Heap Paradox in Fish Schools

EasyChair Preprint 1807

Abstract

The heap paradox is an enduring problem in complex systems. One variation of the heap paradox considers how many parts of a whole are required to generate group behaviour. The original heap paradox indicates that the recursive adding grain process finally makes a heap exceeding at a certain point; however, in this study, we insist that this recursive operation must involve ontological judgement (i.e. anticipation for the forthcoming heap from non-heap in every procedure). Applying integrated information theory (IIT) 3.0 provides two solutions to this paradox. Here, the group behaviour of P. altivelis is analysed with group sizes ranging from 2–5 fish. Resultingly, the subgroup embedded in the whole group has qualitatively different group integrity compared with a whole group of the same size: 2-fish subschools lose the followership property, but gain the leadership property, which is never observed in a 2-fish whole school. Thus, our result suggests that each fish tentatively solves the heap paradox according to its own ontological judgements concerning its group size.

Keyphrases: Integrated information theory 3.0, The paradox of the heap, collective behaviour

@booklet{EasyChair:1807,
  author    = {Takayuki Niizato and Kotaro Sakamoto and Yoh-Ichi Mototake and Hisashi Murakami and Yuta Nishiyama and Toshiki Fukushima},
  title     = {Heap Paradox in Fish Schools},
  howpublished = {EasyChair Preprint 1807},
  year      = {EasyChair, 2019}}