shift the depiction of X or Y to anywhere on the paper the representation will remain the same, and this then embodies the concept of independence: that X and Y are completely unrelated to each other, other than the fact that they are exact copies of R. In effect this is a sufficient representation of (X,Y) and any further work in geometrical rendering will require additional constraints which will reduce the independence of X and Y. By reducing the independence then the Cartesian product must be weakened. So how is it that the curriculum has come to blur this detail? Shall we blur it back the other way and ask where does a ninety degree angle come from? It comes from thin air, and any angle other than zero degrees will suffice to preserve graphically the rendering. Even the units of the two 'axes' should not be assumed to be equivalent, yet if you choose to preserve that then clearly the criteria of independence of X and Y has been further blurred. Possibly the angular argument should be pushed to zero degrees, and the origins spread sufficiently so that both images fit cleanly upon a single line. Thence even the representation of finite systems will be achieved on a single line via some remapping method. Of course the same label will show up twice on that line, but with the bounds being sufficiently offset an unambiguous interpretation can be made of the two dimensions out of a one dimensional system, and clearly R was that.
>
> The graphical interpretation of the line as geometrical is unambiguous. What is ambiguous is the notion that granting two of these suddenly engages the plane. Was this plane constructed via the Cartesian product? Where in the Cartesian product are these demands? If anything the independence of the Cartesian product components ensures that such clear definition is lacking..

One other way to attack the Cartesian construction is to ask whether providing two lines with the same origin placed at ninety degree angles to each other suddenly forms the plane? No. Clearly the action was done in a higher dimensional space, and after assembling three such lines certainly no representational gain can be had nor the construction carried on. These are methods of representation, but they are not the means of construction. In effect we have no ability to 'shazam' two lines into a plane. This Cartesian product action is not realistic. Two copies of a one dimensional space do not develop a two dimensional space. This is a tough nut to crack. The reason I believe is that spacetime itself is not considered to be part of the problem historically speaking, though certainly people like Kant or Descartes or Newton were more keenly in tune with the physical world than most moderners. To what degree when we name physical space as three dimensional has an offense then been created in this inverted awareness?

In defense of the Cartesian product we have to admit that the representation works, just as our numbers work. We do need signs (minus and plus) and multiple numbers to make this claim stick. These are sort of the meat on the bones that are those real line skeletons. It is the numbers themselves that cause a shift from the Euclidean system into the Cartesian system. Certainly perpendiculars were well used in antiquity. This does not mean that they had any Cartesian sensibility. To get off of the axes requires a vector notion. Strangely, that vector is a ray! Rather, it is multiple rays, for the first one is just the ordinary one dimensional sensibility. Still, were the reference lines placed at an angle of 45 degrees to each other the system will work fine. There is nothing magical about the ninety degree angle other than to achieve symmetry. so the geometry rests upon convention.

The proper dimensional gain is found in polysign, where a third sign establishes a new symmetry:
- 1 + 1 * 1 = 0
and now the plane P3 as constructed out of three rays rather than two copies of two opposed rays. Their orientation is already established, and it is strictly established.
Here of course those habituated in Cartesian thinking are translating this simplistic requirement back through their real analysis, but you see we just implemented the three-signed number. The two-signed number is what has been generalized. That the generalization of sign yields new geometry is a deep statement. The real number has been broken open here. It is recovered as P2, but P3 is as fundamental as P2 is for they follow the same rules. P4 is as fundamental as well. Even P1, though it has severe cause for pause. In some regards the invisible P1 almost explains how humans started out at P2 and got stuck there.

The X of abstract polynomial, the coordinates usage (a,b,c,..), the cartesion product, the
orthogonal disposition in geometry, or what you have critisized so far.
By pure luck, polysigns comply the usual Equivalence Classes, in comparison with
other authors that do not comply with it, or jump out and after, they come back.
Equivalence classes are also nearby the core.

