Re: SUO: The Plumbing Theorem(s)
>To answer the questions about dyads and triads as simply as
>possible, I would like to explain the issues in terms that
>anyone can verify just by going down to the basement and
>examining the plumbing.
An excellent analogy for following the graph-theoretic result, but
not one that translates into questions of relational reducibility. If
you look instead at the electrical wiring, you will find that while
triple-conductor cable is often used to save time and copper, you
*can* do it all using 2-conductor Romex.
>Let us suppose that you had the following resources:
>
> 1. Long lengths of water pipe and the option of ordering
> more whenever you need it.
>
> 2. The ability to cut the pipe to any desired length and to
> finish the ends with whatever threading is needed to link
> it with suitable connectors.
I wouldnt recommend threaded iron pipe for water. Use copper with
soldered capillary fittings, or plastic with solvent welding.
> 3. A large supply of dyadic connectors: sleeves, which let
> you link two pipes in a straight line; and elbows, which
> let you link two pipes at an angle (usually a right angle,
> but other angles may be permitted).
>
>With those resources, you can direct water from the point of
>entry into your house to at most one faucet elsewhere in the
>house. You cannot direct the water to any additional faucets,
>bathtubs, showers, or toilets.
>
>But if you were given some triadic connectors (T shape or
>Y shape), you could connect one additional faucet or other
>facility for each triadic connector you use.
>
>Connectors with more than 3 links would be unnecessary.
>A tetrad (+ shape) could be used instead of two triads.
>But if you had enough triads, dyads, and straight pipe,
>you wouldn't need any tetrads, pentads, hexads, etc.
True. Actually they do make tetrads, in the form of a cross, for
convenience in tight spaces, but they are usually only used by
professionals.
Pat
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