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From: George Dishman on 23 Aug 2005 14:37 "Henri Wilson" <H@..> wrote in message news:d3qkg1heo89vgbdej1stb6bu3c1tq5o708(a)4ax.com... > On Mon, 22 Aug 2005 20:02:34 +0100, "George Dishman" > <george(a)briar.demon.co.uk> > wrote: >>"Henri Wilson" <H@..> wrote in message >>news:9k1ig11oa73n2ln6mcgf2e72dl135d0efn(a)4ax.com... >>> On Sun, 21 Aug 2005 11:46:50 +0100, "George Dishman" >>> <george(a)briar.demon.co.uk> >>> wrote: >>But the velocity curve will have double the >>amplitude, that's why it is essential that >>you put scales on the curves. > > The shapes are the most revealing feature but, yes, I can do that fairly > easily. The maximum velocity and the zero are provided at present so it > isn't > hard to work out. Excellent, thanks. > I suppose I can now do that. I wanted to avoid negative values but it > doesn't > really matter. > Trouble is, I will have to make assumptions about the star's actual > luminosity. No, just show the scale as the relative change. If the actual luminosity is 1 and motion reduces it to 1%, the Y coordinate would be +5. Remember positive numbers represent reduced brightness. That would be important if the reference is in mag as it might invert the graph from what you expect. >>If my intuition is correct, for a circular orbit >>the mininimum of the intensity curve should >>correspond to the velocity curve passing through >>the midpoint and changing from blue shift to >>red shift. I could be wrong though. Disregard that guess, I now think I was wrong. > I've just written a program to try to work out how an emission line would > appear doppler shift according to the huff puff principle. > Light from the middle, would have te maximum shift but light from the > edges > would have none....because the expansion would be normal to LOS. > It turns out that there is a sinusoidal distribution of radial velocity > with > maximum at 45 degrees. > This means that a spectral line would appear broadened from zero to > maximum > with maximum intensity at 1/root2 from the max. Remember there will also be thermal broadening and that the lines are from a range of depths and hence temperature. >>No, it is correspondence of both shapes, both >>amplitudes and the phase, otherwise you have >>too many adjustable parameters for the result >>to have any meaning. You should have all that >>information produced by your model anyway, just >>add the scales so everyone can see. > > It will take time but I can do it. Great. That will allow a serious discussion. George
From: George Dishman on 23 Aug 2005 15:29 "Henri Wilson" <H@..> wrote in message news:9lnkg1da8etbdgtjmmknitfpks36406pmv(a)4ax.com... > On Mon, 22 Aug 2005 21:26:11 +0100, "George Dishman" > <george(a)briar.demon.co.uk> > wrote: > >> >>"Henri Wilson" <H@..> wrote in message >>news:plefg11qsoapu2dc2u7mgs53jjg5mt4o20(a)4ax.com... >>> On Fri, 19 Aug 2005 14:51:53 +0100, "George Dishman" >>> <george(a)briar.demon.co.uk> >>> wrote: > >>> George, can you not get away from the idea that 'lengths' have to be >>> measured >>> to be LENGTHS. >> >>I have to educate you somehow. If you split the >>distance between two points into x and y >>components, the values measured along those axes >>depend on the orientation of the axes. You know >>that Henri. It is splitting the distance into >>components for measurement that creates the >>variation. > > Why would you want to do that? It doesn't matter, you asked why I continue to point out that length is a measurement. Lengths of objects don't magically change 'physically' because different observers look at them, they change if the observers are measuring the lengths against different axes. However, I'll also answer that question later. > .. Why not just measure the distance directly by > placing a rod between the two points then checking the rod's length > against a > standard metre stick? > >> >>> The length of space occupied by a rod does not change with speed. The >>> proof is >>> trivial...as I have pointed out many times. >> >>I haven't seen that one but all your proofs so >>far have simply assumed 3-space and time are >>absolute, you haven't offered any proofs at all, >>just assertions. > > George, if you give a rod a short shove, does its length increase or > decrease? The pressure you apply would decrease its proper length. > Also see: www.users.bigpond.com/hewn/contraction.exe Lay a stick on the ground like this: | Measure its length with two rulers, the first like this: \ and the second like this: / In each case the method is to draw lines from the ends of the stick to the ruler, both lines being perpendicular to the ruler. Now rotate the stick slightly clockwise. The measurement on the first ruler decreases while that on the second ruler increases at the same time, yet the 'proper length' of the stick didn't change. Acceleration is a