The Mechanisms of Abstraction

I. Introduction.

We come to know about reality through our perceptions: reality impresses the senses, and perception emerges as an abstraction of that reality. Perception is itself reflected upon and analyzed through the conscious and subconscious mind. Associations between stimuli and various abstract representations get imprinted in memory. These associations get referenced and updated continuously as new stimuli occur and thoughts ruminate. How much information is in this narrative? How much understanding can be squeezed from this process of perception and reflection? What are the mechanisms of our understanding?

Abstraction depends intimately on the notion of information, and to meaningfully talk about the issues given above requires that these concepts be well-defined and thought-out. That shall be the purpose of the next two sections. Once we have a good grasp of the natures of abstraction and information, we can tackle the problem of how organisms abstract information from the external environment through the senses. After that will be a shallow description of my conception of low-level perception, followed by an explanation of how we might recursively abstract information from more generalized perceptual data sets. I will not offer a computational model of human abstraction, only a rough outline of what one might expect the mechanisms to be like.


II. What is information?

While information at one point in time may have been inadequately defined and fraught with confusion, it is now very well-defined and quantifiable thanks to Claude E. Shannon (1948), the father of Information Theory. To help explain the theory, I will start with an intuition pump or thought experiment. Suppose we have a string of events, a string of coin flips using a supposedly unbiased coin. The outcome of a single event is either a head or a tail. Statistically, as the number of events grows, we should expect the number of heads outcomes and tails outcomes to be the same. If the coin is truly unbiased, we should not be able to predict any outcome or subset of outcomes in the entire string of outcomes no matter how much we know about past outcomes. Essentially, very little can be learned from any flip of a truly unbiased coin. All we can do is estimate the bias of the coin based on the past outcomes, and this estimation should approach zero as we accumulate more and more outcomes. Such a system is said to have an information entropy [1] of one bit, i.e. it takes one bit per outcome to represent the entire string of outcomes. Since there are only two possible states for an outcome of a coin flip and only two possible states of a bit, the strings of outcomes and bits in this example are isomorphic and may as well be identical. Thus there is virtually no information content in a string of unbiased coin flips; if randomness has a coherent definition, it must surely be this, the lacking of information. Conversely, if we flip a coin that has two heads, then the outcome will always be the same, and we can predict the outcomes of all future coin flips. The information entropy in this case is zero, and we can represent an unbounded number of coin flips with zero bits: the outcome of each coin flip can be taken for granted, and thus representation is unnecessary.
[1] Information entropy is a metric that represents the lack of information in a string of data.

Information Theory characterizes the limits of abstract representation of data sets. Any arbitrary finite data set can be represented by a string of bits of at least the same dimensionality as the data set. If a data set has structure or statistical correlations between the data points, then there exists a pattern within the data that can be represented by a string of bits that is of a lower dimensionality than the data set. For instance, most electrical data sets acquired in America have a very typical and predictable time varying component with a frequency of around 60 Hz due to the Electro-Magnetic Interference (EMI) from the power grid infrastructure. This 60 Hz structure can symbolically be represented by a trigonometric function of two numbers (of arbitrary but finite precision), amplitude and frequency, regardless of the size of the data set. The data set can be reduced or compressed from N dimensions to 2 dimensions without theoretically losing any information about the 60 Hz structure. In practice, however, no simple function is able to precisely represent most real data sets, so some information is inevitably lost through data compression. The loss of information through abstraction is known as lossy data compression. It may sound bad to lose relevant information, but usually the loss is so minor in effect as to be unnoticeable in most applications. When a data set can be perfectly recovered from an abstract representation, this is known as lossless data compression, which can normally only be achieved in a digital environment.


III. What is abstraction?

I mentioned abstraction and representation a few times in the previous section, and now it's time to explain what I mean by those terms. There have been centuries-worth of debates over what exactly abstraction is. For my part, I tend to view abstraction from a Nominalist perspective, meaning that I don't privilege abstraction with its own special ontological status separate from physical reality like Plato, Descartes, or Frege. Given the potential for confusion over terms, I will offer my own definition of abstraction.

Abstraction is the process of paring down larger-dimensional data sets to smaller-dimensional data sets while preserving the information of interest. A representation or abstractum is the end result of the process of abstraction; it is a smaller-dimensional problem derived from a larger-dimensional problem. There is in general a lot of information in raw sets of data, but at any given moment only a small subset of that information is relevant for a particular end or goal. The information that is not relevant can be ignored or destroyed by reducing or compressing the dimensionality of the problem at hand. Interestingly, the smaller problem implies a set or class of larger problems through an inverse process or relation. Thus the smaller problem is a generalization of a class of larger problems that can potentially be reduced to the smaller problem. This generalization increases the power and speed of data processing, takes less memory to store, and allows decisions to be made more quickly and easily. It also enables the breaking-up of very difficult problems into much smaller and easier chunks.

