# A New Kind of Aesthetics —The Mathematical Structure of the Aesthetic

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## Abstract

**:**

## 1. Introduction

## 2. Method of Research

## 3. Elementary Process of the Aesthetic

## 4. Introduction of the Environmental Condition

P | observer |

Q | aesthetic object |

X | aesthetic concept |

Y | aesthetic state |

M | generation factor of aesthetic object |

F | analysis results of aesthetic state |

## 5. Introduction of Time

## 6. Triangulated Category and Octahedron Structure

${P}^{\u2022}$ | observer |

${Q}^{\u2022}$ | aesthetic object |

${X}^{\u2022}$ | aesthetic concept |

${Y}^{\u2022}$ | aesthetic state |

${M}^{\u2022}$ | generation factor of aesthetic object |

${F}^{\u2022}$ | analysis result of aesthetic state |

## 7. Aesthetic Activity and Time Evolution

**Aesthetic contemplation**

**Artwork criticism**

**Artwork production**

**Aesthetic experience**

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Shelley, J. The Concept of the Aesthetic. In The Stanford Encyclopedia of Philosophy; Zalta, E.N., Ed.; Stanford University: Stanford, CA, USA, 2015; Available online: http://plato.stanford.edu/archives/win2015/entries/aesthetic-concept/ (accessed on 30 June 2017).
- Baumgarten, A.G. Aesthetica-Aesthetik: Lateinisch-deutsche Ausgabe; Fink Wilhelm Gmbh + Co. KG: Paderborn, Germany, 2016. [Google Scholar]
- Maanen, H. How to Study Art Worlds: On the Societal Functioning of Aesthetics Values; Amsterdam University Press: Amsterdam, The Netherlands, 2009. [Google Scholar]
- Danto, A. The Artworld. J. Philos.
**1964**, 61, 571–584. [Google Scholar] [CrossRef] - Gell, A. Art and Agency: An Anthropological Theory; Clarendon Press: Gloucestershire, UK, 1998. [Google Scholar]
- Clark, T.J. The Conditions of Artistic Creation. Times Lit. Suppl.
**1974**, 3768, 561–562. [Google Scholar] - Stecker, R. Aesthetics and the Philosophy of Art: An Introduction, 2nd ed.; Rowman & Littlefield Publishers: Lanham, MD, USA, 2010. [Google Scholar]
- Naruse, M.; Berthel, M.; Drezet, A.; Huant, S.; Aono, M.; Hori, H.; Kim, S.-J. Single-photon decision maker. Sci. Rep.
**2015**, 5. [Google Scholar] [CrossRef] [PubMed] - Naruse, M.; Kim, S.-J.; Aono, M.; Berthel, M.; Drezet, A.; Huant, S.; Hori, H. Category theoretic foundation of single-photon-based decision making, 2016. Available online: https://arxiv.org/abs/1602.08199 (accessed on 30 June 2017).
- Hori, H. Category Theory for Optical Functionalities. Photonics News
**2016**, 5, 115–124. (In Japanese) [Google Scholar] - Adajian, T. The Definition of Art. In The Stanford Encyclopedia of Philosophy; Zalta, E.N., Ed.; Stanford University: Stanford, CA, USA, 2016; Available online: http://plato.stanford.edu/archives/sum2016/entries/art-definition/ (accessed on 30 June 2017).
- MacLane, S. Categories for the Working Mathematician, 2nd ed.; Springer: Berlin, Germany, 1978. [Google Scholar]
- Iversen, B. Cohomology of Sheaves, 1st ed.; Springer: Berlin, Germany, 1986. [Google Scholar]
- Spivak, D.I. Category Theory for the Sciences, 1st ed.; The MIT Press: Cambridge, MA, USA, 2014. [Google Scholar]
- Fulton, W. Algebraic Topology: A First Course, 1st ed.; Springer: Berlin, Germany, 1995. [Google Scholar]
- Levi-Strauss, C. The Elementary Structures of Kinship, Revised ed.; Beacon Press: Boston, MA, USA, 1969. [Google Scholar]
- Birkhoff, G.D. Aesthetic Measure; Harvard University Press: Cambridge, MA, USA, 1933. [Google Scholar]
- Moles, A. Th orie de l’information et perception esth tique (Information Theory and Aesthetical Perception); Deno l: Paris, France, 1973. [Google Scholar]
- Nake, F. Thetik als Informationsverarbeitung (Aesthetics as Information Processing); Grundlagen und Anwendungen der Informatik im Bereich sthetischer Produktion und Kritik; Springer: New York, NY, USA, 1974. [Google Scholar]
- Bense, M. Einfhrung in die informationstheoretische thetik(Introduction to Information Theoretical Aesthetics); Grundlegung und Anwendung in der Texttheorie; Rowohlt: Reinbek, Germany, 1969. [Google Scholar]
- Kawano, H. Computer and Aesthetics: Searching for the Art of Artificial Intelligence; The University of Tokyo Press: Tokyo, Japan, 1984. (In Japanese) [Google Scholar]
- Schmidhuber, J. Low-complexity art, Leonardo. J. Int. Soc. Arts Sci. Technol.
**1997**, 30, 97–103. Available online: http://people.idsia.ch/~juergen/beauty.html (accessed on 30 June 2017). - Huston, J.P.; Nadal, M.; Mora, F.; Agnati, L.F.; Cela Conde, C.J. Art, Aesthetics, and the Brain; Oxford University Press: Cambridge, MA, USA, 2015. [Google Scholar]
- Lauring, J.O. An Introduction to Neuroaesthetics: The Neuroscientific Approach to Aesthetic Experience, Artistic Creativity, and Arts Appreciation; Museum Tusculanum: Enhavn, Denmark, 2015. [Google Scholar]
- Danto, A. The Transfiguration of the Commonplace. J. Aesthet. Art Crit.
**1974**, 33, 139–148. [Google Scholar] [CrossRef]