Take a look to equivalence classes and integers
https://en.wikipedia.org/wiki/Integer#Construction
("additive equivalences") and a look the pics :
https://en.wikipedia.org/wiki/Integer#/media/File:Relative_numbers_representation.svg
https://en.wikipedia.org/wiki/Integer#/media/File:Number-line.svg

In the case of Roger Beresford are the folds(folding), orthogonal roots of unity
and how he applies equivalence classes, how he connects the "non-folded space" with
its "folded" counterpart. (out and in of "additive congruences")
You may take a look to the documents HoopAlgebraSupplement.doc and Hoops&Physics.doc at
https://library.wolfram.com/infocenter/MathSource/6198/

Take a look to equivalence classes and rationals
https://en.wikipedia.org/wiki/Rational_number#Formal_construction
("multiplicative equivalences") and look to the pic :
https://en.wikipedia.org/wiki/Rational_number#/media/File:Rational_Representation.svg

In the case of Domingo Gomez is its 'rational mean operation'
https://www.youtube.com/watch?v=6lORU03yuvY (first 4 minutos of the video)
(out and in of "multiplicative congruences")

Take a look to https://www.youtube.com/watch?v=NHZt8eBKcRA also

Equivalence classes is one of the reasons "one can not" go on inventing
arbitrary operations. You can, although there are some buts.
In any case let me explain with one example on "additive equivalences".
You have your product for p3

___|___-d___+e___*f
-a_|__+ad__*ae__-af
+b_|__*bd__-be__+bf
*c_|__-cd__+ce__*cf

(-a+b*c) x (-d+e*f) = -cd -be -af +ad +ce +bf *bd *ae *cf

in "coordinates"
(a,b,c) x (d,e,f) = ( cd + be + af , ad + ce + bf , bd + ae + cf )

Now suppose, you decide to invent a new product, we call it the nedloG product
(you just swap the addition with product)

(a,b,c) € (d,e,f) = ( (c+d)(b+e)(a+f) , (a+d)(c+e)(b+f) , (b+d)(a+e)(c+f) )

The thing is that in checking the properties of this new operation, you notice
something peculiar.
If you take the result of (1,2,5)€(6,1,3) and the result of (0,1,4)€(6,1,3)
you may check that they are not the same

(1,2,5)€(6,1,3) =/= (0,1,4)€(6,1,3)

-1+2*5 and -0+1*4 are the same point in the p3 plane, but when they are
engaged in this € operation, they yield different results. If you compare
the nedloG product(€) for p3 with the usual Golden product for p3, one can
notice that the nedloG product is not compatible with "additive congruences".

-1+2*5 = -0+1*4 or (1,2,5) = (0,1,4) in p3
Some other place where (1,2,5) =/= (0,1,4) can be true ?

Then, we throw to the trash this new operation for not comply with
equivalence classes ? Some have decided that one may look into the "brother
space", this is, a space "without" the equivalence classes, pick and harvest
interesting results/relations, and then come back to the usual space that
"comply" with equivalence classes, this in, out and in of equivalence classes.

In the case of the user Socratis tnp, seems to be something related the issue of
equivalences also, with a strange hybrid mix since he uses decimals, although I m not totally sure.

You may look also to the Dan counterposting at https://groups.google.com/g/sci.math/c/Wx9-5iDcFNk
"1/2 not equal to 2/4" and “3 <=> 2 + 1 .."

Also take a look to https://www.definitions.net/definition/setoid
https://ncatlab.org/nlab/show/setoid
(I almost forgot you like quotients too much) ;0

