Insta-Reich

Tonematrix by André Michelle is a function defined on the two-dimensional vector space over the field . And yet, it’s so much more; though self-explanatory, it might save you three seconds to know that the axes correspond to time and pitch, with the latter staggered non-linearly to prevent dissonance. It seems possible that Tokyo / Vermont Counterpoint could be produced directly from this tool if the latter were extended further in time.

A more interesting challenge would be to create a devolution from the audio to tonematrix form. I claim such reverse engineering, followed by a Fourier transform to draw out the particular periodicities in frequency and time, can be used to generate an infinte family of pleasant sounding meanderings of arbitrary length. I would also like to consider the possibility of randomly placing and removing structures on the map at different positions: most of the early random and fractal music was interesting but sounded very much like garbage, whereas by forcing tonality on the output, tonematrix minimises the potential for something awful.

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Moving houses

Until now, it has passed unremarked that Brendon is about to take up his post-doctoral position at UCSB with Tommaso Treu. What it is that Brendon will be working on remains mysterious (i.e. to me)! Along with Matt’s journey to SISSA in Trieste, fully 100% of the LtN team now blog from exotic international locations such as those in the image above.

To make matters more dynamic, Luke & I will be reporting to new locations in a few months’ time. I suppose we shall have to announce these in maximally dramatic fashion in a little while after the extended blog post that is my dissertation meets the binders. For now, I think we must investigate a WordPress/Facebook interface to ensure more of Brendon’s prolific literary output finds its way into these august digihalls.

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Very Drunk Photons: A Challenge for Probability Boffins

I’ve been beating my head against a random walk problem for a few days now. I’ve become so muddled that I can’t even place it in the right formalism to begin looking for a solution.

For those who don’t know about these things, the stereotypical random walk problem involves a drunk man trying to walk home. He bravely steps away from the lamppost that he was using to steady himself. However, he is completely disoriented and thus each step is in a new direction. How far, on average, will be away from the lamppost after N steps?

The answer is the length of each step, multiplied by the square root of the number of steps. This result is ably proven here. There are, I am discovering, numerous ways to complicate this scenario, in ways that are relevant to physical situations. The particular problem I am looking at is within radiative transfer. Photons emitted from, say, stars will bounce around in the surrounding gas on their way to our telescopes. This will affect the spectrum and appearance of the source. In this case, the length of each drunken photon step is not constant, but depends on the photon’s frequency, the surrounding gas density and velocity, and good old-fashioned chance.

I’ve given the details of the particular challenge I’m facing here, or as a pdf here. I’m hoping that someone with more statistical brains than me will help me out. Feel free to ask questions in the comments.

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