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collegekid
Jan 25, 2007, 3:50 AM
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miademus wrote: is it possible that parallel cross, you tihnk so?!? are you thinking of beyond? "changed the thread,in some ways so that everyone gets the meaning"
Step 1: Draw parallel lines on a peice of paper.
Step 2: Cut the lines off of the paper.
Step 3: Cross the lines.
TADA!
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miademus
Jan 25, 2007, 10:41 AM
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..well yeah good ole' power of magic.
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rrrADAM
Feb 2, 2007, 11:35 PM
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Oh yea... petsfed:
In regards to your interest in the CMB and its clues to the perturbations that formed what we see today in the cosmos...
You may want to check out a Portugeuse(sp?) Cosmologist and Theoretical Physicist named
Joao Magueijo.
He has a great theory called Variable Speed of Light (VSL), and he's published a paper in the Physical Review D: "Time Varying Speed of Light As a Solution to the Cosmological Problems"... He also has published a book outlining this theory called Faster Than The Speed Of Light, c.2003. His theroy makes very strong mathmatical and theoretical arguments, and it solves the horizon and homogeneity problems of cosmology.
Its a pretty good read, and pretty funny too.
(This post was edited by rrradam on Feb 2, 2007, 11:37 PM)
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petsfed
Feb 3, 2007, 8:08 AM
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rrradam wrote: Oh yea... petsfed: In regards to your interest in the CMB and its clues to the perturbations that formed what we see today in the cosmos... You may want to check out a Portugeuse(sp?) Cosmologist and Theoretical Physicist named Joao Magueijo. He has a great theory called Variable Speed of Light (VSL), and he's published a paper in the Physical Review D: "Time Varying Speed of Light As a Solution to the Cosmological Problems"... He also has published a book outlining this theory called Faster Than The Speed Of Light, c.2003. His theroy makes very strong mathmatical and theoretical arguments, and it solves the horizon and homogeneity problems of cosmology. Its a pretty good read, and pretty funny too.
I'm familiar with it, but its too soon to really profess my faith in it. Clever stuff though. Most people are not really prepared to deal with time variable constants, but hey, that's not really my problem. It throws an interesting wrench in radiological dating, as you might be aware.
What I mean when I say perturbations on the CMB, the consensus view is that the clumps in the CMB eventually formed the galactic superclusters we see today.
(This post was edited by petsfed on Feb 3, 2007, 8:11 AM)
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pjdf
Feb 3, 2007, 3:42 PM
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petsfed wrote: rrradam wrote: Oh yea... petsfed: In regards to your interest in the CMB and its clues to the perturbations that formed what we see today in the cosmos... You may want to check out a Portugeuse(sp?) Cosmologist and Theoretical Physicist named Joao Magueijo. He has a great theory called Variable Speed of Light (VSL), and he's published a paper in the Physical Review D: "Time Varying Speed of Light As a Solution to the Cosmological Problems"... He also has published a book outlining this theory called Faster Than The Speed Of Light, c.2003. His theroy makes very strong mathmatical and theoretical arguments, and it solves the horizon and homogeneity problems of cosmology. Its a pretty good read, and pretty funny too. I'm familiar with it, but its too soon to really profess my faith in it. Clever stuff though. Most people are not really prepared to deal with time variable constants, but hey, that's not really my problem. It throws an interesting wrench in radiological dating, as you might be aware. What I mean when I say perturbations on the CMB, the consensus view is that the clumps in the CMB eventually formed the galactic superclusters we see today.
I remember reading some stuff about possible time variations in the fine structure constant 6 or 7 years ago. But, at that time, the thought was that changes would have been much larger much closer to the start of the universe so that radiological dating wouldn't be particularly effected (most of what we date is < ~4.6 Ga, given that our solar system had all of its isotope system reset at that time). Is the thinking on that different now?
