Quick Definition
Mathematics
A formal constraint (what I consider to be analogous with Hofstadter'sGödel, Escher, Bach- An Eternal Golden Braid
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Read the Wikipedia article on GEB.
Background
I first encountered this book by Douglas Hofstadter in high school and became enraptured. The concepts from Gödel, Escher, Bach that have most influenced my thinking and artistic practice are summarized in the notes to "Creativity and Constraint: Queering the Formal System."
Gödel, Escher, Bach (also abbreviated as GEB) usually proves too difficult for me to adequately summarize in conversation; I'll try to be... "rule of production" or "rule of inference") is a method for transforming one result of a formal system into another result. In mathematics, we can use mathematical induction to derive a theorem from an axiom or from another theorem. Because we trust that our rules of induction will preserve the truth of our mathematical statements, following the rules of inference from axiom to theorem to theorem and so on helps us to build a logically consistentGödel, Escher, Bach- An Eternal Golden Braid
Purchase a copy on IndieBound.
Read the Wikipedia article on GEB.
Background
I first encountered this book by Douglas Hofstadter in high school and became enraptured. The concepts from Gödel, Escher, Bach that have most influenced my thinking and artistic practice are summarized in the notes to "Creativity and Constraint: Queering the Formal System."
Gödel, Escher, Bach (also abbreviated as GEB) usually proves too difficult for me to adequately summarize in conversation; I'll try to be... framework of ideas.
Music
In music, we might use a variation technique to derive a new development of a musical idea from an earlier one. In this case we likely don't think of our initial material and its developed variations as being "true"Axiom
Quick Definition
An axiom is a logical presupposition that cannot be proven to be true – instead, we take it on faith that it is true.
Use in Mathematics
In mathematics, subjects like Geometry rely on a set of axioms that mathematicians "take on faith" in order to begin using mathematical induction to draw conclusions and develop more advanced theorems. Changing these axioms can lead to dramatically different results – for example, you can obtain spherical geometry and hyperbolic geometry ..., however we will likely find that the use of a variation technique to derive one musical idea from another will give the whole work a sense of unity, consistency, organicismOrganicism
The concept of organicism is wily and potentially problematic – it has a history of being a useful aesthetic descriptor, but it can also be attached to a variety of oppressive ideologies. The most salient discussions for my thinking have surrounded organicism in music.
Heinrich Schenker devised influential theories for describing and analyzing works of Western classical music from the "common practice period."[[This time period is from roughly 1650 to 1900.::rsn-transclude]] These theories w..., or meaning that might be lacking otherwise. In this sense, the piece of music will posses a certain "inner logic" that governs how the work develops and progresses. I find this to be somewhat similar to the way that a more rigorous mathematical formal system preserves the truth value of its subsequent statements through mathematical induction.
Exclusivity
The use of constraint techniques necessitates the exclusion of some potential options or outcomes. This is a good and desirable result and is in fact the purpose of a formal system. For Gödel, this meant that some propositions in a formal system might not be permitted because they are inconsistent with other propositions that have already been derived. For Bach, this meant that some technical or stylistic choices would not be available when completing a canon or fugue.
The danger for this view can come in prematurely foreclosing the role of creativity. When we see a constraint and impose a false binary where none exists, we have cut ourselves off from a wide range of possible outcomes or solutions that truly do match our constraints but might otherwise seem impossible or extraordinary.
Discussion – Margo Jefferson and Ari Shapiro
The following interview with Margo Jefferson about her book, Constructing a Nervous System includes a brilliant description of creative constraint. Listen starting at about 4:15 for Jefferson's reading of an excerpt from her book: "A writer works with what she lacks…"
Just for fun: if you're interested in some of the variation techniques that composers use, take a look at this list from Larry Solomon. Related Note: Disambiguation – Constraint vs. OppressionDisambiguation – Constraint vs. Oppression
FREE FROM CONSTRAINT (Sonnet)
Anthony Etherin
I tried to start
again, and shed
the binding thread
that ruled my art.
I let my heart...
Resources
Last modified on 01-28-2022.