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Date: Sat, 9 May 1992 12:22:53 -0400
From: "Stuart A. Moulthrop"
Subject: Re-posted for Jeff Achter
To: Multiple recipients of list TNC
From: jda@BROWNCS (Jeff Achter)
In-Reply-To: Wes Chapman's message of Thu, 7 May 1992 19:31:52 CDT <>
Subject: topology (was: situated knowledges)

Thanks a bunch to everyone who took the time to reply. I kind of wish we were all in some sort of hypertext net now, or at least had an agreed-upon way of marking up documents. In the absence of such tools, I guess I'll use the standard 'net he-sez-she-sez format. My apologies for whatever intellectual terrorism happens in this process....

Wes Chapman writes (among other things) that

If I understand the way people have been using the term "topology," you've got the etymology wrong--the word as it's kicking around in this forum doesn't come from mathematics, but from mapmaking. A topology is a topographical study of a place over the course of a span of time, with "topographical" being defined as a detailed description of the physical feature s of a place (rivers, mountains, etc.).

That's really interesting. I guess I was way off on which "topology" people were using in this context. And I'd certainly agree that topography has a lot to offer as a metaphor for what happens in navigating a (hyper)textual space. You refer to topology as having a notion of temporality built into it; one watches topography evolve over time. To what extent do litcritters (:-) really wrestle with the text's changing over time? I'm not so much concerned with the fact that our reading of something changes; that, it would seem to me, is well-established. Could you give me some refs to interesting topo(graph)(log)ical analyses?

Martin Rosenberg kindly informs me (I think) that what I'm interested in is correspondence theories. He goes on to say that Derrida is particularly cognizant of the analogical ways in which ideas from other disciplines are used to investigate one's own. For example, again in S/Z Derrida writes:

Allusion, or "suggestion" as Mallarme says elsewhere, is indeed that operation we here _by_analogy_ [orig emph] calling undecidable. An undecidable proposition, as Godel... [219]

I guess that's part of why I find his seemingly naive use of the word topology so abandoning. He doesn't situate his notion of topology clearly in any particularly endeavor, at least not for me. And so what I wind up doing is supplying my own context, and as it turns out that isn't particularly helpful. I'm also not convinced that the topographer's topology is germane.

Definitely, we as symbol-using creatures will always try to relate symbols to each other in creative ways; such slippage is to be expected and highly useful.

I agree that this phenomenon is a result of our society's valuing the "knowledge" we get from the sciences. My only quarrel here is with Martin's phrasing, "our traditional sources of truth and value lack power in our society." In what way is science not a traditional source of truth?

[ Brief aside: Martin writes

Course, correspondences also work. Take for example that great correspodence theory Information Theory. I don't know why the same mathematical formula for measuring entropy in a closed system, also works for measuring the amount of noise in a channel connecting messenger and receiver. It just does.

Information theory is a cool subject. Part of the reason the formulas for entropy work the same is precisely so that info-theory could get a leg up by looking like physics. There are some deep reasons why the systems work the same way. But the particular formulation of information entropy we use is just because it looks like something we've seen elsewhere; there's a way in which it's not necessarily canonical. Indeed, Von Neumann was urged to adopt the use of the word "entropy" in his arguments, as it would confuse and intimidate his opponents... ]

Unfortunately, I have to go attend to some matters in the real (other?) world now, so I'm about to give David Durand's message short shrift. He proposes a couple of topologies on a set of nodes and links in a hypertext system. In the first one we let the open sets be the sets which are 1-linked away from each other, 2-linked, etc. This is certainly a basis for a topology, even though it isn't actually closed under union. But that's irrelevant, I suppose. One of my questions is, do we learn anything from thinking about things that way? Connectivity (from graph theory) may provide some useful language to analyze the "complexity" of the interrelationships, but is that really topology? Who knows. I agree with David that maybe we're just talking about ideas in arbitrary relationships to each other, rather than that induced by some "measure":

However, I was thinking of the second sense of the term, in which we are considering the connections of documents in a hypertext without the3 notion of _any_ coordinate system -- thus I used the term topologizing to denote such an organization -- since the only relations between nodes are defined by the links.

Perhaps the ultimate question is his:

Cool, perhaps, but would this be useful? (BTW does anyone know of work done on rendering of views from inside various spaces using the appropriate non-Euclidean optics? It's too weird not to have been worked on, but I've never seen anything on it...

Too early to tell, I suppose. [BTW, at SIGGRAPH ( = special interest group on graphics) last year, someone had a videotape in which we, the viewer, fly around through a projection of some hyperbolic manifold or other. Is that the sort of thing you have in mind?]



Steady State

In complex dynamic systems just the tiniest of motions
Can soon upset a balance long maintained;
As wingflaps Lepidopteral in South Atlantic oceans
Induce the fury of a hurricane.

I set a word upon the windings of our one-to-one relation,
And from my statement chaos soon evolved.
Now the boundaries are conditioned by the error's propagation.
Can bifurcating functions be resolved?

How quickly we're destroyed if simple nuances of notion
Can soon upset a balance long maintained;
As wingflaps Lepidopteral in South Atlantic oceans
Induce the fury of a hurricane.

I'm sorry, how I'm sorry to erred in my regression.
I only saw the pixels, not the screen.
It was nothing predetermined, just a regular expression;
The whole effect completely unforeseen.

David Porush's response