Shuichirou Ike - High Dimensional Space to Formulate Marriage and Birth Functions

Shuichirou Ike

Professor, Department of Sociology, Faculty of Letters Chief of Educational Center for Information Processing Teikyo University

Hachiouji-Shi, Tokyo, Japan

First edition published 2022

by CRC Press

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Library of Congress Cataloging-in-Publication Data (applied for)

ISBN: 978-0-367-18222-9 (hbk)

ISBN: 978-1-032-13471-0 (pbk)

ISBN: 978-0-429-06018-2 (ebk)

DOI: 10.1201/9780429060182

Typeset in Times New Roman

by Radiant Productions

Fertility decline or population decline is now becoming a major problem in all of the developed countries around the world. In order to explain the fertility decline, several demographers, economists, sociologists, feminists and social policy-makers have pointed out many socioeconomic causes and have made proposals to restore the birth rate based on them. However, most of them are based on false assumptions and they cannot explain the real causes of decline in the fertility rate.

This may come as a surprise to some, but this is the startling conclusion that Professor Ike, the author of this book, draws.

According to Ike, marriages occur depending on its neighborhood, and the fertility decline that result from the decline in marriages can be described as an effect of geographic reaction-diffusion system. Ike assumes that the fertility decline is a simple alteration of a three-dimensional surface by its gradients, and it can identify the locations where fertility has historically declined in Europe and reproduce the diffusion of the fertility decline.

Furthermore, Ike argues that the actual number of children is not affected by the ideal number of children or the socioeconomic factors. He concludes that a causal birth model can only be constructed on the time-space dimensional space as a causal chain of the birth behavior.

These conclusions are not only mathematically well-formulated models, but are also falsifiable theories based on empirical data. I hope that this book will intellectually stimulate readers who are interested in the study of fertility decline and to create new academic findings.

Manabu Akagawa

Professor of Tokyo University

https://www.u-tokyo.ac.jp/focus/ja/people/people000194.html#

In 2016, I published Fertility Decline and Background Independence Applying a Reaction-Diffusion System as a Stochastic Process. At the time of writing it, I intended for readers to understand easily the implications of the proposed reaction-diffusion mathematical model and the impact of the model on demographic theory. I understand now that I was wrong.

The reaction-diffusion model is not just a fine-fitted model of fertility decline but requires a fundamental revision of the existing behavioral model. Can we scientifically answer the following questions?

How do marriages occur? Further, how do births occur?

Individual physiological maturation is not a sufficient answer. Today, the number of mature adults who do not marry (common law) has increased. This phenomenon must be considered as having collective emergent properties. Consequently, I ask you another question:

How do these occurrences change dynamically?

Traditionally, we assume that our conscious will and attitudes shift in response to these problems. However, when we question why our will and attitudes shift, we recognize that we have no adequate answers. We typically assume that there is a socioeconomic background causing such shifts. Ordinary social scientists research the relationship between socioeconomic variables and individual fertility behaviors.

Research only implicitly postulates that each individual is affected by socioeconomic variables. We must be skeptical about this postulation. Because the lack of substantial causal behavioral model, many researches cannot help depending on the ready-made statistical methods. We have not achieved clarity for many years under this postulation and these methods. We need to develop comprehensive models of fertility. The concrete model of fertility behaviors which can make quantitative predictions deserves it. The models are the marriage and birth functions, which require us to drastically change our philosophy to analyze phenomena. In addition, models must be built on the stochastic process to help us understand the historical trend of fertility decline.

A.J. Coale recognized that marriages of a cohort occur according with a probability density function for the first time. Namely, he cultivated the object as a stochastic marriage function. He and his colleagues also realized that fertility decline has diffused in space. While this phenomenon has been empirically recognized, stochastic models must be applied to it.

Constructing a stochastic and mathematical model requires us to change our perspective on human behavior. The diffusion process is inevitably the interaction of neighboring spaces (neighboring others). We are perpetually exposed to the affection of neighboring others, whether we are aware of it or not. This is the locomotive power and dynamics of marriage and birth. Thus, marriage and birth functions are constant floating fluids, especially at the micro-scale.

Are you a utilitarian individual, maximizing your own interests? No. This is a false image built by a delusive hypothesis. The eclecticism of utilitarian egos and norms has long prevailed in the social sciences. However, this is simply a programmed feeling. The true law that our behaviors obey is different; however, we are incapable of intuitively understanding such behaviors while they occur. We find it difficult to admit the effects of others on our self-consciousness.

The decisive conception is that previous neighboring marriages stochastically decide the succeeding ones. Neither conscious free will nor individual selection is necessary to build a scientific model of the occurrences of marriage and birth. Clearly, we behave (or respond) according to the behavior of those around us; we are programmed to believe that we think and act as individuals.