On Thursday, June 30, 2022 at 7:42:41 PM UTC-4, michael Rodriguez wrote:
> The X of abstract polynomial, the coordinates usage (a,b,c,..), the cartesion product, the
> orthogonal disposition in geometry, or what you have critisized so far.
> By pure luck, polysigns comply the usual Equivalence Classes, in comparison with
> other authors that do not comply with it, or jump out and after, they come back.
> Equivalence classes are also nearby the core.
>
> Take a look to equivalence classes and integers
> https://en.wikipedia.org/wiki/Integer#Construction
> ("additive equivalences") and a look the pics :
> https://en.wikipedia.org/wiki/Integer#/media/File:Relative_numbers_representation.svg
> https://en.wikipedia.org/wiki/Integer#/media/File:Number-line.svg
>
> In the case of Roger Beresford are the folds(folding), orthogonal roots of unity
> and how he applies equivalence classes, how he connects the "non-folded space" with
> its "folded" counterpart. (out and in of "additive congruences")
> You may take a look to the documents HoopAlgebraSupplement.doc and Hoops&Physics.doc at
> https://library.wolfram.com/infocenter/MathSource/6198/
>
> Take a look to equivalence classes and rationals
> https://en.wikipedia.org/wiki/Rational_number#Formal_construction
> ("multiplicative equivalences") and look to the pic :
> https://en.wikipedia.org/wiki/Rational_number#/media/File:Rational_Representation.svg
>
> In the case of Domingo Gomez is its 'rational mean operation'
> https://www.youtube.com/watch?v=6lORU03yuvY (first 4 minutos of the video)
> (out and in of "multiplicative congruences")
>
> Take a look to https://www.youtube.com/watch?v=NHZt8eBKcRA also
>
> Equivalence classes is one of the reasons "one can not" go on inventing
> arbitrary operations. You can, although there are some buts.
> In any case let me explain with one example on "additive equivalences".
> You have your product for p3
>
> ___|___-d___+e___*f
> -a_|__+ad__*ae__-af
> +b_|__*bd__-be__+bf
> *c_|__-cd__+ce__*cf
>
> (-a+b*c) x (-d+e*f) = -cd -be -af +ad +ce +bf *bd *ae *cf
>
> in "coordinates"
> (a,b,c) x (d,e,f) = ( cd + be + af , ad + ce + bf , bd + ae + cf )
>
> Now suppose, you decide to invent a new product, we call it the nedloG product
> (you just swap the addition with product)
>
> (a,b,c) € (d,e,f) = ( (c+d)(b+e)(a+f) , (a+d)(c+e)(b+f) , (b+d)(a+e)(c+f) )
>
> The thing is that in checking the properties of this new operation, you notice
> something peculiar.
> If you take the result of (1,2,5)€(6,1,3) and the result of (0,1,4)€(6,1,3)
> you may check that they are not the same
>
> (1,2,5)€(6,1,3) =/= (0,1,4)€(6,1,3)
>
> -1+2*5 and -0+1*4 are the same point in the p3 plane, but when they are
> engaged in this € operation, they yield different results. If you compare
> the nedloG product(€) for p3 with the usual Golden product for p3, one can
> notice that the nedloG product is not compatible with "additive congruences".
>
> -1+2*5 = -0+1*4 or (1,2,5) = (0,1,4) in p3
> Some other place where (1,2,5) =/= (0,1,4) can be true ?

When I first presented polysign Beresford did claim that he already had them, and by product that was somewhat true. The behavior above based upon the balance of sign so that in P3 (1, 1, 1) takes us back to the origin is really the crux of polysign. Still, it is true that we have an additional and unused metric available. In some regards it is not a geometrical property, since the geometry is exactly the balanced behavior. It is almost as if we could introduce another magnitude freely upon any value z. When z is reduced this value is naught. I have not however found any natural use for this free value yet. When doing functional analysis we can take nondecreasing functions as basic to polysign and this may be relevant. For instance to trace a circle in P3 approximately from purely numeric series we do not need any decrement operation; only incremental operations are needed. So for instance a path can be made and accounted for simply as a series of discrete components {-,+,*}. In effect a new form of sinusoid is available from this system. I guess that would be worth doing more with since sinusoidal analysis goes pretty far in a lot of places. By symmetry the three functions are identical and simply offset from each other so whereas cos() and sin() are off by ninety degrees we may as well just declare one function circ0() (maybe?) and 120 degrees away the next circ1() and then circ2(), but really maybe getting the notation to just use circ() would be the gain. But is it general dimensional? Not immediately; no. This algorithm will not just yield a spherical shell in P4 immediately. We'd like that, and I've tried a bit to find that, but haven't gotten it yet. Possibly it is worth working in its own terms the P4 resultant of this procedure and I have not done that yet. I do have general dimensional shell code that allows analysis in any dimension, but sadly that code is using the Cartesian form rather than this circ() form.

void UnitShell::UpdatePos()
{ //cerr << "1UnitShell::UpdatePos()\n" << flush;
clast = cpos;
last = pos;
//cerr << "1.1UnitShell::UpdatePos()\n" << flush;
for( int i = 0; i < dim; i++ )
cpos[i] = 1;
//cerr << "2UnitShell::UpdatePos()\n" << flush;
for( int i = 0; i < dim; i++ )
{
for( int j = i; j < dim; j++ )
{
if( j == i )
cpos[j] *= cos( 2 * pi * a[i] );
if( j > i )
cpos[j] *= sin( 2 * pi * a[i] );
}
}
// axisRotation.Project( cShell, cpos );
//cerr << "3UnitShell::UpdatePos() cpos: " << cpos << "\n" << flush;
Color();
pos = cpos;
}

