How to quantify feats involving moving faster than a normal human can see?

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:

• 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.

I would assume that it will be agreed that such a thing can be used as feat and will continue discussing how it should be calculated.

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.

The way I think of it is that Venus is moving FTE, but since it's so far away the distances its covering at FTE speeds (a few meters) isn't noticeable to us. I fail to see any situation in which the second method would be used. If a character is 10 km away and is viewed as FTE over what appears to be 1 meter then all you have to do is angsize and get the real distance and then use the 1/120th timeframe.

I'm in favor of using it but a few problems can arrise depending on the feat or verse.

1. Human (non-superpowered) characters in certain verses might be portrayed as being able to see characters that can move at that speed. This could make the feat meaningless or inconsitent with the real life science you just listed.

2. A blurry effect when a character moves could mean the character is faster than eye but it could also just be there for coolness. People might interprate it as the former when it could just be the later.

etc.

However there are cases that help justify these "faster than eye" feats.

1. If it's consistent with the other speeds of the characters.

2. If it makes sense from a powerscaling perspective (if charcter A is portrayed as far faster than character B, then it might actually be that speed and not just an effect for coolness).

etc.

I don't think "effect for coolness" really matters, if it's a feat it's a feat. Unless of course it's a kind of throwaway gag.

The only real issue is that we can only do this for characters we believe to have human-level senses, we can't use this type of stuff for a supersonic character because then it'd be calc-stacking based on their reactions.

One thing to note is that this can really only be used if it is said that a character can not see the movement. Things like a character just not reacting are another story and artistic things like motion blurs etc. should not be used for such things.

@LordXcano: I don't think you quite understood the explanation. The second method isn't about real distance and what seems to be the distance.

It is more so that are fast enough character could fight another fast enough character in front of a normal human watching for 30 minutes and the human could still not see the characters when they move. Hence when a character is said to move so fast that he can not be seen he either performed the movement in 1/100th of a second or so fast that it could not be recognized by a normal human. The second method is supposed to give the value for moving so fast that it can not be seen. So when calculating such feats both methods would have to be tried and the low end would be taken.

"It is more so that are fast enough character could fight another fast enough character in front of a normal human watching for 30 minutes and the human could still not see the characters when they move."

So from what I understand the second is for fights that go on for extended periods of time rather than 1/100th of a second?

The second method is more universal but you need to know the distance to character. It useless though in case of direct movement to viewer (like Tohka's dash to Origami position in DtL).

The second one is more accurate for sure, but I still think it shouldn't be used. Disappearing from sight is used so often as a visual motif that it isn't even funny. I think free-fall and such are much more reliable, as falling is rarely ever done to look cool. Basically, what I mean to say is that most feats involving moving faster than a person can see are just done because the author thinks it looks badass or cool. It's the perfect example of the one weakness in calcs, the author, getting in the way.

Author intent doesn't matter unless there's an on-panel or WoG thing saying otherwise. The 13 trillion c Flash calc would be okay had there not been the "hair under lightspeed" comment, regardless of the fact that it was the author's intent for it to be 0.99c.

This will boost a LOT of calcs and make a lot of feats calcable. Hell, even human characters will end up above peak human.

And that's perfectly okay. Just look at "peak human" Batman and Captain America.

Obviously gag feats shouldn't count because they're, well, gags. But if Katniss Everdeen moved FTE then I would be perfectly okay upgrading her.

But what if the distance that they stayed out of sight is given and there is no camera angle? This method is fine for manga/anime where we can get a clear view of someone disappearing, but when we work with LNs/VNs, it's a lot harder to quantify something like that.

It still possible though if description is not vague.

Nice idea up there, too bad it doesn't really apply when there's no timeframe ( or people just make up there own timeframe) between action and the object have been showed to go FTL before (despite visual information indicate that it shouldn't go at that speed at present.)

In my opinion, i see method two as more approachable in terms of calculations, more presemtable and more deciesive. However, both are flawed in the way that they don't give us any real speed value. My personal take on 'faster the the eye can see' is that it is given to characters whom we know to have superhuman speed, but no way to know to what degree.

What i believe can be extremly useful, is using the formulas you've developed as an alternate way to calculate speed in apropriete scenes, the problem with that however is that it must be done when the POV is of a normal human, and even then only if there is no other better way to calculate the hypothetical feat in question, because again, authors are not scientists...

