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BT 227.982 767.476 Td /F1 9.8 Tf [(Emergence: Complexity and Organization. Emergence: Complexity and Organization.)] TJ ET
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BT 15.000 745.137 Td /F2 21.0 Tf [(Editorial: Chaos and complexity, branches and trees, and the )] TJ ET
BT 15.000 720.189 Td /F2 21.0 Tf [(advantages of vague concepts)] TJ ET
Q
0.271 0.267 0.267 rg
BT 15.000 702.183 Td /F3 9.8 Tf [(March 31, 2009)] TJ ET
BT 82.431 702.183 Td /F3 9.8 Tf [(·)] TJ ET
0.267 0.267 0.267 rg
BT 87.306 702.183 Td /F3 9.8 Tf [(Editorial)] TJ ET
BT 26.250 690.342 Td /F1 9.8 Tf [(Professor Jeffrey Goldstein)] TJ ET
0.271 0.267 0.267 rg
BT 143.835 694.231 Td /F1 8.7 Tf [(1)] TJ ET
BT 26.250 679.170 Td /F4 9.0 Tf [(1)] TJ ET
BT 31.254 679.170 Td /F1 9.0 Tf [( Adelphi University)] TJ ET
BT 26.250 667.449 Td /F1 9.8 Tf [(Goldstein J. Editorial: Chaos and complexity, branches and trees, and the advantages of vague concepts. Emergence: )] TJ ET
BT 26.250 655.544 Td /F1 9.8 Tf [(Complexity and Organization. 2009 Mar 31 [last modified: 2017 Jul 30]. Edition 1. doi: )] TJ ET
BT 26.250 643.639 Td /F1 9.8 Tf [(10.emerg/10.17357.0bcae8bdd744e93f0d583e637b249146.)] TJ ET
q
15.000 21.955 577.500 619.304 re W n
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BT 26.250 614.537 Td /F4 12.0 Tf [(Abstract)] TJ ET
BT 26.250 594.582 Td /F1 9.8 Tf [( )] TJ ET
BT 26.250 557.980 Td /F4 12.0 Tf [(E:CO has a New Subtitle)] TJ ET
BT 26.250 538.026 Td /F1 9.8 Tf [(This issue signifies the start of volume number 11, a feat showing not just how far )] TJ ET
BT 380.116 538.026 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 403.955 538.026 Td /F1 9.8 Tf [( has come in a relatively short amount )] TJ ET
BT 26.250 526.121 Td /F1 9.8 Tf [(of time, but gives striking evidence that it is still only building steam. Just look at the rich contents of this issue: articles hailing )] TJ ET
BT 26.250 514.216 Td /F1 9.8 Tf [(from diverse countries around the globe and covering a wide variety of fields, and all done in a rigorous, thought-provoking )] TJ ET
BT 26.250 502.311 Td /F1 9.8 Tf [(fashion. This issue also inaugurates a new subtitled for )] TJ ET
BT 265.778 502.311 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 289.617 502.311 Td /F1 9.8 Tf [(: “An International Transdisciplinary Journal of Complex Social )] TJ ET
BT 26.250 490.407 Td /F1 9.8 Tf [(Systems.” That’s quite a mouthful but it more accurately reflects what )] TJ ET
BT 326.989 490.407 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 350.827 490.407 Td /F1 9.8 Tf [( is about and is evolving more and more into.)] TJ ET
BT 26.250 471.002 Td /F1 9.8 Tf [(Three phrases in our new subtitle stand out. First, there is the emphasis on “International.” Of course, internationality was )] TJ ET
BT 26.250 459.097 Td /F1 9.8 Tf [(essential in the journal’s mission right from the start, and even before that with the precursor journal )] TJ ET
BT 457.600 459.097 Td /F5 9.8 Tf [(Emergence)] TJ ET
BT 507.451 459.097 Td /F1 9.8 Tf [(. But we’re now )] TJ ET
BT 26.250 447.192 Td /F1 9.8 Tf [(including it in the title to reaffirm our commitment to a truly international focus in terms of our authors, our readers, and our )] TJ ET
BT 26.250 435.288 Td /F1 9.8 Tf [(article topics. Indeed, this very issue is like a mini United Nations with authors hailing from Australia, Italy, Egypt and Israel \(our )] TJ ET
BT 26.250 423.383 Td /F1 9.8 Tf [(own little peace initiative although it wasn’t planned that way!\), South Africa, China, and the US. Then there’s the term )] TJ ET
BT 26.250 411.478 Td /F1 9.8 Tf [(“Transdisciplinary”. Again that was an indispensible aspect of our initial mission but here it is spelled out overtly. This current )] TJ ET
BT 26.250 399.573 Td /F1 9.8 Tf [(issue is a vivid demonstration of transdisciplinarity as can be seen by considering the fields of research of the authors: cognitive )] TJ ET
BT 26.250 387.669 Td /F1 9.8 Tf [(science, urban planning, environmental studies, architecture, knowledge management, social networks, organizational theory, )] TJ ET
BT 26.250 375.764 Td /F1 9.8 Tf [(operations research, information technology and computer science, and sociology. Moreover, the methods and constructs )] TJ ET
BT 26.250 363.859 Td /F1 9.8 Tf [(utilized herein similarly cut-across a wide range of scientific, mathematical, cultural, and philosophical disciplines.)] TJ ET
BT 26.250 344.454 Td /F1 9.8 Tf [(The third new addition to the subtitle is the intentional mention of “Social Systems.” We are in fact the only existent journal )] TJ ET
BT 26.250 332.550 Td /F1 9.8 Tf [(specializing in complexity applications to social systems. But of course we also supplement this specialization with numerous )] TJ ET
BT 26.250 320.645 Td /F1 9.8 Tf [(phalanges into philosophy, mathematics, education, physics, biology, semiotics, and many other fields related in one way or )] TJ ET
BT 26.250 308.740 Td /F1 9.8 Tf [(another to social systems.)] TJ ET
BT 26.250 289.335 Td /F1 9.8 Tf [(In spite of the long and still unwinding road that )] TJ ET
BT 232.199 289.335 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 256.038 289.335 Td /F1 9.8 Tf [( and complexity studies in general have been on, it comes as a surprise to )] TJ ET
BT 26.250 277.431 Td /F1 9.8 Tf [(me how vexing it can be to pin down, into a concise definition, just what is it that the field of complexity theory or complexity )] TJ ET
BT 26.250 265.526 Td /F1 9.8 Tf [(science covers. I’m sure many of the readers have experienced a version of the following situation. I was recently at a party )] TJ ET
BT 26.250 253.621 Td /F1 9.8 Tf [(where I met some friends that I hadn’t seen in 30 or more years. To catch up on all those years, we asked the customary )] TJ ET
BT 26.250 241.716 Td /F1 9.8 Tf [(questions of what we each had been up to personally and professionally. When my turn came, I again, as I always do in this )] TJ ET
BT 26.250 229.812 Td /F1 9.8 Tf [(situation, became tongued-tied as to how to describe just what it is that complexity theory is about. This elusiveness of a crisp )] TJ ET
BT 26.250 217.907 Td /F1 9.8 Tf [(definition of complexity always reminds me of that famous retort by one of the United States Supreme Court Judges when )] TJ ET
BT 26.250 206.002 Td /F1 9.8 Tf [(asked how he defined obscenity: he said he couldn’t define it precisely in a few words, but he knew it when he saw it! That’s )] TJ ET
BT 26.250 194.097 Td /F1 9.8 Tf [(how I see the study of complex systems, I can’t precisely define it but I’m pretty sure I can recognize it when I see it.)] TJ ET
BT 26.250 174.693 Td /F1 9.8 Tf [(Of course, this kind of response is not particularly enlightening and it brings with it all the vagueness accompanying ostensive, )] TJ ET
BT 26.250 162.788 Td /F1 9.8 Tf [(contextual, and indexical references, a topic I’ll return to below. Moreover, although one tactic could have been to start listing )] TJ ET
BT 26.250 150.883 Td /F1 9.8 Tf [(the varied types of systems considered to be complex, I realized that this would not be of much help. Since, not only were there )] TJ ET
BT 26.250 138.978 Td /F1 9.8 Tf [(too many of them—with the result I would be hard pressed to say what they had in common besides such unilluminating vague )] TJ ET
BT 26.250 127.074 Td /F1 9.8 Tf [(properties as interconnectedness—it would be questionable whether many of the systems I mentioned were in fact complex, or )] TJ ET
BT 26.250 115.169 Td /F1 9.8 Tf [(at least complex all the time, i.e., some systems at certain conditions such as at equilibrium appear quite simple, but may not be )] TJ ET
BT 26.250 103.264 Td /F1 9.8 Tf [(when parameters change.)] TJ ET
BT 26.250 83.859 Td /F1 9.8 Tf [(So, getting back to the situation of trying to explicate for my old friends what complexity theory was about, this time around I )] TJ ET
BT 26.250 71.955 Td /F1 9.8 Tf [(came up with a new strategy \(for me at least\) of asking my well meaning friends if they had ever heard of “chaos theory” and )] TJ ET
BT 26.250 60.050 Td /F1 9.8 Tf [(most of them indeed had. Chaos theory, of course, has entered the popular imagination in many forms, from Jeff Goldblum’s )] TJ ET
BT 26.250 48.145 Td /F1 9.8 Tf [(famous allegory of it in the movie “Jurassic Park”, when he dropped water on the hand of the character played by Laura Dern )] TJ ET
BT 26.250 36.240 Td /F1 9.8 Tf [(and told her to watch its unpredictable flow, to the more recent film “The Butterfly Effect” with Ashton Kutcher, to last year’s )] TJ ET
Q
q
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0.267 0.267 0.267 rg
BT 15.000 745.137 Td /F2 21.0 Tf [(Editorial: Chaos and complexity, branches and trees, and the )] TJ ET
BT 15.000 720.189 Td /F2 21.0 Tf [(advantages of vague concepts)] TJ ET
Q
0.271 0.267 0.267 rg
BT 15.000 702.183 Td /F3 9.8 Tf [(March 31, 2009)] TJ ET
BT 82.431 702.183 Td /F3 9.8 Tf [(·)] TJ ET
0.267 0.267 0.267 rg
BT 87.306 702.183 Td /F3 9.8 Tf [(Editorial)] TJ ET
BT 26.250 690.342 Td /F1 9.8 Tf [(Professor Jeffrey Goldstein)] TJ ET
0.271 0.267 0.267 rg
BT 143.835 694.231 Td /F1 8.7 Tf [(1)] TJ ET
BT 26.250 679.170 Td /F4 9.0 Tf [(1)] TJ ET
BT 31.254 679.170 Td /F1 9.0 Tf [( Adelphi University)] TJ ET
BT 26.250 667.449 Td /F1 9.8 Tf [(Goldstein J. Editorial: Chaos and complexity, branches and trees, and the advantages of vague concepts. Emergence: )] TJ ET
BT 26.250 655.544 Td /F1 9.8 Tf [(Complexity and Organization. 2009 Mar 31 [last modified: 2017 Jul 30]. Edition 1. doi: )] TJ ET
BT 26.250 643.639 Td /F1 9.8 Tf [(10.emerg/10.17357.0bcae8bdd744e93f0d583e637b249146.)] TJ ET
q
15.000 21.955 577.500 619.304 re W n
0.271 0.267 0.267 rg
BT 26.250 614.537 Td /F4 12.0 Tf [(Abstract)] TJ ET
BT 26.250 594.582 Td /F1 9.8 Tf [( )] TJ ET
BT 26.250 557.980 Td /F4 12.0 Tf [(E:CO has a New Subtitle)] TJ ET
BT 26.250 538.026 Td /F1 9.8 Tf [(This issue signifies the start of volume number 11, a feat showing not just how far )] TJ ET
BT 380.116 538.026 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 403.955 538.026 Td /F1 9.8 Tf [( has come in a relatively short amount )] TJ ET
BT 26.250 526.121 Td /F1 9.8 Tf [(of time, but gives striking evidence that it is still only building steam. Just look at the rich contents of this issue: articles hailing )] TJ ET
BT 26.250 514.216 Td /F1 9.8 Tf [(from diverse countries around the globe and covering a wide variety of fields, and all done in a rigorous, thought-provoking )] TJ ET
BT 26.250 502.311 Td /F1 9.8 Tf [(fashion. This issue also inaugurates a new subtitled for )] TJ ET
BT 265.778 502.311 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 289.617 502.311 Td /F1 9.8 Tf [(: “An International Transdisciplinary Journal of Complex Social )] TJ ET
BT 26.250 490.407 Td /F1 9.8 Tf [(Systems.” That’s quite a mouthful but it more accurately reflects what )] TJ ET
BT 326.989 490.407 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 350.827 490.407 Td /F1 9.8 Tf [( is about and is evolving more and more into.)] TJ ET
BT 26.250 471.002 Td /F1 9.8 Tf [(Three phrases in our new subtitle stand out. First, there is the emphasis on “International.” Of course, internationality was )] TJ ET
BT 26.250 459.097 Td /F1 9.8 Tf [(essential in the journal’s mission right from the start, and even before that with the precursor journal )] TJ ET
BT 457.600 459.097 Td /F5 9.8 Tf [(Emergence)] TJ ET
BT 507.451 459.097 Td /F1 9.8 Tf [(. But we’re now )] TJ ET
BT 26.250 447.192 Td /F1 9.8 Tf [(including it in the title to reaffirm our commitment to a truly international focus in terms of our authors, our readers, and our )] TJ ET
BT 26.250 435.288 Td /F1 9.8 Tf [(article topics. Indeed, this very issue is like a mini United Nations with authors hailing from Australia, Italy, Egypt and Israel \(our )] TJ ET
BT 26.250 423.383 Td /F1 9.8 Tf [(own little peace initiative although it wasn’t planned that way!\), South Africa, China, and the US. Then there’s the term )] TJ ET
BT 26.250 411.478 Td /F1 9.8 Tf [(“Transdisciplinary”. Again that was an indispensible aspect of our initial mission but here it is spelled out overtly. This current )] TJ ET
