Is Time an Illusion? Exploring the Block Universe Theory

[puzzled fish]

Science advisor,

1. You deny a big bang first state to the block universe?
2. Time slices in a block universe aren't integers. They have a start and they likely have an end when the universe ends, so your analogy with integers doesn't seem relevant.

Edgar L. Owen

Note that a singularity doesn't imply that there is an end somewhere. In mathematics you can have a curve extending infinitely in the x and y directions and yet its length could be finite. It all depends on how you define the metric.

 

[PeterDonis]

Time slices in a block universe aren't integers.

Time slices are arbitrary spacelike 3-manifolds sliced out of the block universe 4-manifold. The 4-manifold itself is, at least if we are talking about the simplest case, just $\mathbb{R}^4$ with a Lorentz metric on it. In such a manifold there is no "edge" (it's an open set) and hence no "first slice" in any direction, spacelike or otherwise.

 

[EdgarLOwen]

The big bang is not a first state. So yes, I do. The initial singularity is not a state within the big bang model.

No, they do not. It would be good to review the definition of a manifold with particular attention to the part about open sets.

JBriggs,

The point is that in the accepted theory the universe had a beginning called the big bang and so if the universe was a block universe it would have a beginning and the points I made would apply, which makes a block universe extremely unlikely and apparently inconsistent.

Edgar L. Owen

 

[EdgarLOwen]

Time slices are arbitrary spacelike 3-manifolds sliced out of the block universe 4-manifold. The 4-manifold itself is, at least if we are talking about the simplest case, just $\mathbb{R}^4$ with a Lorentz metric on it. In such a manifold there is no "edge" (it's an open set) and hence no "first slice" in any direction, spacelike or otherwise.

Peter,

The point is that the universe had a beginning called the big bang and then it evolved over time, therefore there would be an initial state in a block universe and a causal structure which is unexplained. How would the entire causal structure of the universe come into existence if it didn't causally evolve?

Edgar L. Owen

 

[tophatphysicist]

How would the entire causal structure of the universe come into existence if it didn't causally evolve?

Edgar, you bring out such an important point--a point so important to this discussion. The Block Universe follows logically from the relativity of simultaneity. Einstein once stated in a discussion with one of the leading philosophers, not withstanding his position on the Block Universe, that he was troubled by the overpowering vividness of the personal experience of the 3-D world he lived in evolving over time (quote is not precise, but I can look it up if necessary).

 

[EdgarLOwen]

Edgar, you bring out such an important point--a point so important to this discussion. The Block Universe follows logically from the relativity of simultaneity. Einstein once stated in a discussion with one of the leading philosophers, not withstanding his position on the Block Universe, that he was troubled by the overpowering vividness of the personal experience of the 3-D world he lived in evolving over time (quote is not precise, but I can look it up if necessary).

Tophatphysicist,

Exactly, one can of course come up with a 4D mathematical structure in the form of the mentioned manifold but unless that has a sequential causal structure it's inconsistent with the actual universe and thus cannot be an accurate model of the actual universe.

There are much simpler and more reasonable models of the universe that are consistent with the relativity of simultaneity, and incorporate clock time flows, than a block universe.

Edgar L. Owen

 

[jbriggs444]

The point is that in the accepted theory the universe had a beginning called the big bang

The big bang theory is an extrapolation of the current state of the universe to an earlier denser state. The extrapolation does not go back to a first state.

You claim inconsistency but fail to show one.

 

[Dale]

Just to remind everyone (but especially @EdgarLOwen), thus far we have been discussing BU as an interpretation of SR, not GR. As such it is not a cosmology and does not make any claims about the beginning of the universe. In particular, there is no Big Bang involved in any interpretation of SR.

 

[Dale]

The Block Universe follows logically from the relativity of simultaneity

Do you have a reference for this? It seems false to me so I would like to see the place where this proof is published

 

[PeterDonis]

The point is that the universe had a beginning called the big bang

The Big Bang was not the "beginning" of the unverse, in the sense of being a past "edge" to spacetime. That is an artifact of a particular oversimplified model that is not the one cosmologists actually use. In the model cosmologists actually use, the term "Big Bang" refers to the hot, dense, rapidly expanding state that is the earliest one of which we have reliable knowledge. But what came before that is not known for sure--although it seems most likely that some kind of inflationary epoch preceded it. (But then what came before inflation is not reliably known, and we certainly do not know that an "initial singularity" preceded it.)

