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Excerpt from a thematic paper,

Theoretical Support for Making Computer-Enabled Learning Environments the Core of School Curricula


By Carol Caldwell-Edmonds        

January 29, 2002     

Vermont College Graduate Program



Section I: Computer-enabled Metaphors

The VR metaphor for Consciousness


Computers and medical technology made possible by computers are bringing together philosophers and researchers from the “hard sciences”.  Together they search for connections, referred to as the “neural correlates of consciousness”, between subjective experience and the brain. (Metzinger 2000)  In June 1998, cognitive scientists, neurobiologists, and philosophers from around the world attended a conference intended to launch the study of Neural Correlates of Consciousness. Papers published by the participants include one by philosopher Antti Revonsuo in which he offers a Virtual Reality Metaphor for the philosophical concept of the “phenomenal[1] level” of experience.

The phenomenal level of organization can thus be seen as the brain’s natural virtual reality system, a level of organization the purpose of which is to construct a real-time simulation of the organism and its place in the world. This simulation is modulated by sensory information during waking perception, but during dreaming it is realized off-line, by recombining materials from experiences stored in long-term memory. (Metzinger 2000 65)


Revonsuo offers “the dreaming brain” as a model system[2] for understanding the phenomenal level of organization based on extensive empirical data about dreaming. (Revonsuo in Metzinger 2000 64 65)  The model system of “the dreaming brain” allows the phenomenal level of experience to be isolated and studied as follows:  Dreaming demonstrates that sensory input from the body is not necessary for the brain to be able to perceive a scene accurately.  Studies show dream scenes resemble real scenes in the waking world.  Dream descriptions almost always begin with a description of a physical place where the dream occurred, but the sleeping dreamer was obviously not observing the place with his or her own eyes.  Furthermore, while there is an illusion of activity in dreams, no motor output or actual acting out of the events occurs. Studies about dreaming during REM sleep have revealed that while motor commands are active in the brain, voluntary muscles are “virtually paralyzed”.  People suffering from RBD, a REM sleep behavior disorder, do not suppress motor responses and can injure themselves when they act out the experiences they are dreaming about.  (Revonsuo in Metzinger 2000 64-66)  Finally, the phenomenal level of organization is considered isolated in dreaming because the dreamer is aware of not being in the dream scene.  Revonsuo calls this awareness “virtual presence” and likens it to experiencing a technologically-based virtual reality scenario.  A person using a virtual reality system may be in a special suit, room, or wearing special goggles in the real world, but the brain perceives and responds to the virtual world as though the body were present in that place.

Dreaming about an event is not the same as experiencing the actual event, but the imagery and language used to describe remembered dreams point to the idea of an “‘out-of-the-brain’ experience: the sense of presence in and the immersion in a seemingly real world outside the brain”.  (Revonsuo in Metzinger 2000 65) Revonsuo believes the virtual reality metaphor may help to discover the neural correlates of the phenomenal level of organization. Based on his VR metaphor, phenomenal experience may be mapped to chemical states of networked neurons, or to a complex of electrophysiological states, or to certain features of the brain that current technology cannot yet detect or represent.  “Progress in cognitive neuroscience appears to be closely linked to our ability to visualize phenomena with the help of computer technology.” (Ibid. 72 73)

Revonsuo expressly credits the computer technology community with giving consciousness researchers terms like virtual reality.  However, he points out that such terms in their “normal” sense describe the subjective experience of “presence or immersion in multimodal experiential reality”. (Ibid. 65) The terms were not invented for computer science. His observation demonstrates how technology-based metaphors can be used reflexively.  Concepts guide inventions.  The invented technology enables people to use new metaphors.  The metaphors then help redefine the inventors.  A reflexive view of the brain’s creations finds further support in a cognitive science approach to the metaphor of mathematics.


The Grounding Metaphors of Mathematical Thinking

George Lakoff and Rafael Nuņez are two cognitive scientists who teamed up to create a Theory of Embodied Mathematics: a description of mathematical concepts as metaphors that are based on bodily experience.  

