Das lied von das Universum

I just read “The life of Galileo”, by Bertolt Brecht. Brecht, a man of his time, was worried about the ethics of the scientific work. My personal opinion is that it is not science itself that has to be under scrutiny, but its uses. Science has improved our lives in general, when used properly. And knowledge is a treasure for us all. Only us can save us from ourselves, and knowledge is the way to go. 

A sentence was highlighted by somebody else in the version I have been reading: “Unhappy the land that has no heroes!”. Galileo´s recantation has been cried. However, I would stick to another one, by Galileo later on in the play, which is not highlighted: “Unhappy the land where heroes are needed”.

1616: The Copernican theory is censored by the church. But, 400 years later, we “hear” the music of the Universe. When Galileo oriented the newly invented telescope to Jupiter, he started a journey, the scientific journey, that led us up to the historical moment we are living now. Much has been said and explained everywhere about gravitational waves. I am only echoing what has been on the news since last February 11^th 2016. As all good music, the timing is perfect: 100 years after they were predicted by Einstein, another science´s giant. And, of course, everybody in the planet can have a ringtone with the “music” of two black holes dancing in space. 

Since Galileo, astronomers started to see a silent movie, in black and white. Then there came the colours, with all sorts of wavelengths in the electromagnetic spectrum. Now, we can hear the sound, the soundtrack of the Universe. And now, all humanity can participate in the celebration of this gigantic step towards our understanding of the Universe. 

 We are happy, and we have our heroes.

Mind the gap

An international team of researchers have demonstrated that the spectral gap problem is algorithmically undecidable. The spectral gap, or the difference between the energy of the ground state and the first excited state, is fundamental to understanding the properties of a quantum many-body system. The question posed in their paper is: given a quantum many-body system, is it gapped or gapless? And they find out that that question is undecidable in the same form encountered in Gödel’s incompleteness theorem.

An important consequence of this study is that it has been demonstrated that there exists a physical problem where the reductionist approach is not possible, that is, the macroscopic properties of a system cannot be derived from its detailed microscopic description.  Even if we can perfectly describe all the parts, the properties of the whole cannot be predicted. Nature seems to dodge our immature science.

Emergent properties belong to the realm of complex systems. As Anderson puts it, “More is different”. There seems to exist a hierarchy in the description of nature, and that there is not straightforward way of going from one to the other.

This hierarchic structure has been recently found in our brains when we process language. Apparently, we keep track of different abstract linguistic structures (words, phrases and sentences) at different timescales. The authors of the research found thus a basis for Chomsky’s ideas about how we have a grammar in our head, which underlies our processing of language.

A similar idea permeates the Schenkerian analysis of a passage of music. This analysis shows the hierarchical relationships among its pitches, drawing conclusions about the structure of the analysed passage. Music is another kind of language, with different compositional time scales. I wouldn’t be surprised if a similar kind of analysis for music would led to finding a musical grammar in our heads.

Music, the ultimate abstract language, the one that Kandinsky tried to translate into visual art. To completely disembody lines and colours from their figurative meaning. Just a feast to the eyes.

A complex work of art, created by a complex system, the painter, apprehended by a complex system, us humans. How could ever the beauty of a piece of art be deduced from something so simple as an equation?

Earthquakes in music

I already have written about earthquake records transformed into music (here and here). However, I did not realized that earthquakes could also have inspired music compositions. As I was reading The Melodies of Monsoons: Weather in Indian Classical Music, I was wondering if earthquakes also inspired classical music. 

And, certainly, a few works have been composed after these natural disasters. Among them, the beginning of Handel’s Messiah and Telemann’s Die Donnerode. The later particularly interests me because it was inspired by the 1755 Lisbon earthquake. 

The Lisbon earthquake struck in the height of the Age of Enlightenment. Two opposing ideas, the orthodox religiousness, and the prevalence of the reason, tried to explain such a natural disaster. It inspired Voltaire’s Candide, which would be later transformed into a Bernstein’s operetta, and a strong debate about the existence or not of a benevolent deity. Rousseau found in this earthquake grounds for returning to the natural life, far from the cities. The Lisbon earthquake inspired the creation of the Portuguese fados (fate), so embedded now into their culture. And here I leave you, with Amália Rodrigues:

Music from the spheres

This is a composition by Burak Ulas based on the pulsations of a star called Y Cam A. Isn´t it beautiful?

 From here.

Quantum music

It is not surprising that I was interested in this article in MIT Technology Review. Those who usually read this blog are used to my posts about arts related to science. With a particular interest in music. 

So, this work, by Karl Svozil, a theoretical physicist at the University of Technology in Vienna and his pal Volkmar Putz, got my attention. Basically, each note in a composition would have a probability of being heard, depending on the person who listens to it, and the time they listen to it. 

The music itself would be written with probabilities for each note, and, supposedly, it would be played all together, but each person would have a different experience about it. 

Don’t be surprised by science influencing music. From the beginning of music, it was closely connected to mathematics. And modern science has inspired compositors such as Xenakis. 

I am not sure how this kind of composition could be performed in the raw way it is described, but I thought it would be easy enough to create a computer program that would simulate it. 

I used Ken Schutte’s programs to make one myself with notes with different probabilities in each step. Here you have the program, and here you have one of the realisations of it.

I hope you enjoy the experience.

The Poseidon Ensemble

They made a composition with earthquakes. Isn´t it beautiful?

 

The Poseidon Ensemble — 2014 by Struct on Mixcloud

Seen here :)

The music of a tree ring

It is not a Crhistmas tree, nor a Christmas carol, but this is how a tree ring sounds like when played as a record.

