What does it mean for something to be "logically possible"?

[beero1000]

I'm not sure I understand, but let me answer and you tell me where I missed the point, lol.

If a second (according to my super duper never lose time clock) is a day/24/60/60, then the amount of time is exact and corresponds directly with how long a particular animal times 120 can and must hold his breath when submerging under water.

Again, let's take my state of the art watch that never loses or adds time no matter how we might otherwise fiddle with time. A second times 60 times 60 times 24 gives us what I'll call a permi-day--the number of seconds in a permanent day.

Well, it just so happens that the thingamabopper doesn't rotate around the other thingamabopper with such exact precision, so, and over time (oh, about four years), there is a difference in the number of actual seconds. That leaves us with the option of either altering the second (which is a no no to the child, and surprisingly to the scientists as well) and adding on another whole day which can mathematically be compared in seconds.

Let's go back to the animal. When it goes under, it stays under for exactly 120 child seconds, no more, no less. If it stayed under for less, it dies. If it stays under for more, it dies. The animal never dies, so it stays under for exactly 120 permi-seconds.

If you take a four year period which is 365+365+365+366 days, then the animal dies because a true second doesn't correspond to the calculable second, since the sum of the previous figure divided by four/365/24/60/60 is not the same as if the 366 was a 365.

If I change all the clocks in your house to take 2 seconds per tick, you could figure that out by noticing that the sun rises and sets twice in your new 'clock-day', but that's basically comparing your clocks to another timekeeping method that hasn't changed. If I also magically force the earth to rotate at half speed, you wouldn't notice that difference (but other things would start to break... What if I changed those too?)

So, in your story you are comparing multiple "clocks" here: from your watch, to the time it takes earth to rotate, to the time an animal can hold its breath. If you have multiple clocks you can compare them, sure - that gives you a *cough* relative *cough* measurement of time. But if there is only ONE clock (or essentially one relative equivalent), ticking away - how can you figure out that the time between ticks isn't changing without some other 'clock' process to compare them to? What if all of the clock processes we measure change in tandem?

I guess the conclusion is that time is whatever clocks measure.

 

[Speakpigeon]

I'll play.

1. A "clock" is a process that generates a totally ordered set T, called "time". The elements of T are called "moments".
2. A moment m "occurs before" a moment n if m is less than n. Similarly, a moment m "occurs after" a moment n if m is greater than n.
3. The "ticks" of a clock are a set M of moments, indexed by a strictly monotonically increasing function f: Z -> M
4. The "present" is the tick indexed by 0, given by f(0).
5. The "past" is the subset of T that occurs before f(0).
6. The "future" is the subset of T that occurs after f(0).
7. An "interval of time" is a connected subset of T (in the order topology).
8. An interval I of time "has a beginning" if there is a moment m of I that occurs before every other moment of I. m is called the "beginning moment" of I.
9. An interval I of time "has an end" if there is a moment m of I that occurs after every other moment of I. m is called the "end moment" of I.
10. An interval of time is "finite" if it is contained within an interval of time that has a beginning and an ending.
11. An interval of time is "infinite" if it is not finite.

On second thought, a technical amendment for 3: I think I want to require f to be a bijection, and I also want the domain to be allowed to be any connected (in the order topology) subset of Z containing 0.

I don't think I missed any other issues, so I think this should probably work to formally define time, at least for our purposes. It matches the standard intuition for time, allows for different ephemeral clocks in different reference frames, ticking at different (possibly non-constant) rates, discrete time or continuous time, finite or infinite, clocks can have coarser or finer ticks, we can talk about measurable lengths or durations of time by counting clock ticks, we can bring in relativity, etc.

I very much doubt these definitions imply a contradiction for the idea of an infinite past, but I think I'll enjoy watching untermensche completely bungle the attempt.

I think this qualifies as "clear definitions of 'infinite' and 'past'".

I would also agree that it does "express the common usage of these words".

And, crucially, according to these definitions, an interval of time with no beginning will be infinite.


