ansatz

The Crab Nebula, supernova remnant and pulsar located 6500 light years from Earth.  Photo from JPL/NASA Chandra x-Ray satellite. Credit: X-ray: NASA/CXC/ASU/J.Hester et al.; Optical: NASA/ESA/ASU/J.Hester & A.Loll; Infrared: NASA/JPL-Caltech/Univ. Minn./R.Gehrzchandra.harvard.edu

In mathematics and physics, an ansatz is a provisional approach to describe phenomena – an assumption that is later verified, often empirically.  This “onset” is the initial point of inspiration, a creative risk that allows the capacity for potential ideas to blossom by launching a sequence of equations, experiments, and events from hypothesis to conclusion.

                                                                                                                                             

Art and science often express the same phenomena from different viewpoints, initially using broad strokes, then gradually the system is tightened, simultaneously spiraling both inward and outward.  Pure mathematics can define the cardinality of different sets of numbers, actually yielding  a range of different infinities.  A number can be “very large,” as a broad-based term;  within a given construct, we can imagine a ring which defines a specific set of elements in the universe.  If everything inside the space is known, then an incremental shift is explored: add something, subtract something, etc.  What does that that collection now hold? 

As the focus becomes more narrow, the conclusions are more general:  Monet painted a series of haystacks at multiple times of the day and his narrowly focused exploration, almost scientific, enabled a general description of all haystacks, fields, light, and time.  However, unlike mathematics, art requires no well-defined proof system –  its “validation” is exemplified by the consensus of an idea, well-communicated.  Both systems are reductions of Nature to its essential origins, asking the same questions:  Will our expressions stand the test of time?  Is the introduction of a formula succeeded by its elimination?

                                                                                                                                             

The analyticpoem project is a concept map construction, made from participants who select personal affinities related to Nature by ascribing them to specific geometric dimensions.  An overlapping composition of science, art, literature, music, and philosophy will emerge from the map, resulting in both a unique synthesis for each individual and a baseline for universal ideas and intrinsic sources.

Vertices in the graph will be regarded as the representations of phenomena witnessed everyday: objects, experiences, and time.  The overall structure is organized into a hierarchy using a taxonomy of geometric dimensions to discern the common associations and boundaries among our collection of concepts and perceptions.  Thus, affinities will be grouped according to their comprehensive values for each given dimension:  0, 1, 2, 3, 4, and v+, a transcendental state.

In the process, if the contents and connections of our cognitive map were sufficiently powerful and personal, but gradually scaled to be both comprehensive and obtainable, the introspection could result in a type of transformation. The ansatz conjectures that this evolved insight is possible through the vehicle of geometry:  linear, planar, spatial, and temporal.  If we substitute subject for geometric pre-image and object for image, the transformation can include all phenomena as “signs,” the intersection of meaning and manifestation.  The map holds multiple dimensions that can speak as one voice from a similarity of impressions, effecting a true consilience.

 

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ENDNOTES

Note:  The Crab Nebula, also known as M1, is a remnant of polarized gas from a supernova, having first been observed by astronomers in 1054AD.  It is 6500 light years distant and is expanding at a rate of 1500 km/second.  At the time that it was first observed and recorded by Arabic and Chinese astronomers, it was brighter than any other object in the sky except for the moon and could be seen for two years.  The collapsed central core, a neutron star, rapidly emits regular pulses of radiation, every 33 milliseconds.

consilience:  As Edward O. Wilson describes it, “Consilience is the key to unification. I prefer this word over ‘coherence’ because its rarity has preserved its precision, whereas coherence has several possible meanings, only one of which is consilience. William Whewell, in his 1840 synthesis The Philosophy of the Inductive Sciences, was the first to speak of consilience, literally a ‘jumping together’ of knowledge by the linking of facts and fact-based theory across disciplines to create a common groundwork for explanation.”
Edward O. Wilson, “Consilience – The Unity of Knowledge.” Alfred A Knopf, New York, 1998, page 8.