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has anyone applied golden mean

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Greetings,

Has anyone applied to the golden mean to bed design? Is it a concept that is yet useful to permaculture? I realize that it is a principle long used in architectural applications. Are any of these applications specifically useful in terms of the perme framework? Thanks for any insight! Rickster

Rick Freeman

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Irene Kightley

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Rickster, we use when we're building but I've never thought of using it to shape the raised beds.

For our house roof :

For our chicken shed :

It's an interesting question ! I wonder how using it would affect anything apart from the aesthetics of the bed - I'm off to have a look and see if I can find anything out about it.

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Irene! Most. Beautiful. Chicken. Shed. EVER!

Rickster, go find the book The Power of Limits. It will blow your mind on how the golden mean is used in nature. I think you'll get a lot of inspiration there that will go farther than the basic rectangle.

The golden mean was used to addres what "pleasing to the eye" is. But the book goes into structure as well, and math and pattern. It's in EVERYTHING, and sure it is worth consideration re permaculture.

This book is in my top 10 life changing books.

http://www.amazon.com/Power-Limits-Gyorgy-Doczi/dp/0877731934
Product Description(quote from Amazon)
One of the delights of life is the discovery and rediscovery of patterns of order and beauty in nature—the designs revealed by slicing through a head of cabbage or an orange, the forms of shells and butterfly wings. These images are awesome not just for their beauty alone, but because they suggest an order underlying their growth, a harmony existing in nature. What does it mean that such an order exists; how far does it extend? The Power of Limits was inspired by those simple discoveries of harmony. The author then went on to investigate and measure hundreds of patterns—ancient and modern, minute and vast. His discovery, vividly illustrated here, is that certain proportions occur over and over again in all these forms. Patterns are also repeated in how things grow and are made—by the dynamic union of opposites—as demonstrated by the spirals which move in opposite directions in the growth of a plant. The joining of unity and diversity in the discipline of proportional limitations creates forms that are beautiful to us because they embody the principles of the cosmic order of which we are a part; conversely, the limitlessness of that order is revealed by the strictness of its forms. The author shows how we, as humans, are included in the universal harmony of form, and suggests that the union of complementary opposites may be a way to extend that harmony to the psychological and social realms as well.

My Blog, Natural History and Forest Gardening
www.dzonoquaswhistle.blogspot.com
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posted 14 years ago

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Another fascinating angle on this is origami. There was a great show on PBS about using origami in science and design, I'm sorry I can't remember the title. Basically they are applying origami to thinking about theoretic physics, etc(well, among other things). It has an unusual intersection of design, process, pattern, thought, aesthetic, etc and is the hot "new" way to think.

For instance, solving the problem of how to pack an airbag and have it unfurl in a second was VERY difficult. The person who came up with the solution used origami.

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here's the PBS show
http://www.pbs.org/independentlens/between-the-folds/

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Irene, Wyldthang, thanks for your responses. Irene, in regard to the roof, is slope (rise over run) defined by the ratio? Wyldthang, I'll definitely be on to that book. A friend/mentor intro'd me to it back in the 90s in a seminar on forestry and aesthetics. At the time, I let it go (as my interests were elsewhere), but I'm tuned in, now. Also, I'll watch the vid asap. I really appreciate this information.

Brenda Groth

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i did early on but it is basically a visual thing rather than a practical thing, if you are fussy about design then you might want to do it..but mine all filled in with more and more plantings and i just abandoned the entire idea of using it.

Brenda

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Just off the cuff I would say there's not so much application so much functionally in laying out a garden(though aesthetics is certainly it's domain there), but rather perhaps for predicting future growth and expansion of plants, shade etc. Trees are something that need extra consideration for future size. That prediction deals with fractals, and fractals do indeed go back to the golden mean.

