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Natural Science Forum / Physics / Relativity / August 2006Poincare conjecture
This has been in the news of late: http://en.wikipedia.org/wiki/Grigori_Perelman It has been fleshed out by many since he posted it on arxiv.org. What effects will it have on GR? David A. Smith > What effects will it have on GR? Probably none - it's about classifying 3D manifolds by altering them so they support certain geometries. In GR OTOH the (4D) geometry is already fixed by the Einstein equation. -- Jan Bielawski Dear JanPB: >> What effects will it have on GR? > > Probably none - it's about classifying 3D manifolds > by altering them so they support certain geometries. > In GR OTOH the (4D) geometry is already fixed by > the Einstein equation. Some of the made-for-public-consumption descriptions of this indicated that removing knots or singularities had to occur in 3D, with time as an evolution parameter but not as some sort of necessary degree-of-freedom. So you wouldn't have to resolve an "event horizon" by "rotating" r into t necessarily (just a wag)... Your analysis accepted. Thanks, Jan. David A. Smith > Dear JanPB: > [quoted text clipped - 9 lines] > 3D, with time as an evolution parameter but not as some sort of > necessary degree-of-freedom. The basic idea that Hamilton came up with was to sort of let the 3D manifold evolve according to its (Ricci) curvature. So the more curved portions would tend to "unflex" faster than the flatter portions and the whole thing would sort of tend toward becoming a round 3-sphere. This "tending to" is guaranteed to continue for a short time and AFAICT Perelman showed that continuing this process does not mess things up too badly in the sense that the singularities that occur can be taken care of. Although I remember Hamilton talking already in the '80s that his approach could be used to prove the Poincare conjecture. > So you wouldn't have to resolve an "event horizon" by "rotating" > r into t necessarily (just a wag)... No, the whole setup in Hamilton/Perelman is Riemannian (i.e., not semi-Riemannian, IOW positive definite metric only and no notion of light cones, horizons, none of that). -- Jan Bielawski "N:dlzc D:aol T:com \(dlzc\)" <N: dlzc1 D:cox T:net@nospam.com> wrote: > This has been in the news of late: > http://en.wikipedia.org/wiki/Grigori_Perelman > It has been fleshed out by many since he posted it on arxiv.org. > What effects will it have on GR? Probably not much, assuming "it" means "proof of the Poincare conjecture." There are two places I can think of where it could be relevant. First, if the Poincare conjecture had been shown to be wrong, it would have presumably been possible that a spatial slice of our Universe was a "fake" three-sphere. There's been a fair amount of work on the question of whether other, simpler "strange" topologies might be observable, for example through characteristic patterns in the cosmic microwave background. Now, assuming Perelman is right, no one will have to ask about homology three-spheres. Second, in some path integral approaches to quantum gravity, one should not just "sum over geometries," but "sum over topologies" as well. It's possible that the presence or absence of "fake" three-spheres could affect those sums. (There are a few instances in which it is known that sums over topologies can have drastic effects on path integrals -- see http://arxiv.org/abs/gr-qc/0310002, for example -- and there has been interesting work on, for example, the role of exotic differentiable structures in more than 3+1 dimensions -- see http://arxiv.org/abs/gr-qc/9903086, for example.) More broadly, if Perelman has really proven Thurston's geometrization conjecture, that might have implications for the sum over topologies in quantum gravity as well, but no one that I know of has thought about this very deeply. Steve Carlip Dear carlip-nospam: > "N:dlzc D:aol T:com \(dlzc\)" <N: dlzc1 D:cox T:net@nospam.com> > wrote: [quoted text clipped - 42 lines] > one that I know of has thought about this very > deeply. Yet. Thanks for the $1000 answer... David A. Smith My goodness, 4 years ago a thread like this would generate many replies and I particularly like the topological maneuvering to make 2D look like 3D but that was then and this is now . The first time I came across the conjecture I recognised it as a blur between faculties which recognise the difference between 2D and 3D just as one would know the difference between television images an object and seeing the same object in reality.I even presented the entire relativistic concept and its geometry as an extension of this . How axial rotation to a celestial sphere morphed into orbital motion to 'absolute space' can actually be presented graphically and it really is at the core of Newton's work and its exotic 20th century extension - http://www.opencourse.info/astronomy/introduction/02.motion_stars_sun/celestial_ sphere_anim.gif Dumping an aether on Newton as 'absolute space' was a masterstroke but not half as good as Newton's original masterstroke of creating the