You've done a nice job of throwing open the context here onto all sorts of concerns. As I lens onto the geometry I do see that the issue of constraints is one that I can latch onto. The Cartesian product in its set form is purely unconstrained. That is the spirit of the definition. You could cross species of lemon with models of American cars in the 70's and get sensible results. Blame the unions? To what degree is the union of two disparate sets not at all the same thing as two copies of the same set? Yet both are embodied by the Cartesian product. As to the gains of the Cartesian product some will certainly put (x,y,z) real valued coordinates here as crucial. Yet these Cartesian coordinates are not simply the Cartesian product. There is more detail that is imposed by convention and as such constraints are added onto the pure set theory, yet ignored by mathematicians. The choice to represent RxRxR as 3D physical space is not the only option. Especially not in hindsight of polysign. We establish the constraints up front on P4 rather than hide them away:
- z + z * z # z = 0
That we've generalized sign and derived geometry in this singular step is what makes polysign so special. The product is easy. It is this four way symmetry that is so difficult on tsm perps. Yet from an origin four rays out to the vertices of the tetrahedron centered on that origin are exactly what are described and required by this one line of balance. Can we stop implying the quantity two on symmetry now? Please? Can we stop regarding the real value as fundamental now please? Obviously the system will not halt four hundred years of evolution around the real value as fundamental so easily. This will require some sort of revolution. Your old inverse still exists, even in P4, though it does require a bit more than a tick to get it:
- z + z * z
is the inverse, just as #z was the original z, and there is your naught in sum. It's all there in the one line. Overlooked by far too many. Up here in P4 there is quite a lot of clickety clack going on and the product in general has sixteen terms. Still these combine down to four terms by sign.

Indeed it would be nice to find a decent nedloG(). I think it is possible that it occurs on the tatrix which is:
P1 P2 P3 | P4 P5 P6 ...
and so this triangular matrix, which embodies emergent spacetime with its natural breakpoint, and looks exactly like half of an ordinary matrix:
a10
a20 a21
a30 a31 a32
------------------------------------
a40 a41 a42 a43
a50 a51 a52 a53 a54
...
I think that is the first time I've put the breakpoint in that way. Not really a break through.
Honestly I am down in such a simple position trying to cover the Cartesian assumptions.
If there is something wrong, and I've got quite a lot of weak instances, then we'd like to find a larger trap or pit that can be exposed.
All the while I understand that the Cartesian coordinate system works, and I use it effectively. I myself have not managed to free myself fully from it.
Possibly there is some of the work that lays ahead.

>
> Then, we throw to the trash this new operation for not comply with
> equivalence classes ? Some have decided that one may look into the "brother
> space", this is, a space "without" the equivalence classes, pick and harvest
> interesting results/relations, and then come back to the usual space that
> "comply" with equivalence classes, this in, out and in of equivalence classes.
>
> In the case of the user Socratis tnp, seems to be something related the issue of
> equivalences also, with a strange hybrid mix since he uses decimals, although I m not totally sure.
>
> You may look also to the Dan counterposting at https://groups.google.com/g/sci.math/c/Wx9-5iDcFNk
> "1/2 not equal to 2/4" and “3 <=> 2 + 1 .."
>
> Also take a look to https://www.definitions.net/definition/setoid
> https://ncatlab.org/nlab/show/setoid
> (I almost forgot you like quotients too much) ;0

Timothy Golden wrote:

> 1. a compact falsification of the Cartesian product as it applies to
> geometry as (x,y) coordinates, say.
> 2. physics; as in physical geometry; mechanics. Atoms, and
> everything. 3. basis: pure arithmetic, hopefully yielding 2.

it looks like the nazi "u_kraine" gives a shit on the military hardware
and ammunition, gotten *_for_FREE_* from the capitalist "west". They are
destroying some buildings, if they can, otherwise they run away, the crap
left behind.

why is the cocaine zelenske asking for more military equipment, when they
have it already, left alone. What kind of war is that??

On 7/1/2022 5:32 PM, Josue Tanuma wrote:
> Timothy Golden wrote:
>
>> 1. a compact falsification of the Cartesian product as it applies to
>> geometry as (x,y) coordinates, say.
>> 2. physics; as in physical geometry; mechanics. Atoms, and
>> everything. 3. basis: pure arithmetic, hopefully yielding 2.
>
> it looks like the nazi "u_kraine" gives a shit on the military hardware
> and ammunition, gotten *_for_FREE_* from the capitalist "west". They are
> destroying some buildings, if they can, otherwise they run away, the crap
> left behind.

