The same room. The same arrangement. Mr Blottisham appears invigorated, as though the previous difficulties have only sharpened his resolve.
Blottisham:
I believe I have now grasped the relation between the systems.
Quillibrace:
That would be a first.
Blottisham (undaunted):
They are, of course, aspects of a single underlying system.
Quillibrace:
No.
Blottisham nods, as though confirming a suspicion.
Blottisham:
Yes, yes—you will say no. But it is unavoidable. We have biological, social, and semiotic constraints all operating within the same instantiation. They must therefore belong to a single unified structure.
Quillibrace:
They do not.
Blottisham:
But they clearly interact.
Quillibrace:
They do not.
Blottisham leans forward.
Blottisham:
Then they must at least be layered. Biology at the base, society above it, language above that.
Quillibrace:
No.
Blottisham:
Very well—reversed, then. Meaning first, then social structure, then biological realisation.
Quillibrace:
No.
A pause.
Blottisham:
You leave me very few options.
Quillibrace:
I remove only the incorrect ones.
Elowen speaks gently.
Elowen:
You are trying to relate the systems by placing them in the same dimension.
Blottisham:
Where else could they be?
Elowen:
They are not in a shared dimension. They are orthogonal.
Blottisham sits back.
Blottisham:
Orthogonal. Yes. I had wondered when that word would appear.
Quillibrace:
You were hoping it would clarify matters.
Blottisham:
It usually does.
A brief silence.
Blottisham:
Very well. Orthogonal means independent. So the systems do not affect one another.
Quillibrace:
No.
Blottisham:
But that is what independence means.
Quillibrace:
Not here.
Blottisham exhales.
Blottisham:
Then what does it mean?
Quillibrace:
It means that the constraint structures are non-reducible to one another.
Blottisham considers this.
Blottisham:
So they are separate.
Quillibrace:
No.
Blottisham closes his eyes briefly.
Blottisham:
Independent, but not separate. Non-reducible, but co-present. This is becoming unnecessarily intricate.
Elowen:
Only because you are trying to place them somewhere.
Blottisham gestures impatiently.
Blottisham:
Let me try to make sense of this. In a single instantiation, all three systems operate simultaneously.
Quillibrace:
Yes.
Blottisham:
They do not interact.
Quillibrace:
They do not cause one another.
Blottisham:
They do not belong to a single system.
Quillibrace:
Correct.
Blottisham:
They are not layered.
Quillibrace:
Correct.
Blottisham pauses.
Blottisham:
Then in what sense are they related at all?
Quillibrace:
They are jointly constrained.
Blottisham seizes on this.
Blottisham:
Ah! Then there must be a higher-order constraint system that governs them all.
Quillibrace:
No.
Blottisham sighs.
Blottisham:
You cannot deny every attempt at unification.
Quillibrace:
I can deny every incorrect one.
Elowen leans forward slightly.
Elowen:
You are treating “jointly constrained” as if it required a common source.
Blottisham:
Does it not?
Elowen:
No. It requires only that the selections across systems are mutually compatible within the same instantiation.
Blottisham frowns.
Blottisham:
So the systems do not connect to one another, but their selections must align?
Quillibrace:
Not align.
Not contradict.
A pause.
Blottisham:
That sounds suspiciously like alignment.
Quillibrace:
It is considerably weaker.
Blottisham taps the table thoughtfully.
Blottisham:
Let me attempt an analogy. Three different maps of the same territory—biological, social, and semiotic.
Quillibrace:
No.
Blottisham:
But that is precisely what this is.
Quillibrace:
It is not.
Elowen interjects.
Elowen:
That analogy assumes a shared underlying territory.
Blottisham:
And we do not have one?
Quillibrace:
We have instantiation.
Blottisham:
Which is the territory.
Quillibrace:
No.
Blottisham laughs softly.
Blottisham:
Then it is difficult to say what it is.
Quillibrace:
Yes.
A brief silence.
Blottisham:
Very well. No maps, no territory, no hierarchy, no interaction, no unifying system. What remains of orthogonality?
Quillibrace:
Distinct constraint geometries co-actualised in the same instantiation.
Blottisham nods slowly.
Blottisham:
And these geometries do not overlap.
Quillibrace:
They do not reduce to one another.
Blottisham:
But they must intersect somewhere.
Quillibrace:
They intersect in the instantiation.
Blottisham brightens.
Blottisham:
At last! A point of intersection.
Quillibrace:
Do not make it a point.
Elowen smiles.
Elowen:
It is not a place where the systems meet. It is the condition under which their selections are simultaneously viable.
Blottisham pauses, then nods.
Blottisham:
So orthogonality means that each system defines its own constraint space, and these spaces do not collapse into one another, even though their selections must be compatible in each instantiation.
Quillibrace:
Acceptable.
Blottisham leans back, satisfied.
Blottisham:
Then we have preserved both unity and difference.
Quillibrace:
We have preserved neither.
Blottisham looks startled.
Blottisham:
What, then, have we preserved?
Quillibrace:
Constraint.
A quiet settles.
Blottisham (after a moment):
It is doing a great deal of work.
Quillibrace:
It is the only thing doing any work.
Elowen glances between them.
Elowen:
And the only thing that allows them to remain distinct without separating.
Blottisham considers this, his earlier confidence now tempered.
Blottisham:
I shall resist the urge to unify them.
Quillibrace:
You will not.
End of Dialogue IV
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