The Thickness of Boundaries

[Loki]

I know, weird topic title, but bear with me.

The mind boggling thing I was thinking about today is the "thickness" of a boundary.

I was imagining flying to a given edge of the universe, flying as far out in a particular direction as I could, and then hitting a black wall. What if this black wall had no thickness? Wouldn't that mean that there was nothing beyond it?

Is it logically possible for a thing to have zero thickness? Or is it impossible?

If it's impossible, then yes, reality must be infinite.

[DHodges]

I was imaging flying to a given edge of the universe, flying as far out in a particular direction as I could, and then hitting a black wall. What if this black wall had no thickness? Wouldn't that mean that there was nothing beyond it?

If you can only see one side of the "wall," it is meaningless to talk about its thickness.

Is it logically possible for a thing to have zero thickness? Or is it impossible?

Mathematical objects (lines and planes) can have zero thickness. Real physical objects are made of something - particles - and so have a certain thickness. (Well, kind of. I'm sure Vic D. could answer this more completely - but I'm not sure a more complete answer is actually relevant here.)

So I would say it is not a logical impossibility, but it is a physical impossibility (if by "thing" we mean a physical object).

Boundaries, in general, are mental constructs. When looked at more closely, most boundaries have a fuzzy area and we find we have drawn a line, rather than observed it.

[Loki]

I was imaging flying to a given edge of the universe, flying as far out in a particular direction as I could, and then hitting a black wall. What if this black wall had no thickness? Wouldn't that mean that there was nothing beyond it?

If you can only see one side of the "wall," it is meaningless to talk about its thickness.

Ok, well is it meaningful to talk about this wall having an opposite side?

If I can see only one side of a wall, does this mean that by logical necessity there must be an opposing side?

Is it logically possible for a thing to have zero thickness? Or is it impossible?

Mathematical objects (lines and planes) can have zero thickness. Real physical objects are made of something - particles - and so have a certain thickness. (Well, kind of. I'm sure Vic D. could answer this more completely - but I'm not sure a more complete answer is actually relevant here.)

So I would say it is not a logical impossibility, but it is a physical impossibility (if by "thing" we mean a physical object).

Boundaries, in general, are mental constructs. When looked at more closely, most boundaries have a fuzzy area and we find we have drawn a line, rather than observed it.

Most boundaries? So you think there are exceptions?

[DHodges]

If I can see only one side of a wall, does this mean that by logical necessity there must be an opposing side?

In your scenario, talking about the edge of the universe, no.

Most boundaries? So you think there are exceptions?

I don't know.

[Loki]

Are you enlightened, Dhodges?

If not, do you believe enlightenment is attainable?

Do you have a clear definition of what enlightenment is?

Also, have you realized that reality is infinite?

[brokenhead]

Loki: If I can see only one side of a wall, does this mean that by logical necessity there must be an opposing side?
DHodges: In your scenario, talking about the edge of the universe, no.

Dave is answering this as Stephen Hawking would. Hawking says that this is the question he is asked most often. His answer is that it is like asking what lies ten feet north of the North Pole.

In another recent thread I referred to the quote that the most amazing thing about mathematical representation of things we perceive is that it has any relation to them at all, let alone that it can be astoundingly predictive.

What we do know is that any mathematical representation we can construct to mode the real world cannot be exact, in the sense that it always remains a model.

As an example, take a globe resting on a square table. We can measure the sides of the table to determine the surface area. We can measure the diameter of the globe to compute its surface are an volume. There will always be uncertainty in measurement, but this does not stop us from using exact equations to compute a quantity based on another quantity, the ones we have measured.

These simple exact equations could not in principle give us exact answers, no matter how small the uncertainty or error in measurement, even if we cold get it to zero.

This is because these equations are abstractions or idealizations. Simple reasoning bears this out. According to the mathematical definitions of a sphere and a flat surface, a sphere resting upon a flat surface would touch this surface at exactly a point, something that has exactly zero area or extension because it has zero dimensions. Simple rational thought tells you that since the sphere is resting upon the table, in the real world the point of contact cannot be zero-dimensional.

So while Hawking is right in explaining his mathematical model, keep in mind that it is only a model.

[Loki]

Loki: If I can see only one side of a wall, does this mean that by logical necessity there must be an opposing side?
DHodges: In your scenario, talking about the edge of the universe, no.

Dave is answering this as Stephen Hawking would. Hawking says that this is the question he is asked most often. His answer is that it is like asking what lies ten feet north of the North Pole.

Aw, but I see no reason why our universe isn't like a bubble which has an exterior. I wonder if hawking thinks there is anything beyond the bubble of our universe. It's expanding, so you would think that it's expanding into some surrounding empty space at least.

Here's an interesting question. When we come up against an end of a universe, what is this wall made of? I'd be curious to hear Hawkings answer on that one. If it's made of particles, then the universe definitely has an exterior. We can know that with absolute certainty.

In another recent thread I referred to the quote that the most amazing thing about mathematical representation of things we perceive is that it has any relation to them at all, let alone that it can be astoundingly predictive.

What we do know is that any mathematical representation we can construct to mode the real world cannot be exact, in the sense that it always remains a model.

