ONT Re: My Dictionary Is Bigger Than Your Dictionary
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| Stand and unfold yourself.
|
| 'Hamlet', Francisco 1.1.2
Aside to Edwina: The bigger dictionary is in French, of course.
HP = Howard Pattee
JA = Jon Awbrey
JA: It's Friday and I'm about as burned out on serious
stuff as I've ever been in this all too brief life,
so -- you have been warned if you read any further.
HP: The simplest case of symbol manipulation in my view is the gene. DNA is copied
sequentially one-base-at-a-time and translated one-codon-at-a-time. This is called
copying, reading, and translating just because it has the form of a language. So far
this is all structural or syntactic activity. Only when the linear sequences fold into
three-dimensional allosteric shapes do we have any biological function, and folding is
not a one-at-a-time sequential (or linear) process, but an everything-happens-at-once
(or nonlinear) process.
JA: Again, you are punning on the word "linear" in ways
that has me doubled and folded over with convulsions,
but I have yet to meet a person who will thank me for
telling them that. You're welcome.
HP: If you do not relax and treat my word usage as you do your own, to wit,
as a normative creative art tinged with personal associations and fraught
with ambiguities I'm afraid your convulsive resources soon will be exhausted.
HP: In the above paragraph I mean by a linear system one that can be usefully viewed
as the sum of its parts. Therefore we often say that linear systems are decomposable.
Guess what; a non-linear system is a system that is not linear. Therefore, we often
say it is not decomposable. I don't think this is an eccentric usage. Most formal
systems try to be linear and nearly succeed. Most physical systems also try, but
usually fail. They are partially decomposable or nonlinear.
JA: Here's some more puns for the kicker, imported from just over the far side
of that exorbitant abridgement over turbulent whatevers, the Puns Asinorum:
JA: Linear. For me personally, the first thing that comes to mind, after all this time,
is a linear function or transformation, to wit, an f that obeys a distributive rule:
JA: f(x + y + z) = f(x) + f(y) + f(z).
JA: So, in some sense or other of the words thus invoked:
JA: linear = distributive = morphism = arrow.
JA: Now, morphisms are notable for being "structure-preserving mappings",
where the particular structure exhibited in the special case above
is the structure known as the "adds" table or the "sum" relation,
a 3-adic relation that is inyoked by means of the "plus" sign "+".
JA: So, accumulating the subtotal so far, and sorting lexicographically, we have:
JA: arrow = distributive = linear = morphism = structure-preservative.
JA: Well, that almost compells me, subject as I am to convulsive compulsions,
to add a few more terms that come to mind, quite freely associative,
however much bound by ironic bands of some unknown associative law.
The following are semantically equivalent in some semse (TFASEISS:
| analogy
| arrow
| distributive
| example
| icon
| idol
| linear
| model
| morphism
| paradigm
| structure-preservative
JA: The briar patch grows thicker at this point ...
HP: Only in the context of formal mathematics would this come to my mind.
There would also come to my mind other formal definitions of linear,
e.g,. having no variable raised to a power, linear dependence, etc.
But I was not speaking in a formal context. You are throwing yourself
into this briar patch. I'm not following you.
JA: All kidding aside, no throwing is required --
this is where I have been living all along.
HP: Beginning with formalism is not healthy for inquiry.
In this particular inquiry, I am not just beginning.
HP: I still do not understand your convulsions over the above informal usage.
Is my general meaning that obscure?
JA: Yes, I'm afraid that it is. As hard as I try, I have no way
of guessing with much chance of success what you mean by the
following words and contrasting pairs of words:
| 1. eccentric >>>--->>> centric?
| 2. indecomposable >>>--->>> decomposable
| 3. informal >>>--->>> formal
| 4. nonlinear >>>--->>> linear
| 5. ??? >>>--->>> physical
| 6. ??? >>>--->>> system
| 7. ??? >>>--->>> sum
JA: All of these are words that I know (what I used to consider as being)
standard customs, definitions, and practices for, but I just cannot
match up any of these interpretations with the way that you appear
to be using them. And I really have tried.
HP: I believe everything I was trying to suggest in my admittedly imprecise statement
can be correctly interpreted by using a dictionary. If they don't "match up" with
any of your interpretations, I can only conclude (1) that you don't agree with the
dictionary usages, (2) that you don't think I have used the words properly in
a sentence, (3) that you don't agree with what you interpret as the meaning
of the sentences, or (4) that you find my sentences meaningless.
Howard, I have ordinary dictionaries, technical dictionaries, textbooks,
web resources, and several years of advanced graduate training in math
beyond a Master's degree in that subject. All of the connections and
definitions stemming from the word "linear" that I outlined above are
routine textbook knowledge. I know the meaning of the word "linear".
HP: I will be glad to elaborate on what I meant, but it will help
if you can identify the obstacle(s).
JA: Maybe it would help to back up and to try to tackle one dimension at a time --
not that I would be dream of conceding to RD on that account! -- for instance,
this dimension that ranges from the "casual" to the "formal", or this spectrum
that reaches from the "formative" to the "formalized", as I have of late come
to re-view it. For me it is not a 2-tomy of either/or, but a continuum, one
that begins with a bit of grit on a grotto wall, the inchoative narration of
the past, the present, or the prospective day's hunt, and works its way up,
bit by bit, to the likes of Lie Algebras and Recursive Functions. From
that long view of it, the difference between what you related to me:
| In the above paragraph I mean by a linear system one that can be usefully viewed
| as the sum of its parts. Therefore we often say that linear systems are decomposable.
| Guess what; a non-linear system is a system that is not linear. Therefore, we often
| say it is not decomposable. I don't think this is an eccentric usage. Most formal
| systems try to be linear and nearly succeed. Most physical systems also try, but
| usually fail. They are partially decomposable or nonlinear.
and what I related to you:
| Linear. For me personally, the first thing that comes to mind, after all this time,
| is a linear function or transformation, to wit, an f that obeys a distributive rule:
|
| f(x + y + z) = f(x) + f(y) + f(z).
is only a matter of style, not substance.
HP: I am disappointed that you think our differences might degenerate to
a mere matter of style. I was quite sure our brains have different
operating systems. I am interested in these differences.
I said nothing about our differences. I said something about the differences
between two samples of text. I write many different sorts of text, so do you.
The differences between these textile samplers, that makes us call one of them
less formal and one of them more formal, are comparative, complex, and relative,
and do not justify drawing any kind of absolutely simple dichotomy. Semiotics
is partly a concern with the transformation of texts from one genre to another.
From my point of view, the account that I gave of what "linear" means is much
clearer, in the sense that it supports effective technical discussion, and so
I prefer it for that purpose. Perhaps you prefer yours for the same purpose,
perhaps you prefer it for some other purpose. A person is not one purpose.
Jon Awbrey
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