Suppose we have an elastic string (or a line) and we elongate it at certain 'rate'. How can we express its rate of elongation? We cnnot make any line continuous without introducing the idea of 'elongation' and 'contraction' of lines in coordinate geometry.
> Suppose we have an elastic string (or a line) and we elongate it > at certain 'rate'. How can we express its rate of elongation? > We cnnot make any line continuous without introducing the idea of > 'elongation' and 'contraction' of lines in coordinate geometry.
Lines are infinitely long. Line segments are no problem to anybody but you.
Location, velocity, acceleration, jerk, snap, crackle, pop - in that order, distance/time^n.
General Relativity is a tensor theory - no coordinate background at all. When did topology ever care about length? You are a loud boring flaming imbecile.
-- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) "Quis custodiet ipsos custodes?" The Net!
"V.Gopal" wrote: > Suppose we have an elastic string (or a line) and we elongate it > at certain 'rate'. How can we express its rate of elongation? > We cnnot make any line continuous without introducing the idea of > 'elongation' and 'contraction' of lines in coordinate geometry.
That is a geometric necessity question or a mathematics set question. Elongation of a set is possible and might exist for real, but it sure is not common. Not common because the cause of the set itself must occur by the elongation of a cause of all sets. Meaning the cause of all differentials. And graphs do not cause differentials.
To express the differential of its own cause is the abstracted relation, you likely are thinking of. And an example is one made by an engineer. Take a spring and cause the material to alter as the spring is compressed, and use a spring to alter that spring. Making a highly nonlinear differential.
So, in the end you are simply adding another independent variable. A common occurance, now.
Geometric necessity and set theory was not really examined. If I have any question like this, it means do I need a nonlinear protractor. And someday we just might. How do you know when you need one? If you find a relation without identifiable variables a hidden constant may cause one to be needed. Or just say, you want to try to observe the constant, to allow normal protractors. A true hidden variable means a function is not going to define the relation, except it means the abstract function will be missing.
Right now a very serious variable is missing, the cause to all differentials. A universal abstract physical constant. Except you do not need to look to hard, look to the rereading of the Greek schools.
> > Suppose we have an elastic string (or a line) and we elongate it > > at certain 'rate'. How can we express its rate of elongation? > > We cnnot make any line continuous without introducing the idea of > > 'elongation' and 'contraction' of lines in coordinate geometry.
> That is a geometric necessity question or a mathematics set > question. Elongation of a set is possible and might exist for real, > but it sure is not common. Not common because the cause > of the set itself must occur by the elongation of a cause > of all sets. Meaning the cause of all differentials. And graphs > do not cause differentials.
> To express the differential of its own cause is the abstracted > relation, you likely are thinking of. And an example is one > made by an engineer. Take a spring and cause the > material to alter as the spring is compressed, and use > a spring to alter that spring. Making a highly nonlinear > differential.
> So, in the end you are simply adding another independent > variable. A common occurance, now.
> Geometric necessity and set theory was not really examined. > If I have any question like this, it means do I need > a nonlinear protractor. And someday we just might. > How do you know when you need one? If you find > a relation without identifiable variables a hidden > constant may cause one to be needed. Or just say, > you want to try to observe the constant, to allow > normal protractors. A true hidden variable means > a function is not going to define the relation, except it > means the abstract function will be missing.
> Right now a very serious variable is missing, the cause > to all differentials. A universal abstract physical constant. > Except you do not need to look to hard, look to the > rereading of the Greek schools.
> Douglas Eagleson > Gaithersburg, MD USA >Geometric necessity and set theory was not really examined. > If I have any question like this, it means do I need > a nonlinear protractor. And someday we just might. > How do you know when you need one? If you find > a relation without identifiable variables a hidden > constant may cause one to be needed. Or just say, > you want to try to observe the constant, to allow > normal protractors. A true hidden variable means > a function is not going to define the relation, except it > means the abstract function will be missing.