Alakabamm said:

But what if the distance that they stayed out of sight is given and there is no camera angle?

Click to expand...

The method doesn't involve camera angle. Both in text form or anime form the second method cam be used equally. One just has to approximate teh distance between viewer and moving character, which is possible. Especially it is possible if one knows the distance the character moved that should be possible (After all either their start or end point would have to be of a similar distance to the human viewer (except they run in circles)).

That aside one method being hard to use doesn't justify using the other one getting higher results. If the calculation doesn't approximate an appropiate low end then it isn't useable.


@LordXcano: The second can be used for long as well as short scenes. The difference is that it will often lead to lower results than the 1/100th of a second method.

What if they run up a wall?

Alakabamm said:

What if they run up a wall?

Click to expand...

They reasonably are at least height of the wall away from the POV of a normal human at the end of their path. (technically a bit more given that the people likely not stand directly below the wall)

So for that it would give about 1/5th of the result using 1/100th of a second.

It's been 2 days, has any sort of conclusion been met on this?

Illuminati478 said:

In my opinion, i see method two as more approachable in terms of calculations, more presemtable and more deciesive. However, both are flawed in the way that they don't give us any real speed value. My personal take on 'faster the the eye can see' is that it is given to characters whom we know to have superhuman speed, but no way to know to what degree.
What i believe can be extremly useful, is using the formulas you've developed as an alternate way to calculate speed in apropriete scenes, the problem with that however is that it must be done when the POV is of a normal human, and even then only if there is no other better way to calculate the hypothetical feat in question, because again, authors are not scientists...

Click to expand...

^^^ this

I made a thread on the OBD about it to see what they think.

If I may ask could you give example calcs for both criteria in Method 2? I understand things far better if an example is presented. Just make up the distance and such.

After some thinking, I have come up with two major issues in both methods.

Neither of them factor in two relatively important properties of the moving object:

1.) Size

2.) Brightness/luminosity

For example, take a look at the .50 caliber tracers seen in the video below. These rounds are traveling over 870 m/s out of the muzzle, which is only 2-3 meters away from the camera.

50 CAL FIRING TRACERS IN AFGHANISTAN

According to the methods listed above, the FTE speed should be (unless I'm misunderstanding something):

0.52371843138*3 = 1.57115529414 m/s

3/0.05 = 60 m/s

By this logic the tracers should be invisible, yet they're clearly visible despite being much faster. And non-tracer rounds would be effectively invisible. So the relative brightness/luminosity of the object is a significant factor.

I don't have a video for the issue of size, but that's easy to understand anyways. Imagine you're playing baseball and someone throws a 120 mph (54 m/s) fastball towards you. Since you're not a professional baseball player, you probably won't be able to see it. Now imagine a car coming towards you at 120 mph from the same distance. You'll probably be able to see it (even though you still won't have time to do anything about it) because of how much bigger it is compared to the baseball.

Actualy we do not see tracer - we see after-images. The bullet itself is invisible.

About the baseball and the car. They have different angle sizes. That's why second method is better. It uses not frames but instead rely on biology processes like PoV and angle sizes.

LordXcano said:

I made a thread on the OBD about it to see what they think.

Click to expand...

Yes, I have read the thread. You could just have posted your doubts about that here, would be easier for me to notice.

Well, I have to say you are right in that the approximation gives strange results for short distances. Welp, empirical evidence takes precedence so either I improve the approximation or I will have to drop it.

Given that prospect I have read up a bit more about the topic of invisibility through speed. Strictly speaking invisibility through speed seems to only be possible if one would move so fast that the blur would be indistinguishable from the background. In that sense contrast takes up a large role.

If you posses a fan (one with grey vanes like I have preferably) and look at it in the dark while it is running you will notice that the edges of the vanes (where they are the fastest) can turn invisible. (at least as I tried out they did to a large bit).

So for a low contrast environment the possibility of invisibility for speeds seems to be empirically proven (at least for me).

Now contrast in environments can be larger (for a sufficiently bright object even the 120 fps approach will be inaccurate as the article also mentions IIRC), but of course our characters are also many times faster and the area they move through, and by that can the area they can disperse their blur through, is larger as well.