It is possible to reduce the dimensionality of a problem without losing information, but in that case, the information that would normally be lost must be encoded in the process of abstraction somehow. Computer lossless compression algorithms have this feature of being able to reduce data sets without losing information due to the fact that the information is partially encoded in the algorithm itself. The compressed data might possibly be considered a generalization of a class of larger data sets, but the decompression algorithm will only ever produce one unique larger data set.

In order to have an abstractum, there must be something or set of somethings being abstracted from. Consider a specific person, such as Abraham Lincoln. What I really mean to say is "consider the referent or exemplification of the name or denotation Abraham Lincoln." The real person being referred to is a concrete object, whereas the image or idea or knowledge of the real person is an abstract object, abstractum, or representation. There is much information about the concrete Abraham Lincoln that we can abstract into more general traits. For instance, based on the definitions of the following terms, we know that he was a US President, a person, a mammal, an animal, and a living organism. Each successive term is a respectively more general trait of Abraham Lincoln, containing less and less distinctive information. If we remove all information pertaining to Abraham Lincoln, perhaps the only thing we can say is that he existed, if even that. The important thing to note is that these traits can be recursively abstracted from each other: living organism is an abstraction of animal, which is an abstraction of mammal, and so on all the way down to the concrete Abraham Lincoln. [2]
[2] On a semi-related note, doesn't it seem that cladistic phylogeny is a taxonomy of abstracta in the field of biology?


IV. Abstraction by the senses: how neurons work.

Neurons are cells within the nervous system that transmit and store information throughout the body (see Image 1 near the end of the essay for a detailed picture of a neuron). They accomplish this feat in a rather elegant and interesting way. A neuron has dendrites for the input of stimuli, a cell body or soma for the production of action potential signals to be transmitted, an axon to propagate signals along, and synapses at the end of the axon that interface with dendrites of other neurons over synaptic clefts. The neuron maintains a voltage potential difference across its membranes through the use of ion pumps/channels embedded in the cell membrane. This voltage potential changes when the dendrites of the cell are stimulated and ion channels are opened in the cell membrane. When this voltage potential is increased beyond a certain threshold, the soma or body of the neuron produces what is called an action potential, which is simply a narrow voltage spike. This spike in voltage results in a spiked electric field which induces ion channels in the membrane of the axon to open up and allow ions to flow through. As the ions flow through the ion channels in the axon, the voltage potential in that localized area spikes and induces more ion channels further down the axon to open. Thus the action potential propagates down the axon through this process of induced ion channel opening. When the action potential reaches the synapses, an amount of chemical neurotransmitter is released across the synaptic clefts which binds to and activates receptors in the post-synaptic membrane of the dendrites of other neurons. The more stimulated the first neuron is, the faster it generates action potentials to send to the next neurons. As a neuron transmits action potentials more and more over the course of its life, its synapses become better and more efficient at producing and releasing neural transmitter. This effectively reinforces the neural pathway, making a particular set of neurons more likely to fire, and is the basis for memory. (Kandel, Schwartz 2000)

There are different kinds of neurons that have different geometries and purposes within the nervous system, but they all operate by the same principles given above. Sense and perception start with the stimulation of sensory neurons by analog signals in the immediate external environment. For instance, light (in the visible spectrum) stimulates the neural photoreceptors in the eye, starting a chain reaction of neurons generating action potentials which eventually makes its way to the visual cortex in the occipital lobe of the brain for neural image processing. The first level of abstraction in the body occurs at these sensory neurons; sense is the most basic mechanism of abstraction. Analog signals from the environment get converted into essentially digital pulse-trains of action potentials. It is important to note that these action potentials don't represent anything in particular absent a context within a neural framework. In other words, the action potentials don't have any semantic meaning except to say that a particular neuron got stimulated. It is not possible to infer the external stimulus or even the type of external stimulus from an action potential. We cannot say that an action potential represents the light reflecting off of the surface of some object, for instance. We cannot even say that a set of action potentials or neural firings represents light reflecting off of some object unless we have a mechanism that can interpret this set of neural firings as such. So where is the abstraction? The conversion of analog environmental stimulus into digital neural firings is the very first level of abstraction. All we can say at this point is that some neurons fired due to some kind of external stimulus that the body sensed.

