Hierarchical Brain

Symbol schema

A symbol schema is my name for a network of neurons that, when activated, represents a concept in the brain. The total of all the symbol schemas and the connections between them in my brain is, in effect, a model of my world (including my body and my brain itself), and encompasses all my memory, knowledge and intelligence. Symbol schemas are the most important intermediate level (level four) in my seven hierarchical levels of description of the brain, and they are crucial to all higher-level functions.

Symbol schemas are created as the end result of afferent processing of incoming data (from both external and internal senses and from within the brain), and they are given meaning by the process of reinstatement which uses efferent connections back towards the origin of the data.

History and other names

• Many people have proposed similar structures in the past and given them various names, and some researchers have found evidence that they do exist. This is not intended to be a complete history of the subject, but I have selected areas that I think are most relevant.

• The pioneer psychologist William James, in his 1890 book The Principles of Psychology, used various rather vague terms (such as mental modes, nervous arrangements and mental units) to refer to elements in the brain that might be representations of things in the real world. He also proposes a central or “pontifical” cell to which consciousness is attached¹.
• The term “Cell Assembly” (CA) was used first in 1949 by Donald Hebb to describe a network of neurons that fire together and therefore become more strongly connected by the process of synaptic plasticity, although at that time a CA was not necessarily thought of as something that could represent a concept².
  • Since then, a CA (or sometimes “Neural Cell Assembly” (NCA)) has been frequently referred to in the field of neuropsychology as a network of neurons that represents a concept, and quite strong evidence for their existence has been obtained³.
• The name engram had been coined in 1921 by the biologist Richard Semon to mean a set of neurons that are activated by learning, have lasting cellular changes, and are reactivated by a part of the original stimuli for recall⁴.
  • The term was popularised in the 1950s by Karl Lashley by his research on the brains of rats to try to locate the source of a memory, which he failed to do.
  • Many scientists have since spent much of their careers investigating the details of where and how memories are created, consolidated and retrieved, but sometimes the close relationship between an engram and a Cell Assembly that represents a concept in the brain has not been taken into account.
  • The term engram has been misappropriated by Scientology for a pseudoscientific usage that is nothing to do with this definition.
• In 1967, the Polish neurophysiologist Jerzy Konorski published a book⁵, in which he described “gnostic cells” or “gnostic units” in the brain that represented concepts, although this work was not well known worldwide at the time^{6, 7, 9}.
• The strange term grandmother cell was first coined by Jerry Lettvin (without knowing of the work of Konorski) around 1969⁸ to describe one or more neurons that, when activated, somehow represent the concept of “grandmother” in a specific human brain, with the assumption therefore that all other concepts were similarly represented.
• In 1972, Horace Barlow wrote a paper in which he rejected the idea from William James (above) that there was a single “pontifical” cell that represented the consciousness, and instead proposed that a large number of “cardinal” cells could represent a single perception¹⁰.
• In 1979, Douglas Hofstadter popularised the use of the term “symbol” for the representation of a concept in the brain and concluded that a symbol consisted of a number of neurons that fired together, and that there had to be what he called a “funneling” process to create, update or activate these symbols. He also gave ideas on how they linked together, how they could not fire in isolation and how they could together form a model of the world¹¹.
• From the 1980s onwards, researchers were using electrodes embedded in live brains to try to understand when neurons fired in relationship to each other within a neuronal assembly or cell assembly¹².
  • Electrodes for recording in brains had first been used in the 1950s.
  • These electrodes were usually inserted into the brains of animals, but there were some opportunities to get data from human brains when wires were put into patients for the purposes of investigation into intractable epilepsy.
• The neuroscientist Antonio Damasio, who is best known for his research and theories on consciousness, has published a number of articles and books that include discussions on how concepts could be stored and used in the brain.
  • In 1989, he published two papers^{13, 14} outlining his model of how concepts in the brain are represented in what he called “convergence zones” which, when activated, trigger neurons in the early sensory cortices, a process he called “retroactivation” (similar to the process I prefer to call reinstatement).
  • Twenty years later, in 2009, another Damasio paper¹⁵ expanded on these ideas with a description of how hierarchical processing could create convergence-divergence zones or CDZs, which are similar to what I call symbol schemas, although this paper does not mention that CDZs could represent concepts, neither does it give any detail on how the hierarchical processing of sense data could create CDZs.
  • In this 2009 paper and his 2010 book, “Self comes to mind”, Damasio uses the terms “image”, “map” and “neural pattern” interchangeably to mean a representative symbol in the brain¹⁶.
  • His most recent book “The strange order of things” also uses these terms, and does discuss them representing concepts¹⁷.
• In 2004, Jeff Hawkins, describing his memory-prediction framework, called stored memory patterns “invariant representations” or “name cells”, with invariance increasing up the hierarchy and lower levels changing more frequently than higher levels¹⁸.
• In 2005, some research that highlighted the apparent existence of a “Jennifer Aniston” neuron in the brain came to public attention (although Bill Clinton and Halle Berry neurons were similarly identified).
  • This particular research was only generally able to consider the effect of a single neuron at a time, because it involved patients who already had electrodes implanted in their brains for the purpose of locating the source of epileptic seizures¹⁹.
  • The title of the published paper included the words “representation by single neurons”¹⁹, which was strictly correct in terms of the findings of the research, but this led some people to assume that one (and only one) neuron took part in this representation, in a similar way to some interpretations of a “grandmother cell”. This seemed unlikely to many scientists, mainly because of the known resilience of the brain.
  • Later research clearly showed that many neurons are involved in the representation of a single concept, and also that any one neuron is likely to be involved in the representation of many related symbols²⁰ (also see “degeneracy” below).
• The term “concept cell” has been used in recent years^{21, 22}.
  • The use of the word “cell” tends to suggest that only one physical neuron is involved in the representation, which, as pointed out above, seemed very unlikely and has now been shown to be incorrect.
• The general term “representation” or mental representation has also sometimes been used to mean a memory stored in the brain which represents something²³.
• In 2016, the term “Grandmother cohorts” was used to mean a set of neural networks that represent different aspects of the same concept²⁴.
• This newspaper article from 2016 referenced research²⁵ that created an “atlas of the brain” - a map of where concepts are stored all over the brain.
  • This research used MRI brain scans, so the resolution was very coarse (a single “voxel”, equivalent to a pixel, in an MRI scan might easily contain 100,000 neurons or more!).
  • The picture below is a small extract from the map produced, which shows that symbols for concepts that we may consider have connections between them are often located physically near to each other in the brain.
  • Many words appear in a number of different places in the brain, presumed to reflect the multiple meanings of those words, but I think representations can sometimes consist of a very widespread set of neurons.
  