Of course here as well speed vertical to the direction the human is looking at is meant, for movement in the direction a person is looking at (like a character running straight at the viewer) the 120 fps thesis seems to be most fitting.


All of that said I am back at square one. I don't trust that characters fighting at speeds so fast that a human can't see or crosses a large distance vertical to the direction the viewer looks has to perform everything he does during that action in 1/120th of a second. But I don't know a way to quantify such movement either. Sooo... if no one has an idea how to quantify that case or a good reason why my "invisibility through fast movement" thought is misleading....

Well, then I would only quantify feats using method one if movement is at or away from the direction the viewer is looking at.

As far as I understand how human eyes works for the second method you need two conditions:

1. The angle size should be less the 3 degrees (there actualy exist minimal angle size that human eye can recognize too - we need to find it). Otherwise eyes can still grab some info via processing.

2. Target does not move directly to viewer.

For the first method we need to consider adjustment abilities of cones and rodes. Twilight enviroment is the worst condition where both cells underperform. Additionaly ~13 ms is the best reaction time for brain to recongnize anything when staring at the fixed PoW and distance. So 1/120 s is kind of iffy for me.

Yamatohime said:

1. The angle size should be less the 3 degrees (there actualy exist minimal angle size that human eye can recognize too - we need to find it). Otherwise eyes can still grab some info via processing.

Click to expand...

Angular resolutio: ╬© = 1.22*(╬╗/D), where ╬© is angular resolution (in rad), ╬╗ is wavelength of light (in mm), and D is the diameter of the lens' (pupil) aperture (in mm).

Diameter of a human pupil: 2―4mm contracted, 3―9mm dilated

Spectrum of visible light: 0.00038―0.00075mm

╬© = 1.22*(0.00038―0.00075mm)/(2―9mm) = 0.0000515111―0.0004575 rad

Minimum distance for "comfortable viewing" is roughly 100mm (any closer and you have to strongly cross your eyes to see something)

Actual diameter derived from angular diameter: d(act) = Tan(╬©)*D, where d(act) is the actual diameter (in mm), ╬© is angular diameter (in rad) and D is the distance (in mm)

d(act) = Tan(0.0000515111―0.0004575 rad)*100mm = 0.00515111―0.04575mm

NOTE: This is assuming ideal conditions otherwise. The optical limitations of the eye (such as diffraction by the lens and light scatter by the neural cells in the retina) limits the resolution of the human eye below the theoretical 'pixel limit' of the eye. Therefore, actual minimum size limits are generally going to be larger than these figures in real world applications.

ALSO: studies have indicated that as little as nine photons hitting individual rods in the human retina triggered a conscious response up to 60% of the time in test subjects.

SUPPORT:

Vision (eyesight): What is the smallest thing a human eye can see, and why?

How small can the naked eye see?

What's the smallest a human eye can see?

Resolution of human eye

The Rayleigh Criterio

The Limits of Human Vision - UK Swift (PDF)

The last article seemed promising at first glance. I recommend taking a closer look at it.

So, at 100 m an object with size of 5-45 mm is "invisible" even if it not moving... In perfect conditions.

Yamatohime said:

So, at 100 m an object with size of 5-45 mm is "invisible" even if it not moving... In perfect conditions.

Click to expand...

Well, considering that 5mm is about the diameter of a standard wooden pencil eraser, and a circle with a diameter of 45mm has only twice the face area of a standard Secure Digital (SD) card... yeah, it's believeable that they'd be practically invisible at 100 meters. The 200mm diameter targets shown here are set at about 100 meters distance, and they're practically dots.

I just tested IRL. I can't recognize RED cube of 5 cm at distance of 103 m. It wasn't visible during daylight. The BG was white wall. It was just white wall... =_=

Yamatohime said:

I just tested IRL. I can't recognize RED cube of 5 cm at distance of 103 m. It wasn't visible during daylight. The BG was white wall. It was just white wall... =_=

Click to expand...

Well, the numbers I calced above would be more along the lines of the "peak human" limits for minimum visual angular size, I'd think.

So we all now know why humans can't dodge bullets. Even .50 caliber woll be dot hardly visible at distance of 100 meters. If it's poonted toward you. The angular size is too small.