 

[PeterDonis]

The Block Universe follows logically from the relativity of simultaneity.

We've already had a long discussion about this--on top of the previous long discussion in the comment thread on my Insights article. So just making this assertion baldly, in the light of all that previous discussion, is pointless. Either back it up with a reference, as @Dale asked, or with some new argument that hasn't already been raised and rebutted in discussions here.

Einstein once stated in a discussion with one of the leading philosophers

Irrelevant (and argument from authority). Please stick to physics in this thread.

 

[PeterDonis]

There are much simpler and more reasonable models of the universe that are consistent with the relativity of simultaneity, and incorporate clock time flows

Do you have references?

 

[Denis]

You are thinking of a necessary condition, not a sufficient condition.
Since EPR's criterion is a sufficient condition that means that all things that meet the condition are "real" but not that all things that are "real" meet the condition. There can still be real things which are not measurable with the EPR criterion.

I know this. But the argument (that using it I can prove a physical prediction) does not depend on this.

Furthermore, I am not sure that the EPR criterion is generally accepted outside of QM foundations, and maybe not even then.

I have never seen anybody questioning it as a criterion of realism. There are, of course, all those who reject realism itself, because accepting realism would destroy their beloved version of relativity that there cannot be any preferred frame.

 

[Dale]

But the argument (that using it I can prove a physical prediction) does not depend on this.

Sure, but in this case "using it" means "using the EPR criterion" and the EPR criterion is not a definition of reality or realism. The EPR criterion is physical, but realism is not.

I have never seen anybody questioning it as a criterion of realism. There are, of course, all those who reject realism itself,

Those who reject realism itself also reject the EPR criterion. For them it is not a sufficient condition.

 

[Ebeb]

What does "occur" mean? How do I test, experimentally, whether an event has "occurred"? The obvious answer is to observe it, but if I observe an event, it must be in my past light cone.

You still ldon't know what my point is.
You told me that an observer doesn't know whether the event he observes did exist before it is observed; your post #56-quote-<<More precisely, you have no way of testing by experiment whether or not the event "existed" before you observed it--because any experiment would involve observation.>>
Hence putting the observed event in your past lightcone is wishfull thinking, because you don't know the event happed before the event of observation.
If one talks of mathematical model, be it SR, then I would like to know what it is based on. The simple fact of making a model with an event "in the past light cone of that model" is based on the premise that the event occurred before the apex event of the light cone. But you doubt -see quote above- whether the event occurred before it is observed. This makes me say that the light cone, the SR model uses the premise "events do occur before observation".
Yes, one should question what 'occur' means. We are certain that the observer's present event does occur. That's a good start. But do you know anything "occurred in the past"? No. Then what is the meaning of 'occurred'?
Besed on the premise that "we don't know whether an event occurred in the past or not" I consider it a fair question asking what the past light cone model is based on. I will agree that the model is based on "observations", but because the premise tells us we don't know whether an event occured/occur(?) before observation, then what do we mean by "observation". Read on.

Meaningless question. Any event in your past light cone is fixed and certain. What events are in your past light cone depends on what event on your worldline you are treating as your "present" event.

I want to know what you mean by that. When you make such a statement you already have your model in hand/in mind. I want to know what the meaning is of an event being in the light cone, as far as observation is concerned. Putting an event in a past light cone of the SR model does automatically mean the event occurred before observation (whether it is later observed or not is irrelevant). Would you agree with that or not?
If the event is only put in the past light cone when 'observing/seeing' the event, then it means we are not allowed to draw any event in the past light cone. Because past light cone means "event occurred in the past", hence event occurred before observation.

There is no "labeling" involved. You are treating "fixed and certain" as something that has to happen to an event, physically. It's not. It's just a property in the model.

I want to know what events you draw in the past light cone. Events you observed, or also those you didn't observe?

When and why may an event be located in the past light cone? How does it get there, and when?
Is it because the event was not in the light cone, and then as time goes by, the past light cone gets bigger, and the event that was outside then gets into the past light cone? If not, then when does the event gets located in the past light cone?