BT 26.250 399.573 Td /F1 9.8 Tf [(issue is a vivid demonstration of transdisciplinarity as can be seen by considering the fields of research of the authors: cognitive )] TJ ET
BT 26.250 387.669 Td /F1 9.8 Tf [(science, urban planning, environmental studies, architecture, knowledge management, social networks, organizational theory, )] TJ ET
BT 26.250 375.764 Td /F1 9.8 Tf [(operations research, information technology and computer science, and sociology. Moreover, the methods and constructs )] TJ ET
BT 26.250 363.859 Td /F1 9.8 Tf [(utilized herein similarly cut-across a wide range of scientific, mathematical, cultural, and philosophical disciplines.)] TJ ET
BT 26.250 344.454 Td /F1 9.8 Tf [(The third new addition to the subtitle is the intentional mention of “Social Systems.” We are in fact the only existent journal )] TJ ET
BT 26.250 332.550 Td /F1 9.8 Tf [(specializing in complexity applications to social systems. But of course we also supplement this specialization with numerous )] TJ ET
BT 26.250 320.645 Td /F1 9.8 Tf [(phalanges into philosophy, mathematics, education, physics, biology, semiotics, and many other fields related in one way or )] TJ ET
BT 26.250 308.740 Td /F1 9.8 Tf [(another to social systems.)] TJ ET
BT 26.250 289.335 Td /F1 9.8 Tf [(In spite of the long and still unwinding road that )] TJ ET
BT 232.199 289.335 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 256.038 289.335 Td /F1 9.8 Tf [( and complexity studies in general have been on, it comes as a surprise to )] TJ ET
BT 26.250 277.431 Td /F1 9.8 Tf [(me how vexing it can be to pin down, into a concise definition, just what is it that the field of complexity theory or complexity )] TJ ET
BT 26.250 265.526 Td /F1 9.8 Tf [(science covers. I’m sure many of the readers have experienced a version of the following situation. I was recently at a party )] TJ ET
BT 26.250 253.621 Td /F1 9.8 Tf [(where I met some friends that I hadn’t seen in 30 or more years. To catch up on all those years, we asked the customary )] TJ ET
BT 26.250 241.716 Td /F1 9.8 Tf [(questions of what we each had been up to personally and professionally. When my turn came, I again, as I always do in this )] TJ ET
BT 26.250 229.812 Td /F1 9.8 Tf [(situation, became tongued-tied as to how to describe just what it is that complexity theory is about. This elusiveness of a crisp )] TJ ET
BT 26.250 217.907 Td /F1 9.8 Tf [(definition of complexity always reminds me of that famous retort by one of the United States Supreme Court Judges when )] TJ ET
BT 26.250 206.002 Td /F1 9.8 Tf [(asked how he defined obscenity: he said he couldn’t define it precisely in a few words, but he knew it when he saw it! That’s )] TJ ET
BT 26.250 194.097 Td /F1 9.8 Tf [(how I see the study of complex systems, I can’t precisely define it but I’m pretty sure I can recognize it when I see it.)] TJ ET
BT 26.250 174.693 Td /F1 9.8 Tf [(Of course, this kind of response is not particularly enlightening and it brings with it all the vagueness accompanying ostensive, )] TJ ET
BT 26.250 162.788 Td /F1 9.8 Tf [(contextual, and indexical references, a topic I’ll return to below. Moreover, although one tactic could have been to start listing )] TJ ET
BT 26.250 150.883 Td /F1 9.8 Tf [(the varied types of systems considered to be complex, I realized that this would not be of much help. Since, not only were there )] TJ ET
BT 26.250 138.978 Td /F1 9.8 Tf [(too many of them—with the result I would be hard pressed to say what they had in common besides such unilluminating vague )] TJ ET
BT 26.250 127.074 Td /F1 9.8 Tf [(properties as interconnectedness—it would be questionable whether many of the systems I mentioned were in fact complex, or )] TJ ET
BT 26.250 115.169 Td /F1 9.8 Tf [(at least complex all the time, i.e., some systems at certain conditions such as at equilibrium appear quite simple, but may not be )] TJ ET
BT 26.250 103.264 Td /F1 9.8 Tf [(when parameters change.)] TJ ET
BT 26.250 83.859 Td /F1 9.8 Tf [(So, getting back to the situation of trying to explicate for my old friends what complexity theory was about, this time around I )] TJ ET
BT 26.250 71.955 Td /F1 9.8 Tf [(came up with a new strategy \(for me at least\) of asking my well meaning friends if they had ever heard of “chaos theory” and )] TJ ET
BT 26.250 60.050 Td /F1 9.8 Tf [(most of them indeed had. Chaos theory, of course, has entered the popular imagination in many forms, from Jeff Goldblum’s )] TJ ET
BT 26.250 48.145 Td /F1 9.8 Tf [(famous allegory of it in the movie “Jurassic Park”, when he dropped water on the hand of the character played by Laura Dern )] TJ ET
BT 26.250 36.240 Td /F1 9.8 Tf [(and told her to watch its unpredictable flow, to the more recent film “The Butterfly Effect” with Ashton Kutcher, to last year’s )] TJ ET
Q
q
15.000 711.449 577.500 53.646 re W n
0.267 0.267 0.267 rg
BT 15.000 745.137 Td /F2 21.0 Tf [(Editorial: Chaos and complexity, branches and trees, and the )] TJ ET
BT 15.000 720.189 Td /F2 21.0 Tf [(advantages of vague concepts)] TJ ET
Q
0.271 0.267 0.267 rg
BT 15.000 702.183 Td /F3 9.8 Tf [(March 31, 2009)] TJ ET
BT 82.431 702.183 Td /F3 9.8 Tf [(·)] TJ ET
0.267 0.267 0.267 rg
BT 87.306 702.183 Td /F3 9.8 Tf [(Editorial)] TJ ET
BT 26.250 690.342 Td /F1 9.8 Tf [(Professor Jeffrey Goldstein)] TJ ET
0.271 0.267 0.267 rg
BT 143.835 694.231 Td /F1 8.7 Tf [(1)] TJ ET
BT 26.250 679.170 Td /F4 9.0 Tf [(1)] TJ ET
BT 31.254 679.170 Td /F1 9.0 Tf [( Adelphi University)] TJ ET
BT 26.250 667.449 Td /F1 9.8 Tf [(Goldstein J. Editorial: Chaos and complexity, branches and trees, and the advantages of vague concepts. Emergence: )] TJ ET
BT 26.250 655.544 Td /F1 9.8 Tf [(Complexity and Organization. 2009 Mar 31 [last modified: 2017 Jul 30]. Edition 1. doi: )] TJ ET
BT 26.250 643.639 Td /F1 9.8 Tf [(10.emerg/10.17357.0bcae8bdd744e93f0d583e637b249146.)] TJ ET
q
15.000 21.955 577.500 619.304 re W n
0.271 0.267 0.267 rg
BT 26.250 614.537 Td /F4 12.0 Tf [(Abstract)] TJ ET
BT 26.250 594.582 Td /F1 9.8 Tf [( )] TJ ET
BT 26.250 557.980 Td /F4 12.0 Tf [(E:CO has a New Subtitle)] TJ ET
BT 26.250 538.026 Td /F1 9.8 Tf [(This issue signifies the start of volume number 11, a feat showing not just how far )] TJ ET
BT 380.116 538.026 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 403.955 538.026 Td /F1 9.8 Tf [( has come in a relatively short amount )] TJ ET
BT 26.250 526.121 Td /F1 9.8 Tf [(of time, but gives striking evidence that it is still only building steam. Just look at the rich contents of this issue: articles hailing )] TJ ET
BT 26.250 514.216 Td /F1 9.8 Tf [(from diverse countries around the globe and covering a wide variety of fields, and all done in a rigorous, thought-provoking )] TJ ET
BT 26.250 502.311 Td /F1 9.8 Tf [(fashion. This issue also inaugurates a new subtitled for )] TJ ET
BT 265.778 502.311 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 289.617 502.311 Td /F1 9.8 Tf [(: “An International Transdisciplinary Journal of Complex Social )] TJ ET
BT 26.250 490.407 Td /F1 9.8 Tf [(Systems.” That’s quite a mouthful but it more accurately reflects what )] TJ ET
BT 326.989 490.407 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 350.827 490.407 Td /F1 9.8 Tf [( is about and is evolving more and more into.)] TJ ET
BT 26.250 471.002 Td /F1 9.8 Tf [(Three phrases in our new subtitle stand out. First, there is the emphasis on “International.” Of course, internationality was )] TJ ET
BT 26.250 459.097 Td /F1 9.8 Tf [(essential in the journal’s mission right from the start, and even before that with the precursor journal )] TJ ET
BT 457.600 459.097 Td /F5 9.8 Tf [(Emergence)] TJ ET
BT 507.451 459.097 Td /F1 9.8 Tf [(. But we’re now )] TJ ET
BT 26.250 447.192 Td /F1 9.8 Tf [(including it in the title to reaffirm our commitment to a truly international focus in terms of our authors, our readers, and our )] TJ ET
BT 26.250 435.288 Td /F1 9.8 Tf [(article topics. Indeed, this very issue is like a mini United Nations with authors hailing from Australia, Italy, Egypt and Israel \(our )] TJ ET
BT 26.250 423.383 Td /F1 9.8 Tf [(own little peace initiative although it wasn’t planned that way!\), South Africa, China, and the US. Then there’s the term )] TJ ET
BT 26.250 411.478 Td /F1 9.8 Tf [(“Transdisciplinary”. Again that was an indispensible aspect of our initial mission but here it is spelled out overtly. This current )] TJ ET
BT 26.250 399.573 Td /F1 9.8 Tf [(issue is a vivid demonstration of transdisciplinarity as can be seen by considering the fields of research of the authors: cognitive )] TJ ET
BT 26.250 387.669 Td /F1 9.8 Tf [(science, urban planning, environmental studies, architecture, knowledge management, social networks, organizational theory, )] TJ ET
BT 26.250 375.764 Td /F1 9.8 Tf [(operations research, information technology and computer science, and sociology. Moreover, the methods and constructs )] TJ ET
BT 26.250 363.859 Td /F1 9.8 Tf [(utilized herein similarly cut-across a wide range of scientific, mathematical, cultural, and philosophical disciplines.)] TJ ET
BT 26.250 344.454 Td /F1 9.8 Tf [(The third new addition to the subtitle is the intentional mention of “Social Systems.” We are in fact the only existent journal )] TJ ET
BT 26.250 332.550 Td /F1 9.8 Tf [(specializing in complexity applications to social systems. But of course we also supplement this specialization with numerous )] TJ ET
BT 26.250 320.645 Td /F1 9.8 Tf [(phalanges into philosophy, mathematics, education, physics, biology, semiotics, and many other fields related in one way or )] TJ ET
BT 26.250 308.740 Td /F1 9.8 Tf [(another to social systems.)] TJ ET
BT 26.250 289.335 Td /F1 9.8 Tf [(In spite of the long and still unwinding road that )] TJ ET
BT 232.199 289.335 Td /F5 9.8 Tf [(E:CO)] TJ ET
BT 256.038 289.335 Td /F1 9.8 Tf [( and complexity studies in general have been on, it comes as a surprise to )] TJ ET
BT 26.250 277.431 Td /F1 9.8 Tf [(me how vexing it can be to pin down, into a concise definition, just what is it that the field of complexity theory or complexity )] TJ ET
BT 26.250 265.526 Td /F1 9.8 Tf [(science covers. I’m sure many of the readers have experienced a version of the following situation. I was recently at a party )] TJ ET
BT 26.250 253.621 Td /F1 9.8 Tf [(where I met some friends that I hadn’t seen in 30 or more years. To catch up on all those years, we asked the customary )] TJ ET
BT 26.250 241.716 Td /F1 9.8 Tf [(questions of what we each had been up to personally and professionally. When my turn came, I again, as I always do in this )] TJ ET
BT 26.250 229.812 Td /F1 9.8 Tf [(situation, became tongued-tied as to how to describe just what it is that complexity theory is about. This elusiveness of a crisp )] TJ ET
BT 26.250 217.907 Td /F1 9.8 Tf [(definition of complexity always reminds me of that famous retort by one of the United States Supreme Court Judges when )] TJ ET
BT 26.250 206.002 Td /F1 9.8 Tf [(asked how he defined obscenity: he said he couldn’t define it precisely in a few words, but he knew it when he saw it! That’s )] TJ ET
BT 26.250 194.097 Td /F1 9.8 Tf [(how I see the study of complex systems, I can’t precisely define it but I’m pretty sure I can recognize it when I see it.)] TJ ET
BT 26.250 174.693 Td /F1 9.8 Tf [(Of course, this kind of response is not particularly enlightening and it brings with it all the vagueness accompanying ostensive, )] TJ ET
BT 26.250 162.788 Td /F1 9.8 Tf [(contextual, and indexical references, a topic I’ll return to below. Moreover, although one tactic could have been to start listing )] TJ ET
BT 26.250 150.883 Td /F1 9.8 Tf [(the varied types of systems considered to be complex, I realized that this would not be of much help. Since, not only were there )] TJ ET
BT 26.250 138.978 Td /F1 9.8 Tf [(too many of them—with the result I would be hard pressed to say what they had in common besides such unilluminating vague )] TJ ET
BT 26.250 127.074 Td /F1 9.8 Tf [(properties as interconnectedness—it would be questionable whether many of the systems I mentioned were in fact complex, or )] TJ ET
BT 26.250 115.169 Td /F1 9.8 Tf [(at least complex all the time, i.e., some systems at certain conditions such as at equilibrium appear quite simple, but may not be )] TJ ET
