I suspect not, because moving forward (or backwards for that matter) is an important part, but I would like to confirm.
UPDATE: Clearly it's possible http://www.youtube.com/watch?v=NuJvH1W7s1Y
Can someone explain why?
[Physics] Would a bicycle stay upright if moving on a treadmill and why
everyday-lifenewtonian-mechanics
Related Solutions
I think the solution has more to do with the tennis racket effect (see: https://physics.stackexchange.com/a/17507/392).
Let me clarify the disk with hole in it has two stable axes of rotation and one unstable one. The unstable one is through the hole and the stable one is across (below in green) and normal to the disk.
I have confirmed that without friction (and from the videos in the link above) when the disk is spun on the unstable axis, it will perdiodically flip. This is what caused it to flip when the disk was falling without friction.
The additional nuiance here is the once it is on the "upsidedown" oriention and friction is present then the unstable axis becomes stable.
If the hole spans from the center to the edge of the disk, then the center of gravity is at $$ \vec{c} = (0,-\frac{R}{6},0)$$ where $R$ is the outside radius of the disk. The principal moments of inertia about the center of mass are $$ \begin{aligned} I_{XX} & = m \left( \frac{\ell^2}{12} + \frac{29 R^2}{144} \right) \approx 0.2 m R^2 \\ I_{YY} & = m \left( \frac{\ell^2}{12} + \frac{5 R^2}{16} \right) \approx 0.31 m R^2 \\ I_{ZZ} & = m \left( \frac{37 R^2}{72} \right) \approx 0.51 m R^2 \end{aligned} $$
where $\ell$ is the thickness of the disk. Since $I_{YY}-I_{XX} = \frac{8}{37} I_{ZZ}$ this means that the y direction is the medium inertia value, x the minimum and z the maximum. Hence the instability about the y axis according to the Tennis Racket Effect.
I am working to qualify the above statement and I am going to update this post with my findings.
In the aquarium tunnel the fish appears smaller because the acrylic with the water behind it creates a diverging lens. You can see in the ray diagram below that fish inside the aquarium appears smaller(you outside will see a diminished or smaller virtual image). The sides of the tunnel taken approximately cylindrical( that is in the arc of a circle).
Using small angle approximations the size of the fish decreases by approximately 30%(factoring in refractive index of water and of acrylic where the refractive index of acrylic cancels out in the mathematics) if you calculate the angle of divergence. Thus the fish do appear smaller in such an arrangement for viewing in a tunnel.
Note: You can think of this scenario like the opposite of a fish bowl where fish look larger inside the bowl but here it's like you are inside the fish bowl and hence the outside world(fish in aquarium) looks smaller by the law of reversibility of light.
Best Answer
Because you can move the bike from left to right, like when you're riding, to balance it.
Whether you're moving or not doesn't matter, just that your wheels are turning so the steering works.