## Steiner, Plato, Golden Mean and the Fibonacci Series

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• Since I was a young and hopeful mathematician I have been fascinated by the Golden mean and the Fibonacci Series, with it s connection to plants and animals,
Message 1 of 85 , Dec 9, 2009
Since I was a young and hopeful mathematician I have been fascinated by the Golden mean and the Fibonacci Series, with it's connection to plants and animals, but I missed a good explanation for the Why.

Plato said that the Golden Mean was the key to the universe, and as the Golden Mean is defined through the Fibonacci Series, it's the characteristics of this series which are interesting.

The formula for the Fibonacci series is
Fn= Fn-1 + Fn-2
where subscript describes the position in the sequence. It's really pretty banal, 5=3+2, how deep is that? The interesting part comes when the formula is used again and again on the result from each iteration. The Golden Mean, Phi = Fn/Fn-1 for n nearing infinity.

The formula is connected to grows, both in connection physical grows of plants, animals, planetary systems, galaxies, but also in breeding, see Fibonacci Numbers and Nature with many good examples and descriptions.

What is the interesting here is that the next value depend on the two preceding values, not the last alone, which explains the grows in plants, that each step always builds on the already existing, and the new is not just a repetition of the previous, it's bigger and better, with a factor of Phi, the Golden Mean.

I read a Theosophic text some years ago where it was stated that in each incarnation man, spiritually seen, was growing with the factor Phi, which I thought was interesting, but I didn't understand why. But the Fibonacci formula tells that one incarnation builds on the two previous incarnations, which following Steiner should be one female and one male incarnation, it sounds reasonable.

The Fibonacci triangles/curve has a connection to more than the physical.

Greetings,
Kim

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html

Self-similar syncopations

And Music.

Pascals Triangle.

Two dimentional geometry and the Golden Section.

The Golden Section.

Some beautiful Math:).

A little history.

• ... Hence the lemon juice-sort of softens it up a bit. ... Probably the key is small pieces. My kids call this the spikey lettuce salad since no one has
Message 85 of 85 , Jan 14, 2010
--- In anthroposophy_tomorrow@yahoogroups.com, dottie zold <dottie_z@...> wrote:
>
> Sounds easy right Val....I know...so okay here's what goes through my mind.....
> Â
> Kale is hard and not really pliable it seems to me.

Hence the lemon juice-sort of softens it up a bit.

>I just saw it at whole foods and even had a taste and I think it did too have cranberries...so, I see they cut it in long strips. and to me it is still hard looking but WF's did not look hard.

Probably the key is small pieces. My kids call this the spikey lettuce salad since no one has figured out(yet)that it is kale and I do serve it with pretty large pieces.

>And then the cranberries...are they candied,Â or not candiedÂ ????

Dried, not fresh or frozen.

>and then the tomoatoes are they cut in slices or are they diced or are they triangled???? I can get the oil and then the pepper and the pine nuts...but how does the kale not look like hard and so green green....its not like Chard which is flexible....well in any case I think I shall try this tomorrow if you tell me what kind of cranberries to get and how i should slice the kale and the tomatoes...and .... well I think I can do this, at least I am going to try.

You can do the tomatoes anyway you want-sometimes I use little grape tomatoes-sometimes I dice them up. I think this salad could be experimented with to make it your own (if you like it). I've done different things with it-put carmelized walnuts in it instead of pine nuts,fe.

> What else you got? d

The usual suspects-there is the baby spinach, beet, red onion, goat cheese one that's always good. You don't see much with kale though.

> "Hence only by means of love can we give real help for karma to work out in the right way." Rudolf Steiner