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petsfed
Feb 3, 2007, 7:02 PM
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pjdf wrote: petsfed wrote: rrradam wrote: Oh yea... petsfed: In regards to your interest in the CMB and its clues to the perturbations that formed what we see today in the cosmos... You may want to check out a Portugeuse(sp?) Cosmologist and Theoretical Physicist named Joao Magueijo. He has a great theory called Variable Speed of Light (VSL), and he's published a paper in the Physical Review D: "Time Varying Speed of Light As a Solution to the Cosmological Problems"... He also has published a book outlining this theory called Faster Than The Speed Of Light, c.2003. His theroy makes very strong mathmatical and theoretical arguments, and it solves the horizon and homogeneity problems of cosmology. Its a pretty good read, and pretty funny too. I'm familiar with it, but its too soon to really profess my faith in it. Clever stuff though. Most people are not really prepared to deal with time variable constants, but hey, that's not really my problem. It throws an interesting wrench in radiological dating, as you might be aware. What I mean when I say perturbations on the CMB, the consensus view is that the clumps in the CMB eventually formed the galactic superclusters we see today. I remember reading some stuff about possible time variations in the fine structure constant 6 or 7 years ago. But, at that time, the thought was that changes would have been much larger much closer to the start of the universe so that radiological dating wouldn't be particularly effected (most of what we date is < ~4.6 Ga, given that our solar system had all of its isotope system reset at that time). Is the thinking on that different now?
Its more than just the fine structure constant. When you make all 25 fundamental constants variable over large time, it radically restructures the game of radiological dating.
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GunksMonkey
Feb 5, 2007, 6:29 AM
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parallel lines will cross if the space they travel through is curved
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rrrADAM
Feb 7, 2007, 9:39 PM
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petsfed wrote: I'm familiar with it, but its too soon to really profess my faith in it. Clever stuff though. Most people are not really prepared to deal with time variable constants, but hey, that's not really my problem. It throws an interesting wrench in radiological dating, as you might be aware.
Not sure what you are familiar with as far as VSL goes, as the main premise of the theory is that its effects were long before the moment of decoupling, thus there was not even one atom to decay yet, so no radiometric dating.
Also, as I said, it accounts for the horizon and homegineity problems that 'inflation' is a possible solution for.
Even the CMB shows a homogenous universe locally, and even cosmologically depending on the detail of resolution you apply to the temperature.
We agree about the fine detail changes shown in the CMB becoming the galaxy clusters we see today... VSL is a possible source for these perturbations through time (thus things happening at different rates) varying from location to location.
'Faith' in any theory which has not proven consistant with observation and experiment would be premature, and ill suited for science... However, the more theoretically and mathmatically consistant theories one is versed with gives him a larger knowledge base (or even imagination) to form their own objective opinions... This is how new theories are born. Those that think inside the box are not theroetical physicists.
(This post was edited by rrradam on Feb 7, 2007, 9:55 PM)
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petsfed
Feb 7, 2007, 10:54 PM
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Ah, I see. The same thing has been proposed to deal with the appearance of "dark matter", and that has the more direct effect on radiometric dating.
I suppose if it could happen in one period of time it could happen in any other period of time. To be certain though, it will drive determinists batty trying to figure out why the rate of change of the speed of light is non-constant.
