ONT Re: The Unsinkable Notion Linear
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HP = Howard Pattee
JA = Jon Awbrey
JA: I know the meaning of the word "linear".
HP: My final point was that no matter how neat and linear the symbol structures
may be (DNA, texts, and all that) their functions (interpretations, meanings)
are generally nonlinear. That is, we can no longer look at one nucleotide in
DNA, one amino acid residue in a protein, one neuron, or one word in a sentence
(or one of three massive bodies) and make much sense of what they are meaningfully
doing in the context of any intepretant system.
JA: Much as I love puns, I simply cannot seriously use the
words "linear" and "non-linear" as you just did in this
paragraph -- I would have to use "sequential" or "serial"
instead of "linear" -- as it would wreak utter havoc with
their mathematical uses and cut me off from communicating
with whole communities who use them in mathematical ways.
HP: As much as I love your puns, I think that is serious stubborness.
Sorry, but it's not my stubborness. Nature and Culture are stubborn, all too stubborn.
Being fragile and flexible, I have learned to respect that, and also to work around it.
HP: All your words have several meanings, and I'm sure everyone in your community
knows your lexically loose, elaborate, context-dependent style only too well
to "cut you off" for mere word abuse.
In being so sure, you would be so wrong.
HP: As Jerry says, you can chose to play with yourself and your friends or
you can chose to be part of a larger cultural community that understands
the first meaning of "linear" is "in a line" ("sequential" and "serial"
are not synonyms). To promote your entering this larger community,
I will even give you low-cost insurance against any "utter havoc"
caused by this occasional usage in context. How much do you
think you need?
You and Jerry can fantasize whatever may please you,
but I know the number of disciplinary borders and
badlands that I have had to cross in my lifetime
just to keep true to the integrity of a subject,
and how many "communities of inquiry" (COI's)
in touch with which I still keep to this day.
This one will cause problems,
more grief than it's worth,
and so I will avoid it.
If we are conversing within automata and formal language contexts,
"serial" is usually better for talking about machines "in a line",
"sequential" is usually better talking about strings and strands.
You cannot use "linear" in this context without short-circuiting
to "linear bounded acceptors" (LBA's), the transducer equivalents
of "context-sensitive languages" (CSL's) in the Chomsky hierarchy.
These are tools that I have to use on a regular basis, and so it
is necessary for me to keep my mechanic's and my poet's licenses
both unexpired, but to show the right one for the job to be done.
Here is an example of how the divergent interpretation of a single sign
has obstructed cross-disciplinary communication, indeed, mutual respect,
among engineers, logicians, and mathematicians, and up to this very day.
I append a note that I have often used before, in vain, to explain this:
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Let me try to illustrate the point another way.
Here is is an example of a case where a lack of
respect for the prior use of a single sign,
to wit, the plus sign "+", led to a schism,
first between mathematics and some circles
of logic, and later between mathematical
and logical researchers on one side and
engineers (comm & comp, signal & switch)
on the other. From my own experience,
as late as the 1980's, this one tiny
speed-bump in the road of inquiry
made an obstacle course out of my
projects for cross-field running,
and rendered it nearly impossible
for me to explore the problems or
to use the language of one group
without being totally disdained
and utterly dismissed by the
other.
| Nota Bene. The usage that one often sees, of a plus sign "+" to
| represent inclusive disjunction, and the reference to this operation
| as "boolean addition", is a misnomer on at least two counts. Boole
| used the plus sign to represent exclusive disjunction (or at least,
| an operation of aggregation restricted in its logical interpretation
| to cases where the represented sets are disjoint [Boo, 32]), as any
| mathematician with a sensitivity to the ring and field properties of
| algebra would do. "The expression 'x + y' seems indeed uninterpretable,
| unless it be assumed that the things represented by 'x' and the things
| represented by 'y' are entirely separate; that they embrace no individuals
| in common" [Boo, 66]. It was only later that Peirce and Jevons treated
| inclusive disjunction as a fundamental operation, but these authors, with
| a respect for the algebraic properties that were already associated with
| the plus sign, used a variety of other symbols for inclusive disjunction
| [Sty, 177, 189]. It seems to have been Schröder who later reassigned the
| plus sign to inclusive disjunction [Sty, 208]. Additional information,
| discussion, and references can be found in [Boo] and [Sty, 177-263].
| Aside from these historical points, which never really count against a
| current practice which has gained a life of its own, this usage does have
| a further disadvantage of cutting or confounding the lines of communication
| between algebra and logic. For this reason, we are forced to avoid it here.
|
| Jon Awbrey, "Differential Logic & Dynamic Systems", October 31, 1994.
Now, I only know of two good ways to deal with these brands of problems.
I have argued till now for what my better judgment tells me is the best
way to go -- but that was yesterday, and yesterday's gone -- and so now
I am down to what remains in the runes, which is simply to pay a whole
lot of attention to the whole history of a sign or word, and to notice
the offenses that have accumulated on its rap-sheet. They will recur.
And this insouciant attitude that you can just wipe the slate clean
and start all over again with "whatever appeases reason" (WAR) --
well, it's been tried before. There are reasons it will fail.
Innovations have be upheld by the strongest branches of the
common stock of etymology.
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I hope this explains how seriously I take this issue.
Being an exile is no joke, and in spite of what some
people think, I never risk it unless it is necessary.
Having a parochial little cargo cult of arcane argot,
of special pleadings for common clature, can also be
fun for a while, but it engenders ineffectiveness in
the long run, and the long run is what matters to me.
It is well said, if mutations are outlawed then only
outlaws will evolve -- we all know the risks evolved.
Jon Awbrey
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