sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G
And another point:
You say four spacial dimensions,
I guess in place of three and time.
We observe three spatial dimensions.
Mathmeticians like to add dimensions to their maths models, fair enough, but we still have three spatial dimensions in which to live.
What is your or Zeno’s fourth spacial dimension ?
sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G
I snipped this out from the first post
It has
Flat Euclidean space
4 space dimensions*
No time dimension*
Particles have an Absolute Velocity (AV) property
But those * do not appear again.
So can you please explain the fourth spacial dimension.?
And does absolute velocity mean “not relative to the observer”?
I think we can agree time is not a thing, but that is loose language. It is also not a spacial dimension.
The model used defines time within the model. Newton uses clock time , yes. It works well. But Einstein uses spacetime for cosmology.
Our brain has at least three timers, rather mysterious, but that’s another subject. The thing about human time is that as far as I know, only life has useful memory and humans excel at memory. The rest of the universe is a state by state entity with nothing communicating faster than light. Always in the local now.
So are my questions still word salad?
Is velocity relative to the observer?
What is the fourth space dimension?
sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G
Culturally there is a lot of baggage that comes with the concept of time. A lot of that comes from movies that involve time travel and similar plot lines. Most of which are totally without any physical foundation. Western cultures are dominated by ideas that suggest that the past and future are 'real' and that if we could go back or forward to those time coordinates that we would see what happened at that time. Needless to say these plot lines are filled with paradoxes and contradictions. One thing that reinforces this thinking is the Block Theory of Time used by SR and GR. Whilst it might be a useful tool for understanding SR and GR there is no evidence that it is true and is even problematic for QM.
Unfortunately when you spend your whole life thinking in these terms it can be very difficult to imagine that time might not even exist. Let us examine what it is that we actually do when we use time to measure somethings speed/velocity.
Consider two sprinters for whom you want to know who is the fastest over 100m. We can put them both at the starting line fire the starting gun they run down to the finish line the first to get there is the fastest. No time measurement is required. But what if we can't have the two sprinters in the same place together. We might use a stop watch to measure the time. But what are we measuring?
When I measure a mass I will compare it to another mass often through some intermediary. When I measure a charge I will compare it to another charge. So why am I recording the sprinters speed by using time which is a different unit.
The definition of a second is
"the duration of 9,192,631,770 [cycles] of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom"
a composite of a distance and a velocity.
When we used the stopwatch we recorded the distance a photon went during the race. We have used the concept of time as a tool to compare the speed of the sprinters with the speed of light. As the speed of light is considered to be constant it is thus a convenient reference to use. So do we need the middleman of time to organize events into a list of causally linked events. No. We just measure how far light has gone between them. No concept of time is needed.
But what about time being relative to the observer? I see comments where you seem to suggest velocity and distance are absolute, but that is directly contradicted by observation. (Incidentally, I notice you haven’t answered profloater’s questions which touch on this issue - I would appreciate some answers.)
Are you arguing against relativity theory?
I see a number of issues here that get more complex if you consider measuring the velocity and deciding the distance of objects where relativity issues become significant. Say, if you have two rockets that accelerate to significant but different fractions of the speed of light and traveling from Earth to the Alpha Centauri system. Clocks on Earth and the two ships won’t agree when compared with each other. Observers on Earth and the two ships won’t agree on the distance to Alpha Centauri.Consider two sprinters for whom you want to know who is the fastest over 100m. We can put them both at the starting line fire the starting gun they run down to the finish line the first to get there is the fastest. No time measurement is required. But what if we can't have the two sprinters in the same place together. We might use a stop watch to measure the time.
So one problem that I see is, how would this be possible without a property we call “time”? How do you deal with relativity issues?
You’re using a simple example where extreme precision isn’t needed. Things get complicated when you make comparisons between observers and consider velocity and gravitational effects on measurements.When we used the stopwatch we recorded the distance a photon went during the race. We have used the concept of time as a tool to compare the speed of the sprinters with the speed of light. As the speed of light is considered to be constant it is thus a convenient reference to use. So do we need the middleman of time to organize events into a list of causally linked events. No. We just measure how far light has gone between them. No concept of time is needed.
