Previous: Reverse Motion: Possible Explanations

The main difference [1] between what we are seeing here and what we would see in our day to day perception is this:

• The light under which we see the oil falling is flickering rapidly. It is a series of flashes, or pulses; it is a strobe.
• This flashing is at a set rate.
• This rate is not detectable by us just by looking: we cannot tell it is flashing on and off. It seems to be a steady light. It is flickering so rapidly that we do not notice it.[2].

This strobe is the main reason why we see the oil flow as drops of oil falling up. The effect is similar to an effect possible in a film of the work.

Wagon Wheel Effect

The ‘wagon wheel effect’ is a result commonly found in film. This is also probably where it got its name, being most noticeable there first in Westerns, where one could see it in the wagon wheels of stagecoaches etc. (it is also sometimes called the ‘stagecoach effect’).

The effect is discussed on Michael Bach’s site on illusions. It is due to a mismatch between the speed of an object in motion and the rate at which we see this in motion. It is most noticeable with wagon wheels because they repeat the same pattern, a pattern which is structured enough that certain changes are readily visible. One can also do it with clocks, which I have chosen to do here.

A Stopped Clock

This video is an animation of the hand of a clock spinning rapidly and clockwise around its face. There are twelves different frames in this animation, repeating a number of times.

This is probably obvious but to be explicit: The difference from frame to frame in the position of the hand gives the sense of motion. So: frame 1 is the hand at 12:

and frame 2 is the hand at 1:

…and so on for another ten frames, until we are back to the 12 position (at the thirteenth frame).

Here is the same animation, except for one important difference: here, the first frame is visible, then every twelfth one afterwards (i.e., the thirteenth frame, the twenty-fifth frame). All the rest are blacked out. Despite the fact that there is a change in the frames underneath the blackout, we don’t see them; we just see a black screen.

— [WARNING: THERE IS FLICKERING/STROBING IN THE FOLLOWING VIDEOS] —

From this, we only see the same frame visible again and again, of the hand at the 12 position:

This seems to be just a flashing screen, through which a stationary hand is visible.  The hand seems to not be moving, even though, underneath, it is.

What gives this appearances of stasis? Our sample rate is the same as the rate at which the clock repeats. As a result, every time we see it (in this case, without any choice in the matter, because the rest is blacked out), it is in the same place.

You could do the same as all this with a real life clock. It would just take much longer. Every minute on the second, look up at at the clock. You will see the seconds hand in the same position. It will seem to you as if the seconds hand is not moving (even if you know it is).  Of course, to get the sort of non-change here, you’d need to do it for a few minutes at least, which might be tedious (and so I have conveniently sped it up for you).

An Out of Step Clock

The blacking out of the frames makes the hand seem to be still. One can manipulate it further.

Slowed forward motion

First, the clock can seem to slow down. To do that, you black out twelve of every thirteen frames (actually, you need not do this specific fraction, but it will do for now). With that situation, then whatever position is first visible (e.g., 12), the cycle will complete and move on a position before the next frame is visible. As a result, what is visible will seem to change. In the clock case, the hand in the first visible frame is at 12. Thirteen frames later, the next frame is visible. But this is of the hand at 1. So, what is visible is the hand at 12, then the hand at 1, and so on:

Note: this is a slower motion of the hand than it actually is going through. It only seems to get halfway round the face in the time you see it; yet, as seen in the first video, it actually goes through several cycles in that time.

In your perception, something similar could happen. Look at a clock every 65 seconds, and it will seem as if the seconds hand advances five ‘seconds’ of position on the clock for every minute of time.

Slowed backward motion

Most importantly here, we can make it seem that the clock goes backward.

To do this, black out the frames at a more rapid rate than the cycling around the face. For example, ten of every eleven frames are blacked out in this film:

Again, whatever the first position might be (here, it’s 12), the next position is a step earlier in the cycle (here, 11). As a result, instead of the hand seeming to move on, as with the last video, it seems to go back.

