Cognitive Daily

You might think humans are equally good at estimating distances no matter which direction they’re looking. After all, we use the same visual tools to make those estimates — binocular disparity (the different views we see from each eye), occlusion (whether one object is in front of or behind another), and so on. But consider the situation depicted to the right. Nora is inching her way down a steep rock column, with near-vertical drops on either side of her. If she underestimates the distance to flat ground below, she might decide she doesn’t need to worry about falling. Overestimating the vertical distance isn’t as big a problem: if she descends too slowly and carefully, she’ll still live to tell the story.

On flat ground, overestimating distances could spell trouble: you might pack too much food for a hike, unnecessarily burdening yourself and perhaps not even making it to your destination. In fact, people do make systematic errors in estimating distance based on how much weight they’re carrying; it’s possible that they might make the same sort of errors estimating vertical distance. Since it takes more effort to climb up a mountain than climbing down, maybe we misjudge up distances as longer than down distances.

Russell Jackson and Lawrence Cormack took college students to the base of a 40-foot-tall wall and asked them to estimate the distance to the top by telling a research assistant to back away from the wall until their distance from the wall was equal to its height. Then they took them to the top of the wall and asked them to estimate the distance down using the same system (actually, half the students estimated the distance down first). This graph shows the results:

If the students had seen the distance as the same in both directions, their responses would have fallen along the diagonal line. If they accurately estimated distances, the responses would have fallen where the three lines intersect. In fact, nearly all respondents overestimated both the distance up and down the wall. Looking closer at the graph, you can see that the estimates for the distance down were nearly always larger than for the distance up. The average estimates for down distance were significantly larger than for up distance.

Jackson and Cormack argue that this overestimation of down-distance is beneficial from an evolutionary perspective. If we think a potential fall is worse than it really is, we’re probably going to be more careful when we’re next to a precipitous drop-off. This danger-avoidance adaptation trumps any overestimation we might make based on the amount of work it might take to climb up a wall. Playing it safe, it seems, is so important that it’s worthwhile for the perceptual system to make systematic errors in judging distance.

Jackson, R.E., Cormack, L.K. (2007). Evolved navigation theory and the descent illusion. Perception & Psychophysics, 69(3), 353-362.

Comments

#1 Russell
January 2, 2008

Does this demonstration of threat awareness surprise any one? I look forward to similar experiments of people estimating the speed of snakes that surprise them, the size of a pistol pointed at them by a mugger, and the number of teeth of a dog attacking them. The use of vertical distance is convenient, because it triggers the psychology of a threat, in a way that is safe and controlled. I’m skeptical, though, that this has anything to do with looking down, per se, as opposed to general mismeasure of what is perceived as a threat. Someone should run some fMRIs and see if they can identify which parts of the brain are kicking the rest, saying “hey, bozo, pay attention to that drop, that viper, that gun, those fangs. They’re important!”
#2 Sam the Centipede
January 2, 2008

Doesn’t this treatment show a large cultural bias deriving from a bookish and map/diagram-oriented approach? Distance (measured a length) and lengths are rarely interesting in their own right. If one is driving somewhere, the important question is “how long will it take?” (and perhaps “how much fuel will I need?”). Similarly, I have no idea how far it is from London to Gothenburg in miles or kilometres, but I do know it’s a two hour flight.

Length is almost always a substitute for more interesting measures. So if we were able to measure lengths in different contexts accurately, one might reasonably ask: why on earth have we evolved that ability when it’s so pointless?

Hence, if one is cycling, on an out-and-back route, there is significantly more downhill than uphill because one will spend much longer cycling slowly and painfully uphill then speeding quickly and gleefully downhill, even without the psychological effect of pain stretching time. It would be a complete red herring to point out that the uphill and downhill distances are identical. It’s a problem of measurement to suggest that they are the same, not a problem of perception to suggest that they are different.
#3 Sanguinity
January 2, 2008

Was one distance more accurate than the other? The “up” and “down” tests don’t seem parallel to me. Once you start backing away from the edge, you can’t see the distance down anymore, whereas when you back away from a wall, you can see the distance up just fine. What’s the odds that, in the process of backing away from the edge, that they simply forgot how deep it had looked?
#4 Dave Munger
January 2, 2008

Sanguinity: They didn’t back away from the edge. They looked down over the edge and then signaled a research assistant to move away from them until the distance to the assistant equaled the distance down.
#5 Dave Briggs
January 2, 2008

This danger-avoidance adaptation trumps any overestimation we might make based on the amount of work it might take to climb up a wall.

It’s easy to see how this could happen. The visual picture you get regarding your final state are either you huffing and puffing for air, while the other one included potential blood loss, broken bones and compound fractures! I have always found it easier to get my breathe, rather than blood back! LOL!
Dave Briggs :~)
#6 Cathy
January 2, 2008

I believe there’s a typo up there. You say they were at the base of a 40-foot wall, but the lines on the graph intersect at 14 feet.
#7 Dave Munger
January 2, 2008

That’s 14 meters — actually about 46 feet.
#8 Dan
January 2, 2008

Is the assistant on the ground in both tests? It seems like that makes the second test harder regardless of up/down; in the first one you’re trying to judge when the assistant is 40 feet away from *you*, whereas in the second one, you’re trying to judge when the assistant is 40 feet away from *a point 40 feet away from you*.

Cathy: the graph is in meters
#9 philip roberts
January 2, 2008

I’ve notices the same effect that this experiment measured. I’ve attributed it to the difference that a person’s height makes. When below a 40 foot wall its about 34-35 feet to the top because of the height of our eyes. While when above its 45-46 feet down to the ground. I wonder if this could account for some of this effect.
#10 Pete
January 2, 2008

@Cathy, it’s about 14 metres which is about 45 feet
#11 Dave Munger
January 3, 2008

Dan,

The assistant was on top of the wall (actually a parking garage) when the student was at the top).