Let's look at how computers work as a comparison. Computers organize, store, and transmit information in the form of bits. Bits, like action potentials, are implemented with voltages: if a voltage at a given time and place is above a certain threshold, it is interpreted (by us, the designers) as "high" or "one", and as "low" or "zero" otherwise. The voltages are manipulated to produce predictable strings of abstract ones and zeroes that don't necessarily represent anything in particular. Computer programs, which are themselves abstract strings of ones and zeroes, provide a context and mechanism of interpretation for other abstract strings. Computers are designed to abstract electricity into binary symbols, binary symbols into algorithms, and algorithms into programs. The output or results of these programs are then communicated (which is another abstraction) out of the system to people and other devices through monitors and speakers and other kinds of media. The first level of abstraction for a computer is turning analog user inputs, such as key presses, into digital bit streams. The computer is essentially sensing the user input through its user interfaces, which are analogous to sensory organs. But none of these abstractions have any meaning absent a context and mechanism of interpretation. How could it be otherwise? A single bit has as much inherent meaning as a single action potential, that is to say no inherent meaning at all. A single bit or action potential could in principle represent anything and everything there is to represent as long as there was a mechanism to interpret it thus. What is the mechanism that abstracts and interprets information from sensory data?


V. Perceptual abstraction from sensory data.

Senses are imperfect, which is to say that they offer incomplete and imprecise reports of the external world. There is a certain maximum and minimum resolution of external phenomena that the senses can reliably detect. For instance, human eyes cannot see light or other RF (Radio Frequency) waveforms outside of the (human) visible spectrum, human ears cannot hear frequencies outside of the (human) audible spectrum, and human smell and taste cannot discern all types of molecules. These limitations are not fundamental, however, as other animals clearly respond to external stimulus undetectable by humans. Human senses are thus incomplete in their reporting of physical reality. But even the data that is reported by the senses is not always reliable. The senses in general have non-linear operating ranges where the data reported is confounded by the channel characteristics of the senses, i.e. the senses report certain ranges of stimuli differently than other ranges, thus leading to an imprecise representation of the physical phenomena. Even if the channel characteristics of the senses were perfectly linear in their operating ranges, the fact that there are only finite sensory neurons which are unevenly distributed in unknowable locations that can only digitize the external phenomena at a fairly slow rate (relative to electronic digitizers) means that the senses are severely limited in their precision. Given the limitations of the data reported by the senses, how can information be abstracted from them? And what kinds of information can be abstracted from the senses?

Once we have all of this sensory data abstracted from the external environment, what happens? What do we do with it? At the most basic level, some sensory data gets used in its raw state and never gets abstracted further. The patellar or knee-jerk reflex is a tendon reflex that controls increasing muscle tension by causing muscle relaxation before tension force becomes so great it may damage the muscle (Wikipedia). It is the result of a sensory neural stimulation traveling from the point of impact below the knee cap to the base of the spinal cord and then back to the quadriceps muscle, which flexes as a result of the neural stimulus, kicking the leg out. In this case, we have an analog external stimulus being converted to digital neural firings which travel a little bit before getting turned into an analog muscle contraction. In this very narrow context, there is no further abstraction of the sensory data. Organisms without complex nervous systems likely don't do any abstraction beyond this simple sensory abstraction, with all their actions being purely reflexive. As the complexity of the nervous system increases, there is a greater potential to abstract information from the senses, allowing the organism to reflexively react to specific patterns in the information rather than just the raw sensory data. This second level of abstraction I will define as (low-level) Perception.

Perception is the abstraction that emerges directly from the senses; it encompasses the mechanisms by which information is extracted from sensory data. This definition is a bit different from other definitions in the philosophical literature which rely on the notion of awareness, so perhaps a different term should be used to avoid confusion. Above I mentioned organisms that might reflexively react to certain patterns detected in the perceptual information abstracted from the sensory data. As a thought experiment, let's imagine that there is an organism that has a sense that reports a small change in the environment at a certain time. As time goes by, more and more neurons of the sense start reporting a change and the originally stimulated neurons start reporting ever greater changes. From this raw sensory data, the organism abstracts information and effectively perceives that there is an object approaching from the rough direction of the perpendicular gradient of the center of the stimulated neurons [3]. The perception of this kind of pattern in the sensory data triggers a reflexive response of the organism which might either be equivalent to avoiding or seeking, depending on the organism and the reports from the other senses. The organism could be said to be aware of motion in the external environment, but this awareness is not necessarily conscious or reflected upon; the organism is perhaps as aware of the environment as a similarly structured robot would be.
[3] The perpendicular of the gradient is not actually calculated by the organism, rather I imagine it sort of emerges as a property of the stimulated neurons through the mechanism of perception.