BT 26.250 103.264 Td /F1 9.8 Tf [(when parameters change.)] TJ ET
BT 26.250 83.859 Td /F1 9.8 Tf [(So, getting back to the situation of trying to explicate for my old friends what complexity theory was about, this time around I )] TJ ET
BT 26.250 71.955 Td /F1 9.8 Tf [(came up with a new strategy \(for me at least\) of asking my well meaning friends if they had ever heard of “chaos theory” and )] TJ ET
BT 26.250 60.050 Td /F1 9.8 Tf [(most of them indeed had. Chaos theory, of course, has entered the popular imagination in many forms, from Jeff Goldblum’s )] TJ ET
BT 26.250 48.145 Td /F1 9.8 Tf [(famous allegory of it in the movie “Jurassic Park”, when he dropped water on the hand of the character played by Laura Dern )] TJ ET
BT 26.250 36.240 Td /F1 9.8 Tf [(and told her to watch its unpredictable flow, to the more recent film “The Butterfly Effect” with Ashton Kutcher, to last year’s )] TJ ET
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BT 291.710 19.825 Td /F1 11.0 Tf [(1)] TJ ET
BT 25.000 19.825 Td /F1 11.0 Tf [(Emergence: Complexity and Organization)] TJ ET
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BT 26.250 767.476 Td /F1 9.8 Tf [(surprisingly good romantic comedy “Chaos Theory”. As a matter of fact, each of these films does include plot elements having )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf [(to do with the property of sensitive dependence on initial conditions that characterizes chaotic systems.)] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf [(So, when the heads of my friends shook “yes” that they had indeed heard of chaos theory as well as the butterfly effect, I then )] TJ ET
BT 26.250 724.262 Td /F1 9.8 Tf [(added that chaos theory was like a branch of a wider and taller tree called “complexity science.” But immediately after offering )] TJ ET
BT 26.250 712.357 Td /F1 9.8 Tf [(that analogy, I thought to myself, uh oh, that doesn’t really help at all for at least two strong reasons. First, it leaves the harder )] TJ ET
BT 26.250 700.452 Td /F1 9.8 Tf [(question of what this wider and taller tree is comprised of yet to be explained, and second, and even more troubling, it dawned )] TJ ET
BT 26.250 688.548 Td /F1 9.8 Tf [(on me that this analogy was simply wrong and misleading in a variety of ways.)] TJ ET
BT 26.250 669.143 Td /F1 9.8 Tf [(First of all, there is a decided sense that chaos theory, at least in the form of its progenitor field of nonlinear dynamical systems )] TJ ET
BT 26.250 657.238 Td /F1 9.8 Tf [(theory \(NDS\), predates much of modern complexity theory, going back over a century to Poincaré and to the great Russian )] TJ ET
BT 26.250 645.333 Td /F1 9.8 Tf [(mathematicians Chebyshev, Lyapunov, and others. Branches can hardly be said to predate their trees! Second, a great deal of )] TJ ET
BT 26.250 633.429 Td /F1 9.8 Tf [(the mathematical apparatuses used by complexity theory, indeed, taken for granted by complexity aficionados, comes right out )] TJ ET
BT 26.250 621.524 Td /F1 9.8 Tf [(of NDS, e.g., phase space, attractors, bifurcations, qualitative dynamics, and so on. Wolfram first classified the dynamics of )] TJ ET
BT 26.250 609.619 Td /F1 9.8 Tf [(cellular automata using NDS types of categories. Furthermore, the continual updating of cellular automata, which underlies the )] TJ ET
BT 26.250 597.714 Td /F1 9.8 Tf [(apparent motion of artificial life, recapitulates the iterations of discrete difference equations as found in the logistic map which is )] TJ ET
BT 26.250 585.810 Td /F1 9.8 Tf [(so emblematic of NDS.)] TJ ET
BT 26.250 566.405 Td /F1 9.8 Tf [(Also, there are the very important differences between chaotic and complex systems, e.g., it is not clear to me at least that )] TJ ET
BT 26.250 554.500 Td /F1 9.8 Tf [(complex systems generally possess sensitive dependence on initial conditions like chaotic systems do. In addition, chaotic )] TJ ET
BT 26.250 542.595 Td /F1 9.8 Tf [(systems can form out of very simple functions whereas it seems complex systems require relatively large networks of interacting )] TJ ET
BT 26.250 530.691 Td /F1 9.8 Tf [(agents where the mathematics of their interactions is typically much more complicated than that of logistic-type maps. On the )] TJ ET
BT 26.250 518.786 Td /F1 9.8 Tf [(other hand, Shaw \(1981\) made a convincing case how chaotic systems can be understood as information generators which it )] TJ ET
BT 26.250 506.881 Td /F1 9.8 Tf [(seems to me is cognate to what Peter Allen talks about as happening in complex systems as micro-level diversity generates the )] TJ ET
BT 26.250 494.976 Td /F1 9.8 Tf [(seeds of emergent order with new properties.)] TJ ET
BT 26.250 475.572 Td /F1 9.8 Tf [(Furthermore, complexity science utilizes many more mathematical tools than what NDS can supply, e.g., there’s all the graph )] TJ ET
BT 26.250 463.667 Td /F1 9.8 Tf [(theory of social networks, the group theory of the renormalization group used to explain phase transitional types of the )] TJ ET
BT 26.250 451.762 Td /F1 9.8 Tf [(emergence of new order, all the computational complexity stuff hovering around, the talk of Turing machines, algorithmic )] TJ ET
BT 26.250 439.857 Td /F1 9.8 Tf [(complexity theory, Bennett’s logical depth, Crutchfield’s computational mechanics, and so forth—a whole host of new )] TJ ET
BT 26.250 427.953 Td /F1 9.8 Tf [(mathematical objects and constructs which include but also exceed chaos theory.)] TJ ET
BT 26.250 391.350 Td /F4 12.0 Tf [(Complexity is Vague and that is a Good Thing)] TJ ET
BT 26.250 371.396 Td /F1 9.8 Tf [(So relating complexity to chaos as tree trunk to branch simply won’t do. And, again, I was still left with the arduous task of trying )] TJ ET
BT 26.250 359.491 Td /F1 9.8 Tf [(to adequately describe the tree. That brings me back to the idea of vagueness. At first impression, it might seem problematic )] TJ ET
BT 26.250 347.586 Td /F1 9.8 Tf [(that an entire field of study appears to be perhaps hopelessly vague. “Vague” though doesn’t necessarily entail being nebulous, )] TJ ET
BT 26.250 335.682 Td /F1 9.8 Tf [(ethereal, or inherently muddled. Indeed, in philosophical circles there has recently been a great deal of interest in exploring the )] TJ ET
BT 26.250 323.777 Td /F1 9.8 Tf [(philosophical ramifications of vagueness. In this regard, the English philosopher M. S. Sainsbury \(1997\) has made a good case )] TJ ET
BT 26.250 311.872 Td /F1 9.8 Tf [(for considering much of our ordinary discourse as composed of words that are fundamentally vague. Thus, we find vagueness )] TJ ET
BT 26.250 299.967 Td /F1 9.8 Tf [(attached to the ordinary idea of “small,” demonstrated in what is called Wang’s paradox after the mathematical logician Hao )] TJ ET
BT 26.250 288.063 Td /F1 9.8 Tf [(Wang, a protegé of Kurt Gödel:)] TJ ET
BT 26.250 268.658 Td /F1 9.8 Tf [(* By mathematical induction,)] TJ ET
BT 26.250 249.253 Td /F1 9.8 Tf [(0 is small,)] TJ ET
BT 26.250 229.848 Td /F1 9.8 Tf [(If )] TJ ET
BT 34.382 229.848 Td /F5 9.8 Tf [(n)] TJ ET
BT 39.803 229.848 Td /F1 9.8 Tf [( is small, )] TJ ET
BT 80.431 229.848 Td /F5 9.8 Tf [(n)] TJ ET
BT 85.852 229.848 Td /F1 9.8 Tf [( + 1 is small;)] TJ ET
BT 26.250 210.444 Td /F1 9.8 Tf [(Therefore, every number is small.)] TJ ET
BT 26.250 191.039 Td /F1 9.8 Tf [(As the British philosopher of mathematics Michael Dummett \(1997:101\) explained about Wang’s paradox, “…since every )] TJ ET
BT 26.250 179.134 Td /F1 9.8 Tf [(natural number is larger than only finitely many natural numbers, and smaller that infinitely many, every natural number is small, )] TJ ET
BT 26.250 167.229 Td /F1 9.8 Tf [(i.e., smaller than most natural numbers.” This kind of vagueness is typically linked with the ancient conundrum of the )] TJ ET
BT 530.208 167.229 Td /F5 9.8 Tf [(heap)] TJ ET
BT 26.250 155.325 Td /F1 9.8 Tf [(known as the Sorites paradox \(Sorensen, 2006\):)] TJ ET
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BT 35.250 125.715 Td /F3 10.5 Tf [(1 grain of wheat does not make a heap)] TJ ET
BT 197.989 125.715 Td /F3 10.5 Tf [(.)] TJ ET
BT 35.250 105.741 Td /F3 10.5 Tf [(If 1 grain of wheat does not make a heap then 2 grains of wheat do not)] TJ ET
BT 332.747 105.741 Td /F3 10.5 Tf [(.)] TJ ET
BT 35.250 85.767 Td /F3 10.5 Tf [(If 2 grains of wheat do not make a heap then 3 grains do not)] TJ ET
BT 289.581 85.767 Td /F3 10.5 Tf [(.)] TJ ET
BT 35.250 65.793 Td /F3 10.5 Tf [(… If 9,999 grains of wheat do not make a heap then 10,000 do not)] TJ ET
BT 314.077 65.793 Td /F3 10.5 Tf [(.)] TJ ET
BT 26.250 36.524 Td /F1 9.8 Tf [(In the context of Sorites’s types of paradox, Sainsbury points to the word and concept “red”—there is no crisply defined set of )] TJ ET
Q
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0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf [(surprisingly good romantic comedy “Chaos Theory”. As a matter of fact, each of these films does include plot elements having )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf [(to do with the property of sensitive dependence on initial conditions that characterizes chaotic systems.)] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf [(So, when the heads of my friends shook “yes” that they had indeed heard of chaos theory as well as the butterfly effect, I then )] TJ ET
BT 26.250 724.262 Td /F1 9.8 Tf [(added that chaos theory was like a branch of a wider and taller tree called “complexity science.” But immediately after offering )] TJ ET
BT 26.250 712.357 Td /F1 9.8 Tf [(that analogy, I thought to myself, uh oh, that doesn’t really help at all for at least two strong reasons. First, it leaves the harder )] TJ ET
BT 26.250 700.452 Td /F1 9.8 Tf [(question of what this wider and taller tree is comprised of yet to be explained, and second, and even more troubling, it dawned )] TJ ET
BT 26.250 688.548 Td /F1 9.8 Tf [(on me that this analogy was simply wrong and misleading in a variety of ways.)] TJ ET
BT 26.250 669.143 Td /F1 9.8 Tf [(First of all, there is a decided sense that chaos theory, at least in the form of its progenitor field of nonlinear dynamical systems )] TJ ET
BT 26.250 657.238 Td /F1 9.8 Tf [(theory \(NDS\), predates much of modern complexity theory, going back over a century to Poincaré and to the great Russian )] TJ ET
BT 26.250 645.333 Td /F1 9.8 Tf [(mathematicians Chebyshev, Lyapunov, and others. Branches can hardly be said to predate their trees! Second, a great deal of )] TJ ET
BT 26.250 633.429 Td /F1 9.8 Tf [(the mathematical apparatuses used by complexity theory, indeed, taken for granted by complexity aficionados, comes right out )] TJ ET
BT 26.250 621.524 Td /F1 9.8 Tf [(of NDS, e.g., phase space, attractors, bifurcations, qualitative dynamics, and so on. Wolfram first classified the dynamics of )] TJ ET
BT 26.250 609.619 Td /F1 9.8 Tf [(cellular automata using NDS types of categories. Furthermore, the continual updating of cellular automata, which underlies the )] TJ ET
BT 26.250 597.714 Td /F1 9.8 Tf [(apparent motion of artificial life, recapitulates the iterations of discrete difference equations as found in the logistic map which is )] TJ ET
BT 26.250 585.810 Td /F1 9.8 Tf [(so emblematic of NDS.)] TJ ET
BT 26.250 566.405 Td /F1 9.8 Tf [(Also, there are the very important differences between chaotic and complex systems, e.g., it is not clear to me at least that )] TJ ET
BT 26.250 554.500 Td /F1 9.8 Tf [(complex systems generally possess sensitive dependence on initial conditions like chaotic systems do. In addition, chaotic )] TJ ET
BT 26.250 542.595 Td /F1 9.8 Tf [(systems can form out of very simple functions whereas it seems complex systems require relatively large networks of interacting )] TJ ET
BT 26.250 530.691 Td /F1 9.8 Tf [(agents where the mathematics of their interactions is typically much more complicated than that of logistic-type maps. On the )] TJ ET
BT 26.250 518.786 Td /F1 9.8 Tf [(other hand, Shaw \(1981\) made a convincing case how chaotic systems can be understood as information generators which it )] TJ ET
BT 26.250 506.881 Td /F1 9.8 Tf [(seems to me is cognate to what Peter Allen talks about as happening in complex systems as micro-level diversity generates the )] TJ ET
BT 26.250 494.976 Td /F1 9.8 Tf [(seeds of emergent order with new properties.)] TJ ET
