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<title>Re: [Fis] Limits of Formal Systems</title>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">Dear
</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">All</span><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">Thank you for th</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">is</span><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">
timely and important discussion that continues the theme </span><span lang="EN-US" style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">of the paradigm shift
</span><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">we started with the New Year Lecture. It seems to me that we are already navigating the turbulent waters of several paradigm shifts in the production and use of knowledge.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">Here is my list of concurrent shifts one can observe:<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpFirst" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:36.0pt;mso-add-space:auto;text-indent:-17.85pt;mso-list:l0 level1 lfo3;layout-grid-mode:char">
<![if !supportLists]><span lang="HR" style="font-family:Symbol;color:black"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="HR" style="font-family:"Avenir Book";color:black">MULTIDISCIPLINARY approaches<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:36.0pt;mso-add-space:auto;text-indent:-17.85pt;mso-list:l0 level1 lfo3;layout-grid-mode:char">
<![if !supportLists]><span lang="HR" style="font-family:Symbol;color:black"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="HR" style="font-family:"Avenir Book";color:black">MULTI-LEVEL ANALYSIS<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:36.0pt;mso-add-space:auto;text-indent:-17.85pt;mso-list:l0 level1 lfo3;layout-grid-mode:char">
<![if !supportLists]><span lang="HR" style="font-family:Symbol;color:black"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="HR" style="font-family:"Avenir Book";color:black">THE ROLE OF THE OBSERVER – declaring an observer's perspective in the given context<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:36.0pt;mso-add-space:auto;text-indent:-17.85pt;mso-list:l0 level1 lfo3;layout-grid-mode:char">
<![if !supportLists]><span lang="HR" style="font-family:Symbol;color:black"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="HR" style="font-family:"Avenir Book";color:black">DYNAMICAL approaches<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:36.0pt;mso-add-space:auto;text-indent:-17.85pt;mso-list:l0 level1 lfo3;layout-grid-mode:char">
<![if !supportLists]><span lang="HR" style="font-family:Symbol;color:black"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="HR" style="font-family:"Avenir Book";color:black">AGENTIAL view of life. Living agents navigating „white-water“ (dynamic, largely unpredictable) environments („Wicked problems“)<br>
Cells as collectives of active parts that „dance“ together to produce common goals, based on choreography constrained by chemistry and physics.<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:36.0pt;mso-add-space:auto;text-indent:-17.85pt;mso-list:l0 level1 lfo3;layout-grid-mode:char">
<![if !supportLists]><span lang="HR" style="font-family:Symbol;color:black"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="HR" style="font-family:"Avenir Book";color:black">LOGIC (such as logic in reality-LIR and other non-standard logics)<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:36.0pt;mso-add-space:auto;text-indent:-17.85pt;mso-list:l0 level1 lfo3;layout-grid-mode:char">
<![if !supportLists]><span lang="HR" style="font-family:Symbol;color:black"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="HR" style="font-family:"Avenir Book";color:black">INFORMATION AND COMPUTATION as conceptual glues<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:72.0pt;mso-add-space:auto;text-indent:-17.85pt;mso-list:l0 level2 lfo3;layout-grid-mode:char">
<![if !supportLists]><span lang="HR" style="font-family:"Courier New";color:black"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="HR" style="font-family:"Avenir Book";color:black">COMPUTING & algorithms beyond Turing model of computation. Non-algorithmic computation<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:72.0pt;mso-add-space:auto;text-indent:-17.85pt;mso-list:l0 level2 lfo3;layout-grid-mode:char">
<![if !supportLists]><span lang="HR" style="font-family:"Courier New";color:black"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="HR" style="font-family:"Avenir Book";color:black">INFORMATION beyond Shannon's model of communication (connects to meaning, that is the role of the observer and agential view of life)<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpLast" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:36.0pt;mso-add-space:auto;text-indent:-17.85pt;mso-list:l0 level1 lfo3;layout-grid-mode:char">
<![if !supportLists]><span lang="HR" style="font-family:Symbol;color:black"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="HR" style="font-family:"Avenir Book";color:black">New MATHEMATICAL approaches<o:p></o:p></span></p>
<ul style="margin-top:0cm" type="disc">
<li class="MsoNormal" style="mso-list:l2 level1 lfo4"><span lang="HR" style="font-family:"Avenir Book";color:black">In the PRODUCTION of knowledge – SHIFT FROM MANUFACURE-STYLE BASED ON HUMAN INTELLIGENCE-ONLY to the extensive use of other, ARTIFICIAL INTELLIGENCES
</span><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">for tasks like data collection, verification, systematization, literature searches, writing, communication, etc.<o:p></o:p></span></li></ul>
<p class="MsoListParagraph" style="mso-margin-top-alt:6.0pt;margin-right:0cm;margin-bottom:6.0pt;margin-left:36.0pt;mso-add-space:auto;layout-grid-mode:char">
<span lang="HR" style="font-family:"Avenir Book";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">The list goes on.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">All the best,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US">Gordana<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:9.0pt;font-family:"Avenir Light",sans-serif;color:black"><a href="https://urldefense.com/v3/__http://gordana.se/__;!!D9dNQwwGXtA!UvTDqp9f46c317buFOwM97xyNQUTyxOP5JY585DPS5QZwXFS33z0ccz40UJBtIU1VKjHJT5kQwN0fKvvX2_uYfI342dNJXnq$" title="http://gordana.se/"><span style="color:#0563C1">http://gordana.se/</span></a><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Avenir Book";mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span style="font-family:"Calibri",sans-serif;color:black">From:
