Re: Fibionacci Sequence and self-ordering systems

[Guest guest]

> Something I've always wondered about is, WHY does the Fibionacci

> sequence turn up so often in organic self-ordering systems?

I dunno but if you do a paper on it I'd love to read it. Fibonacci

fascinated me too.

Genyin

--

" I know the answer! The answer lies within the heart of all mankind!

The answer is twelve? I think I'm in the wrong building. "

M. Schultz

[Guest guest]

Hello Joni

(the math & hat lady, right ?)

> Something I've always wondered about is, WHY does the Fibionacci

> sequence turn up so often in organic self-ordering systems? (eg, pine

> cones, sea shells, flower heads, the genearations of rabbits as in

> Fibionacci's original thought experiment, etc) Is it because it is

> generated by addition yet it approximates a geometric sequence?

Any linear system generates geometric sequences (exponential components)

> Is it the solution to a partial differential equation?

Finite difference equation ! it has discrete time steps, not continuous

time.

> Does it have

> something to do with fractals? I'd like to write a thesis on that and

> I'm wondering what areas of math I ought to study so that I can write

> something intelligent and meaningful.

The general area would be " System Dynamics " and would include

differential equations and finite difference equations. A close newer

extension is the Chaotic Systems Theory.

You are right that new _research_ in pure theory is extremely far

away to common understanding, but it would be very good to use it to

either invent and solve a new _application_ model, or to show how to

_teach_ interrelated concepts. A whole world *needs* to know basics

before it's too late and Civilization itself may collapse !

Like:

- Math modelling in general; from reality to model to solution to

understanding to real action !

- Links between continuous-time and discrete-time, both in math

solving theory and understanding real system behaviours.

- N-variable 1-step-lag systems equivalent to 1-variable N-step-lag.

(Fibonacci is a great example for N=2)

- Systems that can have stable and unstable portions at the same time

- Minor change in model (a sign here and there) may shift to entirely

different models with deeply different real-life meaning.

+ Harmonic oscillators appear everywhere, from air and sea waves

to unemployment cycles... Change a sign and you get into:

- Lanchester model(s), with major military applications

- Logistic growth equations in bio- and eco-modelling; these are

becoming vital, and more important than unfettered exponential

growth, as the world is nearing 'carrying capacity'.

- Extensions under uncertainty (would come under Stochastic

processes, a branch of Probability theory)

Much of what I used to teach under the name of Economic

Cybernetics was this popularization of System Dynamics and applications.

(Quit after unbearable 'between anvil and hammer' human pressures)

I can talk a LOT about these... even done some for my hobby.

I can recommend you search in your library and at least peruse:

Giancarlo Gandolfo - Economic Dynamics

By the way... can you recommend (downloadable, if possible)

clear introductions to Laplace transforms, Transfer functions and

Wavelets for signal analysis ? Did you ever teach things like this ?

The kind modern electronic engineers and a few stock-market

analysts are using... I'm NOT interested in that awful pure math

style of " Definition. Theorem. Lemma. Proof. Corollary "

but in conceptual understanding and powerful tools to think and use.

Thank you for thinking about these,

Mircea Pauca, Bucuresti, Romania

[Guest guest]

Wow, and who ever said Autistics were dumb should definitely read that

I used to be a wiz in math. When I was in high school, I got all 100%

actually 106% average in both Geometry and Algebra 1-2, but because

Algebra 1-2 was from The Blind School, they wouldn't let me take Algebra

3-4,

I was so mad, but I was probably a good thing I didn't take it after all,

for I

cannot see the blackboard, but at one time I was a gifted Math student

myself.

tested post high school (pre-college) level by the 6th grade, was English

I hated, and still can't understand what I read. hehe

but oh, do I wish you lived here, I have forgotten all my math skills now.

I am lucky if I remember how to multiply fractions now. I have forgotten

THAT much in 15 years....

Tom

> Hello Joni

> (the math & hat lady, right ?)

>

>

> > Something I've always wondered about is, WHY does the Fibionacci

> > sequence turn up so often in organic self-ordering systems? (eg, pine

> > cones, sea shells, flower heads, the genearations of rabbits as in

> > Fibionacci's original thought experiment, etc) Is it because it is

> > generated by addition yet it approximates a geometric sequence?

>

> Any linear system generates geometric sequences (exponential components)

>

> > Is it the solution to a partial differential equation?

>

> Finite difference equation ! it has discrete time steps, not continuous

> time.

>

> > Does it have

> > something to do with fractals? I'd like to write a thesis on that and

> > I'm wondering what areas of math I ought to study so that I can write

> > something intelligent and meaningful.