"The problem with quotes on the Internet is that it is hard to verify their authenticity." — Abraham Lincoln
I say there is an invisible elf in my backyard. How do you prove that I am wrong?
The Leif Ericson Cruiser
Hi Van Rijn
Yes I agree that it is a simplified scenario. It was intended to give profloater and Noclevername something to chew on.
I intend to elaborate on some more details soon.
There's been a bit going on.
Consider your two sprinters:
Alice and Bob,
Alice also measures Bob’s speed relative to hers, during the race, and it is a smaller value than we timekeepers observe. It is relative. This remains true when the race is separated, except if Bob runs the opposite way, Alice sees nearly double the value we see. Light speed is so much greater we can ignore it in this mind experiment.
If we ignore a clock as a time keeper, we need to include the angles between the two runners and also devise a way to start them at the same “time”.
“Simultaneous” was examined by Einstein in his thought experiments and he showed that concept was relative. Indeed it only has meaning at a single point in space and time, hence spacetime.
None of that requires light speed to be a constant, just finite, and only absolute, according to Einstein, in a perfect vacuum.
But we digress, please explain the fourth space dimension.
sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G
Nice understatement there, but we need answers to chew on! If I may comment on the style here, it seems a bit patronising. You appear to setting riddles like whosisname, Rumplstiltskin, as if holding back the secrets we all seek. We have heard of and even studied Zeno. In his time paradoxes were hugely useful in the formation of ideas but we have learned how to understand hares overtaking turtoises, and the paradox collapses.
I remember an O level maths problem: you have to drive two circuits of a track averaging 60 mph. After one circuit you have averaged 30 mph, how fast must you go in the second. A trick question about Time. Not a paradox once you know the correct way to calculate.
I like to separate dimensions from properties or scalars. In Newton Time is a scalar, not a dimension. It is the same everywhere and slow observation will confirm that. It is only at very high speeds or huge distances that we need to correct that assumption. If the universe were just perpetual orbits, God’s clockwork as Plato would have it, we could still find a speed for light, once we invented an instrument, and we could find ways of defining seconds.
QM has raised more questions like is time quantised? Zeno already had worried about that. I would not seek to answer that one, but maybe your oblique questions will get there.
But as has been said, in this ATM section, you should put up an hypothesis or idea, not ask cryptic questions. I am just an engineer, the physics heavyweights have not joined in. And I am not sure how many academic philosophers we have.
Looking forward to hearing about that fourth dimension.
sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G
Follow me down the rabbit hole if you dare.
Once upon a time European civilizations thought that they were the center of the universe. They then realized that the Earth was round. So they then figured that the Sun, Stars and Planets revolved around Earth until Copernicus described a model where the Sun was at the center of the solar system with the Planets going around it in circles. This was not a viral hit at the time. One of the reasons for this, maybe even the primary reason, was that circular orbits resulted in a poorer fit to what was calculated using the Ptolemaic system. It appears that if you add enough epicycles to anything you can model anything you want.
After Kepler resolved this little problem with ellipses Newton came along and we had time and distances that were absolute and you had to be careful if you sat under an apple tree. Until finally Einstein came along and made everything relative and decidedly rubbery with one exception. The Speed of Light! Why is the speed of light about 300,000km/s not 3km/s or 300,000,000 km/s? Yes I know its just our units but why is it what it is?
Have we got a modern version of the Ptolemaic System?
So down the rabbit hole we go.
Lets assume that the speed of light can have any value at all.
What does that mean and what is required to make it possible?
For that to make any sense there needs to be some sort of reference. What is the Speed of Light relative to? SR and GR don't have that problem as the Speed of Light is framed differently with everything moving through space time with the magnitude c. To deal with this assume that we have 4 space dimensions and there is a state in which a particle, if it could be in this state would have a zero Absolute Velocity (AV). As it stands this has no value whatsoever. Agreed. But it is supplied as an anchor point for how to think about what is to follow. (Just a note Van Rijn stated above that this is "directly contradicted by observation". I think it is more a lack of evidence combined with a lack of a need for it in SR)
Now if we had one particle with an arbitrary AV and a second particle with twice that and they collided, what would happen to the kinetic energy? How do we conserve energy in this system.
