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The question in the title came up in a thread recently, so I want to discuss it.
While it is a general rule that moving faster than an superhuman opponent can see is not quantifiable no such a thing was agreed upon for moving faster than normal human can see.
With that we get to the first question.
Should we use moving faster than a normal human can see as a feat?
The question is the most basic one and the pros and cons are quickly laid out:
Method 1: Timeframe
This is a method one sees at the OBD at times. It relates to this article about how many frames a human can see.
Based on that article it is assumed that whichever action the characters performed was performed in 1/100th or 1/120th of a second so that a human can not notice it.
That is simple enough to calc, but does such a relation make sense for a high speed battle?
To a certain degree it does. I think one can securely say that if a movement for such a short timeframe was seen it would not be noticeable. But is it actually the lowest timeframe a movement can happen in? In other words, is it so that no matter how fast I move around, if I didn't disappear from the field of view of the one watching me in 1/100th of a second it will be seen?
I am skeptical towards that interpretation.
After all we have a frame that changes through movement here.
Let me give an example:
Lets say I have a character moving a distance from point A to point D in 3/100th of a second. We would say he can be seen using the above prediction.
But when would he be seen? Would after the first 1/100th of a second that is invisible to the eye, the rest of his movement become visible?
Lets split that distance in three distances. The distance from A to B (AB), the distance from B to C (BC) and the distance from C to D (CD). Each of those parts the character moves through in 1/100th of a second.
Each of those distances should after the rule of being invisible if a movement only takes 1/100th of a second, be invisible for themself. But the whole distance from A to D should be visible by some means. That seems strange, doesn't it?
To use a second example: I play someone the same 1 second movie running at 100 fps on two screens at the same time. I exchange the 50th image in one movie through a green image and exchange the 51st image in the other movie through a green one.
Now viewing the movies separately one shouldn't notice the one image I manipulated. So what would you think happens if you watch both at the same time?
Well, one would first not see the image manipulated in one movie, so why should one after that see the manipulated image in the second movie that one couldn't see before?
That relates to the movement of a fast character in that way, as that if one doesn't see the first 1/100th second part of the movement the next part at a at that point in time other location should also not be seen with the exact same reasoning.
In other words we can say that a faster than eye movement doesn't have to be shorter than 1/100th of a second, but not that a fast enough movement can not take a longer timeframe.
Method 2: Speed of being faster than one can see in relation to distance (see edit note)
One can not see a bullet being shot at oneself moving at mach 2, but can see Venus in the night sky even though it moves with more than 7 times that speed in the night sky.
Distance plays a role when it comes to being able to see and not see something move, but why?
Well, timeframe one has to see something is one possibility, but I would suggest another influence here.
According to this article in order to become aware of an object in motion the eye movement has to stabilize the object within 3┬░ of visual angle for 100 ms.
That information gives us two criteria to judge the speed.
1. It has to move through 3┬░ visual angle field of a human in under 100 ms.
2. The character has to be faster than the eye movement can follow.
From this two criteria we can derive formulas for the speed necessary in dependence of the distance to the viewer.
Starting with 1:
According to this the formula for visual angle is V = 2*arctan (S/2D), where D is the distance between observer and what he is looking at, V the visual angle and S the distance that lies in the visual angle at given distance.
V = 2*arctan (S/2D) | /2
V/2 = arctan (S/2D) | tan()
tan(V/2) = S/2D | *2D
tan(V/2)*2D = S
Setting in V = 3┬░ = 0.0523598775598299 rad
tan(0.0523598775598299 rad/2)*2D = S = 0.052371843138 * D
That distance is supposed to be crossed in 100 ms = 0.1 seconds.
So speed = 0.52371843138 * D m/s.
Continuing with 2:
This method depends on which direction the character is moving in relative to the viewer. Generally the speed the character has vertical to the viewing direction of the observer has to be this high. How high that has to be I will derive as follows:
According to this (https://en.wikipedia.org/wiki/Saccade) A human eye can turn with 900┬░/s (at most) = 45┬░/0.05s .
Now the eye has to keep up with the movement of the character to see him.
The amount of distance the eye covers (vertikal from the original viewing position) when turning 45┬░ is given by tan(45┬░)*D.
tan(45┬░) = 1, so the total speed a character needs to move in order to be not visible to a normal human would then approximate to D/0.05 m/s. With D being distance from viewer again.
