Plato's Cave

Plato’s Cave – an allegory for all time

The allegory of Plato’s cave has a remarkable permanence in the philosophies of knowledge and of life.  In it we see a collection of prisoners who can only see the shadows of reality as projected by a fire between the truth and the shadows.  They cannot turn around seeing the object so projected.  This is what they know; this is what they see; this is what they believe.  A given prisoner is rescued from the cave and brought into the light of truth.  The prisoner is then returned to the cave to help and instruct the others on what the shadows really depict.  He is rejected by all other prisoners preferring the shadows and consequent conjectures. 

This encapsulates the Plato’s allegory, though not in complete detail.  Our intent here is to reveal or theorize on how we lift shadows to our current versions of truth.   On the physical face of things, what the shadows represent include

• ·         A reduction of spatial dimension – from three or more to two
• ·         A reduction of color – to gray
• ·         A distortion of the truth by the nonlinearity generated by the ever animated flame
• ·         A transformation – from what is to what is observed
• ·         An illusion

What we conjecture is a reconstruction of truth from this reduced image, and an interpretation of what the truth actually is, may not be possible.  It is a common mode of explanation, to lift to a higher dimension of what can be observed.  Yet there must remain aspects that can never be reconstructed.

What is important to realize is that everything in our lives is but a shadow, and therefore everything we perceive is reduced, or projected, in some way. We cannot know the reduction, can only guess.  

What is missing is what we essentially cannot observe what is, and moreover we never may be able to.  We are in the position of the mole trying to see or the fish imagining arms and legs.  And this analogy points to how we understand and explain.

Any investigation to identify the true form can be cast in this way.  The cave is symbolic; the shadows are all that can be perceived; the prisoners are us.  The conveyer of the “truth” has not been extracted from the cave but has divined a truth placed open to inspection. 

In Plato’s allegory, the prisoners choose to remain within the context of their vision.  They do not wish to see a greater truth beyond that.  In our interpretation or modification we assume the prisoners to be open-minded, to understand what they see is but an image or projections and desire to determine the truth.  They do this with cooperation.  This is the nature of modern investigations, particularly in science.  We venture into shadow space and attempt to reconstruct the true objects.    The shadows are feflective light upon the retina.  This is our world.  Optical illusions play a role, such as for the Müller-Lyer illusion which asks which line, irrespective of the arrows, is longer.  Of course, both have the same length. (See Figure 1) This illusion suggests multiple paradigms for the objective truth. There is clear dependency on the use of extraneous information, which can be difficult to filter.

 

Figure 1. The Müller-Lyer illusion

For example, your dentist views the shadows of your teeth by viewing x-ray images on film.  The high energy physicist views the traces of particles in a bubble chamber to infer from these paths the nature of the particle that made them.  This painstaking process over decades led eventually to the discovery of the Higgs-boson, the so-called god particle.  The geologist wishes to explain the substrata of the earth’s lithosphere from observable surface data.  More than a few generations passed before plate tectonics emerged as the accepted model. 

In our modifications, we make assumptions about the prisoners viewing them as members of a society seeking explanation or truth.   First, continuing the allegory we assume all they see are shadows.  We assume they work together to create the object from only the shadows.   That is, the reconstruction or truth is a cooperative effort.

• ·         The object is shown (in shadow) from every possible view available.
• ·         Each prisoner interprets each shadow.  These views are collected, and in the human way, some are preferred at the expense of others.

The natural questions include what objects can they uncover or reconstruct?  What properties, such as color, can never be recovered?  Can even the shape be reconstructed accurately?  Can motion, holes, or anomalies be detected? Can the object be uniquely determined?  In the sense of Kuhn, can a common paradigm be derived?  It is important to note that we humans prefer a single solution.   Multiple solutions lead to uncertainty and indecision, not to theory.  Multiple solutions least to impossible situations. 

The questions are valid, they are topical, and they need answers.  Noting this is a highly simplistic situation with simple geometries, the questions are difficult if not impossible.   Except in rare circumstances, none can be reliably obtained.  Color is beyond the question.  Motion is difficult.  Even the question of shape has but vague and highly restricted answers.  

This short piece has posed some serious questions of how we address the unknown and unknowable.  What are the answers we do not know, except to say we muddle through.  I guess I should give more details, but defer to a later time.