Related resource:

Hi –

I recommend Identity and Control by H. White. He is the godfather of social networks, analysis and leader of the Harvard Revolution. We owe him practically everything. If you can’t read the book, be sure to read the excellent review (attached) by Don Steiny.

http://en.wikipedia.org/wiki/Harrison_White

John-----------------------------

Benoit

--- On

**Tue, 7/22/08, ms@...**wrote:*<ms@...>*From: ms@... <ms@...>

Subject: [holistichelping] Mathematics for our social networks

To: holistichelping@yahoogroups.com, globalvillages@yahoogroups.com

Cc: backtotheroot@yahoogroups.com, learnhowtolearn@yahoogroups.com

Date: Tuesday, July 22, 2008, 6:04 PMJeff,

Thank you for your letter! I'm glad that you are at Arcosanti

http://www.arcosant i.org and also blogging: http://green. onevillage. tv

Thank you for linking me up with Mark Roest and Edward Cherlin.

I include below some letters that I wrote for another group about Stephen

Wolfram and "A New Kind of Science".

Jeff, I think it's great that you are interested in learning math and you

can lead and help as a learner.

This week I want to write him a proposal for a small project ($2,000) that

might lead to bigger ones ($15,000 and $200,000). I will propose a bold

challenge: to discover "minimal principles for distributed social

networking" which is to say, what are the principles needed for different

groups to build on each other's work in a shared culture? This is

relevant for my own interest in organizing a culture of investigation, a

culture of independent thinkers, or simply, a kingdom of heaven, and

learning how we might variously imagine that.

For me, this links with the importance of "intentional community". Global

villagers can be more or less spiritual, but I think it is key, locally,

for them to foster a shared intention, a framework of meaning for

including people and their values. What are principles that might support

all kinds of personal leadership and intentional community so they might

catalyze each other?

I and our Minciu Sodas lab's team will be documenting mathematical

explorations of all sorts of related facts and questions and probabilities

for organizing social networks (we have a lot of experience, history,

content!), such as:

* the paths by which people become more or less involved

* diagrams of how people get to know each other and a network grows

* the geometry that relates people's deepest values (relevant for our

lab), questions, endeavors

* the economic value of activity by participants

* the kinds of content generated and how it gets reused

* various kinds of "civilization networks" and how they overlap

I appreciate our ideas of what we might explore!

Jeff, my plan is to start with math relevant for our own social networks,

then expand that to related questions such as including people with

marginal Internet access, or organizing video bridges, or social questions

that arise for global villagers, and then from there develop the

"mathematical thinking" that might express the values relevant for all

aspects of global village design.

Janet Feldman and I spoke for five hours, which all went by very quickly!

I'm glad that she understood my wish that she regularly share the

questions that she asks herself, and invite us to work with her on them,

because she might lead us most profoundly by engaging us regarding our

values, just as she challenges herself. We can (and should!) learn to

help her respond to others who ask for help. I and I think others would

benefit from Janet's investigations, her example, because that shapes the

culture that we're working towards, the thinking alongside the action. I

encourage us to investigate, to ask ourselves questions, to break them up

into research steps, to think out loud. This is the activity that I want

us to do for Stephen Wolfram, and show how math and his tools are

relevant.

Andrius

Andrius Kulikauskas

Minciu Sodas

http://www.ms. lt

ms@...

+1 312 618 3345

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

Jeff Buderer:

I think math basically is something I am weak in and yet for sustainable

design and community development and research it is very important to have

the math worked out for your projects.

I do think what you are saying may fit with that.

focus on the mathematical challenge of "minimal principles for distributed

social networking" which is to say, what are the principles needed for

different groups to build one each other's work in a shared culture? This

is central to a culture of independent thinkers and even a "kingdom of

heaven".

However could you explain the specifics? Basically my interepretation or

take on all this is how to scale out models of development for social

networks that are more holistic and sustainable as an alternative to the

corporate monoculture model of contemporary society that is killing both

indigenous culture as well as ecological diversity and vitality across the

planet at a shocking pace.

Thus we are connecting systems using ICT to measure viability of systems

to address community needs while preserving or restoring ecological

diversity while offering models that are economically competitive with

existing ones.

At the root level how do we develop a curriculum that engages the student

in a holistic way but with a strong math basis so that they have the

skills to integrate these technologies in an effective way to empower

themselves as well as others in their networks.

Jeff

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

Andrius:

In mathematics one often makes progress by making presumptions about one's

model and then expanding on them. Such presumptions might include:

* in physics, assuming that, locally, a function behaves like a line

(linear) or a well (quadratic), and for that matter, is continuous and

infinitely differentiable

* in economics, that all agents are rational and have perfect knowledge

* in social networks, that people are either "friends" or "not friends"

* in philanthropy, that a solution for some people is going to be a

solution for all people

* in agriculture, that it's the seeds and their genes that matter

* in politics, that people are either left or right

* in society, that every person belongs to a race, a nation, a religion, a

class, typically one from a short list

* in geometry, that everything is made up of simple shapes like triangles,

rectangles, circles

* in communications, that all information can be coded as bits, zeros and

ones

* in biology, that every living thing belongs to a species, and has a

well-defined sex

* in chemistry, that an electron either belongs to an atom or doesn't, or

that matter is either a solid or a liquid or a gas or a plasma

* in mathematics, that knowledge can be written down with abstract symbols

as a true statement

These are simplistic assumptions and they are enormously powerful and

fruitful. They lead to formal models that have structure which can be

tested and then ever expanded to consider all manner of subtleties.