Justification for their existence

• The various pieces of research done over many years referenced in the history section above show that there is strong evidence that there are neurons in the brain that somehow represent a concept or thing to the owner of that brain when they are activated; in other words, they are representational symbols.
  • In particular, the results of research on human epileptic patients, mostly carried out in the last 20 years or so, provides very good evidence for the representations of concepts in networks of neurons.
  • This has been summed-up by Rodrigo Quian Quiroga, a neuroscientist who specialises in this field, in a recent review⁹.
  • The “atlas of the brain”, referenced above, is also very convincing evidence, although based on a very much coarser mapping.
• On my page about the so-called explanatory gap, the difference between the known physical properties of the brain and personal mental experiences, I have examined sensory illusions. This clearly leads to the conclusion that there must be representations of concepts and objects already in the brain before any perception can take place.
• For many years, psychologists have investigated the way that humans define, remember and recall concepts, so there is a pretty good understanding of how symbols in the brain must exist and connect together²⁶. This understanding seems to fit well with my explanation of how symbol schemas exist and connect together.
• My explanation of how symbol schemas are created, by the recursive and hierarchical application of memory-enhanced coincidence detection that I call afferent processing, seems to match well with what is known about the existence and connectivity of representative networks, and is also compatible with what is understood about the low-level processing of sense data (as detailed in afferent processing).
  • Even if you do not agree with my proposals on how symbol schemas are created and updated, the evidence for the existence of such structures in the brain is very clear, and the higher levels of my hierarchical levels of description would still largely be valid.
• It is only useful to propose that there exist symbols in the brain if there is also a method by which those symbols come to have meaning to the owner of the brain (more on this below).
  • I believe that method is reinstatement: it provides an explanation for how concepts and memories have meaning when recalled, and this also seems to fit well with my experience of what happens in my brain.
  • As mentioned above, Antonio Damasio described “retroactivation” in papers in 1989^{13, 14}, but since then further evidence of the reactivation of sensory neurons has been published (see reinstatement).
• Symbol schemas are a crucial part of the explanation of the workings of all the higher-level brain functions in levels 6 and 7 of my levels of description.
  • I propose that a symbol schema that represents the self is created in exactly the same way as all other symbol schemas, but using data largely from the body and inside the brain.
  • When these foundations are put into place, they lead logically towards definitions of perception and attention, my conclusion that I am my self symbol schema and the highest-level definitions of consciousness and free will.

Definition

• A symbol schema is my name for a set of a large number of neurons, and the connections between them, that, when activated, represents a concept in the brain (more on activation below).
  • It seems clear that all the references in the history section above are essentially describing the same thing, but I prefer to use the term “symbol schema”.
    • “Symbol” (as used by Hofstadter¹¹ and others) meaning a representation of a concept, either physical or abstract.
    • “Schema” indicating that it is a model, a cut-down imitation of the real thing. (The word schema is used in psychology to mean a pattern of thought, but the meaning I use here is rather different.)
  • A symbol schema is a real physical entity, consisting of a network of synapse connections joining together a large number of neurons.
    • The neurons involved are not necessarily located physically closely together, but may be quite widely distributed in some cases.
    • The numbers of neurons involved could range from many hundreds through to millions²⁷.
    • The number of synapse connections that make up a symbol schema is likely to be many times higher than the number of neurons, because each neuron will have many connections to many others in the network. This is due to the way that symbol schemas are created by the process of afferent processing.
    • A single neuron can be a part of many different symbol schemas, by virtue of having different synapse connection. One study has suggested that an individual neuron may take part in between 50 and 100 different representations²⁷.
    • Because of the way in which symbol schemas are created through afferent processing, it seems likely that two concepts that are closely related in the real world will be represented by two symbols schemas that have many neurons in common (more on this in activation below).
    • So there is a many-to-many relationship between neurons and symbol schemas.
  • The set of neurons that make up the symbol schema can be described as a degenerate set²⁸.
    • The word degenerate is used here in its scientific sense meaning that the firing of different neurons can cause the same result (not in its non-scientific sense relating to bad morals)²⁹.
    • Degeneracy also provides redundancy, which means that the loss of one or more neurons from a symbol schema is unlikely to make any difference. (Degeneracy and redundancy are related but are not quite the same thing³⁰.)
• Another possible definition for a symbol schema is that it consists of the highest possible level of abstraction or compression for the representation of the concept or object.
  • It can change, if, for example, I discover that my understanding of a concept was slightly wrong or incomplete, in which case changes can be made or new bits can be added.
  • There is always a core of a concept that is unchanging, and the more concrete a concept, the less changes there will be.
  • So my symbol schema for a frisbee is unlikely to change unless someone invents a completely new shape or size of frisbee that is still clearly a frisbee, or perhaps if I see a frisbee from an angle I have never seen one from before.
  • But my symbol schema for beauty, for example, could be relatively fluid, and more dependent on examples.

