A couple of years ago, I was exploring the fastest way to make a concept into something tangible; bridging that apparent gap is always an interest of mine, and especially as of late.
Your video reminded me of an experiment I did. I was exploring analogous physical systems – how electricity has analogues to mechanics, has analogues to hydraulics, etc.
I found a patent for a “fluidic amplifier” that intrigued me. I was investigating the nature of amplification (ultimately trying to comprehend what happens in my own mind as I try to reinforce a thought as it begins to fade so that I don’t forget it) as well as something of the nature of decision-making in the mind itself).
I was able to trace it, using a simulator, convert the fluidiic emplifier from an air fed to a gravity fed system… [I think it was actually a patent for an accoustic amplifier to be used in Orthodox Jewish synagogues now that i think about it]… right on the computer and watch how it works, all within a few short minutes.
I see mathematics as an analogous form itself; yet on a more intellectual side, as long as there is a gap between axiom and proof, it will go far but it will reach a limit when it hits the realm of subjectivity-as-experienced. There is a growing trend to feel that “we are close to the answers” and that all will be explainable via an external view – things-as-objects, and heard from a scientist who is often called as expert witness in court cases give a talk where he was convinced that eventually, all will be explainable through cogsci, potentially rendering the court system as it stands obsolete.
Yet, if you notice, in most fields, they believe their silo has ‘all the answers’ and physics, which happens to work really well with math, and math very well with physics, is heading into a direction of being cut from the tethers of needing validation. My opinion is at that point, it becomes a philosophy and not strictly a science.