Actual Infinity in Reality?

[LadyForCamus]

@steve,

I was a bit confused about this ‘no start’ as well, but I think the relevant distinction here is in how we are viewing time. If time actually flows from moment to moment the way we experience it, then I agree with you that if we assume infinite time, it seems like a logical impossibility to not ever start anywhere, and somehow still get somewhere. But, the point that Poly and Grand are making is that it could very well be true that time does not flow. That there is no, ‘first this one, then the next, and then the next, ect.) but rather, time is a static collection of an infinity of points in existence; past, present, and future. All points exist simultaneously, and every time slice represents a section, or point, in the ‘set’ of infinite time. If that is the case, then infinite time is very much like an infinite set of numbers in mathematics, and completely logically possible. You don’t have to start at a number and actually count one after the other in order to have a completed infinite set of numbers in mathematics. You couldn’t; isn’t that the point? Similarly, you don’t have to start at ‘event one’ in time and wait for the next one to happen in order to have a completed set of infinite time. All the points are already there.

My understanding is that B theory of time is an active competing hypothesis under serious consideration by the scientific community, and not without evidential support. If that is the case, then I have to agree with Poly and Grand that there is no logical contradiction here.

(I’m a dunce in the corner compared to the rest of you, so if I got something wrong above, please jump in and course-correct. Thanks!)

[SteveII]

There are many people that do think the B theory of time is correct (physicist, cosmologists, philosophers).

And in fact, Einstein himself was a B-theorist with regards to time, calling time (or rather, the flow of it) an illusion.

I'm not so sure. Perhaps he was, but relativity/time dilation is not B Theory. From your same article:

According to Einstein, then, time is relative to the observer, and more specifically to the motion of that observer. This is not to say that time is in some way capricious or random in nature – it is still governed by the laws of physics and entirely predictable in its manifestations, it is just not absolute and universal as Newton thought (see the section on Absolute Time), and things are not quite as simple and straightforward as he had believed.

General nor Special Relativity do not entail the B theory of time--it only implies that such a theory my be correct. BUT, more importantly, your belief there is no causal connections is NOT a part of the B Theory of time. If you think it is, it should be easy to post a link from a nice concise article on the subject.

What do you think B-theory means? Have you at least looked up Wikipedia on this?

Here's an article for you to read:
http://www.exactlywhatistime.com/physics...stic-time/

Quoted below is a relevant paragraph from that article:

Modern physicists therefore do not regard time as “passing” or “flowing” in the old-fashioned sense, nor is time just a sequence of events which happen: both the past and the future are simply “there”, laid out as part of four-dimensional space-time, some of which we have already visited and some not yet. So, just as we are accustomed to thinking of all parts of space as existing even if we are not there to experience them, all of time (past, present and future) are also constantly in existence even if we are not able to witness them. Time does not “flow”, then, it just “is”. This view of time is consistent with the philosophical view of eternalism or the block universe theory of time (see the section on Modern Philosophy).

Time does not flow => B-theory of time, which is consistent with the other philosophy of time: eternalism.

With respect to change and events, what does it mean for time to not really be flowing? And what do you think the symmetry of time implies (as entailed by the laws of physics)?

I understand B Theory of Time just fine. I have actually seen the video and read at least a dozen articles on it. My problem with you is that you think that the theory does away with causation. It does not. Even if you believe that all time slices (past, present, future) are equally real, they are all ordered by a causal connections in one direction. Fruit rots in one direction. Baby horses always preceded adult horses. These connections can be drawn with exact precision--that is literally what science does. There is nothing in B Theory that gets around this. You are adding a layer on top and calling it B Theory.

That does not answer the question. Yes or no--are you the same person you were in 2010 or will be in 2020? If not, you have temporal parts that are causally connected in a specific direction--from earlier than to later than.

I am not the exact same person I was in 2010 nor will I be the exact same person in 2020 (if I'm alive then). However, by convention and because we are wired to do so, we perceive the self to be this enduring entity that actually crosses time. It doesn't mean, however, that it does. Each instance of me is stuck in one of the time moments that are a part of this space-time reality.

No, it does not mean that I have temporal parts that are really causally connected, just connected. And direction, even if there is one in the objective sense, does not necessarily imply causal connection.

I think your theory (which is not B Theory) is a real fringe theory and you would be hard pressed to find an article on. The business of science is exactly opposite of what you just said in that last sentence. For some reason, you got it in your head that B Theory of Time entails this. Find an article. 