BT 26.250 475.572 Td /F1 9.8 Tf [(Furthermore, complexity science utilizes many more mathematical tools than what NDS can supply, e.g., there’s all the graph )] TJ ET
BT 26.250 463.667 Td /F1 9.8 Tf [(theory of social networks, the group theory of the renormalization group used to explain phase transitional types of the )] TJ ET
BT 26.250 451.762 Td /F1 9.8 Tf [(emergence of new order, all the computational complexity stuff hovering around, the talk of Turing machines, algorithmic )] TJ ET
BT 26.250 439.857 Td /F1 9.8 Tf [(complexity theory, Bennett’s logical depth, Crutchfield’s computational mechanics, and so forth—a whole host of new )] TJ ET
BT 26.250 427.953 Td /F1 9.8 Tf [(mathematical objects and constructs which include but also exceed chaos theory.)] TJ ET
BT 26.250 391.350 Td /F4 12.0 Tf [(Complexity is Vague and that is a Good Thing)] TJ ET
BT 26.250 371.396 Td /F1 9.8 Tf [(So relating complexity to chaos as tree trunk to branch simply won’t do. And, again, I was still left with the arduous task of trying )] TJ ET
BT 26.250 359.491 Td /F1 9.8 Tf [(to adequately describe the tree. That brings me back to the idea of vagueness. At first impression, it might seem problematic )] TJ ET
BT 26.250 347.586 Td /F1 9.8 Tf [(that an entire field of study appears to be perhaps hopelessly vague. “Vague” though doesn’t necessarily entail being nebulous, )] TJ ET
BT 26.250 335.682 Td /F1 9.8 Tf [(ethereal, or inherently muddled. Indeed, in philosophical circles there has recently been a great deal of interest in exploring the )] TJ ET
BT 26.250 323.777 Td /F1 9.8 Tf [(philosophical ramifications of vagueness. In this regard, the English philosopher M. S. Sainsbury \(1997\) has made a good case )] TJ ET
BT 26.250 311.872 Td /F1 9.8 Tf [(for considering much of our ordinary discourse as composed of words that are fundamentally vague. Thus, we find vagueness )] TJ ET
BT 26.250 299.967 Td /F1 9.8 Tf [(attached to the ordinary idea of “small,” demonstrated in what is called Wang’s paradox after the mathematical logician Hao )] TJ ET
BT 26.250 288.063 Td /F1 9.8 Tf [(Wang, a protegé of Kurt Gödel:)] TJ ET
BT 26.250 268.658 Td /F1 9.8 Tf [(* By mathematical induction,)] TJ ET
BT 26.250 249.253 Td /F1 9.8 Tf [(0 is small,)] TJ ET
BT 26.250 229.848 Td /F1 9.8 Tf [(If )] TJ ET
BT 34.382 229.848 Td /F5 9.8 Tf [(n)] TJ ET
BT 39.803 229.848 Td /F1 9.8 Tf [( is small, )] TJ ET
BT 80.431 229.848 Td /F5 9.8 Tf [(n)] TJ ET
BT 85.852 229.848 Td /F1 9.8 Tf [( + 1 is small;)] TJ ET
BT 26.250 210.444 Td /F1 9.8 Tf [(Therefore, every number is small.)] TJ ET
BT 26.250 191.039 Td /F1 9.8 Tf [(As the British philosopher of mathematics Michael Dummett \(1997:101\) explained about Wang’s paradox, “…since every )] TJ ET
BT 26.250 179.134 Td /F1 9.8 Tf [(natural number is larger than only finitely many natural numbers, and smaller that infinitely many, every natural number is small, )] TJ ET
BT 26.250 167.229 Td /F1 9.8 Tf [(i.e., smaller than most natural numbers.” This kind of vagueness is typically linked with the ancient conundrum of the )] TJ ET
BT 530.208 167.229 Td /F5 9.8 Tf [(heap)] TJ ET
BT 26.250 155.325 Td /F1 9.8 Tf [(known as the Sorites paradox \(Sorensen, 2006\):)] TJ ET
0.965 0.965 0.965 rg
26.250 46.048 555.000 99.396 re f
0.267 0.267 0.267 rg
0.267 0.267 0.267 RG
26.250 145.444 m 581.250 145.444 l 581.250 144.694 l 26.250 144.694 l f
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0.271 0.267 0.267 rg
BT 35.250 125.715 Td /F3 10.5 Tf [(1 grain of wheat does not make a heap)] TJ ET
BT 197.989 125.715 Td /F3 10.5 Tf [(.)] TJ ET
BT 35.250 105.741 Td /F3 10.5 Tf [(If 1 grain of wheat does not make a heap then 2 grains of wheat do not)] TJ ET
BT 332.747 105.741 Td /F3 10.5 Tf [(.)] TJ ET
BT 35.250 85.767 Td /F3 10.5 Tf [(If 2 grains of wheat do not make a heap then 3 grains do not)] TJ ET
BT 289.581 85.767 Td /F3 10.5 Tf [(.)] TJ ET
BT 35.250 65.793 Td /F3 10.5 Tf [(… If 9,999 grains of wheat do not make a heap then 10,000 do not)] TJ ET
BT 314.077 65.793 Td /F3 10.5 Tf [(.)] TJ ET
BT 26.250 36.524 Td /F1 9.8 Tf [(In the context of Sorites’s types of paradox, Sainsbury points to the word and concept “red”—there is no crisply defined set of )] TJ ET
Q
q
15.000 22.238 577.500 754.762 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf [(surprisingly good romantic comedy “Chaos Theory”. As a matter of fact, each of these films does include plot elements having )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf [(to do with the property of sensitive dependence on initial conditions that characterizes chaotic systems.)] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf [(So, when the heads of my friends shook “yes” that they had indeed heard of chaos theory as well as the butterfly effect, I then )] TJ ET
BT 26.250 724.262 Td /F1 9.8 Tf [(added that chaos theory was like a branch of a wider and taller tree called “complexity science.” But immediately after offering )] TJ ET
BT 26.250 712.357 Td /F1 9.8 Tf [(that analogy, I thought to myself, uh oh, that doesn’t really help at all for at least two strong reasons. First, it leaves the harder )] TJ ET
BT 26.250 700.452 Td /F1 9.8 Tf [(question of what this wider and taller tree is comprised of yet to be explained, and second, and even more troubling, it dawned )] TJ ET
BT 26.250 688.548 Td /F1 9.8 Tf [(on me that this analogy was simply wrong and misleading in a variety of ways.)] TJ ET
BT 26.250 669.143 Td /F1 9.8 Tf [(First of all, there is a decided sense that chaos theory, at least in the form of its progenitor field of nonlinear dynamical systems )] TJ ET
BT 26.250 657.238 Td /F1 9.8 Tf [(theory \(NDS\), predates much of modern complexity theory, going back over a century to Poincaré and to the great Russian )] TJ ET
BT 26.250 645.333 Td /F1 9.8 Tf [(mathematicians Chebyshev, Lyapunov, and others. Branches can hardly be said to predate their trees! Second, a great deal of )] TJ ET
BT 26.250 633.429 Td /F1 9.8 Tf [(the mathematical apparatuses used by complexity theory, indeed, taken for granted by complexity aficionados, comes right out )] TJ ET
BT 26.250 621.524 Td /F1 9.8 Tf [(of NDS, e.g., phase space, attractors, bifurcations, qualitative dynamics, and so on. Wolfram first classified the dynamics of )] TJ ET
BT 26.250 609.619 Td /F1 9.8 Tf [(cellular automata using NDS types of categories. Furthermore, the continual updating of cellular automata, which underlies the )] TJ ET
BT 26.250 597.714 Td /F1 9.8 Tf [(apparent motion of artificial life, recapitulates the iterations of discrete difference equations as found in the logistic map which is )] TJ ET
BT 26.250 585.810 Td /F1 9.8 Tf [(so emblematic of NDS.)] TJ ET
BT 26.250 566.405 Td /F1 9.8 Tf [(Also, there are the very important differences between chaotic and complex systems, e.g., it is not clear to me at least that )] TJ ET
BT 26.250 554.500 Td /F1 9.8 Tf [(complex systems generally possess sensitive dependence on initial conditions like chaotic systems do. In addition, chaotic )] TJ ET
BT 26.250 542.595 Td /F1 9.8 Tf [(systems can form out of very simple functions whereas it seems complex systems require relatively large networks of interacting )] TJ ET
BT 26.250 530.691 Td /F1 9.8 Tf [(agents where the mathematics of their interactions is typically much more complicated than that of logistic-type maps. On the )] TJ ET
BT 26.250 518.786 Td /F1 9.8 Tf [(other hand, Shaw \(1981\) made a convincing case how chaotic systems can be understood as information generators which it )] TJ ET
BT 26.250 506.881 Td /F1 9.8 Tf [(seems to me is cognate to what Peter Allen talks about as happening in complex systems as micro-level diversity generates the )] TJ ET
BT 26.250 494.976 Td /F1 9.8 Tf [(seeds of emergent order with new properties.)] TJ ET
BT 26.250 475.572 Td /F1 9.8 Tf [(Furthermore, complexity science utilizes many more mathematical tools than what NDS can supply, e.g., there’s all the graph )] TJ ET
BT 26.250 463.667 Td /F1 9.8 Tf [(theory of social networks, the group theory of the renormalization group used to explain phase transitional types of the )] TJ ET
BT 26.250 451.762 Td /F1 9.8 Tf [(emergence of new order, all the computational complexity stuff hovering around, the talk of Turing machines, algorithmic )] TJ ET
BT 26.250 439.857 Td /F1 9.8 Tf [(complexity theory, Bennett’s logical depth, Crutchfield’s computational mechanics, and so forth—a whole host of new )] TJ ET
BT 26.250 427.953 Td /F1 9.8 Tf [(mathematical objects and constructs which include but also exceed chaos theory.)] TJ ET
BT 26.250 391.350 Td /F4 12.0 Tf [(Complexity is Vague and that is a Good Thing)] TJ ET
BT 26.250 371.396 Td /F1 9.8 Tf [(So relating complexity to chaos as tree trunk to branch simply won’t do. And, again, I was still left with the arduous task of trying )] TJ ET
BT 26.250 359.491 Td /F1 9.8 Tf [(to adequately describe the tree. That brings me back to the idea of vagueness. At first impression, it might seem problematic )] TJ ET
BT 26.250 347.586 Td /F1 9.8 Tf [(that an entire field of study appears to be perhaps hopelessly vague. “Vague” though doesn’t necessarily entail being nebulous, )] TJ ET
BT 26.250 335.682 Td /F1 9.8 Tf [(ethereal, or inherently muddled. Indeed, in philosophical circles there has recently been a great deal of interest in exploring the )] TJ ET
BT 26.250 323.777 Td /F1 9.8 Tf [(philosophical ramifications of vagueness. In this regard, the English philosopher M. S. Sainsbury \(1997\) has made a good case )] TJ ET
BT 26.250 311.872 Td /F1 9.8 Tf [(for considering much of our ordinary discourse as composed of words that are fundamentally vague. Thus, we find vagueness )] TJ ET
BT 26.250 299.967 Td /F1 9.8 Tf [(attached to the ordinary idea of “small,” demonstrated in what is called Wang’s paradox after the mathematical logician Hao )] TJ ET
BT 26.250 288.063 Td /F1 9.8 Tf [(Wang, a protegé of Kurt Gödel:)] TJ ET
BT 26.250 268.658 Td /F1 9.8 Tf [(* By mathematical induction,)] TJ ET
BT 26.250 249.253 Td /F1 9.8 Tf [(0 is small,)] TJ ET
BT 26.250 229.848 Td /F1 9.8 Tf [(If )] TJ ET
BT 34.382 229.848 Td /F5 9.8 Tf [(n)] TJ ET
BT 39.803 229.848 Td /F1 9.8 Tf [( is small, )] TJ ET
BT 80.431 229.848 Td /F5 9.8 Tf [(n)] TJ ET
BT 85.852 229.848 Td /F1 9.8 Tf [( + 1 is small;)] TJ ET
BT 26.250 210.444 Td /F1 9.8 Tf [(Therefore, every number is small.)] TJ ET
BT 26.250 191.039 Td /F1 9.8 Tf [(As the British philosopher of mathematics Michael Dummett \(1997:101\) explained about Wang’s paradox, “…since every )] TJ ET
BT 26.250 179.134 Td /F1 9.8 Tf [(natural number is larger than only finitely many natural numbers, and smaller that infinitely many, every natural number is small, )] TJ ET
BT 26.250 167.229 Td /F1 9.8 Tf [(i.e., smaller than most natural numbers.” This kind of vagueness is typically linked with the ancient conundrum of the )] TJ ET
BT 530.208 167.229 Td /F5 9.8 Tf [(heap)] TJ ET
BT 26.250 155.325 Td /F1 9.8 Tf [(known as the Sorites paradox \(Sorensen, 2006\):)] TJ ET
0.965 0.965 0.965 rg
26.250 46.048 555.000 99.396 re f
0.267 0.267 0.267 rg
0.267 0.267 0.267 RG
26.250 145.444 m 581.250 145.444 l 581.250 144.694 l 26.250 144.694 l f
26.250 46.048 m 581.250 46.048 l 581.250 46.798 l 26.250 46.798 l f
0.271 0.267 0.267 rg
BT 35.250 125.715 Td /F3 10.5 Tf [(1 grain of wheat does not make a heap)] TJ ET
BT 197.989 125.715 Td /F3 10.5 Tf [(.)] TJ ET
BT 35.250 105.741 Td /F3 10.5 Tf [(If 1 grain of wheat does not make a heap then 2 grains of wheat do not)] TJ ET
BT 332.747 105.741 Td /F3 10.5 Tf [(.)] TJ ET
BT 35.250 85.767 Td /F3 10.5 Tf [(If 2 grains of wheat do not make a heap then 3 grains do not)] TJ ET
BT 289.581 85.767 Td /F3 10.5 Tf [(.)] TJ ET
BT 35.250 65.793 Td /F3 10.5 Tf [(… If 9,999 grains of wheat do not make a heap then 10,000 do not)] TJ ET
BT 314.077 65.793 Td /F3 10.5 Tf [(.)] TJ ET
BT 26.250 36.524 Td /F1 9.8 Tf [(In the context of Sorites’s types of paradox, Sainsbury points to the word and concept “red”—there is no crisply defined set of )] TJ ET
Q
q
0.000 0.000 0.000 rg
BT 291.710 19.825 Td /F1 11.0 Tf [(2)] TJ ET
BT 25.000 19.825 Td /F1 11.0 Tf [(Emergence: Complexity and Organization)] TJ ET
Q
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q