I salute you for your reply! It is excellent, clear and explicit. I believe that the difficulty arises because here 'elongation'is an idea that involves 'self-reference'. We always think the problem of self-reference in terms of negative effect leading to a dead-lock, e.g. "I am a lier." In this case, from what I say no one can decide whether what I am saying is true or false. It does not demonstrate the logic behind self-reference. Nothing can demonstrate the logic involved in self-reference. The formula for 'Rate of elongation' has to reveal universally applicable logic involved in self-reference - this would become the law of thought or the law of investigation of truth. "Velocity proportional to distance" (expansion of universe) involves self-reference - here use of the term 'velocity' is wrong; it must be 'acceleration'. Similarly 'gravity inversely proportional to hight' makes gravity (g) at a point, inexpressible. The working of a predictable system involves self-reference. 'Elongation' involves a quality like elasticy and also environment e.g. force, and, 'elongation' represents state of change. State of change involves self-reference. Geometrical curves represent state of change, and state of change involves cntinuous falsification of the past. Therefore geometry of continuous lines represents nature. This is the reason why in statistics IF the resulting curve is smooth prediction 'becomes' accurate with zero-error.
> > > Suppose we have an elastic string (or a line) and we elongate it > > > at certain 'rate'. How can we express its rate of elongation? > > > We cnnot make any line continuous without introducing the idea of > > > 'elongation' and 'contraction' of lines in coordinate geometry.
> > That is a geometric necessity question or a mathematics set > > question. Elongation of a set is possible and might exist for real, > > but it sure is not common. Not common because the cause > > of the set itself must occur by the elongation of a cause > > of all sets. Meaning the cause of all differentials. And graphs > > do not cause differentials.
> > To express the differential of its own cause is the abstracted > > relation, you likely are thinking of. And an example is one > > made by an engineer. Take a spring and cause the > > material to alter as the spring is compressed, and use > > a spring to alter that spring. Making a highly nonlinear > > differential.
> > So, in the end you are simply adding another independent > > variable. A common occurance, now.
> > Geometric necessity and set theory was not really examined. > > If I have any question like this, it means do I need > > a nonlinear protractor. And someday we just might. > > How do you know when you need one? If you find > > a relation without identifiable variables a hidden > > constant may cause one to be needed. Or just say, > > you want to try to observe the constant, to allow > > normal protractors. A true hidden variable means > > a function is not going to define the relation, except it > > means the abstract function will be missing.
> > Right now a very serious variable is missing, the cause > > to all differentials. A universal abstract physical constant. > > Except you do not need to look to hard, look to the > > rereading of the Greek schools.
> > Douglas Eagleson > > Gaithersburg, MD USA > >Geometric necessity and set theory was not really examined. > > If I have any question like this, it means do I need > > a nonlinear protractor. And someday we just might. > > How do you know when you need one? If you find > > a relation without identifiable variables a hidden > > constant may cause one to be needed. Or just say, > > you want to try to observe the constant, to allow > > normal protractors. A true hidden variable means > > a function is not going to define the relation, except it > > means the abstract function will be missing.
> I salute you for your reply! It is excellent, clear and explicit. > I believe that the difficulty arises because here 'elongation'is an > idea that involves 'self-reference'. We always think the problem of > self-reference in terms of negative effect leading to a dead-lock, > e.g. "I am a lier." In this case, from what I say no one can decide > whether what I am saying is true or false. It does not demonstrate > the logic behind self-reference. Nothing can demonstrate the logic > involved in self-reference. The formula for 'Rate of elongation' has to > reveal universally applicable logic involved in self-reference - this > would become the law of thought or the law of investigation of truth. > "Velocity proportional to distance" (expansion of universe) involves > self-reference - here use of the term 'velocity' is wrong; it must be > 'acceleration'. Similarly 'gravity inversely proportional to hight' > makes gravity (g) at a point, inexpressible. The working of a > predictable system involves self-reference. > 'Elongation' involves a quality like elasticy and also environment > e.g. force, and, 'elongation' represents state of change. State of > change involves self-reference. Geometrical curves represent state > of change, and state of change involves cntinuous falsification of > the past. Therefore geometry of continuous lines represents nature. > This is the reason why in statistics IF the resulting curve is smooth > prediction 'becomes' accurate with zero-error.
Thanks for liking my reply.
A quote from yours:
"Geometrical curves represent state of change, and state of change involves cntinuous falsification of the past. Therefore geometry of continuous lines represents nature. This is the reason why in statistics IF the resulting curve is smooth prediction 'becomes' accurate with zero-error."
In simple test wording you appear to state that geometry is a cause of the world or a knowledge of the world. It is a real nice dilemma! Thanks
> > > > Suppose we have an elastic string (or a line) and we elongate it > > > > at certain 'rate'. How can we express its rate of elongation? > > > > We cnnot make any line continuous without introducing the idea of > > > > 'elongation' and 'contraction' of lines in coordinate geometry.
