No meaning to go backwards in time

[Flatland]

Look at it this way. If we treat time as a dimension just like space then there is no meaning to go backwards into time. You cannot go "back" in time just like you cannot go "back" in space. Think about it. No matter what direction an object is moving, it's direction of motion is always forward. You can say the object may turn around and move the opposite way, but it's direction of motion is still forward! No matter which direction the object moves, it's direction of motion will always be forward! Get it? To technically go "backwards" in space means to arrive at your destination before you left (see the connection?). No matter which direction you travel in space, your direction of motion is always forward. Therefore, no matter which direction you travel in time, you are always moving "forward!"

 

[DaveC426913]

"To technically go "backwards" in space means to arrive at your destination before you left"

No. To technically go backwards in space is to arrive at your starting point in space, not in time. You can easily do this by turning around and going "forward" to your starting point.


You're arguing semantics. You are playing on an ambiguous use of the word "forward". Sometimes you use it to mean "direction my vehicle is travelling" and sometimes you use it to mean "direction in which I make headway".

Just becasue your vehicle is always moving forward does not mean that you are always making headway. If you are pointed back towards where you came from, you'll end up there, not "forward".



So you're going forward through space, and you turn your ship around and go forward in the opposite direction until you end up at your starting point again.

You're going forward through time, and you ...what ? turn your ship around and go forward in the opposite direction through time until you end up back at your starting time again?

 

[MeJennifer]

space[/I] is to arrive at your starting point in space, not in time. You can easily do this by turning around and going "forward" to your starting point.

I agree, and it is similar with time.

I think there is a definite meaning for to go backwards in time.
Another question of course is if that is at all possible.

In my opinion it is not possible at all to go backwards in time.
Even in the case of a hypothetical closed loop situation in GR would we univocally have to conclude that something went back in time? I do not think so, since we could alternatively interpret the results as an effect of non-locality.

 

[setAI]

I agree with the emerging view that Time is a QUANTUM concept- the arrow of time in classical physics is invariant- the Page and Wooters idea being advanced by quantum computer science works better: that the universe is an ensemble of all possable static states and some are related by being the output of specific physical rule-systems [ Page, D.N. and Wooters, W.K. (1983), Phys. Rev. D 27, 2885-2892]- and in the case of our universe our states are the output of a quantum algorithm determined by Entropy- which emerges to observer states within the larger world-states as the illusory 'flow' of time into the future-

this would mean that flowing time is wholly determined by the causal structure of related states- and certainly quantum histories with 'backward' or 'sideways' [i.e. parallel time-like degrees of freedom] are likely in the ensemble- but these worlds would be nothing like ours-

 

[Flatland]

"To technically go "backwards" in space means to arrive at your destination before you left"

No. To technically go backwards in space is to arrive at your starting point in space, not in time.

That does not make sense. If you arrive at your starting point, you still went forwards in motion. For example, I can walk around the planet Earth and arrive back at my starting point without ever having to turn around. Does that mean I went backwards?

"You can easily do this by turning around and going "forward" to your starting point.

Exactly, you still went "forward" to your starting point. You didn't go backwards, you went forwards. My point precisely.

"You're arguing semantics. You are playing on an ambiguous use of the word "forward". Sometimes you use it to mean "direction my vehicle is travelling" and sometimes you use it to mean "direction in which I make headway".

In this case, we are talking about direction of motion. Please read my original post, I have stated so many times.

You're going forward through time, and you ...what ? turn your ship around and go forward in the opposite direction through time until you end up back at your starting time again?

Uhh that's what I'm trying to say...you can't do that. Am I missing something?

 

[pervect]

In modern langualge, "going backwards in time" would be replaced with "a closed timelike curve" for the reasons you describe. The two concepts arent quite totally equivalent, a CTC is more like a time-loop the jargon of time-travel.

 

[George Jones]

I think there is a definite meaning for to go backwards in time.

Going backwards in time means going into the past while traveling forwards in time.

Let p be an event in spacetime, Event q is in the (chronological) past of p if there exists a future-directed timelilke curve from q to p.

Suppose that event p is on the worldline of an observer, and that there is an event q is in the past of p such that a future-directed timelike curve from p to q. Then, it is possible for an observer to travel into his own past.