15.000 29.451 577.500 747.549 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf [(referents that could be considered red without also including colors that blend off into yellow. For instance, we might find on a )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf [(shelf in an art store, a row of red oil paint tubes that go from a strong, bright, blood red all the way to something approaching )] TJ ET
BT 26.250 743.667 Td /F1 9.8 Tf [(orange yellow. There is a continuum of possible colors between red and yellow depending on the scale of resolution, although )] TJ ET
BT 26.250 731.762 Td /F1 9.8 Tf [(from a distance we can discern, in a prism, or example, a band separating red from yellow. Ralph Stacey has his well-known )] TJ ET
BT 26.250 719.857 Td /F1 9.8 Tf [(diagram distinguishing three zones of a coordinate plane into simple, random, and complex in relation to the degree of certainty )] TJ ET
BT 26.250 707.952 Td /F1 9.8 Tf [(on the horizontal axis and agreement on the vertical one. As helpful as this diagram can be, in my experience it turns out that )] TJ ET
BT 26.250 696.048 Td /F1 9.8 Tf [(the complexity region is itself highly complex, containing mini-regions, fractally embedded, of more random and more simple )] TJ ET
BT 26.250 684.143 Td /F1 9.8 Tf [(regions, like the pockets of order within the famous bifurcation diagram of the logistic map \(ah ha! We’re back to chaos theory )] TJ ET
BT 26.250 672.238 Td /F1 9.8 Tf [(after all that!\).)] TJ ET
BT 26.250 652.833 Td /F1 9.8 Tf [(As a prototypical example of vagueness, the philosopher Achille Varzi \(2001\) cites a wild passage from the many populating )] TJ ET
BT 26.250 640.929 Td /F1 9.8 Tf [(Saul Bellow’s great novel )] TJ ET
BT 137.878 640.929 Td /F5 9.8 Tf [(Herzog)] TJ ET
BT 169.302 640.929 Td /F1 9.8 Tf [(:)] TJ ET
0.965 0.965 0.965 rg
26.250 541.678 555.000 89.370 re f
0.267 0.267 0.267 rg
0.267 0.267 0.267 RG
26.250 631.048 m 581.250 631.048 l 581.250 630.298 l 26.250 630.298 l f
26.250 541.678 m 581.250 541.678 l 581.250 542.428 l 26.250 542.428 l f
0.271 0.267 0.267 rg
BT 35.250 611.319 Td /F3 10.5 Tf [(Remember the story of the most-most? It’s the story of that club in New York where people are the most of every type. There is )] TJ ET
BT 35.250 598.845 Td /F3 10.5 Tf [(the hairiest bald man and the baldest hairy man; the shortest giant and the tallest dwarf; the smartest idiot and the stupidest )] TJ ET
BT 35.250 586.371 Td /F3 10.5 Tf [(wise man. They are all there, including honest thieves and crippled acrobats. On Saturday night they have a party, eat, drink, )] TJ ET
BT 35.250 573.897 Td /F3 10.5 Tf [(dance. Then they have a contest. And if you can tell the hairiest bald man from the baldest hairy man—we are told—you get a )] TJ ET
BT 35.250 561.423 Td /F3 10.5 Tf [(prize)] TJ ET
BT 56.250 561.423 Td /F3 10.5 Tf [(.)] TJ ET
BT 26.250 532.154 Td /F1 9.8 Tf [(Varzi points out how vagueness runs through this passage because not only is there no sharp boundary exactly demarcating )] TJ ET
BT 26.250 520.249 Td /F1 9.8 Tf [(the category of bald men and no precise number of hairs separating hairy from the bald, it also makes no sense to think one can )] TJ ET
BT 26.250 508.344 Td /F1 9.8 Tf [(identify the hairiest bald man. Even though some men are obviously bald and some are clearly hairy, between the two there are )] TJ ET
BT 26.250 496.440 Td /F1 9.8 Tf [(a host of borderline cases including baldish guys, men with toupees, hirsute beatniks with a shiny bald spot on the top of their )] TJ ET
BT 26.250 484.535 Td /F1 9.8 Tf [(heads, and so on and on. Accordingly, the concepts of bald and hairy are vague with ranges of application having vague )] TJ ET
BT 26.250 472.630 Td /F1 9.8 Tf [(boundaries.)] TJ ET
BT 26.250 453.225 Td /F1 9.8 Tf [(As another philosopher Max Black \(1997\) put it, vagueness does not necessarily indicate a conceptual defect just as an )] TJ ET
BT 26.250 441.321 Td /F1 9.8 Tf [(impressionist painting is not adequately understood as a flaw of precision in technique:)] TJ ET
0.965 0.965 0.965 rg
26.250 342.070 555.000 89.370 re f
0.267 0.267 0.267 rg
26.250 431.440 m 581.250 431.440 l 581.250 430.690 l 26.250 430.690 l f
26.250 342.070 m 581.250 342.070 l 581.250 342.820 l 26.250 342.820 l f
0.271 0.267 0.267 rg
BT 35.250 411.711 Td /F3 10.5 Tf [(The impressionist painting of a London street in a fog is not a vague representation of what the artist sees, since his [sic] skill )] TJ ET
BT 35.250 399.237 Td /F3 10.5 Tf [(consists in the accuracy with which the visual impression is transcribed. But the picture is called vague in relation to a )] TJ ET
BT 35.250 386.763 Td /F3 10.5 Tf [(hypothetical laboratory record of the wave lengths and positions of the various objects in the street, while it is forgotten that )] TJ ET
BT 35.250 374.289 Td /F3 10.5 Tf [(that record, in supplying additional detail, obliterates just those large scale relations in which the artist or another observer )] TJ ET
BT 35.250 361.815 Td /F3 10.5 Tf [(may be interested)] TJ ET
BT 109.317 361.815 Td /F3 10.5 Tf [(. \(71\).)] TJ ET
BT 26.250 332.546 Td /F1 9.8 Tf [(Related to Black’s contention, the computer scientist Mark Changizi \(1999\) has made a good argument that vagueness is )] TJ ET
BT 26.250 320.641 Td /F1 9.8 Tf [(intimately related to the issues of undecidability and noncomputability in mathematical logic and computational complexity )] TJ ET
BT 26.250 308.736 Td /F1 9.8 Tf [(theory. Changizi interprets vagueness as resulting from bounds on computability, and not from human fallibility for it would exist )] TJ ET
BT 26.250 296.832 Td /F1 9.8 Tf [(even with the computer HAL from )] TJ ET
BT 173.641 296.832 Td /F5 9.8 Tf [(2001: A Space Odyssey)] TJ ET
BT 278.239 296.832 Td /F1 9.8 Tf [(. Instead, vagueness is what we are ultimately left with in the case of )] TJ ET
BT 26.250 284.927 Td /F1 9.8 Tf [(all natural languages. According to Changizi, “given that you are computationally bound, avoiding vagueness brings in greater )] TJ ET
BT 26.250 273.022 Td /F1 9.8 Tf [(costs than accepting it.” \(345\).)] TJ ET
BT 26.250 253.617 Td /F1 9.8 Tf [(Hence, I believe we can presume that complexity and complex system are in fact vague notions, but those designations have a )] TJ ET
BT 26.250 241.713 Td /F1 9.8 Tf [(silver lining. To see what the advantages can be to vagueness, it is helpful to distinguish it from the ideas of either ambiguity or )] TJ ET
BT 26.250 229.808 Td /F1 9.8 Tf [(generality. Concerning, ambiguity, the term “complexity” is definitely a candidate. Seth Lloyd at MIT several years back had )] TJ ET
BT 26.250 217.903 Td /F1 9.8 Tf [(identified at least 30 different definitions of “complexity.” This could be taken as indicating there is something fishy about the )] TJ ET
BT 26.250 205.998 Td /F1 9.8 Tf [(whole field if it can mean so many things. But, vagueness is not the same as ambiguity. Whereas ambiguity is about words )] TJ ET
BT 26.250 194.094 Td /F1 9.8 Tf [(possessing many equivocal meanings, vagueness has more to do with the referents to which the word applies. Thus, )] TJ ET
BT 26.250 182.189 Td /F1 9.8 Tf [(vagueness makes a concept more inclusive, allowing all sorts of borderline cases, in effect, manifesting the fact that it deals )] TJ ET
BT 26.250 170.284 Td /F1 9.8 Tf [(with systems whose boundaries are themselves essentially vague, permeable, fractally bounded, and so forth. Moreover, as a )] TJ ET
BT 26.250 158.379 Td /F1 9.8 Tf [(vague notion, in this philosophical sense, complexity continually resists formulation in terms of this or that discrete mathematical )] TJ ET
BT 26.250 146.475 Td /F1 9.8 Tf [(formalism such as set theory, or graph theory, or whatever theory. This of course doesn’t imply that we abandon such )] TJ ET
BT 26.250 134.570 Td /F1 9.8 Tf [(formalisms. On the contrary, it suggests instead that we go the whole length in utilizing such formalisms, but with the )] TJ ET
BT 26.250 122.665 Td /F1 9.8 Tf [(expectation that at some point we will need to transcend each formalism and devise new constructs and terms and methods to )] TJ ET
BT 26.250 110.760 Td /F1 9.8 Tf [(further our study of complex systems. This also means that vagueness doesn’t imply that anything goes in describing and )] TJ ET
BT 26.250 98.856 Td /F1 9.8 Tf [(studying complex systems, i.e., vagueness is not some kind of a license for unbridled post-modernist \(misunderstood )] TJ ET
BT 26.250 86.951 Td /F1 9.8 Tf [(postmodernism\) claptrap. Rather, it is marker that context is a crucial factor in determining the scope of inquiry.)] TJ ET
BT 26.250 67.546 Td /F1 9.8 Tf [(Vagueness is also not to be conflated with the idea of generality. Thus, although there are a multitude of types of complex )] TJ ET
BT 26.250 55.641 Td /F1 9.8 Tf [(systems, trying to get at what is complex about them by extracting some common element that could then be put into the form )] TJ ET
BT 26.250 43.737 Td /F1 9.8 Tf [(of a generalization would miss the boat by a country mile, since the highly important role that context plays in understanding )] TJ ET
Q
q
15.000 29.451 577.500 747.549 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf [(referents that could be considered red without also including colors that blend off into yellow. For instance, we might find on a )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf [(shelf in an art store, a row of red oil paint tubes that go from a strong, bright, blood red all the way to something approaching )] TJ ET
BT 26.250 743.667 Td /F1 9.8 Tf [(orange yellow. There is a continuum of possible colors between red and yellow depending on the scale of resolution, although )] TJ ET
BT 26.250 731.762 Td /F1 9.8 Tf [(from a distance we can discern, in a prism, or example, a band separating red from yellow. Ralph Stacey has his well-known )] TJ ET
BT 26.250 719.857 Td /F1 9.8 Tf [(diagram distinguishing three zones of a coordinate plane into simple, random, and complex in relation to the degree of certainty )] TJ ET
BT 26.250 707.952 Td /F1 9.8 Tf [(on the horizontal axis and agreement on the vertical one. As helpful as this diagram can be, in my experience it turns out that )] TJ ET
BT 26.250 696.048 Td /F1 9.8 Tf [(the complexity region is itself highly complex, containing mini-regions, fractally embedded, of more random and more simple )] TJ ET
BT 26.250 684.143 Td /F1 9.8 Tf [(regions, like the pockets of order within the famous bifurcation diagram of the logistic map \(ah ha! We’re back to chaos theory )] TJ ET
BT 26.250 672.238 Td /F1 9.8 Tf [(after all that!\).)] TJ ET
BT 26.250 652.833 Td /F1 9.8 Tf [(As a prototypical example of vagueness, the philosopher Achille Varzi \(2001\) cites a wild passage from the many populating )] TJ ET
BT 26.250 640.929 Td /F1 9.8 Tf [(Saul Bellow’s great novel )] TJ ET
BT 137.878 640.929 Td /F5 9.8 Tf [(Herzog)] TJ ET
BT 169.302 640.929 Td /F1 9.8 Tf [(:)] TJ ET
0.965 0.965 0.965 rg
26.250 541.678 555.000 89.370 re f
0.267 0.267 0.267 rg
0.267 0.267 0.267 RG
26.250 631.048 m 581.250 631.048 l 581.250 630.298 l 26.250 630.298 l f
26.250 541.678 m 581.250 541.678 l 581.250 542.428 l 26.250 542.428 l f
0.271 0.267 0.267 rg
BT 35.250 611.319 Td /F3 10.5 Tf [(Remember the story of the most-most? It’s the story of that club in New York where people are the most of every type. There is )] TJ ET
BT 35.250 598.845 Td /F3 10.5 Tf [(the hairiest bald man and the baldest hairy man; the shortest giant and the tallest dwarf; the smartest idiot and the stupidest )] TJ ET
BT 35.250 586.371 Td /F3 10.5 Tf [(wise man. They are all there, including honest thieves and crippled acrobats. On Saturday night they have a party, eat, drink, )] TJ ET
BT 35.250 573.897 Td /F3 10.5 Tf [(dance. Then they have a contest. And if you can tell the hairiest bald man from the baldest hairy man—we are told—you get a )] TJ ET
BT 35.250 561.423 Td /F3 10.5 Tf [(prize)] TJ ET
BT 56.250 561.423 Td /F3 10.5 Tf [(.)] TJ ET
BT 26.250 532.154 Td /F1 9.8 Tf [(Varzi points out how vagueness runs through this passage because not only is there no sharp boundary exactly demarcating )] TJ ET
BT 26.250 520.249 Td /F1 9.8 Tf [(the category of bald men and no precise number of hairs separating hairy from the bald, it also makes no sense to think one can )] TJ ET
