I am fascinated with unifying theories such as the periodic table (Mendeleev's) and the Copernican view of planets orbiting the sun. The previous, Earth-centric model had more deviations than predictive power. The periodic table is also an example of a structure with tremendous predictive power.
I think it's also interesting to distinguish between systems that reveal intrinsic order (e.g. periodic table), and systems that superimpose external order (e.g. a performance review framework).
Behavioural economics is an example of a field that desperately needs a modern-day equivalent of Mendeleev to come around and structure.
I am craving more examples of this, please, anyone, share!
I can't find it now but I recently read of one or two guys who systematically tabulated juggling tricks. Gaps in the table led to new tricks which astonished experienced jugglers -- the way gaps in the periodic table led Mendeleev to predict properties of undiscovered elements. One guy gives talks on juggling at math conferences and on math at juggling conferences.
Newton’s theory of gravitation unified the motion of apples falling from a tree, cannonballs thrown into walls, the motion of planet earth around the sun, and even motion of all the known planetary bodies.
Electromagnetic waves gives us one understanding of X-rays, gamma radiation, visible light, infrared, radio waves, etc.
Quantum field theory unifies every microscopic theory of matter and energy we have ever known.
Here's an eclectic mix of examples from various perspectives across multiple domains. Understanding the representation of knowledge and the fundamental structure that underpins the connective essence of things is one of the prime ideas that drives my thinking, and as a consequence much of what I post about on here is related to that in some way. Below is a brief sampling of examples related to this idea, and for a more extensive list, browse through my postings (and if you can see how they all connect, let me know!).
In general, see the Classification of Finite Simple Groups [0]. In terms of specific examples, the minimal classifications of knots [1], trees [2], and braids [3] are 3 instances that popped to mind. From a number-theoretic perspective, the paper Enumerating the Rationals and its derivative works are interesting reads. In terms of spatial structure and spatial decomposition, look at the classification of crystal structures [4], lattices, polytopes (zonotopes are particularly interesting), periodic and aperiodic tilings, the classification of space-filling curves, and the classification of closed surfaces [5]. From a relational perspective, look at the classification of topological spatial relations [6] and Allen's interval algebra [7]. And the one my intuition finds most intriguing is the classification of Group Theory Single Axioms and its relation to my conjecture that division is primary.
P.S. Clifford Algebra / Geometric Algebra [00] unifies much of mathematics, e.g. in GA, Maxwell's equations can be reduced to one equation and expressed on one line [01]:
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I think it's also interesting to distinguish between systems that reveal intrinsic order (e.g. periodic table), and systems that superimpose external order (e.g. a performance review framework).
Behavioural economics is an example of a field that desperately needs a modern-day equivalent of Mendeleev to come around and structure.
I am craving more examples of this, please, anyone, share!