Re: [holistichelping] Mathematics for our social networks
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.
--- On Tue, 7/22/08, ms@... <ms@...> wrote:
From: ms@... <ms@...>
Subject: [holistichelping] Mathematics for our social networks
To: email@example.com, firstname.lastname@example.org
Cc: email@example.com, firstname.lastname@example.org
Date: Tuesday, July 22, 2008, 6:04 PM
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
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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
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
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.
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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
* 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,
* in communications, that all information can be coded as bits, zeros and
* in biology, that every living thing belongs to a species, and has a
* 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
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
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
* 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
* 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
* 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
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
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