 

Seen here.

 Happy Christmas :)

Music from the LHC

Again, more music by Domenico Vicinanza (see our post about the Voyager 1 and 2 duet). Now, with data collected from the Large Hadron Collider.

Seen here.

Voyager 1 and 2 duet

This beautiful piece is made from data from the Voyager 1 and 2, mixed in a duet, by Domenico Vicinanza. Here you have more information. Via Microsiervos. 

From Supersymmetry to Schoenberg

Professor James Gates on Supersymmetry. The talk starts at around minute 12. He goes from symmetry concepts to the music of Arnold Schoenberg. What I found most interesting is the finding about doing calculus by means of graphs, or by coding the operations into binary code. They transform equations into what they called Adinkramat. Simply genius.

How does the Little Prince sound?

In their work, Hannah Davis at New York University and Saif Mohammad at the National Research Council Canada have developed a computer program that translates the emotions shown in a novel into a piece of music.
See here for further explanations, and check here for listening to the novels they analyzed.

Isn't it cool?

Music in the DNA

I have read this article and I found it very interesting. It summarizes the different ways in which our DNA can be translated into music. Read it if you are interested in the topic. One of the ways to create music is translating the 22 amino acids that can be obtained from our DNA bases into microtones. 

One of the composers that use DNA is Stuart Mitchell. Check this composition. It is absolutely beautiful:

The music of the spheres

It is said that the idea of the harmony of the spheres is attributed to Pythagoras, that the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony. Well, Pythagoras was probably the first person to notice the remarkable relationship between music and mathematics. 

In another post I already mentioned the topic, but now I want to show you the work by Dmitri Tymoczko, which I fond through this link. In his works, which are published in Science, he describes harmony in a geometric way. He explains how the possible paths between cords are influenced by the symmetries of his mathematical constructions. 

So now we not only can listen to the music of the spheres, we also can see it!

A review of "Gödel, Escher, Bach: An Eternal Golden Braid"

I think the most interesting way (at least for me) of learning about the Gödel’s Incompleteness Theorems is by reading Douglas Hofstadter´s book "Gödel, Escher, Bach: An Eternal Golden Braid". 

Both content and form are carefully chosen, in such a way that you are introduced to very difficult concepts in a, let´s say, artistical way. And of course it is completely intentional. The structure of the book is, as it has been said, a counterpoint between Dialogues and Chapters.

The author makes a explicit analogue of Bach´s music in his book. And, I think, it shows the universality of the concepts he wants to show.

As a fugue, he first shows the main themes, and masterly proceeds to makes variations of it. He presents the concept of recursivity and isomorphism from an artistic point of view. He presents what he calls a "strange loop" in terms of music and painting. As he defines them it is a phenomenon that occurs whenever, by moving upwards (or downwards) through the levels of some hierarchical system, we unexpectedly find ourselves rightback where we started. You can find this in Bach´s music and in Escher paintings. 

He also explains that implicit in the concept of Strange Loops is the concept of infinity, and the conflict between the finite and the infinite in Bach´s and Escher´s works.

He introduces the main theme as the so-called Epimenides paradox, or liar paradox. Epimenides was a Cretan who made one immortal statement: "All Cretans are liars." What can be said about that statement? It is true or false? 

Godel´s idea was to use mathematical reasoning in exploring mathematical reasoning itself, and came up with the conclusion that "All consistent axiomatic formulations of number theory include undecidable propositions.

Hofstadter masterly shows the importance of strange loops in Gödel´s proof of his theorem. Once a formal system ask about its consistency and completeness, it cannot reach a conclusion. The equivalent of Epimenides paradox in mathematics it´s "This statement of number theory does not have any proof". Whereas the Epimenides statement creates a paradox since it is neither true nor false, the Gödel sentence is unprovable (inside its own formalization) but true. 

As Hofstadter concludes, Gödel’s Theorem shows that there are fundamental limitations to consistent formal systems with self-images. In particular, it cannot proves its own consistency. 

It has been used to prove that we cannot compute the human mind, because we would be incomplete. There is the argument against this of humans not being consistent, so we could be inconsistent Turing machines, and therefore computable. Read more about the computability of the mind and the Gödel´s theorems here.

 

I must say that it is not an easy book to read. You have to pay a lot of attention to it. But it is worth reading. 

As a mathematical representation of one of Bach´s compositions, here you have the "Crab canon", from his Musical Offering, with which Hofstadter starts his book. 

Earthquake music

The other they we had a visit from a high school student that wanted to study maths or physics. We were explaining him what we did. He said that he also liked music, so we came up with some music related entertainment: fractal music. 

There are some authors that play with physical models and convert it into music, like Xenakis, for example. We played a little bit, and we ended up creating a program that translates fractals into music. Here you have the result: 

We used the MATLAB scripts written by Ken Schutte, but with fractals. This fractal in particular has a Hurst exponent of 0.8. The timing is equal, but we can choose random or fractal timing too.

Then, at home, I thought that it would be cool to create a movie with an earthquake. The result is this: 

This is what the Lorca (Spain) 2011 earthquake would sound like. The sound is scaled, so this is not a real sound. But I thought it would be nice to see how the earthquake signal could be translated into sound. I am not the first one to think about it. You can look at NOAA , for example. 

Here you have the sound of seismic ambient noise, recorded at Almería (Spain), for a seismic campaign: 

The sound is also scaled.They are very different, don´t you think?

The movies and sounds are nothing special (I don´t think I will win an oscar), but I had fun making them. And I think that´s all that matter.