And again, just like the last video, the rate of motion is slower than it is normally perceived.

Again, we can see this in real life with a clock: glance up every fifty-five seconds at the clock, and you will see it as if the seconds hand is moving around the clock at five seconds a minute.

So we have two general differences between appearances and reality. By making some frames not visible (e.g., by blacking them out) at a rate comparable to the frames themselves:

1. The seconds hand seems to slow down, even to freeze in place.

2. The seconds hand can reverse in direction.

The reversing explains the cartwheel effect on film. The cartwheel spokes move through a cycle at a certain rate, but this rate does not match the rate at which the film captures the images of the spokes. As a result, in many cases, depending on how fast they move, like the seconds hand, a cartwheel spoke will seem to be at a previous or successive position in each frame.

For example,

i. When a cartwheel moves forward left to right, it moves by rolling forward and down, moving  clockwise when viewed from the street (and not, e.g., from under the carriage).

ii. If it is at the ’12’ in the first frame, due to how quickly the spoke rotates, and how quickly the film captures it, the spoke might be at ’11’ in the next frame.

iii. If this happens over and over, then even though it is, in fact moving all the time from ’12’ the long clockwise route to ’11’, the cartwheel will seem to move the shorter counter-clockwise route, from ’12’ to ’11’, i.e., counter-clockwise, and so backward.

Multiple objects in motion

There is a complication with this account, and with Supermajor. This complication is not there in the seconds hand examples above.

With the seconds hand examples, only one object is being observed to move. There is a single seconds hand rotating. But what if another seconds hand, otherwise identical, followed it? What effect would that have on freezing, reversing and so on?

Call the first hand the first hand and the other hand the following hand. In keeping with Supermajor and the cartwheel effect, assume that:

(a) The following hand has the same rate as the first hand.

(b) The two hands are equally distant from each other on all sides (i.e., the distance from the hands clockwise and counterclockwise is the same).

— This is how it is with the cartwheel: the spokes are at the same rate being locked in position in the wheel, and they are equidistant apart on both sides. They are regularly placed apart. Some spokes are not heaped up in one area of the wheel, the rest empty. This isn’t necessarily true. Some might be very badly designed and be uneven, even noticeably; my bet is that in such a case the cartwheel effect is more complicated.

— This is also how it is with Supermajor, although not as obviously. All the drops are falling at the same rate, and equidistant from each other. If the pump unevenly pushed the drops out, this wouldn’t be the case, and again the effects would be more complicated.

One might wonder how we can compare change in the clock or cartwheel — which rotate in a circle– with change in the stream of oil drops — which fall in a straight line. The difference between, on the one hand, the clock and cartwheel, and, on the other hand, Supermajor, is that there is not necessarily a finite number of drops falling. But take any region of space, and the result is very similar to the clock positions.

Take, for example, halfway between the hole and the pool. Call this ’12’. There is a steady change here. Drops enter and leave this position at a constant rate. This change in a succession of different drops is equivalent to the cycle of the hands passing through a point on the clock. E.g., at position ’12’, of the first hand leaving it, followed by: the following hand entering (and then leaving) it followed by: the first hand entering (and then leaving) it, and so on.

Given we have this succession of different but otherwise identical things entering and leaving a position, what do we get once we start blacking out certain frames?

Consider the clock again. We get almost the same as what we get with just one hand passing repeatedly through that space. The difference is this: the point at which the position is occupied by successive hands is a shorter cycle, one shorter than that of the first hand’s own motion through that position. This is because the following hand reaches that position before the first hand gets back there.

So, for the clock:

1. Say, as it does in the video, it takes twelve frames for one hand to return to a position on a clock.
2. Say the following hand is six frames behind (and in front) of the first hand.
3. Then it takes six frames after the first hand leaves a position for the following hand to get to it. Further, it takes six more frames for the first hand to get to the position after the following hand has left.
4. This means that we have a different rate of replacement: whereas with just the first hand, it took twelve frames to have the frame reached again, with two hands, it only takes six frames for it to be reached.