So, now, anybody thinks s/he can do better? Maybe shorter?
EB

 

[beero1000]

On second thought, a technical amendment for 3: I think I want to require f to be a bijection, and I also want the domain to be allowed to be any connected (in the order topology) subset of Z containing 0.

I don't think I missed any other issues, so I think this should probably work to formally define time, at least for our purposes. It matches the standard intuition for time, allows for different ephemeral clocks in different reference frames, ticking at different (possibly non-constant) rates, discrete time or continuous time, finite or infinite, clocks can have coarser or finer ticks, we can talk about measurable lengths or durations of time by counting clock ticks, we can bring in relativity, etc.

I very much doubt these definitions imply a contradiction for the idea of an infinite past, but I think I'll enjoy watching untermensche completely bungle the attempt.

I think this qualifies as "clear definitions of 'infinite' and 'past'".

I would also agree that it does "express the common usage of these words".

And, crucially, according to these definitions, an interval of time with no beginning will be infinite.


So, now, anybody thinks s/he can do better? Maybe shorter?
EB

Minor caveat and subtlety here: According to my definitions, you can have intervals without beginning or ending that still count as finite, as long as they are contained within a finite interval of time.

The classic example being a variant of Zeno's paradox: If I perform actions over halving intervals, i.e. for 1 min, for 1/2 min, for 1/4 min, etc. The total interval of time described there would count as finite even though it has no end, because it is contained in a finite interval of time. You could similarly describe intervals with no beginning that would count as finite as well. I thought a little about it, and I think I do want to count those intervals as finite, but I'd be interested in seeing opinions one way or the other.

 

[untermensche]

What is the time span from some present time to time with no beginning?

You question doesnt make sense. ”Time with no beginning” is description of time itself. Not a timepoint.

This whole nonsense of "no beginning" makes no sense.

If you have no beginning exactly how do you get to an end?

 

[fast]

I'm not sure I understand, but let me answer and you tell me where I missed the point, lol.

If a second (according to my super duper never lose time clock) is a day/24/60/60, then the amount of time is exact and corresponds directly with how long a particular animal times 120 can and must hold his breath when submerging under water.

Again, let's take my state of the art watch that never loses or adds time no matter how we might otherwise fiddle with time. A second times 60 times 60 times 24 gives us what I'll call a permi-day--the number of seconds in a permanent day.

Well, it just so happens that the thingamabopper doesn't rotate around the other thingamabopper with such exact precision, so, and over time (oh, about four years), there is a difference in the number of actual seconds. That leaves us with the option of either altering the second (which is a no no to the child, and surprisingly to the scientists as well) and adding on another whole day which can mathematically be compared in seconds.

Let's go back to the animal. When it goes under, it stays under for exactly 120 child seconds, no more, no less. If it stayed under for less, it dies. If it stays under for more, it dies. The animal never dies, so it stays under for exactly 120 permi-seconds.

If you take a four year period which is 365+365+365+366 days, then the animal dies because a true second doesn't correspond to the calculable second, since the sum of the previous figure divided by four/365/24/60/60 is not the same as if the 366 was a 365.

If I change all the clocks in your house to take 2 seconds per tick, you could figure that out by noticing that the sun rises and sets twice in your new 'clock-day', but that's basically comparing your clocks to another timekeeping method that hasn't changed. If I also magically force the earth to rotate at half speed, you wouldn't notice that difference (but other things would start to break... What if I changed those too?)

So, in your story you are comparing multiple "clocks" here: from your watch, to the time it takes earth to rotate, to the time an animal can hold its breath. If you have multiple clocks you can compare them, sure - that gives you a *cough* relative *cough* measurement of time. But if there is only ONE clock (or essentially one relative equivalent), ticking away - how can you figure out that the time between ticks isn't changing without some other 'clock' process to compare them to? What if all of the clock processes we measure change in tandem?

I guess the conclusion is that time is whatever clocks measure.

Time exists, and we are able to measure it, but the existence of time, though measurable, does not depend on our ability to measure it for it to exist. The elementary perspective is just that, time exists whether we can measure it or not. The more advanced notion of time (a conception I disagree with) is that where there is no ability to measure time, no time exists.