>
>
> --- On Wed, 1/13/10, val2160 <wdenval@...> wrote:
>
>
> From: val2160 <wdenval@...>
> Subject: [anthroposophy_tomorrow] Re: Love
> To: anthroposophy_tomorrow@yahoogroups.com
> Date: Wednesday, January 13, 2010, 3:05 PM
>
>
>
> Dottie-this is a great salad-even better than a Waldorf salad! It sounds
> kinda mundane but it's addictive. -Val
>
> Raw Kale
> Dried Cranberries
> Raw Pine Nuts
> Tomatoes
> Olive Oil
> Black Pepper
> Lemon Juice (lots of it!)
>
> --- In anthroposophy_tomorrow@yahoogroups.com, dottie zold
> <dottie_z@> wrote:
> >
> > Hi Christopher, isn't that beautiful and isn't it true! whew.
> > Ã
> > For me it seems this suffering is really a non knowledge of oneself in
> connection to ongoing incarnations and the what the soul needs in
> relations to these ongoing incarnations. Once I realized that I had
> brought myself to this moment to confront myself and this insane fear I
> have of asking for what I need from one who has the possibility to
> control my fate in a materialist point of view way, or so I considered
> in my scaredycat self, I determined to meet it and them as friends who
> were dancing with me and helping me to grow:whether they realized it or
> not was and is besides the point. But what a great love I have for both
> of these gentlemen for being the ones who I would have to work this and
> stretch this soul out with. These two men are incredibly humane with me
> and they proved it once again by meeting me way more than half way in
> what is going on in my rental situation and agreement.
> > Ã
> > I first spoke with Robin, my friendly daily owner friend, on Friday
> and he shared that his mother had passed away on Christmas Eve and he
> had not gone on vacation after all. I said 'Oh I am so glad for her' as
> she is 93 and he said 'no she went too soon' :))) he is so beautiful
> really. And we had a really nice conversation and then it turned to my
> 'situation' and he said 'its out of my hands, if we had only given the
> other one money he woulda been fine but we didnt' do that' and I said
> 'no Robin please you have to fight for me, please you have to stand up
> for me and I have a plan and I will pay \$500 each Monday and then on the
> first of each month I will give \$1000 from the little funds I get once a
> month. And my Rabbi is going to help me with a loan from the Jewish Free
> Loan Association and others are trying to figure a way to help and...and
> he started to laugh when he found my Rabbi was the dancing Rabbi with
> the big beard and belly!. He knew of him.
> >Â  And we ended it there.
> > Ã
> > Initially I thought it was all good and we would be able to stay and
> work it out. And then I realized I might be hearing what I want to hear
> and not the part where he said it was out of his hands. The next day he
> came by and did not come in my store and had to see another tenant. He
> never does not pass by without entering into Elderberries, ever. And so
> I realized maybe he was just going to let the other owner take care of
> it and as he was a little more sensitive right now he just didnt' want
> to deal with it. And I started to be concerned again. BUT I recognized I
> met my burden wonderfully. I met my greatest fear, not losing
> Elderberries but asking Robin to believe in me. And I passed. And
> something shifted for me in that I stopped being a victim in this in my
> mind.
> > Ã
> > I went to bed asking how I could meet this and I started to figure
> this and then that and then I told myself to shut up. And I did.
> > Ã
> > So Monday I wake up with a list of To Do today and one by one I hit it
> including writing a letter to the other owner as I did not want to
> bother Robin.. And then Robin came in. And he said 'honey, what are we
> gonna do here, when are we gonna say enough'. I said 'Robin I said I
> have a plan and this is what I am gonna do and...' and he said 'Okay,
> you said \$500 on Monday, how muchÃÂ  you got?' And I said 'I have \$200
> and...' "200!, he says, what happened to the five hundred?' and I said
> 'but I had to get my jeep out and I meant to begin next Monday and...'
> And he says' when is enough enough' and I said 'Robin I am good for it
> and we opened in October and the holidays and it was a horrible time to
> open and people are coming in and...' And he said 'when are we gonna say
> enough' and I said 'we said enough on Friday and now I am going to make
> this place fly' and he waved his cigar and I had a big smile on my face
> and he walked away saying '\$200, when is it gonna
> >Â  be enough' and my next door boxer Maca got up from the table and gave
> me a big ol smile and a high five and I realized we got a reprieve.
> Elderberries is gonna make its committment of \$500. each Monday and
> that's that.
> > Ã
> > And then I called my friend to help me design a few sandwiches and
> salads as you know I look at arecipe and its a foreign language and I am
> so not kidding at all. It's awful. :People say 'oh just put a lttle
> green salad and cut some tomatoes' and I'm thinking they just don't get
> it. I have to worry what kinda dressing and then how big to cut the
> lettuce and then what...and its insane for me to be a girl really is all
> I can think....but in any case we made over a hundred dollars today and
> everyone loves us and if you are into stocks I think a goodlooksee would
> be peanut butter and jelly along with bananas as that's been going like
> wild...:)))) i am so not kidding.
> > Ã
> > So, I am going to hold the balance and keep the foot drumming steady
> and remember the words Jesus spoke 'why do you call me good, only God is
> good'. For this means to me that we never know what is around the corner
> from out of the past moving into the future and the best we can do is
> > Ã
> > And to consider the spiritual worlds in all of this. Really. To
> consider its' all aligned....that is truly so amazing and humbling and
> keeps me considering them all the time.
> > Ã
> > All good things my friends,
> > Dottie
> >
> >
> > "Hence only by means of love can we give real help for karma to work
> out in the right way." Rudolf Steiner
> >
> >
> >
> > --- On Sat, 1/9/10, Christopher Bodame transintelligence@ wrote:
> >
> >
> > From: Christopher Bodame transintelligence@
> > Subject: Re: [anthroposophy_tomorrow] Re: Love
> > To: anthroposophy_tomorrow@yahoogroups.com
> > Date: Saturday, January 9, 2010, 1:14 AM
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > Ã
> > Ã
> > Ã¢â¬Å"All true understanding is born of pain and sorrow.
> Ã¢â¬Â¦.Without suffering, without suffering a great deal and having
> thereby become free from that element in pain which drags one down, one
> cannot come to know and understand the spiritual world.Ã¢â¬ï¿½ Ã
> Ã Dr. Rudolf Steiner
> > Ã
> > Ã
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