Self-discriptive system within time change.

The simplest example of self-discriptive systems is the exponential increase. This is because the simplest “change” of a variable $x$ is a first derivative of its time $dx/dt$, and the simplest form of the function “$f(x)$” determined by a variable $x$ is a linear one $Cx$.

• Case1: Growth is constant with the current state (state is invariant over time)

$$ \frac{dx}{dt} = C $$

• Case2: Growth is linear with the current state (state changes exponentially)

$$ \frac{dx}{dt} = Cx $$

• Case3: Growth is complex but relative to the current state (generalization)

$$ \frac{dx}{dt} = f(x) $$

Actual situations

1. Money/Capital creates new money/capital

This is the principle of capital markets and investment. Or what is called Capital Gain. Source of motivation on the lender side.

これは資本市場と投資の原理．いわゆるキャピタルゲイン．貸し手の動機の源泉．

2. Trust/Credit creates new trust/credit

The most obvious example is banking. Actually, there is a word of credit creation. Lending is gradually increased based on credit. This is the principle of the borrower.

わかりやすい例は銀行業． 実際，信用創造という言葉があるくらい．信用をもとに，少しずつ貸出を増やす．これは借り手の原理．

The modern financial system is supported by the principle that capital and credit increase/decrease exponentially. This principle creates a dynamic phenomenon (spiral) that motivates lenders and borrowers and that “lending and borrowing exponentially increases/decreases.” This is inflation and deflation.

現代金融システムは，「資本と信用が指数増加/減少する」という原理によって支えられる．この原理は，貸し手と借り手に動機を与え「指数増加/減少する貸金と借金」という現象（スパイラル）を生む．これがインフレとデフレ．

A vested interest (a large corporation or a large political party) can be established as a vested interest by reproducing credit and achievement in the future by accumulating past credit and achievement.

既得権益（大企業や大政党）は，過去の信用と実績の積み重ねにより，将来の信用と実績を再生産することで，既得権益として成立する．

To make matters difficult, “trust” and “achievement” are complementary. “Trust” provides an opportunity to unlock new achievements. The new “achievement” repairs and strengthens trust. In other words, vested interests are invincible unless environmental changes occur.

厄介なことに「信頼」と「実績」は相補関係にある．「信頼」は新たな実績解除への機会を提供する．新たな「実績」は信頼を補修・強化する．つまり，既得権益は環境変化が起きない限り無敵．

The first step for new powers (ventures and youth) to scale up is to win trust or to make some achievements. In addition, it is even better as it causes environmental changes and innovation.

新興勢力（ベンチャーや若者）がスケールアップするための第一歩は「信頼」を勝ち取るか，「実績」で黙らせるか． 加えて，環境変化やイノベーションを起こすとなお良い．

As a result, The risk-loving youths first try to walk the cycle from the trust to the achievement, but The risk-averse youths first try to walk the cycle from the achievement to the trust.

結果として， リスク選好的な若者は，信頼から実績へというサイクルを歩もうとし， リスク回避的な若者は，実績から信頼へというサイクルを歩もうとする．

4. Follower/Fan creates new follower/fan

In order for super popular corporate brands, entertainers, celebrities, and influencers to be born, their fans/followers need to create new fans/followers.

超人気な企業ブランドや芸能人，セレブ，インフルエンサーが生まれるためには，彼らのファン/フォロワーが新たなファン/フォロワーを生む必要がある．

Nowadays, this mechanism has been strengthened in the entertainment industry where globalization by the Internet has been achieved, and in platforms where search and recommendation algorithms that strongly fit past trends are dominant.

近年，インターネットによるグローバル化が達成されたエンタメ産業や，過去の傾向に強くfitする検索や推薦のアルゴリズムが支配的なプラットホームにおいて，このメカニズムは強化されている．

The more followers/fans there are, the more followers/fans there are. The services with more registrants/subscribers tend to have more registrants/subscribers.

フォロワー/ファンが多い人ほど，フォロワー/ファンが増えやすい． 登録者/購読者の多いサービスほど，登録者/購読者が増えやすい．

3. Popularity/Evaluation creates new popularity/evaluation

For products that sell well, the “selling” state itself becomes valuable.

売れているものは，売れているということ自体が価値になる．

This phenomenon is often explained by René Girard’s triangular desire from the perspective of consumer sentiment, and by the network externality from the perspective of industrial organization theory.

この現象は，消費者心理の観点からはルネ・ジラールの欲望の三角形，産業組織論の観点からはネットワーク外部性でよく説明される．

Additionally, this schema is often misused for stealth marketing, hype, information products, affiliates, etc.

また，このスキーマは，しばしばステマ，偽客(サクラ)，誇大広告，情報商材，アフィリエイトなどで悪用される．