To solve this problem will will assume that the energy of a particle is proportional to the AV squared. This is equivalent to the E = mc2 of SR except that we replace c with the AV.
So what about Maxwell's Equations that predict that light always travels at the speed of light?
If we view Maxwell's Equations from a different direction and think of a particles AV as being c in its local reference frame, then c defines the scale of Maxwell's Equations along with other processes at an atomic level. SR and GR show that time, length, mass etc are all changed when a particle is viewed from a different reference frame from that of the particle, yet in the particles reference frame physics continues as usual. Same here.
So if we have a particle in Zenos 4 dimensional universe, what happens when it emits a photon?
The photon will have a relative velocity of c the same as the particles AV. If the photon is emitted in the same direction as the AV then it would require 4 times as much energy as that available. If it tries to emit the photon backwards then its energy would be zero. Clearly a photon cannot be emitted with a direction that includes a component in the direction of the AV. It can only be emitted perpendicular to the AV. Therefore the particle will not experience that dimension via the EM forces. Only three spacial dimensions will be apparent.
What would be the results of the primary experiments used to support SR?
The measurement of the speed of light in laboratory situation would always return a constant because the light source and detector are kept at the same AV.
The MM experiment would likewise always show a null result.
With the De Sitter Double Star experiment the detector may not have the same AV but the two source stars will have a very similar AV, a lot smaller than that indicated by there relative velocities, simple Pythagoras between c and the relative velocity. In this case there is an additional factor that also comes into play. There is a lot of random thermal motion on the surface of the stars resulting in each atom having a slightly different AV these are not just different in magnitude but more importantly direction in the four dimensions. Consequently any photons emitted with a different velocity will miss the detector. The further the light source is away from the detector the tighter that filter is. This same filter will occur with supernovas.
So if the AV determines the physical size of an object then a galaxy could be as small as a mouse or so big that our galaxy could be as small as a mouse in comparison! For a galaxy to be this small it would have to have a relative velocity extremely close to c. The energy that it would have available to be detected just wouldn't be available. It would be undetectable. So what would be detectable or more precisely, observable? To observe something you need a reasonably large number of photons to conclude that you have made an observation. You need a first and a last photon and essentially a stream of photons in between. I the original post I showed what was required, the outcome was that the light source and the detector must be in the same plane which includes the AV vector for both the source and detector. And the ratio of the AVs of the source and the observer must be the cosine of the angle between these vectors (alpha). This makes the number of observable objects very small.
So you've discovered time is relative, congratulations. But that doesn't mean it doesn't exist.
I think your understanding of the mainstream of physics needs work. Your explanations are a layman's simplified Wikipedia descriptions of more complex work based on centuries of evidence and experimental verifications. Where's your supporting data? Any evidence at all? All I see is walls of text saying how "flawed" established theories are, despite them being based on repeatable observation that's been tested again and again.
Somehow you've discovered something that the most brilliant minds in the world have missed for their entire careers, without you giving a single equation or any direct observation that matches it? "Extraordinary claims require extraordinary evidence" - Carl Sagan
"I'm planning to live forever. So far, that's working perfectly." Steven Wright
Quoll, I'm asking you directly: What implications of your "fourth spatial dimension" make it testable, in other words what factors should we be looking for in established observations that we aren't already seeing?
Answer that, and you'll be doing the job of trying to convince us scientifically.
"I'm planning to live forever. So far, that's working perfectly." Steven Wright
Predictions
Time Dilation
The Lorentz time dilation would apply if a simple rotation of the AV vector occurred, though the length contraction would not. The situation is a lot more complicated in Zeno's Universe. If the AV increases then the length of a ruler would increase regardless of its orientation in the 3 dimensions perpendicular to the AV. You can't align the ruler in the direction of the AV.
