OUR KNOWLEDGE AND BELIEFS ARE LIKE A ROAD MAP WHICH HELPS US AVOID WRONG TURNS, BUT WHICH NEEDS TO B Essay, Research Paper

?OUR KNOWLEDGE AND BELIEFS ARE LIKE A ROAD MAP WHICH HELPS US AVOID

WRONG TURNS, BUT WHICH NEEDS TO BE CORRECTED WHENEVER IT IS CONTRADICTED

BY OUR EXPERIENCE OF THE WORLD? Discuss this simile from the point of

view of three of the fields you have examined during your TOK course, and of

your experience of the TOK course itself. Since the dawn of mankind, Man has striven first to understand, and later to

control, the World that surrounds him. Patterns have been noticed, connections

inferred, questions asked and answers proposed. “Why are the stars always in

the same place when the Nile floods?” That?s the way our brains work, we are

nothing less -and nothing more- than symbolic computers. We see things, we draw

conclusions, we build up simplified versions of reality, models, that we

can understand. And, more often that we?d like to admit, we get it wrong. Having

some form or the other of “failsafe” is, therefore, vital if we are to stay on

track…

The distinction between reality and model, between Truth and metaphor,

however, is all too often blurred, or ignored entirely. Often we consider

Models, mere derivations, and Reality itself, to be one and the same. ?Tis not

so: the map is not the territory! All our knowledge amounts to is a simplified,

digested, approximate, accessible bastardisation of reality. It is our

map, marking out the straight and narrow. Of the “path less trodden” it

says nothing.

From the moment we first open our eyes to the moment we breath our last, we

are immersed in a flood of sensory information; and we do more than passively

wallow in this sea of input. We (subconsciously, more often than not) select,

edit, and subtly modify the data that our senses feed us; we simply cannot deal

with it all, not in detail, at least. Thus, perception is very much an

active affair: we build our vision of the world. We spot

relationships, pick out familiar features; associate the sweet scent of roses

with the red flowers we see before us. We choose what features to draw on our

map.

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, the “Queen of Sciences”, 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 edifice 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 corpus 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? Indeed, such embarrassing situations do arise, where the

theories of relativity -gravity- and quantum theories -matter and

most other forms of energy- meet… such as at the core of a black hole. General

Relativity, a “classical” theory, predicts an infinitely dense “singularity”, or

point with zero volume. Furthermore, it predicts that this point, this

thing, is absolutely stationary (because there is no time for it to move

“through”). Unfortunately, Heisenberg?s Uncertainty Principle, one of the basic

tenants of Quantum Field Theory, states that it is impossible to know both the

position and velocity of an object accurately, as measuring one

parameter automatically interferes with the other. 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

coastline. It has been shown by G?del in his famous incompleteness

theorems, that any formal mathematical system is unable to

self-explain itself; there must exist within it theorems (”true

statements”) that cannot be proven to be true. However, one can prove such a

statement to be undecidable by referring out of the system that contains

it, and, provided that it is impossible to prove false statements, then the

undecidable statement is proven true by proxy.

Granted, this may seem a rather academic problem far removed from every-day

reality. But what, then, about numbers with an infinite number of decimal

places, those that cannot be expressed as a fraction, irrational numbers?

Could they, too, be a mere artefact of our mathematical system, a simple

counting system devised to number sheep? How can such numbers exist in a

finite universe, one where there are insufficient objects to represent them. Are

they some form of necessary evil, some little quirk not worth worrying about,

something that emerges from the model itself, and not the reality that model is

based upon?

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. 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.