Further details

• The boundary of a symbol schema is a purely logical one, and depends on the semantic definition of what is being represented. Clearly there will be no boundary visible in the brain, and the degree of separation between one symbol schema and another will vary.
• Many symbol schemas could be “super-sets” because they contain other symbol schemas.
  • Two or more symbol schemas that were created at different times could later have become merged together to form a larger one, but the original smaller ones are still valid symbol schemas in representing a smaller, more refined, sub-concept of the larger one.
  • Or the larger one may have existed first and become fragmented when multiple meanings were realised.
• Many concepts are stored in the brain in hierarchical networks, so, for example, the symbol schemas for “classroom”, “playground” and “teacher” might be linked in a hierarchy “below” the symbol schema for “school”. This is because, when we first learn a new concept, the recursive and hierarchical afferent processing of sense data will create the “higher level” concept from the “lower” ones (and not the other way round).
• Each symbol schema will have two different types of afferent links, one type coming from sense data when the symbol schema was originally created, and another type from other symbol schemas that are “lower” in the hierarchy and which represent the connection between symbols in the real world. Some connections in the first type could disappear and be pruned quite quickly, unless they are reinforced by being recalled.
• Each symbol schema will also have two different types of efferent links, one for reinstatement, and one for links to other symbol schemas that are “lower” in the hierarchy.
• Given that a symbol schema is a symbol that represents something, it is easy to see how easily and naturally language can be catered for.
  • Spoken words are also symbols that represent things, and written words are symbols that represent the spoken words.
  • So a symbol schema for the written word “frisbee” is a symbol for the spoken word “frisbee” which itself is a symbol for the concept of a “frisbee” in the real world, which is also exactly what the symbol schema for “frisbee” is.
• Language provides a huge advantage to improve understanding, meaning and intelligence.
  • It would be far more difficult to differentiate closely related concepts without language.
  • Abstract concepts (such as truth, beauty, freedom, evil etc.) would be almost impossible for the brain to define without multiple levels of reference and comparison.
  • The growth of human culture, I believe, relies very heavily on the ability to use language, and with culture came intelligence, the ability to pass on knowledge, and the ability to define difficult concepts (see the page on language for more on this).
• There is a particular category of symbol schema that is useful to differentiate when it comes to looking at representation and meaning (below) provided by reinstatement.
  • I define an “elemental” symbol schema as one that is created directly from sensory input and does not need any other connections to define its meaning.
    • Elemental symbol schemas are likely to be the first symbol schemas created in the brain of a child.
    • An elemental symbol schema could consist of a set of neurons that are directly connected to a single particular type of sensory neurons related to a single sense, or those which are activated by a specific pattern or firing frequency of these neurons.
    • Examples of elemental symbol schemas include:
      • “Red” created from the input from particular cone cells in the retina.
      • “Bright light” for a lot of light detected by many of the cells in the retina.
      • “Loud noise” from the input of many hair cells in the ear.
      • “Sounds of a specific pitch” from input from a specific range of hair cells (most people do not retain the ability to access these symbol schemas - see perfect pitch below).
      • “Sweet taste” from input from specific taste buds on the tongue.
      • “Pain of a specific type” from input from pain receptors in a specific place.
  • Non-elemental symbol schemas are all those that are created not directly from sensory input, or those that need other qualification.
    • Non-elemental symbol schemas will always be connected to other symbol schemas, including probably some elemental ones, via efferent connections, because they were created with reference to other concepts or objects.
    • The symbol schemas for more abstract concepts and ideas will be more distant from elemental symbol schemas in terms of the number of connections away.
    • The connections run in both directions, afferent (inwards) for the processing of data, and efferent (back outwards) for prediction, reinstatement and a number of other functions.
• Perfect pitch is a particularly interesting example that starts as a set of elemental symbol schemas, but later in life it seems that most people lose the ability to access them.
  • A young child almost certainly has a form of perfect pitch in that they will unconsciously remember exact pitches rather than relative pitches.
  • But after some time of exposure to versions of music that are the same, but in different keys, access to the symbol schemas for the exact frequencies will not be retained, but symbol schemas for relative pitches will be.
  • A small number of people do retain perfect pitch; this ability seems to have both a genetic and an educational component.
  • Since hair cells in the ear respond to absolute pitch, I am pretty sure that we all have symbol schemas for individual pitches, but that direct access to them is lost when we use relative pitches instead.
• I propose the following notation as a shorthand way of describing symbol schemas, and I use this below as well as on several other pages.
  • A symbol schema can be written as a pair of curly brackets (or braces) with the name of the object or concept that the symbol schema represents within the brackets.
  • So I can write, as a shorthand for the symbol schema that represents a frisbee, {frisbee}.
  • The self symbol schema can be written as {self}.
  • This has parallels with the notation used for a mathematical set. The set of neurons that makes up a symbol schema is well-defined at any moment in time, but neurons can be part of many different symbol schemas, so it is actually the network of connections that defines the symbol schema better than the set of neurons.
  • Using this notation makes some rather complex statements about symbol schemas easier to understand.

Activation and deactivation

• The activation and deactivation of symbol schemas is the process that drives higher-level behaviours such as the workings of the model of my world, the flow of my thoughts and imagination and the process of attention, and also is a major factor in free will.
  • The underlying mechanism of activation and deactivation is the excitatory and inhibitory synapse connections between the many neurons that make up a symbol schema.
  • The crucial component at any one moment is the balance of strength between the many excitatory and inhibitory connections. Since I know that my thoughts or attention can sometimes move between different things many times a second, this balance can clearly change very quickly over time.
  • The overall balance of excitatory and inhibitory connections between two symbol schemas is a feature that emerges from the balance of them between individual neurons.
  • Overall, it is believed that a general balance is maintained between the strengths of excitatory and inhibitory connections between neurons (see Scholarpedia: Balance of excitation and inhibition), although the mechanisms behind this are not yet understood.
• The activation of a symbol schema means that most, perhaps all, the neurons in the network fire (generate an action potential) at, or very near, the same time, and all continue to fire for a period of time, up to several seconds because of mutual excitation.
  • This activation will take place because there are synapse connections between one or more neurons in this symbol schema and one or more in another symbol schema that has been activated (see diagram below of multiple overlapping symbol schemas).
    • Connections between different symbol schemas are all due to neurons being part of more than one symbol schema.
    • These connections reflect, to a large extent, connections between the concepts represented in the real world.
  • It is possible that if only one neuron in a symbol schema fires, it may trigger many others to fire, and then the firing will spread across the whole symbol schema.
    • This, I suspect, is likely to be why a number of experiments on living experimental subjects who already had electrodes implanted in their brains for the purpose of locating the source of epileptic seizures seemed to show that the stimulation of a single neuron caused a thought, memory or action to take place in the subject.
    • This is probably how the concept of the grandmother cell (see above) and other so-called single-cell representation theories came to be proposed.
    • It is also possible that an implanted electrode, although intended to activate only one neuron, could actually activate a number of other nearby ones, because of the voltage leaking into the surrounding areas.
    It is more likely, though, that many are needed to fire together in order to activate the symbol schema.
  • Once the threshold for activation has been passed, the firing of all the neurons becomes self-perpetuating, for at least two reasons:
    1. With the many synapse connections in multiple directions between the neurons, there will be relatively small circuits or loops of connections between neurons within the symbol schema that trigger each other (see animation in this diagram).
    2. There will be larger circuits or loops of connections from neurons in the symbol schema via efferent connections back towards sensory neurons and thence back to the symbol schema. This is what I call reinstatement.
    This self-perpetuation is what allows attention or a conscious thought on the symbol schema to last for several seconds.
• The deactivation of a symbol schema is generally brought about by the activation of another one.
  • The self-perpetuating process of activation will be brought to an end by the process of lateral inhibition or selection, which are described in levels 2 and 3.
    • The inhibitory signals most likely come from another symbol schema that has been activated partly from signals from this symbol schema because of connections between the two concepts (see diagram below of multiple overlapping symbol schemas).
    • In effect, there is a form of competition between symbol schemas trying to become active. More than one can be active at a time, but only one can connect to the self symbol schema at any one time (see attention).
    • The overall architecture of the brain can be described as fractal, or chaotic, meaning that only a small disturbance can cause one activated symbol schema to be deactivated, and another one to become activated (see model of my world).
• There is evidence that chemical synapses that are part of a commonly-activated symbol schema may encourage the growth of electrical synapses between the neurons involved (see synapse groups for the evidence).
  • This would allow much quicker mutual activation of neurons that make up the symbol schema (one of the statistics on synapses shows that electrical synapses are very much quicker than chemical ones).
  • This could come about because it has been shown that chemical and electrical synapses interact and influence each other.
• This process of activation and deactivation described above is how our thoughts and attention flow from one thing to another, either consciously or unconsciously. One thought about one subject triggers a related thought.
• This illustrative diagram shows five symbol schemas that overlap, with many links within each schema and also many links between schemas.

