MAG LEV
walk on a flexible surface floating over thin air

Solution

This floor is composed of individual tiles linked only by powerful magnets.  The joins are allowed to flex and reflex as needed.  The floor surface rides a few centimeters above grade on a permanent magnetic field.  The magnetic field effectively replaces padding or other methods of making a floor soft to relieve stress and fatigue on those using it.  Unlike padding, it doesn't trap dirt or ever need replacing.  There is no high technology magic here.  It is just a very specific arrangement of common magnets that creates a strong springy integrated web structure.  Because there is empty space between the walking surface and subfloor, you can vacuum clean from above.  There are ventilation holes to allow this.  The same holes can be used as part of an updraft or downdraft system for room temperature control or to take away fumes.  The system consists of  a basic tile and two edge tiles.  The edge tiles define the space the floor surface occupies and are also what keeps the floating surface confined over the fixed floor magnets.  The defined space need not be rectangular; an irregular edge is just as easy to make.  You can also create holes within the defined space without the need for edging.  Absent tiles will not break the magnetic integrity of the array.  So the floating floor surface can wrap freely around structural columns or other possible obstructions without physical contact.  Tiles that occur under furniture legs can be made stationary and act as neutral islands within the floating floor structure.