Red shift
All observable objects have to meet the Observability Criteria outlined previously. Consequently the light received will be red shifted by a factor of at least cos(alpha) ^ 2.With alpha having the range 0 to pi/4. In other words most things observable will be red shifted. Objects that are gravitationally bound may be blue shifted.
The brightness will also decrease with increased values of alpha in addition to that resulting from the increased distance. So the inverse square rule relating distance and brightness will fail. This puts Hubble's Law in jeopardy.
Causality and the Arrow of Time
Zeno's Universe allows particles to move anywhere and any direction without encountering any causality issues unlike the current models of time. Entropies Arrow of Time is simply the constant progress from a low probability state to a higher probability state.
Dark Matter, Dark Energy, Virtual Particles and the CMB
As most of the matter in Zeno's universe isn't visible the obvious answer to the quest of what is Dark Matter is simply that it is ordinary matter that doesn't fit the observability criteria. Although this matter isn't observable it doesn't mean that all of the photons emitted by it aren't. It should exist as a constant background, though I don't see any reason for a peak in any particular frequency.
There would of course be some particles that almost fit the observability criteria. These would seem to pop into existence and promptly disappear again. The bigger the energy difference the shorter they would be around. Dark Energy could be the consequence of any of many measurement assumptions.
Gravity
GR has the speed of light constant and thus space must be considered to be bent. In Zeno's universe the reverse applies.
The Big Bang
The initial post described a process where interactions between particles results in a migration of particles from large values of AV to progressively smaller values of AV. This process enables the universe to have always existed and to always exist whilst at the same time entropy continues to increase! No Big Bang, No Big Freeze.
The Center of the Universe
Zeno's Universe would seem to complete the transition from us being the center of the universe to there be nothing special about anything except that one state of zero velocity where nothing can be and may be nothing more than a philosophical talking point.
From Large Scale processes to Small Scale processes
Many of the explanations for what is observed in our universe are attributed to processes that take place on large scales The Big Bang, Inflation, Dark Energy etc. The processes described in Zeno's Universe all occur at the particle interaction level which removes the need for totally new physics to explain it.
The Voyager Problem
The Observability criteria is not a two way street. Unless the object and the observer are close or fit the criteria then it isn't possible for the object to observe the observer. This would suggest that two way communications with a fast moving distant space craft shouldn't be possible. Yet it is.
Which means either
1. The distance/speed constraints for two way communications isn't as tight as I would have thought.
2. There is a criteria that I have applied which isn't correct. Earlier on in this thread I mentioned Copernicus assumed that the orbits were circular. The broad predictions of the theory were right but the detail was wrong.
3. Zeno's Universe only exists in my mind (The most likely possibility)
Should Zeno's universe be hyperbolic?
I have stuck with a flat Euclidean model because I can visualize it and I have never learnt hyperbolic geometry. Given time and motivation I could do it but I don't have sufficient of either these days. I hope you have enjoyed this one, Maybe it will inspire someone to think outside the box.
So any particle is travelling at its own light speed. Scale is local so we cannot judge the size of distant objects and photons emitted “backwards” stand still. If we then observe macro objects close to us, we can only see their front? That is on the basis their surfaces are moving toward us or vibrating? This is indeed a rabbit hole. I see that the night sky becomes very different in interpretation but now local objects are changed. There is still no fourth space dimension, but maybe you are describing a scaling effect of locality? I am struggling to grasp the predictions of this interpretation. Snooker balls become interesting. If two collide one or both disappear as their photons stop, or they jump into view. The local world sparkles like dust in a sunbeam. Doppler effects are magnified, an object coming towards you disappears as it passes.
If I turn my hand over quickly enough, it vanishes! The world is a facade with no depth.