Up to now, I've claimed that there is such a thing as perception without explaining where it comes from. Quite simply, once we have data in the realm of abstraction thanks to the senses, the data can be manipulated and interpreted in the same way a finite-state machine (read: computer) would do it. In other words, once the information has passed from the realm of the concrete to the realm of the abstract, all we need is a neural network to perceive the patterns in the data and to do further abstractions. We already know we can artificially simulate biological neurons with computers, to a degree, in order to abstract complex bits of information from the environment. And we already know how to make robots with senses that can use this information in useful, natural, and interesting ways to interact with the environment. In fact, many of the techniques we use in robotics and computer science were inspired by models of how our own minds might work. So it's not a great leap to suppose that perception should naturally emerge from a collection of neurons in a network (or several networks), assuming that the networks capable of such a feet are evolutionarily viable.


VI. Thoughts on recursive abstraction and feedback.

Now we're approaching the limits of what we know and can usefully describe. Sense is a direct abstraction of physical reality, and perception is a direct abstraction of sensory data. As long as there is sufficient enough information in the perceptual data, it should be possible to recursively abstract bits and pieces of that information over many iterations. For the uninformed, recursion is the process of iteratively transforming a data set by repeatedly using the same function or process. The basic idea is this: 1) get sensory data; 2) abstract information from sensory data through the mechanism of perception; 3) abstract more information from the perceptual data; 4) recursively apply 3). In order for this process to work, there has to be a feedback mechanism to allow the output of a neural network to influence its own behavior and perhaps the behaviors of neural networks at other points in the chain of abstractions. In other words, the outputs of some neural networks must partially function as their own inputs. There are a couple of ways to accomplish this: 1) the neural network can have its output connected to its input, either directly or via other neurons; or 2) the neural network can have a built in mechanism of memory where each neuron keeps a running and exponentially decaying tally of how often it gets stimulated. Both of these mechanisms are used in brains. Not only are these mechanisms necessary for recursive abstraction, but I daresay they are sufficient as well, i.e. recursive abstraction will naturally occur given these mechanisms of neural network feedback.

Here is a just-so story of human abstraction. We acquire information about the world first through the senses. There are some reflexive reactions at this point, but we are largely unconscious of them. As the sensory information reaches specialized processing centers, the process of perception starts to occur, though still not necessarily anything we are consciously aware of. The transmission of this information through the nervous system partially gets stored in the efficiency of the synapses of the stimulated neurons. This memory combined with new external stimuli and the stimuli still ruminating in higher brain functions dynamically alters the behavior of the neural networks. New and perhaps more general abstractions emerge from the interplay of the cognitive faculties as manifest in the dynamically changing neural networks. The genesis of consciousness lies in these recursive and dynamic abstractions.


VII. Concluding remarks.

To understand how our minds work requires us to understand the ontological nature of abstraction and information, the ways in which these concepts are bound to reality. In this analysis, I have taken the Nominalist stance of supposing the abstract to have an ontology that is unified with that of the physical realm. Many have disputed this position, and many would still dispute this position today, but I fail to see a viable alternative that allows us as much expressive explanatory power. That being the case, I have lobbied that the neuron should be considered the physical interface between the concrete and the abstract, and that further simple levels of abstraction are emergent from perceptual mechanisms. From this, it is not difficult to suppose that memory and feedback lead to recursive levels of abstraction that are more complex and interesting while ironically being concerned with less and less detailed information. If there is a viable alternative to this viewpoint, it is not clear to me what it could possibly be.


A. Images.

Image 1: Anatomy of a neuron.
http://upload.wikimedia.org/wikipedia/commons/a/a9/Complete_neuron_cell_diagram_en.svg

B. Bibliography.

• D'Ambrose, Chris (2003), "Frequency Range of Human Hearing", The Physics Factbook, http://hypertextbook.com/facts/2003/ChrisDAmbrose.shtml
  

• Kandel ER, Schwartz JH, Jessell TM (2000), "Principles of Neural Science", 4th ed. McGraw-Hill, New York
  

• Mahoney, Matt (Aug. 20, 2006), "Rationale for a Large Text Compression Benchmark", http://cs.fit.edu/~mmahoney/compression/rationale.html
• Rosen, Gideon (2001), "Abstract Objects", Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/abstract-objects/
  
• Shannon, Claude E., (1948), "A Mathematical Theory of Communication", Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656.
• Stufflebeam, Robert (2008), "Neurons, Synapses, Action Potentials, and Neurotransmission", http://www.mind.ilstu.edu/curriculum/neurons_intro/neurons_intro.php
  