As an example, take a globe resting on a square table. We can measure the sides of the table to determine the surface area. We can measure the diameter of the globe to compute its surface are an volume. There will always be uncertainty in measurement, but this does not stop us from using exact equations to compute a quantity based on another quantity, the ones we have measured.

These simple exact equations could not in principle give us exact answers, no matter how small the uncertainty or error in measurement, even if we cold get it to zero.

This is because these equations are abstractions or idealizations. Simple reasoning bears this out. According to the mathematical definitions of a sphere and a flat surface, a sphere resting upon a flat surface would touch this surface at exactly a point, something that has exactly zero area or extension because it has zero dimensions. Simple rational thought tells you that since the sphere is resting upon the table, in the real world the point of contact cannot be zero-dimensional.

So while Hawking is right in explaining his mathematical model, keep in mind that it is only a model.

hmmm. interesting thoughts, broke. A little over my head, but interesting.

[brokenhead]

Aw, but I see no reason why our universe isn't like a bubble which has an exterior. I wonder if hawking thinks there is anything beyond the bubble of our universe. It's expanding, so you would think that it's expanding into some surrounding empty space at least.

I am certainly not claiming I can visualize adequately the physical model suggested by any of the solutions to Einsteins GR equations. I say this because there have been times when I could do it better or more clearly than others, so this means I cannot do it perfectly, that I could always do it better if I really tried. It always eludes me.

The simplest way to envision it is to use an analogy in fewer dimensions. If all space were limited to two dimensions, say the surface of a sphere, then no matter where you traveled in that space, you would encounter no edges.

People that must work with hyperspace models more often than not cannot picture the model which they are constructing mathematically. It is by exploring equations believed to be correct, finding and examining solutions that satisfy these [GR] equations, then trying to interpret what the the solutions would imply in the real world that cosmologists come up with a notion of a universe with no exterior, just an interior.

Models are not required to have any reality other than the abstractions which they are. They are required to be self-consistent logically, and are then modified and forced to evolve to correspond with new empirical observations. They either evolve, get subsumed into a larger framework, or are discarded.

It is amazing to me that the model of the atom that consists of a nucleus containing protons and neutrons surrounded by a distribution of electrons has been the standard model of ordinary matter for less than one hundred years. It's acceptance is due to the overwhelming success of predictions made based on it. We are taught it in school, and rightly so. We take it as a fact. Yet it is not even twice as old as I am.

[Shahrazad]

broken,

It is amazing to me that the model of the atom that consists of a nucleus containing protons and neutrons surrounded by a distribution of electrons has been the standard model of ordinary matter for less than one hundred years. It's acceptance is due to the overwhelming success of predictions made based on it. We are taught it in school, and rightly so. We take it as a fact. Yet it is not even twice as old as I am.

You are aware that this simple model is very outdated, aren't you?

[Loki]

Yeah, I was told that the Rutherford planetary model of the atom no longer holds weight. But that's just what I've heard.

[MySuicide.X.MyBride]

I know, weird topic title, but bear with me.

The mind boggling thing I was thinking about today is the "thickness" of a boundary.

I was imagining flying to a given edge of the universe, flying as far out in a particular direction as I could, and then hitting a black wall. What if this black wall had no thickness? Wouldn't that mean that there was nothing beyond it?

Is it logically possible for a thing to have zero thickness? Or is it impossible?

If it's impossible, then yes, reality must be infinite.

"Space" is a product of the universe, therefore there is no boundary. Everything is within the universe, or at least in this closed system.

[Loki]

How do you know the universe isn't a product of space?

[Ignius]

The mind boggling thing I was thinking about today is the "thickness" of a boundary.

That strikes me as nonsensical. However, upon further contemplation, I saw this: we all have boundaries for many reasons. Some have more reasons than others and therefore the boundary can be seen as thicker.

I was imagining flying to a given edge of the universe, flying as far out in a particular direction as I could, and then hitting a black wall. What if this black wall had no thickness? Wouldn't that mean that there was nothing beyond it?

If there was nothing beyond it, then that would mean that it isn't the edge of the universe. But, if it was the edge of the universe, then it must have a thickness, though we would not know about it, unless we were to find a door...

Is it logically possible for a thing to have zero thickness? Or is it impossible?

I would assume that there is no end to the universe... It's sort of like the concept of infinity. If it isn't, then there must be something behind it.

If it's impossible, then yes, reality must be infinite.

Depends what you mean by reality. For instance, when I'm dreaming, THAT is my reality for that time period.

[MySuicide.X.MyBride]

How do you know the universe isn't a product of space?

Spacetime was created by the big bang and is the relationship of the dimensions to matter.

Edit: Of course this is all according to theory. I'm not saying that's how it is, but that's what the best evidence suggests.

[David Quinn]

Loki: If I can see only one side of a wall, does this mean that by logical necessity there must be an opposing side?
DHodges: In your scenario, talking about the edge of the universe, no.

This issue can never resolved because it is firmly enmeshed in the realm of empirical uncertainty.

