Draft Essay here EssayDraft
Concepts of interest
The angular defect "What is non-Euclidian space? The space that Gauss, Bolyai, and Lobachevsky discovered, hyperbolic space, is the space that results from replacing the parallel postulate (Euclid’s Elements) by the assumption that for any line, there are not just one, but many parallel lines through any given external point. One consequence, as Gauss wrote (Taurinus, is that the sum of the angles in a triangle is always less that 180 degrees, by a number Gauss called the angular defect. Another, the one stumbled upon by Wallis, is that similar triangles do not exist. The two are related, for the angular defect varies with the size of the triangle. Larger triangles have greater angular defects: smaller triangles are more nearly Euclidian. In hyperbolic space, the Euclidian form is approachable but not attainable, like the speed of light, or your ideal weight. Though but a minor change in a simple axiom, the alteration of the parallel postulate produced a wave that propagated through the body of Euclidian theorems, changing each and every one that pertained to the shape of space. It was as if Gauss had removed the glass from Euclid's Window and replaced it with a distorting lens."
Similar Triangles in real space
Euclid's Window by Leonard Mlodinow p.121 (it is time to put this book away I think) -what are some local examples of this exponential shift. Do architects attempt to attain the Euclidian form? Are there parallels to the human defect or human imperfection? Could it be a metaphor for what is real and what is not? Euclidian being utopian and Non-Euclidian being real - defective being real
IngerSays : I don't know if metaphor is the word you are looking for here. Maybe you could tackle this one from the angle (sic) of representation and "real". I like the ideas about imperfection, are we imperfect? What is the perfect human? In what way do you think human "impection" might effect their experience of architecture?
JessText: This is great. I thought perhaps I could look at how the change in space (being only an abstract analytical tool) affect other abstract concepts in art and architecture that was generated at the time. Whether or not this shift could be read as a return to defective celebration. How this shift could become a visual as well. Perhaps the image of curved space busting through it's architectural, euclidian envelope. Is this what happened in art? Did artist's feel (at the turn of the century) that they could also burst out of there euclidian envelopes and explore a more defective side of expression. I might try drawing these curved junctions. Also this idea of the Euclidian form being nearly attainable at the infintesimal, how when you begin to zoom out, you might begin to see the greater curvature.
Defect n. - a deficiency; an imperfection.
Synonyms - inequality, inferiority, decrement, deficit, shortcoming, requirement, insufficiency, imperfection erroneousness, delectability, fallibility
Here I need a potent local observation (like Lani's clever Yellow Peril example) if it is to go anywhere. Please edit this if there are any suggestions or criticism for me.
IngerSays: Maybe try looking at Howard Raggatt's work, Storey hall has some richness with respect to math theory. Also some of his writing on knots and malapropos
Also there is a danger of stepping into the realm of fashionable nonsense through abusing the sophistication of the mathematics.
IngerSays: I think the danger they are pointing up is it is pointless it is used as a way of saying nothing while appearing to say something. I have to say that I think D and G are being more slippery then that (and they never ask you to accept it as "truth", unlike some others). However the temptation to effectively say absolutly nothing while appearing to say something profound is one to be avoided for sure.
-The powers of 10 this seems to be wholly related to scalability in an abstract form. Could scalability be an analytical tool or architectural intervention (Alice in wonderland - trying to get through a door that is too small)? What is the relationship of scalability to the defect? Is scalability defective - I have argued that in terms of text it is? And that in the realms of the infinitesimal and monumental there are defects. But still it seems a mute point at this stage until I find something to test it on.
Affect in the evolutionary sense. That evolution can be non-linear. re: "mating Game" Similarly technology is non-linear. Is evolution defective, in the sense perhaps that you can over evolve, as Inger said, to the point of extinction.
IngerSays: Defective or Affective, that is the question.
Am I defective in writing this crap? Don't answer that one!
IngerSays: At least you have done your homework Jess!
Liveness- Salam Pax's blog??? Let me think.
Visual Essay
God is in the detail
Or in the refect
The consequences of Curved Space
Distributed Architecture
It is difficult to assess the impact of the angular defect on architecture because in the scheme of things, architecture remains in the infintesimal realm on earth, it could be explored through the subtle "curved space busting through the euclidian envelope" in the detail (wall joining roofetc) so that the greater implications of this curved void could start to be expressed in the entire building. But in this way it remains a (not particularly constructive) metaphorical and aesthetic. However 2000 years from now when we a constructing in outerspace the impact of the defect will be blatant.
An interesting avenue that could parralel it's use in architecture is the evolution of telescopes. The main difference between telescopes now (please exceuse my very basic knowledge) and telescopes twenty years ago is firstly, that they are electronic rather than optical, but secondly that they are arrays, a matrix of sensors. This makes them non-euclidian in the sense that they are not nodes but planes, they are multi-focal. They are distributed.
The very Large Array
link to the sacred http://psycho-ontology.net/sacred/