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Wyldthang, thanks again. Interesting response on the fractals. Lots of work being done with fractals on modeling tree dispersal (regen) in forest stands. Also, I do understand your argument on function. I need to look into it more before I agree or disagree, but I definitely won't dismiss your hunch. I'll keep ya posted.

Joel Hollingsworth

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An interesting point on the golden mean:

It is one option in the toolbox for describing an intricate physical structure (like an organism) in a small amount of information (like a set of genes).

IMOO, it doesn't really shine unless the relationships that generate the ratio are important to the function of the system in question. For example, a sheet of paper might be folded or cut in half an unknown number of times, and it makes sense that it should have a similar aspect ratio to other sheets of paper, so that our customs for using paper can still operate on the enlarged or reduced scale.

If you have a system like Mel Bartholomew, where garden beds are sub-divided into regularly-shaped plots down to an un-specified size, the sensible options I'm aware of are squares, rectangles scaled to the golden ratio, and equilateral triangles. I don't see an advantage to the rectangles here, though, because the long direction of the rectangle switches each time you scale up or down.

"the qualities of these bacteria, like the heat of the sun, electricity, or the qualities of metals, are part of the storehouse of knowledge of all men. They are manifestations of the laws of nature, free to all men and reserved exclusively to none." SCOTUS, Funk Bros. Seed Co. v. Kale Inoculant Co.

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Interesting point, Joel. Lots to be said for Euclidean forms, of course. That more or less describes my current garden, though it's not designed in relationship to the golden ratio. But, I'm interested in moving towards irregular shapes determined more by everyday foot-travel routes, practical (habitual) access, and use -- zones... as well as "sector" considerations... and site considerations (terrain, alternative uses, etc.)... But, I would like to compliment direct access with a low path-to-bed ratio (area) (but, I lumber like an ox and like plenty of path)... for example I am experimenting with dendritic patterns.

When I have time, I want to look into this a tad more. I've heard of a golden-ratio based spiral that sounds intriguing. (I'm not particularly spellbound by spirals, but I notice that several people employ them, as did Mollison. But, that's off-topic.) I'd like to know more about that, and see what else might be useful. Perhaps none of it, in a practical sense.

I'm interested in the book Wyldthang recommended and will read it when time permits. But... the days are long and I have much to do. Thanks for the comments.

Irene Kightley

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Rickster,

As you say, the days are long and the winter's the time to reflect on great stuff like this !

To answer your question about our roof, we've tried to use the golden mean in any decision we had to make regarding shapes and distances between them but we've based a lot of heights and forms on local architecture because we want to make our house look as though it's old and "belongs" in it's site.

Our beds and paths as wyldthang says are shaped more for functionality.

I had to look up "dendritic patterns" and I've come to the conclusion that that's how my beds function. My potager is on a slope and I use that as a way of allowing the compost at the top of the slope to flow down into the paths to keep them clear. The area at the top is wide to allow for wheelbarrow turning then the paths become narrower towards the bottom of the slope as the vegetation has grown out from the beds - their size depends on the use the paths get from us, five dogs and fifty or so chickens.

This is the compost from the goat shed at the top of the hill:

The chickens and I disturb the compost and it flows downwards like a river :

Me, the dogs and the chickens decide where we want to walk to get where we're going and the beds are raised on sloping areas to keep the soil in and flatter where the slope is gradual :

The paths get narrower and narrower as the zones become woodland :

I realise now that I make my beds following the size and shape of the paths which have developed from using them to get somewhere - something I never realised before.

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Irene, those beds are beautiful. Speaking of beautiful, my friend and mentor (forestry and planning) hypothesized a functional relationship between our aesthetic sense and our sense of "healthy" or "functional" forest structure (which might be helpful in designing a treatment or target stand). Come to think of it, he introduced me to the idea of the golden mean during a seminar on forestry and aesthetics. In relationship to this statement, "I make my beds following the size and shape of the paths which have developed from using them to get somewhere," I wonder if aesthetics don't have a strong influence on where we choose (unconsciously or consciously) to walk -- in a decision between paths or in an environment without paths -- or where we choose to plant, other factors notwithstanding.

