# Re: Using the RM for ADTs

Date: Wed, 8 Jul 2009 23:33:46 -0700 (PDT)

Message-ID: <48a4205b-e46f-4cb7-8c9e-d2a923135c80_at_x5g2000prf.googlegroups.com>

> > 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.
**>
**> They are not indistinguishable. Just pick an arbitrary component lead, and
**> the rest can be described in terms of it because each has different paths to
**> it.
*

Well, obviously some things won't be indistinguishable anymore after you "just pick" one. Picking one means distinguishing it from all others.

Note that distinguishing one of the nodes is insufficient to break all symmetry. Call it "top". This immediately distinguishes a node on the opposite corner (call it "bottom"). However there remains 3-way symmetry in the nodes adjacent to "top", and a further 2-way symmetry from any one of these nodes to the next three adjacent nodes as we proceed towards the bottom of this lattice structure.

In your case picking a component lead can be regarded as picking an ordered pair of adjacent nodes. That still leaves a 2-way symmetry as described above. Received on Thu Jul 09 2009 - 08:33:46 CEST