Again, you have not shown that to be part of the theory. Can you explain why science is almost entirely focused on causation if it is an illusion.  It seem the claim that it is an illusion is driven by something else rather than science.

Then you haven't read enough articles on the B-theory of time. It is logically entailed by the theory. If the flow of time is an illusion, then what we are perceiving is an illusion. All the changes and events we supposedly witness are not really happening. It's all psychological. But it nevertheless serves an evolutionary benefit for us to perceive changes and events.

And, of course, science is going to focus on causation and changes and events much of the time, because much of the time, we are analyzing the world from a temporal perspective, assuming the flow of time, and because it's not a useless way of analyzing the world from such a perspective. Saying that causality is an illusion, fundamentally and ultimately, does not mean it is a waste of time to understand how this actual local universe works from a temporal perspective. Different aims/purposes, and different questions about the world, mean different ways of studying the world. It's normally when you need to answers questions regarding time itself that you jump some levels and analyze the world from a vastly different perspective, one that is atemporal.

I see one of your problems. You said "causality is an illusion". You will not find that phrase anywhere in an article of B Theory. The typical description is the "flow of time is an illusion". 

How many times have I asked this: " We could not have gotten to our current universe without an infinite amounts of universes already being created. We would still be waiting for an infinite amount of universe to be sparked before ours could be sparked--which will never happen, because there still needs to be an infinite more that need to come first. Why can't you address this!?"

I don't adhere to such a model of cosmology. I think all universes exist eternally and simultaneously.

That is a metaphysical claim with very thin reasoning. We only know about the laws of physics in our universe. Extrapolating what appears to be a finite universe into a spacetime manifold for all universes ever is a stretch. HOWEVER, that doesn't really answer the question. Regardless of your insistence, there would still be measurable causal connections all the way back through the time slices and you are back up against my point above. 

NOT SO. The B theory of time does not entail an actual infinite. The standard big bang models all have our spacetime manifold with a definite beginning.

If time does not really flow, then what can one say about "past", "present", and "future" time moments, other than what I have been arguing the whole time about them?

And even if there was what we may call the "beginning" moment, this is being said from a temporal first-person perspective.

Not so at all. If the universe had a beginning, the spacetime manifold had an absolute beginning. Has nothing to do with observer position. The fact that all timeslices were created at once does not mean there was a first time slice in the sequence. 

Anything with a beginning is by definition not an actual infinite.

Actually, not true.

Remember this set?

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... }

This is an example of an infinite set that has a starting number.

Your example is a potential infinite set -- not an actual infinite. Two very different things. This distinction is important for this whole discussion. 

If something were to "start existing" it most certainly can be counted.

Which is irrelevant to everything I've been saying here.

One man's "counter-intuitive outcomes" is another man's absurdities. Notice the word I marked above - assume. If you assume an actual infinite, you are question begging.

We're assuming it in order to see if we can disprove it, via a reductio ad absurdum argument. Since you have failed to disprove it, then it's fair to say that an actual infinity seems logically possible. Or at least, we haven't seen a logical argument that proves it is not logically possible. And I'm being very generous here.

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Bold mine.

I think what Steve means is, if we have time moving in a forward direction, how do we get to that one point in time from an infinite past?  How do you get to that single event in time without beginning somewhere?  If events are happening in succession, and time is infinite into the past, how would we ever arrive at a singular point in time?  Wouldn’t you have to start somewhere to get there?   I’m confused! Lol

Steve is assuming the A-theory of time, which is very problematic and a clear contradiction of modern science. What he seems to be doing is treating time as if it's this one entity (NOT a stream, but a "something" like a point/dot or whatever) which actually moves along from "somewhere" to "somewhere else", and wherever it hits, that is the "present moment". But according to science, time isn't anything like that. It's more of a dimension of space itself (similar to the x, y coordinates in high school algebra graphs), and all things in existence are already there and have already "happened". So there is no "arrival" to worry about. This "present moment" exists because it's always been there, being experienced by its corresponding instance of "you".

For this discussion, I assumed all along B Theory (even though I don't believe it) because it does not matter to my point. Time is one thing. Space is another. They both exist. Treated together, we have spacetime. You can break them back up and do equations and put them back together again. You think I am talking about A theory, but its because you don't understand B theory. 

"Arriving" to the present is a handy placeholder. You still have causal connections all the way to whatever "present" you want to observe. You can't avoid it by mincing words.