OK, coffee break is over. Enjoy the day.

PS, I just now checked out your website. You've created a beautiful homesite and a nice website.

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Rickster wrote:
Irene, those beds are beautiful. Speaking of beautiful, my friend and mentor (forestry and planning) hypothesized a functional relationship between our aesthetic sense and our sense of "healthy" or "functional" forest structure (which might be helpful in designing a treatment or target stand). Come to think of it, he introduced me to the idea of the golden mean during a seminar on forestry and aesthetics. In relationship to this statement, "I make my beds following the size and shape of the paths which have developed from using them to get somewhere," I wonder if aesthetics don't have a strong influence on where we choose (unconsciously or consciously) to walk -- in a decision between paths or in an environment without paths -- or where we choose to plant, other factors notwithstanding.

OK, coffee break is over. Enjoy the day.

PS, I just now checked out your website. You've created a beautiful homesite and a nice website.

If you follow deer paths they always make nice ones, both functionally and aesthetically--from a human's point of view, I think the paths they make are nice wandering rambles which results from browsing as they go, and also having to be able to have good field of vision for predators.

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Rickster wrote:
Interesting point, Joel. Lots to be said for Euclidean forms, of course. That more or less describes my current garden, though it's not designed in relationship to the golden ratio. But, I'm interested in moving towards irregular shapes determined more by everyday foot-travel routes, practical (habitual) access, and use -- zones... as well as "sector" considerations... and site considerations (terrain, alternative uses, etc.)... But, I would like to compliment direct access with a low path-to-bed ratio (area) (but, I lumber like an ox and like plenty of path)... for example I am experimenting with dendritic patterns.

When I have time, I want to look into this a tad more. I've heard of a golden-ratio based spiral that sounds intriguing. (I'm not particularly spellbound by spirals, but I notice that several people employ them, as did Mollison. But, that's off-topic.) I'd like to know more about that, and see what else might be useful. Perhaps none of it, in a practical sense.

I'm interested in the book Wyldthang recommended and will read it when time permits. But... the days are long and I have much to do. Thanks for the comments.

hey! pictures please!

Anonymous

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This is an interesting thread, I like the part about creating pathways after discovering were you will walk.

BUT can someone please explain "The golden mean"? I have not heard of this before

Irene Kightley

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This is good site for some information on the golden mean and ratios Dianne :

http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

Don't anyone let the geometry put you off, keep looking at the photos and diagrams and you'll see why it's important.

This is a simpler one I've just found :

http://goldennumber.net/goldsect.htm

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Thanks Irene,

I think I do remember this now from art class.
D

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@ Diane, thanks for these links!
@wyldthang, I'll post pics asap. My battery charger had died so I'm w/o camera temporarily. (Replacement charger costs barely less than the entire camera, which itself retails for far less than it did when I bought it. What a world.) I'm assuming you want photos of my typically Euclidean garden?

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Rickster wrote:
@ Diane, thanks for these links!
@wyldthang, I'll post pics asap. My battery charger had died so I'm w/o camera temporarily. (Replacement charger costs barely less than the entire camera, which itself retails for far less than it did when I bought it. What a world.) I'm assuming you want photos of my typically Euclidean garden?

yup

now I'm going to check out your foresty link

rose macaskie

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I had a teacher at art school who was crazy about the golden mean and spent his time counting sunflower bits and such, activities that made me a bit impatient though i liked his paintings and he was nice. He got run over by a bus which killed him. That is not to say that i could not get into it myself one day. Does not it get not it fairly complicated and varied so it gives people a fair amount of lee way.
The only architectural idea I remember is that the height of you with one arm held up is good for doors, and the reason for using such a measurement is that human heights are agreable they don't dwarf you. I like to keep things from looking narrow, in the house at anyrate, just to keep conscious of the importance of things not looking narrow and oppressive.
My grandmother said, put paths were people make them, if you don't you will just be flying in the face of what happens and is likely to go on happening. Seems like in life i fly in the face of the paths others make, on the mental plane at anyrate. rose macaskie.