name we give to rotation in the x-t plane. Incidentally, aether theory says there _is_ a physical shrinkage due to the interaction with the aether but it is undetectable your program doesn't falsify that either because clock effects come into play that you disregard. <snip> > ... There are techniques now available for accurately > measuring the lengths of moving rods. They should give the same answer as > that > for the rod at rest. What methods are you thinking of? >>>>>>Precisely, that is exactly what I am saying. >>>>>> >>>>>>> 'Lengths of space' and 'intervals of time' are natural phenomena. >>>>>> >>>>>>No they aren't, 'space' and 'time' or 'spacetime' >>>>>>is the natural phenomenon while 'Lengths of space' >>>>>>and 'intervals of time' are numbers read off >>>>>>rulers and clocks and those relate back to axes. >>>>>>Change the orientation of the axes and you change >>>>>>only the measurement, not the underlying reality. >>>>> >>>>> ..but George, a 'length of space' can be specified very easily without >>>>> being >>>>> measured. >>>> >>>>No, a region of space can be defined but the >>>>length of that region is a measurement. >>> >>> OK, call it a region of space if you want to include more than one >>> spatial >>> dimension.. >> >>That wasn't my intention, just that "a region" is >>unquantified until you measure it. However, you >>make a good point, it is fact that there is no >>absolute direction in space that allows us to >>trade off x and y components. > > True...but we can rotate a rod in any direction and know it will occupy > the > same absolute length of space. If measured by a ruler at rest wrt the rod, that is true. If the ruler is moving wrt the rod then the axes along which the measurement is made are rotated so the measured length changes even though the proper length (absolute if you like) doesn't. > We can also construct three axes at 'right angles' even if we are hurtling > along in a sealed space capsule. We can. Now think about this observer compared to one he hurtles past. Let's say they align the x axis with the direction of movement and they use the point and time at which the pass as the origin of their x and t axes. A vector drawn from (0,0) to (0,1), one second later is a unit vector lying along the time axis. Each of them says that the (0,1) point is located with them of course since the x coordinate is zero. Can you see that these unit time vectors have an angle between them on the x-t plane which depends on the speed? If the time axes have that angle between them and each considers the x axis perpendicular to the time axis, then the x axes also have that angle between them. In other words one observer is using axes that are rotated relative to the other's. That is the answer to your "Why would you want to do that?" earlier, you don't want to but it is unavoidable. > Interestingly, even though rotation direction is not absolute, rotation > itself > IS absolutely detectable. What is really interesting is that acceleration is also absolute and acceleration is a rotation in the x-t plane. >>>>> Just take a piece of wood......that defines a length of space. >>>>> >>>>> It doesn't need a number to be a 'length of space'.. >>>> >>>>Yes it does, otherwise it is just "some space". >>> >>> Like an orbit is just 'some time'. >>> That's all it has to be for my experiment. The 'some' part is constant. >> >>Constant, but not single valued. You can trade >>space and time by rotating the x-t axes just as >>you can trade space-space by rotating the axes >>in the x-y plane. > > It IS single valued....magnitude ONE. No, it has two values, you just want to call them both "one" but I won't let you :-) >>>>When are you going to start litening to what I >>>>say instead of inventing alternatives? Look >>>>back through this post and see if you can find >>>>why I say that. >>> >>> You are repeating over and over that the orbit duration depends on who >>> measures >>> it. >> >>No, that's a nice strawman too. I am repeating that >>the values measured along an axis depend on the >>orientation of that axis. > > I really don't see the relevance of that argument. Hopefully the earlier discussion of axes has clarified that. >>> I am trying to convince you that no matter what figure you out n the >>> orbit >>> duration, it will n ot change due to clock movement. >> >>And I am trying to get you to listen when I say I >>have never disputed that each of the values is >>constant, they are just not the same value. > > I know what you are claiming. I am also trying to tell you that it can > have > only one REAL value no matter how many values it is measured to have. It has only one "proper" value which is measured at rest relative to the object but that translates to many measured values on different axes. > Measurement differences indicate measurement errors, that's all. > >>> Define the orbit duration