RE: SUO: The Plumbing Theorem(s)
Pat and John
The plumbing analog was an excellent set of examples to bring to light
dyads and triads. Tetrads however we may need if we desire to shorten the
path of flow between different layers and some more elaboration is in order
but I will quit while I'm ahead.
On the lighter side:
Since I plan to remodel my house this summer I am looking for some good
plumbers and electrician. I would love to hire you guys. However I'm not
sure about 'triple cable' and '2-conductor Romex'.
Keep up the great work.
and
John thank you for the pointer on the early 20th century intuitionists.
Edward
US Army, CECOM, RDEC
Command and Control Directorate
Tel: (732) 427-4122 DSN 987-4122
Fax (732) 427-3440
E-Mail edward.dawidowicz@mail1.monmouth.army.mil
-----Original Message-----
From: pat hayes [mailto:phayes@ai.uwf.edu]
Sent: Wednesday, March 21, 2001 12:11 PM
To: John F. Sowa
Cc: standard-upper-ontology@ieee.org
Subject: 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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