BT 26.250 508.344 Td /F1 9.8 Tf [(identify the hairiest bald man. Even though some men are obviously bald and some are clearly hairy, between the two there are )] TJ ET
BT 26.250 496.440 Td /F1 9.8 Tf [(a host of borderline cases including baldish guys, men with toupees, hirsute beatniks with a shiny bald spot on the top of their )] TJ ET
BT 26.250 484.535 Td /F1 9.8 Tf [(heads, and so on and on. Accordingly, the concepts of bald and hairy are vague with ranges of application having vague )] TJ ET
BT 26.250 472.630 Td /F1 9.8 Tf [(boundaries.)] TJ ET
BT 26.250 453.225 Td /F1 9.8 Tf [(As another philosopher Max Black \(1997\) put it, vagueness does not necessarily indicate a conceptual defect just as an )] TJ ET
BT 26.250 441.321 Td /F1 9.8 Tf [(impressionist painting is not adequately understood as a flaw of precision in technique:)] TJ ET
0.965 0.965 0.965 rg
26.250 342.070 555.000 89.370 re f
0.267 0.267 0.267 rg
26.250 431.440 m 581.250 431.440 l 581.250 430.690 l 26.250 430.690 l f
26.250 342.070 m 581.250 342.070 l 581.250 342.820 l 26.250 342.820 l f
0.271 0.267 0.267 rg
BT 35.250 411.711 Td /F3 10.5 Tf [(The impressionist painting of a London street in a fog is not a vague representation of what the artist sees, since his [sic] skill )] TJ ET
BT 35.250 399.237 Td /F3 10.5 Tf [(consists in the accuracy with which the visual impression is transcribed. But the picture is called vague in relation to a )] TJ ET
BT 35.250 386.763 Td /F3 10.5 Tf [(hypothetical laboratory record of the wave lengths and positions of the various objects in the street, while it is forgotten that )] TJ ET
BT 35.250 374.289 Td /F3 10.5 Tf [(that record, in supplying additional detail, obliterates just those large scale relations in which the artist or another observer )] TJ ET
BT 35.250 361.815 Td /F3 10.5 Tf [(may be interested)] TJ ET
BT 109.317 361.815 Td /F3 10.5 Tf [(. \(71\).)] TJ ET
BT 26.250 332.546 Td /F1 9.8 Tf [(Related to Black’s contention, the computer scientist Mark Changizi \(1999\) has made a good argument that vagueness is )] TJ ET
BT 26.250 320.641 Td /F1 9.8 Tf [(intimately related to the issues of undecidability and noncomputability in mathematical logic and computational complexity )] TJ ET
BT 26.250 308.736 Td /F1 9.8 Tf [(theory. Changizi interprets vagueness as resulting from bounds on computability, and not from human fallibility for it would exist )] TJ ET
BT 26.250 296.832 Td /F1 9.8 Tf [(even with the computer HAL from )] TJ ET
BT 173.641 296.832 Td /F5 9.8 Tf [(2001: A Space Odyssey)] TJ ET
BT 278.239 296.832 Td /F1 9.8 Tf [(. Instead, vagueness is what we are ultimately left with in the case of )] TJ ET
BT 26.250 284.927 Td /F1 9.8 Tf [(all natural languages. According to Changizi, “given that you are computationally bound, avoiding vagueness brings in greater )] TJ ET
BT 26.250 273.022 Td /F1 9.8 Tf [(costs than accepting it.” \(345\).)] TJ ET
BT 26.250 253.617 Td /F1 9.8 Tf [(Hence, I believe we can presume that complexity and complex system are in fact vague notions, but those designations have a )] TJ ET
BT 26.250 241.713 Td /F1 9.8 Tf [(silver lining. To see what the advantages can be to vagueness, it is helpful to distinguish it from the ideas of either ambiguity or )] TJ ET
BT 26.250 229.808 Td /F1 9.8 Tf [(generality. Concerning, ambiguity, the term “complexity” is definitely a candidate. Seth Lloyd at MIT several years back had )] TJ ET
BT 26.250 217.903 Td /F1 9.8 Tf [(identified at least 30 different definitions of “complexity.” This could be taken as indicating there is something fishy about the )] TJ ET
BT 26.250 205.998 Td /F1 9.8 Tf [(whole field if it can mean so many things. But, vagueness is not the same as ambiguity. Whereas ambiguity is about words )] TJ ET
BT 26.250 194.094 Td /F1 9.8 Tf [(possessing many equivocal meanings, vagueness has more to do with the referents to which the word applies. Thus, )] TJ ET
BT 26.250 182.189 Td /F1 9.8 Tf [(vagueness makes a concept more inclusive, allowing all sorts of borderline cases, in effect, manifesting the fact that it deals )] TJ ET
BT 26.250 170.284 Td /F1 9.8 Tf [(with systems whose boundaries are themselves essentially vague, permeable, fractally bounded, and so forth. Moreover, as a )] TJ ET
BT 26.250 158.379 Td /F1 9.8 Tf [(vague notion, in this philosophical sense, complexity continually resists formulation in terms of this or that discrete mathematical )] TJ ET
BT 26.250 146.475 Td /F1 9.8 Tf [(formalism such as set theory, or graph theory, or whatever theory. This of course doesn’t imply that we abandon such )] TJ ET
BT 26.250 134.570 Td /F1 9.8 Tf [(formalisms. On the contrary, it suggests instead that we go the whole length in utilizing such formalisms, but with the )] TJ ET
BT 26.250 122.665 Td /F1 9.8 Tf [(expectation that at some point we will need to transcend each formalism and devise new constructs and terms and methods to )] TJ ET
BT 26.250 110.760 Td /F1 9.8 Tf [(further our study of complex systems. This also means that vagueness doesn’t imply that anything goes in describing and )] TJ ET
BT 26.250 98.856 Td /F1 9.8 Tf [(studying complex systems, i.e., vagueness is not some kind of a license for unbridled post-modernist \(misunderstood )] TJ ET
BT 26.250 86.951 Td /F1 9.8 Tf [(postmodernism\) claptrap. Rather, it is marker that context is a crucial factor in determining the scope of inquiry.)] TJ ET
BT 26.250 67.546 Td /F1 9.8 Tf [(Vagueness is also not to be conflated with the idea of generality. Thus, although there are a multitude of types of complex )] TJ ET
BT 26.250 55.641 Td /F1 9.8 Tf [(systems, trying to get at what is complex about them by extracting some common element that could then be put into the form )] TJ ET
BT 26.250 43.737 Td /F1 9.8 Tf [(of a generalization would miss the boat by a country mile, since the highly important role that context plays in understanding )] TJ ET
Q
q
15.000 29.451 577.500 747.549 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf [(referents that could be considered red without also including colors that blend off into yellow. For instance, we might find on a )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf [(shelf in an art store, a row of red oil paint tubes that go from a strong, bright, blood red all the way to something approaching )] TJ ET
BT 26.250 743.667 Td /F1 9.8 Tf [(orange yellow. There is a continuum of possible colors between red and yellow depending on the scale of resolution, although )] TJ ET
BT 26.250 731.762 Td /F1 9.8 Tf [(from a distance we can discern, in a prism, or example, a band separating red from yellow. Ralph Stacey has his well-known )] TJ ET
BT 26.250 719.857 Td /F1 9.8 Tf [(diagram distinguishing three zones of a coordinate plane into simple, random, and complex in relation to the degree of certainty )] TJ ET
BT 26.250 707.952 Td /F1 9.8 Tf [(on the horizontal axis and agreement on the vertical one. As helpful as this diagram can be, in my experience it turns out that )] TJ ET
BT 26.250 696.048 Td /F1 9.8 Tf [(the complexity region is itself highly complex, containing mini-regions, fractally embedded, of more random and more simple )] TJ ET
BT 26.250 684.143 Td /F1 9.8 Tf [(regions, like the pockets of order within the famous bifurcation diagram of the logistic map \(ah ha! We’re back to chaos theory )] TJ ET
BT 26.250 672.238 Td /F1 9.8 Tf [(after all that!\).)] TJ ET
BT 26.250 652.833 Td /F1 9.8 Tf [(As a prototypical example of vagueness, the philosopher Achille Varzi \(2001\) cites a wild passage from the many populating )] TJ ET
BT 26.250 640.929 Td /F1 9.8 Tf [(Saul Bellow’s great novel )] TJ ET
BT 137.878 640.929 Td /F5 9.8 Tf [(Herzog)] TJ ET
BT 169.302 640.929 Td /F1 9.8 Tf [(:)] TJ ET
0.965 0.965 0.965 rg
26.250 541.678 555.000 89.370 re f
0.267 0.267 0.267 rg
0.267 0.267 0.267 RG
26.250 631.048 m 581.250 631.048 l 581.250 630.298 l 26.250 630.298 l f
26.250 541.678 m 581.250 541.678 l 581.250 542.428 l 26.250 542.428 l f
0.271 0.267 0.267 rg
BT 35.250 611.319 Td /F3 10.5 Tf [(Remember the story of the most-most? It’s the story of that club in New York where people are the most of every type. There is )] TJ ET
BT 35.250 598.845 Td /F3 10.5 Tf [(the hairiest bald man and the baldest hairy man; the shortest giant and the tallest dwarf; the smartest idiot and the stupidest )] TJ ET
BT 35.250 586.371 Td /F3 10.5 Tf [(wise man. They are all there, including honest thieves and crippled acrobats. On Saturday night they have a party, eat, drink, )] TJ ET
BT 35.250 573.897 Td /F3 10.5 Tf [(dance. Then they have a contest. And if you can tell the hairiest bald man from the baldest hairy man—we are told—you get a )] TJ ET
BT 35.250 561.423 Td /F3 10.5 Tf [(prize)] TJ ET
BT 56.250 561.423 Td /F3 10.5 Tf [(.)] TJ ET
BT 26.250 532.154 Td /F1 9.8 Tf [(Varzi points out how vagueness runs through this passage because not only is there no sharp boundary exactly demarcating )] TJ ET
BT 26.250 520.249 Td /F1 9.8 Tf [(the category of bald men and no precise number of hairs separating hairy from the bald, it also makes no sense to think one can )] TJ ET
BT 26.250 508.344 Td /F1 9.8 Tf [(identify the hairiest bald man. Even though some men are obviously bald and some are clearly hairy, between the two there are )] TJ ET
BT 26.250 496.440 Td /F1 9.8 Tf [(a host of borderline cases including baldish guys, men with toupees, hirsute beatniks with a shiny bald spot on the top of their )] TJ ET
BT 26.250 484.535 Td /F1 9.8 Tf [(heads, and so on and on. Accordingly, the concepts of bald and hairy are vague with ranges of application having vague )] TJ ET
BT 26.250 472.630 Td /F1 9.8 Tf [(boundaries.)] TJ ET
BT 26.250 453.225 Td /F1 9.8 Tf [(As another philosopher Max Black \(1997\) put it, vagueness does not necessarily indicate a conceptual defect just as an )] TJ ET
BT 26.250 441.321 Td /F1 9.8 Tf [(impressionist painting is not adequately understood as a flaw of precision in technique:)] TJ ET
0.965 0.965 0.965 rg
26.250 342.070 555.000 89.370 re f
0.267 0.267 0.267 rg
26.250 431.440 m 581.250 431.440 l 581.250 430.690 l 26.250 430.690 l f
26.250 342.070 m 581.250 342.070 l 581.250 342.820 l 26.250 342.820 l f
0.271 0.267 0.267 rg
BT 35.250 411.711 Td /F3 10.5 Tf [(The impressionist painting of a London street in a fog is not a vague representation of what the artist sees, since his [sic] skill )] TJ ET
BT 35.250 399.237 Td /F3 10.5 Tf [(consists in the accuracy with which the visual impression is transcribed. But the picture is called vague in relation to a )] TJ ET
BT 35.250 386.763 Td /F3 10.5 Tf [(hypothetical laboratory record of the wave lengths and positions of the various objects in the street, while it is forgotten that )] TJ ET
BT 35.250 374.289 Td /F3 10.5 Tf [(that record, in supplying additional detail, obliterates just those large scale relations in which the artist or another observer )] TJ ET
BT 35.250 361.815 Td /F3 10.5 Tf [(may be interested)] TJ ET
BT 109.317 361.815 Td /F3 10.5 Tf [(. \(71\).)] TJ ET
BT 26.250 332.546 Td /F1 9.8 Tf [(Related to Black’s contention, the computer scientist Mark Changizi \(1999\) has made a good argument that vagueness is )] TJ ET
BT 26.250 320.641 Td /F1 9.8 Tf [(intimately related to the issues of undecidability and noncomputability in mathematical logic and computational complexity )] TJ ET
BT 26.250 308.736 Td /F1 9.8 Tf [(theory. Changizi interprets vagueness as resulting from bounds on computability, and not from human fallibility for it would exist )] TJ ET
BT 26.250 296.832 Td /F1 9.8 Tf [(even with the computer HAL from )] TJ ET
BT 173.641 296.832 Td /F5 9.8 Tf [(2001: A Space Odyssey)] TJ ET
BT 278.239 296.832 Td /F1 9.8 Tf [(. Instead, vagueness is what we are ultimately left with in the case of )] TJ ET
BT 26.250 284.927 Td /F1 9.8 Tf [(all natural languages. According to Changizi, “given that you are computationally bound, avoiding vagueness brings in greater )] TJ ET
BT 26.250 273.022 Td /F1 9.8 Tf [(costs than accepting it.” \(345\).)] TJ ET
BT 26.250 253.617 Td /F1 9.8 Tf [(Hence, I believe we can presume that complexity and complex system are in fact vague notions, but those designations have a )] TJ ET