as 1, 100, 1000 or 1000000 'time units' and >>> that >>> value will not change due to any observer activity. >> >>Of course, but you are still trying to define >>two different durations as the same 1, or 100 >>or whatever number of units. You can't do that >>and your attempt at a proof fails as a result. > > George, an orbit occupies a duration of time. No, it occupies as many durations as there are angles for the time axis for it to be measured against. > We can try to place a figure on > that duration with clocks. > The clocks are calibrated according to another time duration standard...in > our > case it is still basically the Earth's rotation period (although we now > have > something slightly more accurate). > So when you measure Jupiter's orbit with a clock, you are really comparing > it > with Earth's daily rotation. > > There has been and there will remain a constant ratio between the periods > of > Jupiter and the daily rotation of Earth. It is a dimensionless number > around > 4332.59. > Any measured difference in that ratio reveals a measurement error. > The obvious conclusion one must reach is that the clocks are not perfect. .... assuming time is absolute. An alternative philosophy is that spacetime is absolute (if you like) but that time is a measurement made along an axis can be rotated by changing the speed of the clock which is doing the measuring. >>>>>>Different components for x and y only signifies >>>>>>what you said before, that direction in space >>>>>>is not absolute. The same applies to z, y, z, t >>>>>>components in the spacetime of GR. >>>>> >>>>> 't' doesn't have a spatial direction. >>>> >>>>Inventing more things for me to say Henri? >>>>At no time did I suggest 't' was spatial. >>> >>> The 't' in GR is actually 'ct' (c=1) which has the dimensions of length. >>> ... >> >>Don't try to tell me about relativity until you >>learn it yourself Henri. You forgot that the sign >>of the terms differs. The 't' part is "-ct^2" so >>it would be 'ict' and have units of imaginary length >>whatever that might mean. Time is not the same as >>space and the equations always reflect that. I won't >>waste my time educating you any more on this, if you >>want to understand, study the subject. > > The time axis is made imaginary to keep it orthogonal. Yes, empirically we find it has to have the opposite sign from spatial dimensions. > 'c' is actually just a > scaling factor. Very good Henri, I thought that would be beyond you. Saying 299792458m = 1s has essentially the same meaning as saying that 25.4mm = 1 inch. > This is a perfectly sound mathematical treatment...but it has no physical > significance. > Space and Time are not related in any way. You can't combine furlongs and Fahrenheit, but as long as you correct the units using 299792458m=1s, you can combine time and space exactly as we can combine distance north and distance east using Pythagoras, while the negative sign distinguishes space from time. That has to be telling us something significant about the nature of our universe. George
From: Henri Wilson on 23 Aug 2005 17:59 On Tue, 23 Aug 2005 11:28:42 +0200, "Paul B. Andersen" <paul.b.andersen(a)deletethishia.no> wrote: >Henri Wilson wrote: >> On Mon, 22 Aug 2005 10:18:48 +0200, "Paul B. Andersen" >> <paul.b.andersen(a)deletethishia.no> wrote: >> >> >>>Henri Wilson wrote: >>>> >>>>The idea is indeed very stupid...and it is obviously hard for you to accept the >>>>fact that such stupidity underlies your own belief system. >>>>You have ben fooled Paul, by the world's greater ever hoaxer. >>> >>>So you know the idea: >>>"the invariance of the speed of light >>> implies the existence of a preferred frame" >>>is stupid, but you claim it anyway? >> >> >> Don't lie. I do not claim any universal preferred frame exists. >> I am one of the few TRUE relativists here. > >Can't you read? >I did NOT say that you claim a preferred frame exists. > >I said you claim that invariance of the speed of light >_implies_ that a preferred frame exist. Look Paul, the 'invariance of light speed' is a meaningless expression anyway. Do you mean invariance wrrt the source? Do you mean invariance wrt little planet Earth? Do you mean invariance of light's 'closing speed' between two objects? To me, the claim that light speed wrt all observers is invariant is a sign of some kind of mental disorder akin to acute self-delusion. However the claim doesn't necessarily require a preferred frame. Distorting space will achieve the same result. Trouble is, the same space will need an infinite number of distortions to accommodate all events that take place in it. > >Which you do. >And which is an idea so stupid that only a full blown >crank like you can claim it. > >Paul HW. www.users.bigpond.com/hewn/index.htm Sometimes I feel like a complete failure. The most useful thing I have ever done is prove Einstein wrong.