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baja_java
Feb 7, 2007, 11:59 PM
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one problem with the "debate" so far is the assumption that if you drew two parallel lines on Earth, the lines would inherently curve around the globe following exactly the curvature of the Earth. this is only true if the table on which you drew the lines has a subtle warped curvature that is exactly concentric with that of the Earth. i've never seen a table that matches the curvature of the Earth that precisely, and can be placed so perfectly
short answer: if you drew two parallel straight lines on a flat surface, then yes, they're parallel, and the lines defined by their abstract extensions will stay parallel as they shoot off into space in either direction, across the universe that we've assumed infinite. and each of these parallel lines can touch a perfectly spherical Earth only at one tangential point if you were to lower them from your desk and onto the surface of this hypothetically spherical Earth
In reply to: 1) It is some time usefull when thinking about continuity to consider the real plane as including "the point at infinity". Parrallel lines do intersect at this point but you have to ask if it is really a point
parallel straight lines converge at this point only as an approximation. but actually, in the infinite universe that is assumed, if you hop into a taxi and follow the abstract extensions of the two parallel lines to wherever said "point at infinity" you've selected, arriving at that point, when you step out of the taxi and look, you'll again see space stretching out into infinity in all directions, and the parallel lines are still parallel at that point. if you must, you can again select another point in the far distance where the parallel lines would converge via the same mathematical approximation and deem that as your next "point at infinity." you can get back into the taxi and go all the way out there again and experience the same thing. that's if you don't first run out of cab fare
and please make the distinction between light and lines abstractly drawn. the former has energy and momentum, hence coupled to gravity and hence the observable bending of light by gravity of stars or black holes as well as whatever other dense holes. and the latter has no energy or momentum, and no mass unless you're actually going to hire a contractor and build parallel lines that would stretch into infinity, piercing through however many abdomens and tv sets as they stretch across the Earth and hopefully at some point into space and pierce through asteroids shaped like the melon heads of idiots who don't know what the hell they're talking about
c'mon, people, not like any of this is rocket science
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ryanb
Feb 8, 2007, 12:44 AM
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In reply to: parallel straight lines converge at this point only as an approximation. but actually, in the infinite universe that is assumed, if you hop into a taxi and follow the abstract extensions of the two parallel lines to wherever said "point at infinity" you've selected, arriving at that point, when you step out of the taxi and look, you'll again see space stretching out into infinity in all directions, and the parallel lines are still parallel at that point. if you must, you can again select another point in the far distance where the parallel lines would converge via the same mathematical approximation and deem that as your next "point at infinity." you can get back into the taxi and go all the way out there again and experience the same thing. that's if you don't first run out of cab fare
You misunderstand. The point at infinitey is not identified with any point in R2 instead it and R2 make up R2+ (or it and C1 make up C1+). It is a well defined construction comeing out of the need or desire to project things on to the sphere.
http://en.wikipedia.org/wiki/Stereographic_projection
http://en.wikipedia.org/wiki/Riemann_sphere
Depeding on the map to the sphere parrallel lines either cross or cross and are perpendicular there.
Also I believe light "bends" because (in a vacume) it travells in geodesics which are the closest thing we get to lines in the curved (by mass) space we live in. The exsistence of some underlying flat space as suggested by your proposed parrallel construction project is an unfounded assumption i am unwilling to make.
(This post was edited by ryanb on Feb 8, 2007, 12:46 AM)
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baja_java
Feb 8, 2007, 1:19 AM
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ryanb wrote: Also I believe light "bends" because (in a vacume) it travells in geodesics which are the closest thing we get to lines in the curved (by mass) space we live in.
so abstractly drawn lines follow geodesics like light do?
ryanb wrote: the curved (by mass) space
in other words, space with a gravitational field, which bends light because light has energy and momentum which are coupled to gravity and hence, once again, the bending
ryanb wrote: The exsistence of some underlying flat space as suggested by your proposed parrallel construction project is an unfounded assumption i am unwilling to make.
the infinite parallel lines in question exist only as an abstract, so they can only be constructed on an abstract flat surface, with an abstract ruler that has two edges that are abstractly parallel
think straight first, before curving it into spherical space or whatever the like
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petsfed
Feb 8, 2007, 4:19 AM
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You misunderstand me. Its easy to postulate abstractions away from reality to argue such a thing, but i'm loathe to do such a thing. I just know what works, and what's (apparently) true, and I try to argue from that.
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ryanb
Feb 8, 2007, 6:48 AM
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Geodesics are a generalization of straight lines to curved space. If we are the ants on the surface of a sphere they are the straight lines we try and walk in (or build abstract parrallel lines along). Straight lines are infact the geodesics of flat space.
http://en.wikipedia.org/wiki/Geodesic
Of course math sidesteps this whole discustion by defineing to geodesics in an non euclidian plane geometry to be parrallel iff they don't intersect, makeing this whole discusion an entertaining circle jerk.