 

[ryan]

Think about other dimensions except for time. Your home, for example, does it have a beginning and an end?

Most definitely. In several ways. It's size is defined and static. It has a beginning and end. The building of the home had a beginning and like all human structures it will have an end.

I said without time. Your home's beginning and end in space is arbitrary. Objects extending through the dimension of time are no different.

There is a very specific and unalterable order to the events in the past.

Order of events depends on the observer observing them. Time order of events is relative.

That is what it means that time has a direction. The events have a direction. The paper burnt does not unburn.

The direction of time is based on it being asymmetric (entropy for example). Geometrically, asymmetry still does not have an absolute beginning or end.

 

[untermensche]

There is a very specific and unalterable order to the events in the past.

Order of events depends on the observer observing them. Time order of events is relative.[/ quote]

We are talking about events that have no observer. Just events. Not the observation of events.

 

[ryan]

Order of events depends on the observer observing them. Time order of events is relative.

We are talking about events that have no observer. Just events. Not the observation of events.

Relativity is not only saying that we observe events in different order, but also that there is no order. Event A happens after event B for observer C; the opposite may be true for observer D. Neither C nor D is wrong.

 

[untermensche]

There are two things.

The order of events and the observed order of events.

The observed order can vary but not the order of the events themselves.

 

[ryan]

There are two things.

The order of events and the observed order of events.

The observed order can vary but not the order of the events themselves.

So then what is the actual order: A before B or B before A? Which observer is right, are they both wrong?

The question above should not be answered with anything other than they are both right. And this part of relativity is not controversial like other implicit theories stemming from relativity. There is no single timeline.

 

[untermensche]

There are two things.

The order of events and the observed order of events.

The observed order can vary but not the order of the events themselves.

So then what is the actual order: A before B or B before A? Which observer is right, are they both wrong?

The question above should not be answered with anything other than they are both right. And this part of relativity is not controversial like other implicit theories stemming from relativity. There is no single timeline.

The observation is subjective. The events only look different between observers because they observe them from a different place.

Remove the observer and the events can only have one order.

 

[beero1000]

So then what is the actual order: A before B or B before A? Which observer is right, are they both wrong?

The question above should not be answered with anything other than they are both right. And this part of relativity is not controversial like other implicit theories stemming from relativity. There is no single timeline.

The observation is subjective. The events only look different between observers because they observe them from a different place.

Remove the observer and the events can only have one order.

Your ignorance is showing again. Maybe take some time to learn relativity?

 

[untermensche]

The observation is subjective. The events only look different between observers because they observe them from a different place.

Remove the observer and the events can only have one order.

Your ignorance is showing again. Maybe take some time to learn relativity?

One of us does not know it.

Probably the moron that thinks "no beginning" is some kind of explanation.

 

[fast]

I think this qualifies as "clear definitions of 'infinite' and 'past'".

I would also agree that it does "express the common usage of these words".

And, crucially, according to these definitions, an interval of time with no beginning will be infinite.


So, now, anybody thinks s/he can do better? Maybe shorter?
EB

Minor caveat and subtlety here: According to my definitions, you can have intervals without beginning or ending that still count as finite, as long as they are contained within a finite interval of time.

The classic example being a variant of Zeno's paradox: If I perform actions over halving intervals, i.e. for 1 min, for 1/2 min, for 1/4 min, etc. The total interval of time described there would count as finite even though it has no end, because it is contained in a finite interval of time. You could similarly describe intervals with no beginning that would count as finite as well. I thought a little about it, and I think I do want to count those intervals as finite, but I'd be interested in seeing opinions one way or the other.

If it took a millions years to watch each 1 second of a movie, I'm afraid I will have missed the forest for the trees.