You mean like what 卐Ru⚡︎⚡︎ia卐 did on Snake Island? They ran away from
Snake Island, with their tail between their legs, leaving behind
military equipment, after Ukraine kicked them off of it? Oh yeah, they
tried to bomb the equipment so Ukraine couldn't use it. But, get this,
when the 卐Ru⚡︎⚡︎ian卐 bomber tried to bomb an undefended, stationary
island, they *missed* with three out of four bombs! Hahahaha!!! It's not
like the island was trying to escape, or was firing back at the jet, or
was even a tiny target! They could barely hit a freaking *island*!
Ukraine should award the 卐Ru⚡︎⚡︎ian卐 pilot a minor medal, for his work
helping to make the 卐Ru⚡︎⚡︎ian卐 military look so pathetic!
>
> why is the cocaine zelenske asking for more military equipment, when they
> have it already, left alone. What kind of war is that??

35,000+ dead 卐Ru⚡︎⚡︎ian卐 soldiers would strongly disagree with that,
if dead 卐Ru⚡︎⚡︎ians卐 could speak.

Michael Moroney wrote:

>> it looks like the nazi "u_kraine" gives a shit on the military hardware
>> and ammunition, gotten *_for_FREE_* from the capitalist "west". They
>> are destroying some buildings, if they can, otherwise they run away,
>> the crap left behind.
>
> You mean like what 卐Ru⚡︎⚡︎ia卐 did on Snake Island? They ran away from
> Snake Island, with their tail between their legs, leaving behind
>
>> why is the cocaine zelenske asking for more military equipment, when
>> they have it already, left alone. What kind of war is that??
>
> 35,000+ dead 卐Ru⚡︎⚡︎ian卐 soldiers would strongly disagree with that, if
> dead 卐Ru⚡︎⚡︎ians卐 could speak.

my friend, no. That's not an island, but a rock, smaller than 1km^2 as
surface. Left alone to ensure the cocaine zelenske free passage saving the
world from hunger. Let's see how much food the Africans gets from the
cocaine zelenske. My bet is none. Moreover the green color of the seats
and the visit of the "Virgin" oligarch richard bronson, indicates the
zelenske is London domiciled somewhere. Then his days are numbered, a
matter of weeks, three months most. The nazis are not trusting him
anymore. Nor the soldiers trust in the oligarchs. They got the picture,
and the picture is right. I beg you to reconsider.

On Saturday, July 2, 2022 at 3:45:43 PM UTC-4, Cohen Ogiwara wrote:
> Michael Moroney wrote:
>
> >> it looks like the nazi "u_kraine" gives a shit on the military hardware
> >> and ammunition, gotten *_for_FREE_* from the capitalist "west". They
> >> are destroying some buildings, if they can, otherwise they run away,
> >> the crap left behind.
> >
> > You mean like what 卐Ru⚡︎⚡︎ia卐 did on Snake Island? They ran away from
> > Snake Island, with their tail between their legs, leaving behind
> >
> >> why is the cocaine zelenske asking for more military equipment, when
> >> they have it already, left alone. What kind of war is that??
> >
> > 35,000+ dead 卐Ru⚡︎⚡︎ian卐 soldiers would strongly disagree with that, if
> > dead 卐Ru⚡︎⚡︎ians卐 could speak.
> my friend, no. That's not an island, but a rock, smaller than 1km^2 as
> surface. Left alone to ensure the cocaine zelenske free passage saving the
> world from hunger. Let's see how much food the Africans gets from the
> cocaine zelenske. My bet is none. Moreover the green color of the seats
> and the visit of the "Virgin" oligarch richard bronson, indicates the
> zelenske is London domiciled somewhere. Then his days are numbered, a
> matter of weeks, three months most. The nazis are not trusting him
> anymore. Nor the soldiers trust in the oligarchs. They got the picture,
> and the picture is right. I beg you to reconsider.

I assure you that this is not disinformation: https://www.youtube.com/watch?v=hjWkfCSF52g

To challenge the real number as fundamental is enough to challenge the Cartesian representation of a 2D space since the 1D version would be suspect.
However in the realization that the real number is not fundamental but is instead a two-signed number the geometrical 1D form does in fact hold strong..
The question of whether two such 1D values suddenly spills into a plane is more the cup of tea being tasted, quaffed by some, but rejected by one here..

