I had this idea, that maybe one way of looking at the problem is through calculus. For instance, consider the Fibonacci sequence:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34….

∑* x* = ∑ *(x-1)* + ∑ *(x-2)*

where ∑*x* is the Fibonacci number;

or maybe you could just rewrite the formal solution into the equation itself which is: n+(n+1)

Then take a look at the classical labyrinth (Cretean):

It’s almost a visual expression of a Fibonacci sequence, where *n* is the center of the labyrinth and *n+1* is the additional expansions of route towards the solution/route of *n+(n+1)*.

So I was thinking, this is a really fantastic example of how architecture of the mind/intangible is constructed visually. Was there any other theorems I could apply, where the geometry produced could be reduced to equations?

Of course, yes. Behold one of my favourites — the binomial theorem!

The thing about binomial is that it isn’t really expressed as a limit or set, it’s expressed as a total area (because the formula for binomial is to distribute the powers i.e.

*(a+b)* power *n *where* n* can be any real number….. Since it expresses an area and not a route, it isn’t a labyrinth or maze but an object. Although if you were to express the limits (outer shell) of all it emcompasses it would be like Ka.power.(k-1)b where k is the size of set

So I was thinking, is it possible to express the model of Pathways in the form of equations? Because right now I have all this discrete parts, and maybe being able to express it as a formal equation might give an idea of how it would really work potentially… and also tie nicely with the extinction concept. (the only difficulty is that typing equations are bloody hard…. where is all those super/sub-script when you need them?)

I touched on this briefly, but maybe a way to rethink is to prototype it as an equation. Can all the ideas I have be reduced to pure equations? I mean, I already know how it looks like. I know it in terms of units, but missing the forest for trees. So I think it might be good to aspect some of this out.

So maybe start with something simple;

*A* = initial website i.e. google, facebook, yelp, wtv

the successor to *A *can be expressed as A U {A} where it contains all elements of A+A’s elements{}. It will be denoted as *B*.

therefore, the set size of one intersection = *A ∩ B*

assume f(t) >0 where t = time;

so to express the extinction rule….

c = counter, or 365.25 x 25

therefore….

(*c*-1) = !(*A ∩ B*)

since the counter counts downwards everytime an intersection is **not** made

therefore…

*t* = (c-1) limit–> f(A *∩ B)*

where t is the range (hyperbola) between the limits of (c-1) and f(A *∩* B)

If I can figure out the set size of one intersection, maybe I can work out all the possibilities of elements within an intersection etc etc etc and figure a way to combine all of them to a reduced equation? yes? as a prototype?

Otherwise I’ve been reading a lot of Borges’ and trying to figure out what to do next for thesis. I’m personally excited about adding the extinction process in (needs to be refined) but so far here’s what I’ve come up with:

**the project will only exist if it can prevent it’s own extinction**

**therefore, it will be evaluated based on expansion**

rationale:

1.** if a need exists, then it exists** i.e. if it never reaches critical mass in the early beginning, it goes extinct. also: if the technology for webgl becomes unnecessary or obsolete (i.e. Internet Explorer) then it will also go into extinction.

2. **if it remains itself, then it exists** i.e. something ZG said earlier (in my interview of him) that the revolutionary always becomes re-appropriated or absorbed into the capitalist machine. For instance, Google started as the alternative web media against giants like Yahoo! and Microsoft but now it has become the very monopoly it tried not to be.

3. **if it becomes extinct, then it is a sign of progress** this is an idea I’ve been toying with for a while, that technological extinction is a sign of progress i.e. a signifier for a change in age, or a new movement appearing. For instance the early version of facebook is friendster, and friendster is similar to an ‘end of era’ much like archeological ruins….. it also ties nicely with Deleuze, which is when something is fully actualised it is dead. (Simondon also makes a similar claim, via the crystallisation process)

So in a way, it’s like the way people plan product life cycles – planned obsolescence.

**Secondary rules:**

1. a counter is inbuilt into the system so when it hits zero it will automatically become extinct.

2. new pathways must be opened for the timer to be stopped

3. if no path is opened in a day, the count will start (n – 1)

4. there is no reversal or count upward.

Okay it’s 2.30am…. I think I need sleep!!!