</span></b><span style="font-family:"Calibri",sans-serif;color:black">Fis <fis-bounces@listas.unizar.es> on behalf of "Pedro C. Marijuán" <pedroc.marijuan@gmail.com><br>
<b>Date: </b>Wednesday, 7 February 2024 at 20:59<br>
<b>To: </b>"fis@listas.unizar.es" <fis@listas.unizar.es><br>
<b>Subject: </b>Re: [Fis] Limits of Formal Systems<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Dear All,<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Thanks to Carlos for his kickoff text and indeed to Karl and Lou for their elegant duet . And also to Plamen.<o:p></o:p></p>
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<p class="MsoNormal">The historical road to logics and formal systems has been drafted, somehow, in these interventions and in the previous NY Lecture--at least cursorily. Some mentions of our naming capabilities and biological limits have also been made by
the above parties. It is in this aspect that I will briefly enter.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">I worked in the 90s in some neuroscience themes with Ken Collins ("El Cerebro Dual", book we published in Spanish). One of the themes then emerging was the role of cerebellum in "higher functions". Also related to logics? My own contention
after the work during those years (sorry to be insufficiently updated) is that language logic could be a byproduct of the way our cerebellum contributes to organize the myriad combinatory muscular modules and percept complexes involved in movement. I mean
to achieve effective closure of an action, a congruence with the ongoing perception (and associated memories) has to be achieved. For a trivial grasping of, say, a mug, dozens and dozens of muscles activation/inhibition processes, in a fiendish combinatorics
of high precision changing terribly fast, has to be orchestrated. <u>"True" efficient motion when a closure is achieved, versus "False" or failed motion when sensory-motor constellations do not match properly.</u> Well, if we go to language, the muscles of
phonation (particularly tongue and vocal cords) are supporting the physical part of linguistic combinatorics, necessarily coupled with percepts and ad hoc memories related to the involved occurrences. Thus, there should also be a (logical) closure in the
way our concepts or "cognits" (as Joaquin Fuster put) are verbally organized, so to achieve not only phonatory or lexical congruence but also an
<u>efficient adaptive matching</u> with previous conceptual/perceptual experiences. Otherwise language would have never evolved.<o:p></o:p></p>
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<p class="MsoNormal">I have always had trouble with logic. I think it is needed, beyond computation and formal systems, for communication & explanatory purposes, for making acceptable the new pieces of knowledge; but it would stand far away from the obtention
part: the creative, visionary, intuition leaps that lead to real knowledge novelty. Nevertheless, the fascinating thing, tribute to human ingenuity, is the amazing historical development grounded in logics and formal systems that has been able to approach
most physical events with uncanny precision. But concerning the bio-logics specifically, it is for me something not well solved yet. Joseph Brenner, a senior philosopher in FIS list, has developed a Logic in Reality, LIR, that tries to transcend formal logic
limitations. I would be curious of hear from him in the present juncture. <o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Best wishes,<o:p></o:p></p>
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<p class="MsoNormal">--Pedro<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">PS. Several new parties have joined FIS list these days. They are very welcome to express their views, always taking into account the general limitation of 2 messages per week (except the presenter), or sometimes 3 messages (for urged parties).
The counting of messages follows the international business week (Monday to Sunday)... In any event, it is quite nice receiving fresh minds in our discussion community!<o:p></o:p></p>
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<p class="MsoNormal">El 05/02/2024 a las 16:43, Carlos Gershenson escribió:<o:p></o:p></p>
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<p class="MsoNormal">In the 1920s, David Hilbert's program attempted to get rid once and for all from the paradoxes in mathematics that had arisen from the work of Cantor, Russell, and others. Even when Hilbert’s PhD student — John von Neumann — was working
avidly on demonstrating that mathematics were complete, consistent, and decidable, Kurt Gödel proved in the early 1930s that formal systems are incomplete and inconsistent, while Alan Turing proved in 1936 their undecidability (for which he proposed the "Turing
Machine", laying the theoretical basis for computer science).<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Digital computers have enabled us to study concepts and phenomena for which we did not have the proper tools beforehand, as they process much more information than the one our limited brains can manipulate. These include intelligence, life,
and complexity.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Even when computers have served us greatly as "telescopes for complexity", the limits of formal systems are becoming even more evident, as we attempt to model and simulate complex phenomena in all their richness, which implies emergence,
self-organization, downward causality, adaptation, multiple scales, semantics, and more.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Can we go beyond the limits of formal systems? Well, we actually do it somehow. It is natural to adapt to changing circumstances, so we can say that our "axioms" are flexible. Moreover, we are able to simulate this process in computers.
