The mechanical outlook on the natural world is the foundation of physics and influential to all sciences. The stuff of the world grow, shrink, move around, and the quest to understand these kinematics motivated the concept of mass, the quantification of matter, the extra dimension beyond those of space and time. From different combinations of matter, space and time, many offspring emerged: force, momentum, energy, power, action, stiffness, pressure, viscosity, etc. These standard mechanical quantities can be in turn pushing or pulling, impelling or impeding motion. 

In this series on mechanics, we will see how kinematics can be understood from the interplay of the dimensions of underlying mechanical quantities: 

• From pairs of mechanical quantities emerge length scales, time scales, and more generally scaling laws governing dynamics from the quantum realm to the astronomical arena. 

• From trios of mechanical quantities can emerge special events, turning points of the dynamics, which can be used as units of space and time, more objective than the traditional standards like meters and seconds. These units are based solely on the phenomena at play, not on the viewpoint of any bystander. 

• From combinations of four mechanical quantities emerge domains with six possible topological structures. These domains are associated with dimensionless numbers, nature's numbers, which provide mechanical numbering systems beyond base 10. 

This general series on mechanics showcases the breadth of dimensional analysis, its ability to capture the mechanisms at play behind motion, but also its invitation to remove ourselves from the description of the world. Our seconds, meters and even the 10 digits we use for counting obscure the scale invariant similarities of the universe. Nature can express herself in her own units, with her own numbers. 

This series provide the general framework behind the notions introduced in topical series like the one focused on explosions. We generalize the notions of kinematic and mechanical quantities, of regime, of system of units, of index and radix. And we also talk about a few topics at the frontier of this standard framework. This series presents mechanics from a kinematic perspective, were motion is measured and the mass-carrying quantities are constant parameters working behind the scene. L and T are the apparent dimensions and M is the extra dimension. Other approaches are possible and will be the subject of their own series.

For a summary of episodes 1-8 check out our recent preprint.