Joining the future-directed timelike curve form p to to q with the future-directed timelike curve from q to p, shows that, as already mentioned by pervect, this is completely equivalent to the existence of a closed timelike curve.

Another question of course is if that is at all possible.

Its certainly allowed by general relativity, as there are numerous solutions to Einsten's equations that have closed timelike curves.

How does one deal with the paradoxes associated with time travel? Also as mentioned (in another thread), Matt Visser has written http://arxiv.org/abs/gr-qc/0204022" about this. He talks about four possibilies:

1. Radically rerwite physics from the ground up;

2. Permit time travel, but also invoke consistency constraints;

3. Quantum physics intervenes to prevent time travel;

4. the Boring Physics Conjecture, where we assume (until forced not) that our particular universe is globally hyperbolic, and thus doesn't have closed timelike curves.

In the past 4. was often assumed, but since global hyperbolicity is a very strong global condition and Einstein's equations are (local) differential equations, many physicists have moved to 2. and 3. Stephen Hawking likes 3., for example, and has formulated the Chronology Protection Conjecture, "It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians."

This roughly states that near a chronology horizon (horizon at which spacetime becomes causally ill-behaved), expectation values of stress-energy tensors for quantum fields blow up, thus preventing (by wall-of-fire barriers) physical objects from crossing chronology horizons. There seems to be some semi-classical evidence for this conjecture, but a http://arxiv.org/abs/gr-qc/9603012" by Kay, Radzikowski, and Wald muddies the picture a bit. Their analysis shows that the semi-classical stress-energy tensor is ill-defined, but not necessarily infinite, at a chronology horizon.

This may be just an indication that the semi-classical theory breaks down at chronology horizons, and that full quantum gravity is needed for definitive predictions.

 

[Tzemach]

This discussion shows why we need mathematics to clarify discussion, if we consider time now as Tn anything less than Tn is the past anything greater than Tn is the future we can now at least describe which direction in time we are travelling.

Time travel is possible in some ways even with our limited knowledge, the "twins paradox" describes a form of time travel. Relative to each other one twin is traveling forward in time faster than the other, however both will arrive at a time greater than Tn but one will appear to have "jumped" forward to that time.

 

[DaveC426913]

Originally Posted by DaveC426913
"To technically go "backwards" in space means to arrive at your destination before you left"

No. To technically go backwards in space is to arrive at your starting point in space, not in time.

That does not make sense. If you arrive at your starting point, you still went forwards in motion. For example, I can walk around the planet Earth and arrive back at my starting point without ever having to turn around. Does that mean I went backwards?

What you suggest is another way of returning to your starting point (and an excellent exmaple of how it IS possible to return to your starting point without going backwards through the medium). Nobody said there was only one way. But this has nothing to do with the example originally posed.

What exactly does not make sense to you about returning to your starting point in space?




Again, you are playing on an ambiguous definition of the words "forward" and "backward". Sometimes you mean "relative to the ship" and sometimes you mean "relative to the medium".

If any doubt, replace the ambiguous words in your statements with more succinct terminology. You'll find the paradox goes away (mostly because the claim makes no sense anymore, you'd have to change the wording, and that would make the paradox go away):

Look at it this way. If we treat time as a dimension just like space then there is no meaning to "return to a point where you've already been" in time. You cannot "return to a point where you've already been" in time just like you cannot "return to a point where you've already been" in space*. Think about it. No matter what direction an object is moving, it's direction of motion is always "pointing in the direction of travel". You can say the object may turn around and move the opposite way, but it's direction of motion is still "pointing in the direction of travel"! No matter which direction the object moves, it's direction of motion will always be "pointing in the direction of travel"! Get it? To technically "return to a point where you've already been" in space means to arrive at your destination before you left ** (see the connection?). No matter which direction you travel in space, your direction of motion is always "pointing in the direction of travel". Therefore, no matter which direction you travel in time, you are always moving "pointing in the direction of travel"***

* This makes no sense now.
** This statement is still plain false, as pointed out previously.
*** And this says nothing we didn't already know.

Disambiguation of words shows the logical flaws.

 

[Farsight]

To technically go "backwards" in space means to arrive at your destination before you left (see the connection?). No matter which direction you travel in space, your direction of motion is always forward. Therefore, no matter which direction you travel in time, you are always moving "forward!"

Yup. Love it. Nice one Flatland.