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Why (Almost All) Cosmologists are Atheists

Interestingly, here's what Sean Carroll had to say on causality from the paper linked to in the quote:

In particular, we should emphasize that there is no place in this view for common philosophical concepts such as “cause and effect” or “purpose”. From the perspective of modern science, events don’t have purposes or causes; they simply conform to the laws of nature. In particular,
there is no need to invoke any mechanism to “sustain” a physical system or to keep it going; it would require an additional layer of complexity for a system to cease following its patterns than for it to simply continue to do so. Believing otherwise is a relic of a certain metaphysical way of thinking; these notions are useful in an informal way for human beings, but are not a part of the rigorous scientific description of the world. Of course scientists do talk about “causality”, but this is a description of the relationship between patterns and boundary conditions; it is a derived concept, not a fundamental one. If we know the state of a system at one time, and the laws governing its dynamics, we can calculate the state of the system
at some later time. You might be tempted to say that the particular state at the first time “caused” the state to be what it was at the second time; but it would be just as correct to say that the second state caused the first. According to the materialist worldview, then, structures and patterns are all there are — we don’t need any ancillary notions.

So it's not an idiosyncratic view I just happen to personally hold. This is the view on causality that physicists themselves adhere to as well.

He didn't say anything i haven't been saying. I understand the B Theory of Time. But we still have "connections" (see highlighted). I called them "causal connections" for convenience. A rotting apple is still connected to the good apple. The baby horse always precedes the adult horse in these connections. You are grasping onto a couple of phrases and reading things into it. Of course if time slices are equally real, you cannot say one caused the next. But you cannot say they are not linked!!!! Those links can be followed backwards through the slices.

[polymath257]

At least as far as I understand it, Einstein's views were not *exactly* in line with the B theory of time. But they certainly were not at all in line with the A theory. Let me explain.

The B theory seems to suggest that time is a universal, objective thing in a way that contradicts general relativity.  For example, if I measure the time between two events to be 5 seconds, so will everyone else. But that is NOT the case in relativity! It is quite possible in relativity for one observer to measure 5 seconds between events and another to measure 3 seconds between those same two events. From what I can see, the B theory isn't very comfortable with this aspect of reality.

General relativity, on the other hand, considers time and space together to be a single entity: spacetime, which has an objective reality. So, while distances in space and durations between events are not separately well-defined (they depends on the motion and position of the observers), a combination of them *is* objective and is agreed upon by all observers. In this system, time does NOT 'flow'. ALL of space and ALL of time are, together, the geometry of spacetime. Time, like space, simply exists. Neither is well-defined in and of itself. BOTH are required for a consistent system.

One of the issues here is that it is possible that one observer will see event A as happening before event B and another may see it the other way around. So the idea of causality needs to be somewhat modified: instead of causes only having to be in the past (which is observer dependent), they have to be in the *past light cone* (which all observers agree to). The past light cone is the collection of events in spacetime from which light could reach the event in question. Nothing outside of this light cone can be a cause for an event.

With this modification, however, causality *is* a central aspect of general relativity. But it isn't in the sense that time flows from one set of events to another. It is that the particular distribution of particles in spacetime has to obey certain rules that reflect this causality. The spacetime is *still* one complete entity, but the 'pictures' on that manifold are not completely random: they reflect constraints on the solutions of the basic dynamical equations.

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OK, we have a good question here:

Is {1,2,3,4,5....} an actual infinity or a potential infinity?

Steve claims it is a potential infinity. I claim it is an actual infinity. The difference is that Steve seems to think of it as a process of creating that set and I see the set as simply there and our attempts to *list* it are doomed to failure.

But I can tell what is in and what is not in that set with perfect precision. For example, the number 59749873 is in that set and the number 82.389587 is not. That is *all* that is required to completely define the set: to know what is in and what is not. You don't have to list the elements, just know how to tell when something *is* an element.

So the set {1,2,3,4,5....} is an actually infinite set. It is the *complete* collection of counting numbers. Nothing is being added or taken away from it.

And we are NOT taking the succession of finite sets
{1}, {1,2}, {1,2,3}, {1,2,3,4},....
NONE of those is the set above. THAT I certainly agree with. At no finite stage in this progression do you get the set above. I agree with that also.

But that isn't the same question. The question is whether the completed set
{1,2,3,4,.....}
is an actually infinite set or not. Since it is well defined and since it is none of the finite sets above, it is.