From: Henri Wilson on 23 Aug 2005 18:25 On Tue, 23 Aug 2005 19:37:05 +0100, "George Dishman" <george(a)briar.demon.co.uk> wrote: > >"Henri Wilson" <H@..> wrote in message >news:d3qkg1heo89vgbdej1stb6bu3c1tq5o708(a)4ax.com... >> On Mon, 22 Aug 2005 20:02:34 +0100, "George Dishman" >> <george(a)briar.demon.co.uk> >> wrote: >>>But the velocity curve will have double the >>>amplitude, that's why it is essential that >>>you put scales on the curves. >> >> The shapes are the most revealing feature but, yes, I can do that fairly >> easily. The maximum velocity and the zero are provided at present so it >> isn't >> hard to work out. > >Excellent, thanks. > >> I suppose I can now do that. I wanted to avoid negative values but it >> doesn't >> really matter. >> Trouble is, I will have to make assumptions about the star's actual >> luminosity. > >No, just show the scale as the relative change. >If the actual luminosity is 1 and motion reduces >it to 1%, the Y coordinate would be +5. Remember >positive numbers represent reduced brightness. >That would be important if the reference is in >mag as it might invert the graph from what you >expect. Yes I think I can do that without too much trouble. I will work on it today. My graphs will probably remain upside down though.....brightness increasing downwards. > >>>If my intuition is correct, for a circular orbit >>>the mininimum of the intensity curve should >>>correspond to the velocity curve passing through >>>the midpoint and changing from blue shift to >>>red shift. I could be wrong though. > >Disregard that guess, I now think I was wrong. Actually you were basically correct...although the phase changes slightly with observer difference. Near the critical distance, two peaks may occur, one on each side of the above point. It is a little more complicated for ellipses. >> I've just written a program to try to work out how an emission line would >> appear doppler shift according to the huff puff principle. >> Light from the middle, would have te maximum shift but light from the >> edges >> would have none....because the expansion would be normal to LOS. >> It turns out that there is a sinusoidal distribution of radial velocity >> with >> maximum at 45 degrees. >> This means that a spectral line would appear broadened from zero to >> maximum >> with maximum intensity at 1/root2 from the max. > >Remember there will also be thermal broadening >and that the lines are from a range of depths >and hence temperature. I know. It all adds up to the plain fact that 'huff puff' theories about cepheids that rely on radial velocity data will be pretty vague at best. > >>>No, it is correspondence of both shapes, both >>>amplitudes and the phase, otherwise you have >>>too many adjustable parameters for the result >>>to have any meaning. You should have all that >>>information produced by your model anyway, just >>>add the scales so everyone can see. >> >> It will take time but I can do it. > >Great. That will allow a serious discussion. OK. ,,,but the relative magnitudes are markedly dependent on distance and radial velocity anyway....and both of these are generally uncertain. >George > HW. www.users.bigpond.com/hewn/index.htm Sometimes I feel like a complete failure. The most useful thing I have ever done is prove Einstein wrong.
