Brownian thought space

Cognitive science, mostly, but more a sometimes structured random walk about things.

My Photo
Location: Rochester, United States

Chronically curious モ..

Wednesday, December 23, 2009

Primates and walking

In a previous issue of the lovely journal Mindfields, I wrote an article about baby robots. In this, happily ignoring various dynamical systems approaches to the issue, I wrote:
Do we think that the ability to walk comes out of experience? Clearly not. It’s not like the human newborn, upon encountering flattish surfaces, gravity, friction, two (semi-)controllable limbs extending below the waist and other similar-looking beings walking around, figures out from scratch that putting this limb so, and then the other one so (controlling for any number of external factors), it can walk. Instead, walking seems to follow its own developmental program, just like facial hair, zits, breasts and those curious feelings for members of a certain gender. So, typically, you cannot walk when you are two months of age, and people around you would be very worried if you were not walking by the age of three.
Just to be clear, this contrasts with dynamical systems in a deep way, as this quote from a random article* shows:
Dynamical systems theory, as we prefer, views walking as an emergent behavior that arises from the collective dynamics of all contributing subsystems, including the central nervous system and musculoskeletal system. Other constraints, such as those found in the environment (e.g., gravitational forces, slippery walking surfaces) and the task itself (e.g., walking fast or slow), also contribute to shaping the behavior.
Note that these authors contrast this with versions of "maturational and neurophysiological approaches." In the most radical version of this stance, something like walking is not pre-destined, but arises through an interaction between various sub-systems. That is, walking is not something that the organism "knows" in any sense of the word, but is a novel generation by each individual (see e.g., Lewkowicz & Lickliter's review of the Thelen & Smith book**).
Now there are other reasons to suspect that walking and the like are indeed things that (certain) animals can look forward to. For example, pigeons who are restrained from birth can still fly.
(There's also an interesting salamander story for another day)
But the new issue of the PNAS has yet another interesting story to tell.
*Jane E. Clark and Sally J. Phillips (1993) A Longitudinal Study of Intralimb Coordination in the First Year of Independent Walking: A Dynamical Systems Analysis. Child Development, Vol. 64(4), pp. 1143-1157
**Esther Thelen and Linda B. Smith (1994) A dynamic systems approach to the development of cognition and action. The MIT Press, Cambridge, MA

Saturday, December 12, 2009

Why a watched pot never boils

Simple answer: phase transitions are relatively rapid.
Let the time when you set the pot/kettle on the fire to be t_0.
Let the time when the contents are at a rolling boil be t_b.
Imagine you're watching TV, and going to the kitchen every once in a while to watch if the contents are actually boiling...
The essence of the observation is that, given the rapidness of a phase transition, in this case between the non-boiling and the boiling phases, the most likely observation is either one or the other, as shown in this mockchart: only in the pink-magenta region will you actually see the transition from one state to the next.
So, in all the 'n' trips where t_n is less than the lower bound of the pink-magenta region, the pot won't be boiling. And if you miss the narrow transition window, then on the (n+1)th trip, where t_(n+1) is beyond the pink-magenta region, you'll see the water boiling. And conclude, "a watched pot never boils."
That or the Quantum Zeno effect...