One of the great findings of cognitive science is that our ideas are shaped by our bodily experiences—not in any simpleminded one-to-one way, but indirectly through the grounding of our entire conceptual system in everyday life.  The cognitive perspective forces us to ask, ‘Is the system of mathematical ideas also grounded indirectly in bodily experiences? And if so, exactly how?’ (Lakoff and Nuņez 2000 xiv)


The Theory of Embodied Mathematics rests on “4 Grounding Metaphors”, so-called because they ground mathematical concepts in sensory motor experiences of the body.  These “4 G’s” or 4 Grounding Metaphors are: collecting objects, constructing objects from other objects, measuring segments, and motion along a path.  All mathematical ideas arise through blending and symbolization of concepts originating in these grounding metaphors.  Higher-level metaphors are used to further understand our universe mathematically. An example of a higher-level metaphor, “numbers are things that exist”, demonstrates the same reflexive tendency I described in reference to virtual reality systems:

The metaphor Numbers Are Things in the World has deep consequences.  The first is the widespread view of mathematical Platonism.  If objects are real entities out there in the universe, then understanding numbers metaphorically as Things in the World leads to the metaphorical conclusion that numbers have an objective existence as real entities out there as part of the universe.  This is a metaphorical inference from one of our most basic unconscious metaphors.  As such, it seems natural.  We barely notice it.

…What is particularly ironic about this is that it follows from the empirical study of numbers as a product of mind that it is natural for people to believe that numbers are not a product of mind! (Lakoff and Nuņez 2000 80 81 emphasis theirs)


People perceive mathematics, a created abstraction, as something as real in the universe as the planets.  However, Lakoff and Nuņez explain mathematics, not as a set of truths to be discovered, but as a metaphorical language of explanation for our brain’s interaction with the universe.  The content and symbols representing mathematical ideas are what they are because they are the products of an embodied mind. 

Ultimately, mathematical meaning is like everyday meaning.  It is part of embodied cognition.  This has important consequences for the teaching of mathematics.  Rote learning and drill is not enough.  It leaves out understanding.  Similarly, deriving theorems from formal axioms via purely formal rules of proof is not enough.  It, too, can leave out understanding.  (Lakoff and Nuņez 2000 49)


What is taught in grade school as arithmetic is, for the most part, not ideas about numbers but automatic procedures for performing operations on numerals—procedures that give consistent and stable results.  Being able to carry out such operations does not mean that you have learned meaningful content about the nature of numbers, even if you always get the right answers!

There is a lot that is important about this.  Such algorithms [the procedures for performing operations on numbers, described above] minimize cognitive activity while allowing you to get the right answers.   (Lakoff and Nuņez 2000 86)


Lakoff and Nuņez present a theory of embodied mathematics based on metaphors of concrete manipulation of objects, measurement, and movement in space.  In their comments about how math is taught in the early years of school, I sense a call for educators to redirect the emphasis in early mathematical education from the manipulation of symbols to the exploration of concepts.  There are also implications for new ways of understanding how different individuals may construct metaphors differently. 

The process of collaboration between these two scientists, Lakoff from a linguistics background and Nuņez from psychology, taking on the task of creating a new field—cognitive mathematics—highlights an integrated and fluid connectivity that is increasing because of the findings of cognitive science.  Data obtained from several types of brain imaging scans, animal experimentation and cases from brain–damaged human patients in the neurosciences are used by these researchers as their “way of knowing metaphorical mappings work”. (Lakoff and Nuņez 2000 100)  These are the same tools that link the neurosciences with philosophy in the search for neural correlates of consciousness. 

In his introduction to the essay collection, Neural Correlates of Consciousness, Thomas Metzinger writes about his concerns with the cultural ramifications of “subjective experience [as it] becomes technologically accessible, in a way it has never been in the history of mankind.” (Metzinger 2000 8) He expresses a need to integrate both the ideas arising from NCC (Neural Correlates of Consciousness) studies and technologies that make researching the ideas possible in human culture in an inclusive way allowing “a maximum of people free access to them”.  He expresses a concern over the widening gap between the scientific community and less educated people and points to the potential for ideas from NCC research to collide with an image of the human from a religious perspective.  NCC studies are attempting to find the Self, the phenomenal experience of being, the soul, in the brain itself—in embodied cognition.  Metzinger offers no suggestions for how to include himself and his colleagues and their work in the general culture; he intends only to acknowledge the issue.   Understanding and constructive dialog about this kind of information about ourselves is a “meta-goal” for the kind of computer-enabled microworlds of learning I discuss in Section II.  More than a method, a microworld models the process of integrated research and the idea of free access to information that these researchers use and wish to share. 


[1] “Phenomenal” has a specific meaning in philosophy linking the foundation of knowledge to visual perception (DK Illustrated Oxford Dictionary 1998 612) Revonsuo’s VR metaphor points to a link between mental images and visual perception.

[2] A “model system” allows the phenomenon of interest to be (1) isolated from other phenomena with which it may be confused and (2) easily observed and manipulated by researchers.  (Revonsuo in Metzinger 2000 64)