Cholewiak, S. A., Fleming, R. W., & Singh, M. (2013). Visual perception of the physical stability of asymmetric three-dimensional objects. Journal of Vision, 13(4), 1–13. doi: 10.1167/13.4.12

Here’s the abstract:

Visual estimation of object stability is an ecologically important judgment that allows observers to predict the physical behavior of objects. A natural method that has been used in previous work to measure perceived object stability is the estimation of perceived “critical angle”—the angle at which an object appears equally likely to fall over versus return to its upright stable position. For an asymmetric object, however, the critical angle is not a single value, but varies with the direction in which the object is tilted. The current study addressed two questions: (a) Can observers reliably track the change in critical angle as a function of tilt direction? (b) How do they visually estimate the overall stability of an object, given the different critical angles in various directions? To address these questions, we employed two experimental tasks using simple asymmetric 3D objects (skewed conical frustums): settings of critical angle in different directions relative to the intrinsic skew of the 3D object (Experiment 1), and stability matching across 3D objects with different shapes (Experiments 2 and 3). Our results showed that (a) observers can perceptually track the varying critical angle in different directions quite well; and (b) their estimates of overall object stability are strongly biased toward the minimum critical angle (i.e., the critical angle in the least stable direction). Moreover, the fact that observers can reliably match perceived object stability across 3D objects with different shapes suggests that perceived stability is likely to be represented along a single dimension.

Want to cite us? Click through for the BibTeX source.

[code]@ARTICLE{Cholewiak2013,
author = {Cholewiak, Steven A. and Fleming, Roland W. and Singh, Manish},
title = {Visual perception of the physical stability of asymmetric three-dimensional
objects},
journal = {Journal of Vision},
year = {2013},
volume = {13},
pages = {1–13},
number = {4},
abstract = {Visual estimation of object stability is an ecologically important
judgment that allows observers to predict the physical behavior of
objects. A natural method that has been used in previous work to
measure perceived object stability is the estimation of perceived
“critical angle” — the angle at which an object appears equally
likely to fall over versus return to its upright stable position.
For an asymmetric object, however, the critical angle is not a single
value, but varies with the direction in which the object is tilted.
The current study addressed two questions: (a) Can observers reliably
track the change in critical angle as a function of tilt direction?
(b) How do they visually estimate the overall stability of an object,
given the different critical angles in various directions? To address
these questions, we employed two experimental tasks using simple
asymmetric 3D objects (skewed conical frustums): settings of critical
angle in different directions relative to the intrinsic skew of the
3D object (Experiment 1), and stability matching across 3D objects
with different shapes (Experiments 2 and 3). Our results showed that
(a) observers can perceptually track the varying critical angle in
different directions quite well; and (b) their estimates of overall
object stability are strongly biased toward the minimum critical
angle (i.e., the critical angle in the least stable direction). Moreover,
the fact that observers can reliably match perceived object stability
across 3D objects with different shapes suggests that perceived stability
is likely to be represented along a single dimension.},
doi = {10.1167/13.4.12},
eprint = {http://www.journalofvision.org/content/13/4/12.full.pdf+html},
file = {Article:http:\semifluid.com\wp-content\uploads\2013\\03\Cholewiak-Fleming-Singh-2013-Visual-perception-of-the-physical-stability-of-asymmetric-three-dimensional-objects.pdf:URL},
owner = {Steven A. Cholewiak},
url = {http://www.journalofvision.org/content/13/4/12.abstract}
}
[/code]

It seems as though billbalance practices the art of Rock Balancing:

Rock balancing is an art, discipline, or hobby (depending upon the intent of the practitioner) in which rocks are balanced on top of one another in various positions. There are no tricks involved to aid in the balancing, such as adhesives, wires, supports, or rings.

Which appears to be a very short-term example of cairns:

Cairn is a term used mainly in the English-speaking world for a man-made pile (or stack) of stones. It comes from the Scottish Gaelic: càrn (plural càirn). Cairns are found all over the world in uplands, on moorland, on mountaintops, near waterways and on sea cliffs, and also in barren desert and tundra areas. They vary in size from small stone markers to entire artificial hills, and in complexity from loose, conical rock piles to delicately balanced sculptures and elaborate feats of megalithic engineering. Cairns may be painted or otherwise decorated, e.g. for increased visibility or for religious reasons.

In modern times, cairns are often erected as landmarks, a use they have had since ancient times. Since prehistory, they have also been built as sepulchral monuments, or used for defensive, hunting, ceremonial, astronomical and other purposes.

…
Plans were drawn, crayons sharpened and collaborators consulted to come up with a reception desk that would put “small and routine” in its place for once and for all. This is the result of months of planning and some fairly heavy scientific research.

A company called Twisted Image finally started production in February. Their job was to fabricate permanent hot air balloons strong enough to carry the weight of the desk. A new type of rubber composite was used to make balloons that were genuinely air-tight and would never degrade, and Caltech were called upon to supply a Heluim/Hydrogen [sic] hybrid gas with an atomic weight 150 times lighter than Helium alone.

Ribbons reinforced with Carbo-Titanium (and in pretty colours) were used to secure the table top to the balloons, tied off on an aerospace grade titanium cleat.
Finally, giant Jenga blocks were carved from solid wood and placed on the reinforced floor.
…

I’m sure it’s pretty obvious that the claims of a “Helium/Hydrogen hybrid gas” and “Carbo-Titanium ribbons” are dubious (to say the least ;-)), but still, a very nice piece of artwork that makes you go, “Hmmm.”

From the designer:

…
The chair is tilted at 9,5 degrees. By tilting the chair and then elevating one end of the seat back to a straight angle, a triangle was created. This actually made the construction stronger and reduced the need for a stabilising cross rod.
In conclusion, it’s not always wrong to be wrong. The deconstruction of the original design served a higher purpose.
…

B°Fex also created a fantastic “unstable” table (8,5°) that compliments the chair:

8,5° is a work table designed for the chair 9,5°, created in the same mindset as the chair.
When the table is tilted at exactly 8,5 degrees, the transverse pin meet the tabletop which makes a very strong construction. The table tilts opposite to the chair, for visual balance.