Anonymous

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Actually it was Irene who provided the links.

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@Diane, yes, I see. Thanks.
@Irene, Thanks for the links!

Emerson White

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Just because it shows up again and again that doesn't mean it has any advantages. In development many times one cell will have some change occur, then it will stimulate the cells next to it, and the patches will get bigger and bigger, each patch stimulating one about as long as it is wide. If you do that you will follow the Fibonacci sequence and get Phi as a result. But your bed isn't going to be an iterative spiral. Any well tended garden bed or bee hive will produce well, regardless of any magic numbers evoked or not evoked.

If you look at what makes a garden bed or a chicken house, or an orchard, or any of the things that humans make you will notice that their wild counterparts follow the golden ratio no better than chance. The golden ratio is only up held really within the tissues of living things. If you have some iterative process that you follow for designing your system Phi will have a good chance of coming out, but forcing the system to look like phi in order to garner some sort of advantage in an interplay with nature is a bit like building a bamboo tower in hopes that a plane will land and carry cargo, it's going about it backwards.

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So Rickster,
I'm not a math person, in fact I hated doing this formula in Art class, so I cheated by guessing at the configurations & points & ratios, I was lucky that I kind of have an eye for "the Golden flow" so I still passed the course.

If math were something I had an aptitude for I might be very into this, I can surely understand that you see value in it.
I would be interested in hearing you tell us what you get out of using this formula (or principles there of) ?

Do you feel like it is more than the fact that, perhaps even on the deepest levels, our minds tend to be pleased by theses configurations?

Do you feel like it give your space a more natural flow?

Is it something like the feelings folks get when the Feng Shui of a space is really good?

Are there structural benefits when you use it in building?

rose macaskie

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i just did not like the paintings that use the golden rule like claude lorrains paintings that put m eoff the golden rule. I quite likes the idea.
I should like claude lorrains painings they are of the decidiouse woods that i so like in real life. i suppose constable is even better at that. .
the landscapes painted in art are important, people do change landscapes for asthetic reasons or because they want to produce such and such an impression though ugly, whether you like it or not, so it is hiding your head in the sand to say i don't think asthetics is seriouse and so i will not use it to promote healthy farming methods.
i think people here want to look northern european for example and so are crazy about beeches and don't like meditereanean trees that need less water.
I do like Pierro de la Franchescas paintings, and he is as big on the golden rule as claude lorraine is. He is a favourite painter of mine but i dont like his painting the flagelation the one teachers most use ton use to when they were talking of the golden rule with. On that sort of subject i much prefer the crucifixion of Grunewald. or the crucifixion of Ucello. with its weird and unhinging color a ziggy lines of perturbed vegetation and people who are also agitated and ziggy looking, all that a picture of extreme violence should be, perturbed. The picture i like of Pierro de la Francescas is his baptism of christ for example, I imagine everyone but very turbulent people would love that picture, full of light, calm and airey.

The only bit of the golden rule i know of is the sequence of numbers that is part of it, in which you add the preceeding figure to the last figure in your list to get the next figure . I will tell it for those who have not done art.
It starts o i suppose and then 1 and the third figure is 1 because one and zero is 1 and goes on to 2 because one and one is two and then three because one and two is three, the next number is five one and two are five, etc. 1, 1, 2, 3, 5, 8. this ladder of numbers gives It gives according to its followers the ratio in which snail shells get bigger and if you are drawing the space between lamposts going away down a road in the distance, as percieved by a person standing in the middle of the road not in reality , the space between each lampost reduces in that ratio in a drawing were the distances lamps seem to get smaller each time.so the distance between the first and second post may be 8 and between the second an third 5 etc.,

