On 2/1/2013 3:52 PM, Craig Weinberg wrote:



On Friday, February 1, 2013 2:29:21 PM UTC-5, Stephen Paul King wrote:

    On 2/1/2013 8:07 AM, Craig Weinberg wrote:


    On Friday, February 1, 2013 12:12:17 AM UTC-5, Stephen Paul King
    wrote:

        On 1/31/2013 6:12 PM, Craig Weinberg wrote:


        On Thursday, January 31, 2013 5:38:28 PM UTC-5, Stephen Paul
        King wrote:

            On 1/31/2013 4:46 PM, Telmo Menezes wrote:
            What's an entity?

                Any system whose canonical description can be
            associated with some kind of fixed point theorem.


        Nice. Interestingly this just came up on another list five
        minutes ago. Some interesting etymology too:

        entity (n.)
            1590s, from Late Latin entitatem (nom. entitas), from
        ens (genitive entis) "a thing," proposed by Caesar as prp.
        of esse "be" (see is), to render Greek philosophical term to
        on "that which is" (from neuter of prp. of einai "to be;"
        see essence). Originally abstract; concrete sense in English
        is from 1620s.

        entire (adj.)
            late 14c., from Old French entier "whole, unbroken,
        intact, complete," from Latin integrum (nom. integer; see
        integer).

         A slightly different meaning when we formalize it... a
        literal entity has a thingness definable by position. A more
        figurative or casual reference could mean like a 'the aspect
        of a presence or representation which emphasizes its closure'.

        Craig
        Hi Craig,

            Position is one kind of dimension that is identifiable
        via a fixed point, for example: Craig is at such and such an
        address.


    Hi Stephen,

    I would tend to consider address just another kind of position
    though. Is there an example of something which fixed point
    theorem addresses which is not a dimension which can be defined
    by position? Isn't the act of fixing a point the same as
    formalizing a position?

    Craig

    Hi Craig,

        No, its about the relation between object and context in a
    dynamic sense. Look at the variability in fixed points here:
    http://en.wikipedia.org/wiki/Fixed-point_theorem
    <http://en.wikipedia.org/wiki/Fixed-point_theorem>

    Look at what all have in common: Some transformation on a
    collection, some closure of that which is transformed and some
    invariant - the fixed point.


Oh, sorry I didn't realize that was a specifically defined term. F-p theorem seems too narrow to me to contain the casual use of 'entity', as x or f(x) is already an entity regardless of any operations of coordination of values. A ghost in a dream can be an entity, or a legal entity can be purely conceptual. Unless you are looking at 'entity' as a mathematical description only.

Craig

Hi Craig,

What ever the entity is, it is its representation that we actually discuss, thus it is 'purely conceptual'. I am going for a broad strokes definition that can be adapted to specific cases...

--
Onward!

Stephen

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