Even if a person were to travel to what seemed like the edge of the universe and observed nothing beyond, he would have no way of knowing whether he really was looking at the universe's edge. Perhaps the universe does extend beyond the edge, but on a much larger scale, quite invisible to a human's smaller scale of seeing things? Perhaps the nothingness he observes is an hallucination or a delusion of some kind? It isn't possible to resolve such a question in any absolute sense.

All we can say is that wherever there is existence, there is ultimate reality. There can never be anything beyond ultimate reality.

Is it logically possible for a thing to have zero thickness? Or is it impossible?

If it's impossible, then yes, reality must be infinite.

Things with zero thickness can only exist in the realm of the imagination.

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[Ignius]

Duh.

[brokenhead]

broken,

It is amazing to me that the model of the atom that consists of a nucleus containing protons and neutrons surrounded by a distribution of electrons has been the standard model of ordinary matter for less than one hundred years. It's acceptance is due to the overwhelming success of predictions made based on it. We are taught it in school, and rightly so. We take it as a fact. Yet it is not even twice as old as I am.

You are aware that this simple model is very outdated, aren't you?

No it's not. I am not talking about the planetary model of the atom. I am talking about the existence and behavior of nuclei and the quanum behavior of electrons. The central nuclues/outer electron model is not outdated at all.

[Shahrazad]

broken,

No it's not. I am not talking about the planetary model of the atom. I am talking about the existence and behavior of nuclei and the quanum behavior of electrons. The central nuclues/outer electron model is not outdated at all.

I was taught a more sophisticated atom model in school, in the mid 70s. That's well over 30 years ago that I've known that electrons do not revolve around the protons and neutrons in a neat little orbit.

However, I still find your planetary model extremely useful in chemistry. It's just that there are other scientific fields besides chemistry where the old model doesn't deliver.

Edit to add: I just reread your post, and noticed you said you are not talking about the planetary model. Sorry, I misread you, and now I'm not sure what model you are talking about.

[Ignius]

You see, you post like me! *shocked*

[marcothay]

Interesting how almost every pondering about "existence of something" goes directly
to the question about the nature of space, isn't?

Is this physical universe limited or unlimited?
Olber's paradox explains very well why this universe can't be infinite!

By the way, what is your definition of "DIMENSION"?

Again, what is the commune denominator between "appearance" and "illusion"?

[Sapius]

David: All we can say is that wherever there is existence, there is ultimate reality. There can never be anything beyond ultimate reality.

Which seems to leave open the possibility of when and where there is no existence, then what happens to ultimate reality? However, I don’t see the need to introduce an “ultimate reality” to know that there can never be anything beyond existence itself, or say beyond space, (to keep Marco happy) ;) Or to know that non-existence is not possible.

[David Quinn]

David: All we can say is that wherever there is existence, there is ultimate reality. There can never be anything beyond ultimate reality.

Which seems to leave open the possibility of when and where there is no existence, then what happens to ultimate reality? However, I don’t see the need to introduce an “ultimate reality” to know that there can never be anything beyond existence itself, or say beyond space, (to keep Marco happy) ;) Or to know that non-existence is not possible.

If you want to encourage people to comprehend the true nature of existence, then it can help to introduce terms such as "ultimate reality".

For example, we can define "ultimate reality" to mean existence as it really is, as opposed to what deluded people imagine existence to be.

-

[Ignius]

If you want to encourage people to comprehend the true nature of existence, then it can help to introduce terms such as "ultimate reality".

For example, we can define "ultimate reality" to mean existence as it really is, as opposed to what deluded people imagine existence to be.

How do deluded people imagine it to be?

[Ignius]

Just because you don't see what another sees, doesn't mean that that which is seen doesn't exist, even though it doesn't exist in your reality. Right? Someone may have once mentioned this: a homeless man siting on the street talking to the voices in his head. Any reasonable person would assume (or know) that this guy is mentally ill, but according to you, David, this man may actually be going through a real experience, though, there is no evidence for this in the real world (or one's perspective of the real world, or the group-agreement that this is the way things are, etc). Now take that example, and make it a little more clearer, a homeless man taking an imaginary shower out on the street. He's got an imaginary sponge, soap, running water, etc... Everything except for the actual setup. He strips down, etc...

Question: could it be that this man, in his head, is actually washing himself? Of course, but is that something that is really happening? No, but this is according to your perspective. Perhaps, that whole "scene" is in your head, and perhaps, you're the man that's taking the shower out on the side of the street? Go, ultimate reality!

Obviously, this isn't true, and you won't know unless you wakeup, but before you do wakeup, you are already awake... Or so you think.

What do you think of that?

[David Quinn]

If you want to encourage people to comprehend the true nature of existence, then it can help to introduce terms such as "ultimate reality".

For example, we can define "ultimate reality" to mean existence as it really is, as opposed to what deluded people imagine existence to be.

How do deluded people imagine it to be?

Their primary fault is imagining things to be inherently existing and objectively real. And then on top of that, other delusions are constructed. For example, most people believe the universe to be warm, caring and purposeful, or alternatively, cold, inhospitable and meaningless.

So it's a case of delusions being piled on top of other delusions.

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