AU through the RA/Dec system.The later guys are just pale imitators of Isaac and that remains my objection,if you cannot contend with what Isaac was actually up to you will always be caught up in his calendrically driven clockwork solar system I give you the short version of how axial rotation to celestial sphere geometry morphed into orbital motion to absolute space and how many men died without knowing that.You have a chance to get out of a mentally damaging cult just as a few have managed to do. > Dear carlip-nospam: > [quoted text clipped - 50 lines] > > David A. Smith > "N:dlzc D:aol T:com \(dlzc\)" <N: dlzc1 D:cox T:net@nospam.com> wrote: > > Now, assuming Perelman is right, no one will have to ask > about homology three-spheres. A minor nit: it's "homotopy sphere". Homology spheres OTOH do exist and in fact Poincare constructed one himself (I think his example was the +1 surgery on the trefoil knot in S^3) and then on the same breath - ever so innocently - he asked: "OK, that was that, so how about homotopy 3-spheres now"? Hee hee... > Second, in some path integral approaches to quantum gravity, > one should not just "sum over geometries," but "sum over [quoted text clipped - 7 lines] > dimensions -- see http://arxiv.org/abs/gr-qc/9903086, for > example.) Vehrrrry interesting, thanks. -- Jan Bielawski >> "N:dlzc D:aol T:com \(dlzc\)" <N: dlzc1 D:cox T:net@nospam.com> wrote: >> Now, assuming Perelman is right, no one will have to ask >> about homology three-spheres. > A minor nit: it's "homotopy sphere". Homology spheres OTOH do exist and > in fact Poincare constructed one himself (I think his example was the > +1 surgery on the trefoil knot in S^3) and then on the same breath - > ever so innocently - he asked: "OK, that was that, so how about > homotopy 3-spheres now"? Hee hee... Ouch! I knew that... taht's what I get for posting after not enough sleep. Steve Carlip Steve son,you have been sleeping all your existence, a silly attempt to fit a 1898 science fiction novel into a formal framework should now look plain silly . Look out into the great celestial arena and draw you gaze away from the silly 20th century excesses.Look out with the eyes of Kepler and then compare it with that diseased Newtonian mind - Epitome Of Copernican Astronomy by JOHANNES KEPLER Finally by what arguments do you prove that the centre of the Sun which is at the midpoint of the planetary spheres and bears their whole system - does not revolve in some annual movement,as Brahe wishes,but in accordance with Copernicus sticks immobile in one place,while the centre of the Earth revolves in an annual movement. Argument 10 " The 10th argument,taken from the periodic times, is as follows; the apparent movement of the Sun has 365 days which is the mean measure between Venus' period of 225 days and Mars' period of 687 days.Therefore does not the nature of things shout out loud that the circuits in which those 365 days are taken up has a mean position between the circuits of Mars and Venus around the Sun and thus this is not the circuit of the Sun around the Earth -for none of the primary planets has its orbit arranged around the Earth,as Brahe admits,but the circuit of the Earth around the resting Sun,just as the other planets,namely Mars and Venus,complete their own periods by running around the Sun." Johannes Kepler _______________________________________________ PHENOMENON IV. "That the fixed stars being at rest, the periodic times of the five primary planets, and (whether of the sun about the earth, or) of the earth about the sun, are in the sesquiplicate proportion of their mean distances from the sun. This proportion, first observed by Kepler, is now received by all astronomers; for the periodic times are the same, and the dimensions of the orbits are the same, whether the sun revolves about the earth, or the earth about the sun. And as to the measures of the periodic times, all astronomers are agreed about them. But for the dimensions of the orbits, Kepler and Bullialdus, above all others, have determined them from observations with the greatest accuracy; and the mean distances corresponding to the periodic times differ but insensibly from those which they have assigned, and for the most part fall in between them; as we may see from the following table." newton * http://members.tripod.com/~gravitee/phaenomena.htm > >> "N:dlzc D:aol T:com \(dlzc\)" <N: dlzc1 D:cox T:net@nospam.com> wrote: > [quoted text clipped - 11 lines] > > Steve Carlip For the time being, as along that moment, Henri Poincaré has had lights, a mathematical physics as it has had received along himself, its first a powerful ideal among and from especially the gravity, however, which it has had been, just specified as follows : Every body in the universe, every grain of sand, every star was attracted to every other body by a force inversely proportional to the square of their separation. However, that kind of a stipulation has had always varied and applied to a different kinds of a forces, but a definitely as always, a new principles were needed, a principles that