• Wikipedia, (2010), "Patellar Reflex", http://en.wikipedia.org/wiki/Patellar_reflex
  

Emergence and Cognition

I. What is emergence?

The study of the nature of the universe happens at several different levels. Cosmology studies the universe at the macro level, Quantum Theory studies the universe at the micro level, and in between there are various ways to look at semi-closed systems: Anthropology studies the nature of Human social interaction, Biology studies the nature of living organisms, Chemistry studies the nature of atoms and molecules, etc. At each level of inquiry there are properties of the system that are not easily relatable or reducible to other levels: the properties are purely abstract artifacts of the particular level of inquiry, and thus have little to no meaning or application at other levels. Daniel Dennett gives an excellent example:

"...a center of gravity is not an atom or a subatomic particle or any other physical item in the world. It has no mass; it has no color; it has no physical properties at all, except for spatio-temporal location. It is a fine example of what Hans Reichenbach would call an abstractum. It is a purely abstract object. It is, if you like , a theorist's fiction. It is not one of the real things in the universe in addition to the atoms. But it is a fiction that has nicely defined, well delineated and well behaved role within physics." (Dennett 1992)

The center of gravity is an emergent property of a system. One could figure-out the center of gravity of a system by adding-up the centers of gravity of all disjoint subsets of the system, which means that the center of gravity property is reducible to the sum of its parts. Reducibility implies Supervenience, thus the center of gravity property of a system also supervenes on the subsets of the system. The property is thus to be considered by some to be weakly emergent (Bedau, 1997). Dennett goes on to say that the concept of self is analogous to the concept of center of gravity, that it is a purely abstract artifact, a center of conscious narrative. It is not readily apparent, however, if and how the self is reducible to constituent parts. Does the abstract property of self even supervene on the constituent parts? In other words, do the physical properties of the brain imply the psychological properties of the mind? Dualism is founded on the assumption that the self is not reducible to and does not supervene on its parts, i.e. the mind is not equal to the brain. But in order for the mind and brain to interact, does not supervenience at least have to hold? Do not changes in brain matter lead to changes in psychological state? If the supervenience of the mind on the brain does hold in the absence of the possibility of reducing mental phenomena to physical brain phenomena, then the abstract property of the self or consciousness is said to be strongly emergent.

Given these definitions of strong and weak emergence, it is tempting to see emergence everywhere and in everything. Everything that is a metric or a property that we measure is emergent from some underlying physical basis. The properties of structure and pattern that are observed in everyday objects like chairs and toothpaste are emergent. The properties of language that we use to communicate ideas with others and ourselves are emergent. Indeed, all conceivable formalisms are emergent, for the necessary abstraction involved in forming concepts must have some sort of basis that they are abstracted from; there can not be an abstraction without there also being a thing or set of things being abstracted from. The brain is a vehicle of abstraction, and the mind is the representation of this abstraction to itself, a multilayered automorphism of abstraction. All of conscious experience is an abstraction of some underlying reality, and the trick of science and philosophy is inferring through induction and deduction the properties of this underlying reality from the emergent abstractions of our conscious experience.

II. Is there a great distinction between strong and weak emergence?

David Chalmers claims that it is vital to keep the concepts of strong and weak emergence separate; weakly emergent properties do not challenge our currently accepted physical laws, whereas strongly emergent properties do:

"Strong emergence, if it exists, can be used to reject the physicalist picture of the world as fundamentally incomplete. By contrast, weak emergence can be used to support the physicalist picture of the world, by showing how all sorts of phenomena that might seem novel and irreducible at first sight can nevertheless be grounded in underlying simple laws."

"...with the exception of consciousness, it appears that all other phenomena are weakly emergent or are derived from the strongly emergent phenomenon of consciousness." (Chalmers, 2002)

Does Chalmers mean to say that current physicalist models can account for all emergent properties except for consciousness, or does he mean that physicalist models can never even in principle account for properties of consciousness? It's telling that Chalmers claims that the only strongly emergent property that he can think of is consciousness, setting it alone on a pedestal above and beyond other emergent properties. This conception of consciousness as a strongly emergent property that is not representable with physicalist laws implies that it is as much or more fundamental than physicalist laws. Chalmers describes the property of consciousness as possibly having a downward causality, originally conceived by Donald T. Campbell:

"all processes at the lower level of a hierarchy are restrained by and act in conformity to the laws of the higher level" (Campbell, 1974)

