Plato’s caves all the way up! — no ultimate limits to complexity?

Many have heard of the allegory of Plato’s cave, of the wonderment, or more likely bewilderment, that the tortured souls experience when they first leave the cave and see the ‘actual world’ versus the mere projected shadows they had subsisted on.

There is an interesting unstated assumption, with corollary possibility, here. 

That there is only one level of cave, that what is ‘outside’ of the cave are not the projections of an even greater cave. 

i.e. the cave dwellers, who originally took the shadows at face value, realize their true nature with the help of a new frame of reference. Yet this does not automatically confer on them the capability to competently assess this more complex environment which after all could be higher level shadows!

To make the assumption of a single cave layer, if you’ll bear with me, seems like dimensional arrogance. Assuming that what is outside Plato’s cave constitutes ‘reality’ makes about as much sense from the perspective of the fourth spatial dimension as to assume that the cave shadows constitutes ‘reality’. In both cases they are indistinguishable from, and likely are, the projections of higher dimensional ‘reality’.

This leads to the possibility of an infinite number of ever greater, dimensionally nested, caves. As there are no mathematical or logical reasons to limit how many there could be.

Which leads to a conundrum doesn’t it? 

After all we universally accept without question the existence of 2D projections from a 3D object, and mathematicians and physicists likewise for 3D projections. There shouldn’t be an arbitrary limit on this right?

The following idea is potentially so enormous that it is difficult to even put to words.

If it’s possible for the ‘outside’ to be the shadows of a greater cave, how do we know we are not projected shadows? 

Furthermore, it’s understood that a single 3D object can take on many different 2D forms on Plato’s cave wall. To infer the object from any given cave shadow can be highly misleading. 

So how do we know what objects are at all? 

In fact, given arbitrary volume and projection energy, it seems likely a sufficiently complex 3D object can produce all possible lower dimensional shadows. (As a corollary I wonder if there is, or could be, a proof for this.)

Given these heady ideas it’s comforting to note, if true, the absence of any ultimate cutoffs. 

Possibilities are truly boundless!

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