would, at least, characterize the whole of the process without any specification to any detail along any machine. Therefore, a new principles has had included that a stipulation, like for instance, that the mass of a system always stayed the same, whether, that the energy of a system remained constant along a time, and this is what it has had been all about. -- Ahmed Ouahi, Architect Best Regards! > Steve son,you have been sleeping all your existence, a silly attempt to > fit a 1898 science fiction novel into a formal framework should now [quoted text clipped - 67 lines] > > > > Steve Carlip Look,if you can believe the fiction then good for you. As a compromise I have often posted an excellent article from the mid 19th century from genuine theorists who realised they had reached a dead end ,50 years later they created a fiction to overcome the dilemma existing in Newton's calendrically driven clockwork solar system. Look at the top right column - http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id=bm.1 843.10.x.54.336.x.425 They dumped an aether on Newton through 'absolute space' anyway and pretended to reject it all over again. These dusty characters from the 20th century were well pleased with themselves and their localised solution for planetary motion but this was before the solar system's motion in one direction around the galactic axis was discovered.Do you not think that after 80 years that some bright spark might consider grafting in the affects of compound motions such as planetary motion around the Sun and simultaneously moving with the solar system in one direction around the galactic axis. > For the time being, as along that moment, Henri Poincaré has had lights, a > mathematical physics as it has had received along himself, its first a [quoted text clipped - 92 lines] > > > > > > Steve Carlip Therefore, what would follows, has ha beed addressed to the foundations of a geometry, geodesy, physics and philosophy, by Henri Poincaré himself as it would be an other fiction for you : 1 - There is no absolute space, and we only conceive of relative motion, and yet in a most cases mechanical facts are enunciated as if there is an absolute space to which they can be refered. 2 - There is no absolute time. When we say that two periods are equal, the statement has no meaning, and can only acquire a meaning by a convention. 3 - Not only have we no direct intuition of the equality of two periods, but we have not even direct intuition of the simultaneity of two events occurring in two different places. I have - Henri Poincaré - exolained this in an article entitled " Mesure du Temps ". 4 - Finally, is not Euclidean geometry in itself only a kind of convention of language? -- Henri Poincaré -- Ahmed Ouahi, Architect Best Regards! Look,if you can believe the fiction then good for you. As a compromise I have often posted an excellent article from the mid 19th century from genuine theorists who realised they had reached a dead end ,50 years later they created a fiction to overcome the dilemma existing in Newton's calendrically driven clockwork solar system. Look at the top right column - http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id= bm.1843.10.x.54.336.x.425 They dumped an aether on Newton through 'absolute space' anyway and pretended to reject it all over again. These dusty characters from the 20th century were well pleased with themselves and their localised solution for planetary motion but this was before the solar system's motion in one direction around the galactic axis was discovered.Do you not think that after 80 years that some bright spark might consider grafting in the affects of compound motions such as planetary motion around the Sun and simultaneously moving with the solar system in one direction around the galactic axis. Ahmed Ouahi, Architect wrote: > For the time being, as along that moment, Henri Poincaré has had lights, a > mathematical physics as it has had received along himself, its first a [quoted text clipped - 96 lines] > > > > > > Steve Carlip > Therefore, what would follows, has ha beed addressed to the foundations of a > geometry, geodesy, physics and philosophy, by Henri Poincaré himself as it > would be an other fiction for you : He is indeed another cartoon character in this charade,yes. > 1 - There is no absolute space, and we only conceive of relative motion, and > yet in a most cases mechanical facts are enunciated as if there is an > absolute space to which they can be refered. Absolute and relative space ,at least in Newtonian terms,represent his idiosyncratic resolution for retrogrades and his false conclusion that planetary orbital motion is Not seen directly from Earth when it is . The Newtonian mutation of the Copernican resolution for heliocentric motion is not at all complex but it is geometric therefore this business of the existence and non existence of 'absolute space' is a waste of time. > 2 - There is no absolute time. When we say that two periods are equal, the > statement has no meaning, and can only acquire a meaning by a convention. Again,the creation