From: Henri Wilson on 23 Aug 2005 19:34
On Tue, 23 Aug 2005 20:29:46 +0100, "George Dishman" <george(a)briar.demon.co.uk> wrote: > >"Henri Wilson" <H@..> wrote in message >news:9lnkg1da8etbdgtjmmknitfpks36406pmv(a)4ax.com... >> On Mon, 22 Aug 2005 21:26:11 +0100, "George Dishman" >> <george(a)briar.demon.co.uk> >> wrote: > >> .. Why not just measure the distance directly by >> placing a rod between the two points then checking the rod's length >> against a >> standard metre stick? >> >>> >>>> The length of space occupied by a rod does not change with speed. The >>>> proof is >>>> trivial...as I have pointed out many times. >>> >>>I haven't seen that one but all your proofs so >>>far have simply assumed 3-space and time are >>>absolute, you haven't offered any proofs at all, >>>just assertions. >> >> George, if you give a rod a short shove, does its length increase or >> decrease? > >The pressure you apply would decrease its >proper length. Why do you introduce irrelevancies, George. My use of the term 'short shove' is just a concise way of saying, "a force is applied to one end of the rod for a short period of time so as to accelerate it to a different speed relative to the initial one. The force is then released." The question is, after the force is released, has the rod's length 'physically' increased or decreased? The point of the question is that the 'v' in SR's gamma term will have both increased and decreased depending on observer velocity. Therefore the rod will have both increased and decreased its length, according to SR. Can you see now why the proof is trivial? The rod's length cannot PHYSICALLY increase and decrease simultaneously. .. > >> Also see: www.users.bigpond.com/hewn/contraction.exe > >Lay a stick on the ground like this: | > >Measure its length with two rulers, >the first like this: \ > >and the second like this: / > >In each case the method is to draw >lines from the ends of the stick to the ruler, >both lines being perpendicular to the ruler. > >Now rotate the stick slightly clockwise. The >measurement on the first ruler decreases while >that on the second ruler increases at the same >time, yet the 'proper length' of the stick >didn't change. Acceleration is a name we give >to rotation in the x-t plane. George I cannot see any point in what you are doing. > >Incidentally, aether theory says there _is_ a >physical shrinkage due to the interaction with >the aether but it is undetectable your program >doesn't falsify that either because clock >effects come into play that you disregard. Contractions can be REAL if an aether exists. I have pointed that out many times. If the 'velocity component' of the 'GR correction' of GPS clocks is correct, as claimed by Andersen, then the Earth must have some kind of 'aether' around it...since the effect is REAL and not illusiory as demanded by SR. >> ... There are techniques now available for accurately >> measuring the lengths of moving rods. They should give the same answer as >> that >> for the rod at rest. > >What methods are you thinking of? Running its ends past a couple of accurately spaced photocells .... >>> >>>That wasn't my intention, just that "a region" is >>>unquantified until you measure it. However, you >>>make a good point, it is fact that there is no >>>absolute direction in space that allows us to >>>trade off x and y components. >> >> True...but we can rotate a rod in any direction and know it will occupy >> the >> same absolute length of space. > >If measured by a ruler at rest wrt the rod, that >is true. If the ruler is moving wrt the rod then >the axes along which the measurement is made are >rotated so the measured length changes even though >the proper length (absolute if you like) doesn't. That merely shows that the measuring technique is faulty...if not plainly stupid. > >> We can also construct three axes at 'right angles' even if we are hurtling >> along in a sealed space capsule. > >We can. Now think about this observer compared to >one he hurtles past. Let's say they align the x >axis with the direction of movement and they use >the point and time at which they pass as the origin >of their x and t axes. A vector drawn from (0,0) >to (0,1), one second later is a unit vector lying >along the time axis. Each of them says that the >(0,1) point is located with them of course since >the x coordinate is zero. Can you see that these >unit time vectors have an angle between them on >the x-t plane which depends on the speed? Can you not see that reality can only be determined if the travel time of human communication is corrected out? It is not hard to do that. I have described how with my 'instantaneous universe' concept. If two dolphins performed your experiment under water, using sonar to line up the axes, the angle would be very different from your visually determined one. What does that prove? >If >the time axes have that angle between them and >each considers the x axis perpendicular to the >time axis, then the x axes also have that angle >between them. In other words one observer is using >axes that are rotated relative to the other's. That >is the answer to your "Why would you want to do >that?" earlier, you don't want to but it is >unavoidable. You are talking about an experiment that relies on EM communication, which we know requires finite time. The fact that we don't always SEE things precisely as they are doesn't imply that the things ARE exactly as we see them....unless one applies the relativist logic.... > >> Interestingly, even though rotation direction is not absolute, rotation >> itself >> IS absolutely detectable. > >What is really interesting is that acceleration >is also absolute and acceleration is a rotation >in the x-t plane. That is a mathematical concept only. It has no physical meaning. Obviously, a constant speed is represented on an x-t diagram as a straight line. An acceleration has a constantly changing gradient. I don't see how this kind of graphical