We don't know whether an event was outside the lightcone before it entered the light cone, isn't it?
If there did occurr an event before it entered the lightcone, then it would be correct stating the event gets labeled 'fixed and certain' when it enters the light cone. And in that case the event gets labeled before the observer observes the event yet. but you don't agree with my labeling scenario. Hence I still don't understand your "fixed and certain".

I haven't said anything about "know".

I'll rephrase it. When I said <<the above doesn't mean that you know that the event occurred before you observed it.>> I mean that you use the premise that you don't know whether an event occurred before observation.

Once again: you have a model, and the model treats events in the past light cone of some chosen event, the one you are calling the "present" event on your worldline, as fixed and certain.

That doesn't answer my question. My point is that you cannot make/construct a past light cone model if it doesn't use a premise "events occur before observation".
You keep on repeating we don't know whether an event occurred before observation or not, -and I agree, in principle-, I then wonder what the past light cone of the SR model is based on if the option "events do not occur before observation" is used.

Strictly speaking, they are events you could have observed, at some event on your worldline prior to the event you are calling your "present" event, just looking at the causal structure of spacetime. Whether you actually observed them depends on things that are irrelevant to this discussion, like whether you were paying attention.

They are not irrelevant to the discussion. They are at the core of the discussion to know whether relativity of simultaneity requires Block Universe or not. But you don't seem to understand why. I don't question causality of the past light cone. That's not what is being discussed (actually I should, because if one doesn't know whether events occurred before observation, then what is the meaning of causality (f.ex event occurs, light travellingfrom event, then hitting my eye... but I won't push it that far yet)
I concentrate on the meaning of your post #56-quote-<<More precisely, you have no way of testing by experiment whether or not the event "existed" before you observed it--because any experiment would involve observation.>> and what it means for constructing a light cone model, and then using the model.

Nope. You still don't understand what a model is. A model is a tool for making predictions. You don't have to predict what happened in your past light cone, at some chosen event you are calling your "present" event, because those events are fixed and certain in the model. You only have to predict events outside your past light cone. That's what the model is for.

I know, that's why I want to concentrate on the meaning of putting events in the past light cone. I don't know how you interpret your own words, but for me your post #56-quote-<<More precisely, you have no way of testing by experiment whether or not the event "existed" before you observed it--because any experiment would involve observation.>> means one doesn't know whether there are events in such a thing as past lightcone model. I think the whole SR model based is construced on loose sand if one uses the option "events don't occur in the past before observation". But the SR mode does make sens if one uses the premise "events do occur in the past before observation".

Any event in the model that is not in the past light cone of whatever event you are calling your "present" event is not fixed and certain in the model; it's predicted, and the prediction is not 100% guaranteed to be correct. That is true. Any model will have the same property--there will be some things that are fixed and certain, and some things that are predicted and might be wrong.

It still doesn answer the question about the past lightcone and "fixed and certain" events.
You cannot put an event in the past light cone if you don't use the premise "events do occur before observation". If you would consider the option "events do not exist before observation", then there cannot even be such a thing as 'past light cone'. Don't you understand that?

I haven't said anything about "know". See above. You need to get rid of your preconceptions and stop reading things into my posts that I didn't put there.

When I said <<They are fixed and certain, but you don't know whether those events actually occurred before observation that event of observation.>>, I meant "one doesn't know". I thought it was obvious, but obviously one has to be very careful what's obvious or not. Mea culpa.
Yes, I still I wonder what you mean by fixed and certain. Can event can be fixed and certain, irrelevant of whether the event is observed or not? In that case you mean by fixed and certain: all events in the past light cone. then my question is: when are you allowed to put an event in the past light cone model?

I feel sorry that you have the impression that I am reading things into your posts that you didn't put there. I only try to find out what you put in there. Hence I try to formulate what I think you put in there. You shouldn't be upset that I might read things you didn't put in there. It's part of the game of discussions, and getting at the bottom of things? Or not?

We are talking about SR here, not about theories of consciousness. You are making this way too difficult.

I'm not talking about theories of consciousness. Every time the word 'consciousness' popps up in science topics somebody starts panicking. Look, I try to understand what observations are if one considers the option events do not occur before it's observed, based on your post #56-quote-<<More precisely, you have no way of testing by experiment whether or not the event "existed" before you observed it--because any experiment would involve observation.>> Please explain what observations are if one considers the option events do not occur before it's observed.