This means that we can treat it just like a faster version of the situation with one hand. As such, adjusting for how quickly the cycle takes with two hands, we can get all the same effects. We just need frames to be visible more frequently, in keeping with the increased frequency of hands reaching that position.

Let the frequency of visible frames in the number of frames (the rest of which are blacked out) be the frequency of flashes, flickers or strobes; or the strobing rate,  or simply the strobe. So, for all three situations, we have the following:

Frozen in space

For the clock, if the rate at which the first hand exits and its following hand enters a position is in time with the strobe, then:

• If it takes six frames for ’12’ to be occupied, five of six frames are blacked out for the strobe.
• This has the same effect as the first hand completing a cycle in time with the strobe. The following hand simply replaces it before the other gets there.
• So, we get the freezing of a hand at that position (as outlined above). The only difference is that two hands are moving here, not one.
• E.g., if the first hand is in position 12 the first time a frame is visible, and the following hand is in position 12 the second time a frame is visible, nothing in position 12 will seem to change. There will always be a hand positioned there.

And for the other effects:

— The Cartwheel Effect: If the cart’s spokes replace each other at a position at the same rate as the film records by frames, (again, assuming all spokes seem identical to the observer), then there will seem to be no change in what is at that position. Given we see the wheel overall, it will not look as if the wheel is moving.

— The Supermajor scenario (or what I’ll just call ‘Supermajor’ from now on): If the drops replace each other at any location at the same rate as the strobe, (again, assuming all drops seem identical to the observer[3]), then there will seem to be no change in what is at that position. Given we see the stream of the drops overall, it will not look as if the stream is moving. The drops will seem to be hanging in space.

Slow Forward Motion

For the clock example, if the strobe rate is slower than the cycle of the two hands, we get a slower apparent motion to the hands than they actually have; however, we still get them moving in the same direction as they are actually moving,

• It now takes six frames for a position to be replaced; six of every seven frames are blacked out.
• As a result, in frame one, the first hand is at position ’12’; the following hand is at position ‘6’.
• In the next visible frame, frame eight (seven frames later), the first hand is at position ‘7’ and the following hand is at position ‘1’. This will seem to be a movement of hands from positions ’12’ to ‘1’, and from ‘6’ to ‘7’.
• It takes seven frames for this motion to be apparent. But, in fact, each hand gets through those positions in one frame.

With the other effects,

— The Cartwheel Effect: If the cart’s spokes replace each other at some position faster than the film records by frames, (again, assuming all spokes seem identical to the observer), then if we see the wheel overall, there will seem to be a slow advance of the spokes around the wheel.

— Supermajor: If the drops replace each other at a position faster than the strobe, (again, assuming all drops seem identical to the observer), then there will seem to be a slow advance through the positions. Given we see the stream of the drops overall, it will look as if the stream is slowly moving downwards. Individual drops will seem to be slowly falling through space.

Slow Reversed Motion

Finally, we get to the effect which gives rise to what is seen in Supermajor.

For the clock example, if the rate of the strobe is faster than the cycle of the two hands, we get a slow reversal of the hands, i.e., they move slowly in the opposite direction to which they are actually moving,

• It takes six frames for a position to be occupied by the following hand; four of every five frames are blacked out.
• As a result, in frame one, the first hand is at position ’12’; the following hand is at position ‘6’.
• In the next visible frame, frame six (five frames later), the first hand is at position ‘5’ and the following hand is at position ’11’. This will seem to be a movement of a hand from position ’12’ to ’11’, and the movement of another hand from ‘6’ to ‘5’.
• It takes five frames for this motion to be apparent. But, in fact, each hand gets through these positions, in the opposite direction, in eleven frames.

With the other effects:

— The Cartwheel Effect: If the cart’s spokes replace each other at a position at a slower rate than the film records by frames, (again, assuming all spokes seem identical to the observer), then if we see the wheel overall, there will seem to be a slow reversal of the spokes around the wheel.

