Homo Sapiens Sapiens, however, is a creature wrought by merciless Nature to fulfil a task, and that task alone: to survive in the Savannah. That the skills evolved for outwitting various predators and prey are any use for anything but hunting/gathering is one of the most fascinating and incomprehensible quirks of natural selection. And sometimes, our "information processing systems", designed with lion-detection in mind, are fooled. Who hasn’t seen the optical illusion of the "Penrose Triangle", and, more importantly, who hasn’t been fooled by it? We can see the "triangle", but, until we look at it, its impossibility fails to register. Once we become aware that it "is weird", the source of the weirdness is immediately apparent, but, in passing, our subconscious fails to notice anything special. This is because understanding the Penrose Triangle requires a holistic judgement, only when we consider the "big picture" does it become evident that the shape is not self-consistent when considered as a whole. Each individual corner, however, taken as a self-contained unit, makes perfect sense.
This simple optical illusion is one of many that demonstrate just how fallible our interpretation of the surrounding world is. It is indeed an example of our model, our metaphor, our map, leading us astray. If we don’t look closely at the errant frame, we will not notice that we’re off track, and the implications of such a statement are truly horrific: how many things do we fail to notice, with what certainty can we ascertain that what we in passing perceive as being self-consistent is indeed so? How much of our knowledge contradicts itself? We, or our visual system at least, seem to be worryingly pragmatic in our perception of the world. Reassuringly, Science, based upon a rigorous foundation, is immune to such obscenities. Or isn’t it?
Science is a tool. A powerful tool to map the world around us, based upon the scientific principles of coherence, correspondence and reproducibility. But a mere tool nonetheless, it does nothing by itself, someone has to wield it. Let us consider, for example, physics. It is hard to argue against it’s universal significance: whatever process our eyes fall upon, Physics has something to say about it. An idea laboriously constructed over the past three hundred years, observation upon observation, all cemented together by rigorous logic. A (reasonably) coherent whole. Reassuring, objective, monolithic, eternal: theories may be written and disproved, measurements taken and discarded, but Physics will remain, always.
And yet, Physics too is nothing but a particularly successful model, a collection of Russian dolls, approximation within approximation, each successive level of mathematical complexity accounting for glitches in the previous theories; first Newton, then Einstein, then, well, who knows? Quantum gravity?
How much of this vast bundle of knowledge is nothing but an artefact of its formulation, how much of it is a product of the underlying language -mathematics- in which it happens to be written? Mathematics is very much the metaphor of physics, physics depends upon maths. But they are not the same thing, in the same way that, although Shakespeare’s Romeo & Juliet is written in English, it is not "English" itself. It has been said that "[The greatest misconception about black holes is] that they actually exist [...] the black holes that [...] physicists study are only approximations [...] of these collapsed stars. In the strictest sense of the word, there are no black holes." Ideal black holes, whether their real counterparts exist or not, arise from, quite simply, divisions by zero.
Thus we are presented with a model of extreme conditions, the basic "ingredients" of which come from far less "extreme" conditions. Is it possible that just as the corners of the Penrose Triangle "disagree with each other", bits of physics might also not fit together well? Can our map be distorting the picture? Just as the case of religion and science. Clash; who are we to believe? The theory of the immensely big or that of the unimaginably small? Does this single contradiction invalidate all their predictions? Again our map has led us astray, again conflicting counter-claims to knowledge spoil our fun.
Even mathematics itself, it turns out, suffers such maladies, although of a subtly different kind: not incoherence, but rather incompleteness. It is impossible for us to "map" every corner of a mathematical system from within that system itself, sometimes one must "refer out" of the system itself, just as if we needed aerial photographs to accurately map a
It seems obvious that there cannot be knowledge without symbols to represent that knowledge; thus all knowledge must be presented as some kind of metaphor. What escapes our feeble minds all too often is that all symbols for representing information necessarily alter (or distort) that information. To further the simile, it is impossible to "roll out" the Earth’s curved surface onto a flat map without warping it somehow.
This is the only way we can manage information; all that we know is the result of a laborious process of collection, collation and simplification. Paradoxically, it is this very process that allows us to understand the world that surrounds us, to impose a semblance of order upon all those random nervous impulses delivered to our cortex. Maps, it seems, are truly ubiquitous.
The danger, however, is that we let ourselves be led astray by our imperfect understanding of the world, that we seek Truth in the metaphor and not where it truly lies, in Reality. Is it not possible that at least some of our purported knowledge of the world amounts to nothing but mere features of the model used to describe reality?
This is the very essence of correspondence: if our model diverges from reality (or, more pragmatically, if it diverges significantly from reality), then it’s out, it is nothing but a curious collection of ideas. This ruthless housekeeping is essential if our maps are to be as accurate as possible, it is vital that we discard any inaccurate view of the world as soon as it fails to agree with what we see. Otherwise we risk confusing reality and our models of it. One of the most famous examples of a model being wrong is the universal knowledge that the world is flat. This is wrong, it is “proven” to be wrong.
Of course, even if the model "works", this tells us nothing about the actual principles that make the model tick, the clockwork inside. "As long as it works", one can hear the pragmatists scream, "does it even matter?"
We may well know the map like the back of our hand, but of the world we know nothing. By Samantha Barber