## Information Mathematics Seminar

Seminar information archive ～09/10｜Next seminar｜Future seminars 09/11～

Date, time & place | Thursday 16:50 - 18:35 128Room #128 (Graduate School of Math. Sci. Bldg.) |
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Organizer(s) | Toshiyuki Katsura |

### 2022/10/06

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

On a New Quantitative Definition of the Complexity of Organized Matters (Japanese)

**Tatsuaki Okamoto**(NTT)On a New Quantitative Definition of the Complexity of Organized Matters (Japanese)

[ Abstract ]

Scientific problems are classified into three classes: problems of simplicity, problems of disorganized complexity, and problems of organized complexity. For example, classical dynamics can be used to analyze and predict the motion of a few ivory balls as they move about on a billiard table. This is a typical problem of simplicity. Imagine a large billiard table with millions of balls rolling over its surface, colliding with one another and with the side rails. This is a typical problem of disorganized complexity. Problems of organized complexity, however, deal with features of an organization such as living things, ecosystems, and human societies. The quantitative definition of complexity is the most fundamental and important notion in problems of (organized and disorganized) complexity. The quantitative definition of disorganized complexity has been established to be entropy. In contrast, there is no agreed-upon quantitative definition for organized complexity, although many definitions have been proposed for this aim. In this talk, first, I will show the shortcomings of the existing definitions for organized complexity. I will then introduce a new definition and present that the new definition has solved all problems with the existing definitions. Finally, I will show some applications. This talk is based on the following paper.

Tatsuaki Okamoto, ‘‘A New Quantitative Definition of the Complexity of Organized Matters,’’ Complexity, Volume 2022, Article ID 1889348 (2022)

https://www.hindawi.com/journals/complexity/2022/1889348/

Scientific problems are classified into three classes: problems of simplicity, problems of disorganized complexity, and problems of organized complexity. For example, classical dynamics can be used to analyze and predict the motion of a few ivory balls as they move about on a billiard table. This is a typical problem of simplicity. Imagine a large billiard table with millions of balls rolling over its surface, colliding with one another and with the side rails. This is a typical problem of disorganized complexity. Problems of organized complexity, however, deal with features of an organization such as living things, ecosystems, and human societies. The quantitative definition of complexity is the most fundamental and important notion in problems of (organized and disorganized) complexity. The quantitative definition of disorganized complexity has been established to be entropy. In contrast, there is no agreed-upon quantitative definition for organized complexity, although many definitions have been proposed for this aim. In this talk, first, I will show the shortcomings of the existing definitions for organized complexity. I will then introduce a new definition and present that the new definition has solved all problems with the existing definitions. Finally, I will show some applications. This talk is based on the following paper.

Tatsuaki Okamoto, ‘‘A New Quantitative Definition of the Complexity of Organized Matters,’’ Complexity, Volume 2022, Article ID 1889348 (2022)

https://www.hindawi.com/journals/complexity/2022/1889348/