Wow, as each finite second passes, there (according to my grasp of the conception you describe), a seemingly infinite number of precision points in time will pass per second. In other words, after 3 minutes and 8 seconds begins and before 3 minutes and 9 seconds arrive, there will be a point in time at 3 minutes and 8.7473020394736820294774389202836482283739283739293738847302833892937483027374730283636392937362792833928373827384732792837483029322 seconds

 

[Juma]

You question doesnt make sense. ”Time with no beginning” is description of time itself. Not a timepoint.

This whole nonsense of "no beginning" makes no sense.

If you have no beginning exactly how do you get to an end?

Time goes on and any timepoint is an end. What is the problem with that?

Any time span is between to timepoints and thus finite even if time has always been going on.
That time itself has always been doesnt mean that there are infinite timespans.

 

[untermensche]

This whole nonsense of "no beginning" makes no sense.

If you have no beginning exactly how do you get to an end?

Time goes on and any timepoint is an end. What is the problem with that?

Any time span is between to timepoints and thus finite even if time has always been going on.
That time itself has always been doesnt mean that there are infinite timespans.

Time goes on from where?

How do you go on if you have no beginning?

 

[fromderinside]

Think of it as "time is". That way there is no need for a beginning. If there were a need for a beginning then time is wouldn't apply would it. Why would there be need for the concept of eternal if there were a need to specify a time beginning?

I disagree with Juma to some extent. Time between two points can be infinite. Consider time points as being on a line. Lines are made up of infinite points else there would be no continuous line between those two points.

 

[beero1000]

Your ignorance is showing again. Maybe take some time to learn relativity?

One of us does not know it.

Obviously.

Probably the moron that thinks "no beginning" is some kind of explanation.

I suspect your perspective might be relative.

Time exists, and we are able to measure it, but the existence of time, though measurable, does not depend on our ability to measure it for it to exist. The elementary perspective is just that, time exists whether we can measure it or not. The more advanced notion of time (a conception I disagree with) is that where there is no ability to measure time, no time exists.

Minor caveat and subtlety here: According to my definitions, you can have intervals without beginning or ending that still count as finite, as long as they are contained within a finite interval of time.

The classic example being a variant of Zeno's paradox: If I perform actions over halving intervals, i.e. for 1 min, for 1/2 min, for 1/4 min, etc. The total interval of time described there would count as finite even though it has no end, because it is contained in a finite interval of time. You could similarly describe intervals with no beginning that would count as finite as well. I thought a little about it, and I think I do want to count those intervals as finite, but I'd be interested in seeing opinions one way or the other.

If it took a millions years to watch each 1 second of a movie, I'm afraid I will have missed the forest for the trees.

Maybe an analogy can help: My PC runs on crystals that give the 'ticks' of the computer's clocks. To the CPU, those cycles define 'time', 1 cycle is 1 unit of time, always. But I can modify my computer, making the crystals run faster or slower - from my perspective. To the CPU though, everything still runs at the same rate, 1 cycle per cycle - it cannot tell that what it sees as 1 cycle today was 2 cycles yesterday. So I can ask, how would you know if what you measure as a second today was what you measured as a million years yesterday?

I brought it up because this 100% happens ALL the time. Well, maybe not 1 second to a million years, but you get the idea even if the changes are smaller. Sure, you'll measure a second as a second everywhere you go, but the second that you measure at sea level won't be the second that you measure at altitude, which won't be the second that you measure when accelerating in your car. To you they all look like a second though, you need an outside perspective to be able to compare them to tell the difference.

Wow, as each finite second passes, there (according to my grasp of the conception you describe), a seemingly infinite number of precision points in time will pass per second. In other words, after 3 minutes and 8 seconds begins and before 3 minutes and 9 seconds arrive, there will be a point in time at 3 minutes and 8.7473020394736820294774389202836482283739283739293738847302833892937483027374730283636392937362792833928373827384732792837483029322 seconds

That's a possibility, but not a necessity. Time could be discrete, or it could be continuous.

 

[ryan]

So then what is the actual order: A before B or B before A? Which observer is right, are they both wrong?

The question above should not be answered with anything other than they are both right. And this part of relativity is not controversial like other implicit theories stemming from relativity. There is no single timeline.

