Universe Rule №30 | 第30號規則宇宙
What is the truth about the universe? A big bang? A high-dimensional experiment? Or a code?
Sometimes interesting imagination may also be the truth of the universe:
Imagine that our universe may be composed of a simple rule plus a certain algorithm. What does this mean?
First, let’s describe the background history:
While working at Los Alamos National Laboratory in the 1940s, Stanislaw Ulam studied crystal growth using a simple lattice network as a model. At the same time, Ulam’s colleague at Los Alamos, John von Neumann, was working on the problem of self-replicating systems. Von Neumann’s original design was based on the concept of one robot building another robot. This design is called a kinematic model.
By the end of the 1950s, Ulam and von Neumann had created a method for calculating liquid motion. The driving concept of this method is to treat the liquid as a set of discrete units and calculate the motion of each unit based on the behavior of its neighbors. Thus the first cellular automaton system was born.
In the 1970s, a two-state two-dimensional cellular automaton called the “Game of Life” was invented by John Conway and described by Martin Gardner in Scientific American Promotion in the article, the rules are as follows:
- Any living cell with fewer than two neighbors will die, as if it were underpopulated.
- Any living cell with two or three neighbors will survive to the next generation.
- Any living cell with more than three neighbors will die, as if it were overpopulated.
- Any dead cell with exactly three live neighbors will become a live cell, as if by reproduction.
Stephen Wolfram began working independently on cellular automaton in mid-1981 after considering how the formation of complex patterns in nature violates the second law of thermodynamics. His research was initially motivated by a desire to model systems such as neural networks in the brain. In June 1983, he published his first paper in Reviews of Modern Physics, studying basic cellular automaton (specifically Rule 30). The unexpected complexity led Wolfram to suspect that the properties might be due to a similar mechanism.
For more complete content, please refer to the wiki’s description of cellular automaton.
Okay, it doesn’t matter if you don’t read the history. Let’s first understand the algorithm of elementary cellular automaton:
An illustration of a cellular automaton designed by Wolfram. An elementary cellular automaton is a one-dimensional cellular automaton in which there are two possible states (labeled 0 and 1), and the rules for determining the next generation cellular state depend only on The current state of this cell. To put it simply, the conditions that determine the current cell state are the states of the previous generation and its left and right neighbors.
Take Rule 30 as an example:
The Rule 30 algorithm assumes that the arrangement of the previous generation and its neighbors is 010, and in the Rule 30 universe the 010 algorithm will be equal to 1, and the state of this cell is 1. And when we start from a point in sequence and follow the algorithm of Rule 30, the picture of universe №30 at the beginning of the article will appear. Yes, a certain rule and algorithm generates a series of irregular cells, and superposing the cell states of the same generation can generate a disordered sequence.
One cell, two states, and three mothers can give birth to an ever-changing universe. Those who are familiar with Chinese Taoism may be surprised to say, isn’t this the 42nd chapter of Laozi [Dao De Jing]: “Dao gives birth to One, One gives birth to two, two gives birth to three, and three gives birth to all things.”
And how many such universes can there be? There are 0–255 universes in total, and each universe has its own mirror image and complement, as well as the complement of the mirror image, that is, 4 similar universes. That is, there are 64 categories. We are currently thinking about the issue of boundaries and infinity, because if the boundaries overlap, it will cause interference, but the correct information of the previous generation can be obtained, otherwise the universe will expand with each generation cycle, from 1 Toward infinite expansion. It may also be that boundary interference occurs and then shrinks, and then changes back to a point.
If you are interested, you can go to Wolfram’s MathWorld, where there are 256 detailed universes. Some are blank, others are filled with cells. What is so special about the Rule 30 universe? The Rule 30 universe has many properties similar to the universe we live in. For example, it looks orderly from one side, but chaotic from the other side. There are regular laws and a clear past, but there is no regular future… There are many interesting things left for everyone to explore on their own.
Science is good at observing phenomena and finding laws and principles from phenomena. However, in the face of the vast universe, more and more phenomena have no laws, but operate based on a simple rule. How should we understand them?
As an aside, the definition of π is the circumference/diameter of a circle. This is a simple but irregular definition. π is an infinitesimal number that does not cycle. So, is it the circumference that cannot be determined or the diameter that cannot be determined? How can we create a circle in the real world whose circumference or diameter cannot be determined? Or We are determined by irregular infinitesimal number?
宇宙的真相是甚麼? 一個大爆炸? 一場高維度的試驗? 還是一個程式碼? 有時有趣的想像也有可能就是宇宙的真相 :
試想我們的宇宙可能是由一個簡單的規則加上確定的演算法，這是什麼意思呢?
