An important quality of ‹ob› is that it is a proper mathematical structure. In particular all functions, Of, of ‹ob› are well-defined. This condition of well-definedness accounts for the mathematical and logical straightforwardness of ‹ob› in contrast to typical interpretations of mathematical structures in computational systems.
As much as it preserves the application of mathematics to computational interpretations of ‹ob›, well-definedness creates some difficulties for "natural" manifestations of ‹ob› in computational systems. This note describes the nature of that bind and its relationship to the maintenance of distributed identity among potentially-cooperating manifestations.
The "bind" is illustrated by a simple and appealing function, ob.proc, one that encapsulates arbitrary Obs as individuals. Since encapsulation under ‹ob› is important for manifestation of other structures in ‹ob› itself (and hence in manifestations of ‹ob›), understanding the preservation of well-definedness is crucial to development of principles for Miser extensionality. It appears that there are also implications for the trustworthiness of cooperative arrangements and the "interchange" of Obs (i.e., manifestations) among cooperating Miser systems.
Content
Define well-definedness and illustrate its application to ‹ob›.
Emphasize the case of ob.ap and oApInt.
Allude to the other cases.
- See also:
- Taming ‹ob› Blog
Define it to produce an individual
Define it to be well-defined and a homomorphism to unique individuals. The identity is based on identity or distinctness of the operands of the encapsulation function.
Make them different than any others we have defined.
In the Miser system,
An essential quality
What the rules have to be and how we keep ourselves out of trouble. The ways that oMiser delivers descriptions of Obs, including constructed individuals.
How the identity oracle works. At least, how we want it to work.
The necessity to deliver construction schemes rather than something else, for it to work with oMiser.
The ob.proc function as an example.
The need to communicate the rules of construction, because you can't communicate the individual.
Or can you?
N000901: Distributed Identity for Ob Manifestations, when written
N010200: Identity and Individuals, when written
- Version 0.00: Initial Draft (orcmid)
- Sketch the basic situation and what it implies for the manifestation of Obs with oMiser.
created 2002-10-18-15:46 -0700 (pdt) by orcmid
$$Author: Orcmid $
$$Date: 04-01-06 13:03 $
$$Revision: 9 $