Ahh... perhaps the vector that I am looking for lays in the deconstruction of higher spaces. If for instance we pop in on a 1D space, and by this I mean a populated version. Populated with what? Well, this is a physical problem isn't it? Did we merely have a single point in R? After all, this is the Cartesian representation. So to what degree then is the representation merely of a point versus a space? Is RxR then a space? Or is it merely a point? That point of course being a zero dimensional entity now requiring two dimensions as I've quipped on here in the past. As a geometer fills his plane with whatever suits his interest can we do the same on the real line? Even that will betray the level of possibilities, for a thickness of point distribution should entirely be possible, as when a and b have the same coordinate the density of the trace would be twice what either singleton would be.. No wonder physics rests so far away from mathematics. But they take the same root. They as well decompose down to just a few interacting objects, reduce back down to one dimension; such simplistic instances are ideal to the textbook approach. As creatures of habit these methods are getting old now.. Reused for generations. Then along comes some complicated text that takes it all to another level. Should we have had the complicated version first then all of those simplistic depictions will appear fraudulent won't they? In that reality is not RxRxR (the real number cubed somehow), ignoring it's two-signed nature, being unappreciated by apes who barely were even able to accept that version of the number whose purity in prior times was less questionable...

Then to wind up with physical systems whose point particles engage spin tactics, as if to admit these point's solidity, does not receive discussion why exactly?
Is it because this realization will take the entire system apart? Is it because Cartesian thought was already known to fail? In that future constructions are best defended as variations on the failed past constructions; in avoiding such combative situations academia has speared itself through the foot into soft ground, the spear going down deeply into the soil so not to be pulled out easily. I suppose there is room to pivot around, but that is about it.

I find those who speak so highly and deferentially about books to be frauds.. They must be nearly the same ones who bow to academia. What of they who do not fit in to that structure? It's actually rather a lot of people. Do people of good common sense of physical reality not fit in? Of course the sheer quantity of genera of language that have devolved over time in overlapping identical words that mean completely different things such as the word 'group', or 'ring'; the escapement of such as such are such that their obscurity is welcome in the stifling towers. "We have AC.", said one academician to the other academician. "Yes, but for how long. You know the grid has issues..." said the other to the first. A third, overhearing the first two, interjects: "It's a perfectly good reason that we should have a student run nuclear power plant on campus." The other academician, being a bit earthy, says: "Well, that would close the loop, though Uranium doesn't just grow on trees." The first responded: "Well, maybe a student run chip burning power plant would do." The other says "You know, going undergound would solve all of this..." - https://www.rt.com/shows/going-underground/

On Saturday, July 2, 2022 at 3:45:43 PM UTC-4, Cohen Ogiwara wrote:
> Michael Moroney wrote:
>
> >> it looks like the nazi "u_kraine" gives a shit on the military hardware
> >> and ammunition, gotten *_for_FREE_* from the capitalist "west". They
> >> are destroying some buildings, if they can, otherwise they run away,
> >> the crap left behind.
> >
> > You mean like what 卐Ru⚡︎⚡︎ia卐 did on Snake Island? They ran away from
> > Snake Island, with their tail between their legs, leaving behind
> >
> >> why is the cocaine zelenske asking for more military equipment, when
> >> they have it already, left alone. What kind of war is that??
> >
> > 35,000+ dead 卐Ru⚡︎⚡︎ian卐 soldiers would strongly disagree with that, if
> > dead 卐Ru⚡︎⚡︎ians卐 could speak.
> my friend, no. That's not an island, but a rock, smaller than 1km^2 as
> surface. Left alone to ensure the cocaine zelenske free passage saving the
> world from hunger. Let's see how much food the Africans gets from the
> cocaine zelenske. My bet is none. Moreover the green color of the seats
> and the visit of the "Virgin" oligarch richard bronson, indicates the
> zelenske is London domiciled somewhere. Then his days are numbered, a
> matter of weeks, three months most. The nazis are not trusting him
> anymore. Nor the soldiers trust in the oligarchs. They got the picture,
> and the picture is right. I beg you to reconsider.

This has gotten me to thinking that Zelensky will be the first to step aboard a new sort of elevator that Elon Musk has built. He will be a rocket man..
When they outlawed the 'Z' it was destined, Mr. Elensky. Kiev to London: ten minute trip. Scramble the fighter jets. Yes, you can bring your cat and your tooth brush.