首先我們先來描述一下背景歷史 :
20 世紀 40 年代，斯坦尼斯瓦夫·烏拉姆 (Stanislaw Ulam ) 在洛斯阿拉莫斯國家實驗室工作時，使用簡單的晶格網絡作為模型研究了晶體的生長。 與此同時，烏拉姆在洛斯阿拉莫斯的同事約翰·馮·諾依曼正在研究自我複製系統的問題。馮·諾依曼的最初設計是基於一個機器人建造另一個機器人的概念。這種設計稱為運動學模型。
至50 年代末烏拉姆與馮·諾依曼創建了一種計算液體運動的方法。此方法的驅動概念是將液體視為一組離散單元，並根據其鄰居的行為計算每個單元的運動。第一個元胞自動機系統就這樣誕生了。
在 1970 年代，由約翰·康威 (John Conway)發明了一種名為「生命遊戲」的二態二維元胞自動機，並由馬丁·加德納 (Martin Gardner)在《科學美國人》文章中推廣，其規則如下：
任何少於兩個鄰居的活細胞都會死亡，就像人口不足造成的一樣。
任何有兩個或三個鄰居的活細胞都會生存到下一代。
任何具有超過三個鄰居的活細胞都會死亡，就像人口過剩一樣。
任何具有恰好三個活鄰居的死細胞都會變成活細胞，就像透過繁殖一樣。
Stephen Wolfram於 1981 年中期開始獨立研究元胞自動機，此前他考慮了自然界中複雜模式的形成是如何違反熱力學第二定律的。他的研究最初是出於對大腦中的神經網路等系統建模的願望。 1983年 6 月，他在《現代物理學評論》上發表了他的第一篇論文，研究基本元胞自動機（特別是規則 30 ） 。的意外複雜性使Wolfram 懷疑性質可能是由於類似的機制。
更完整的內容可以參照wiki對元細胞自動機的說明。
好的，就算不了解這些歷史也沒有關係，我們先了解元細胞自動機的演算法則:
Wolfram設計的元細胞自動機的說明，初等元胞自動機是一維元胞自動機，其中有兩種可能的狀態（標記為0 和1），並且確定下一代元胞狀態的規則僅取決於該元胞的目前狀態。簡單來說，決定現在細胞狀態的條件，是上一代與其左右鄰居的狀態。
以規則30為例 :
假設上一代與其鄰居的排列為 010，而在規則30的宇宙中010演算會等於1，這個細胞的狀態就是1。而當我們依序從一個點開始生成，並依照規則30的演算法，就會出現文章開頭的30號宇宙的圖。
是的，一個確定的規則與演算法，生成了一連串的無規律細胞，而將同一代的細胞狀態疊加就能生成一個無序的數列。
一個元細胞，兩種狀態，三個母代，就能誕生出千變萬化的宇宙，如果熟捻中國道家的人可能會驚訝地說，這不就是老子〔道德經〕第四十二章：「道生一，一生二，二生三，三生萬物。萬物負陰而抱陽，沖氣以為和。」
而這樣的宇宙到底能有多少個呢?
共有0–255個宇宙，每個宇宙都有自身的鏡像與補集，以及鏡像的補集，也就是4個相似宇宙。也就是64個類別，目前也在思考邊界與無窮大的問題，因為如果邊界迴疊會造成干擾，但可得到正確的上一代資訊，不然就是隨著每一代循環發生宇宙就要擴大一次，從1邁向無窮大的擴張。也可能就是邊界干擾產生進而發生收縮，然後又變回一點。
有興趣可以至Wolfram的數學世界，那裏有詳盡的256個宇宙。有些是一片空白，有些則是填滿了細胞。而規則30宇宙有什麼特別的呢? 規則30宇宙與我們所處的宇宙有許多性質相似之處。例如從一邊看是有序，從另一邊看則是渾沌，有規律的法則與明確的過去，卻沒有規律的未來…還有許多有趣之處就留給大家自行去探討。
科學擅長於觀察現象，並從現象中找到規律與原理，但面對浩瀚的宇宙，越來越多現象並不存在著規律，卻又基於一個簡單的規則運行，我們又該如何去理解呢?
題外話，圓周率π的定義為一個圓的周長/直徑，這是一個簡單規則卻沒有規律的定義，π是一個不循環的無窮小數，那麼究竟是周長不能確定，還是直徑不能確定呢? 我們又如何在真實世界中創造出一個不能確定周長或是直徑的圓呢? 又或是我們確定在不循環的無窮小數之上呢?
