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
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:
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.
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'.
Position is one kind of dimension that is identifiable via a
fixed point, for example: Craig is at such and such an address.
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?
No, its about the relation between object and context in a dynamic
sense. Look at the variability in fixed points here:
Look at what all have in common: Some transformation on a collection,
some closure of that which is transformed and some invariant - the fixed
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