Holistic Detective Agency

Have you ever needed a holistic detective agency? And do you know what a holistic detective agency is? If you do not know, don't panic: I am going to say what it is this strange agency.

The term ‘holistic’ refers to my [detective's] conviction that what we are concerned with here is the fundamental interconnectedness of all things. I do not concern myself with such petty things as fingerprint powder, telltale pieces of pocket fluff and inane footprints. I see the solution to each problem as being detectable in the pattern and web of the whole. The connections between causes and effects are often much more subtle and complex than we with our rough and ready understanding of the physical world might naturally suppose.

And what are its secret origins?

Well, some researchers were once conducting such an experiment [Schroedinger's cat], but when they opened up the box, the cat was neither alive nor dead but was in fact completely missing, and they called me in to investigate. I was able to deduce that nothing very dramatic had happened. The cat had merely got fed up with being repeatedly locked up in a box and occasionally gassed and had taken the first opportunity to hoof it through the window. It was for me the work of a moment to set a saucer of milk by the window and call “Bernice” in an enticing voice -- the cat’s name was Bernice, you understand -- and the cat was soon restored. A simple enough matter, but it seemed to create quite an impression in certain circles, and soon one thing led to another as they do and it all culminated in the thriving career you see before you.

If this was the case for Dirk Gently and his holistic agency, perhaps the most important was the investigation into the murder of Gordon Way, a computer science magnate, as well as friend of Susan’s boyfriend (and Susan is Gordon’s sister), Richard MacDuff. Richard, a well-known programmer and author of the popular article Music and Fractal Landscapes, which sets the foundation for modern fractal music⁽¹⁾, the only investigated about the murder, is lucky enough to know Dirk, his old college companion, and the misfortune of being his client, seen that a Dirk’s investigation implies a rescue mission of the universe, obviously thanks to the time machine, which is the old house of Richard’s professor.
And if that was not enough to convince you (to do what, then, I don’t know), you must hear that an electric monk who crosses the worlds thanks to the door of the bath left open by the professor in one of his trips is a more than sufficient reason to do anything (but I don’t know precisely what you must do).
So, dont’ panic: it’s towel day! And thanks to Douglas Adams.

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1. Fractal music is a mathematical deviation in the study of fractals in which one seeks to understand how these can be used to generate music. Or even how these can be in music apparently composed without the use of any mathematical knowledge about fractals. For example Harlan Brothers argues that there is a fractal structure based on the Cantor set in Bach Suite no. 3.
   
   Reading the article that Ivars Peterson written about Brothers’ work, one finds out how these, by examining the score, determines an AAB structure, where section B is twice that of A.
   
   According to Brothers, the composition of Bach has a symmetric four-tier structure, which has not always been correctly performed. However, the researcher concludes

   The fact that Bach was born almost three centuries before the formal concept of fractals came into existence may well indicate that an intuitive affinity for fractal structure is, at least for some composers, an inherent motivational element in the compositional process.⁽²⁾

   And something like that seems to be discovered by Daniel Levitin with his research team:

   Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a $1/f$ [where $f$ is the frequency] power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm’s contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a $1/f^\beta$ power law across 16 subgenres and 40 composers, with $\beta$ ranging from $\sim 0.5 - 1$. Notably, classical composers, whose compositions are known to exhibit nearly identical $1/f$ pitch spectra, demonstrated distinctive $1/f$ rhythm spectra: Beethoven’s rhythms were among the most predictable, and Mozart’s among the least. Our finding (…) demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a $1/f$ spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in $1/f$ rhythms to give their compositions unique identities.⁽³⁾ ↩

2. Brothers HJ (2007). Structural scaling in Bach’s Cello Suite No.3, Fractals, 15 (01) 89-95. DOI: 10.1142 / S0218348X0700337X (sci-hub) ↩
3. Levitt DJ, Chordia P. & Menon V. (2012). From the Cover: Musical rhythm spectra from Bach to Joplin obey at 1 / f power law, Proceedings of the National Academy of Sciences, 109 (10) 3716-3720. DOI: 10.1073 / pnas.1113828109 (pdf) ↩