BT 26.250 241.713 Td /F1 9.8 Tf [(silver lining. To see what the advantages can be to vagueness, it is helpful to distinguish it from the ideas of either ambiguity or )] TJ ET
BT 26.250 229.808 Td /F1 9.8 Tf [(generality. Concerning, ambiguity, the term “complexity” is definitely a candidate. Seth Lloyd at MIT several years back had )] TJ ET
BT 26.250 217.903 Td /F1 9.8 Tf [(identified at least 30 different definitions of “complexity.” This could be taken as indicating there is something fishy about the )] TJ ET
BT 26.250 205.998 Td /F1 9.8 Tf [(whole field if it can mean so many things. But, vagueness is not the same as ambiguity. Whereas ambiguity is about words )] TJ ET
BT 26.250 194.094 Td /F1 9.8 Tf [(possessing many equivocal meanings, vagueness has more to do with the referents to which the word applies. Thus, )] TJ ET
BT 26.250 182.189 Td /F1 9.8 Tf [(vagueness makes a concept more inclusive, allowing all sorts of borderline cases, in effect, manifesting the fact that it deals )] TJ ET
BT 26.250 170.284 Td /F1 9.8 Tf [(with systems whose boundaries are themselves essentially vague, permeable, fractally bounded, and so forth. Moreover, as a )] TJ ET
BT 26.250 158.379 Td /F1 9.8 Tf [(vague notion, in this philosophical sense, complexity continually resists formulation in terms of this or that discrete mathematical )] TJ ET
BT 26.250 146.475 Td /F1 9.8 Tf [(formalism such as set theory, or graph theory, or whatever theory. This of course doesn’t imply that we abandon such )] TJ ET
BT 26.250 134.570 Td /F1 9.8 Tf [(formalisms. On the contrary, it suggests instead that we go the whole length in utilizing such formalisms, but with the )] TJ ET
BT 26.250 122.665 Td /F1 9.8 Tf [(expectation that at some point we will need to transcend each formalism and devise new constructs and terms and methods to )] TJ ET
BT 26.250 110.760 Td /F1 9.8 Tf [(further our study of complex systems. This also means that vagueness doesn’t imply that anything goes in describing and )] TJ ET
BT 26.250 98.856 Td /F1 9.8 Tf [(studying complex systems, i.e., vagueness is not some kind of a license for unbridled post-modernist \(misunderstood )] TJ ET
BT 26.250 86.951 Td /F1 9.8 Tf [(postmodernism\) claptrap. Rather, it is marker that context is a crucial factor in determining the scope of inquiry.)] TJ ET
BT 26.250 67.546 Td /F1 9.8 Tf [(Vagueness is also not to be conflated with the idea of generality. Thus, although there are a multitude of types of complex )] TJ ET
BT 26.250 55.641 Td /F1 9.8 Tf [(systems, trying to get at what is complex about them by extracting some common element that could then be put into the form )] TJ ET
BT 26.250 43.737 Td /F1 9.8 Tf [(of a generalization would miss the boat by a country mile, since the highly important role that context plays in understanding )] TJ ET
Q
q
0.000 0.000 0.000 rg
BT 291.710 19.825 Td /F1 11.0 Tf [(3)] TJ ET
BT 25.000 19.825 Td /F1 11.0 Tf [(Emergence: Complexity and Organization)] TJ ET
Q
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BT 26.250 767.476 Td /F1 9.8 Tf [(complex systems would be sacrificed. Complex systems are related to other complex systems, but this relation is better thought )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf [(of in terms of a Wittgensteinian family resemblance than some common essence that they share in general.)] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf [(For a moment, let’s assume the opposite, i.e., that the complexity of a complex system, indeed, the realm of complex systems in )] TJ ET
BT 26.250 724.262 Td /F1 9.8 Tf [(general are not vague notions but instead can be exactingly and precisely defined. This would entail that it would always be )] TJ ET
BT 26.250 712.357 Td /F5 9.8 Tf [(decidable)] TJ ET
BT 67.980 712.357 Td /F1 9.8 Tf [( whether a system was or was not complex, no borderline cases allowed. But this would paradoxically turn complexity )] TJ ET
BT 26.250 700.452 Td /F1 9.8 Tf [(into a simple notion for surely a crucial aspect of simplicity is the presence of crisp, uncontroversially so, boundaries. This, )] TJ ET
BT 26.250 688.548 Td /F1 9.8 Tf [(though, would in turn imply that complexity as simplicity must run up against Rice’s theorem in mathematical logic and )] TJ ET
BT 26.250 676.643 Td /F1 9.8 Tf [(computatability theory, which suggests that only trivial problems are decidable or computable, i.e., there are algorithms to solve )] TJ ET
BT 26.250 664.738 Td /F1 9.8 Tf [(them \(Rice’s Theorem, Weisstein\).)] TJ ET
BT 26.250 645.333 Td /F1 9.8 Tf [(“Trivial” in this sense is closely related to properties that are always true or always false, i.e., tautologically demonstrable )] TJ ET
BT 26.250 633.429 Td /F1 9.8 Tf [(properties such as that bachelors possess the property of being non-married. More formally, Rice’s theorem holds that for any )] TJ ET
BT 26.250 621.524 Td /F1 9.8 Tf [(non-trivial property of partial functions \(we’ll put aside for the sake of brevity the technical definition of such functions\), there is )] TJ ET
BT 26.250 609.619 Td /F1 9.8 Tf [(no general and effective method to decide whether an algorithm computes a partial function with that property \(Rice’s Theorem, )] TJ ET
BT 26.250 597.714 Td /F1 9.8 Tf [(Wikipedia\). Turing’s famous noncomputability results turn out to be a special case of Rice’s Theorem which states the more )] TJ ET
BT 26.250 585.810 Td /F1 9.8 Tf [(general case that every nontrivial decision problem regarding the function computed by a given Turing machine has no )] TJ ET
BT 26.250 573.905 Td /F1 9.8 Tf [(algorithmic solution \(Goldreich, 2008\). Rice’s theorem is an important result for computer science because it sets up boundaries )] TJ ET
BT 26.250 562.000 Td /F1 9.8 Tf [(for research in that area.)] TJ ET
BT 26.250 542.595 Td /F1 9.8 Tf [(If complexity and complex were in actuality nonvague, crisp ideas, then according to Changizi’s linkage of vagueness to )] TJ ET
BT 26.250 530.691 Td /F1 9.8 Tf [(undecidability described above, most matters involving complex systems, by involving only nonvague, crisp areas of delineation, )] TJ ET
BT 26.250 518.786 Td /F1 9.8 Tf [(would therefore be decidable. But according to Rice’s Theorem, this would suggest that most matters involving complex )] TJ ET
BT 26.250 506.881 Td /F1 9.8 Tf [(systems would be trivial. But clearly they’re not, as our readers and authors and anyone else for that matter researching )] TJ ET
BT 26.250 494.976 Td /F1 9.8 Tf [(complex systems clearly knows. Rather, complex systems are difficult to research, difficult to measure, difficult to construct )] TJ ET
BT 26.250 483.072 Td /F1 9.8 Tf [(viable theories of, indeed difficult to determine if or if not they are in fact complex! A case could be made, I believe, that the )] TJ ET
BT 26.250 471.167 Td /F1 9.8 Tf [(more difficult it is to define a specific field of study, ultimately the more interesting it is precisely because it eludes preconceived )] TJ ET
BT 26.250 459.262 Td /F1 9.8 Tf [(constructs, frameworks, and pat answers.)] TJ ET
BT 26.250 439.857 Td /F1 9.8 Tf [(Ultimately, the best strategy I could have followed in trying to describe to my friends what complexity theory was about was to )] TJ ET
BT 26.250 427.953 Td /F1 9.8 Tf [(simply show them a copy of this issue of E:CO and gone through it, weaving around the more arcane mathematical constructs, )] TJ ET
BT 26.250 416.048 Td /F1 9.8 Tf [(and pointing to the kinds of systems and the issues being investigated and the conclusions being drawn. I can think of no better )] TJ ET
BT 26.250 404.143 Td /F1 9.8 Tf [(way to describe what makes up complexity theory than these examples.)] TJ ET
BT 26.250 367.541 Td /F4 12.0 Tf [(References)] TJ ET
BT 26.250 340.086 Td /F1 9.8 Tf [(1.)] TJ ET
BT 38.132 340.086 Td /F1 9.8 Tf [(Black, M. \(1997\). “Vagueness: An exercise in logical analysis,” R. Keefe and P. Smith \(eds.\), Vagueness: A Reader, ISBN )] TJ ET
BT 26.250 328.182 Td /F1 9.8 Tf [(9780262112253. pp. 69-81.)] TJ ET
BT 26.250 308.777 Td /F1 9.8 Tf [(2.)] TJ ET
BT 38.132 308.777 Td /F1 9.8 Tf [(Changizi, M. \(1999\). “Vagueness, rationality and undecidability: A theory of why there is vagueness,” Synthese, ISSN 0039-)] TJ ET
BT 26.250 296.872 Td /F1 9.8 Tf [(7857, 120: 345-374.)] TJ ET
BT 26.250 277.467 Td /F1 9.8 Tf [(3.)] TJ ET
BT 38.132 277.467 Td /F1 9.8 Tf [(Dummett, M. \(1997\). “Wang’s paradox,” in R. Keefe and P. Smith \(eds.\), Vagueness: A Reader, ISBN 9780262112253, pp. )] TJ ET
BT 26.250 265.563 Td /F1 9.8 Tf [(99-118.)] TJ ET
BT 26.250 246.158 Td /F1 9.8 Tf [(4.)] TJ ET
BT 38.132 246.158 Td /F1 9.8 Tf [(Goldreich, O. \(2008\). Computational Complexity: A Conceptual Perspective, ISBN 9780521884730.)] TJ ET
BT 26.250 226.753 Td /F1 9.8 Tf [(5.)] TJ ET
BT 38.132 226.753 Td /F1 9.8 Tf [(Hyde, D. \(2005\). “Sorites paradox,” Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/sorites-paradox/.)] TJ ET
BT 26.250 207.348 Td /F1 9.8 Tf [(6.)] TJ ET
BT 38.132 207.348 Td /F1 9.8 Tf [(Rice’s Theorem \(Wikipedia\). http://en.wikipedia.org/wiki/Rice%27s_theorem.)] TJ ET
BT 26.250 187.944 Td /F1 9.8 Tf [(7.)] TJ ET
BT 38.132 187.944 Td /F1 9.8 Tf [(Sainsbury, M.S. \(1997\). “Concepts without boundaries,” in R. Keefe and P. Smith \(eds.\), Vagueness: A Reader, ISBN )] TJ ET
BT 26.250 176.039 Td /F1 9.8 Tf [(9780262112253, pp. 251-264.)] TJ ET
BT 26.250 156.634 Td /F1 9.8 Tf [(8.)] TJ ET
BT 38.132 156.634 Td /F1 9.8 Tf [(Shaw, R. \(1981\). Strange attractors, chaotic behavior, and information theory,” Zeitschrift für Naturforschung, ISSN 0932-)] TJ ET
BT 26.250 144.729 Td /F1 9.8 Tf [(0784, 36a: 80-112.)] TJ ET
BT 26.250 125.325 Td /F1 9.8 Tf [(9.)] TJ ET
BT 38.132 125.325 Td /F1 9.8 Tf [(Sorensen, R. \(2006\). “Vagueness,” Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/vagueness/.)] TJ ET
BT 26.250 105.920 Td /F1 9.8 Tf [(10.)] TJ ET
BT 43.553 105.920 Td /F1 9.8 Tf [(Varzi, A. C. \(2001\). “Vagueness, logic, and ontol-ogy,” The Dialogue: Yearbooks for Philosophical Hermeneutics, 1: 135-)] TJ ET
BT 26.250 94.015 Td /F1 9.8 Tf [(154.)] TJ ET
Q
q
15.000 76.634 577.500 700.366 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf [(complex systems would be sacrificed. Complex systems are related to other complex systems, but this relation is better thought )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf [(of in terms of a Wittgensteinian family resemblance than some common essence that they share in general.)] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf [(For a moment, let’s assume the opposite, i.e., that the complexity of a complex system, indeed, the realm of complex systems in )] TJ ET
BT 26.250 724.262 Td /F1 9.8 Tf [(general are not vague notions but instead can be exactingly and precisely defined. This would entail that it would always be )] TJ ET
BT 26.250 712.357 Td /F5 9.8 Tf [(decidable)] TJ ET
BT 67.980 712.357 Td /F1 9.8 Tf [( whether a system was or was not complex, no borderline cases allowed. But this would paradoxically turn complexity )] TJ ET
BT 26.250 700.452 Td /F1 9.8 Tf [(into a simple notion for surely a crucial aspect of simplicity is the presence of crisp, uncontroversially so, boundaries. This, )] TJ ET
BT 26.250 688.548 Td /F1 9.8 Tf [(though, would in turn imply that complexity as simplicity must run up against Rice’s theorem in mathematical logic and )] TJ ET
BT 26.250 676.643 Td /F1 9.8 Tf [(computatability theory, which suggests that only trivial problems are decidable or computable, i.e., there are algorithms to solve )] TJ ET
BT 26.250 664.738 Td /F1 9.8 Tf [(them \(Rice’s Theorem, Weisstein\).)] TJ ET
BT 26.250 645.333 Td /F1 9.8 Tf [(“Trivial” in this sense is closely related to properties that are always true or always false, i.e., tautologically demonstrable )] TJ ET
BT 26.250 633.429 Td /F1 9.8 Tf [(properties such as that bachelors possess the property of being non-married. More formally, Rice’s theorem holds that for any )] TJ ET
BT 26.250 621.524 Td /F1 9.8 Tf [(non-trivial property of partial functions \(we’ll put aside for the sake of brevity the technical definition of such functions\), there is )] TJ ET
