Experiment with smaller children

[WackyTaffy]

There has been an experiment with smaller children. First, there was a smaller container which had a certain amount of liquid (Let's say 355 mL, the same as a coke can). Then, there was a taller glass, with the same amount. Without saying which had more, they were asked which one had more liquid in it. They chose the taller glass.

There was also some experiment where they had to guess which one had more liquid, and then had to pour it from one size glass to another.

I forgot the experiment exactly, but I still feel this way with certain things. Why?
For example, Jones Co Soda (The best soda company in the world, in my opinion) makes glass bottles, 355 mL each, with a resealable lid. Now, coke cans have the same amount of liquid. Yet I swear, it seems like the Jones Co ones have more. Is this because of the illusion that it being taller it has more liquid?

 

[hypnagogue]

This clearly involves some kind of visual illusion or another. Probably what is going on is that the visual system processes information in such a way as to implicitly assume that taller things have greater volume than wider things (all other things being more or less equal). Another way of saying that might go as follows: if there exists some perceptual estimate of volume based on an object's perceived height, length, and width, the visual system might be inherently biased to give the height dimension more weight to its volume estimate than it does to the length or width dimensions.

For a more detailed and qualified explanation, you should try to track down the paper describing this study. If you can find the article reference but can't view the paper online, I'd be willing to access the article myself and see what their explanation of this effect is.

 

[selfAdjoint]

As I recall Piaget did a lot of experiments like this, and hypothesized that the ability to estimate the relative amount of liquid in different shaped containers, which he held to require a certain level of abstraction, didn't develop until the children were older. Piaget's theories have had a lot of influence on educational thought in the USA.

 

[hypnagogue]

I haven't found the original paper, but here's a new article (Dec 2005) discussing essentially the same effect: Shape of glass and amount of alcohol poured: comparative study of effect of practice and concentration.

Results: Aiming to pour a "shot" of alcohol (1.5 ounces, 44.3 ml), both students and bartenders poured more into short, wide glasses than into tall slender glasses (46.1 ml v 44.7 ml and 54.6 ml v 46.4 ml, respectively). Practice reduced the tendency to overpour, but not for short, wide glasses. Despite an average of six years of experience, bartenders poured 20.5% more into short, wide glasses than tall, slender ones; paying careful attention reduced but did not eliminate the effect.

So it looks as if learning can improve our ability to estimate volumes of various shapes, but even as adults with extensive experience we still tend to be fooled by certain shapes (specifically, our tendency to underestimate the volume of short, wide containers seems particularly resistant to learning). The authors of this paper don't propose any explanation for why this occurs though.

 

[DaveC426913]

This clearly involves some kind of visual illusion or another. Probably what is going on is that the visual system processes information in such a way as to implicitly assume that taller things have greater volume than wider things (all other things being more or less equal).

Yes. Hold that thought...

Another way of saying that might go as follows: if there exists some perceptual estimate of volume based on an object's perceived height, length, and width, the visual system might be inherently biased to give the height dimension more weight to its volume estimate than it does to the length or width dimensions.

Note that, from a single viewpoint, we see objects as areas. Volume is only implied.

A round glass that is twice as tall really does fill twice as much of our vision. A round glass that is shorter but fatter does not actually fill twice as much of our vision - it only fills root(2) as much. We can't explicitly see the added front-to-back depth.

Really, the experiment is cheating in a sense. A truly objective experiment would use two glasses that have identical front-to-back depths.

 

[DaveC426913]

Demonstration:

2 ROUND glasses, each holds 1 litre

Glass A:
height: ~16cm
Thus, width, depth = ~8cm


Glass B:
We give it a height = half of glass A, so: ~8cm
Thus, width,depth = ~5cm (to hold same volume as glass A)

Note that Glass A (128cm^2) actually DOES look smaller than glass B (40cm^2).

A PROPER glass B would be:
Height: 8cm
Width: ~16cm
Depth: ~8cm (same as Glass A)

In a proper experiment, Glass B would be much wider than it is.

 

[TheStatutoryApe]

So it looks as if learning can improve our ability to estimate volumes of various shapes, but even as adults with extensive experience we still tend to be fooled by certain shapes (specifically, our tendency to underestimate the volume of short, wide containers seems particularly resistant to learning). The authors of this paper don't propose any explanation for why this occurs though.

When I worked at a coffee house I generally measured out what I poured into containers with an imaginary mark off point because I was familiar with the containers and approximatly where the proper amount should fill them to. I don't remember having ever tried to observe the actual volume itself.
This may be part of what happened with the bartenders but I think DaveC has a better theory of the overall issue.