Again, we are talking about SR here,

The talking involves the second premise of your BU article.

not about theories of consciousness or metaphysical questions about how we can observe or know anything at all. You are making this way too difficult.

My impression is that you might be making it too easy in your BU article.
I'm not interesed about theories of consciousness or metaphysical questions. I want to know what the implications of your statement -whether or not the event "existed" before it's observed- are for constructing the SR model, and then using that model. You know why. In your BU article a second premise is introduced, to be able to refute Block Universe. I try to understand that second premise. What the exact meaning is of that premise. And to do that I have to understand the meaning of your "fixed and certain". I still don't understand what it means. Because it involves the problem whether events occurred before observation or not. Hence I want to know what "occurred before observation" means for the past light cone. If you insist that there is an option that events not occur before observation, the how can there be events in a past light cone if one considers the option events do not occur before observation?

Because you keep on wandering off into the weeds of theories of consciousness and metaphysics,

Don't put things into my words that I didn't put in there.
Because you seem getting very nervous about reading the word 'consciousness'. I'll keep it safe and rephrase it: If one considers the option events didn't occur before observation, then what do you mean by 'observation'? Please answer that question. Observation involves something/event that is observed and did occur before observation. If not, then please tell me what observation means for using that SR model. Is that -your quote- "making it too difficult"?
My point is that 'observation' doesn't mean anything if one doesn't use the premise "events do occur before observation". But for that option I tried to rescue the word by introducing it may be just all happening in the mind...because I guess we still want to go on using models and observations. But I shouldn't have done that. I had better stated: If one doesn't use the premise "events do occur before observations" then 'observation' cannot mean anything. Would you prefer this? 'Observation' of an event implies the event occurred (as an observer independent unit) before observation. Can I get agreement on that?

instead of just looking at the simple model I am describing.

If I 'just look at the model', then it requires Block Universe. But your article tells me that's a too easy way of putting things. In your article refuting block universe you didn't 'just look' at the model. A second premise is introduced, and I want to know what you mean 'exactly' what that second premise means. It leads to some "fixed and certain" qualification of events, questions about whether events do exist before observation or not, what it means for the past light cone, and what observation means. If you consider this making it too difficult, feel free, but I like to get to dig things a bit further. May I?

In the model, there is some event that you call your "present" event. Events in the past light cone of that event, in the model, are treated as fixed and certain. Events not in the past light cone of that event, in the model, are not treated as fixed and certain. That's it. That's all there is to it.

I want to know what the meaning of a model with past light cone is if you don't know whether events exist or not before observation, hence considering the option events do not occur before observation.
If I would state that the SR model (let's concetrate on the past lightcone) is based on the premise events do exist before observation, I guess you don't agree?

Your approach, taken to its logical conclusion, would say that we cannot do physics at all unless we first understand how consciousness works. That's absurd.

I won't push it that far. We can base models for making predictions. I want to know the premise(s) the model is based on. At its core it's based on observing the past. Agreed? "Observation" means: observing something that was there before observation. But if one considers there is an option that events didn't occur before observation, then what is the meaning of observation? Please answer that question. I tried to answer that question, but I had to use the word "consciousness", which makes you think I want to get involved in -your quote-<< theories of consciousness or metaphysical questions>>. I don't. But if one considers there is an option that events didn't occur before observation, then please tell me what the meaning of observation is?
Just trying to understand what you post. Nothing else.

People have been doing physics for centuries without knowing how consciousness works, except for the basic rough and ready pragmatic knowledge that everybody has just by being conscious and going through their daily lives. That is enough for what we're discussing here.

No, it isn't. For the discussion here it's important to know what you mean by fixed and certain, and what the implications of your post #56-quote-<<More precisely, you have no way of testing by experiment whether or not the event "existed".>> are for the light cone model. We can then deal with your BU article

If it isn't enough for you, then I'm afraid nothing anyone could possibly say in this discussion is going to satisfy you. Sorry.

You know, that might indeed be the case. But I do understand other participant's posts, probably because they have the same premise in mind as I do.

The other point of your article I don't understand: in that article you refute solipsism, but your post #56-quote-<<More precisely, you have no way of testing by experiment whether or not the event "existed" before you observed it--because any experiment would involve observation.>> leaves the option 'solipsims' still open, because in case the events do not occur before they are observed, there is nothing left but your present now event.