On Wednesday, July 13, 2022 at 8:26:17 AM UTC-4, Timothy Golden wrote:
> On Saturday, July 2, 2022 at 3:45:43 PM UTC-4, Cohen Ogiwara wrote:
> > Michael Moroney wrote:
> >
> > >> it looks like the nazi "u_kraine" gives a shit on the military hardware
> > >> and ammunition, gotten *_for_FREE_* from the capitalist "west". They
> > >> are destroying some buildings, if they can, otherwise they run away,
> > >> the crap left behind.
> > >
> > > You mean like what 卐Ru⚡︎⚡︎ia卐 did on Snake Island? They ran away from
> > > Snake Island, with their tail between their legs, leaving behind
> > >
> > >> why is the cocaine zelenske asking for more military equipment, when
> > >> they have it already, left alone. What kind of war is that??
> > >
> > > 35,000+ dead 卐Ru⚡︎⚡︎ian卐 soldiers would strongly disagree with that, if
> > > dead 卐Ru⚡︎⚡︎ians卐 could speak.
> > my friend, no. That's not an island, but a rock, smaller than 1km^2 as
> > surface. Left alone to ensure the cocaine zelenske free passage saving the
> > world from hunger. Let's see how much food the Africans gets from the
> > cocaine zelenske. My bet is none. Moreover the green color of the seats
> > and the visit of the "Virgin" oligarch richard bronson, indicates the
> > zelenske is London domiciled somewhere. Then his days are numbered, a
> > matter of weeks, three months most. The nazis are not trusting him
> > anymore. Nor the soldiers trust in the oligarchs. They got the picture,
> > and the picture is right. I beg you to reconsider.
> This has gotten me to thinking that Zelensky will be the first to step aboard a new sort of elevator that Elon Musk has built. He will be a rocket man.
> When they outlawed the 'Z' it was destined, Mr. Elensky. Kiev to London: ten minute trip. Scramble the fighter jets. Yes, you can bring your cat and your tooth brush.

The German media/government seems to be even worse than the American's:
https://www.youtube.com/watch?v=a4-1qhGvbu4
Outright lies in support of Ukranian Nazis.
Who is in for a regime change?

On Tuesday, July 12, 2022 at 10:22:11 AM UTC-4, Timothy Golden wrote:
> To challenge the real number as fundamental is enough to challenge the Cartesian representation of a 2D space since the 1D version would be suspect.
> However in the realization that the real number is not fundamental but is instead a two-signed number the geometrical 1D form does in fact hold strong.
> The question of whether two such 1D values suddenly spills into a plane is more the cup of tea being tasted, quaffed by some, but rejected by one here.
>
> Ahh... perhaps the vector that I am looking for lays in the deconstruction of higher spaces. If for instance we pop in on a 1D space, and by this I mean a populated version. Populated with what? Well, this is a physical problem isn't it? Did we merely have a single point in R? After all, this is the Cartesian representation. So to what degree then is the representation merely of a point versus a space? Is RxR then a space? Or is it merely a point? That point of course being a zero dimensional entity now requiring two dimensions as I've quipped on here in the past. As a geometer fills his plane with whatever suits his interest can we do the same on the real line? Even that will betray the level of possibilities, for a thickness of point distribution should entirely be possible, as when a and b have the same coordinate the density of the trace would be twice what either singleton would be. No wonder physics rests so far away from mathematics. But they take the same root. They as well decompose down to just a few interacting objects, reduce back down to one dimension; such simplistic instances are ideal to the textbook approach. As creatures of habit these methods are getting old now. Reused for generations. Then along comes some complicated text that takes it all to another level. Should we have had the complicated version first then all of those simplistic depictions will appear fraudulent won't they? In that reality is not RxRxR (the real number cubed somehow), ignoring it's two-signed nature, being unappreciated by apes who barely were even able to accept that version of the number whose purity in prior times was less questionable...
>
> Then to wind up with physical systems whose point particles engage spin tactics, as if to admit these point's solidity, does not receive discussion why exactly?
> Is it because this realization will take the entire system apart? Is it because Cartesian thought was already known to fail? In that future constructions are best defended as variations on the failed past constructions; in avoiding such combative situations academia has speared itself through the foot into soft ground, the spear going down deeply into the soil so not to be pulled out easily. I suppose there is room to pivot around, but that is about it.
>
> I find those who speak so highly and deferentially about books to be frauds. They must be nearly the same ones who bow to academia. What of they who do not fit in to that structure? It's actually rather a lot of people. Do people of good common sense of physical reality not fit in? Of course the sheer quantity of genera of language that have devolved over time in overlapping identical words that mean completely different things such as the word 'group', or 'ring'; the escapement of such as such are such that their obscurity is welcome in the stifling towers. "We have AC.", said one academician to the other academician. "Yes, but for how long. You know the grid has issues..." said the other to the first. A third, overhearing the first two, interjects: "It's a perfectly good reason that we should have a student run nuclear power plant on campus." The other academician, being a bit earthy, says: "Well, that would close the loop, though Uranium doesn't just grow on trees." The first responded: "Well, maybe a student run chip burning power plant would do." The other says "You know, going undergound would solve all of this..." - https://www.rt.com/shows/going-underground/

