Paul Cereghino wrote: Physiologically, what exacly is it that a spiral does for a snail, and what does that mean for design.
The logarithmic spiral has the unique property that the curve is everywhere 'similar', differing in size but not in shape. In other words, as the curve rotates through a fixed angle, it grows uniformly in scale. This, and the description above, help us to see what are the fundamental generating mechanisms of such a form. Some things remain constant, for example the angular speed of the curve's tip, and the shape of the curve, while other things, for example the linear (tangential) speed of the tip, change in a well-defined way. We can then generate a form like this by proposing that the deposition of new fabric at the shell's rim follows a growth mechanism that produces these characteristics. A mechanism of this sort that generates a three-dimensional mollusc shell with the cross-section of a logarithmic spiral is as follows: the existing shell rim provides a template on which new shell material is laid down, so it stays the same shape, but the rim is expanded in scale at a constant rate. If, in addition, the growth happens initially to be slightly faster on one side of the embryonic rim than the other, this imbalance is maintained proportionately as the shell gets bigger, and it curves into a spiral. It does not take too much imagination to see that a mechanism like this is a rather 'natural' one to be expected from a creature making a shell that needs to keep pace with its own growth, and doesn't require any mysterious geometrical knowledge or an ability to figure out what on earth equation 1.2 means. The imbalance that leads to spiral growth could come from any source - any imbalance will produce a logarithmic spiral. If there is no imbalance, the shell instead has a cone shape, just as one can find in some species of mollusc.
Burra Maluca wrote:You don't need to know anything about math to appreciate the beauty in this, just watch it and enjoy.
to be expected from a creature making a shell that needs to keep pace with its own growth
Janet Dowell wrote:
I have kept up with the reading, so am very glad for this group....I am motivated to keep up with the schedule! Chapter 5 starts on Sunday...has gone fast so far!
Burra Maluca wrote:
We're actually going to have 'catch-up week' next week. Quite a few people, including myself, seem to be a bit behind on the reading, and chapter 4 has been a bit 'heavy'! Hopefully we can use that week for pulling our ideas together and sharing them. Also it gives any latecomers a chance to catch up, too.
Burra Maluca wrote: Together they make a reticulated network - you can, for the most part, get to anywhere from anywhere.
Ya can't git thar, frum here.
Michael Cox wrote:
I guess overall I've struggled to find the relevance of this chapter because the scale he is talking on seems vastly inappropriate for my conditions ...
I have to say that there were things that Geoff mentioned in the PDC that are in the PDM which I had sort of glossed over when reading but were super interesting when told in narrative form.
Best example? Page 96, Figure 4.26.
"An experienced man lowers his testicular sac into the sea to accurately gauge water mass temperature."
Honestly, I may have glanced at the drawing and the text but it did not make the same impression at all as when Geoff explained that and the reasons for it!
Stuart Davis wrote:
Another example is the spiral galaxy or vortex ring. If Mollison explained the underling law behind why a galaxy is shaped like a spiral, I missed it, given my lack of being able to focus on this chapter. However, a vortex and galaxy shape results from the law of conservation of angular momentum.
Stuart Davis wrote:
I can think of at least one very purposeful good use of a vortex in permaculture - the vortex filter commonly used in aquaponic and pond systems.
Cj Verde wrote:
So here's my question:
If growth is often depicted as a spiral, how is contraction depicted?
Janet Dowell wrote:Is there a link to Chapter 5 up yet? Aren't we at the end of the week for Chapter 5 (e.g. aren't we supposed to start Chapter 6 tomorrow?) Or did I miss something (entirely possible)?
Paul Cereghino wrote:I suspect that most of the "pattern" we put into gardens in pursuit of harmony with nature are actually meaningless to nature. In an intensively managed system like the annual portion of your garden, you are an integral part of the ecosystem, you are the animal causing disturbance to benefit plants with an annual life history strategy, and so the "pattern" needs fits the mental ruminations and movement patterns of that animal that is the disturbance vector (you). If the pattern needs to change, it is because the interaction between you and the system isn't optimal or is leaking energy in some way. I'd look for leaks (water nutrients energy (including your labor)), and then adjust pattern to plug those leaks.