This is the Cartwheel effect. This is where the spokes don’t replace each other in positions on the wheel at a rate of 24 frames or less. At frame one, the first spoke might be at the top, at position ’12’; at the next visible frame where a spoke occupies anything near ’12’, the cartwheel effect is because it is at position ’11’. A consistent rate of this means the next visible spoke near there is at position ’10’, and so on, in the opposite direction to the actual motion.

There are complications here, which I’ve not needed to address until now.

In actual films, it isn’t as simple as the clock example. First this is because carts slow down and speed up, changing the rate of the visible wheels. Second and more important, the standard rate of individual frames in filming is 24 per second. The spokes don’t move through position at anything close to that rate. If they did, the wheel would be turning very fast. Take, for example, a six-spoked frame roughly three feet high. For one spoke to replace another at a position on this wheel, e.g., for one spoke to be replaced by another at position ’12’, the spokes need to move through about half a metre. To match the filming rate, they would need to move through half a metre in 1/24 of a second. That’s 12 metres a second, or about thirty miles an hour. Cartwheels don’t move that fast.

The answer for particular cases involves maths such as ratios and factors. I don’t need to get into the details, however. I’ll just reiterate my original point: what matters is what each successive frame shows. It is the difference between them that gives the direction of change (and speed). Say we have a cartwheel which moves clockwise. If the visible positions of the cartwheels — e.g., what is captured on each film frame — are a succession of positions closer in distance counter-clockwise than clockwise, we will get this effect.

(This works particularly for cartwheels because there is empty space between the spokes; it is much less obvious with rubber tyres, etc. For each position, e.g., position 12, for some proportion of the twenty-four frames, there is nothing noticeably near it, either clockwise or counter-clockwise. If, after this empty period, another spoke appears at a counter-clockwise location before anywhere else, it will seem as if the first spoke has moved to that location, and thus in that direction (and then, keeping the same rate, this appearance continues).

— Supermajor:

• If the drops replace each other in some position at a slower rate than the strobe, (again, assuming all drops seem identical to the observer), then there will seem to be a slow retreat through the positions.
• Given that we see the stream of the drops overall, it will look as if the stream is slowly moving backwards.

• In this case, ‘slowly moving backwards’ means that individual drops seem to slowly rise through space. And so we get the illusion as seen in ‘Supermajor’.

The Illusion

The illusion (I think, at least) in ‘Supermajor’ is this:

• We seem to see a series of individual drops continuously and slowly moving upwards through space.
• But we don’t see the continuous rate of the motion; nor do we see the individual drops in motion.
• Otherwise, everything is how it seems.

What we do see: a series of oil drops occupying different positions at different successive times in a particular region of space due to their passage through that space. This is not an illusion.

But

— We do not see the drops continuously:  strobe lights mean that a great deal of the motion of any of the drops we see is not visible; it is ‘blacked out’. Only the drops when the light flashes are visible to us. (They might very well move then but not enough to be noticeable).

— We do not see the drops fall at the rate at which they fall: each drop we see is moving much faster than it seems to move. From one flash to the next, each drop, and thus the stream, is moving a much greater distance than anything visible to us seems.

— We do not see the same individual drops in nearby positions from moment to moment. Each time the strobe flashes, and we can see the display, we see one set of drops at certain positions. When the strobe flashes again, we see a different set of drops near those original positions.

Again, to repeat the reason:

• The rate of the strobe is faster than the rate[4] at which the drops fall.
• As such, for a particular position, one particular drop may occupy it at one flash of the strobe. But, when the next flash happens, that drop has left and may not be visible anywhere in the space (i.e., it may have fallen into the pool already). Given the rate of flow, as well, a multiple series of further drops may have fallen through the location during the blackout. But when that position in the stream is visible, it is after some drop has left and another drop has yet to reach it.
• However, we do not see just that position. We see other positions in the stream as well. And the nearest visible drop is about to fall into that position. This nearest visible drop to that position is a little above it in space. This nearest drop is not the same as the first drop (which could be anywhere below). But it seems to be the same drop because it is the nearest position.
• And so, for each position in the space between hole and pool, what is

(a) A succession of one drop followed by another drop in a position just above it

seems to be

(b) One drop moving to a position just above it.