BT 26.250 609.619 Td /F1 9.8 Tf [(no general and effective method to decide whether an algorithm computes a partial function with that property \(Rice’s Theorem, )] TJ ET
BT 26.250 597.714 Td /F1 9.8 Tf [(Wikipedia\). Turing’s famous noncomputability results turn out to be a special case of Rice’s Theorem which states the more )] TJ ET
BT 26.250 585.810 Td /F1 9.8 Tf [(general case that every nontrivial decision problem regarding the function computed by a given Turing machine has no )] TJ ET
BT 26.250 573.905 Td /F1 9.8 Tf [(algorithmic solution \(Goldreich, 2008\). Rice’s theorem is an important result for computer science because it sets up boundaries )] TJ ET
BT 26.250 562.000 Td /F1 9.8 Tf [(for research in that area.)] TJ ET
BT 26.250 542.595 Td /F1 9.8 Tf [(If complexity and complex were in actuality nonvague, crisp ideas, then according to Changizi’s linkage of vagueness to )] TJ ET
BT 26.250 530.691 Td /F1 9.8 Tf [(undecidability described above, most matters involving complex systems, by involving only nonvague, crisp areas of delineation, )] TJ ET
BT 26.250 518.786 Td /F1 9.8 Tf [(would therefore be decidable. But according to Rice’s Theorem, this would suggest that most matters involving complex )] TJ ET
BT 26.250 506.881 Td /F1 9.8 Tf [(systems would be trivial. But clearly they’re not, as our readers and authors and anyone else for that matter researching )] TJ ET
BT 26.250 494.976 Td /F1 9.8 Tf [(complex systems clearly knows. Rather, complex systems are difficult to research, difficult to measure, difficult to construct )] TJ ET
BT 26.250 483.072 Td /F1 9.8 Tf [(viable theories of, indeed difficult to determine if or if not they are in fact complex! A case could be made, I believe, that the )] TJ ET
BT 26.250 471.167 Td /F1 9.8 Tf [(more difficult it is to define a specific field of study, ultimately the more interesting it is precisely because it eludes preconceived )] TJ ET
BT 26.250 459.262 Td /F1 9.8 Tf [(constructs, frameworks, and pat answers.)] TJ ET
BT 26.250 439.857 Td /F1 9.8 Tf [(Ultimately, the best strategy I could have followed in trying to describe to my friends what complexity theory was about was to )] TJ ET
BT 26.250 427.953 Td /F1 9.8 Tf [(simply show them a copy of this issue of E:CO and gone through it, weaving around the more arcane mathematical constructs, )] TJ ET
BT 26.250 416.048 Td /F1 9.8 Tf [(and pointing to the kinds of systems and the issues being investigated and the conclusions being drawn. I can think of no better )] TJ ET
BT 26.250 404.143 Td /F1 9.8 Tf [(way to describe what makes up complexity theory than these examples.)] TJ ET
BT 26.250 367.541 Td /F4 12.0 Tf [(References)] TJ ET
BT 26.250 340.086 Td /F1 9.8 Tf [(1.)] TJ ET
BT 38.132 340.086 Td /F1 9.8 Tf [(Black, M. \(1997\). “Vagueness: An exercise in logical analysis,” R. Keefe and P. Smith \(eds.\), Vagueness: A Reader, ISBN )] TJ ET
BT 26.250 328.182 Td /F1 9.8 Tf [(9780262112253. pp. 69-81.)] TJ ET
BT 26.250 308.777 Td /F1 9.8 Tf [(2.)] TJ ET
BT 38.132 308.777 Td /F1 9.8 Tf [(Changizi, M. \(1999\). “Vagueness, rationality and undecidability: A theory of why there is vagueness,” Synthese, ISSN 0039-)] TJ ET
BT 26.250 296.872 Td /F1 9.8 Tf [(7857, 120: 345-374.)] TJ ET
BT 26.250 277.467 Td /F1 9.8 Tf [(3.)] TJ ET
BT 38.132 277.467 Td /F1 9.8 Tf [(Dummett, M. \(1997\). “Wang’s paradox,” in R. Keefe and P. Smith \(eds.\), Vagueness: A Reader, ISBN 9780262112253, pp. )] TJ ET
BT 26.250 265.563 Td /F1 9.8 Tf [(99-118.)] TJ ET
BT 26.250 246.158 Td /F1 9.8 Tf [(4.)] TJ ET
BT 38.132 246.158 Td /F1 9.8 Tf [(Goldreich, O. \(2008\). Computational Complexity: A Conceptual Perspective, ISBN 9780521884730.)] TJ ET
BT 26.250 226.753 Td /F1 9.8 Tf [(5.)] TJ ET
BT 38.132 226.753 Td /F1 9.8 Tf [(Hyde, D. \(2005\). “Sorites paradox,” Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/sorites-paradox/.)] TJ ET
BT 26.250 207.348 Td /F1 9.8 Tf [(6.)] TJ ET
BT 38.132 207.348 Td /F1 9.8 Tf [(Rice’s Theorem \(Wikipedia\). http://en.wikipedia.org/wiki/Rice%27s_theorem.)] TJ ET
BT 26.250 187.944 Td /F1 9.8 Tf [(7.)] TJ ET
BT 38.132 187.944 Td /F1 9.8 Tf [(Sainsbury, M.S. \(1997\). “Concepts without boundaries,” in R. Keefe and P. Smith \(eds.\), Vagueness: A Reader, ISBN )] TJ ET
BT 26.250 176.039 Td /F1 9.8 Tf [(9780262112253, pp. 251-264.)] TJ ET
BT 26.250 156.634 Td /F1 9.8 Tf [(8.)] TJ ET
BT 38.132 156.634 Td /F1 9.8 Tf [(Shaw, R. \(1981\). Strange attractors, chaotic behavior, and information theory,” Zeitschrift für Naturforschung, ISSN 0932-)] TJ ET
BT 26.250 144.729 Td /F1 9.8 Tf [(0784, 36a: 80-112.)] TJ ET
BT 26.250 125.325 Td /F1 9.8 Tf [(9.)] TJ ET
BT 38.132 125.325 Td /F1 9.8 Tf [(Sorensen, R. \(2006\). “Vagueness,” Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/vagueness/.)] TJ ET
BT 26.250 105.920 Td /F1 9.8 Tf [(10.)] TJ ET
BT 43.553 105.920 Td /F1 9.8 Tf [(Varzi, A. C. \(2001\). “Vagueness, logic, and ontol-ogy,” The Dialogue: Yearbooks for Philosophical Hermeneutics, 1: 135-)] TJ ET
BT 26.250 94.015 Td /F1 9.8 Tf [(154.)] TJ ET
Q
q
15.000 76.634 577.500 700.366 re W n
0.271 0.267 0.267 rg
BT 26.250 767.476 Td /F1 9.8 Tf [(complex systems would be sacrificed. Complex systems are related to other complex systems, but this relation is better thought )] TJ ET
BT 26.250 755.571 Td /F1 9.8 Tf [(of in terms of a Wittgensteinian family resemblance than some common essence that they share in general.)] TJ ET
BT 26.250 736.167 Td /F1 9.8 Tf [(For a moment, let’s assume the opposite, i.e., that the complexity of a complex system, indeed, the realm of complex systems in )] TJ ET
BT 26.250 724.262 Td /F1 9.8 Tf [(general are not vague notions but instead can be exactingly and precisely defined. This would entail that it would always be )] TJ ET
BT 26.250 712.357 Td /F5 9.8 Tf [(decidable)] TJ ET
BT 67.980 712.357 Td /F1 9.8 Tf [( whether a system was or was not complex, no borderline cases allowed. But this would paradoxically turn complexity )] TJ ET
BT 26.250 700.452 Td /F1 9.8 Tf [(into a simple notion for surely a crucial aspect of simplicity is the presence of crisp, uncontroversially so, boundaries. This, )] TJ ET
BT 26.250 688.548 Td /F1 9.8 Tf [(though, would in turn imply that complexity as simplicity must run up against Rice’s theorem in mathematical logic and )] TJ ET
BT 26.250 676.643 Td /F1 9.8 Tf [(computatability theory, which suggests that only trivial problems are decidable or computable, i.e., there are algorithms to solve )] TJ ET
BT 26.250 664.738 Td /F1 9.8 Tf [(them \(Rice’s Theorem, Weisstein\).)] TJ ET
BT 26.250 645.333 Td /F1 9.8 Tf [(“Trivial” in this sense is closely related to properties that are always true or always false, i.e., tautologically demonstrable )] TJ ET
BT 26.250 633.429 Td /F1 9.8 Tf [(properties such as that bachelors possess the property of being non-married. More formally, Rice’s theorem holds that for any )] TJ ET
BT 26.250 621.524 Td /F1 9.8 Tf [(non-trivial property of partial functions \(we’ll put aside for the sake of brevity the technical definition of such functions\), there is )] TJ ET
BT 26.250 609.619 Td /F1 9.8 Tf [(no general and effective method to decide whether an algorithm computes a partial function with that property \(Rice’s Theorem, )] TJ ET
BT 26.250 597.714 Td /F1 9.8 Tf [(Wikipedia\). Turing’s famous noncomputability results turn out to be a special case of Rice’s Theorem which states the more )] TJ ET
BT 26.250 585.810 Td /F1 9.8 Tf [(general case that every nontrivial decision problem regarding the function computed by a given Turing machine has no )] TJ ET
BT 26.250 573.905 Td /F1 9.8 Tf [(algorithmic solution \(Goldreich, 2008\). Rice’s theorem is an important result for computer science because it sets up boundaries )] TJ ET
BT 26.250 562.000 Td /F1 9.8 Tf [(for research in that area.)] TJ ET
BT 26.250 542.595 Td /F1 9.8 Tf [(If complexity and complex were in actuality nonvague, crisp ideas, then according to Changizi’s linkage of vagueness to )] TJ ET
BT 26.250 530.691 Td /F1 9.8 Tf [(undecidability described above, most matters involving complex systems, by involving only nonvague, crisp areas of delineation, )] TJ ET
BT 26.250 518.786 Td /F1 9.8 Tf [(would therefore be decidable. But according to Rice’s Theorem, this would suggest that most matters involving complex )] TJ ET
BT 26.250 506.881 Td /F1 9.8 Tf [(systems would be trivial. But clearly they’re not, as our readers and authors and anyone else for that matter researching )] TJ ET
BT 26.250 494.976 Td /F1 9.8 Tf [(complex systems clearly knows. Rather, complex systems are difficult to research, difficult to measure, difficult to construct )] TJ ET
BT 26.250 483.072 Td /F1 9.8 Tf [(viable theories of, indeed difficult to determine if or if not they are in fact complex! A case could be made, I believe, that the )] TJ ET
BT 26.250 471.167 Td /F1 9.8 Tf [(more difficult it is to define a specific field of study, ultimately the more interesting it is precisely because it eludes preconceived )] TJ ET
BT 26.250 459.262 Td /F1 9.8 Tf [(constructs, frameworks, and pat answers.)] TJ ET
BT 26.250 439.857 Td /F1 9.8 Tf [(Ultimately, the best strategy I could have followed in trying to describe to my friends what complexity theory was about was to )] TJ ET
BT 26.250 427.953 Td /F1 9.8 Tf [(simply show them a copy of this issue of E:CO and gone through it, weaving around the more arcane mathematical constructs, )] TJ ET
BT 26.250 416.048 Td /F1 9.8 Tf [(and pointing to the kinds of systems and the issues being investigated and the conclusions being drawn. I can think of no better )] TJ ET
BT 26.250 404.143 Td /F1 9.8 Tf [(way to describe what makes up complexity theory than these examples.)] TJ ET
BT 26.250 367.541 Td /F4 12.0 Tf [(References)] TJ ET
BT 26.250 340.086 Td /F1 9.8 Tf [(1.)] TJ ET
BT 38.132 340.086 Td /F1 9.8 Tf [(Black, M. \(1997\). “Vagueness: An exercise in logical analysis,” R. Keefe and P. Smith \(eds.\), Vagueness: A Reader, ISBN )] TJ ET
BT 26.250 328.182 Td /F1 9.8 Tf [(9780262112253. pp. 69-81.)] TJ ET
BT 26.250 308.777 Td /F1 9.8 Tf [(2.)] TJ ET
BT 38.132 308.777 Td /F1 9.8 Tf [(Changizi, M. \(1999\). “Vagueness, rationality and undecidability: A theory of why there is vagueness,” Synthese, ISSN 0039-)] TJ ET
BT 26.250 296.872 Td /F1 9.8 Tf [(7857, 120: 345-374.)] TJ ET
BT 26.250 277.467 Td /F1 9.8 Tf [(3.)] TJ ET
BT 38.132 277.467 Td /F1 9.8 Tf [(Dummett, M. \(1997\). “Wang’s paradox,” in R. Keefe and P. Smith \(eds.\), Vagueness: A Reader, ISBN 9780262112253, pp. )] TJ ET
BT 26.250 265.563 Td /F1 9.8 Tf [(99-118.)] TJ ET
BT 26.250 246.158 Td /F1 9.8 Tf [(4.)] TJ ET
BT 38.132 246.158 Td /F1 9.8 Tf [(Goldreich, O. \(2008\). Computational Complexity: A Conceptual Perspective, ISBN 9780521884730.)] TJ ET
BT 26.250 226.753 Td /F1 9.8 Tf [(5.)] TJ ET
BT 38.132 226.753 Td /F1 9.8 Tf [(Hyde, D. \(2005\). “Sorites paradox,” Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/sorites-paradox/.)] TJ ET
BT 26.250 207.348 Td /F1 9.8 Tf [(6.)] TJ ET
BT 38.132 207.348 Td /F1 9.8 Tf [(Rice’s Theorem \(Wikipedia\). http://en.wikipedia.org/wiki/Rice%27s_theorem.)] TJ ET
BT 26.250 187.944 Td /F1 9.8 Tf [(7.)] TJ ET
BT 38.132 187.944 Td /F1 9.8 Tf [(Sainsbury, M.S. \(1997\). “Concepts without boundaries,” in R. Keefe and P. Smith \(eds.\), Vagueness: A Reader, ISBN )] TJ ET
BT 26.250 176.039 Td /F1 9.8 Tf [(9780262112253, pp. 251-264.)] TJ ET
BT 26.250 156.634 Td /F1 9.8 Tf [(8.)] TJ ET
BT 38.132 156.634 Td /F1 9.8 Tf [(Shaw, R. \(1981\). Strange attractors, chaotic behavior, and information theory,” Zeitschrift für Naturforschung, ISSN 0932-)] TJ ET
BT 26.250 144.729 Td /F1 9.8 Tf [(0784, 36a: 80-112.)] TJ ET
BT 26.250 125.325 Td /F1 9.8 Tf [(9.)] TJ ET
BT 38.132 125.325 Td /F1 9.8 Tf [(Sorensen, R. \(2006\). “Vagueness,” Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/vagueness/.)] TJ ET
BT 26.250 105.920 Td /F1 9.8 Tf [(10.)] TJ ET
BT 43.553 105.920 Td /F1 9.8 Tf [(Varzi, A. C. \(2001\). “Vagueness, logic, and ontol-ogy,” The Dialogue: Yearbooks for Philosophical Hermeneutics, 1: 135-)] TJ ET
BT 26.250 94.015 Td /F1 9.8 Tf [(154.)] TJ ET
Q
q
0.000 0.000 0.000 rg
BT 291.710 19.825 Td /F1 11.0 Tf [(4)] TJ ET
BT 25.000 19.825 Td /F1 11.0 Tf [(Emergence: Complexity and Organization)] TJ ET
Q
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