My solution to a nagging problem in Mathematics

I became intrigued by the variety of ways to establish a coordinate system for representing solid geometry in numeric terms.

https://en.wikipedia.org/wiki/Cartesian_coordinate_system

I remember, as a young person, being amazed at the difficulty of transitioning from plane to solid geometry.  Being comfortable with x-y graphs, I felt that it would be easy to add a z axis and be done with it.  I soon found that confusion prevailed.  Teachers at the blackboard oriented the axes so that y was up and z came out into the room.  My intuitive choice was to have z going up out of the paper at my desk.  I found agreement with my system when describing ‘ground vehicles’, where x is to the front and z is up.  But when working with aircraft I found that x was the same as for ground vehicles but that z pointed down.  And for water vehicles, where z is meaningless (except for submarines), the aircraft convention was adopted.  Space is a different story all together, where up is not defined.

https://en.wikipedia.org/wiki/Aircraft_principal_axes

https://en.wikipedia.org/wiki/Axes_conventions

Mathematics does not settle the confusion, when it accepts any orientation as equivalent, as long as the ‘right hand rule’ convention is followed.

https://en.wikipedia.org/wiki/Right-hand_rule

Most people could care less.  With the introduction of 3d printers and design tools readily available, more people are confused.  Which way is ‘up’?  One of my favorite books from childhood was ‘Flatland’ by Edwin Abbott where a character struggled with the suggestion of ‘up without north’ and concluded that the concept was silly.

https://en.wikipedia.org/wiki/Flatland

I have concluded that this confusion is silly in a system so important, for describing the world we live in.  The solution I chose was to relate the axes to the only meaningful perspective – the individual’s senses.  The x axis points in the direction of visual interest and mobility preference.  X points ahead to the front.  Z is another intuitive sense and must be pointing up.  This requires that Y must be pointing to the Left; to follow the right hand rule and the mathematical definition of orthogonal axes.  We are after all, a ground vehicle.

So to aid in remembering this system, and it’s associated conventions for roll, pitch and yaw; I  have created a structure using my hero Albert Einstein as the model. 

https://en.wikipedia.org/wiki/Albert_Einstein

The x-axis comes out of his head in the region of the eyes, providing for the ROLLing of eyes.

The z-axis comes out of the top of his head, providing for the YAWing of disagreement.  And the y-axis comes out of the left side of his head, providing for the PITCHing of agreement.

I decided to further enhance my Albert Einstein model by allowing us to view into his thoughts; by not completing the construction of the top of his head.  Looking into his head we get a glimpse of his thought processes. We find 4 major areas of concentrated innovations.

Area 1 relates to the ‘Photoelectric Effect’ and is represented by a matrix of similar objects.

I’ll leave it to you, to relate Quantum to the observed impact of light dislodging an electron only if the frequency is appropriate.  He showed that the intensity and duration of the light had no effect upon releasing electrons; only the frequency.  Concluding from that an idea of discrete levels and units.  And that light can influence matter.

https://en.wikipedia.org/wiki/Photoelectric_effect

Area 2 relates to ‘Browning Motion’ and is represented by a rotated normal distribution curve, compared to the Apollo spaceship.  I’ll leave it to you, to relate Statistics to the observed motion of a pollen seed being moved randomly about by impacts with water molecules.

https://en.wikipedia.org/wiki/Brownian_motion

Area 3 relates to the relationship between Time and Space and is represented by the light cones of past and future interacting with the present space plane.  I’ll leave it to you, how the ‘special theory of relativity’ can unify time and space.

https://en.wikipedia.org/wiki/Special_relativity

Area 4 relates to the relationship between Mass and Energy and is represented by the famous equation that almost everyone knows.  I’ll leave it to you, to ponder the enormous amount of energy released by the conversion of even a tiny amount of mass.  Take one of the largest numbers you can think of, the speed of light (very fast), multiply it by itself, then multiply that by the mass converted and you get a really humungous number for the energy released.  So much so, that over many decades of failed attempts to contain it, we still struggle with controlling it.

https://en.wikipedia.org/wiki/Mass–energy_equivalence

My completed model includes an idea of the frustration of living in the shadow of greatness.  We see a smaller pale imitation of the colorful Einstein model standing off to the side, admiring with awe the accomplishments of a hero. 

Yet we know that the effort to assign numbers to physical objects will continue to broaden our understanding and appreciation of nature.

Click on the image to the right for a video of my model.