Philip,

The difference in distance between looking down / looking up is greater than 2x a human height. When looking down, people overestimate the distance by more than 12 meters — they almost double the height of the wall.
#12 Jim Kornell
January 3, 2008

Would be interesting to test people who jump off things–divers, ski-jumpers, downhill bikers–to see if they systematically vary from the normal populace. By analogy, testing the general populace to see if they can hear musical intervals, as contrasted with practicing musicians. I can’t tell if the implication of the experiment is, we’re wired to overestimate falling distances, or only that we’re bad at things we never practice.
#13 Jason
January 3, 2008

“The assistant was on top of the wall (actually a parking garage) when the student was at the top).”

Well in that case you likely had to turn their head further (and thus further distort their frame of refernce) to look down and then turn and look at the assistant. Standing at the base of the wall it would probably be possible to see the wall and the assistant at once.
#14 Alioth
January 5, 2008

First-hand experience: the ski slope immediately under the lift looks a hell of a lot less steep when you’re just looking at it as you ride up, vs. looking down along it from the top or middle. For me, I’d estimate the usual difference at ten degrees or so, but it’s been a while since I last went skiing.
#15 Freiddie
January 6, 2008

Your explanation does make logical sense, but I wonder why I always see things down from an airplane to be, well, closer than usual?
#16 Patrik
January 6, 2008

I have been rock climbing semi-professionaly for about a decade and nowadays I am used to standing next to the edge of a cliff being 10, 50 or 100 meters up without feeling any discomfort. Though, whenever I have climbed together with less experienced climbers and especially beginners I have always been intrigued by the fear in the eyes of a person standing only 10 meters up and looking down into the “abyss”. My experience is that normal people perceive it as very discomfortable to look down when standing next to the edge of a cliff.
However, when you are in a parking garage (as in this case) you might feel safer since there are walls, fences or the like so that you cannot fall over the edge. Still, this discomfort that I am mentioning is at risk of inducing bias in the respondents.

Then of course, I guess that it is this bias that makes us overestimate distance when looking down compared to looking up.

It is my experience that beginners are constantly overestimating how far up on a wall they are. People who are climbing for the first time are frequently stating that they are 6-7 meters up when they have just left the ground being perhaps 2 meters up (+ 1,6-1,8 meters where their eyes are). This error is being reduced as they gain climbing experience.

Remember that I am just speaking out of my own experience here and not any systematic research that I have conducted.
#17 Patrik
January 6, 2008

Coming back to my previous comment above #16; Perhaps the respondents would overestimate the distance when looking down even more if they were not in a “safe” garage but exposed more directly to the unpleasant feelings when standing on the edge of a cliff some 40 feet up.
#18 Skeptic8
January 9, 2008

Many years ago I read of early Anglo horsemen/ explorers who encountered the Grand Canyon of the Colorado and attempted to descend to the bottom by looping a few lariats together. We do get used to the utility of our bi-optic stereovision that just runs out at about 200 ft max. After that we rely on comparisons of objects for distance cues. The system is seamless- we have one eyed drivers- and our estimates are rather good. Few of us encounter the “run out” in our daily lives like those horsemen.
I’m an experienced amateur stereo-photographer who has inserted a “left-left” slide into a series of “left-right” images and questioned the viewer. I truly realised the that “run out” peering into the GC. Had there been a yellow boat shooting the rapids I would have prob’ly not noticed.
#19 Jim Kornell
January 11, 2008

After posting the above, I talked to an “augmented reality” researcher who’d tested people on horizontal distance estimation. People were generally terrible; but when he tested a friend who was a competitive pistol marksman, his friend, and the friend’s father, also a marksman, were bothy excellent. This all anecdotal, of course.

it doesn’t mean that there’s not also an evolutionary explanation, viz., if there is a strong systematic bias to overestimate when looking down, then the “badness at unpracticed estimation” may sit on a foundation of “guess more when looking down.” Seems pretty plausible. Wonder about systematic errors of estimation looking up?
#20 Luna_the_cat
January 13, 2008

I personally learned to overestimate “down” distances by painful experience — in other words, by drastically underestimating a down distance as a child, when I decided to escape a hotel room where my parents had imprisoned me (to my way of thinking, anyway) by jumping out a window.

And also, to Russell @#1 — yes, indeed, and as anyone who has ever done battle re-enactments can tell you, anyone charging you automatically gains a foot in height and about 45 pounds in weight, and anyone charging you wearing plate armor and swinging a battle axe is automatically 9 feet tall and weighs half a ton.
#21 soboco
January 14, 2008

I’m a pilot, and I’ve wondered about that very thing ever since I started flying. I still find myself surprised at the altitude indicated on my altimeter. In relatively low flight, say a 1,500 feet or less above the ground, my visual perception tells me I’m much higher than I am. On approaches to runways I have frequently found myself low on the glide slope which isn’t much of an issue in good weather with good visibility, but at night it increases the chances of landing in trees off the end of the runway.
#22 Mikhail
January 15, 2008

Thank you, Patrick the climber. At least someone sees an alternative to the naive evolutionary explanation. A much more likely explanation is that we grow up and live in a FLAT world – we walk on flat ground and look at things UP! Therefore we learn to estimate the height of things, while very rarely needing to estimate the same thing down. It’s a simple skill difference. I’d bet you good money that if they tested members of mountain tribes or people born and raised in the mountains, the difference would disappear!