of the AU through celestial sphere geometry by borrowing 3 minutes 56 seconds from terrestial longitudes and inserting it into a .986 degree orbital displacement - http://www.pfm.howard.edu/astronomy/Chaisson/AT401/IMAGES/AACHCIR0.JPG Newton correctly identifies the Equation of Time and what it does - "Absolute time, in astronomy, is distinguished from relative, by the equation or correlation of the vulgar time. For the natural days are truly unequal, though they are commonly considered as equal and used for a measure of time" Newton The Equation of Time is what equalises the natural unequal day to the 24 hour day by means of the noon correction and addition or subtraction of minutes and seconds.This pre-Copernican principle was perfectly adapted by the heliocentric astronomers to the principle that the Earth has an independent axial rotation hence the two step process which creates the 24 hour day first and then its Wesytern application to axial rotation at 15 degrees per hour and 24 hours/360 degrees in total. Newton in trying to 'define' time did not even recognise the flaw in John Flamsteed's celestial sphere reasoning and the Earth's rotation. Big mistake Mr Quahi,very,very ugly mistake. > 3 - Not only have we no direct intuition of the equality of two periods, but > we have not even direct intuition of the simultaneity of two events > occurring in two different places. I have - Henri Poincaré - exolained this > in an article entitled " Mesure du Temps ". They had no intuition,period !,not Poincare,not Mach,not Albert,none of them. Now,Newton narrowed the view to suit himself and his own agenda and this is fine,I know his maneuvering and clever do it was,it now shuts the door on genuine investigators who may not wish to make grand sweeping gestures about celestial phenomena but may wish to work with an accurate version of planetary motions for climatological and geological purposes. > 4 - Finally, is not Euclidean geometry in itself only a kind of convention > of language? > > -- Henri Poincaré The house always wins and the geometric house which affirms or rejects concepts based on physical considerations spits out the Newtonian conceptions from the great heliocentric astronomical tradition.You are certainly welcome to discuss the ins and outs of your system but it all goes back to the simple flaw lurking benesth it all -celestial sphere geometry. The Newtonian mutation is harder to spot than the Tychonic but I have done my part to highlight it as absolute/relative space in the matter of retrogrades and how they are resolved . "And though some disparate astronomical hypotheses may provide exactly the same results in astronomy, as Rothmann claimed in his letters to Lord Tycho of his own mutation of the Copernican system,nevertheless there is often a difference between the conclusions because of some physical consideration [causa alicujus considerationis physicae].... But practitioners are not always in the habit of taking account of that diversity in physical matters [in physicisvarietas], . . " KEPLER Thank you for being civil and I enjoyed the polite conversation for all this is not proving people wrong but rather to recover accurate working principles. > -- > Ahmed Ouahi, Architect [quoted text clipped - 126 lines] > > > > > > > > Steve Carlip Yes indeed! But whatsoever, a people they do love a cartoons, at least, it does provides them by a strictly an other and more realistic image of the illusion turning around their existence, as it does also, makes to run farther from anything absolutely a conventional, which is the ultimate structuration of the illusion. However, you mentioned the principles, as I would be very glad to mention to you a dialogue about the principles, which it would be as follows : Lämmel : Is the world picture resulting from the conceptions of the relativity principles an inevitable one, or are the assumptions arbitrary and expedient but not necessary? Einstein : The principle of relativity is a principle that narrows the possibilities, it is not a model, just as the second law of thermodynamics is not a model. Lämmel : The question is whether the principle is inevitable and necessary or merely expedient. Einstein : The principle is logically not necessary, it would be necessary only if it would be made such by experience. But it is made only probable by experience. Therefore, for Henri Poincaré, also, principles were made probable by experience, because, they could be used against the grain of experience and always at the cost of an immense inconvenience. However, something, which it would be a systematically turned to an illusion prefabrication, a definitely as a matter a fact. -- Ahmed Ouahi, Architect Best Regards! Ahmed Ouahi, Architect wrote: > Therefore, what would follows, has ha beed addressed to the foundations of a > geometry, geodesy, physics and philosophy, by Henri Poincaré himself as it > would be an other fiction for you : He is indeed another cartoon character in this charade,yes. > 1 - There is no absolute space, and we only conceive of relative motion, and > yet in a