The observation is subjective. The events only look different between observers because they observe them from a different place.

The time order of events is also about the relative motion of the observer.

Remove the observer and the events can only have one order.

I have found a link that explains this in a very provable way! I took this in university about 3 years ago, and it is said over and over that this is not just an illusion. Nothing in that course made me realize that it is not just an illusion, for each observer, more than this link! It is a brilliant proof! http://www.pitt.edu/~jdnorton/teach...7_Jan_1/Special_relativity_rel_sim/index.html

Normally we start with 2 postulates (I don't think they have this in the link): 1) light always travels at c 2) the laws of physics are the same for all inertial (nonaccelerating) observers/frames of reference.

If you scroll down to the second animation where the point of view is from the ground, you will see that the only way for the light on the far side to still travel at c and only cross a fraction of the distance that the other light had to travel is if the light came after the closer light!

Absolutely amazing!

 

[fast]

One of us does not know it.

Obviously.

Probably the moron that thinks "no beginning" is some kind of explanation.

I suspect your perspective might be relative.

Time exists, and we are able to measure it, but the existence of time, though measurable, does not depend on our ability to measure it for it to exist. The elementary perspective is just that, time exists whether we can measure it or not. The more advanced notion of time (a conception I disagree with) is that where there is no ability to measure time, no time exists.

Minor caveat and subtlety here: According to my definitions, you can have intervals without beginning or ending that still count as finite, as long as they are contained within a finite interval of time.

The classic example being a variant of Zeno's paradox: If I perform actions over halving intervals, i.e. for 1 min, for 1/2 min, for 1/4 min, etc. The total interval of time described there would count as finite even though it has no end, because it is contained in a finite interval of time. You could similarly describe intervals with no beginning that would count as finite as well. I thought a little about it, and I think I do want to count those intervals as finite, but I'd be interested in seeing opinions one way or the other.

If it took a millions years to watch each 1 second of a movie, I'm afraid I will have missed the forest for the trees.

Maybe an analogy can help: My PC runs on crystals that give the 'ticks' of the computer's clocks. To the CPU, those cycles define 'time', 1 cycle is 1 unit of time, always. But I can modify my computer, making the crystals run faster or slower - from my perspective. To the CPU though, everything still runs at the same rate, 1 cycle per cycle - it cannot tell that what it sees as 1 cycle today was 2 cycles yesterday. So I can ask, how would you know if what you measure as a second today was what you measured as a million years yesterday?

I brought it up because this 100% happens ALL the time. Well, maybe not 1 second to a million years, but you get the idea even if the changes are smaller. Sure, you'll measure a second as a second everywhere you go, but the second that you measure at sea level won't be the second that you measure at altitude, which won't be the second that you measure when accelerating in your car. To you they all look like a second though, you need an outside perspective to be able to compare them to tell the difference.

Wow, as each finite second passes, there (according to my grasp of the conception you describe), a seemingly infinite number of precision points in time will pass per second. In other words, after 3 minutes and 8 seconds begins and before 3 minutes and 9 seconds arrive, there will be a point in time at 3 minutes and 8.7473020394736820294774389202836482283739283739293738847302833892937483027374730283636392937362792833928373827384732792837483029322 seconds

That's a possibility, but not a necessity. Time could be discrete, or it could be continuous.

Surrounding the issue we're discussing, a lot of questions can creep up. You happen to be be asking a "how" question. I guess this is what we call an epistemological issue. How do we know, or how can we tell, or how is it that we can figure out. That's fine. Good questions I suppose. I imagine we could mesh it out.

However, before I get to the how, I want to cover the what. I want to show two different conceptions at play. I guess that is an ontological issue. Once we can clearly see the two distinct ontological perspectives, we can switch gears and approximate a game plan for steering us towards tackling the how question.

If the ticks of computer A (a state of the art computer) cycle at precisely one second per tick, then this will serve as a basis of comparison that will help us later to determine the answer to how questions. The time passing between ticks will remain the same no matter the situation, so height nor speed will alter the passage of time between the ticks, now or yesteryear.

More to come later