[SteveII]

@steve,

I was a bit confused about this ‘no start’ as well, but I think the relevant distinction here is in how we are viewing time.  If time actually flows from moment to moment the way we experience it, then  I agree with you that if we assume infinite time, it seems like a logical impossibility to not ever start anywhere, and somehow still get somewhere.  But, the point that Poly and Grand are making is that it could very well be true that time does not flow.  That there is no, ‘first this one, then the next, and then the next, ect.) but rather, time is a static collection of an infinity of points in existence;  past, present, and future.  All points exist simultaneously, and every time slice represents a section, or point, in the ‘set’ of infinite time.  If that is the case, then infinite time is very much like an infinite set of numbers in mathematics, and completely logically possible.  You don’t have to start at a number and actually count one after the other in order to have a completed infinite set of numbers in mathematics.  You couldn’t; isn’t that the point?  Similarly, you don’t have to start at ‘event one’ in time and wait for the next one to happen in order to have a completed set of infinite time.  All the points are already there.

My understanding is that B theory of time is an active competing hypothesis under serious consideration by the scientific community, and not without evidential support.  If that is the case, then I have to agree with Poly and Grand that there is no logical contradiction here.

(I’m a dunce in the corner compared to the rest of you, so if I got something wrong above, please jump in and course-correct.  Thanks!)

You are not a dunce. I observed not too long ago that I didn't know anything about this subject and read quite a few articles. Even the process of this discussion fills in some things for me. 

First, you don't need time to "flow". You still have causal connections from one time slice to another that are countable. A rotting apple has very predictable steps that are easy to plot. You still need a baby horse in a prior time slice to get an adult horse in another. These causal connections are what the whole enterprise of science is about. To say that the theory dismisses this fundamental aspect of reality is to not understand the theory. 

Second, I think it is quite a leap to say that every and all universes ever exist simultaneously in a giant spacetime manifold like the one that we experience in our universe. That just seems to be a convenient assertion. However, as we have been discussing, the B theory of time does not eliminate the aspect of reality that each event is inextricably linked in prior-to and after than relationships/connections. 

Third, the idea that all events that will ever happen are equally real simultaneously is NOT the same as infinite set theory in mathematics. The first is an actual infinite and the second is a potential infinite. To be clear, mathematicians are talking about potential infinities when the talk about sets. This is because one side is bounded and only the open side is potentially infinite. These two terms have very different definitions and cannot be used interchangeably or use one to prove the other.

[polymath257]

Third, the idea that all events that will ever happen are equally real simultaneously is NOT the same as infinite set theory in mathematics. The first is an actual infinite and the second is a potential infinite. To be clear, mathematicians are talking about potential infinities when the talk about sets. This is because one side is bounded and only the open side is potentially infinite. These two terms have very different definitions and cannot be used interchangeably or use one to prove the other.

This is just false. Mathematicians are talking about actual infinities. They even talk about different sizes of actual infinities (for example the difference between countably and uncountably infinite sets).

There is no requirement of having an 'open end' in the description of a set:

N={x: x is a natural number}

is a perfectly well defined, infinite set. No 'open side' and no 'bounded side'. The description in terms of a list,

N={1,2,3,4,...}

is more a convenience for those who cannot read mathematics than anything else.

What you seem to think is that the second is some sort of process. It isn't. It *does* appeal to your understanding to know what things are in the set and what are not. But the list itself is just a notational convention and nothing else. In the same way, we can define an uncountbaly infinite set

R={x: x is a real number}

or

[0,1]={x: x is a real number and 0<=x<=1}.

Both of these are uncountably infinite sets.

There is no such thing as a 'potentially infinite set' in math. Sets are either finite or infinite. In the latter case, they are actually infinite. They can be countably infinite or uncountably infinite. For the uncountbaly infinite sets, there are infinitely many different possible cardinalities (although very few are used in practice)

Look in *any* math book and you will find NO distinction made between potential and actual infinity. The reason? Those notions have been replaced. They are no longer used because they are confused and ill defined.

So, I will make a challenge. Look in *any* advanced level math book produced in the last half century. Find *any* reference that discusses *at all* the notion of 'potential infinity'. I challenge you to find a single source *in math* for your claims from the last 50 years (I'll even go 75 years).

