Agility as the fundamental concept of classical mechanics
In this paper, we introduce a mathematical formalism that demonstrates how concepts are implemented in physical theories, with a focus on the agility concept. We define a concept manifestation as a process, in which a concept is assigned to an object (e.g., a body or a particle). In the implementation stage, a physical theory is spanned, and we demonstrate how the implementation of the concept of agility generates the rules of classical mechanics and, in some aspects, general relativity. Using this approach, we show that both expressions for momentum— <mml:math display="inline"> <mml:mover accent="true"> <mml:mi>p</mml:mi> <mml:mo></mml:mo> </mml:mover> <mml:mo>=</mml:mo> <mml:mi>m</mml:mi> <mml:mover accent="true"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mo></mml:mo> </mml:mover> </mml:mrow> <mml:mo></mml:mo> </mml:mover> </mml:math> and <mml:math display="inline"> <mml:mover accent="true"> <mml:mi>p</mml:mi> <mml:mo></mml:mo> </mml:mover> <mml:mo>=</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="italic"></mml:mi> <mml:mo>/</mml:mo> <mml:mi>λ</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mover accent="true"> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mo></mml:mo> </mml:mover> </mml:math> —originate from the same source-time derivative of an agility operator. We conclude that physical laws that can serve as representative concepts may be useful in artificial intelligence systems.