1. | All the elements of G can be divided without redundancy using normal Subgroup H of Group G. |

2. | If the sequence $0\to A\to B$ is exact at A, that map is a monomorphism (injective or one-to-one). If the sequence $B\to C\to 0$ is exact at C, that map is an epimorphism (surjective or onto). |

Artwork Criticism | Aesthetic Experience | ||||||||
---|---|---|---|---|---|---|---|---|---|

0 | 0 | ||||||||

↓ | ↓ | ||||||||

0 | → | generation factor of aesthetic object | → | aesthetic concept | → | observer | → | 0 | Aesthetic contemplation |

↓ | ↓ | ↓ | |||||||

0 | → | generation factor of aesthetic object | → | aesthetic object | → | aesthetic state | → | 0 | Artwork production |

↓ | ↓ | ||||||||

analysis result of aesthetic state | → | analysis result of aesthetic state | |||||||

↓ | ↓ | ||||||||

0 | 0 |

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**MDPI and ACS Style**

Kubota, A.; Hori, H.; Naruse, M.; Akiba, F. A New Kind of Aesthetics —The Mathematical Structure of the Aesthetic. *Philosophies* **2017**, *2*, 14.
https://doi.org/10.3390/philosophies2030014

**AMA Style**

Kubota A, Hori H, Naruse M, Akiba F. A New Kind of Aesthetics —The Mathematical Structure of the Aesthetic. *Philosophies*. 2017; 2(3):14.
https://doi.org/10.3390/philosophies2030014

**Chicago/Turabian Style**

Kubota, Akihiro, Hirokazu Hori, Makoto Naruse, and Fuminori Akiba. 2017. "A New Kind of Aesthetics —The Mathematical Structure of the Aesthetic" *Philosophies* 2, no. 3: 14.
https://doi.org/10.3390/philosophies2030014