I decided to pass history of art by concentrating on the things i liked and not things that at that stage did not interest me. There were lots of things that did.
i don't specially like the design of sunflowers how the seeds spiral into the centre though i dont believe that everyone should like what i do so it could be fantastic for another person. much though i do like spirals as in spiral herb beds and spiral piers, the last totally impractical , maybe not for growing seawed between the spirals .
I agree with diane keest that some things please us maybe rounded shapes please us at some deep level because of cultural experience that has engraved an expectation of pleasure on us from things shaped like that, like apples and peaches and the curves of the body if the starry eyed don't mind the mention of bodies.
A spiral is an energetic form like a spring it talks of energy. These things have so many sides to them that it is hard to know which one has appealed to us. hindu painters use th espiral more than we do. ,S forms strike me as gracefull the arebesques of Mattise for example bottecellis painting have s lines in them. they can be energetic as are tadpoles tails.
It may depend on your experience, whether you saw art you liked or did not like influenced by the golden rule.
I like fat rooms, i paint lines round the walls or the top part of the wall in a different color in places that are narrow to make it look as if they only come up to the line aren't half as high as they really are and therefore not half as narrow when it is height that makes th e place look narrow. On th eother hand i get the garden thoroughly overcrowded and constricting so i just forget my own rules.
There are probably structural benefits or at least, if some idea makes you investigate you are likely to discover things of strusctural importance because you are looking for them in new places, in plants for example. agri rose macaskie .

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Wow Rose, that's a lot of great info., I'd enjoy seeing some pic of the paintings posted here.

Have you seen it used or used it yourself for gardening of landscaping or building?

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Here's a little video portraying the beauty of the fibonacci numbers and how they relate to spirals and the golden mean, and also how they are used in nature.

http://vimeo.com/moogaloop.swf?clip_id=9953368

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rose macaskie

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dianne keast, yes i have a plcae to try out my ideas limited by my strengeth, pretty good for a woman of fifty five, money and the short time i am there so i cant carry out all my ideas quickly. I have mostly just tried to plant trees and get them through the first dry summers. If you don't plant trees quickly you wont see them grow so they come first. I seem to be addicted to buying trees so is brenda groth.she is more so. I am now trying vegetables not easy if you weekend occasionally in a place that is so hot an dry in summer except this summer that is rainy i wonder what has happened in the garden.? I reckon it will take me about five years to learn to grow vegetables. If i was there all the time it might be quicker.

I put in some swales last year. and this. It is suprisingly easy to pull earth towards you to make a flat space on a slope, easier than digging earth out of the ground. I have noticed some wetness that never used to be there in one place below the hill with swales on it my garden is all slopes it is a ravine, so maybe springs do begin to appear if you put in swales. If i build i may remember the golden rule and try to get it in a bit.
the hut in the photos at the begining o fthis thread had the two squares in the dooor the upper and lower that are the one and one of the first part of the golden rule sequencei suppose
and the other bits of the house must be proportional have the areas the size of two squares and another of three squares.

