Abstract Spaces and Their Superposition on Physical Reality

An interesting point was made in the reading that I thought was worth discussing here. Borgo mentions the habit that people have of using sensory verbs out of context; for example, "I see what you mean," or "can you shed some light on this subject for me." Such uses of the words or phrases are not coincidental to me. My understanding of consciousness and its ties with physical reality (whatever that means) is that though the two cannot be separated, it seems to me that there are things outside of a conscious mind (physical objects, for example) that are observed by the senses of a sentient being and there are symbols in the mind (not letters, or even real objects, but merely something that happens in the brain when a word is said, or an action is perceived) that are slowly built up and interconnected in such a way that rational thought is then possible by the "communication" between such symbols.

It is sensible then that we should describe ways of understanding things with verbs associated with the senses, since our senses are our source of input, our way of connecting with external stimuli. What we typically refer to is our actions within space and time. However, when we start using sensory terminology within music, we are not particularly using our senses in the same manner as with physical space. Rather, we are giving this "musical space" properties of its own. The sound we perceive begins to take on texture, volume has its highs and lows, and note duration is discrete or continuous.

Though this is not a physical space in terms of space and time, it is nonetheless visible in our minds and we should thus be unafraid to explore it in its entirety. Perhaps it is infinite, or perhaps there are boundaries, but surely we have a long way to go before we find them, for music is continuously evolving and taking on new sounds everyday. I think writing a piece of music can be likened to charting a map, and each detailed note implies a more specific route in our musical space. Improvisation, then, is a highly exploratory method of traversing this space. It's as though you're flown to this magical land, dropped off, and told to have fun. Of course, the route is not fixed, and every spot is accessible in one way or another by any given location.

While this space seems abstract, it is not unlike an abstract mathematical space such as a Hilbert space. We can operate on it in numerous ways and we can chart particular shapes or patterns by well-defined rules. We can even create abstract objects that accurately describe physical phenomena, all by using abstractions that originate in the mind. In a similar fashion, we can create musical objects and patterns in our musical space that correspond to triggered thoughts of physical reality or even emotions which elicit physical reactions in our bodies. In this sense the musical space and physical reality are interconnected by means of the mind, in the same way mathematical spaces are attached to physical realities.

This analogy is important, in my opinion, because much in the same way we can predict physical phenomena through mathematical reasoning, we should be able to chart new territory in a musical space that is capable of manipulating thoughts and emotions in new ways. I also think that perhaps the collective consciousness of a group of improvising performers is due to exploring the same local regions of musical space and perhaps even traveling together through the space, which establishes a connection between two or more different conscious minds.