Stephen Wolfram champions an alternative which he calls "A New Kind of

Science". Computers make it more and more possible for us to exhaustively

review certain computational spaces. This approach can help us see

complex but interesting phenomena that may be in the blindspots of our

simplistic assumptions.

A classic case is the 2-color, 3-cell cellular automata. There are 256

such automata. Here are diagrams of output from each one, where the input

is a line of cells where one cell is black and the rest are all white.

http://www.wolframs cience.com/ nksonline/ page-55

http://www.wolframs cience.com/ nksonline/ page-56

It's surprising (at least to me) that among these automata there are a few

of extraordinary complexity, such as rule 30 and rule 110. It would be

very easy for a mathematician like me to study the 2-color, 3-cell

automata for months or years and never realize that these particular rules

are noteworthy. So I'm grateful to him for making the point.

I imagine that Stephen Wolfram's approach with computational explorations

is similar to Aristotle's approach in biology. I imagine Aristotle

reveling in the enormous variety of forms that he found in nature, the

varieties of shapes and characteristics for leaves, flowers, organs.

Aristotle's categories, I imagine, came from such a bottom-up, exhaustive

approach, and hence they are quite hodge podge. Whereas Plato, as a lover

of mathematics, and an idealist, was impressed by the conceptual limits of

the mind (much like I am). The two approaches seem to benefit from each

other.

Stephen Wolfram has gone out on a limb and I'm sympathetic to that.

* After achievements in quantum physics, one of the most regarded

disciplines, he dedicated himself to cellular automata, one of the least

regarded.

* Driven by his vision of computational exploration, in 1988 he created

Mathematica, a software designed with an intellectual clarity and

integrity that allows mathematicians to reach definitive conclusions to

many deep research questions (whereas the typical calculator or computer

can - thanks to rounding errors which build - draw the most erroneous,

useless conclusions) .

* He argued that complex data is fundamentally more interesting than

simple data, that we should look for complexity instead of simplicity.

* He developed a methodology in which computational exploration is the

formal framework for studying complexity in the world, just as mathematics

is the formal framework for studying simplicity in the world.

* He pushes his methodology to the limits by applying it encyclopedically

to all disciplines.

* He's reached out to encourage practictioners in all disciplines (which

made the summer school immensely stimulating, much more than graduate

school)

* He's brought that methodology directly to the public with a book

(available online), software, forum, summer schools, which is to say, he's

taken an open, nonesoteric, nonacademic, noninsider, nonmonopolistic

approach.

* He's succeeded as an entrepreneur to fund his tools and his research so

that he and they stay independent.

I learned a lot at his summer school, not only how to program Mathematica

(a functional paradigm) and about cellular automata, but also to witness

people doing what for me is a new kind of research: imagine somebody

leafing through thousands of pictures in minutes, looking for something

"interesting" , much like an astronomer scanning the sky, except that the

pictures are not of the natural world, but of the formal world, parts of

computational space.

I found him personable, sociable, very excited to get to know people and

their diverse projects, help them find their niche.

I organize independent thinkers. I think he's one of the greatest. He

may not be the brightest, but he shines bright.

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

I find it helpful to realize that the cells in my toe, in my kidney,

in my heart, in my brain, all have the same DNA, even though they end

up so different.

The distinction between the rule and it input - which is the source of

complexity? also came up for me at the Stephen Wolram summer camp.

Both the rule and its input are key for complexity.

I doubted Stephen Wolfram's point in his book "A New Kind of Science"

that a single black square is "simple input". Actually, I pointed out

that in the context of cellular automata, simple input is anything

periodic, such as all black cells, all white cells, alternating

black-white, or black-black- white, or black-white- white, and so on,

which is to say, infinitely repeated Lyndon words. Periodic input

gives periodic output (of the same or smaller period). Whereas "a

single black square" is input of infinite period. (It turns out that I

was reproducing Stephen Wolfram's work from his 1984 paper "Algebraic

Properties of Cellular Automata"). So what is simple depends also on

the point of view, ours or the automata.

It seems that the period attractor states that input heads towards -

the kinds of wallpaper that the automata generates - are key to the

behavior of the automata (perhaps there is an analogy with how genes

can be turned on or off). So I considered if it is possible to create

a wallpaper built up from two different wallpapers. (In Christopher

Alexander's and Nikos Salingaros's work, the wallpaper is important

because it is "open space" that allows for "levels of scale".) I got

lucky and actually stumbled upon a "gene splicing" effect which I hope

to investigate further - the building blocks of the input have the

form AB and CD and then one pair gets cut and rearranged to give AC

and BD and that change then propagates through the whole system

yielding the beautiful activity.

http://www.worknets .org/wiki. cgi?LawsOfArchit ecture

So that's an example of the point of Stephen Wolfram's methodology -

that by scouring the data, the outputs it is possible to come across

behavior that one wouldn't plan for if they simply focused on their

own models.

Andrius

Andrius Kulikauskas

Minciu Sodas

http://www.ms. lt

ms@...

+1 312 618 3345