most cases mechanical facts are enunciated as if there is an > absolute space to which they can be refered. Absolute and relative space ,at least in Newtonian terms,represent his idiosyncratic resolution for retrogrades and his false conclusion that planetary orbital motion is Not seen directly from Earth when it is . The Newtonian mutation of the Copernican resolution for heliocentric motion is not at all complex but it is geometric therefore this business of the existence and non existence of 'absolute space' is a waste of time. > 2 - There is no absolute time. When we say that two periods are equal, the > statement has no meaning, and can only acquire a meaning by a convention. Again,the creation of the AU through celestial sphere geometry by borrowing 3 minutes 56 seconds from terrestial longitudes and inserting it into a .986 degree orbital displacement - http://www.pfm.howard.edu/astronomy/Chaisson/AT401/IMAGES/AACHCIR0.JPG Newton correctly identifies the Equation of Time and what it does - "Absolute time, in astronomy, is distinguished from relative, by the equation or correlation of the vulgar time. For the natural days are truly unequal, though they are commonly considered as equal and used for a measure of time" Newton The Equation of Time is what equalises the natural unequal day to the 24 hour day by means of the noon correction and addition or subtraction of minutes and seconds.This pre-Copernican principle was perfectly adapted by the heliocentric astronomers to the principle that the Earth has an independent axial rotation hence the two step process which creates the 24 hour day first and then its Wesytern application to axial rotation at 15 degrees per hour and 24 hours/360 degrees in total. Newton in trying to 'define' time did not even recognise the flaw in John Flamsteed's celestial sphere reasoning and the Earth's rotation. Big mistake Mr Quahi,very,very ugly mistake. > 3 - Not only have we no direct intuition of the equality of two periods, but > we have not even direct intuition of the simultaneity of two events > occurring in two different places. I have - Henri Poincaré - exolained this > in an article entitled " Mesure du Temps ". They had no intuition,period !,not Poincare,not Mach,not Albert,none of them. Now,Newton narrowed the view to suit himself and his own agenda and this is fine,I know his maneuvering and clever do it was,it now shuts the door on genuine investigators who may not wish to make grand sweeping gestures about celestial phenomena but may wish to work with an accurate version of planetary motions for climatological and geological purposes. > 4 - Finally, is not Euclidean geometry in itself only a kind of convention > of language? > > -- Henri Poincaré The house always wins and the geometric house which affirms or rejects concepts based on physical considerations spits out the Newtonian conceptions from the great heliocentric astronomical tradition.You are certainly welcome to discuss the ins and outs of your system but it all goes back to the simple flaw lurking benesth it all -celestial sphere geometry. The Newtonian mutation is harder to spot than the Tychonic but I have done my part to highlight it as absolute/relative space in the matter of retrogrades and how they are resolved . "And though some disparate astronomical hypotheses may provide exactly the same results in astronomy, as Rothmann claimed in his letters to Lord Tycho of his own mutation of the Copernican system,nevertheless there is often a difference between the conclusions because of some physical consideration [causa alicujus considerationis physicae].... But practitioners are not always in the habit of taking account of that diversity in physical matters [in physicisvarietas], . . " KEPLER Thank you for being civil and I enjoyed the polite conversation for all this is not proving people wrong but rather to recover accurate working principles. > -- > Ahmed Ouahi, Architect [quoted text clipped - 7 lines] > > Look at the top right column - http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id= > bm.1843.10.x.54.336.x.425 > [quoted text clipped - 113 lines] > > > > > > > > Steve Carlip Excuse me for recycling the mid 19th century article which presents a real dilemma and not the exotic fictional ones that appeared later to support the emergence of the 1905 concept - http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id=bm.1 843.10.x.54.336.x.425 These men were reaching the walls of Newton's celestial sphere geometry and could not find a way out,rather than criticising these people I comprehend completely the situation they inherited from many different viewpoints and especially their ability to admit that whatever rut they found themselves in,there appeared to be no way out of the diemma. There actually is a way out but apparently nobody has the courage to deal with the celestial sphere core lurking behind the Newtonian system which influenced all later attempts to deal with planetary motion and solar system structure.I put it down to unfamiliarity with the original astronomical working principles