ego cogito, ergo sum
[Descartes]
The statement I think, therefore I am has become a sort of philosophical ground truth. In fact, neural systems show that this is backwards. More appropriate would be I am represented, therefore I am. All that we are is a system that takes numerical input from sensors and produces numerical motor output. The largest and most important part of that system consists of representing the external environment. Parts of that system are so important and complex that large areas of the brain are dedicated to the various stages of processing necessary. The most important part of this is visual processing. What the visual system in particular shows is that most sensor information is integrated into a representational space. The external environment is represented in a simplified and systematic way, the most important element of which is object-based representation. Much of the literature on perception assumes that the world of perception accurately reflects the physical environment; that the external environment somehow imprints itself onto perception. This is a mistaken assumption which gives rise to fundamentally mistaken thinking when perception turns inward to represent itself. A great deal of attention is given in the literature to these types of objects of perception, whereas very little attention is given to the internal mechanics of how perception must function. The mistaken assumption that the world of perception reflects the real world leads to a disregard to how perception is produced from the information produced by the sensors. It is often assumed this step is trivial, whereas careful reasoning about how the objects of perception must be produced is the key to understanding the nature of what we think we are.
The assumption that the external environment imprints itself onto the senses has a long tradition and seems an intuitive ground truth. It requires that the information produced by the sensors is rich in information about the physical environment. In fact the opposite is true. The information produced by the sensors is in fact very limited. It is only by attempting to build perceptual systems ourselves that it becomes clear exactly how difficult the problem is and which direction any perceptual system must follow. What is immediately clear is that trying to recognize objects in the external environment or relying on oracles to detect objects is a hopeless approach. An oracle may detect an object, but that is not helpful in representing an object – no matter how simple. This becomes evident when considering simplifed perception. One of the most simple perceptual systems would be a two-dimensional system which is capable of representing only triangles. It is immediately apparent from this simplified geometry that an oracle would be useless when considering how such a simplified visual system would work. Even for the most simple geometry which allows for only line segments that must form part of a triangle (the object of perception) leads to intractible complexity such as implicit triangles, triangles which consist of other triangles and triangles obscured by other triangles.
For even the most simple of possible geometries, it is evident that a perceptual system must first rigorously define the representational space. A perceptual system does not draw bounding boxes in the sensor data and it cannot rely on oracles that amount essentially to little more than bug detection. The output of the simplest of possible perceptual system should be the parameters necessary to represent the underlying geometry. Fortunately a great deal of work has already been done on systems which support simplified geometries. This demonstrates that a formal geometry is an essential part of any possible perceptual system. The output of the perceptual system is necessarily in terms of the implicit geometry. A formal geometry and a sparse
The difference between this systematic way of representing the external environment is readily apparent when comparing olfaction (the sense of smell) with other more integrated senses such as vision or audition. Olfaction is equivalent to a chemical analysis, but the perception of smell is not integrated into the perceptual construct of the external environment. Audition and vision on the other hand are linked to such a degree that dogs may be seen to bark, pianos play and people appear to talk. Indeed, when watching a movie a non-technical viewer might have some difficulty understanding that the system that produces sound and the system which reproduces images are very different and unrelated systems. A movie without sound would be greatly disruptive to the viewer, whereas a viewer would rarely, if ever, notice the lack of smell. Olfaction may therefore be seen as a sense that has remained more or less unchanged from the distant evolutionary past. In the very distant past our amphibian ancestor may have used vision, audition and olfaction to guide its tongue toward its food source, but without having any genuine representation of the external world. It would be a simple creature similar to that represented in Figure XXX. It does not live in a perceptual world where the external environment is reprented abstractly, but is merely a set of pre-programmed responses which are triggered by certain stimuli. A feeding response, for example, might be triggered by movement, and all three senses would simply provide input to calculating directionality to the target. That target might be the next meal, but it also might be something quite inapropriate like a finger or it might even be a trap laid by a predator – the amphibian cannot know the difference. As our ancestors became more complex they began to represent the external world to help them distinguish prey from predator and also to solve a multitude of other problems posed by the need to survive. In a complex environment this is best achieved by a general system which integrates sensor input into a general perceptual representation. This integration was achieved with the visual sensors and auditory sensors, but the chemical sensors remained more or less as they were, providing cues to whether something is edible or not or driving a behaviour tendency (such as a feeding frenzy) but without being integrated in general perception.