Representation and meaning

• There are two aspects by which a symbol schema can be said to represent a concept in the brain, both of which come about because of the way the symbol schema is created by afferent processing:
  1. Whenever a particular concept or object is sensed or recollected, the same symbol schema will be activated. So there is a one-to-one relationship (an isomorphism) between the symbol schema and the concept or object.
  2. Whenever this symbol schema is activated the same efferent connections will be activated via reinstatement each time. This means that every activation has the same “meaning”, when meaning is manifested, and meaning is only manifested when the sensing becomes conscious, i.e. it connects to the self symbol schema.
  Over time, however, as new neurons are added to a symbol schema by new encounters, and old ones are removed because of inactivity, the reinstatement links can change.
• In theory there could be many reinstated connections from every neuron in the symbol schema, where each neuron represents a multi-sensory memory of the particular encounter that caused that neuron to be added; however in practice some memories are not retained for long because the connections are not reinforced and so may be pruned.

Creation and update

• Simplistic examples of how a symbol schema may be created and updated are given in my afferent processing examples.
  • Example 1 shows how, when a frisbee is seen, existing synapse connections between existing neurons are strengthened by the hierarchical and recursive coincidence detection process resulting in a neuron at the “top” of the hierarchy becoming part of the symbol schema representing a frisbee; or, if a frisbee had never been seen before, the start of a new symbol schema.
  • Example 2 shows the same thing for the sense of touch or feel, and example 3 shows how the senses of sight and touch can be combined.
  • Example 4 and example 6 show how further neuron(s) are added to the existing symbol schema when the frisbee is seen on later occasions.
  • Exactly the same process will take place for all other data from external and internal senses, and comparisons can easily be drawn with the examples for sight and touch already given.
    • Take, for example, the sense of hearing. Different hair cells in the ear response to different frequencies of sound, so frequency for hearing can be thought of as the equivalent of colour for sight. Two frequencies that often occur together, or close together, will cause new connections to be created between neurons connected to those hair cells, or existing connections to be strengthened.
    • A lot of other sense data does not have a continuous spectrum (spatial movement, colour frequency, sound pitch and balance are examples of ones that have) so the coincidence detection and compression process will be different for these.
  • A neuron will be considered to be part of a symbol schema if, for a given instance of a sensing of the thing being represented, it is at the “top” of the hierarchy of afferent processing i.e. no more coincidence matching or compression is possible for that instance.
    • So, for example, with reference to afferent processing example 1, neurons A-G are not considered to be in the symbol schema for a frisbee because they represent only a small part of the view of the frisbee, but neuron X is, because it represents the whole frisbee for this view, and no further coincidence detection or compression is possible for the concept of frisbee for this instance of the viewing of it.
    • Clearly neurons A-G in afferent processing example 1 could represent a part of any red thing, so could contribute to the creation or update of many other symbol schemas; neuron X, even though it is part of the symbol schema for a frisbee, could also be part of other symbol schemas for red, round things, but for those purposes it will have additional connections to other neurons.
• All this afferent processing happens subconsciously, so a symbol schema can be created and updated without any attention on the thing being sensed. When or if attention is paid to the thing, then a perception takes place, but this can only happen once the symbol schema exists.
• In the simplified examples referenced above, one neuron is added to a symbol schema for each new sensing of the thing being represented if there is a different angle, distance, attribute or context for the thing. This could amount to a total of many thousands of neurons for even a simple object; however in practice the number of neurons in a given symbol schema will stabilise over time: if synapse connection are not reinforced, then they will weaken and may be pruned, which may remove some neurons from that symbols set; new ones will only be added when novel situations are encountered.
• Synapse connections that are not used will be pruned over time, so if not used, a symbol schema could shrink and eventually disappear. All the neurons will still exist, but the connections that made the symbol schema no longer exist.
• When looking at a frisbee and a bicycle, the frisbee is seen as an object and the bicycle is seen as a separate object. They do not move together, they are not attached to each other, they have different characteristics, etc.. The only connection between them is that they are seen at the same time, and that they have been seen to exist close to each other in their particular storage area.
• Considering the way a symbol schema is created with afferent processing, it will often happen that what seems at first to be a new symbol later transpires to be the same as, or similar to, another already-existing symbol, so the two will get linked together. This will result in a symbol schema consisting of multiple neurons. Each of these neurons could have different efferent connections back to different “memories” of when the object or concept was encountered, so when the symbol schema is activated, many different reinstatements are also activated, and the whole nuanced, detailed picture of the symbol in question is available to the brain.
• The most important symbol schema, which must also probably be the biggest set with the most links, is the one that relates to the self, which I call the self symbol schema. It is the main requirement for self-awareness and attention, and therefore consciousness.
• There is evidence that abstract concepts are stored in an associative network³¹, so, for example, the symbol schema for “danger” would be linked to the symbol schemas for “lion” and “snake”. This is because the only way we have to recall abstract terms is via connections to concrete terms which have links (via reinstatement) to the original sense data input.