 

[JesseM]

Look at it this way. If we treat time as a dimension just like space then there is no meaning to go backwards into time. You cannot go "back" in time just like you cannot go "back" in space. Think about it. No matter what direction an object is moving, it's direction of motion is always forward.

I would say that if you really "treat time as a dimension just like space", then from the perspective of spacetime nothing is "moving" forward or backwards in time, you just have a bunch of worldlines on 4D spacetime which don't move any more than lines drawn on a piece of paper. If the paper has x and y axes drawn on you can say that as you vary the y-coordinate, the x-coordinate of the corresponding point on the line may change, and likewise you can say that as you vary the t-coordinate in spacetime, the space coordinates x,y,z of a given worldline may change, but that's all.

Really, all "travelling backwards in time" means in relativity is that a worldline's path enters the past light cone of an earlier point on the worldline. If you want to argue that I can meet my own past self and yet I have not really "travelled backward in time" because from my perspective the event of meeting my younger self still lies in the future of actually having been that younger self, then you're just not using language in the way physicists would use it.

 

[Hurkyl]

Therefore, no matter which direction you travel in time, you are always moving "forward!"

"Going forwards in (coordinate) time" simply means:

$$\frac{d\tau}{dt} > 0$$

similarly, "Going backwards in (coordinate) time" simply means:

$$\frac{d\tau}{dt} < 0$$

That's all there is to it.

 

[MeJennifer]

Let p be an event in spacetime, Event q is in the (chronological) past of p if there exists a future-directed timelilke curve from q to p.

Suppose that event p is on the worldline of an observer, and that there is an event q is in the past of p such that a future-directed timelike curve from p to q. Then, it is possible for an observer to travel into his own past.

Joining the future-directed timelike curve form p to to q with the future-directed timelike curve from q to p, shows that, as already mentioned by pervect, this is completely equivalent to the existence of a closed timelike curve.

I know what you are saying but that is simply a particular interpretation.
Spacelike becoming timelike and vice versa is a coordinate dependent interpretation.
After all the square root of a negative number is not a negative number.
Furthermore as I already wrote we could alternatively interpret this case as a non-local interaction.

 

[lokofer]

- I think you're missing something... "time travel" at classical or semiclassical scale perhaps is impossible since you're dealing with Geodesic Tensor and other "Geommetric" entities..

- HOwever it's different at the scale of quantum world , where time and space are just "Eigenstates" of a certain Unknown operator, so if you are on an "state" let's call $$|t_0 >$$ and you want to travel forward or backwards in time to an state $$|t_1 >$$ you should use some kind of "teleportation" to reconstruct a reality that's on state $$|t_1 >$$ then the "time travel probability" is just $$| <t_1 | t_0 >|^{2}$$ unfortunately in most of cases this (semiclassical limit) will be almost 0 ...i think that perhaps if "time travel" exist or will exist perhaps it will be made similar to "teleportation" so they pick up you that are on an initial state and "reconstruct" you on a final state... similar to electron teleportation.

 

[George Jones]

Spacelike becoming timelike and vice versa is a coordinate dependent interpretation.

Whether a curve is timelike, lightlike, or spacelike at a particular event is independent of coordinates.

 

[MeJennifer]

Whether a curve is timelike, lightlike, or spacelike at a particular event is independent of coordinates.

Yes, but what is the relevance of that comment?

 

[DaveC426913]

Yes, but what is the relevance of that comment?

Its relevance is that it negates your earlier comment in Post #13.

 

[MeJennifer]

Its relevance is that it negates your earlier comment in Post #13.

Oh, looks like the sun is getting to me here in Pasadena.

So let me turn this upside down, can we construct a coordinate independent description of a situation where time goes into the negative and not the complex plane?

 

[Flatland]

What you suggest is another way of returning to your starting point (and an excellent exmaple of how it IS possible to return to your starting point without going backwards through the medium).

are you saying space and time are mediums?

What exactly does not make sense to you about returning to your starting point in space?

Because you can't return to your starting point in space, does that help? You can only return to a starting point relative to something. There's no such thing as a starting point in space unless there's a relative reference. And I also fail to see how much more definite "forward motion" can get. Does anyone else see any ambiguity in that term? Maybe this is going way over your head.