@Dont Yeah sorry about that. If I'm very convincing I may be able to get my grandfather to make something that'll speed objects across 1 meter at 120+ m/s to test this, but I think it's a bit of a stretch.

Yamatohime said:

So we all now know why humans can't dodge bullets. Even .50 caliber woll be dot hardly visible at distance of 100 meters. If it's poonted toward you. The angular size is too small.

Click to expand...

Yeah, according to the numbers it would need to be closer to the size of a 30-40mm autocannon round.

The last parameter... How fast eye can refocus... At most.

LordXcano said:

@Dont Yeah sorry about that. If I'm very convincing I may be able to get my grandfather to make something that'll speed objects across 1 meter at 120+ m/s to test this, but I think it's a bit of a stretch.

Click to expand...

For the sake of your grandfathers time and money I would stop there and think a bit of what you can proof with such a device.

You can proof that something that is only for 1/120th of a second in the field of view is invisible, by moving an object 120 m/s in such a way that it is only visible over the distance of 1 meter.

That we already know from the article. Of course if the article is false than it could also disproof the article, but that is unlikely IMO, so just for that I would not bother doing such an experiment.


Next one could try moving the object at 120 m/s and let it remain in the field of view of a spectator (moving vertical to the direction looked at) and see if the object turns invisible.

If it doesn't we only now that FTE characters are at least 120 m/s. That is subsonic. I believe nobody would doubt that.

If it does we would know that 120 m/s is sufficicent for invisibility and through that know that we can basically drop the issue about trying to quantify them. But that result is also an unlikely one IMO.

Additionally even if that result would happen I don't think we would have really won anything as it means that FTE characters are subsonic, which we can rank them at just because cars are generally visible. The only difference is that instead of not ranking them higher due to not knowing how high they should be ranked we don't rank them higher by knowing that they don't have to be higher ranked.

In the end it is entirely your decision wether or not you want to have fun with mach 0.35 objects, but I personally wouldn't spend my time and money on an experiment that doesn't turn out any meaningful results.

After some thought, I think it's important to break down the "faster than eye" phenomenon into obvious tiers(?) so we can work towards defining tose individually, potentially eliminating confusion regarding the term "faster than the eye" once and for all. Ideally, anyways.

Here are example tiers, listed from (assumed) slowest to fastest.

1.) Faster than Tracking: The character moves out of an observer's field of view faster than s/he can move their eyes/head to follow their movement. The observer can see and react to their movement but can't follow it in time, quickly losing track of them.

2.) Faster than Reaction: The character moves out of an observer's field of view faster than s/he can react to. The observer can see their movement but can't react to it in time, losing track of them the moment s/he realized they had moved.

3.) Faster than Processing: The character moves out of an observer's field of view so fast that s/he can only see delayed afterimages and/or momentarily appears in multiple places simultaneously. The observer can technically see their movement but can't react to it, losing track of them long before s/he realized they had moved.

4.) True Faster than the Eye: The character moves out of an observer's field of view faster than s/he can actually see. The observer cannot see their movement nor react to it, completely losing track of them instantly.

Have I missed anything?

@Jaften:

Things like reaction vary greatly depending on circumstances, but that said this thread is strictly speaking only about Fatser than eye in the sense on:

"The character moves (wether out of the Field of vision or not) so fast that the observer cannot see their movement nor react to it, completely losing track of them instantly."

To use your words partly.

I'm gonna have to go with distance-relation in this one. Imo, timeframe may not always be given and humans can percieve various things depending on distance and angle of movement of the one being viewed.

E.g. a bullet train moving at top speed moving by in front of you would barely register in your eyes but some few tens to hundred meters away, you'd be able to percieve it and follow it with your eyes.

Soooo... This thread should somehow reach an conclusion.

Would everyone be okay with only using method one for movement roughly in the direction of viewing (towards or away from the viewer) and leaving the rest at an unquantified "Subsonic (Faster than Eye)" (at least until we have found a more secure method of approximation)?

DontTalk said:

Soooo... This thread should somehow reach an conclusion.
Would everyone be okay with only using method one for movement roughly in the direction of viewing (towards or away from the viewer) and leaving the rest at an unquantified "Subsonic (Faster than Eye)" (at least until we have found a more secure method of approximation)?

Click to expand...

i guess that can work (sorry im not able to give too much input due to the time of the year)