Similar to an interpreter or a compiler, we can define a formal system where some aspects of it can be modified/adapted. And if we need more adaptation, we can generalize the system so that a constant becomes a variable (similar to oracles in Turing Machines).
Certainly, this has its limits, but our adaptation is also limited: we cannot change our physics or our chemistry, although we have changed our biology with culture and technology.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Could it be that the problem lies not in the models we have, but in the modeling itself? We tend to forget the difference between our models and the modeled, between the map and the territory, between epistemology and ontology; simply because
our language does not make a distinction between phenomena and our perceptions of them. When we say "this system is complex/alive/intelligent", we assume that these are inherent properties of the phenomenon we describe, forgetting that the moment we name anything,
we are already simplifying and limiting it. It is clear that models/descriptions will never be as rich as the modeled/phenomena, and that is the way it should be. As Arbib wrote, “a model that simply duplicates the brain is no more illuminating than the brain
itself”. [1]<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Still, perhaps we're barking up the wrong tree. We also tend to forget the difference between computability in theory (Church-Turing's) and computability in practice (what digital computers do). There are non-Turing-computable functions
which we can compute in practice, while there are Turing-computable functions for which there is not enough time in the universe to compute. So maybe we are focussing on theoretical limits, while we should be concerned more with practical limits.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">As you can see, I have many more questions than answers, so I would be very interested in what everyone thinks about these topics.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">I'll just share some idea I've been playing with recently, although it might be that it won't lead anywhere. For lack of a better name, let's call them "multi-axiom systems". For example in geometry, we know that if we change the 5th axiom
(about intersecting parallel lines), we can go from Euclidean to other geometries. We can define a "multi-axiom geometry", so that we can switch between different versions of the 5th axiom for different purposes. In a similar way, we could define a multi-axiom
system that contains several different formal systems. We know we cannot have all at once universal computation and completeness and consistency. But then, in first-order logic, we can have completeness and consistency. In second-order logic we have universal
computation but not completeness. In paraconsistent logics we sacrifice consistency but gain other properties. Then, if we consider a multi-axiom system that includes all of these and perhaps more, in theory we could have in the same system all these nice
properties, but not at the same time. Would that be useful? Of course, we would need to find rules that would determine when to change the axioms. Just to relate this idea to last month's topic — as it was motivated by Stu's and Andrea's paper [2] — if we
want to model evolution, we can have "normal" axioms at short timescales (and thus predictability), but at longer (evolutionary) timescales, we can shift axioms set, and then the "rules" of biological systems could change, towards a new configuration where
we can use again "normal" axioms.<o:p></o:p></p>
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<p class="MsoNormal">[1] Michael Arbib, The Metaphorical Brain 2. Neural Networks and Beyond (1989)<o:p></o:p></p>
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<p class="MsoNormal">[2] Stuart Kauffman, Andrea Roli. Is the Emergence of Life an Expected Phase Transition in the Evolving Universe?
<a href="https://urldefense.com/v3/__https:/arxiv.org/abs/2401.09514v1__;!!D9dNQwwGXtA!Q9Wf2QzNb33Rbcm_rxf9I_P4EziZ3qwzNM9drNcS2M856SZcvJx6al-U8ZnYt5Fj0OfDWnNsNDd2RoZgOmc$">
https://arxiv.org/abs/2401.09514v1 </a><o:p></o:p></p>
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<p class="MsoNormal">Carlos Gershenson<o:p></o:p></p>
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<p class="MsoNormal">SUNY Empire Innovation Professor <br>
Department of Systems Science and Industrial Engineering<br>
<span class="apple-converted-space">Thomas J. Watson College of Engineering and Applied Science</span><br>
<span class="apple-converted-space">State University of New York at Binghamton</span><br>
<span class="apple-converted-space">Binghamton, New York 13902 </span>USA<o:p></o:p></p>
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<p class="MsoNormal"><a href="https://urldefense.com/v3/__https:/tendrel.binghamton.edu__;!!D9dNQwwGXtA!Q9Wf2QzNb33Rbcm_rxf9I_P4EziZ3qwzNM9drNcS2M856SZcvJx6al-U8ZnYt5Fj0OfDWnNsNDd2yTKmSVg$">https://tendrel.binghamton.edu</a><o:p></o:p></p>
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<p class="MsoNormal"><br>
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<o:p></o:p></p>
<pre>_______________________________________________<o:p></o:p></pre>
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