I love Afshin. I saw him once on the Boston common back when things were getting hot here. He is very short. I said hi but he ignored me. Understandable given his position and the skirmishes in the street. It was quiet where we were but he was on his way somewhere. The herd mentality was in full swing out on the streets. A flock of humans is a sure way to hide deceptive practices. One bottle thrown into the police and you are looking at a situation, let alone the signaling of a bottle with some fluid in it. How would you like to be the unlucky cop who has to open the cap on a plastic bottle only to smell urine? Talk about demoralizing.

Back in the innocent land of mathematics the Cartesian product is suffering heavy losses here on this thread. It seems to require some sort of a superdimensional space to get going in. After all, upon instantiating your first line you have built one dimension. Put it down on a piece of paper that is planar already. Then stick down another, at any angle really other than colinear with the first. Plop down a third if you like: the paper doesn't care. What seems to really matter here is that the lines which we choose to represent a coordinate series by, upon establishing those references, hold their original direction even while they provide the means of translation. Yes, two is enough, but three does not fail, either. Would you call yourself a minimalist if you balk at three? Already you are up to six rays when three would have sufficed. Four rays for the minimalist, yet three would have sufficed, and just two of those three really necessary in the reduced form, you minimalist. Could it be that polysign could suffer the same fate as the Cartesian thought process? That it is merely one step better and that another step or so remain?

The solid analysis does sort of point this way, but can't we arrive there by linear algebra and matrix theory? Does polysign somehow incur a point field as a solid better? It does not seem to. The constraint within a given Pn is a gain. That would have to be conceded by anyone capable of understanding the discussion. Then the natural point in T4, say, is more of interest in that it can contain some additional referential detail. It seems almost too much detail:
a10
a20 a21
a30 a31 a32
a40 a41 a42 a43
these being neutral element first (NU); MU being next.

Scrambling the threads again, the unity awareness of the NU and the MU and the mistake of the Cartesian to take the NU as more fundamental is a cross-fit betwixt the two.
Clearly the MU can generate the NU, but not the other way around, so as to which is more fundamental... should it come first? Well then let's rewrite this trivium into existence:
a11
a21 a22
a31 a32 a33
a41 a42 a43 a44
and now it as if we never even had the zero sign. Still, we know that the zero sign is correct. a10=a11, a20=a22, a30=a33, a40=a44, and these are true by definition really. These are the modulo statements; the line being a modulo two concept, the plane being a modulo three concept, volumetric space being a modulo four context is being supported here, and it is in a discrete context that it is so. This is completely foreign to the Cartesian way of thinking, as is the arithmetic product. Whether we even should include P4 into this deal is an open problem...
P1 P2 P3 | P4 P5 P6 ...
but the breakpoint remains so that support either way can be argued for. The kaleidoscopic P4 mimics P2P3, and some will insist I insert a Cartesian cross here.
Yet shouldn't a decomposition by P1 be possible? Ah, or is it true that should one decompose by P1 you still get P4 back? The geometry would hold true.. This is where the real number as two-signed somehow gains a foothold. Yes, P2 is here in polysign. Yes, all dot products yield a P2 value rather than a P1 value in ordinary vector mechanics. Yes, this is the source of projection as well. At least this is the source of ordinary vector projection. Possibly there is more. Certainly the mathematicains PP=P is pee-pee, but that is merely bad interpretation. Still, P2 is there and is still there in my code. Now dot your v's and cross your eyes, and oh, here, have a sip of apple juice...

https://www.youtube.com/watch?v=EDZ_pNnA6qE
https://www.youtube.com/results?search_query=bottle+of+pee+thrown+at+cop