demonstration can change the nature of space and time. >>> >>>Constant, but not single valued. You can trade >>>space and time by rotating the x-t axes just as >>>you can trade space-space by rotating the axes >>>in the x-y plane. >> >> It IS single valued....magnitude ONE. > >No, it has two values, you just want to call them >both "one" but I won't let you :-) According to you, it has an infininte number of values....because you can have an infinite number of observers. I agree, it can have an infinite number of MEASURED values. However, the fact remains none of those values will change during the course of the experiment... The rotation period has an inherent constancy. >>>>>When are you going to start litening to what I >>>>>say instead of inventing alternatives? Look >>>>>back through this post and see if you can find >>>>>why I say that. >>>> >>>> You are repeating over and over that the orbit duration depends on who >>>> measures >>>> it. >>> >>>No, that's a nice strawman too. I am repeating that >>>the values measured along an axis depend on the >>>orientation of that axis. >> >> I really don't see the relevance of that argument. > >Hopefully the earlier discussion of axes has >clarified that. It has clarified it but makes no more sense. One doesn't rely on one's eyes in physical experments. >> >> I know what you are claiming. I am also trying to tell you that it can >> have >> only one REAL value no matter how many values it is measured to have. > >It has only one "proper" value which is measured >at rest relative to the object but that translates >to many measured values on different axes. We obviously have a different approach to this whole topic. I say the rotation period occupies a fixed time duration, which doesn't need to have a value placed on it to BE a time duration. I say it is the same time duration in all frames. You (and Einstein) are claiming that if its duration is measured using manmade clocks and if the readings are different for different frames or circumstances, then this is an indication that TIME itself must vary according to those circumstances. You are not even prepared to consider the possibility that the clocks are not perfect and might have malfunctioned under the different conditions. .......Very strange logic if you ask me.... >>>Of course, but you are still trying to define >>>two different durations as the same 1, or 100 >>>or whatever number of units. You can't do that >>>and your attempt at a proof fails as a result. >> >> George, an orbit occupies a duration of time. > >No, it occupies as many durations as there are >angles for the time axis for it to be measured >against. You are introducing measurement errors, mainly due to EM's finite travel time. You have to eliminate that. >> We can try to place a figure on >> that duration with clocks. >> The clocks are calibrated according to another time duration standard...in >> our >> case it is still basically the Earth's rotation period (although we now >> have >> something slightly more accurate). >> So when you measure Jupiter's orbit with a clock, you are really comparing >> it >> with Earth's daily rotation. >> >> There has been and there will remain a constant ratio between the periods >> of >> Jupiter and the daily rotation of Earth. It is a dimensionless number >> around >> 4332.59. >> Any measured difference in that ratio reveals a measurement error. >> The obvious conclusion one must reach is that the clocks are not perfect. > >... assuming time is absolute. An alternative >philosophy is that spacetime is absolute (if you >like) but that time is a measurement made along an >axis can be rotated by changing the speed of the >clock which is doing the measuring. What I said above makes no such assumption. The ratio of Earth's rotation period to Jupiter's orbit period is constant no matter how anyone wants to measure it, in any frame, with any form of 'space time' or whatever. The ratio compares two durations of absolute time. So if a GPS clock gets a different ratio than the GC then it shows that the clock(s) are faulty. >>>Don't try to tell me about relativity until you >>>learn it yourself Henri. You forgot that the sign >>>of the terms differs. The 't' part is "-ct^2" so >>>it would be 'ict' and have units of imaginary length >>>whatever that might mean. Time is not the same as >>>space and the equations always reflect that. I won't >>>waste my time educating you any more on this, if you >>>want to understand, study the subject. >> >> The time axis is made imaginary to keep it orthogonal. > >Yes, empirically we find it has to have the opposite >sign from spatial dimensions. empirically? Since when was anything in relativity backed up by things 'empirical'? > >> 'c' is actually just a >> scaling factor. > >Very good Henri, I thought that would be beyond >you. Saying 299792458m = 1s has essentially the >same meaning as saying that 25.4mm = 1 inch. > >> This is a perfectly sound mathematical treatment...but it has no physical >> significance. >> Space and Time are not related in any way. > >You can't combine furlongs and Fahrenheit, but as >long as you correct the units using 299792458m=1s, >you can combine time and space exactly as we can >combine distance north and distance east using >Pythagoras, while the negative sign distinguishes >space from time. That has to be telling us >something significant about the nature of our >universe. But you are not combining space and time at all. You are subtracting space, as specified in terms of 'light's time to get there', from space Euclidean. What is the purpose of doing that? Relativity says, "the length AB does not appear to be AB because it takes different times for light to go from A to O and from B to O. This implies that AB is not a fixed length of space". > >George > HW. www.users.bigpond.com/hewn/index.htm Sometimes I feel like a complete failure. The most useful thing I have ever done is prove Einstein wrong. |