The ranaiscance pictures like, "The Birth of Venus" of Boticelli and the his picture of "Spring" have some very dreamy poetic qualities that make them especially memorable that where inspired by a crazy reainaiscance philosophy called neoplatonism. The storm by Georgione may be were inspired by them too as are lot of pictures. No one really know what Georgiones picture is about. Neoplatonism is not much appreciated as good philosophy now but the paintings are apreciated. It inspired great art.
I don't know how great the golden rule is as a true engineering force or canon of beauty but anything that pushes humans out of learnt patterns to creative search can get us finding out usefull things.
We are at one moment brilliant and at other we get bogged down, not with the whole of past ideas but with some part of them that thas lost its vitality, our cleverest moments blinds us to our stupididity in other moments. We see our cleverness so clearly that our stupidity takes us of guard.
Buckminster Fuller found that the hexagonal or the triangle were a strong forms, i don't know if the golden rule pushed him to think more about them i have not studied him much, hexagonals appear in nature in honey combs for example. He said the native americans using the force of diagonals in their tents, if my memory serves me. Hexagonals and diagonals exert pressure against each other so each hold the other up, whilst square things are simlpy one thing piled on top of another, beams on posts, they are not a equal counter force like two diaingonal bars of the same length at the same angle that lean against each other as the sticks of a native american tent do. The roman arch uses the rounded diagonal in upper corners to strengthen the structure.
Buckminster Fuller says verticals and horizontals are not really a strong form and if you think we do need to put in some diagonals between corners to strengthen up our pergolas. The idea that we all should live in tents of Buckminster Fullers was echoed in the film I like a lot, "Mars Attacks", the nice young hippy heroe of the fim suggests we could all start right, after the destruction by the marcians, by living in tents this time. Which is a joke because of our nature which makes his hopeful bid for modest living on our part sound ridiculouse.
Talking of modest living, I say the native iamericans had kilometres of land variouse places in which to put their tents overlordship or use of a lot of places and objects and animals though they had an idea of iquality with animals. It is us who do with very little gained with a lot of work in exchange for warm water proof houses. rose macaskie

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Wow Rose you are a bank of knowledge!!

Interesting stuff!

I thought I had paid attention in art history but clearly I would have learned more if I had a teacher like you.

I think if my mother had better health she too would be addicted to planting trees she just loves them & taught us to love them too.

As for growing your veggies, I grow lettuce in boxes in the shade on my porch, its a good way to get started & easy for me to care for because its right by the door. We find that square foot gardening is pretty easy for us, we stay pretty busy with other stuff so not much time for a garden, yet it is important to us so we find a way to grow some of our own food every year.

This winter we are going to try a hydroponic window farm & see how it does her with our cold dark winters. I'm already wondering how far the plants will need to be from the glass to prevent frost damage.

I've never done anything like a swale before, never had land to try it on.

As always Rose your post is illuminating.

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One use of golden mean in interior design - the usual height for chair rail molding on an 8 foot tall wall is at 3 feet, leaving the upper part of the wall at 5 feet so it follows the 3, 5, 8 sequence.

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@ Diane, I'm really not sure about any of these questions... but:

Do you feel like it is more than the fact that, perhaps even on the deepest levels, our minds tend to be pleased by theses configurations?

Perhaps. That was definitely Alan's theory. (Mentor and friend.) But, he retired before he could study it. I'm still considering the question but won't ever have the means to do primary research. (That domain is under tight regulation.) I'd like to know more. Perhaps our minds being pleased is an outcome of another determinant this is related to plant propagation and morphology (a possibility that this math stuff speaks to). It would be interesting to see a spatial, analytical comparison of a forest stand after I've marked and treated it, an untreated stand with a history of fire suppression, and an untreated stand with a history of frequent fires (in-line with it's natural fire regime).

Do you feel like it give your space a more natural flow?

I'm not yet that strong on it... but I would (weakly) hypothesize such.

Is it something like the feelings folks get when the Feng Shui of a space is really good?

Perhaps. That statement would be consistent with the theory that our aesthetic sense is structured. I tend to believe that it is structured by evolution (genetics) and by culture... (similar, _maybe_, to Chompsky's grammatical structures, work he did in the 40s and 50s before going to "Orwell's problem"... but for another thread, another forum).

Are there structural benefits when you use it in building?

Some say yes. I don't know.

@ Rose: whether or not aesthetics plays an important role in garden design is still an open question, to me, but my hunch is that it should and does for the reasons above. But... only a hunch.

btw, it's a simple rule: b is to a as a is to a+b. The ratio has a value of 1.61803399.

I also have a hunch that if such a rule is applicable, it will be so in ways not discussed in this thread, particularly designing rectangular beds in mathematical sequence (resulting from values), as suggested by Emerson.