But maybe I have not graped the predictions correctly, can you please explain that fourth space dimension?
sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G
Ah posted before i saw your latest.
sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G
Having seen your post 50, distant objects are less testable and about half invisible, you say mostly invisible, but it sounds Gaussian. Local objects should have different properties. But the prediction of macro objects from particles is still not clear. We assume temperature involves chaotic vibration and emitting photons. Would not Zeno have self cancellation of those photons? So as an interpretation of distant objects it challenges the standard model but is paradoxical when I can feel both sides of a coin at the same time. Of course that is electron behaviour and you have not explained what Zeno makes of electrons.
sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G
So far, all known experimental results support length contraction, not length increase. https://www.physicsclassroom.com/mmedia/specrel/lc.cfm
How would you explain the discrepancy?
Observable objects are redshifted, but that is also consistent with mainstream models of expansion. What distinguishes your model's results?Red shift
All observable objects have to meet the Observability Criteria outlined previously. Consequently the light received will be red shifted by a factor of at least cos(alpha) ^ 2.With alpha having the range 0 to pi/4. In other words most things observable will be red shifted. Objects that are gravitationally bound may be blue shifted.
In jeopardy how exactly?The brightness will also decrease with increased values of alpha in addition to that resulting from the increased distance. So the inverse square rule relating distance and brightness will fail. This puts Hubble's Law in jeopardy.
How would this be measured? What experiments could be designed to show this?Causality and the Arrow of Time
Zeno's Universe allows particles to move anywhere and any direction without encountering any causality issues unlike the current models of time. Entropies Arrow of Time is simply the constant progress from a low probability state to a higher probability state.
And how would one determine this? We know the Universe is diffused with EM energy that does have a particular frequency, the Cosmic Microwave Background.Dark Matter, Dark Energy, Virtual Particles and the CMB
As most of the matter in Zeno's universe isn't visible the obvious answer to the quest of what is Dark Matter is simply that it is ordinary matter that doesn't fit the observability criteria. Although this matter isn't observable it doesn't mean that all of the photons emitted by it aren't. It should exist as a constant background, though I don't see any reason for a peak in any particular frequency.
There would of course be some particles that almost fit the observability criteria. These would seem to pop into existence and promptly disappear again. The bigger the energy difference the shorter they would be around. Dark Energy could be the consequence of any of many measurement assumptions.
Please expound on what you mean by "the reverse applies".Gravity
GR has the speed of light constant and thus space must be considered to be bent. In Zeno's universe the reverse applies.
'The Big Bang
The initial post described a process where interactions between particles results in a migration of particles from large values of AV to progressively smaller values of AV. This process enables the universe to have always existed and to always exist whilst at the same time entropy continues to increase! No Big Bang, No Big Freeze.
And what are the implications of entropy without beginning or end? What observations might support this?
Mainstream models also say the Universe's has no special center, but we have observed that everything the Universe has relative velocity. How does this differentiate from your claim?The Center of the Universe
Zeno's Universe would seem to complete the transition from us being the center of the universe to there be nothing special about anything except that one state of zero velocity where nothing can be and may be nothing more than a philosophical talking point.
Please expand this explanation. Provide whatever supporting data you need.From Large Scale processes to Small Scale processes
Many of the explanations for what is observed in our universe are attributed to processes that take place on large scales The Big Bang, Inflation, Dark Energy etc. The processes described in Zeno's Universe all occur at the particle interaction level which removes the need for totally new physics to explain it.
Thank you for acknowledging that you might be incorrect. I've seen many - most - who post on ATM who lack this quality of self-reflection, it's a good basis for science.The Voyager Problem
The Observability criteria is not a two way street. Unless the object and the observer are close or fit the criteria then it isn't possible for the object to observe the observer. This would suggest that two way communications with a fast moving distant space craft shouldn't be possible. Yet it is.
Which means either
1. The distance/speed constraints for two way communications isn't as tight as I would have thought.
2. There is a criteria that I have applied which isn't correct. Earlier on in this thread I mentioned Copernicus assumed that the orbits were circular. The broad predictions of the theory were right but the detail was wrong.