Numbers

• An estimate of the number of symbol schemas in your brain is always going to be vague because the boundaries between and within sets are fuzzy, and there will be overlaps between categories, but I think there must be at least many hundreds of thousands and quite possibly millions. In your brain there must be a symbol schema for each of the following:
  • Every physical object, or part of one, that you have every come across in real life, or in pictures or films or videos, or even in verbal or literal description. One estimate from some years ago came to the conclusion that there are about 30,000 readily discriminable objects in this category alone³².
  • Every abstract concept that you have every encountered.
  • Every single word you know, whether or not you know the meaning of it, plus every combination of more than one word that you remember as a “concept” in its own right, every phrase, quotation, proverb, book title, lyric, picture title, etc.
  • Every person you remember or have some knowledge of, alive, dead or fictional (including a very large one for yourself - see above).
  • Every place you remember visiting, seeing, or reading about, or have some knowledge about (e.g. that it is on the way to somewhere else or has a particular feature), including scenes and pictures.
  • Every number that means anything to you.
  • Every noise you can distinguish or remember, whether or not it has a name.
  • Every piece of music you remember, plus every phrase of music, every piece of harmony and every interval (and, if you have perfect pitch, every note).
  • Every smell you can distinguish or remember, whether or not it has a name.
  • Every taste you can distinguish or remember, whether or not it has a name.
  • Every touch or feeling from every part of your body that you can distinguish or remember (which could be considered to be part of the self symbol schema).
  • Every temporal, spatial or abstract relationship, whether or not you know its name.
  • Many other technical concepts that might be in your specialist field, or an area of interest.
  • Concepts of relative time, such as “last week”, “when I was younger” or “next year” are difficult to imagine, but they must exist.

Summary

• A symbol schema is an emergent concept, but a symbol schema is a structure that physically exists and has cause and effect.
• It is very difficult to find a good analogy, because the brain is such a complex structure, but it can usefully be compared to a cloud, although a symbol schema has more permanence than a cloud.
  • A cloud is made up of millions of tiny individual ice particles, water droplets, or dust; a symbol schema may consist of a similar number of synapses.
  • A cloud has a physical area, shape, structure and position in the sky and its existence is defined by its constituent particles and environmental factors within that area; a symbol schema does not occupy a single space, its existence is defined by connections between neurons that may be widely spread.
  • The boundary of a cloud is fuzzy - when you get close in you cannot easily specify where it starts and finishes, but away from its edges the centre is more definitely always part of the cloud; the boundary of a symbol schema is also fuzzy to a certain extent, and there is a logically central core that is unlikely to change.
  • The boundaries of both a cloud and a symbol schema can change quite rapidly, but they can also be quite stable; a cloud can be stable for perhaps hours, a symbol schema can be stable for years.
  • A cloud can form apparently out of nothing, and fade and disappear into apparently nothing, when viewed from a distance; a symbol schema could be the same if viewed “from a distance”.
  • Clouds have real effects by casting shadows and affecting the climate both nearby and at a distance; symbol schemas also have real effects when activated by causing action and thoughts.
  • It is useful to be able to talk about both clouds and symbol schemas. And in fact we do - we talk about the speed, shape and effects of clouds and we also talk about the concept of something, our knowledge of something and we have names for abstract and concrete concepts.

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References For information on references, see structure of this website - references

1. ^ The Principles of Psychology - William James 1890
   viewable here, downloadable here: Volume I and Volume II or see GoogleScholar.
   In Chapter 2, “The Functions of the Brain”, James quotes John Hughlings Jackson: “Brain and mind alike consist of simple elements, sensory and motor. 'All nervous centres,' says Dr Hughlings Jackson, 'from the lowest to the very highest (the substrata of consciousness), are made up of nothing else than nervous arrangements, representing impressions and movements... I do not see of what other materials the brain can be made.'”
   In Chapter 6, “The Mind-Stuff Theory”, bottom of page 173 to 175: “Now take the other cases alleged, and the other distinction, that namely between 'having' a mental state and knowing all 'about' it. ...A faint feeling may be looked back upon and classified and understood in its relations to what went before or after it in the stream of thought. But it, on the one hand, and the later state of mind which knows all these things about it, on the other, are surely not two conditions, one conscious and the other 'unconscious', of the same identical psychic fact. It is the destiny of thought that, on the whole, our early ideas are superseded by later ones, giving fuller accounts of the same realities. But none the less do the earlier and the later ideas preserve their own several substantive identities as so many several successive states of mind. To believe the contrary would make any definite science of psychology impossible. The only identity to be found among our successive ideas is their similarity of cognitive or representative function of the same objects.”
   In Chapter 6, “The Mind-Stuff Theory”, middle of page 179: “Every brain-cell has its own individual consciousness, which no other cell knows anything about, all individual consciousness being 'ejective' to each other. There is, however, among the cells one central or pontifical one to which our consciousness is attached. But the events of all the other cells physically influence this arch-cell; and through producing their joint effects on it, these other cells may be said to 'combine'.”
2. ^ The Organization of Behavior - Hebb 1949
   downloadable here or see GoogleScholar.
   See particularly Chapter 4 “The First Stage of Perception: Growth of the Assembly”, starting on page 60. For example, first paragraph:
   “This chapter and the next develop a schema of neural action to show how a rapprochement can be made between (1) perceptual generalization, (2) the permanence of learning, and (3) attention, determining tendency, or the like. It is proposed first that a repeated stimulation of specific receptors will lead slowly to the formation of an 'assembly' of association-area cells which can act briefly as a closed system after stimulation has ceased; this prolongs the time during which the structural changes of learning can occur and constitutes the simplest instance of a representative process (image or idea). The way in which this cell-assembly might be established, and its characteristics, are the subject matter of the present chapter.”
3. ^ A review of cell assemblies - Huyck and Passmore 2013
   doi: 10.1007/s00422-013-0555-5 downloadable here or see GoogleScholar.
   Page 1, start of Abstract: “Since the Cell Assembly (CA) was hypothesised, it has gained substantial support and is believed to be the neural basis of psychological concepts. A CA is a relatively small set of connected neurons, that through neural firing can sustain activation without stimulus from outside the CA, and is formed by learning. Extensive evidence from multiple single unit recording and other techniques provides support for the existence of CAs that have these properties, and that their neurons also spike with some degree of synchrony. Since the evidence is so broad and deep, the review concludes that CAs are all but certain. CAs are found in most cortical areas and in some sub-cortical areas, they are involved in psychological tasks including categorisation, short-term memory and long-term memory, and are central to other tasks including working memory.”
4. ^ Memory engrams: Recalling the past and imagining the future - Josselyn and Tonegawa 2020
   doi: 10.1126/science.aaw4325 downloadable here or see GoogleScholar.
   Start of background: “The idea that memory is stored as enduring changes in the brain dates back at least to the time of Plato and Aristotle (circa 350 BCE), but its scientific articulation emerged in the 20th century when Richard Semon introduced the term 'engram' to describe the neural substrate for storing and recalling memories. Essentially, Semon proposed that an experience activates a population of neurons that undergo persistent chemical and/or physical changes to become an engram. Subsequent reactivation of the engram by cues available at the time of the experience induces memory retrieval. After Karl Lashley failed to find the engram in a rat brain, studies attempting to localize an engram were largely abandoned. Spurred by Donald O. Hebb’s theory that augmented synaptic strength and neuronal connectivity are critical for memory formation, many researchers showed that enhanced synaptic strength was correlated with memory. Nonetheless, the causal relationship between these enduring changes in synaptic connectivity with a specific, behaviorally identifiable memory at the level of the cell ensemble (an engram) awaited further advances in experimental technologies.”
5. ^ Integrative Activity of the Brain: An Interdisciplinary Approach - Konorski 1967
   I have not been able to get a copy of this book, so my knowledge of the contents is based on the review in reference 6 below.
6. ^ Looking back at Jerzy Konorski’s book “Integrative Activity of the Brain”, 45 years after - Srebro 2013
   downloadable here or see GoogleScholar.
   First page, under the heading “How 'Integrative Activity of the Brain' was received”: “To some disappointment of the author, the book did not receive a worldwide attention. Indeed, only a handful of reviews of 'Integrative Activity of the Brain' appeared in scientific journals following the publication.”
   Page 455, under the heading “A brief description of the book”: “...the central concept of the proposed theory was idea of 'gnostic units' as a high level of representation of sensory stimuli by a single neuron or a small network of neurons.”
   