[Jenny A]

I am not asking if there is a concept in mathematics that deals with infinity or if there exists sets with an infinite number of members (although you might use the concept in a larger argument). I am not asking if we can theoretically divide something an infinite amount of times (although you might use the concept in a larger argument). I am not asking about a potential infinite. 

I am asking about an actual infinite of something concrete (not abstract). Can it logically exist? Why or why not? 

No mention of God either. Philosophy subforum--let's stick with pure metaphysics.

Anything may exist as a posibility unless there is an inherent logical contradiction built into the possibility of it's existence. For example, invisible bachelors might exist (though not probably) without defying logic, as might 1000 year old bachlors. But married bachlors may not logically exist. What exactly is it about an infinity that makes you think it is logically impossible? And why do you think an infinite number of objects or time is illogical but an infinite division of an object or period of time is not?

[GrandizerII]

And in fact, Einstein himself was a B-theorist with regards to time, calling time (or rather, the flow of it) an illusion.

I'm not so sure. Perhaps he was, but relativity/time dilation is not B Theory.

He may not have called himself explicitly a B-theorist, but the things he did say about time clearly indicate that he was. The B-theory of time, by the way, is consistent with relativity and time dilation and such (see the video). It doesn't contradict it, as it doesn't strictly assert that every observer must observe the same moment in time, or anything like that.

From your same article:

According to Einstein, then, time is relative to the observer, and more specifically to the motion of that observer. This is not to say that time is in some way capricious or random in nature – it is still governed by the laws of physics and entirely predictable in its manifestations, it is just not absolute and universal as Newton thought (see the section on Absolute Time), and things are not quite as simple and straightforward as he had believed.

Yes, and? The B-theory of time goes a bit beyond the science, but it is the one philosophy of time that is consistent with modern science (unlike the A-theory of time, with which you would have to come up with heaps of unwarranted assumptions to get it to even remotely account for relativity and such).

Again, see the video that links relativity and time dilation and length contraction to the B-theory of time (and eternalism, which is virtually equivalent to the B-theory of time).

I understand B Theory of Time just fine. I have actually seen the video and read at least a dozen articles on it. My problem with you is that you think that the theory does away with causation. It does not. Even if you believe that all time slices (past, present, future) are equally real, they are all ordered by a causal connections in one direction. Fruit rots in one direction. Baby horses always preceded adult horses. These connections can be drawn with exact precision--that is literally what science does. There is nothing in B Theory that gets around this. You are adding a layer on top and calling it B Theory.

Not adding any layer on top of what is clearly an implication of the B-theory of time. Maybe it's the word "illusion" that puts you off, but if you want "causality" to still be implied by the B-theory of time, you do have to redefine the word to mean something that doesn't indicate the flow of time or actual change or actual motion. Fresh fruit does not cause rotten fruit in the sense that it morphs into it; the "antecedent" fresh fruit is still there and the "consequent" rotten fruit is there as well (just in different time moments). Baby horses do not actually eventually morph into adult horses; the baby horse still exists along with the adult version of it. And the key reason we have this one perceived direction happening in this one particular local universe is because of the increase of entropy from one state of this universe to the next, with entropy being at its lowest in the moment closest to the supposed "Big Bang singularity". But otherwise, as far as the laws of physics themselves are concerned, there is no direction of time. And even then, direction does not mean temporal causation anyway; both "cause" and "effect" simultaneously and eternally exist.

I see one of your problems. You said "causality is an illusion". You will not find that phrase anywhere in an article of B Theory. The typical description is the "flow of time is an illusion".

You can say "illusion" or you can say "derived/emergent", same thing, different words. Let's not get into an argument over semantics. Physicists don't geenrally agree with you that causality is a fundamental part of reality.

That is a metaphysical claim with very thin reasoning. We only know about the laws of physics in our universe. Extrapolating what appears to be a finite universe into a spacetime manifold for all universes ever is a stretch.

Then why are you acting like you know what would happen if there were multiple universes as opposed to just this universe? The view I hold to is nothing more but a logical extension of what is very well-accepted in both scientific and philosophical fields. Rather than denigrate me for having a "bold" view that, AFAIK, isn't contradicted by modern cosmology, why not just stick to challenging my view? After all, you're one to talk, considering your insistence that God exists against all odds.

HOWEVER, that doesn't really answer the question. Regardless of your insistence, there would still be measurable causal connections all the way back through the time slices and you are back up against my point above.

