A Jewel at the Heart of Quantum Physics
This is a very astounding article and discovery, quite readable. However, the intent of this essay is not the physics or math. I explore how humans come to radical and significant insights; looking at some metaphors we may use to better comprehend what we might do to enable our own insights.
The role of “geometry” (whatever “it” is) in science is intriguing. This math is well beyond visualizable geometry, but the mathematicians may have access to a brain process more fundamental to visualization. In the history of mathematical physics, there was a tumultuous centuries long transition from the geometry based mathematics, most noted in Greece, and the algebraic based mathematics that eventually replaced it. Computers are moving us through a transition to a third math mode, where calculations can be performed without access to algebraic functions – and the philosophical abandonment of algebraic functions as the holy grail for the “fundamental components of reality”.
Physical construction and measurements (using rulers, protractors, compass, and divider) and then computed areas and volumes were essential in geometry math. Geometrical proofs (from HiSchool geometry – my first intro to logic) served as the medium for deduction. They had formulas for computations in geometric math but they were simply tools for action and not mathematical entities themselves; as in algebraic math – where geometric diagrams are relegated to mere illustrations. Analogous formulas must be involved for computing quantitative volumes in an amplituhedron.
This opens the issue for new thinking on the meaning of “fundamental” and “reality” and our continuing dependence on linear logic. The mathematical representation for the data of particle physics, whether by Feynman’s diagrams or volumes in the amplituhedron multidimensional “crystal”, is far from a “theory of everything” – as it ignores life and “consciousness” and implies a reductionism to physics/math. That human minds are capable of creating means for comprehending amplituhedron and its associated contexts is a fact that can’t be ignored. This new “geometry” hasn’t “caused” space-time to become less “fundamental”. Creative mathematical play, deep in human mind/brain systems, is what today we call theoretical physics – seeking conceptual formulations to more accurately represent patterns in empirical data (more and more from computer mediated instrumentation). My “gut” informs me that these are more “curve fitting techniques” to satisfy our math/logic minds than fundamentals of an objective/external reality beyond our minds (which doesn’t imply a solipsism to “everything is self/mental”).
I won’t go into detail here, but this dove tails with my recent thinking about our needed transitions to new “reality contexts” for better comprehending ourselves and our worlds-in-collapse/transition.
The intuitive math insights referred to may be analogous to our experience of stereograms.
Nose to image, relax focus, pull back keeping focus relaxed.
We relax our viewing of very complex 2D patterns and a 3D images will slowly emerge which can be maintained and examined. It takes a procedure each time to experience the 3D pattern. I experience the feeling-of-insight when the 3D image emerges akin to what I experience when I have an insight. I speculate that the emergence of insights involves an analogous process – where data/knowledge in memory/mind rearranges and brings the insight to consciousness. These “insights” may not appear directly in consciousness, but in deeper levels which provide contexts for conscious experiences. Contextual insights are powerful in that they can be applied in many different situations. We may have “insightful experiences” associated with them. When new data accumulates in our collective mind/brains, a few persons with a unique distribution of that knowledge, personally, and a special receptivity, will first experience the insight. The experience is so moving that they are driven to share. The difficulty we have in maintaining the stereogram 3D image is analogous to difficulty we have in keeping “focus” on new insights and attempts to apply them.
Some populations will never have a sufficient subset of essential data to permit the insight – which will be absent from the contexts they apply in comprehending their experiences. Other populations may need training in “relaxing their minds” to enable the insight to emerge, even when they have a sufficient set of essential data. “Relaxing their minds” may involve disengaging from deep thought patterns constantly being reinforced in their informational milieu. Other populations may be lacking a few critical pieces of data/knowledge, where the insight may remained locked into a “tip-of-the-tongue” experience – almost emerging.