Another Way Of Viewing The Flat Lander

One of the most daunting claims made by modern mathematical physicists is that they can infer the existence of dimensions more than the 3 by taking measurements while stuck in the 3d so call manifold. Many people fall into the temptation due to the desire to find a place to hid god, angels, demons and santas to the extend that they never bother to check if the breath taking claims by the mathematicians conduct electricity. Does it even make sense? What if someone tells you that he is going to prove to you that devil is inside your shoe polish can. Surely, before you open the can, he must first tell you how the devil look. What if he says that he can't even imagine the devil? What is he going to prove by opening the can? Allright you have gotten, he will not be knowing what the hell he is doing!GEOMETRY IS NOT MATHEMATICSIt all begun when mathematicians cheated themselves that geometry is mathematics. In other words, geometry is NOT a purely 'HOW MUCH' issue. It has a very meaningfull 'WHAT IS' issue that falls outside the juridiction of pure mathematics. A mathematician will want to understand PARRALEL LINES as lines that never meet no matter how far they extend. He is trying to answer a 'WHAT IS' question with an 'HOW FAR' answer! He is not trying to simple contemplate on WHAT parallel lines are. He is busy wondering how far he will get with his neverending tape measure before he conclude that the two lines are indead parallel, sidestepping the MEANING of parallel lines! Mathematician is an idiot when it comes to a 'WHAT'. He is not interested with what things are. He is just interested with how big they are!No matter how sharp your pencil is, how smooth your paper is, how white it is, lines, triangles, dots etc are THINGS and not mere abstract concepts. a line is a SOLID. It is not 1d. It is a genuine 3d OBJECT. Geometry is PHYSICS, an empirical science done by OBSERVATION. The only way to define parallel ines, straight ones, triangles, perpendicular lines etc is to SHOW them! No words or equations can adequately express these concepts. Therefore a flat lander traped in a 2d tissue paper trying to INFER 3d is a meaningless idea.An equation of the form s^2=x^2 y^2 does not mean that s,x and y are sides of a triangle a right angled triangle! The only way to determine the othorgonality of s,x and y is to look at the triangle! Yet this is the only reason Minkowsky ends up claiming that time is a fourth dimension!To add insult to injury, mathematician ends up thinking that an equation of the form z=Ax^2 By^2 necesarily describe a curved surface so that z must be a fourth dimension relative to x and y!ALTERNATIVE TO FLAT LANDERIt is at this point where I step in to introduce another way of understanding a curved space. This is designed to show that it is impossible for a flat lander to conclusively infer a third axis while trapped in 2d. And then of course all the modern physics speculations of 'multidimensional reality' goes on its way to dustpin!At the centre of a piece of paper, draw a series of equaly spaced concentric circles. Then draw a cartecian grid whose origin is that concenter of those circles. If z is the radius of an abitrary concentric circle, it is possible to have an equation of the form z=Ax2 By2 by simply chosing an apropriate values of A,B, x and y. The gist of my argument is that since the flat lander cannot imagine the z axis, he can as well conclude that the information supposedly containg the curvarture of the piece of paper(A&B) rather shows how lines are related to each other within the flat piece of paper!It is even far more apt in general relativity because I can take z as the unknown length of a ruler under no gravity (in free space), x is the length of the same ruler placed horizontaly near a gravitating object (so the length contracts) and y is the length of the same ruler placed vertically. So the relation dz/dx gives the relativist length contraction etc and A=D^z/dx^2 and B=D^2z/dy^2 contains information about curvature of the manifold which you have now seen that it is just rates at which lenghts in various orientations are contracted to the second derivative. Einstein's field equations is just about relating such values as A and B to the mass and the energy of gravitating objects.FLAT LANDER IN THE BALOONThis is truely curious case where the flat lange head straight bearing neither to the left nor to the right only to land at the very place he started! Will the flat lander still not conclude that he leaves traped on the surface of the cylinder? The answer is 'no' simply because relativity brings ambiguity as to what 'bearing neighther to the left nor right' supposed to mean.To illustrat it, consider consider a sun with several planets orbiting aroun it. Let the farther away the planet, the faster it revolves around the sun. So we have our 'flat lander' doing geometry on the the space he is moving past. Remember that in relativity, the faster we move, the more the length contracts. So as we move farther and farther from the sun, we eventually hit at the one revolving around the sun at the speed of light. What would be the circumfrence of its orbit as measured by the 'bed bug' in that planet? Allright, it will be zero! So it realy doesn't matter if the the flatlander uwittingly moved around all the way to the other end since any such distance amounts to zero in his frame of referance. So he can still amuse himself that he is bearing neither to the left nor to the right but voila! He is comming from the other end of the cosmos!!

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"Good blog here Drekx :) some of what you talked about was not mentioned in the Your Galactic Neighbors book by Sheldan that I'm reading again so it's good to see new info available."

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