This seems to me to be a rather confused idea. What distinguishes higher level laws from lower level laws? Don't we presume the higher level to supervene on the lower level? How else do we construct a higher-lower hierarchy? I imagine Neurology would be considered to be lower level than Psychology, so according to the theory of downward causality, the neurological processes would be constrained by and act in accordance with the psychological processes. But if psychological properties are emergent in the way described above, then we know that many different neurological configurations and processes could lead to or map to the same psychological properties: different people with different brains and different neurological configurations can nevertheless sympathize and empathize and come to the same conclusions and become aware of the same phenomenal events, and we can imagine the biological neurons being replaced with non-biological neurons without there being a change in psychology; analogous is the many different configurations of matter that could map to the same center of gravity. So in what sense is the lower level constrained by the upper level? Does this not flip the order of supervenience? In what way is this relationship causal?

Causality as originally (and unfortunately) conceived by Aristotle was meant to answer the question "why?": (1) to what purpose (final cause), (2) from what means (material cause), (3) in what order of implication (efficient cause), (4) by what intent (formal cause). Science is mainly concerned with the efficient cause, or "cause and effect": if A, then B; if there is fire, then there is smoke. We want to know what we should expect when we have 'A'. Downward causality in cognition essential claims "if there is a certain mental process, then there is a certain configuration of neural firings". More importantly, the implication is that given a certain mental process, we should be able to predict a certain configuration of neural firings. What other implication could there be? Proponents of strong emergence and its corresponding mechanism of downward causality claim that it is impossible even in principle to arrive at or predict mental processes from neural firings, so clearly the converse must be true. But the converse is clearly not true, and even if it were, then in what sense would the mental processes be emergent?

Let's go back to the supposed irreducibility of strongly emergent properties. The distinction between weak and strong emergence is perhaps by orders of nested abstraction. The self may be strongly emergent in the context of neural analysis, but is it not weakly emergent in the context of memory? Does the self supervene on memory and is it reducible to memory? There are many examples of people losing their memory and consequently modifying their behavior out of character (Schacter, 1996). It is very clear that the notion of self and personal identity depends heavily on memory. If you were able to modify a person's memory and give them the recollection of murdering someone, then the person would suppose that she was a murderer. If you gave the person the memory of playing classical piano music with virtuosity at Carnegie Hall, then the person would suppose that she was a great musician. If you completely replaced this person's memories with your own memories, then wouldn't this person "feel" like she was you in some way? Perhaps the self is not completely reducible to memory, but certainly a large subset of mental processes comprised within the self are reducible to memory, and thus this subset of the self is weakly (not strongly) emergent from memory.

Memory is itself perhaps weakly emergent in the context of perception and experience, and so on and so forth. Following this chain of weak emergence, would it not be possible to thus reduce a supposedly strongly emergent property to an arbitrarily lower level of inquiry? In computer programming, high-level languages use nested class and metaclass structures to abstract complicated objects and algorithms from more basic machine instructions which are themselves abstracted from physical properties and structures of the computer. The behavior of any advanced program is thus emergent from the physics of the computer. Is this emergence strong or weak? We can't explain the behavior of the program (easily) in terms of switching transistors, and so it would seem to be strongly emergent. But on the other hand, we know that the behavior is reducible to transistors because that's how we designed it, which indicates that it is weakly emergent. In this interpretation, there is no great distinction between strong and weak emergence. If there is no great distinction between weak and strong emergence, then the implication is that there is no great distinction between Reducibility and Supervenience either. In the end, these distinctions may not be that important or useful. For now, I will assume that if A-properties supervene on B-properties, then A is phenomenally reducible to B, and thus all emergent properties are of the weak variety.


III. The mechanism of emergence.

What is the mechanism of emergence? How does emergence work? Are emergent properties fundamental and inherent in some way, or merely useful fictions as Dennett put it? Plato may be the earliest recorded thinker to tackle this issue. He devised a theory of Forms, abstractions that he presumed to be more fundamental than substance or matter. For Plato, these abstractions were the objects of reality, and perceptual knowledge was merely an illusion, the shadows cast by these perfect, ideal objects. One did not learn or come to know about the Forms, but rather one would "remember" the Forms from some place in the immortal soul. Was Plato onto something, or just on something?

Lets suppose there were no Humans or other conscious agents, for the sake of argument. Would there still be abstract emergent properties? This is not an easy question to answer. The natural logic and language of our minds has a physical basis in our brains, so these abstractions have a physical representation, and they are not represented to merely some hypothetical omniscient being but also to themselves. This is an important point. If we look, from an omniscient perspective, at a relatively random string of zeroes and ones represented by transistors in a computer, we can interpret it in near-infinite ways as long as we have a mechanism to decode the string for each way we want to interpret it. If we change the decoding mechanism, then we effectively change what the string represents. But does the string inherently represent anything in particular absent a mechanism to decode it, or does it represent everything that is possible for it to represent? Does any configuration of matter inherently have emergent properties absent some emergent property reading mechanism to interpret it? And what about that mechanism? What is its ontological status?