I haven't seen a good way to define parrallel in higher dimensions (equadistant doesn't work as one might not be a geodesic).
In reply to: think straight first, before curving it into spherical space or whatever the like
Not really good practice mathematically as there exsist many interesting curved spaces that can not be completely (smoothly) covered by curving up a flat space.
For example the sphere can be covered except for one point (think about trying to strech a flat piece of rubber around an apple completely covering its skin).
A curved space (smooth manifold) simply must have a complete covering of curved up patches of flat rubber. Every point is in one of these patches so locally it is similar to flat space (possibley streched a bit). However, it is quite possible for things that would never happen in flat space to happen on a scale larger then one of these patches.
Good discussion so far, its been forever since I looked at this stuff. Nice to try and remember it.
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baja_java
Feb 8, 2007, 7:00 PM
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ok, first a clarification that's somewhat critical regarding where you're looking for the solution set of points at infinity:
In reply to: 1) It is some time usefull when thinking about continuity to consider the real plane as including "the point at infinity". Parrallel lines do intersect at this point but you have to ask if it is really a point
In reply to: You misunderstand. The point at infinitey is not identified with any point in R2 instead it and R2 make up R2+ (or it and C1 make up C1+). It is a well defined construction comeing out of the need or desire to project things on to the sphere.
this latter is only true if you're looking for points infinitely away from a plane or lines that span the R2 space. in the case of a plane, the solution points exist at infinite distance away from the frontside of this plane and also away from the backside of this same plane. the solution space is therefore indeed noncoplanar and out of R2 space, in R2+, namely R3. but in the case of the two parallel lines, we're not looking for the set of points that are infinitely far away from the plane spanned by the two parallel lines, nor infinitely away from these infinite lines themselves. the solution set we're actually looking for is just the two points the pair of parallel line are each pointing at out at infinity in one direction, plus the two other points the other ends of the parallel lines are pointing at in the opposite direction. all four of these points at infinity are still coplanar with the lines themselves, in R2, because they lie on the two parallel lines. even if the two points pointed at in one direction by the parallel lines could move toward each other and become one point (likewise for the other two points pointed at in the opposite direction), the two resulting merged points (one in each direction) are still coplanar with the lines, and what i'm saying is that this convergence to become one point doesn't actually take place at infinity. that it only happens at infinity because you applied the mathematical limit to obtain a convergence.
also, if by "point at infinity" you had meant an abstract point at infinity, instead of a physical point at a great enough distance that approximates infinity, then what i said before still holds true, that a pair of abstract parallel lines would converge at this abstract point of infinity only as a mathematical approximation. in actuality, at this abstract point of infinity where the set of parallel lines have extended to, if you could actually be there to see for yourself as they arrive, the lines would still come in parallel, coming in from a point of origin that would now be, from that other perspective, equally abstract and infinitely distant
this drawing of parallel lines according to light paths along parallel geodesics in a gravitational field, just because that's the closest you have doesn't mean they actually are.
these parallel geodesics the light paths will follow, are they actually parallel geodesics that are generated by all the actual gravitational sources of the actual universe and free of any mathematical approximations of any order? because we don't have an actual gravitational model of the actual universe. just theoretical approximations. if parallel lines drawn in that particular way turn out the slightest bit abstract because they're based on any abstract approximations, you'd have to reject them as well. and by definition, parallel geodesics stay parallel, and would only converge in the limit to infinity, as in parallel lines drawn according to this mathematical model would only converge via a mathematical approximation, unless they're ultra parallel geodesics, in which case they'll never ever touch, not even in the limit to infinity, like strangers in the night, exchanging glances along separate ultra parallel geodesics that would never ever really be exchanged
now if you're comfortable with abstract parallel lines, so yeah, i know for sure that a set of parallel lines does indeed stay parallel all the way to a point of infinity because, and i swear that this is the truth and nothing but the truth, i've seen this first hand, that i've been to such a point of infinity, that i've seen this, numerous times. way the hell out there at infinity, i've seen bunches of sets of parallel lines all over the place, going to and from different directions, reaching whichever point of infinity each pair was constructed to reach. so obviously others out there have been pondering this too, whoever they are. and they've actually been able to physically construct perfectly parallel lines out of whatever super stiff and super strong material that each is made of and stretching them all the way to wherever to prove that a pair of parallel lines does indeed stay parallel. and i was able to go and have a look at all this because, yeah, our space program is actually further along than most people are aware. we've already found another life-supporting planet, by the way, at a distant star system, and have the transportation to get there in couple of hours. this is important because we also know exactly when the next big comet will completely destr-- uh i mean -- impact the Earth. tickets have already been issued to those who are, hmm, how can i delicately put this, uh, worth saving. well, i have my ticket. hope you have yours too
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ryanb
Feb 8, 2007, 7:41 PM
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No. Parrallel lines don't converge together in an infinite limit. By definition this would mean that for every esilon greater than zero there exsistes some large number D such that beyond D the lines are closer then epsilon. But the lines are a fixed distance P apart so this is not true for Epsilon less then P and they don't converge.
R2+ is not R3 though it can be embeded in R3. R2+ is topologicaly equivelent to the sphere and thus fundementally diffrent from R2 or R3 which is where you are getting confused. In R2+ a line is just a circle through the point at inifinity and all lines projected from the real plane into R2+ cross at said point. It might feel like the plane if you are sitting on it but it is not the plane, it has a different topology and can be given diffrent metrics (ie you can squish and strech a sphere into lots of diffrent shapes).
Lines projected from the plane might even fail to be geodesics in some cases... parallel certainly has a diffrent definition (not crossing till the point at inifinity).
The point at inifinity is a physical point in R2+. Since we have so far only experienced our universe locally it might not be topologically flat R4...even if our best estimates of its total curvature indicate that it is, on the whole, flat there might be some region out there that violates that, where it wraps around in odd ways.
I have no ticket off this place, if I hear a comet comeing I think I'll go hop on the Bachar-Yerian, I mean there'd be no excusse not to.
Though perhapse this route:
http://www.stanford.edu/~clint/yos/quantum.gif
would be more apropriate for this discusion (Id have to be a fair bit stronger to do that one comet or no)
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baja_java
Feb 8, 2007, 11:13 PM
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yes, R2+ not the same as R3. went too quick there. was just trying to say out of R2 space and in R2+
and you're right, parallel lines don't converge at all. tried too and could only prove they stay parallel in the infinite limit. had thought you were suggesting their convergence at infinite limit with:
In reply to: 1) It is some time usefull when thinking about continuity to consider the real plane as including "the point at infinity". Parrallel lines do intersect at this point but you have to ask if it is really a point
because above sounds odd. clarify? be as precise and descriptive as you like (pm if you like), esp about how exactly does that "intersect" occur, and what that "point/non-point" is. that plane still a real plane if it includes "the point at infinity?" meant as the one and only possible "point at infinity?"
so, parallel lines don't intersect at all. they do stay parallel to infinity. not sure if drawing parallel lines with an abstract geodesic model is really that less abstract than drawing two parallel lines with an abstract ruler with parallel edges on an abstract flat surface
i'm just curious, and yeah, think this is fun too
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jeremy9876543
Feb 9, 2007, 2:09 AM
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miademus wrote: is it possible that parallel cross, you tihnk so?!? are you thinking of beyond? "changed the thread,in some ways so that everyone gets the meaning"
Anyone ever see my ski tracks?
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oldsalt
Feb 10, 2007, 4:52 AM
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rrradam wrote: Also, I for one believe that space is granular and discrete, thus it IS an un-understood medium, but this line of thinking is 'taboo', as it smaks of the ether. It is accepted that space behaves as if it were a something and this is consistant with experiment and observation, but it is also accepted to be a nothing despite this, and that is a contradiction.... But that is another topic for discussion all together.
I agree, and I believe that the solution to the multi-dimensional excesses required to make superstrings work is due to the idea that the strings themselves move. Not to mention link and break and ....
If space is granular, and particles emerge from harmonic vibrations, and "The sum of all of the energy in the Universe is zero" (intended to quote, not paraphrase Hawking), and by substitution:
The sum of all of the mass in the Universe is zero - e=mc^2 -> sum(e) = sum(m)*c^2 -> setting sum(e)=0 yields sum(m)=0/c^2 -> sum(m) = 0,
I see the strings as "pixels" which pass particles along like a person walking across a TV screen. The pixels don't move, just the image. Reality is an emergent phenomenon of moving harmonics across an aether-like space. Michelson and Morley were right, of course, the aether doesn't move, just the signals through it.
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rrrADAM
Feb 14, 2007, 5:03 AM
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oldsalt wrote: rrradam wrote: Also, I for one believe that space is granular and discrete, thus it IS an un-understood medium, but this line of thinking is 'taboo', as it smaks of the ether. It is accepted that space behaves as if it were a something and this is consistant with experiment and observation, but it is also accepted to be a nothing despite this, and that is a contradiction.... But that is another topic for discussion all together. I agree, and I believe that the solution to the multi-dimensional excesses required to make superstrings work is due to the idea that the strings themselves move. Not to mention link and break and .... If space is granular, and particles emerge from harmonic vibrations, and "The sum of all of the energy in the Universe is zero" (intended to quote, not paraphrase Hawking), and by substitution: The sum of all of the mass in the Universe is zero - e=mc^2 -> sum(e) = sum(m)*c^2 -> setting sum(e)=0 yields sum(m)=0/c^2 -> sum(m) = 0, I see the strings as "pixels" which pass particles along like a person walking across a TV screen. The pixels don't move, just the image. Reality is an emergent phenomenon of moving harmonics across an aether-like space. Michelson and Morley were right, of course, the aether doesn't move, just the signals through it.
Thanx for the 'nod', so to speak, but I am not of the 'stringy' point of view of reality...
Please refer to the detailed replies in this thread for starters:
http://www.rockclimbing.com/...ring=string;#1491004
Personally... I think we are amiss somewhere in our understanding of the fine details of quantum mechanics, even far above the Plank levels... As we all know: the finer detail the resolution, the more chaotic it gets.
Robert Laughlin (Nobel Prize 1995?, for his work on the quantum hall effect) makes very strong arguments for the end of 'The Age of Reductionalism' and the dawn of the 'Age of Emergence' in his recent book A Different Universe: Reinventing Physics From the Bottom Down. Basically, he makes argues/shows that at quantum levels only what emerges, usually through selforganization, is important and relevant to reality...
As an example: Think quantum mechanically about the computer you're reading this thread on right now, as we don't know the location of all the electrons within it, but instead the 'bulk' of them, and what the 'bulk' of them will do or are doing, and the emergent effects of that... Thus, we can make reliable computers.
Or... Consider matter before and after a phase transition, as water is liquid then steam, there is no 'gray inbetween'... The changes are abrupt, and happen at a clearly defined temperature (and pressure). Reducing the molecules and atoms tells you nothing about it, as a molecule of H2O is the same whether it is ice, water or steam-it only moves differently, so reductionalism tells you nothing about it in regards to its state.
(This post was edited by rrradam on Feb 14, 2007, 5:40 AM)
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carabiner96
Feb 14, 2007, 5:44 AM
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I know it's a little late for my .02, but I can't believe this thread has come to this.
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the_climber
Feb 14, 2007, 5:49 AM
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carabiner96 wrote: I know it's a little late for my .02, but I can't believe this thread has come to this.
UUuughhh! I am way to drunk to make any responce other than...
Hellloooooooooooo!!!!!!!!!!!!!!!1 as soon as they cross, they ain't parallel any more!
and,
if it were on a plain of glass and you looked directly in line with the plain... they would apear to cross the whole distance....
and I don't care about spelking right now,
aahahahaha
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