Month: November 2016

Beethoven’s Pastoral Symphony & Nature

We are now going to talk about Beethoven’s 6th symphony, the Pastoral symphony. It is widely regarded as one of the greatest pieces of the orchestral repertoire, and certainly one of the most played.

This was written in 1808, during one of the most difficult periods in Beeythoven’s life. By this time he was completely deaf and had seriously considered suicide. He was saved, however, by his passion for music and for nature, and often enjoyed long walks across the forests in the outskirts of Vienna.

The Pastoral symphony is one of a handful of works by Beethoven containing explicit programatic content, i.e. a piece of music that is intrisically connected to a extra-musical content, and in the example of this particualr movement, it depicts a walk in a forest, which precedes a storm (3rd movement). This depicts a walk across the forest, similar to the walks Beethoven often enjoyed. The first thing that is noticeable about this piece is the smooth, peaceful melody, which ineviatbly transmits the sensation of being surrounded by nature.

 

In the example above, we can hear the imitation of bird sounds: a nightingale, depicted by a flute, a quail, depicted by an oboe, and lastly, a cuckoo, depicted by a clarinet:

In conclusion, Beethoven’s 6th symphony is a perfect example of how music can (and indeed often does) depict the most diverse situations and moods, and can really take us to other places, sometimes unknown.

Superposition of Quantum States and Qubits

In quantum mechanics, the probabilistic replaces the deterministic. This means that, for instance, an electron can’t be in a well defined position. This is due to a small uncertainty regarding its speed and its position, which means that an electron can actually be in two places at once, pop in and out of existence, and teleport instantly from a place to another, amongst other strange phoenomena. We then stop talking about well defined states and enter the realm of probability, and about the superpositions of those same states, which are described in the Schrödinger equations.

In classical computing, an electrical impulse can either and exclusively represent a 0 or a 1, which are differentiated by their respective voltage (low voltage represents a 0, and a high voltage represents a 1). In quantum computing, however, since we can not know the state of a quantum object until we observe it, then what will happen is a superposition of all the possible states. If we attribute, for instance, the spin of an electron to a bit (spin up=1, spin down=0), we can not know its definite spin, and thus a superposition of all possible spins is created. The bit that is generated is called a quantum bit, or a “qubit”.

Let us now compare the computational power of classical computers and of quantum computers: If we take two bits, each one can only have the value of either 0 or 1. The possible combinations are, therefore, 00, 01, 10 and 11. If we take two electrons, since their spin can correspond to both 0 and 1 at the same time, the number of possible combinations is exponentially larger than the number of bits allowed by classical computing. This then implies a far greater computational power than even our best super computers are capable of.

There is, however, a problem with quantum computing: Even though multiple quantum states can coexist, when observed, only one of those states can be shown. What a quantum computer then does is choose the combination of qubits that best fits the goal of the user. For instance, when running a simulation, a quantum computer is capable of testing all the possible combinations at once, but only one of those combinations is showed. This shows us the immense power of quantum computers relative to classical computers which can only test one combination at a time.