3. Zeno's Universe only exists in my mind (The most likely possibility)
Understood, we're all very occupied these days! If you do choose to learn something of HG and other relevant fields of mathematics and physics, you can certainly use that to hone your hypothesis, and perhaps return to the Forum to share it. We always welcome any knowledgeable scientific box-leaving.Should Zeno's universe be hyperbolic?
I have stuck with a flat Euclidean model because I can visualize it and I have never learnt hyperbolic geometry. Given time and motivation I could do it but I don't have sufficient of either these days. I hope you have enjoyed this one, Maybe it will inspire someone to think outside the box.
I think this post is a useful beginning to understanding your concept. We can use this as a basis for trying to find answers.
"I'm planning to live forever. So far, that's working perfectly." Steven Wright
Ok lets see what my "layman's simplified Wikipedia descriptions" say "direct experimental confirmations of length contraction are hard to achieve".
In other words there is no direct experimental evidence. There is only indirect evidence.
I think I prefer Wikipedia to you Kindergarten Cartoon.
You have also simplified the intent of the statement. If the AV is gets smaller then the length also gets smaller and it doesn't talk about what an external observer would measure. As stated its a lot more complicated. The model doesn't have to predict the same result as existing theories it has to match the experimental results.
You complain when the prediction is not the same as mainstream physics then complain when it is!
In fact you have misinterpreted what has been said again.
The redshift is fine but the brightness of a distant light source changes with both the distance and the AV thus breaking the astronomical distance ladder.
If my information is up to date there are two main ways that the Hubble constant is measured and they both give different answers which don't match within their error bars. Additionally we keep finding galaxies closer and closer to the Big Bang already completely formed with high metal content. Is another epicycle required?
The Observability Criteria tells you what can be objects can be observed which is in fact a very small part of what is predicted to exist. Actual measurements would be via some indirect method. Mainstream Physics still can't directly detect Dark Matter even that it has been aware of it for decades. Zenos Universe says that it would just be ordinary Baryonic so we wouldn't realize that we had detected it when we do.
Clearly if the speed of light was not constant then GR would have to be revisited as it assumes that it is constant. Its predictions have been well borne out by experiment. So you would need to turn it inside out, take its inverse what ever term you like to use. Maybe it will allow it to get around those nasty divide by zero type problems so that it works beyond the event horizon. This would not be a job for the faint hearted.
This would take it one step further. Its not a physical center that I'm referring too. But the special status that the speed of light has. Why is should it be what it is?
Mainstream Physics is increasingly relying on processes that span the vastness of space to explain what we are observing. Dark Energy, Inflation and the Big Bang are examples for which we have absolutely no known Physics to explain. Newtonian Gravity assumed that it operated at infinite speed everywhere similarly with the Electric field. Mainstream Physics now uses force carrying particles to model how these work. For inflation it would be much more elegant, and possibly wouldn't require any new physics, if the homogeneity of the universe could be explained by a simple process that occurred at the particle level.
I'm still waiting for you to ask a question that shows that you actually understand this ATM. Most of your questions seem to be the same old tired cut and paste ones and often miss the mark, maybe its my poor ability to explain the concepts.
Science progresses not by patting ourselves on the back and congratulating ourselves on doing such a great job but by digging into those dirty cracks to see what the problems are. I have presented an ATM, admittedly a flawed one, that by assuming the speed of light is variable and following through to its logical conclusion without any really off the mark assumptions. I get a model that passes the experiments that are used as the primary evidence that the speed of light is constant. Doesn't that give you cause for concern?
But you only need to suggest lightspeed is affected by spacetime to achieve that. So why attack time rather than light speed? There are two classes of observed evidence, those we manipulate on Earth and those we rely on photons from outside. I should add gravity waves into the latter class. That recent evidence about observed star velocity and observed density of galaxies does shift the interpretations in the way you want.
sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G
I am reminded about Hamilton and his quaternians, is that what you mean? Ways to handle vectors ? Are you conflating four dimensions in maths to handle vector products in three dimensional space? I believe quaternians have made a comeback, I am afraid I am still at vector products but suddenly I see something about your OP that was not, IMO well introduced. Or is that all wrong?
sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G