however rather than react,as Newtonians were once want to do,it is becoming a pleasure to see glimpses of dialogue beginning to appear. > Yes indeed! > [quoted text clipped - 277 lines] > > > > > > > > > > Steve Carlip Nothing really matter, as I would be recycling, a little bit more deeper, as however for instance, along the physics or along an intuitive physics, which is used to keep any fastidious a track of how objects fall, bounce, and bend. Therefore, along that matter, its core intuition is a definitely the concept of the object, which occupies one place or a specific corner along a specific space, whether, it would exists for a continuous portion of a time, and follows all the directions of a motion and a force. However, these are a strictly and absolutely not a Newton's directions but something a definitely more and more closer to the medieval conception, of an energy or a momentum of a moving object, that a definitely keeps an object in a motion and gradually dissipates, and this is a simply what is all about. -- Ahmed Ouahi, Architect Best Regards! Excuse me for recycling the mid 19th century article which presents a real dilemma and not the exotic fictional ones that appeared later to support the emergence of the 1905 concept - http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id= bm.1843.10.x.54.336.x.425 These men were reaching the walls of Newton's celestial sphere geometry and could not find a way out,rather than criticising these people I comprehend completely the situation they inherited from many different viewpoints and especially their ability to admit that whatever rut they found themselves in,there appeared to be no way out of the diemma. There actually is a way out but apparently nobody has the courage to deal with the celestial sphere core lurking behind the Newtonian system which influenced all later attempts to deal with planetary motion and solar system structure.I put it down to unfamiliarity with the original astronomical working principles however rather than react,as Newtonians were once want to do,it is becoming a pleasure to see glimpses of dialogue beginning to appear. Ahmed Ouahi, Architect wrote: > Yes indeed! > [quoted text clipped - 143 lines] > > > > Look at the top right column - http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id= > > bm.1843.10.x.54.336.x.425 > > [quoted text clipped - 129 lines] > > > > > > > > > > Steve Carlip > Nothing really matter, as I would be recycling, a little bit more deeper, as > however for instance, along the physics or along an intuitive physics, which [quoted text clipped - 5 lines] > specific space, whether, it would exists for a continuous portion of a time, > and follows all the directions of a motion and a force. The mathematicians idea of 'intuition' is often a poor imitation of real intuitive intelligence.Intuitive intelligence affirms or rejects notions based on physical considerations therefore it encompasses all intellectual reasoning and facts brought to bear on topics such as solar system motion and structure.The celestial sphere structure of Newtonian ballistics is unworkable hence there is never a real need to work with the later exotic notions such as relativity as other such junk. The empirical world of Newton is all arrows pointing somewhere rather than dealing with planetary geometry in motion,insofar as the core of that Newtonian agenda is the wrong value for axial rotation or what amounts to the same thing,the justification of a return of a star to a meridian in 23 hours 56 min through the axial and orbital motions of the Earth.You seem perfectly happy and comfortable with celestial sphere geometry and its 'warped ' nature so have a ball. > However, these are a strictly and absolutely not a Newton's directions but > something a definitely more and more closer to the medieval conception, of [quoted text clipped - 336 lines] > > > > > > > > > > > > Steve Carlip For the time being, this is a precisely, what it has had been and it is in the meantime all about, the geometry of the space! However, along that time, already Poincaré, has had discovered a magical new attempt to a celestial mechanics along a differential equations, which would be, about anything as about any moment and how anything and any moment would and can a definitely change from that moment to an infinitesimal other things or a moment. Therefore, usually as a French it is always a full of thinkers, they do know already, that along that matter, there is no need to turn around any predictions or any intuitions neither, as Poincaré also emphasized along and again, however, that a mathematical statements would be made in the language of non-Euclidean just as well as in an Euclidean geometry. However, whether, along the philosophical matter of Poincaré, has had been mentioned the limits of a scientific knowledge, and the restricted power of an observation and the active purpose and what the mind must as would as can play along a making science. -- Ahmed Ouahi, Architect Best Regards! Ahmed Ouahi, Architect wrote: > Nothing really matter, as I