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Deduce Geometry from Network
Given a conceptual network, it is possible, in theory, and sometimes, in practice, to deduce a conceptual geometry.
The Conceptual Space of Deepest Values
In July, 2004, I asked Franz Nahrada, what was his key concept? (Global Villages) Since then, I have collected unique answers from more than 500 people to the question What is your deepest value in life, which includes all of your other values? I also organized two dozen working groups around the deepest values of our Minciu Sodas leaders, such as Janet Feldman's Holistic Helping, Pamela McLean's Learning From Each Other, John Rogers's Participatory Society (Cyfranogi), Samwel Kongere's Motivation through Sacrifice (Mendenyo = "Men without Food"). I think this proved to be a healthy way to organize ourselves in that each person is a natural leader regarding their deepest value, which they intuit better than anybody else.
I wanted to create a map of our deepest values so that I and others might understand how to naturally divide up our conceptual space. The map would clarify how to match stronger leaders with weaker leaders they might foster.
I realized that given any pair of deepest values, I could rank which one I personally felt closer to, and thus I could give them a total rank, more or less. Other people would rank them differently, in accord with their own deepest values. Our rankings function like sonar readings. Given several respondents, it should be possible, with some work, to calculate the number and kind of dimensions that the conceptual space entails.
July 26, 2006, Marcus Petz (Meaningful Inclusion) and I visited John Rogers on our road trip through the UK. I gave them thirty deepest values which they ranked for me, as best they could, as did Eluned Hurn (Fighting Peacefully) and later, Franz Nahrada and Pamela McLean. My own deepest value is Living by Truth. I tried to make the data fit in two dimensions, more or less, as follows:
My efforts make it clear that two dimensions is insufficient, but perhaps six or fewer dimensions might suffice. That would mean that millions of deepest values could be represented as locations in a handful of dimensions, like stars in the sky, each seeing the whole sky from some corner of it, and perhaps a spherical sky at that, so that no point is privileged.
I also noted, that although our deepest values seem very stable across our lives, but our rankings may change significantly, in that we learn to see the world from a friend's eyes, a friend who may be very different. For example, I've grown to see Franz's Global Villages as very important for my life. This suggests that mature people who know themselves well, who ask questions by which they go beyond themselves, who engage people quite different from themselves, end up with an altered metric of the conceptual geometry, whereby certain points far away (across the sphere, so to speak), become much closer, creating ripples of closeness. They can thereby engage and appreciate larger parts of the conceptual space. If so, this makes it quite a bit harder to calculate the underlying geometry. However, it should be possible, especially if we include many points of view, including people who are less mature and perhaps less sensitive but simpler in their appraisals. In 2006, I wrote a proposal to Stephen Cayzer of Hewlett-Packard's Bristol Labs to pursue this research, but they decided not to fund it. It's an open problem.
Here, it's clear that there are at least three steps:
Ways of Figuring Things Out
In 2010, I used this method to help me make my map of the "ways of figuring things out". I had a list of 200 ways and I had noted various "threads" that each belonged to. For example, some ways belonged to one or another stage of my structural research; some were relevant in the "good will exercises"; some helped me grow in various areas of my personal life.
I wrote a database query that calculated, given two threads, how many ways they had in common. If threads shared at least a few ways, then I considered them neighbors. I laid out the ways in the following diagram. Larger labels (in yellow) indicate threads with a greater number of ways. Thicker arrows indicate more ways shared.
The diagram helped me just a bit to confirm that there were some threads, like the good will exercises, my faith in Jesus Christ, and my lab Minciu Sodas, that served as bridges between my theoretical work and my personal growth.
This method is, I think, most relevant when there are hundreds or thousands of data points. It can make absolute sense (through geometry) of relative data points (each of which may be idiosyncratic). Thus it can be a great bridge between theory and practice, the absolute and the relative. I expect to make more use of it as I investigate languages of argumentation and verbalization and I diagram the many ways of figuring things out.
Valdis Krebs provides a very telling example: Political Polarization During the 2008 Presidential Campaign. He considers two books on US politics, A and B, to be close to each other if Amazon says those who bought A also bought B. This yields a network, which, interestingly, form two camps that are linked by only one or two books, if at all. The two camps are, it turns out, Republicans and Democrats, or however you may term them. Books that link the camps, such as "The True Story of the Bilderberg Group", can be used as a reference point (0) to lay out a one-dimensional spectrum based on the number of links away a book is from it. I note that Terror and Consent (about market-states as drivers of terrorism) is 7 steps deep into the far left and Moment of Truth in Iraq (about heroic American warriors) is 4 steps deep into the far right. See also: Networks on the Radio. I look forward to studying Valdis's Social Network Analysis, A Brief Introduction.
Mapping Science by Iris Monica Vargas writes about Richard Klavans and Kevin Boyack of SciTech Strategies, Inc., who made a Map of Science of 7.2 million papers published in 16,000 journals from 2001 to 2005. They organized the journals on a three-dimensional sphere which they later projected with a Mercator projection onto a two-dimensional map. They used shared citations as a measure of how close different journals are. This metric allowed them to distinguish various regions in the space for biology, physics, math, earth science, chemistry and so on, to which they assigned different colors.
Linked In Maps let you visualize and analyze your own social network at LinkedIn.