It is common and appealing to think of abstractions and emergent properties as existing in their own universe separate from the material world, as Plato did. And yet, the act of thinking about these things has a physical basis in the brain! When we write these ideas down on paper, they have a physical basis in the ink and paper. When we communicate these ideas to other people, we communicate them through physical media. We do not communicate them through some other immaterial universe. The ink on the paper and the syllables in the air do not pull abstraction and meaning out of the ether. Do our equations written in ink on paper have emergent properties? Is there a center-of-gravity emergent property, and a just-off-center-of- gravity emergent property, and a bit-more-off-center-of-gravity emergent property ...? Where does all of this meaning, abstraction, and emergence come from? Does emergence have any meaning outside of the mechanism used to discern/determine it?

The mechanism of emergence is homomorphic to the property of emergence. The property inheres in the mechanism, not in the physical basis of the property, and the mechanism can inhere in itself as an automorphic property. This may sound technical, but the concept should not be terribly difficult to grasp. We even have idioms that more or less express this very sentiment: "beauty is in the eye of the beholder", "it's a matter of interpretation", "everything is relative". These all basically mean that emergent properties inhere in the mechanism of emergence; the mechanism of emergence is the source of emergent properties [1]. The mechanism itself is evolved. Lots of mechanisms get tried out, and only the ones most useful for survival and proliferation manage to propagate. These mechanisms are effectively sensual, perceptual, or extensions thereof. They also tend to compress higher dimensional data sets into lower dimensional data sets using lossy compression or perceptual coding schemes, as is the nature of abstraction. The more these mechanisms compress data, the more complex and higher-order these mechanisms must be [2].

[1: Note how this unintentionally jives with the Turing Test. (Turing, 1950)]
[2: Wikipedia has a good article about data compression, including a section about Machine Learning, which notes that data compression might be a good metric for general intelligence. Data Compression and Machine Learning are both extremely interesting topics in themselves, and have a lot to offer in the consideration of emergence, but they are beyond the scope of this paper. (http://en.wikipedia.org/wiki/Data_compression)]


IV. The necessary conditions of emergent consciousness.

In cognitive science, we are concerned with explaining the properties of the mind. The properties of the mind supervene on the brain, which supervenes on the nervous system, which supervenes on biology, and so on all the way down to the quantum level presumably. These properties are all emergent in some way, but how? What are the necessary conditions for the emergence of mental properties, or the emergence of any property in general? We already know that no individual neuron or even sets of neurons is necessary for consciousness. We also know that severely crippled senses does not prohibit the development of a conscious mind (see Helen Keller). People survive all sorts of traumatic brain injuries with a level of self-awareness intact. Even diseases such as Chronic Inflammatory Demyelinating Polyneuropathy (CIPD), which hinders the conduction of action potentials along the axons of neurons, do not prohibit self-awareness.

But people do lose consciousness temporarily sometimes, as in the case of syncope. Syncope is usually caused by insufficient blood flow to the brain. Neurons require oxygen to power their ion pumps, so if the blood does not supply enough oxygen to the brain, then the neurons can't function and the person loses consciousness. It seems obvious that consciousness depends on neurons being able to fire, but it also depends on the coherence of neuron firings. People who experience epileptiform seizures also lose self-awareness / consciousness. Even petit mal seizures, which are mildly manifested, cause a loss of awareness. These epileptiform seizures are a result of a massive amount of neurons firing all at once, during which time the person has no conscious control over her body or awareness of her surroundings. This makes sense since in order to respond to stimuli, one needs a mechanism of response through the neural network. But if the neural network is preoccupied firing in an incoherent or confounded way, then there is no way for the stimuli to produce a predictable response. There are other ways to lose consciousness through concussions and comas, the result of traumatic events in the brain, or through certain kinds of dementia and memory loss. In all of these cases, though, there must be some set of factors or elements in the brain being hindered that leads to a loss of consciousness. What are these things being lost that are necessary for the emergence of consciousness?