Note that in nature 1 and two here complement each other so that the speed of a character being invisible being above both. Method 1 and method 2 on the other hand do not complement each other, so that only the lower speed of the two is securely proven.
End result
So both this methods have justifications to exist in certain cases, but work fundamentally different.
Now the discussion about this should start, arguing about flaws in the methods, when which should be used, cases where the feats may not be used at all and similar. That is the purpose of the thread.
Lastly let me say that this thread of course was made, because it recently came up in another thread about a specific verse. But like usual, whenever I discuss a topic coming up in a specific case in a thread for doing a general decision on the method, I would like to ask not to bring up specific feats of verses and how this would influence, as that will introduce bias towards verses into the discussion which I want to avoid.
Now is the time to write your opinions.
Edit
I am leaving the rest intact to not cause confusion about what is going in in the thread at this point, but just for those people who don't read through the whole thread:
LordXcano brought up some severe flaws in method 2. For the simple case of 1 meter it would suggest that a movement with 20 m/s (about 72 km/h) is invisible. We can easily see cars moving that fast on the road.
Another problem is that the formula strictly speaking only outputs speed necessary to be so fast as not to be properly recognizeable (that is if it did what it is supposed to do, which it doesn't seems to do (problem mentioned before)), not the speed to be completly invisible.
The problem that remains is that I still don't believe, that Method 1 is suited for suited for movement vertical to the direction the observer (that is not supposed to percieve the character moving), out of the given reasons. Method 1's timeframe is so short that what happens is that the "blur" caused by a frame is so faint that the brain doesn't recognize the blur at all. Similary a vertical speed should be possible at which the moving character stays in the field of view, but the blur of his movement is so faint that the eye doesn't recognize it, similar to how it happens in method 1.
The problem with this line of reasoning is that I don't know a method which could decide on how fast a character has to be, but without such a method or a good reason why staying invisible while staying in the field of view is actually ot possible at all, we can only use method 1 for non-vertical movement.
While it is a general rule that moving faster than an superhuman opponent can see is not quantifiable no such a thing was agreed upon for moving faster than normal human can see.
With that we get to the first question.
Should we use moving faster than a normal human can see as a feat?
The question is the most basic one and the pros and cons are quickly laid out:
- Pro: If we can quantify it we should use it and such feats are made by the author with the intent to make the characters move fast.
- Con: It is almost impossible for an author to know how fast this is making characters given that it is actually a very complicated issue. Characters that are so fast that they seem to disappear is a common trope.
Method 1: Timeframe
This is a method one sees at the OBD at times. It relates to this article about how many frames a human can see.
Based on that article it is assumed that whichever action the characters performed was performed in 1/100th or 1/120th of a second so that a human can not notice it.
That is simple enough to calc, but does such a relation make sense for a high speed battle?
To a certain degree it does. I think one can securely say that if a movement for such a short timeframe was seen it would not be noticeable. But is it actually the lowest timeframe a movement can happen in? In other words, is it so that no matter how fast I move around, if I didn't disappear from the field of view of the one watching me in 1/100th of a second it will be seen?
I am skeptical towards that interpretation.
After all we have a frame that changes through movement here.
Let me give an example:
Lets say I have a character moving a distance from point A to point D in 3/100th of a second. We would say he can be seen using the above prediction.
But when would he be seen? Would after the first 1/100th of a second that is invisible to the eye, the rest of his movement become visible?
Lets split that distance in three distances. The distance from A to B (AB), the distance from B to C (BC) and the distance from C to D (CD). Each of those parts the character moves through in 1/100th of a second.
Each of those distances should after the rule of being invisible if a movement only takes 1/100th of a second, be invisible for themself. But the whole distance from A to D should be visible by some means. That seems strange, doesn't it?
To use a second example: I play someone the same 1 second movie running at 100 fps on two screens at the same time. I exchange the 50th image in one movie through a green image and exchange the 51st image in the other movie through a green one.
Now viewing the movies separately one shouldn't notice the one image I manipulated. So what would you think happens if you watch both at the same time?
Well, one would first not see the image manipulated in one movie, so why should one after that see the manipulated image in the second movie that one couldn't see before?
