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Topology is a swath of mathematics that investigates the properties preserved under a continuous transformation. Originating from an in depth study of the real line, this field equips the analyst with the ability to abstract beyond the familiar, in addition to generating a convenient link between analysis and the other major fields of mathematics -- algebra and geometry.
The most commonly used tool of a topologist is a homeomorphism. Essentially defining topological equivalence, two spaces are said to be homeomorphic if one can be deformed into the other in a well-behaved manner. As such, topology is frequently called "rubber sheet geometry". For instance, in jest, a topologist is said to not know the difference between a donut and a coffee mug. Put as simply as possible, topologies allow mathematicians to "stretch", "cut", and "glue" abstract spaces
The applications for this field are countless outside of pure mathematics, and in titling this album so, Joe McPhee supplies an interesting and unforeseen context to examine his music. I had grown accustom to thinking of jazz as a means of expression, with free jazz and its sub-genres as the liberal extension. From the spiritual revelry of Pharoah Sanders to the existential musings of Sachiko M, I had been caught up in this tautology. However, through this Po Music, I was able to break free and view each passage as a deformation of another. The free improvisation of "Age" blends seamlessly into the reinterpretation of older styles of "Blues for new Chicago". Before the listener can grasp what has occurred, all structure is cut away in the titular final track, through Radu Malfatti's electro-acoustic explorations.
In many ways, this topological framework is useful to understand the traditional role of an improviser. They extract motifs from their conscious, then instantaneously stitch them back together. Although Topology is said to be a non-idiomatic session, the interpretation is similar. And this fantastic cast (the aforementioned Malfatti and McPhee, Irène Schweizer, and others) do not disappoint.
Sorry for the stodgy math!
The most commonly used tool of a topologist is a homeomorphism. Essentially defining topological equivalence, two spaces are said to be homeomorphic if one can be deformed into the other in a well-behaved manner. As such, topology is frequently called "rubber sheet geometry". For instance, in jest, a topologist is said to not know the difference between a donut and a coffee mug. Put as simply as possible, topologies allow mathematicians to "stretch", "cut", and "glue" abstract spaces
The applications for this field are countless outside of pure mathematics, and in titling this album so, Joe McPhee supplies an interesting and unforeseen context to examine his music. I had grown accustom to thinking of jazz as a means of expression, with free jazz and its sub-genres as the liberal extension. From the spiritual revelry of Pharoah Sanders to the existential musings of Sachiko M, I had been caught up in this tautology. However, through this Po Music, I was able to break free and view each passage as a deformation of another. The free improvisation of "Age" blends seamlessly into the reinterpretation of older styles of "Blues for new Chicago". Before the listener can grasp what has occurred, all structure is cut away in the titular final track, through Radu Malfatti's electro-acoustic explorations.
In many ways, this topological framework is useful to understand the traditional role of an improviser. They extract motifs from their conscious, then instantaneously stitch them back together. Although Topology is said to be a non-idiomatic session, the interpretation is similar. And this fantastic cast (the aforementioned Malfatti and McPhee, Irène Schweizer, and others) do not disappoint.
Sorry for the stodgy math!
6 comments:
Great post! Looking forward to this.
PB
You should call me unobservant because I didn't realize until just a few minutes ago that there was a new person posting here!
I really enjoyed the prepared piano album you posted. Also, you brought to my attention the Tetuzi Akiyama/Toshimaru Nakamura album Which I didn't even know know existed.
there's another toshi/tetuzi (with others) out on bombax bombax. i highly recommend it.
also, i don't think topology is in print anymore. but i did notice available copies on amazon.
Iacus,
Yeah, he's doing great. Awesome to have him on board. There are a couple other people that will be in the mix the next week or so.
P
Amazing
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