# Footnote: Angle of View

Simple motion can seem complicated and difficult to resolve when viewed from an awkward angle. Unfortunately, it is not always possible to change one's viewing position in order to find a more amenable direction from which to view it. Understanding its motion consequently takes more effort.

If I observe a planet, it appears to move in a very complicated way. It proceeds along a smooth orbit for a long time. Then suddenly it decides to back-track for a short while before continuing along its original smooth orbit. That is how I perceive its motion when observing from where I am on the surface of the Earth. However, if I transform my point of view to that of a hypothetical observer on the sun, the planet's orbit becomes beautifully simple. It is an almost circular ellipse.

The complication comes from the awkward viewing position on the Earth to which I am physically bound. My perceived view is of a planet, moving in a simple elliptical orbit, as seen from another planet (the Earth) moving at a different speed in a dif­ferent elliptical orbit. This perceived view is indeed very awkward and complicated. Yet the reality of the planets' orbits is comparatively simple.

### Awkward Complexity

If I can "look down" on a planet making a circular orbit, its motion appears very simple. It is moving in a circle at a constant speed. Its speed (in metres per second) is given by multiplying two real numbers: ω and R, where ω is the anglar velocity of the planet around the centre of its orbit (in radians per second) and R is the radius of its orbit in metres. Notwithstanding, a simple circular or­bit appears very complicated when observed from an awkward point of view. If I can only view the planet's or­bit edge-on, the planet seems to be moving in a very pe­culiar way. In the absence of the necessary back­ground knowledge, this motion makes no sense.

The planet appears to be accelerating backwards and forwards in a straight line, speeding up as it crosses the central part of its journey and slowing down before turn­ing back again at either end. Its speed at any time is given by the formula shown on the left. R is half the len­gth of the planet's path in metres. π is the ratio be­tween the circumferance and diameter of the planet's orbit. t is the time elapsed since the planet last passed the centre point of its track while travelling in the left-to-right direction. P is the total time of its cycle of movement, starting from when it passes the centre point of its track in the direction left-to-right until it does this again.

To most people who have studied school level mathematics, the cosine function (cos in the above formula) is very familiar. It is nonetheless the sum of an infinite series of terms, which is a cumbersome piece of ar­ithmetical paraphernalia. Each of the terms of this infinite series contains the constant π, which is itself the sum of an infinite series of terms. The total complexity of the whole calculation is therefore horrendous.

Some mathematicians think things like these infinite series are beautiful. I think they are ugly and complicated compared with the simple multiplication that ex­plains the motion of the planet when it is possible to look downwards on its circular orbit.

Grasping the maths is unimportant here. I am just using it to illustrate the follow­ing. Because I am constrained (by space, time and sensual limitation) to view my universe from an awkward angle, it appears to me to be unnecessarily complicated.

On the other hand, I have, within my conscious self, the strong intuitive feeling that reality has a beautiful simplicity. I sense that all could be described by a simple uni­fied equation that I could easily understand, if only my conscious perception were not hampered by the physical constrains of time, space and restrictive senses.

But my conscious perception is hampered by the physical constrains that time, space and restrictive senses unavoidably impose on upon me. This is one of many factors that forcibly complicates my view of human society, the world and the uni­verse beyond. It makes my quest to understand what I see more difficult and more prone to error.

© June 2005, Sept-Nov 2014, Jan-Apr 2017 Robert John Morton
Parent Document