Representing the external environment has in modern humans become so sophisticated that it is often indistinguishable from the external environment itself. In fact there are various strands of philosophy which entertain the view that the perceptual environment is real or that it might be illusion. This is a sterile debate, because perception can both accurately represent the external environment but yet be a purely internal representation. Perception is both illusion and reality. Perception is inherently an illusion; reality cannot of course be created by representation. But at the same time it is representation of the external environment. Despite the credibility of the representation produced by the visual system, a careful study of the physical external environment demonstrates that it is fundamentally very different from how our perceptual system presents it to be. It is clear from the physics of the very small that the underlying physics of our environment is fundamentally very different from our object-based perception. Important aspect of visual perception, such as colour, demonstrate conclusively that perception consists of elements which are inconsistent with the physical environment. The perceptual representation of the external environment has at the beginning of the processing chain the numerical input of the sensors, and these numbers are measurements of certain properties of the external environment. A visual system cannot know the external environment as it is, merely how it is presupposed it might be. In the same way chemist has no means to see atoms and molecules directly, but rather has available only the a variety of empirical measurements that provide fleeting and inconsistent clues about the nature of the building blocks of the environment. Atoms and molecules are therefore not things in themselves, but are a product of a general theory of matter which it is hypothesised accurately reflects the physical environment. In the same way that a chemist who begins with simple observations and measurements of the external world and from these hypothesises the structure of matter, the visual systems of complex organisms must have developed in a similar fashion. In the same way that a chemist might produce visualization tools that turn the raw data of empirical measurements into a useful representation, so too a visual system populates the perceptual world on the basis of raw sensor data. The crucial aspect of this is that the perceptual world and the perceptual objects that exist within it are arbitrary constructs of a specific approach which is chosen to interpret the raw data. There may be a wide variety of ways to consistently interpret the sensor data, and any practical system (or any practical theory) must make a design choice. Our visual system is a product of hundreds of millions of years of evolution, and it reflects the design choices made along the way. Perception is representation, and the system of representation is a construct of the visual system to make sense of the vast flow of sensor data. That construct has been shaped by evolution and as a result it is consistent with the needs of the organism to navigate the external environment, but it is something which represents the physical environment, it cannot be the environment.
An atomic theory of matter is also a theoretical construct, which however useful is know to be a simplification of the actual physical environment (with the sub-atomic quantum nature of matter being inherently much more complex). A theoretical construct is a product of a hypothesis, which is a type of invention. A formal system capable of invention is induction. Induction can be used to It is produced by a system of induction rather than a system which veridically translates the external environment as it really is into perception. This belief that perception represents the external environment as it really is may be seen almost universally in the literature, and it is the root cause for much of the mistaken thinking about ourselves; specifically the mind-brain problem.
What can be created, on the other hand, at very little cost with respect to the ground truth of the external environment is a representation of self. The simplest self-representation is simply representing the physical, mechanical self – the parts of the self that are revealed by the sensors.
One entertaining strand of philosophical thinking is the brain in a vat thought experiment [Hofstadter]. This is implausible because the sensors and the motor outputs are in extensions of the brain. This is particularly so with vision, and this is the reason that the disembodied brain is often pictured with the eyes attached. The purpose of a brain is to take the input from the sensors and to produce motor output. Indeed the brain of the simplest possible organism consists just of sensor neurons which drive the motor neurons directly. The disembodied brain of such an organism would not be very useful. It would be somewhat more plausible to imagine entire nervous systems in a vat, where an input for each sensor is provided and the output of each motor neuron is measured.
While some animals live lonely isolated lives, only rarely interacting with other members of their species, many animals are social. While it may be helpful for a predator to model the internal states of its prey, for a complex social animal this can readily become of vital importance. A social animal will succeed only if it is able to effectively model other members of its social group. Where can we find evidence of this modelling? In fact we see this every night in our dreams, although these dreams are usually forgotten once we wake up. But from the dreams we can from time to time remember, it is clear that they are populated with characters we find important in real life. These characters tend to act and speak as their real-life counterparts. In real life these models help us predict what other individuals in our social environment would do or say, they allow writers to speak on behalf of their characters and they make possible for us to know what other people are thinking. This model may be seen as a kind of animating spirit which drives the characters. It is easy for us to think this because we produce working models for those characters that animate our dreams or our stories. We can call this unseen agent which animates the individuals in our social group a mind. If we are able to represent the minds of others, it is then a simple (and indeed necessary) step to represent our own mind. We represent not only our own body as it is presented to us by the sensors, but we place the representation of our own mind into the representation of our environment. Once we are represented in the perceptual world we can begin to look at ourselves. We can look at our physical structure by for example looking into a mirror, and we can also turn our gaze inwards in an attempt to look at our mind. What we see is representation of our own self and thereby we become aware of ourselves – we become self-aware, conscious of our own self.
Equation example with MathJax: When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are
\[x = {-b \pm \sqrt{b^2-4ac} \over 2a}\]
And as MathML: