Hopefully my last post on infinite regress.

[jumbojak]

I'm really not good at maths, so I might be making a total mess here, but what about the common example used to describe infinity, where in a hotel with an infinite amount of rooms will always be able to cram in one more room, thus making infinity equal to infinity plus 1?

Also, there are different types of infinities, and even contained within a finite set. Decimals, for instance, between finite and well defined numbers.

Hilbert's Hotel relies on there being an actually infinite number of rooms and the way infinite arithmetic works out you don't seem to be actaually adding one to infinity to make room for new guests. Infinite set theory is a bit counter-intuitive, for example, imagine that all the guests in odd numbered rooms check out. Because the hotel contains an actual infinite number of rooms the owner can shift each remaining guest by dividing their room number by two and leave his hotel fully occupied

It's weird that a hotel filled with infinitely many guests could have an infinite number of guests check out, shuffle the remaining occupants around and still be completely full. That's the problem with infinity, it doesn't work like everyday experience.

[Ali]

My understanding that as a concept, time is infinite, both ways.  Infinate future, infinate past.  Of course infinate past is incredibly hard to grasp, because our brains aren't built to deal with that concept.  But if you think about it, it's just as hard to think of time having a true start either.  What happened before time?  If it was "before" isn't it still part of time? 

[jumbojak]

My understanding that as a concept, time is infinite, both ways.  Infinate future, infinate past.  Of course infinate past is incredibly hard to grasp, because our brains aren't built to deal with that concept.  But if you think about it, it's just as hard to think of time having a true start either.  What happened before time?  If it was "before" isn't it still part of time? 

I think the problem is that we don't have a good grasp on causation in the absence of time and you seem to be right that our brains are not built to deal with these concepts intuitively. This is the reason why we clung to aritotelian physics for so many years. This is bad physics, but I think it is understandable that we would see things that way. In the same way, I believe the widely held view that time has no beginning is mistaken, and is based on our personal bias

Asking what happened before time seems a bit like asking why the Sun orbits the Earth. When you can see that all the facts and physical intuitions point to a heliocentric solar systemthe original question becomes irrelevant. In the same sense I do not think we have anywhere near sufficient facts or physical intuition to answer the question of how time came into being. The fact that time had a beginning does not provide an explanation for its existence and the fact that we do not know how it began does not change the fact that it did begin to exist.

[Recusant]

I'm not quite sure what you mean by outside of any chain of events.

A hard vacuum exists. A pair of particles pops in and out of existence in that vacuum. This is an example of an occurrence for which no cause can be ascribed. Can we say that the fact that a continuum exists (in which those particles might appear) is itself a cause? That doesn't seem to qualify as classical causality.

If you mean an event outside of time, which is what I think you mean by un-caused, I certainly think that events can occour outside of time, however I do not believe that our common sense view of how things happen in time will be of much use to us in that situation. It seems that an event would merely happen, and that perhaps only very simple events could occour.

No, as you can see above, an un-caused event doesn't necessarily have to occur outside of time.

The idea that a raging tiger could pop into existence at a singularity ( if a singularity is the best explanation for the origin of our universe ) seems quite absurd. The idea that something very simple, like fundamental particles and our four-force laws, seems much more reasonable given the very primitive machinery that would be availible in such a state.

I never mentioned tigers.    Standard cosmology describes a very simple thing emerging from the initial singularity, so it seems to meet your idea of what is reasonable.

And I don't think that our understanding of the concept of infinity is hindering us in this endeavor.  It is precicely because I realise that we cannot really count to infinity, that I conclude the idea of an actually infinite series of events in time is impossible. You could redefine infinite in some different way I suppose, but that wouldnt be infinity in the sense that I am using the word.

I'm not saying that our understanding of infinity is a hindrance. On the other hand, perhaps our existence as beings who perceive time in a particular way affects how we approach the concept of infinity.  Attempting to count infinity makes no sense, as you say, but I think you're making a leap when you say that this uncountable quality makes an infinite timeline impossible. Perhaps I've failed to grasp your meaning, but I don't see where you've actually proved that.

Another approach: Addition is a process, and adding indefinitely is one description of infinity. An actual infinity isn't a static thing, therefore, but a process. Yet you try to treat it as a static thing like a number; something which can be "created" as something complete. That approach seems incorrect to me.

As for the arrow of time, I think that thermodynamics indicates that events happen in a certain direction. We could certainly imagine that a glass of water spontaneously boils when it is put in the freezer, but that isn't what normally happens. Thermofynamics has in intrinsically irreversible nature.

Yet the article says that Newton's laws would work just as well in reverse, and that our perception of time may be something that emerges in the macroscopic scale, but has no validity on the quantum level.

That article could be a little misleading if the last few weeks are any indication. Many scientists and philosophers have adopted the B-Theory of time which treats time as a "static" quantity, with events described in terms of relationships with other events. It's the result of an effort to describe events without making use of tensed verbs, and I have seen a few places where its implications were confused to mean no time. I will try to contact the scientists and inquire more on their specific views.

That would be interesting.

For the side question, I do think that our future could never actually be considered infinite, even if the universe goes on expanding forever. It would still just be one event happening after another and thus could not actually be infinite.

Again, it seems that you're attempting to approach infinity as something that should be static, something that, since we can never actually reach, we must conclude doesn't exist. ("If it's not finished then it's not infinity." As if infinity could be finished.) I think this is not correct, as explained above. In the realm of time (assuming for the moment that time actually exists  ), infinity is exactly one thing happening after another, without end; it's a process, not a quantity. It doesn't have to be something that you can point at ("See, there is infinity!") to be "actual."

[Genericguy]

Perhaps...

In counting units of time in either direction, from any random starting point, we really are not starting at 1. We are starting at infinity. Today, for example would not be 1 if we move ahead 2 million years and counted backwards. Today would be day 2 million. if we moved ahead indefinitely, we would not be able to quantify the distance as anything other than infinite.

[Ali]

Asking what happened before time seems a bit like asking why the Sun orbits the Earth. When you can see that all the facts and physical intuitions point to a heliocentric solar systemthe original question becomes irrelevant. In the same sense I do not think we have anywhere near sufficient facts or physical intuition to answer the question of how time came into being. The fact that time had a beginning does not provide an explanation for its existence and the fact that we do not know how it began does not change the fact that it did begin to exist.

Is that a fact (that time did indeed begin to exist, that there was a time before time? LOL) Do you have any evidence or even just logic that would back that up?  Because my brain insists that the time before time, would still time, as "before" is a time based construct. 

[jumbojak]

I'm not quite sure what you mean by outside of any chain of events.

A hard vacuum exists. A pair of particles pops in and out of existence in that vacuum. This is an example of an occurrence for which no cause can be ascribed. Can we say that the fact that a continuum exists (in which those particles might appear) is itself a cause? That doesn't seem to qualify as classical causality.

If you mean an event outside of time, which is what I think you mean by un-caused, I certainly think that events can occour outside of time, however I do not believe that our common sense view of how things happen in time will be of much use to us in that situation. It seems that an event would merely happen, and that perhaps only very simple events could occour.

No, as you can see above, an un-caused event doesn't necessarily have to occur outside of time.

The idea that a raging tiger could pop into existence at a singularity ( if a singularity is the best explanation for the origin of our universe ) seems quite absurd. The idea that something very simple, like fundamental particles and our four-force laws, seems much more reasonable given the very primitive machinery that would be availible in such a state.

I never mentioned tigers.    Standard cosmology describes a very simple thing emerging from the initial singularity, so it seems to meet your idea of what is reasonable.

And I don't think that our understanding of the concept of infinity is hindering us in this endeavor.  It is precicely because I realise that we cannot really count to infinity, that I conclude the idea of an actually infinite series of events in time is impossible. You could redefine infinite in some different way I suppose, but that wouldnt be infinity in the sense that I am using the word.

I'm not saying that our understanding of infinity is a hindrance. On the other hand, perhaps our existence as beings who perceive time in a particular way affects how we approach the concept of infinity.  Attempting to count infinity makes no sense, as you say, but I think you're making a leap when you say that this uncountable quality makes an infinite timeline impossible. Perhaps I've failed to grasp your meaning, but I don't see where you've actually proved that.

Another approach: Addition is a process, and adding indefinitely is one description of infinity. An actual infinity isn't a static thing, therefore, but a process. Yet you try to treat it as a static thing like a number; something which can be "created" as something complete. That approach seems incorrect to me.