Let's say we have a normal person with normal mental properties. What would happen if we completely removed or froze the mechanism of memory? What would be the behavior of the person? We can imagine that perception would still work, meaning that there would still be sensory inputs into the brain. These inputs would activate some network of neurons, which would evoke a response from the person. But none of the preceding would change the synapses, or the weights of the neurons, or the neural network, and thus the exact same response could be evoked given the same sensory inputs. The person would be reduced to an automaton, perfectly predictable given a set of inputs. Would this person still have self-awareness? What mental properties if any would this person have? We could torture the person and evoke responses that might be interpreted as pained perhaps, but would there be any cognition of pain? If we plunged a knife into the person's hand, the person would have no recollection of the knife approaching the flesh, or of the knife penetrating the skin, or of any of the moments prior to the current perceptual indication that there is a knife in the hand. Any response to this event could only be reflexive, and not reflected upon. These considerations imply that some kind of memory is a necessary condition for the emergence of consciousness: the interpretation of sensory stimuli in the context of memory is a necessary condition for the emergence of consciousness.

What else is necessary for the emergence of consciousness? As I noted in section (III), emergent properties inhere in mechanisms of emergence, which I then claimed evolve and are perceptual in nature. Thus consciousness, being an emergent property, requires (self?) perception. If we hypothetically removed or confounded the perceptual information in the brain, then consciousness would cease to emerge, as in the case of epileptiform seizures. Even people who do not normally suffer from epileptiform seizures can lose consciousness from sensory overload. The evolutionary component of this point is also very important. Consider the fetus, infant, and toddler. How is consciousness emergent at these different stages of Human development, and how do we account for differences? Remember, consciousness inheres in the mechanism of emergence, which itself must evolve. The early stages of Human development do not have the requisite mechanisms of emergence evolved yet for higher cognition. Is that not why it is very difficult if not impossible for people to remember anything from those earlier stages of life? All memories from those early stages would be couched in terms of inferior and simplistic mechanisms of emergence, which become overwhelmed later on by the memories informed by more advanced mechanisms of emergence. The evolution of these mechanisms occurs through competition internal to the mind; new mechanisms get created, slightly modified from parent mechanisms, and the ones that are most successful are maintained, while the least successful get discarded (hopefully). Thus people gradually become more and more perceptive, making sense of things they weren't able to before, and sometimes seeing more than is really there (see a list of fallacies, http://en.wikipedia.org/wiki/List_of_fallacies).

Memory and perception require a lot of hardware, complexity, and redundancy. There assuredly must be a minimum neurological requirement for the emergence of consciousness, and maybe there is a way to evaluate what that limit must be and in what terms. It would be an interesting problem to try to solve, but for the moment, the best we can do is note that the limit is there and leave it to bigger and better minds to figure out. As for other necessary conditions of consciousness, it is not readily apparent to me what they might be. Memory, perception, and neurological complexity are necessary, but may not be sufficient. Perhaps there is a limiting spatiotemporal component that is based on physical principles?


V. Concluding remarks.

Admittedly, this paper has merely provided a rough outline of the characteristics of emergence and its relationship to consciousness. My most important claim is that emergent properties inhere in the mechanisms of emergence, not in the physical basis of the properties. In this conception, these mechanisms that are the product of evolution should allow us to explain how knowledge is acquired and how language is developed, how children and machines learn, how rationality and cognitive dissonance emerge, how perception is extended, and how science progresses. I feel there is much explanatory power in this idea, and many testable predictions that it could make. Most importantly, this theory of emergence unifies ontologies, as opposed to others that separate the ontology of the mind from the brain; it opposes the dualism inherent in the distinction between strong and weak emergence, and the attendant implication of magical qualia of what it is like to be conscious.


VI. Bibliography.

Aristotle, "Metaphysics".
Bedau, Mark A. (1997), "Weak Emergence".
Campbell, Donald T. (1974), "Evolutionary Epistemology", in P.A. Schilpp, ed., The Philosophy of Karl Popper (Open Court, LaSalle, Il, 1974). Pp. 413-463.
Chalmers, David J. (2002) "Strong and Weak Emergence" Republished in P. Clayton and P. Davies, eds. (2006) The Re-Emergence of Emergence. Oxford: Oxford University Press.
Dennett, Daniel C. (1992) "The Self as a Center of Narrative Gravity". In: F. Kessel, P. Cole and D. Johnson (eds.) Self and Consciousness: Multiple Perspectives. Hillsdale, NJ: Erlbaum.
Plato, "Meno", "Parmenides".
Schacter, D.L. (1996). "Searching for memory: The brain, the mind, and the past". New York: Basic Books.
Tomberlin, J., ed., "Philosophical Perspectives: Mind, Causation, and World", Vol. 11 (Malden, MA: Blackwell, 1997), pp. 375-399.
Turing, Alan (October 1950), "Computing Machinery and Intelligence"