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Re: [holistichelping] Mathematics for our social networks

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  • Benoit Couture
    Related resource:   Hi –   I recommend Identity and Control by H. White. He is the godfather of social networks, analysis and leader of the Harvard
    Message 1 of 1 , Jul 27, 2008
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      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@... <ms@...> wrote:

      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 PM

      Jeff,

      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


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