would be recycling, a little bit more deeper, as > however for instance, along the physics or along an intuitive physics, which [quoted text clipped - 5 lines] > specific space, whether, it would exists for a continuous portion of a time, > and follows all the directions of a motion and a force. The mathematicians idea of 'intuition' is often a poor imitation of real intuitive intelligence.Intuitive intelligence affirms or rejects notions based on physical considerations therefore it encompasses all intellectual reasoning and facts brought to bear on topics such as solar system motion and structure.The celestial sphere structure of Newtonian ballistics is unworkable hence there is never a real need to work with the later exotic notions such as relativity as other such junk. The empirical world of Newton is all arrows pointing somewhere rather than dealing with planetary geometry in motion,insofar as the core of that Newtonian agenda is the wrong value for axial rotation or what amounts to the same thing,the justification of a return of a star to a meridian in 23 hours 56 min through the axial and orbital motions of the Earth.You seem perfectly happy and comfortable with celestial sphere geometry and its 'warped ' nature so have a ball. > However, these are a strictly and absolutely not a Newton's directions but > something a definitely more and more closer to the medieval conception, of [quoted text clipped - 9 lines] > real dilemma and not the exotic fictional ones that appeared later to > support the emergence of the 1905 concept - http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id= > bm.1843.10.x.54.336.x.425 > [quoted text clipped - 173 lines] > > > > > > Look at the top right column - http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id= > > > bm.1843.10.x.54.336.x.425 > > > [quoted text clipped - 144 lines] > > > > > > > > > > > > Steve Carlip > For the time being, this is a precisely, what it has had been and it is in > the meantime all about, the geometry of the space! [quoted text clipped - 19 lines] > Ahmed Ouahi, Architect > Best Regards! The French mathematician Blaise Pascal expressed something of the great Western civilisation and its balance between intuitive intelligence and intellectual intelligence before the anti-intuitive empirical doctrines or the 'scientific method' emerged.Free to 'define' whatever they liked,mathematicians even defined 'intuition' to suit their agenda and the great Western civilisation has been descending to this ridiculous level ever since. There is no such thing as counter-intuitive,there is such a thing as counter-productive and that now stands as the difference between the intuitive mind and the mathematical mind,in this dark era of black holes and blacker hearts,the great balance is now almost lost with an anonymous pseudo-authority at the helm. "But the reason that mathematicians are not intuitive is that they do not see what is before them, and that, accustomed to the exact and plain principles of mathematics, and not reasoning till they have well inspected and arranged their principles, they are lost in matters of intuition where the principles do not allow of such arrangement. They are scarcely seen; they are felt rather than seen; there is the greatest difficulty in making them felt by those who do not of themselves perceive them. These principles are so fine and so numerous that a very delicate and very clear sense is needed to perceive them, and to judge rightly and justly when they are perceived, without for the most part being able to demonstrate them in order as in mathematics, because the principles are not known to us in the same way, and because it would be an endless matter to undertake it. We must see the matter at once, at one glance, and not by a process of reasoning, at least to a certain degree. And thus it is rare that mathematicians are intuitive and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning. Not that the mind does not do so, but it does it tacitly, naturally, and without technical rules; for the expression of it is beyond all men, and only a few can feel it." Pascal Pensees > Ahmed Ouahi, Architect wrote: > > Nothing really matter, as I would be recycling, a little bit more deeper, [quoted text clipped - 405 lines] > > > > > > > > > > > > > > Steve Carlip As you have had end it beautifully, it is that way it would be! Otherwise, it would take to swin along the topology, something maybe it would be mentioned soon enough... -- Ahmed Ouahi, Architect Best Regards! Ahmed Ouahi, Architect wrote: > For the time being, this is a precisely, what it has had been and it is in > the meantime all about, the geometry of the space! [quoted text clipped - 19 lines] > Ahmed Ouahi, Architect > Best Regards! The French mathematician Blaise Pascal expressed something of the great Western civilisation and its balance between intuitive intelligence and intellectual intelligence before the anti-intuitive empirical doctrines or the 'scientific method' emerged.Free to 'define' whatever they liked,mathematicians even defined 'intuition' to suit