7. ^ Genealogy of the “Grandmother Cell” - Gross 2002
   doi: 10.1177/107385802237175 downloadable here or see GoogleScholar.
   Bottom of page 512 (the first page of the paper) under the heading “Jerzy Konorski’s Gnostic Units”: “Although unknown to Lettvin, the grandmother cell idea had actually been set out in detail as a serious scientific proposal a few years earlier by the Polish neurophysiologist and neuropsychologist Jerzy Konorski in his 'Integrative Activity of the Brain' (1967), [see reference 5 above] a wide-ranging set of speculations on the neurophysiology of perception and learning.”
8. ^ Ibid. Genealogy of the “Grandmother Cell”
   See top-right of page 512 (the first page of the paper) under the heading “Jerry Lettvin and the Birth of Mother and Grandmother Cells”: “Jerry Lettvin originated the term ‘grandmother cell’ around 1969 in his M.I.T. course titled ‘Biological Foundations for Perception and Knowledge.’”.
9. ^ ^ Gnostic cells in the 21st century - Quiroga 2013
   downloadable here or see GoogleScholar.
   This paper is an excellent review looking back over the history of the proposal and discovery of, and various names for, networks of neurons in the human brain that represent concepts.
   Conclusion on page 469: “Concept cells are the link between perception and memory; they give an abstract and sparse representation of semantic knowledge that constitutes the building blocks for declarative memory functions. So, concept cells may then be the neural base for our thoughts, for leaving aside countless details and extracting meaning, for creating new associations and memories. They encode what is critical to retain from our experiences. ... Concept cells are not quite like the gnostic cells that Konorski once envisioned but they may be a key neural substrate for the power of human reasoning.”
10. ^ Single Units and Sensation: A Neuron Doctrine for Perceptual Psychology? - Barlow 1972
    doi: 10.1068/p010371 downloadable here or see GoogleScholar.
    Barlow agrees with Sir Charles Sherrington that James’ ideas about single pontifical cells (see last quote of reference 1 above) cannot be correct, and that many cells in a network are needed.
    Page 390, under the heading “12.3 Pontifical cells”: “Thus the whole of subjective experience at any one time must correspond to a specific combination of active cells, and the 'pontifical cell' should be replaced by a number of 'cardinal cells'. Among the many cardinals only a few speak at once; each makes a complicated statement, but not, of course, as complicated as that of the pontif if he were to express the whole of perception in one utterance.”
11. ^ ^ Godel, Escher, Bach - Douglas Hofstadter Penguin Books UK 1979
    This fascinating book, despite its title, is mostly about the functioning of the brain, although it covers many other subjects as well.
    See page 340 onwards for a discussion on symbols.
    Page 347 under the heading “Funneling into Neural Modules”: “One possible alternative to the grandmother cell [i.e. a single cell representation] might be a fixed set of neurons, say a few dozen, at the thin end of the 'funnel', all of which fire when Granny comes into view. And for each different recognizable object, there would be a unique network and a funneling process that would focus down onto that network. ... Such networks would be the 'symbols' in our brains.”.
    Page 348 under the heading “Modules Which Mediate Thought Processes”: “Thus we are led to the conclusion that for each concept there is a fairly well-defined module which can be triggered - a module which consists of a small group of neurons - a 'neural complex' of the type suggested earlier.”
    Page 359 under the heading “Can One Symbol Be Isolated?”: “Is it possible that one single symbol could be awakened in isolation from all other? Probably not. Just as objects in the world always exist in the context of other objects, so symbols are always connected to a constellation of other symbols.”
    Page 360 still under the same heading: “The network by which symbols can potentially trigger each other constitutes the brain’s working model of the real universe, as well as of the alternate universes which it considers (and which are every bit as important for the individual’s survival in the real world as the real world is).”
    Hofstadter also uses the term (tongue-in-cheek) “superhypercomplex cell” for a grandmother cell (page 344).
12. ^ The brain from inside out - Gyorgy Buzsaki 2019 Oxford University Press
    doi: 10.1093/oso/9780190905385.001.0001 or see GoogleScholar.
    In Chapter 4, entitled “Neuronal Assembly”, page 92 under the heading “Reader Mechanism-Defined Cell Assembly”: “By the 1990s, my group and other laboratories worked out methods to record sufficiently large ensembles of neurons so that we could address a critical question: What determines the precise timing of a neuron’s spikes? We hypothesized, as did Hebb, that the recorded neurons take part in different assemblies, but not all assembly members are active on each occasion. We also reasoned that members of the assembly should work together within a measurable time window. ... So we tried to determine the time window within which neurons can best predict the timing of each other’s spikes. By varying the analysis window experimentally, we found that the best prediction of spike timing of single hippocampal neurons from the activity of their peers was when the time window varied between 10 and 30ms.”
13. ^ ^ Time-locked multiregional retroactivation: a systems-level proposal for the neural substrates of recall and recognition - Damasio 1989
    doi: 10.1016/0010-0277(89)90005-X downloadable here or see GoogleScholar.
    This paper (which is quite difficult to make sense of) describes a theory of how neurons can store information about entities and events in “convergence zones” and how they can have meaning when recalled. The paper does not mention that these could be symbols for concepts, which is odd considering the subject of the next reference below, published in the same year. It does touch on where and how these convergence zones might be created, for example page 43, last paragraph: “The key to regionalization is the detection, by populations of neurons, of coincident or sequential spatial and temporal patterns of activity in the input neuron populations.”
14. ^ ^ Concepts in the Brain - Damasio 1989
    doi: 10.1111/j.1468-0017.1989.tb00236.x (download not available).
    Page 25, second sentence: “The neural basis for the reconstructed representations is the activation of many separate neural population ensembles, distributed in various cortical regions. They constitute a related set because the activations occur within the same time-window and are co-attended.”
    and Page 26, last sentence: “The mechanism that permits coactivation of representations depends on devices I have called convergence zones, which are ensembles of neurons that 'know about' the simultaneous occurrence of patterns of activity during the perceived or recalled experience of entities and events.”
15. ^ Convergence and divergence in a neural architecture for recognition and memory - Meyer and Damasio 2009
