The following is my first attempt to liveblog ICCS 2007. I arrived at the Quincy Marriott shortly before 8:30 this morning, having driven south on I-93 from Boston. Unlike the first time I drove out here, I didn’t get lost in Braintree, since I took the left fork at the “Braintree split,” where I-93 undergoes mitosis. These things are important to know.

The morning’s plenary talks began with Diana Dabby (Franklin W. Olin College of Engineering), who spoke about chaotic transformations one can apply to music in order to generate musical variations, as in “Variations on a Theme of Beethoven.” Her scheme begins by breaking the musical performance into a sequence of pitches, denoted [tex]p_i[/tex], and then mapping each [tex]p_i[/tex] to a section of a dynamical trajectory on a chaotic attractor like the Lorentz owl/butterfly mask.

One then chooses a different set of starting conditions, which yields a different path through the attractor, and a new sequence of notes is built by recording the regions of space through which the second trajectory passes. (It’s a push-forward, pull-back sort of scheme.) This procedure can produce variations which resemble the original piece fairly closely, or which diverge more radically. It can also be used to fuse two different compositions, for example taking a selection from Bach’s Well-Tempered Clavier and a Gershwin tune to make a “GershBach” composition.

Next, Ed Fredkin (Carnegie Mellon) spoke about the relation between physics and computer science. His thesis was that the absence of nice symmetries and conservation laws in the latter makes it difficult to establish definite rules for what can and cannot be done, computation-wise. I found his direction a little puzzling: to me, there’s not much point in building an elaborate cellular automaton to implement some reversible-gate computer, if you immediately turn around and use that CA to create a plain vanilla Universal Turing Machine. Fredkin devises logic gates which preserve the total number of 1s and 0s, so you could speak of a “Law of Ones Conservation.” However, I think, this doesn’t really get you anywhere, and here’s why. Fredkin notes that you can represent any string you want while still respecting the Conservation of Ones, by using a mapping from two-bit sequences:

[tex]01 \rightarrow A,\ 10 \rightarrow B.[/tex]

[tex]A[/tex] and [tex]B[/tex] can then become the symbols for a higher-level computational device. But at the level of that computation, your bits are no longer necessarily conserved. You haven’t really gained anything, because we already know that an irreversible computer can be built upon fundamentally reversible laws: we build computers in the physical world.

Gyan Bhanot (IBM Research) spoke after Fredkin, expounding the discoveries which mitochondrial DNA sequencing has revealed about human migration and evolutionary history. One item I hadn’t heard before is that Scandinavian mtDNA shows Scot and Irish ancestry — because the Vikings invaded the British isles and brought back Irish wives! Indeed, the founding population of Iceland appears to have been mostly Scandinavian males and British/Irish females.

The final speaker of the morning session was Liz Bradley (University of Colorado), who has worked with Dabby to extend the chaotic transformation to other symbol sequences, such as dance moves. The body of her speech, however, dealt with the fluid dynamics of planar jets, and the question of how small perturbations can be amplified (via sensitive dependence on initial conditions) to excite new regimes of behavior. In her laboratory apparatus, a flat sheet of heated gas 2mm in width is made to rise, carrying atomized droplets of mazola oil (which fluoresces under green laser light, allowing for convenient strobe photography). The sheet of gas passes through a gauntlet of micromechanical air-puffers which can poke the column either symmetrically, pushing on both sides at the same time, or asymmetrically, pushing in alternation. Overall, the situation is rather like a 2D version of the smoke rising from a cigarette or a snuffed candle: the smoke rises vertically for a while and then wobbles back and forth, spreading and wandering all over the place.

Using numerical simulations based on vortex behavior, Bradley and colleagues can exert a measure of flow control over the planar jet’s behavior, exciting different modes of instability. The hope is that such technology would eventually prove useful for improving the operation of devices like fuel injectors.