@Emerson: I don't think the claim is that the GR is applicable to gardening or farming because it shows up repetitively in nature. I've never read nor heard that claim. Using the GR certainly doesn't depend on the claim. Also, I have been looking for the use of the term "magic" on this thread or in the literature, but seem to have missed it. Please direct us to the reference! Otherwise, it seems like a veiled "ad hominem" reference.... not particularly helpful or useful to an educated discourse (IMHO). This characterization has been used repetitively to negate ideas that subsequently gained scientific currency... but the history of science is a topic of another forum and thread. Also, following this thread, I'm not sure that anyone has put forth the claim that one should be

forcing the system to look like phi in order to garner some sort of advantage in an interplay with nature.

Perhaps several (many) other ideas are at play for applying the golden mean?

Emerson White

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I don't see how you got an ad hominem fallacy from that, perhaps you could explain a little more. Examples abound on google of people treating phi like a magic number or fallaciously confusing correlation and causation to attribute one or more of their successes to phi.

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@ Emerson: true, not a correct use of the term. However, characterizing the use of the golden mean, as described in this thread, as "magic" is similar to the ad hominem fallacy in that it doesn't directly deal with the argument (in terms of its validity or truth of its assumptions). Rather, it attempts to associate the argument with an unreasonable character just by saying it's so. Best to deal specifically with the argument or hypothesis in question. No one here, on this thread, even remotely suggested the use of the golden mean in any esoteric way or in any magical rituals or anything of the sort, but rather were speculating on whether or not it might be useful for laying out gardens. My interest, specifically, is in using it to design the dendritic patterns I was otherwise designing by eye. So, perhaps you should be more precise in your characterizations and address specific statement in terms of their validity (logic) and assumptions (truth), just to avoid such misunderstanding.

Emerson White

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I think you are trying to force the fit on that fallacy, and that you should let ad hom go and look at other fallacies if you are sure my comment was fallacious, here are two resources that may help you articulate your concerns better.

I will agree that I should have written my post differently, I think that in retrospect you should see the point I was trying to make and why I found it necessary to make it. My mistake was assuming that others had seen and would recognize the intent to increase the production/sustainability/natural/useful nature of a garden plot by invoking magic numbers or building magic shapes (sometimes neopagans do that).

Phi is an emergent property of iteration, iteration can be useful, but iteration is not an emergent property of phi. Trying to get anything but aesthetics out of phi is a fools errand. It doesn't make it easier to weed, or increase the sun to your plants, or make sure airflow happens in the right ratios. When you apply phi from the top down you absolutely miss the important things that phi is associated with.

Phi is absolutely lovely to look at, and a 5 foot long and 8 foot tall trellis will be very lovely to behold, but since 8 foot materials are more widely available in the western world a 4X8 trellis will use fewer materials, and since humans have such short arms 4 foot wide garden beds make sense too. If you are trying to make dendritic patterns then you should focus on reasonable branch lengths and internodal lengths for what your task is, using phi will not make it any easier to reach in and get to the parts or make it any more structurally sound or make the elements fit together any better. If you are making a picture with a dendritic pattern to hang on a wall making one that fits in a frame that uses the golden ratio might be a good idea, but that will not increase the utility of the patterns for anything other than aesthetics.

Again, going to the number phi has very little utility outside of aesthetics.

Anonymous

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Thanks Rickster for taking the time to answer my questions.

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You're welcome, Diane. The questions are still open, to me. And, I'm not too quick to relegate aesthetics to the junk heap of impractical concerns. The question of the utility of aesthetics is still open and interesting, as long as one can think outside of the false dichotomy between aesthetics and utility. (That's true in forestry and planning discourses, to be sure.) We've discussed a really small corner of the golden ratio, which shouldn't be dismissed as a land-use design tool merely because of a misunderstanding or muting of an interesting question.

Emerson White

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Who set up a dichotomy?

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