Again, you are playing on an ambiguous definition of the words "forward" and "backward". Sometimes you mean "relative to the ship" and sometimes you mean "relative to the medium".

If any doubt, replace the ambiguous words in your statements with more succinct terminology. You'll find the paradox goes away (mostly because the claim makes no sense anymore, you'd have to change the wording, and that would make the paradox go away):




* This makes no sense now.
** This statement is still plain false, as pointed out previously.
*** And this says nothing we didn't already know.

Disambiguation of words shows the logical flaws.

Your replacement of my words is pretty humorous. You're putting in your own terminology to create the paradox.
It's funny how you state I'm ambiguous, when your explanantions are pretty damn ambiguous.

 

[DaveC426913]

are you saying space and time are mediums?

No. Perhaps a better phrase would be 'coordinate system' (in this case, miles or years).

Because you can't return to your starting point in space, does that help?

I see you're getting snippy and nonresponsive.

You can only return to a starting point relative to something. There's no such thing as a starting point in space unless there's a relative reference.

And what exactly is wrong with a reference?

Take a bearing on 500 stars, fly 1 light year west, then fly one light year east, take a bearing on the same 500 stars to ensure you're in the right spot. Fine-tuning aside, how is that NOT returning to your starting point in space?

And I also fail to see how much more definite "forward motion" can get. Does anyone else see any ambiguity in that term?

Yes. In this case the motion most definitely IS relative. Forward motion with respect to what? So, yes, it's very ambiguous.

If I take a measurement of 500 stars, then move around and take the measurement again, I can determine whether or not I have moved relative to the stars. I CANNOT tell whether my SHIP has moved forward, sideways, backwards or a combination of all of them. I could have moved forward towards a star by one light year, while having my ship in reverse the whole time.

If I were making a trip to Alpha Centauri, I could put my ship in "forward" and drive towards it. I would be making progress forward towards AC. But if my ship got turned around by a meteor storm, I could very well have my ship moving forward while my progress is moving away (backward) from AC. This is a pretty basic concept.

Maybe this is going way over your head.

Ah yes, the "puny mind" gambit.

Your replacement of my words is pretty humorous. You're putting in your own terminology to create the paradox.

Feel free to rewrite it yourself. Since I am refuting your definition of the phrase "moving forward", humour me by substituting something else less ambiguous.

Note that this is in your best interest. If my best shot at refuting your claim is a simple complaint about a term I don't like, and all you have to do is disambiguate that term, I'll have no leg to stand on, and your argument will stand unocontested.

It's funny how you state I'm ambiguous, when your explanantions are pretty damn ambiguous.

Ah yes, the "I know you are but what am I" gambit.
And coupled with the escalation to cuss words - good double play.


I'd be happy to continue to discuss this without the poo-flinging. Let me know.

 

[Flatland]

No. Perhaps a better phrase would be 'coordinate system' (in this case, miles or years).

I did not know that spacetime had a coordinate system. Please let me know when and how you made this breakthrough discovery.

And what exactly is wrong with a reference?

Because, another observer in a difference reference frame may disagree that you have returned to your starting point, therefore, rendering your definition of returning to a starting point meaningless.

Yes. In this case the motion most definitely IS relative. Forward motion with respect to what? So, yes, it's very ambiguous.

Relative to the direction? I have stated that very clearly in my original post. Here, I will post it again below cause I think you somehow missed it:

...You can say the object may turn around and move the opposite way, but it's direction of motion is still forward! No matter which direction the object moves, it's direction of motion will always be forward!

Relative to any observer, your direction of motion is forwards? No? When you see an object travelling, whether it's traveling towards you, away from you, sideways, upside down, or in whatever direction or orientation you want it to be, (now read this very carefully) it's motion in the direction a relative observer see's it is forwards!

 

[J77]

To go backwards in time, would one not have to retravel the path previously traveled in space?

 

[JesseM]

Relative to the direction? I have stated that very clearly in my original post.

You haven't addressed my point that at the level of spacetime, there is no "motion" at all, just frozen worldlines, so the notion of objects having an natural "direction of motion through time" doesn't make much sense (although you can talk about which direction the numbers on their clocks are advancing, I suppose). And you also haven't addressed my point that "going backwards in time" can be given a perfectly reasonable definition in terms of worldlines which bend around to visit points within the past light cone of earlier points on the worldline, it's not relevant to this definition that the clock is advancing forwards at all points on the worldline as seen by comoving observers. It's not as if there's some intrinsic reason why we must define "going backwards in time" your way rather than this way, words and phrases mean whatever they are defined to mean.