This is my suggestion for why we see reverse motion in these cases. Perhaps a lot can be drawn from this. I leave that for later work (this post is long enough).

A Brief Comment on the Experience of Time

I don’t think this work shows much more about the structure of our perception than what we get from similar issues in seeing film. The difference between this situation here and film is that the flickering or discrete visibility from film frames is replaced by flickering or discrete visibility from overall illumination. The flicker is in the light, not in what is lit (the latter which is in film[5]).

This does not show anything new for questions about our own perception and experience generally. It does not show, for example, that our experience of time is discrete any more than the perception appearance of a film as a continuous stream shows our experience of time is discrete. This is not to say that it does not show us something about our perception and experience of time. It just shows what film shows. This might be enough for some issues, e.g., it,involves the phi effect. I have not written about that here yet, but it is often thought to demonstrate an illusion of temporal order (which I think ‘Supermajor’ does not).

Also, I have been told by at least one philosopher of cognitive science and one neuroscientist that the cartwheel effect can be seen in normal light, in the real world, e.g., looking at a car’s wheels as it rolls up to a pedestrian crossing. This could suggest that our perception of the world is discrete.

Given other reasons to think that perception is discrete (and there are many other reasons to think so), the appeal to perception would be sufficient. But there is another possible explanation as well. The alternative explanation is that the light falling on objects even in normal circumstances is discrete. Like the light in Supermajor, it comes in bursts or pulses. Just like the art-work’s strobe, these pulses are the reason for the gaps in what we see. But our own experience or seeing could still be continuous. That is, one could explain a normal daylight perception of motion reversal if one assumed light itself is strobe-like in normal circumstances (remember, we don’t need to notice that it is). However, there are other reasons to think that perception is discrete, so there is no reason from reverse motion to assume anything about the light itself.

In any case, in conclusion, that Supermajor doesn’t say something new about perception is not to diminish the wonder of seeing the work. Nor does it diminish the intent of the artist (which is about something beyond the effect here).

Go see it. The effect, even understood as I present it here, is striking.

And see the other exhibits above, including one which is very similar but on a much larger scale (and in which, like an old film, the flickering of the strobe is obvious).

Notes

1. It may be that this is not a difference. As Einstein proved, light does come in packets of energy — quanta, particles — so it may be that light is not continuously bathing or being reflected by any surface we observe.

As such, light might come in discrete packets in such a way that even daylight is ‘flickering’. Alternatively, this ‘flicker’ is so rapid as to be completely undetectable by any instrument, natural or human-made, including our own visual system. I don’t know.

One consequence of this might be an explanation of the wagon wheel effect which, I’ve been told by many authorities (but no literature), even occurs in our everyday perception.

2. Actually, sometimes, once I was aware of this, it seemed to flicker somewhat, but it didn’t obviously do so when I was actually looking at the exhibit. Also, I’m not sure if it really does seem to flicker at all, or that I’m just imagining it.

3. Again, the drops or spokes will vary. As a result, something will seem to change at those position. The drops may change size, vibrate and so on. But they will not seem to move through the space. Because, again, each time we see that space, it is occupied by a drop.

4. Or, to be exact, some multiple of the rate of the motion of the drops. Many drops of oil can have fallen through a space between one flash and the next. What matters is that the strobe flashes before another drop again occupies a particular position, and that the nearest visible drop is above that position.

5. Classic images of film also have the beam of light flickering. But I think this is because of the frames being discrete, rather than the light itself. In practice, it turns out the same anyhow.