Dear At and dear LO'ers,
Due to hard work and some days off, this reaction appears with some delay.
My apologies for this.
At de Lange made a wonderful contribution to the "=" sign. Whereas I
mentioned in my original contribution some loose statements ('equal to'
and 'generate'), At extended this further. First he pointed our attention
to the whole (both sides of the sign and the middle where the very symbol
is), than he made clear that the meaning of the symbol is only
understandable if we look to both sides. He also introduced other symbols.
I summarise with the items on both sides to make the meaning clear:
= (equal to) being = being
== (corresponds to) being == being OR becoming
"=" (corresponds to, including change) becoming "=" becoming
We are here very close to the discussion of 'Logic'.
This whole theme of interacting subjects reminded me of still something
else. This is probably a helpful addition to those readers who have some
hasitations with the understanding of the mathematical backgrounds. Let me
spend some words on this other area. It is the area of the thesaurus, the
helpful relational dictionary, known to database searchers in libraries.
Please, if your library has some lierature databases on CD-ROM, consult
the thesaurus. It will open your eyes. I am very fond of the thesaurus of
INSPEC (a database focussed on mathematics, physics and computersciences).
I will give first a simple example.
It is a probable thesaurus term, which means that this word might occur as
descriptor (controlled keyword). The common abbriviation of descriptor is
DE. So
DE precipitation
The word precipitation is in this case a keyword in a database. But as
fresh user of this database, we like to know something more. We need some
explanation (see the very nice contribution of Winfried Deijmann
about VERFLUCHT, LO21712).
Precepitation might be related to several disciplines, e.g. chemistry or
meteorology.
So the thesaurus must give us an extra clue. Therefore the abbriviation UF
is introduced: Used For. Sometimes even a scope note is included. In the
Georef database (mainly earth science literature)
In our example:
precipitation USE 'chemical precipitation' or 'atmospheric precipitation'.
I will use the latter, so the subject or descriptor changed into:
DE atmospheric precipitation
The next level of the thesaurus is RT: Related Terms. These are synonyms
or near-synonyms. But commonly the related terms are much broader
interpreted. It looks nearly to free associations. The thesaurus is ment
te be used as search instrument and could be used very creatively. So we
may find:
RT atmosphere, drainage basin, drought, evapotranspiration,
hydrologic cycle, hydrology, meteorology, moisture, rainfall, retention,
water. (mainly based on the GEOREF-thesaurus)
You see, a variety of terms. Difficult to find the proper mathematical
symbol. Maybe we might use the following (using At's symbols):
(atmospheric precipitation) == (atmosphere + drainage basin + drought +
evapotranspiration + hydrologic cycle + hydrology + meteorology + moisture
+ rainfall + retention + water).
But some readers may say: "You forget the rain and the snow". Well, in a
thesaurus these are so-called narrower terms (NT). Thus:
NT rain, snow, hail
And you will easily think of so-called broader terms (BT):
BT weather
and even a top term (TT)
TT climate
An example from the INSPEC thesaurus looks like:
DE vibrations
SEE ALSO lattice dynamics; molecular vibration; vibrating bodies
UF linear vibrations; modes, vibration
RT acoustic noise; acoustics; damping; earthquakes; elastic waves;
harmonics; lattice dynamics; mechanical oscillations; oscillations;
resonance; vibrating bodies; vibration control; vibration measurement
NT molecular vibration
BT dynamics
I hope you find some new or other thoughts for logic relations and
mathematical symbols. A thesaurus looks like the description of some
thinking techniques used in creativity trainings. Associations, convergent
and divergent thinking.
Therefor, I have played with some other symbols, but I did not succeeded.
The thing is that we need symbols for sentences which have in a language
the following structure:
noun(1) verb noun(2)
The nouns (1 and 2) could be a 'static being', or a 'dynamic being'. But
also, noun (1) could be equal to noun (2) (equal term, ET), or noun (1)
could be either a Broader, or a Narrower term than noun (2).
Thus we could have:
WATER (ET) = H2O (ET)
WATER (BT) > ICE (NT)
WATER (NT) < LIQUID (BT)
WATER (RT) == RAIN (RT) (corresponds to related term)
The verb could be a static relationship (as in the above examples), or it
could indicate a dynamic relationship. But this verb could be further
precised. The dynamic relationship (becoming) could either be an
emergency, or an immergency. So:
^
WATER | ICE (I have tried to compose an arrow upward, indicating an
emergency)
WATER | STEAM (Now it is an arrow downward, indicating an immergency)
V
Now the following, where the nouns could be static or dynamic by
themselves:
FLOWING WATER (dynamic) > RIVER (static, if the river is seen on a
geograohic map)
FLOWING WATER (Dynamic) "=" STREAM (dynamic)
^
FLOWING WATER (dynamic) | (emergency) VORTEX (dynamic)
FLOWING WATER (dynamic) | (immergency) TURBULENCE (dynamic)
v
Well, you may see that I did not have figured out all possible
relationships. The difficulty is that the nouns could be static beings or
becomings, and the relationship could be static or dynamic. If one then
also likes to introduce things like 'smaller' and 'bigger', or emergencies
or immergencies, it becomes very complicated.
The discussion on 'Logic' and the Law of excluded Middle (LEM), or - maybe
- the law of included middle (LIM), is in close relation with all this.
Although I realise that I am not so clear, I thought that it is wise to
share my troubled thoughts with you.
Thank you At for your clear teaching, it generated some extra
turbulent thoughts as you have seen.
dr. Leo D. Minnigh
minnigh@library.tudelft.nl
Library Technical University Delft
PO BOX 98, 2600 MG Delft, The Netherlands
Tel.: 31 15 2782226
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Let your thoughts meander towards a sea of ideas.
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--Leo Minnigh <L.D.Minnigh@library.tudelft.nl>
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