Re: Using the RM for ADTs

On Jul 7, 11:43 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:

> Here is a case in which what defines something is how it stands in relation
> to other things rather than just a collection of properties.

This idea is fundamental to the axiomatic approach to mathematics.

One can draw a parallel with the natural numbers which can be defined using the Peano axioms. This treats the natural numbers as an abstract set. As such one could use abstract identifiers for each of the elements, and define them though their relation to each other.

ISTM that we don't use abstract identifiers for the natural numbers because we don't need to. We can instead encode them using a physical representation that maps to the number of successor operations from 0.

Evidently "tricks" like this cannot be used in more complicated examples.

> ...,it is intuitively obvious
> that each component or node should still be distinguishable from all other
> components and nodes in the same template;

I disagree. Circuits may contain a lot of self-symmetry. One can investigate this mathematically by considering the group of automorphisms in the obvious way.

As an example, consider a circuit consisting of 12 x 1 ohm resistors and 8 nodes wired up in the manner of a 3-dimensional cube. All the resistors are indistinguishable and all the nodes are indistinguishable, even in the context of the circuit that they appear in.

Some circuits have more symmetry than others. For example, one can partially break the symmetry by changing only one of the resistors. This affects the group of automorphisms. Received on Wed Jul 08 2009 - 16:42:31 CEST