By Grant Ocean

To
begin with, let’s get familiarized with a ubiquitous law in the universe,
called the inverse-square law, which governs the behaviors of gravitation,
electrostatics, acoustics, light and other electromagnetic radiations. The
perceived size equation which this paper introduces has been derived from this
universal law.

The
inverse-square law commonly applies when certain energy, force, and some
conserved quantity are evenly radiated outward from a point source in
three-dimensional space. Given that the surface area of a sphere (which is *4πr ^{2}* in mathematical terms)
is proportional to the square of the radius

or

Now we can derive a perceived size
equation from the equation above. The total size of an object (*S*) corresponds to *P*, which can be thought of as the total photons reflecting off the
object. The perceived size (*P _{s}*)
of the object corresponds to

However,
the perceived size of an object is always measured by an active observer. The
point where one places the ruler to measure the object will affect the
perception of the object’s size. Therefore, we need to add a term, the
measure-point (*M _{p})* to the
equation to resemble how the perceived size of an object is actually measured
and materialized in the human situation. The measure-point is where the ruler
is placed away from the eye (or the nodal point to be precise), so that

We can see that the
perceived size (*P _{s}*) is
determined by the measure-point (

To
link our perception with a universal law is a new approach to how our mind
functions. Our brain or mind is envisioned to behave like all the other
entities in the world to obey the universal laws. Instead of treating the size
perception as the geometrical relationship between objects and our eyes, the
new approach envisages the objects’ sizes we perceive as being equivalent to
various magnitudes of energy intensity following the inverse-square law. This
approach might sound far-fetched according to our conventional viewpoint. But, its
validity and appropriateness should be judged by the actual experiments, in
particular by how well the perceived size equation can explain and predict the
mirror images.

The
object’s size (*S*) is the total area
of an object in two dimensions, i.e., vertical and horizontal dimensions. If
both dimensions of an object are doubled, the total area of the object will
increase by fourfold. When the vertical and horizontal dimensions of the object
are tripled, the total area of the object grows by nine times. As a result, the
object’s size increases in the same proportion as the square of distance, i.e., .
If only one dimension of the object is concerned, i.e., the linear size of the
object such as its height, the object’s height (*H*) changes in the same proportion as the distance (*d*), i.e., *. Thus, the perceived
size equation can be simplified as*

It is very simple for you to
verify the above equation. All you need are a measuring tape and a transparent
ruler. Place the measuring tape alongside the edge of a table and set the zero
point at one end of the table. Secure one eye of yours at this end with a chin
spporter and above the zero point of the tape, blind-folding the other eye. Now
find an object (e.g., a book), measure its height (*H*), and put it at certain distance (*d*). Set the ruler at a distance (*M _{p}*)
close to the eye and measure the height of the book. This measurement is the
value of