| Project/Area Number |
09440026
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Hokkaido University |
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Principal Investigator |
TSUJISHITA Toru Grad. School of Science, Hokkaido Univ., Professor, 大学院・理学研究科, 教授 (10107063)
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| Co-Investigator(Kenkyū-buntansha) |
SHIOZAWA Yoshinori Faculty of Economy, Oosaka City University, Professor, 経済学部, 教授 (00109076)
KANEKO Kunihiko Grad. School of Arts and Science, Hokkaido Univ., Professor, 大学院・総合文化研究科, 教授 (30177513)
GUNJI Yukio Faculty of Science, Kobe University Professor, 理学部, 教授 (40192570)
TSUNODA Shuichiro Faculty of Science, Nara Women University, Professor, 理学部, 教授 (60144424)
TSUDA Ichiro Grad. School of Science, Hokkaido Univ., Professor, 大学院・理学研究科, 教授 (10207384)
高橋 陽一郎 京都大学, 数理解析研究所, 教授 (20033889)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥16,300,000 (Direct Cost: ¥16,300,000)
Fiscal Year 1999: ¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1998: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1997: ¥10,600,000 (Direct Cost: ¥10,600,000)
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| Keywords | complex systems / emergency / formal systems / indefiniteness / n-category / molecular machine / natural number / ontological observation / 内部観測 / 2元論 / ミルナーアトラクタ / 関数マップ / 動的認識子 / 複複系 / 形式化 / 内的集合論 / 高次元圏論 / 分散システム / 様相論理 / 翻訳システム |
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| Research Abstract |
Although the development of molecular biology has made it possible to study animals and plants as molecular machines, there are no efforts to formulate such kind of machines mathematically. In fact the nonlinear dynamical systems of huge degrees of freedom seem to be more suitable models than traditional discrete models of machines, and provide us hundreds of rich concrete models in complex systems studies. However we are left with the fundamental question whether it is legitimate to use dynamical systems as the framework in which to understand the plants and animals.
In this research project, we focused our attention on the foundational ones among many motivations in complex systems studies. From discussions among complex systems researchers, mathematicians with various backgrounds and computer scientists, we recognized a new role mathematics might play in complex systems studies and the role can be played only when mathematics itself takes a step into a new direction. The point in the new direction is "the indefiniteness of mathematics", which we confront for example when we abandon the ungrounded conviction of the uniqueness of the natural number series. Since many mathematical constructions rely heavily on this conviction, its abondonment affects the whole modern mathematics. The indefiniteness in mathematics has positive significance and our preliminary investigations lead us to conclude that it is this persistent ubiquitous indefiniteness that is behind the everlasting evolution of mathematics. 'This recognition of the fundamental role played by indefiniteness in mathematics sheds great light on the nature of the so called ontological observational approach.
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