    doi: 10.1016/j.tins.2009.04.002 download not available but see GoogleScholar.
    Page 377, first paragraph: “The convergent-divergent connectivity principle exists at all levels of the processing hierarchy: just as first-order CDZs inscribe records of the combinatorial arrangement of knowledge fragments in early cortices, second-order CDZs inscribe records of the combinatorial arrangement of first-order CDZs, and so forth.”
    Figure 2 on my explanation of a symbol schema and its main linkages.
    This paper uses the terms “map”, “image” and “neural representation” all meaning the same thing (see reference 16 below for a comment on this).
16. ^ Self comes to mind: constructing the conscious brain - Antonio Damasio Pantheon Books USA 2010
    Page 56: “I used to be strict about using the term image only as a synonym of mental pattern or mental image... Throughout this book, I use the terms image, map, and neural pattern almost interchangeably.”
    In general, I find Damasio’s books very readable and informative, but I find it strange that this particular terminology is both inconsistent and misleading; an 'image' is not the same as a 'map' in either technical or non-technical language: both are forms of representation, but a map is a diagrammatic representation and an image is a visual representation. There are some places in the book where it is suggested that a map is something used for actions, whereas an image is used for visual recall, but in other places this usage is not differentiated. I also think the term 'neural pattern' is vague and not helpful - does it mean a pattern in neural connections, or in neural signals, or both, and what is the pattern?
17. ^ The strange order of things: Life, feeling and the making of cultures - Antonio Damasio Pantheon Books USA 2018
    For example, page 61: “The presence of images meant that each organism could create internal representations based on its ongoing sensory descriptions of both external and internal events.”
    Page 89: “All the words we use... are made of mental images. This is true of the auditory images of the sounds and letters and words and inflexions and of the corresponding visual symbol/letter codings that stand for those sounds... Also present in mind are countless other images regarding any object or event that pertain and describe their constitutive properties and relationships.”
    Page 89-90: “The collection of images typically related to an object or event amounts to the 'idea' of that object or event, the 'concept' of it, the meaning of it, semantics of it.”
    Damasio also sometimes uses the term 'map' as if it is only formed when conscious access to it is required. Pages 74-75: “At some point, long after nervous systems were able to respond to many features of the objects and movements that they sensed, both outside and inside their own organism, there began the ability to map the objects and events being sensed. ... Now stretch your imagination and think of maps not just of shapes or spatial locations but also of sounds..., and also think of maps built from touch, smell or taste. Stretch the imagination a bit more and think of maps built from the 'objects' and 'events' that occur within the organism... The depictions produced by this web of nervous activity, the maps, are none other than the contents of what we experience as images in our minds.”
    Damasio is suggesting here that 'maps' are only created much later in evolutionary terms than the ability to recognise and react to internal and external features or influences. But how were these early organisms able to recognise and respond to these features if not by creating (simple) types of 'maps'? Any mechanism that records and remembers a stimulation, so that it can be responded to at a later time, is surely already a 'map', or symbol schema, as I call such things? When self-awareness evolved, this did not mean that the structure of maps had to change.
18. ^ On Intelligence or On Intelligence - Jeff Hawkins with Sandra Blakeslee St. Martin’s Press USA 2004
    For example, middle of page 69: “...the cortex creates what are called invariant representations”.
    Middle of page 153: “The sum of all these mechanisms allows the cortex to learn sequences, make predictions, and form constant representations or 'names', for sequences. These are the basic operations for forming invariant representations.”
19. ^ ^ Invariant visual representation by single neurons in the human brain - Quiroga, Reddy, Kreiman, Koch and Fried 2005
    doi: 10.1038/nature03687 downloadable here or see GoogleScholar.
    Second paragraph: “The subjects were eight patients with pharmacologically intractable epilepsy who had been implanted with depth electrodes to localize the focus of seizure onset. For each patient, the placement of the depth electrodes, in combination with micro-wires, was determined exclusively by clinical criteria.”
20. ^ Brain Cells for Grandmother - Quiroga, Fried and Koch 2013
    doi: 10.1038/scientificamerican0213-30 downloadable here or see GoogleScholar.
    Page 31, first paragraph under the heading “In brief”: “For decades neuroscientists have debated how memories are stored. That debate continues today, with competing theories - one of which suggests that single neurons hold the recollection, say, of your grandmother or of a famous movie star. The alternative theory asserts that each memory is distributed across many millions of neurons. A number of recent experiments during brain surgeries provide evidence that relatively small sets of neurons in specific regions are involved with the encoding of memories.”
    Page 33, second column, end of first paragraph: “Concept cells may sometimes fire to more than one concept, but if they do, these concepts tend to be closely related.”
21. ^ Concept cells: the building blocks of declarative memory functions - Quiroga 2012
    doi: 10.1038/nrn3251 downloadable here or see GoogleScholar.
    From the abstract, page 587: “Intracranial recordings in subjects suffering from intractable epilepsy - made during their evaluation for an eventual surgical removal of the epileptic focus - have allowed the extraordinary opportunity to study the firing of multiple single neurons in awake and behaving human subjects. These studies have shown that neurons in the human medial temporal lobe respond in a remarkably selective and abstract manner to particular persons or objects, such as Jennifer Aniston, Luke Skywalker or the Tower of Pisa. These neurons have been named 'Jennifer Aniston neurons' or, more recently, 'concept cells'. I argue that the sparse, explicit and abstract representation of these neurons is crucial for memory functions, such as the creation of associations and the transition between related concepts that leads to episodic memories and the flow of consciousness.”
22. ^ Concept Cells through Associative Learning of High-Level Representations - Reddy and Thorpe 2014
    doi: 10.1016/j.neuron.2014.10.004 downloadable here or see GoogleScholar.