Except they have always been there (under the view I hold to), so no successive addition occurring at all. Successive implies a flow of time. There is no flow of time at all happening, whether in this local universe or beyond.

Not so at all. If the universe had a beginning, the spacetime manifold had an absolute beginning. Has nothing to do with observer position. The fact that all timeslices were created at once does not mean there was a first time slice in the sequence.

It's clear you don't get it. Let's go with the mathematical analogy again. The infinite set of all positive integers has what we may consider to be a "starting number" (namely, the number '1'), but it doesn't mean that '1' causes or leads to '2', that '2' causes or leads to '3', and so on. If they are already there in the set, then they don't need to begin to exist in order to exist.

And the timeslices weren't created. They're there, and that's that.

Your example is a potential infinite set -- not an actual infinite. Two very different things. This distinction is important for this whole discussion.

No, it isn't. The elements have always been in such a set. How many times do you need to be told this?

[pocaracas]

You guys are doing great. I've learned quite a few things with this thread.

But, to thwart the philosophers, one need only add the possibility that time is not what we intuitively think it is.

Because, if time does not really flow from event to event, then temporal causation may break under certain conditions... which are those? don't know.
What I do know is that Special Relativity narrowed the scope of temporal causation to the speed of light. Prior to that, philosophers would be happy to claim instantaneous causation everywhere, as the speed of light is too fast for our human senses to grasp it as anything else than instantaneous... who knows what lies behind the next stone in the way?
Better not make any definite pronouncement.

[LadyForCamus]

I am not asking if there is a concept in mathematics that deals with infinity or if there exists sets with an infinite number of members (although you might use the concept in a larger argument). I am not asking if we can theoretically divide something an infinite amount of times (although you might use the concept in a larger argument). I am not asking about a potential infinite. 

I am asking about an actual infinite of something concrete (not abstract). Can it logically exist? Why or why not? 

No mention of God either. Philosophy subforum--let's stick with pure metaphysics.

Anything may exist as a posibility unless there is an inherent logical contradiction built into the possibility of it's existence.  For example, invisible bachelors might exist (though not probably) without defying logic, as might 1000 year old bachlors.  But married bachlors may not logically exist. What exactly is it about an infinity that makes you think it is logically impossible? And why do you think an infinite number of objects or time is illogical but an infinite division of an object or period of time is not?

@Jenny, 

The strangest thing; earlier today you randomly popped into my mind and I wondered what ever happened to you (I remembered you being an awesome contributor), and less than eight hours later, here you are!!!

ESP?  😝

[polymath257]

Not adding any layer on top of what is clearly an implication of the B-theory of time. Maybe it's the word "illusion" that puts you off, but if you want "causality" to still be implied by the B-theory of time, you do have to redefine the word to mean something that doesn't indicate the flow of time or actual change or actual motion. Fresh fruit does not cause rotten fruit in the sense that it morphs into it; the "antecedent" fresh fruit is still there and the "consequent" rotten fruit is there as well (just in different time moments). Baby horses do not actually eventually morph into adult horses; the baby horse still exists along with the adult version of it. And the key reason we have this one perceived direction happening in this one particular local universe is because of the increase of entropy from one state of this universe to the next, with entropy being at its lowest in the moment closest to the supposed "Big Bang singularity". But otherwise, as far as the laws of physics themselves are concerned, there is no direction of time. And even then, direction does not mean temporal causation anyway; both "cause" and "effect" simultaneously and eternally exist.

Your example is a potential infinite set -- not an actual infinite. Two very different things. This distinction is important for this whole discussion.

No, it isn't. The elements have always been in such a set. How many times do you need to be told this?

I'm going to push back very slightly here. Even in general relativity, which regards spacetime as a single manifold and time does not flow (so B theory is closest), there is a notion of causality.  There are constraints on how things can be at different time slices. So, we will find the rotten apple time slice after that of the fresh apple and not before (in terms of the time coordinate). We find higher entropy states at later time slices than lower entropy states, etc.

Time is still all 'out there'. It does not 'flow' in the sense of the A theory. But there are still patterns between the time slices and we call *those* patterns causality.


And yes, the set N={1,2,3,4,5....} is an actual infinity. We can say exactly which things are in it and which are not without using a 'counting process'. For example, Graham's number is in this set even though there is no physical way to count up to that number.

https://en.wikipedia.org/wiki/Graham%27s_number

I am curious if Steve thinks it is possible for Graham's number of objects to exist in our universe.