 

[DaveC426913]

I did not know that spacetime had a coordinate system. Please let me know when and how you made this breakthrough discovery.

Do not put words in my mouth. You have introduced spacetime - something not in your original claim, nor in anything we have discussed up to this point - certainly nothing I have mentioned.

I have been treating space and time - as per your lead - as two distinct things that are comparable. Note the coordinates I proposed for each: miles or years.

I suspected early on that you were going to try to slip spacetime in, hoping no one would notice it as a change to your claim. But to try to assign it to me is the height of folly.

Relative to any observer, your direction of motion is forwards? No? When you see an object travelling, whether it's traveling towards you, away from you, sideways, upside down, or in whatever direction or orientation you want it to be, (now read this very carefully) it's motion in the direction a relative observer see's it is forwards!

You have introduced an external observer (I'm not sure what you mean by 'relative observer'. I'm going to assume you mean external observer, but correct me if I'm presumptuous). External observation is something not in your original claim, nor in anything we have discussed up to this point.

I would be interested to hear your thoughts on where you would post this "external observer" (or "relative observer") so that he may observe a spaceship that is traveling backward through time.



Your story is beginning to change. Please free to take time to rewrite it at your leisure. I am confident that, as you insert these less ambiguous terms 'spacetime' and 'external observer', the paradox will disappear.

Meanwhile, as it stands, your claim is false.



P.S. Your emotional, snippy remarks are a classic indication that logic is beginning to fail and irrational emotion is taking over. If you want to continue to be taken seriously, attack the argument, not the arguer. That's rule #1 of logical debate.

 

[Flatland]

Do not put words in my mouth. You have introduced spacetime - something not in your original claim, nor in anything we have discussed up to this point - certainly nothing I have mentioned.

Why should I have to mention the term spacetime to imply that it is 1 entity? My argument is one based off of relativity, doesn't that in itself imply that spacetime is 1 entity?

I have been treating space and time - as per your lead - as two distinct things

That is your fault to treat them as distinct things. My original post had nothing to do with comparasons. Simply how space and time should be treated the same. Again, you don't understand my arguement.

I suspected early on that you were going to try to slip spacetime in, hoping no one would notice it as a change to your claim. But to try to assign it to me is the height of folly.

What is that suppost to mean? You suspected that I would slip in spacetime? Hmm, sounds like something you just made up as a last ditch effort to save your arguement.

You have introduced an external observer (I'm not sure what you mean by 'relative observer'. I'm going to assume you mean external observer, but correct me if I'm presumptuous). External observation is something not in your original claim, nor in anything we have discussed up to this point.

How can you speak of motion without a relative observer (relative observer does not technically have to be an observer. Any external benchmark would do)? What would you be in motion with respect to? Yourself? As I stated already, certain things don't have to be said in order to be implied. Yet agian, you do not understand my arguement.

I would be interested to hear your thoughts on where you would post this "external observer" (or "relative observer") so that he may observe a spaceship that is traveling backward through time.

An "external observer" would always "observe" anything to travel forwards through time. My whole original post was about how you CAN NOT travel back through time. In fact, it was clearly stated in the post title.
By now, I already know that you utterly missed the whole point of my arguement, but I did not know that you didn't even read the title. I should not have to do this but here I'll write it for you again: "No meaning to go backwards in time" Here, let me rephrase it to something you can better understand: "It is ambiguous to go backwards in time"

Your story is beginning to change. Please free to take time to rewrite it at your leisure. I am confident that, as you insert these less ambiguous terms 'spacetime' and 'external observer', the paradox will disappear.

What paradox? Oh you mean the one you created. I thought that already diappeared.

And I also don't understand what your problem is. You're the one that's attacking ME! Not once have I threw a single insult at you and yet all you have done is call me this and that. I even ignored your previous belitting remarks and did not respond to them but you obviously didn't get the point. Your previous emotional outbreak just shows how small of a criticism it takes to hurt your little feelings. Please do not argue if you can't take criticisms.