>

> The general area would be " System Dynamics " and would include

> differential equations and finite difference equations. A close newer

> extension is the Chaotic Systems Theory.

>

> You are right that new _research_ in pure theory is extremely far

> away to common understanding, but it would be very good to use it to

> either invent and solve a new _application_ model, or to show how to

> _teach_ interrelated concepts. A whole world *needs* to know basics

> before it's too late and Civilization itself may collapse !

> Like:

> - Math modelling in general; from reality to model to solution to

> understanding to real action !

> - Links between continuous-time and discrete-time, both in math

> solving theory and understanding real system behaviours.

> - N-variable 1-step-lag systems equivalent to 1-variable N-step-lag.

> (Fibonacci is a great example for N=2)

> - Systems that can have stable and unstable portions at the same time

> - Minor change in model (a sign here and there) may shift to entirely

> different models with deeply different real-life meaning.

> + Harmonic oscillators appear everywhere, from air and sea waves

> to unemployment cycles... Change a sign and you get into:

> - Lanchester model(s), with major military applications

> - Logistic growth equations in bio- and eco-modelling; these are

> becoming vital, and more important than unfettered exponential

> growth, as the world is nearing 'carrying capacity'.

> - Extensions under uncertainty (would come under Stochastic

> processes, a branch of Probability theory)

>

> Much of what I used to teach under the name of Economic

> Cybernetics was this popularization of System Dynamics and applications.

> (Quit after unbearable 'between anvil and hammer' human pressures)

> I can talk a LOT about these... even done some for my hobby.

>

> I can recommend you search in your library and at least peruse:

> Giancarlo Gandolfo - Economic Dynamics

>

> By the way... can you recommend (downloadable, if possible)

> clear introductions to Laplace transforms, Transfer functions and

> Wavelets for signal analysis ? Did you ever teach things like this ?

> The kind modern electronic engineers and a few stock-market

> analysts are using... I'm NOT interested in that awful pure math

> style of " Definition. Theorem. Lemma. Proof. Corollary "

> but in conceptual understanding and powerful tools to think and use.

>

> Thank you for thinking about these,

> Mircea Pauca, Bucuresti, Romania

>

[Guest guest]

Hello,

I do not like math at all but seem to do good in it. Whenever I take a math test

I reach for a

calculator or pencil and paper. (I am unsure of myself because of not liking

math.) If I don't

have those I guess, and usually get it right in that way.

As far as english is concerned: I cannot remember what a preposition, etc. is

but I write and

proofread pretty good.

Kellie

[Guest guest]

Hi, Genyin! I did not know you were in here!

, who knows you from the other list (FB)

Kelsang Genyin wrote:

> Something I've always wondered about is, WHY does the Fibionacci

> sequence turn up so often in organic self-ordering systems?

I dunno but if you do a paper on it I'd love to read it. Fibonacci

fascinated me too.

Genyin

--

" I know the answer! The answer lies within the heart of all mankind!

The answer is twelve? I think I'm in the wrong building. "

M. Schultz

---------------------------------

Never miss a thing. Make Yahoo your homepage.

[Guest guest]

On Joni's *original* question:

> Something I've always wondered about is, WHY does the Fibionacci

> sequence turn up so often in organic self-ordering systems? (eg, pine

> cones, sea shells, flower heads, the genearations of rabbits as in

> Fibionacci's original thought experiment, etc) Is it because it is

> generated by addition yet it approximates a geometric sequence?

I think the physical mechanism in the " Rabbits " model applies for

cell growth giving the " golden ratio " spacing. Growth is controlled

by chemical Start and Stop signals ultimately encoded in DNA.

Suppose cells of constant width; each replicates once (between

existing cells) then at the second replication a " Stop " signal comes.

So we have the Rabbit model:

N t = N t-1 +N t-2

They say chaotic systems and self-similarity also generate

" Power law " distributions. Empirically observed in wealth distribution

across persons, companies etc. even earthquake intensity.

That, again I don't know why.

Thank you for thinking about this,

Mircea Pauca, Bucuresti, Romania

[Guest guest]

> Hi, Genyin! I did not know you were in here!

> , who knows you from the other list (FB)

Only very recently :-)

Genyin

--

" I know the answer! The answer lies within the heart of all mankind!

The answer is twelve? I think I'm in the wrong building. "

M. Schultz

[Guest guest]

Welcome form Me : ~ )

Kelsang Genyin wrote:

> Hi, Genyin! I did not know you were in here!

> , who knows you from the other list (FB)

Only very recently :-)

Genyin

--

" I know the answer! The answer lies within the heart of all mankind!

The answer is twelve? I think I'm in the wrong building. "

M. Schultz

---------------------------------

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