I don't know about other readers of your BU article (although 8 pages of discussion in that other thread discussing your article gives me a hint) , but I need a lot more information for trying to understand the full content of your article.
Thanks for reading this long post.

 

[PeterDonis]

You still ldon't know what my point is

At this point I have no idea how to make things any clearer.

You have a 4-D spacetime manifold, which is a perfectly well-defined mathematical object. You pick an event in that manifold to represent the "present" event of an observer. Events in the past light cone of that chosen event, which is a perfectly well-defined mathematical object, are considered "fixed and certain" in the model. Events not in the past light cone of that chosen event are not.

I've already described this, and I don't see what's so hard to grasp about it.

I don't know what else to say; you keep on harping about things that aren't experimentally testable, like whether events "exist", or whether they "occur", or things that depend on a theory of consciousness, like which events are "known" or "observed", when here we're just discussing a simple physical model. At this point I think you're just never going to be satisfied with anything we say, and continuing discussion is pointless.

 

[PeterDonis]

Events in the past light cone of that chosen event, which is a perfectly well-defined mathematical object, are considered "fixed and certain" in the model.

If you insist on having "fixed and certain" unpacked, events which are fixed and certain in the model are considered "initial data", i.e., they are put into the model, not predicted from the model. Events which are not fixed and certain are predictions of the model.

 

[Ebeb]

If you insist on having "fixed and certain" unpacked, events which are fixed and certain in the model are considered "initial data", i.e., they are put into the model, not predicted from the model. Events which are not fixed and certain are predictions of the model.

I want to know where you got the 'initial data' from to put into the model.
You put data into a past lightcone but if you consider the option that events that are observed might NOT have occurred before the observation, even the past light cone model is constructed on loose sand. If you don't understand this, or consider the issues I threw up being off-topic for discussing your BU article, so be it. I consider it rather an easy way for not wanting to discuss the real issue of your BU article, but that's only a personal feeling you don't have to worry about ;-)

Shame I put in so much time writing my posts. It won't happen again.

 

[PeterDonis]

I want to know where you got the 'initial data' from to put into the model.

Um, from whatever data I am using as initial data?

I'm confused by the question because this is not a question particular to SR or to the kind of model I'm describing. Any model in physics is going to have data that's put into the model, and predictions that come out. So asking this question is tantamount to asking "how do I build a model in physics", which is much too broad a question for a PF discussion.

if you consider the option that events that are observed might NOT have occurred

If I have data about events that I am using as input for my model, how do I "consider the option whether those events might NOT have occurred"? That makes no sense. The data is the data. So this question does not look to me like a question about physics, but a question about either metaphysics or philosophy, both of which are off topic here. It certainly is not a question I need to answer in order to build a physical model and use it to make predictions. (And again, that's not anything particular to the model we're talking about here; it's true of any physical model whatsoever.)

 

[Dale]

The simple fact of making a model with an event "in the past light cone of that model" is based on the premise that the event occurred before the apex event of the light cone

Yes, of course. By definition anything in the past light cone of an event occurred before the event. That is why it is called the "past" light cone.

But do you know anything "occurred in the past"? No.

I have pretty compelling physical evidence of many things that occurred in the past.

in that article you refute solipsism, but your post #56-quote-<<More precisely, you have no way of testing by experiment whether or not the event "existed" before you observed it--because any experiment would involve observation.>> leaves the option 'solipsims' still open,

What is it with BU discussions and solipsism? It seems to be a sort of philosophical name calling or guilt by association ploy. As though by gratuitously throwing the "s-word" into the discussion you can make them back off.

Any further posts discussing solipsism will be summarily deleted. This thread is already too prone to wandering.

 

[Dale]

You put data into a past lightcone but if you consider the option that events that are observed might NOT have occurred before the observation,

You are misstating things here. This is wrong: "you consider the option that events that are observed might not have occurred before the observation". It should be: "before the observation you consider the option that events that are not observed might not have occurred"

you don't know the event happed before the event of observation.

Here is another one. This should be "before the event of observation you don't know the event happened". After the observation you know both that the observed event physically happened and that it happened before the observation

But you doubt -see quote above- whether the event occurred before it is observed

Again this should be "before it is observed you doubt whether the event occurred". You consistently misstate things this way.

Hopefully those examples are sufficient for you to clear up the confusion in your recent posts.

