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  1. #1
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    Default Metaphorically thinking

    Metaphorically thinking

    We commonly think of metaphor as something like analogy. We are trying to explain something to someone and we say this something new is very much like this other something you are familiar with.

    This is one form of metaphor but there is another metaphor that is automatic and unconscious. The child playing with objects has an experience of collecting objects in a pile. This experience results in a neurological network that we might identify as grouping. This neurological structure that contains some sort of logic related to this activity serves as a primary metaphor.

    The child has various experiences resulting from playing with objects. These experiences result in mental spaces with neural structures that contain the logic resulting from the experience. When the child then begins to count perhaps on her fingers these mental spaces containing the experiences automatically map to a new mental space and become the logic and inference patterns to make it possible for the child to count because counting contains similar operations.

    Primary metaphors are the contents of mental spaces developed in experience and the contents then pass to another mental space to become the bases for a new concept. The contents of space A is mapped to space B to then be the foundation for the new concept at space B. This mapping is automatic and unconscious.

    Many years ago, before

  2. #2

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    All of mathematics, pure and applied, is based on metaphor.

    I believe that is what makes math work so well.

    On a tangential note:
    I recommend this book on embodied mathematics.

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  3. #3
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    Quote Originally Posted by ygolo View Post
    All of mathematics, pure and applied, is based on metaphor.

    I believe that is what makes math work so well.

    On a tangential note:
    I recommend this book on embodied mathematics.
    The co-author of both books is Lakoff.

    The concepts of containment and orientation are essential concepts for mathematics. Closed sets, bounded intervals, geometric figures, etc. utilize containment concepts; angles, rotation, tangents, etc. utilize orientation concepts. Mathematics takes advantage of our normal adaptive capacities; adaptive capacities are those neural structures required to sense and to move about in our world.

    Spatial relationssuch as in, on, above, etc. are necessary for language and for sensorimotor neural control networks. Primitive image schemas (structural frame work or plan)--such as above, which is orientational; such as contact, which is topological; such as support, which is force dynamicThe concepts of containment and orientation are essential concepts for mathematics. Closed sets, bounded intervals, geometric figures, etc. utilize containment concepts; angles, rotation, tangents, etc. utilize orientation concepts. Mathematics takes advantage of our normal adaptive capacities; adaptive capacities are those neural structures required to sense and to move about in our world.

    Spatial relationssuch as in, on, above, etc. are necessary for language and for sensorimotor neural control networks. Primitive image schemas (structural frame work or plan)--such as above, which is orientational; such as contact, which is topological; such as support, which is force dynamic
    Last edited by coberst; 10-20-2007 at 02:18 AM. Reason: mistake made

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    This forum seems to cut all posts off in mid post. Is there some reason that almost all my posts get cut off?

  5. #5
    Protocol Droid Athenian200's Avatar
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    Quote Originally Posted by coberst View Post
    This forum seems to cut all posts off in mid post. Is there some reason that almost all my posts get cut off?
    You have to be careful to make sure you don't use any special (Non-ASCII) characters. Avoid long dashes and fancy quotes, especially. Some apostrophes are "fancy" as well, and have to be avoided. The UTF-8/Unicode support is broken somewhere.

    Anyway, I sort of see what you mean. We take one or more kinds of ideas from a situation we've encountered before, and we apply it to another situation to understand it. We group things based on how we understand other things, and can apply that understanding to other things. But what does that tell us about how we learn? It probably means something, but I'm not sure what.

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    Senior Member Hypatia's Avatar
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    @coberst

    Love your threads. Will respond soon.

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