As for the arrow of time, I think that thermodynamics indicates that events happen in a certain direction. We could certainly imagine that a glass of water spontaneously boils when it is put in the freezer, but that isn't what normally happens. Thermofynamics has in intrinsically irreversible nature.

Yet the article says that Newton's laws would work just as well in reverse, and that our perception of time may be something that emerges in the macroscopic scale, but has no validity on the quantum level.

That article could be a little misleading if the last few weeks are any indication. Many scientists and philosophers have adopted the B-Theory of time which treats time as a "static" quantity, with events described in terms of relationships with other events. It's the result of an effort to describe events without making use of tensed verbs, and I have seen a few places where its implications were confused to mean no time. I will try to contact the scientists and inquire more on their specific views.

That would be interesting.

For the side question, I do think that our future could never actually be considered infinite, even if the universe goes on expanding forever. It would still just be one event happening after another and thus could not actually be infinite.

Again, it seems that you're attempting to approach infinity as something that should be static, something that, since we can never actually reach, we must conclude doesn't exist. ("If it's not finished then it's not infinity." As if infinity could be finished.) I think this is not correct, as explained above. In the realm of time (assuming for the moment that time actually exists  ), infinity is exactly one thing happening after another, without end; it's a process, not a quantity. It doesn't have to be something that you can point at ("See, there is infinity!") to be "actual."

Sorry I can't quote your post line by line but I am transfering the long responses from my laptop to my phone because I don't have an internet connection in the house. I will try and respond to the points you made in order.

The idea of a "hard vacuum" is not entirely correct. Modern quantum theory describes a vacuum state as a lowest possible energy state and the mechanism by which virtual particles appear is not settled among physisists today. Combine this with the formulation of deterministic variants of quantum mechanics ( Bohmian Mechanics ) and the idea of particles appearing uncaused from nothing loses some of its significance.

Even if the existense of such a low energy state does not enable us to predict exactly when such particles will come into existence, if I am not mistaken even our current understanding of such events allows us to at least measure the probability that such particles will appear. I understand where you are coming from here, but the existence of even a lowest energy field gives a possible causal explanation for virtual particles.

As for the tiger, it is not uncommon for Christians to cite the absurdity of a "raging tiger" emerging from nothing. Often this happens during a debate with a smug ( and often unprepared ) atheist, and Christian crowds seem to go wild. I've heard it so many times over the last month that I couldn't resist.

When I talk about the difference between an actual infinite collection and an indefinite collection ( earlier I think I mistakenly said "potentially infinite" ) I am referring to the difference between an infinite set, like the natural numbers, and a constantly growing set, like the numbers counted while attempting to reach infinity. There is a difference in what can exist conceptually and what can exist actually.

If we think about the natural numbers, all of them, then we are clearly talking about a set that is actually infinite. No natural number exists which is not a part of the set. Conceptually this is pretty easy to do, and it is clear that no "process" is involved in creating the natural numbers. They exist, only in an abstract way mind you, but they exist all on their own.

As for Newton's laws being time reversible, that is a well documented fact. However, Newton is best known for his work in mechanics, not thermodynamics, and the laws of thermodynamics most definately don't work in reverse. It is certainly possible that time does not exist on some smallest scale and I would welcome the discovery, but conjecture over the interperetation of disputed theoretical results ( which have not yielded any experimental results ) seems like we are getting ahead of ourselves.

Tonight I'm going to see if I can find those scientists email. It's not uncommon for universities and labs to post their staff's contact information so stay tuned for what they have to say. That is assuming they will have anything at all to say to a dumb, uneducated redneck like me!

With regard to your last point, yes I am saying that if we are going to say that a collection is actually infinite, then it does need to be infinite, and not merely growing towards infinity. Conceptual entities, like the set of real numbers, can certainly be said to be both infinite, and static. The set of natural numbers does not grow over time and I think this affords us the right to say that the set is actually infinite as opposed to merely approaching infinity which it can never really reach.

The difference between aleph-null and the lemniscate is a subtle, but crucial difference to make. There really is a difference between the two and according to my findings the difference rules out the possibility of an infinite regress.

[jumbojak]

I found Prof. Krausz email and plan to contact him tonight. I have to run to the store but I hope to send him a request for clarification before bedtime tonight. Bedtime sucks...