That relates to the movement of a fast character in that way, as that if one doesn't see the first 1/100th second part of the movement the next part at a at that point in time other location should also not be seen with the exact same reasoning.
In other words we can say that a faster than eye movement doesn't have to be shorter than 1/100th of a second, but not that a fast enough movement can not take a longer timeframe.
Method 2: Speed of being faster than one can see in relation to distance (see edit note)
One can not see a bullet being shot at oneself moving at mach 2, but can see Venus in the night sky even though it moves with more than 7 times that speed in the night sky.
Distance plays a role when it comes to being able to see and not see something move, but why?
Well, timeframe one has to see something is one possibility, but I would suggest another influence here.
According to this article in order to become aware of an object in motion the eye movement has to stabilize the object within 3┬░ of visual angle for 100 ms.
That information gives us two criteria to judge the speed.
1. It has to move through 3┬░ visual angle field of a human in under 100 ms.
2. The character has to be faster than the eye movement can follow.
From this two criteria we can derive formulas for the speed necessary in dependence of the distance to the viewer.
Starting with 1:
According to this the formula for visual angle is V = 2*arctan (S/2D), where D is the distance between observer and what he is looking at, V the visual angle and S the distance that lies in the visual angle at given distance.
V = 2*arctan (S/2D) | /2
V/2 = arctan (S/2D) | tan()
tan(V/2) = S/2D | *2D
tan(V/2)*2D = S
Setting in V = 3┬░ = 0.0523598775598299 rad
tan(0.0523598775598299 rad/2)*2D = S = 0.052371843138 * D
That distance is supposed to be crossed in 100 ms = 0.1 seconds.
So speed = 0.52371843138 * D m/s.
Continuing with 2:
This method depends on which direction the character is moving in relative to the viewer. Generally the speed the character has vertical to the viewing direction of the observer has to be this high. How high that has to be I will derive as follows:
According to this (https://en.wikipedia.org/wiki/Saccade) A human eye can turn with 900┬░/s (at most) = 45┬░/0.05s .
Now the eye has to keep up with the movement of the character to see him.
The amount of distance the eye covers (vertikal from the original viewing position) when turning 45┬░ is given by tan(45┬░)*D.
tan(45┬░) = 1, so the total speed a character needs to move in order to be not visible to a normal human would then approximate to D/0.05 m/s. With D being distance from viewer again.
Note that in nature 1 and two here complement each other so that the speed of a character being invisible being above both. Method 1 and method 2 on the other hand do not complement each other, so that only the lower speed of the two is securely proven.
End result
So both this methods have justifications to exist in certain cases, but work fundamentally different.
Now the discussion about this should start, arguing about flaws in the methods, when which should be used, cases where the feats may not be used at all and similar. That is the purpose of the thread.
Lastly let me say that this thread of course was made, because it recently came up in another thread about a specific verse. But like usual, whenever I discuss a topic coming up in a specific case in a thread for doing a general decision on the method, I would like to ask not to bring up specific feats of verses and how this would influence, as that will introduce bias towards verses into the discussion which I want to avoid.
Now is the time to write your opinions.
Edit
I am leaving the rest intact to not cause confusion about what is going in in the thread at this point, but just for those people who don't read through the whole thread:
LordXcano brought up some severe flaws in method 2. For the simple case of 1 meter it would suggest that a movement with 20 m/s (about 72 km/h) is invisible. We can easily see cars moving that fast on the road.
Another problem is that the formula strictly speaking only outputs speed necessary to be so fast as not to be properly recognizeable (that is if it did what it is supposed to do, which it doesn't seems to do (problem mentioned before)), not the speed to be completly invisible.
The problem that remains is that I still don't believe, that Method 1 is suited for suited for movement vertical to the direction the observer (that is not supposed to percieve the character moving), out of the given reasons. Method 1's timeframe is so short that what happens is that the "blur" caused by a frame is so faint that the brain doesn't recognize the blur at all. Similary a vertical speed should be possible at which the moving character stays in the field of view, but the blur of his movement is so faint that the eye doesn't recognize it, similar to how it happens in method 1.
The problem with this line of reasoning is that I don't know a method which could decide on how fast a character has to be, but without such a method or a good reason why staying invisible while staying in the field of view is actually ot possible at all, we can only use method 1 for non-vertical movement.