    Page 249, first paragraph: “Concept cells are highly selective neurons that seem to represent the meaning of a given stimulus in a manner that is invariant to different representations of that stimulus. For example, a single neuron in the human hippocampus was found to selectively respond to several different pictures of the actress Halle Berry, even when she was disguised as Catwoman, the role she played in one of her movies. The same neuron also responded to the letter string 'HALLE BERRY' but not to other letter strings. Later studies showed that these 'concept cells' were also activated when stimulus information was provided in other sensory modalities, for example, hearing the name of a person spoken aloud.”
23. ^ Cognition through the lifespan: mechanisms of change - Craik and Bialystok 2006
    doi: 10.1016/j.tics.2006.01.007 downloadable here or see GoogleScholar.
    See for example page 132, under the heading “Lifespan changes in representation”: “It is generally agreed that humans encode and store relevant aspects of the external world and that these internal systems of knowledge representation are organized hierarchically and have evolved phylogenetically.”
24. ^ Grandmother cohorts: Multiple-scale brain compression dynamics during learning of object and sequence categories - Stephen Grossberg 2016
    doi: 10.1080/23273798.2016.1232838 (download not available, although see GoogleScholar).
    This paper is a follow up to papers published in 1976-80 that described the Adaptive Resonance Theory (ART), a neural network model of brain learning. A grandmother cohort is a set of networks that each represent different categories of an object or concept.
    From the final paragraph on page 26: “...ART category learning mechanisms can enable the learning of specific and invariant object categories, and the learning of list chunks that represent sequences of items that are temporarily stored in working memory. ...The categories that are learned by these mechanisms tend to be compact, involving small numbers of cells or cell populations, even perhaps grandmother cells as a limiting case. Balanced against this property, however, is the fact that networks of such categories are often needed to represent multiple aspects of an object or of a stored sequence of events. Such networks are called grandmother cohorts to emphasize the balance between compression and distribution that is needed to learn predictive representations of the world in space and time.”
25. ^ Natural speech reveals the semantic maps that tile human cerebral cortex - Huth, de Heer, Griffiths, Theunissen and Gallant 2016
    doi: 10.1038/nature17637 downloadable here or see GoogleScholar.
    Supplementary Information downloadable here.
    See also accompanying video and interactive tour.
26. ^ Categorization and Concepts - Goldstone, Kersten and Carvalho from Volume 3, Chapter 8 of Stevens’ Handbook of Experimental Psychology and Cognitive Neuroscience - Fourth Edition 2018
    doi: 10.1002/9781119170174.epcn308 downloadable here or see GoogleScholar.
    Page 276, under the heading “What are concepts?”: “... a concept is a mental representation of a class or individual and deals with what is being represented and how that information is typically used during the categorization”.
    Page 278, under the heading “What do concepts do for us?”: “... concepts function as filters. We do not have direct access to our external world. We only have access to our world as filtered through our concepts. Concepts are useful when they provide informative or diagnostic ways of structuring this world.”
    and “Concepts are cognitive elements that combine together to generatively produce an infinite variety of thoughts.”
27. ^ ^ Sparse Representation in the Human Medial Temporal Lobe - Waydo, Kraskov, Quiroga, Fried and Koch 2006
    doi: 10.1523/JNEUROSCI.2101-06.2006 downloadable here or see GoogleScholar.
    Page 10234, second paragraph, concludes that several million neurons represent a typical stimulus, and that each neurons fires in response to 50-100 distinct representations. However, these figures are calculated using a number of assumptions that could in fact be very different from the assumed values.
28. ^ Degeneracy and complexity in biological systems - Edelman and Gally 2001
    doi: 10.1073/pnas.231499798 downloadable here or see GoogleScholar.
    Page 13765, bottom left, last five lines: “Typically, neurons in the brain receive synaptic input from many thousands of other neurons so that in humans, for example, there are approximately one billion synapses in each cubic millimeter of brain gray matter. The pattern of connectivity created by so many synapses within such a tiny volume of tissue in one animal could not be genetically prespecified and, thus, must be unique to each individual. Indeed, the degree of degeneracy in neural connectivity probably dwarfs that of any other system discussed in this review.”
29. ^ Hidden in plain view: degeneracy in complex systems - Mason, Dominguez, Winter and Grignolio 2015
    doi: 10.1016/j.biosystems.2014.12.003 downloadable here or see GoogleScholar.
    Abstract, page 1: “Degeneracy is a word with two meanings. The popular usage of the word denotes deviance and decay. In scientific discourse, degeneracy refers to the idea that different pathways can lead to the same output.”
    Page 4: “Degeneracy is present across multiple scales of brain organization - from neurotransmitters and synapses, through cortical and subcortical regions...”
    and: “for ... brain networks to be functionally robust, structurally different elements must be able to provide similar outputs, that is, they must be degenerate. A degenerate network is thus able to provide reliable output even when the input is neither labeled nor identical across occurrences, and when the input is presented in a noisy environment with a large number of competing stimuli, which overwhelmingly characterizes the conditions under which the brain operates.”
    See also concluding remarks on page 5.
30. ^ Degeneracy and redundancy in cognitive anatomy - Friston and Price 2003
    doi: 10.1016/S1364-6613(03)00054-8 downloadable here or see GoogleScholar.
    This short letter explains the difference between degeneracy and redundancy. Degeneracy is necessary for redundancy, but degeneracy is more than redundancy, it is a relationship between structure and function.
31. ^ Abstract and concrete concepts have structurally different representational frameworks - Crutch and Warrington 2005
    doi: 10.1093/brain/awh349 downloadable here or see GoogleScholar.
    Two-thirds of the way through the Summary: “...abstract concepts, but not concrete concepts, are represented in an associative neural network.”
32. ^ Recognition-by-Components: A Theory of Human Image Understanding - Biederman 1987
    doi: 10.1037/0033-295X.94.2.115 downloadable here or see GoogleScholar.
    This psychological study concludes (Page 127, top of second column) that there are around 30,000 readily discriminable concrete objects, but this does not mean that any single individual has actually come across all of these and therefore created a symbol schema for each. The methodology uses the concept of geons and seems a reasonable estimate as far as it goes, but only includes one category of items in my list of things that must be represented by symbol schemas.

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