> > > That is a geometric necessity question or a mathematics set > > > question. Elongation of a set is possible and might exist for real, > > > but it sure is not common. Not common because the cause > > > of the set itself must occur by the elongation of a cause > > > of all sets. Meaning the cause of all differentials. And graphs > > > do not cause differentials.
> > > To express the differential of its own cause is the abstracted > > > relation, you likely are thinking of. And an example is one > > > made by an engineer. Take a spring and cause the > > > material to alter as the spring is compressed, and use > > > a spring to alter that spring. Making a highly nonlinear > > > differential.
> > > So, in the end you are simply adding another independent > > > variable. A common occurance, now.
> > > Geometric necessity and set theory was not really examined. > > > If I have any question like this, it means do I need > > > a nonlinear protractor. And someday we just might. > > > How do you know when you need one? If you find > > > a relation without identifiable variables a hidden > > > constant may cause one to be needed. Or just say, > > > you want to try to observe the constant, to allow > > > normal protractors. A true hidden variable means > > > a function is not going to define the relation, except it > > > means the abstract function will be missing.
> > > Right now a very serious variable is missing, the cause > > > to all differentials. A universal abstract physical constant. > > > Except you do not need to look to hard, look to the > > > rereading of the Greek schools.
> > > Douglas Eagleson > > > Gaithersburg, MD USA > > >Geometric necessity and set theory was not really examined. > > > If I have any question like this, it means do I need > > > a nonlinear protractor. And someday we just might. > > > How do you know when you need one? If you find > > > a relation without identifiable variables a hidden > > > constant may cause one to be needed. Or just say, > > > you want to try to observe the constant, to allow > > > normal protractors. A true hidden variable means > > > a function is not going to define the relation, except it > > > means the abstract function will be missing.
> > I salute you for your reply! It is excellent, clear and explicit. > > I believe that the difficulty arises because here 'elongation'is an > > idea that involves 'self-reference'. We always think the problem of > > self-reference in terms of negative effect leading to a dead-lock, > > e.g. "I am a lier." In this case, from what I say no one can decide > > whether what I am saying is true or false. It does not demonstrate > > the logic behind self-reference. Nothing can demonstrate the logic > > involved in self-reference. The formula for 'Rate of elongation' has to > > reveal universally applicable logic involved in self-reference - this > > would become the law of thought or the law of investigation of truth. > > "Velocity proportional to distance" (expansion of universe) involves > > self-reference - here use of the term 'velocity' is wrong; it must be > > 'acceleration'. Similarly 'gravity inversely proportional to hight' > > makes gravity (g) at a point, inexpressible. The working of a > > predictable system involves self-reference. > > 'Elongation' involves a quality like elasticy and also environment > > e.g. force, and, 'elongation' represents state of change. State of > > change involves self-reference. Geometrical curves represent state > > of change, and state of change involves cntinuous falsification of > > the past. Therefore geometry of continuous lines represents nature. > > This is the reason why in statistics IF the resulting curve is smooth > > prediction 'becomes' accurate with zero-error.
> Thanks for liking my reply.
> A quote from yours:
> "Geometrical curves represent state > of change, and state of change involves cntinuous falsification of > the past. Therefore geometry of continuous lines represents nature. > This is the reason why in statistics IF the resulting curve is smooth > prediction 'becomes' accurate with zero-error."
> In simple test wording you appear to state that geometry > is a cause of the world or a knowledge of the world. > It is a real nice dilemma! Thanks
> Douglas Eagleson > Gaithersburg, MD USA
I am sorry if I my statement gave you such an impression. 'Geometry' is not a 'cause', nor geometry is 'knowledge' of the real. Geometry gives us a vague idea about cause - effect relation. Geometry tells us that cause and effect are inseparable; cause and effect are contiguous in space; cause and effect are continuous in time, cause and effect are asymmetrical or 'one sided' etc. Geometry gives us an idea about the reason why a system is predictable. It gives a very vague idea about how a predictable system should look like. It tells us that if we want to make prediction about a system then the system to which we want to apply knowledge, the same sysytem must be source of all knowledge that we use to make the prediction. Unfortunately the 'method' turns out to be statistical. In any statistical prediction the 'curve' seems 'move' (acquire a particular shape) on its own without any extrnal cause. In statistics we use 'dead information' and not knowledge drawn from experience. Each information is a state of 'no change' and not the state of change, but the curve as a whole projects the state of change without giving us any knowlege as to why the system is prdictable, and, if we do not know why the system is predictable it means we do not have 'true knowledge' of the system, whether it is a piece of matter or the universe as a whole.
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