 

[Tomsk]

Look at it this way. If we treat time as a dimension just like space then there is no meaning to go backwards into time. You cannot go "back" in time just like you cannot go "back" in space. Think about it. No matter what direction an object is moving, it's direction of motion is always forward. You can say the object may turn around and move the opposite way, but it's direction of motion is still forward! No matter which direction the object moves, it's direction of motion will always be forward! Get it? To technically go "backwards" in space means to arrive at your destination before you left (see the connection?). No matter which direction you travel in space, your direction of motion is always forward. Therefore, no matter which direction you travel in time, you are always moving "forward!"

You seem to be saying that things can travel in either direction through time, but both directions would give the impression of traveling forwards through time. Two particles can travel in two opposite directions through space, so why not time as well...? Ehh, I don't get it. We only observe things traveling in the same direction through time as us, surely? If something were traveling in the opposite direction through time to us, would we even see it? We would exist in the same point of time for an infinitely short time, and we can't see the future or the past, so maybe not... Um, I think I may have missed something here. :yuck:

 

[DaveC426913]

"Why should I have to mention..."

"...certain things don't have to be said in order to be implied..."

"...let me rephrase it..."

"It is ambiguous..."

Finally! All along I have been pointing out that your claim is an attempt to play with words - things you don't 'mention', things to 'imply' without saying them, that it needs to be 'rephrased', that it is 'ambiguous'.

I pointed out these flaws in post 2; it's taken 26 posts for you to acknowledge them.


And again (for future reference) attack the argument, not the arguer.

 

[nealh149]

Flatland, you are treating this problem like the universe has 6 spatial dimensions. This isn't the case there are only three. You can move positive and negative in each of these directions. YOu're acting like moving negative along the horizontal is like moving positive in a totally separate dimension.

Think of it this way. Traveling forward into space you will never return to where you started. I'm talking about 3D space, not the 2D surface of the earth. The only way to get back is to turn around, and go backwards in reference to your original motion.

However, with time you are always going forward, we have no way to turn arounod and go back to where you started.

 

[chronon]

Here, let me rephrase it to something you can better understand: "It is ambiguous to go backwards in time"

Changing from the claim that there are no ways to understand a sentence to claiming that there are more than one is not a 'rephrasing', it is a change in your position.

So there are two ways to understand the phrase 'travelling backwards in time', there's the one that DaveC426913 and me and everyone else in the world who's watched 'Back to the future' uses, and there's the one which you have put forward which is analogous to 'walking backwards'. You conclude that it is hard to make any sense out of the second interpretation.

Now a phrase which has two interpretations, the second of which does not make sense, is not ambiguous, as it is clear that the first interpretation must be taken.

 

[Flatland]

Finally! All along I have been pointing out that your claim is an attempt to play with words - things you don't 'mention', things to 'imply' without saying them, that it needs to be 'rephrased', that it is 'ambiguous'.

I pointed out these flaws in post 2; it's taken 26 posts for you to acknowledge them.


And again (for future reference) attack the argument, not the arguer.

Okay, I'm done arguing with you. No matter what I say you keep throwing in something completely irrelevant. What's the point? You're always right.

 

[Flatland]

Flatland, you are treating this problem like the universe has 6 spatial dimensions. This isn't the case there are only three. You can move positive and negative in each of these directions. YOu're acting like moving negative along the horizontal is like moving positive in a totally separate dimension.

I don't understand what you mean. I am not treating the universe as having six dimension. A dimension by definition is a plane that is completely perpendicular to all the other planes. Ok, not exactly the greatest definition but you get the point.

 

[J77]

If you move a clock's hand forward half a turn, do you not go back in time by moving the clock hand back half a turn.

ie. you have returned the system to it's original position.

I guess this is more a case of what frame you measure time from.

In a lot of dynamical systems you can usually reverse time by setting t=-t. This means that you can go backwards in examine how the system was in the past - even though you only know the present.

In some systems, eg. those which depend on the past - modeled by delay differential equations - you can only do this time reversal when the system is locked to some predictive path, eg. a periodic oscillation.

To this effect, I would say that, in real life, if the future is somehow determined by what happened in the past - in a nontrivial way, you won't be able to go back in time.

Or am I ranting into a Friday philosophical discussion here...

 

[Flatland]

Well, I for one believe there are many reasons why you can't go back in time. This is just one of them.