their agenda and the great Western civilisation has been descending to this ridiculous level ever since. There is no such thing as counter-intuitive,there is such a thing as counter-productive and that now stands as the difference between the intuitive mind and the mathematical mind,in this dark era of black holes and blacker hearts,the great balance is now almost lost with an anonymous pseudo-authority at the helm. "But the reason that mathematicians are not intuitive is that they do not see what is before them, and that, accustomed to the exact and plain principles of mathematics, and not reasoning till they have well inspected and arranged their principles, they are lost in matters of intuition where the principles do not allow of such arrangement. They are scarcely seen; they are felt rather than seen; there is the greatest difficulty in making them felt by those who do not of themselves perceive them. These principles are so fine and so numerous that a very delicate and very clear sense is needed to perceive them, and to judge rightly and justly when they are perceived, without for the most part being able to demonstrate them in order as in mathematics, because the principles are not known to us in the same way, and because it would be an endless matter to undertake it. We must see the matter at once, at one glance, and not by a process of reasoning, at least to a certain degree. And thus it is rare that mathematicians are intuitive and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning. Not that the mind does not do so, but it does it tacitly, naturally, and without technical rules; for the expression of it is beyond all men, and only a few can feel it." Pascal Pensees > > Nothing really matter, as I would be recycling, a little bit more deeper, > as [quoted text clipped - 42 lines] > > real dilemma and not the exotic fictional ones that appeared later to > > support the emergence of the 1905 concept - http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id= > > bm.1843.10.x.54.336.x.425 > > [quoted text clipped - 183 lines] > > > > > > > > Look at the top right column - http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id= > > > > bm.1843.10.x.54.336.x.425 > > > > [quoted text clipped - 167 lines] > > > > > > > > > > > > > > Steve Carlip > Steve son,you have been sleeping all your existence, a silly attempt to > fit a 1898 science fiction novel into a formal framework should now [quoted text clipped - 27 lines] > > Johannes Kepler Below Newton discussed *phenomema*. Newton roughly agreed with Kepler about what really happens. Apparently you argue that the sun exactly "sticks immobile in one place", like Newton apparently assumed for the stars. To what does the sun stick, do you think? Harald > _______________________________________________ > [quoted text clipped - 17 lines] > > * http://members.tripod.com/~gravitee/phaenomena.htm > > Steve son,you have been sleeping all your existence, a silly attempt to > > fit a 1898 science fiction novel into a formal framework should now [quoted text clipped - 34 lines] > > Harald The working principles of Kepler are pure Copernican insofar as he derives his orbital geometry by making comparisons between the orbital motion of Earth and that of Mars - "Copernicus, by attributing a single annual motion to the earth, entirely rids the planets of these extremely intricate coils [spiris], leading the individual planets into their respective orbits [orbitas],quite bare and very nearly circular. In the period of time shown in the diagram, Mars traverses one and the same orbit as many times as the 'garlands' [corollas] you see looped towards the centre, with one extra, making nine times, while at the same time the Earth repeats its circle sixteen times " Astronomia Nova 1609 http://mitpress.mit.edu/journals/pdf/POSC_13_1_74_0.pdf Newton ,and by association all empiricists, mistake the Panis Quadragesimalis diagram on page 86 as being geocentric hence Newton's cockeyed view of retrogrades and their resolution - "For to the earth planetary motions appear sometimes direct, sometimes stationary, nay, and sometimes retrograde. But from the sun they are always seen direct.." Newton The periodic times argument of Kepler in inserting the orbit of the Earth between Venus and Mars is based on orbital comparisons and having nothing to do with the background stars much less a dumb re-introduction of the Sun around the Earth as a valid principle. What Newton is doing is creating the AU by transfering orbital comparisons to mean Sun/Earth distances hence empiricists are known through linking axial rotation directly to celestial sphere geometry or "the fixed stars at rest".It is not just wrong,it is narrow and fraudulent at the same time and the major crack in this 3 century episode of junkl attached to astronomy. At least you are civil and I sincerily thank you for that. > > _______________________________________________ > > [quoted text clipped - 17 lines] > > > > * http://members.tripod.com/~gravitee/phaenomena.htm |
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