 

[Ebeb]

Hopefully those examples are sufficient for you to clear up the confusion in your recent posts.

They help, thanks, but unfortunately they are not sufficient to clear up the confusion.
When you write: <<"before the event of observation you don't know the event happened">>, I fully agree, in the following sense:
Let's say we discuss the event "car hits tree". I fully agree that we don't know whether the car hits the tree or not until observation of such an event. But it's not the issue I wanted to deal with. The issue is: are there (any) events outside of the light cone that are not observed yet? Whether they will be observed or not is irrelevant to the question.
Are there are 'now' events occurring outside of my light cone or not. I'm not interested in what the 'content' is of the events (what they represent, f.ex "car hits tree", "bomb explosion", or whatever). I hope you understand that's a different issue than "We know whether the car hits the tree only after observation of the event 'car hits tree'". The question is whether there happens/occurs anything at all, now, at a spatial distance (elsewhere zone) from me.

To facilitate things I'll give you a possible answer to my question:
(A) strictly speaking I don't know whether at my present now event (let's call it event 'O') there are any events outside of my lightcone. Because strictly speaking it might be possible that in the future I all of a sudden don't see any events anymore, meaning that at event 'O' there are no events in the elsewhere zone, but not knowing it yet. (I should wonder whether physics/physical laws deal with such a possibility?)

The possible answer (A) to my question means we have two options to work with:
(1) there are at my the present now event spatially separated events in the elswhere zone of my present light cone.
Or
(2) there are at my the present now event no spatially separated events in the elswhere zone of my present light cone.

Correct so far?

 

[Dale]

The issue is: are there (any) events outside of the light cone that are not observed yet?

Is there any experimental measurement which could be performed to answer the question?

If not, then it is a philosophical question rather than a physical question.

If yes, then please describe the experimental setup and analysis you have in mind.

The question is whether there happens/occurs anything at all, now, at a spatial distance (elsewhere zone) from me.

Same as above.

 

[Ebeb]

O.K. Dale.
So your answer to my "Correct so far?" would be a '"yes".
Strictly speaking it means: when during the last few seconds you saw your foot, it doesn't imply/mean you will still see it the next second, because there might all of a sudden be no foot anymore!
For millions of years human beings saw events that existed before being observed, but we are not sure there are 'now' any spatially separated events from you that you will observe in the future.
O.K. Dale, I finally got the picture. It sounds too crazy to be true, but obviously I am not allowed to tell the universe to be crazy or not ;-) And it's not what Einstein had in mind (see previous quotes of, and about, Einstein).

 

[Dale]

So your answer to my "Correct so far?" would be a '"yes".

Don't put words in my mouth.

What experiment would you propose to answer the question?

Strictly speaking it means: when during the last few seconds you saw your foot, it doesn't imply/mean you will still see it the next second, because there might all of a sudden be no foot anymore!
For millions of years human beings saw events that existed before being observed, but we are not sure there are 'now' any spatially separated events from you that you will observe in the future.
O.K. Dale, I finally got the picture. It sounds too crazy to be true, but obviously I am not allowed to tell the universe to be crazy or not ;-) And it's not what Einstein had in mind (see previous quotes of, and about, Einstein).

This is wholly irrelevant to MY position on the matter. I understand the appeal of constructing a straw man to ridicule, but that is not what I am claiming.

What I am claiming is that there is no experiment that can answer the question even in principle. Therefore the question is not physical.

 

[Boing3000]

The question is whether there happens/occurs anything at all, now, at a spatial distance (elsewhere zone) from me.

But that question can only be answered when the elsewhere cross your past cone. That's all there is to it. The question of what IS now elsewhere cannot be answered by experimental apparatus.

Nobody here denies that there is an elsewhere full of events. Actually the universe seems to be quite stubborn at blasting them with uncanny regularity(SR) toward your now. But given that you cannot even attribute to them any coordinate, before they reach you, what the point ?

For millions of years human beings saw events that existed before being observed, but we are not sure there are 'now' any spatially separated events from you that you will observe in the future.

If the speed of "seeing" was that of a snail, you would realize how much your "sureness" would reduce accordingly.

"Seeing" does not project you into the future, not event the present, but the past. If it doesn't trouble you for the Andromeda galaxy, why does it for your foot ?

 

[PeterDonis]

The thread is going around in circles and is therefore closed.