Ignore the idiots! In this interesting universe, have fun.
Editor’s note: This article comes from the WeChat public account “Lonely Brain” (ID: lonelybrain) , author Lao Yu In plus.
One
John Conway, a famous mathematician and a professor at Princeton University and Cambridge University, passed away on April 11, 2020 at the age of 82.
Conway is active in the research of finite groups, interesting mathematics, knot theory, number theory, combinatorial game theory, and coding.
He was very interested in mathematics when he was young:
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At the age of four, his mother found him recite the second power;
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At the age of eleven, he went to the middle school interview and was asked what he wanted to do when he grew up. He answered that he wanted to be a mathematician in Cambridge.
Conway really studied mathematics at the University of Cambridge and is currently a professor at Princeton University.
Conway first proposed the surreal numbers (surreal numbers) number system, he himself said that this is his greatest contribution to mathematics.
(The above information comes from Wikipedia and news.)
Conway is an interesting genius, he designed countless games. He said that he has been playing games even if he hasn’t worked in a day.
The most famous one is:
Life game.
Secondary
This game is played on a chess board that is very similar to Go. The difference is that the game of Go is at the intersection, and the life “game” occurs in the grid.
There will be living cells in each square, either dead or alive. Is it a bit like the life and death of Go pieces?
How to play this game?
We know that the rules of the game of Go are very simple: go out of hand and kill each other.
The rules of “Life Game” are also very simple. Before talking about the rules, let ’s talk about the “thoughts” of the rule setting:
Life game is a zero player game. It consists of a two-dimensional rectangular world in which each cell in this world lives a living or dead cell.
The life and death of a cell (black spots in the picture below) at the next moment depends on the number of living or dead cells in the adjacent eight squares (white spots in the picture below).
If there are too many cells alive in the adjacent square (the yellow person in the picture below), this cell (☠️ in the picture below) will die at the next moment due to lack of resources;
On the contrary, if there are too few living cells around, this cell will die because it is too lonely.
In practice, the player can set when the number of surrounding living cells is suitable for the survival of the cells.
From the point of view of life, if this number is set too high, most cells in the world will die because they cannot find too many living neighbors until the whole world is dead;
If this number is set too low, the world will be filled with life without any change.
An overly simple metaphor for “Game of Life” is:
A person who is too lonely will die, and too busy will die.
Conway has set the following rules for “Life Game”:
In a grid world, each grid can grow up to one cell. Cells survive, reproduce or die from generation to generation according to the rules.
Rule 1: Health
The cells adjacent to 2 or 3 cells will survive to the next round, such as the cells with a green tick in the center of the box below;
Rule 2: Dead
Adjacent to 4 or more cells, it will die because of overcrowding; adjacent to 1 or 0 cells, it will die because of loneliness.
Rule 3: Reproduction
If a space is adjacent to 3 cells, in the next round, a new cell will be generated in this space, such as the cells with yellow circles in the center as shown below.
In every generation, life, death, and reproduction occur simultaneously. Each generation of cells constitutes a group, or a small step in “history of life”.
The initial cell structure can be defined as a seed. When all the cells in the seed are processed by the above rules at the same time, the first generation cell map can be obtained. Continue to process the current cell map according to the rules, and you can get the next generation of cell maps.
Three
Take an example (from Dr. Yang Yang) to demonstrate how to play this game:
The first generation (as shown below) randomly selects a state.
We analyze according to the rules of “Life Game”:
According to the rules, the next generation will change as follows.
Second generation (lower right part of the picture below)
Continue to iterate, we will run according to the rules of the game on the basis of the second generation.
The third generation (as shown in the lower left part of the picture below)
Then, you can continue to evolve from generation to generation, and start again and again.
This “life game” seems too simple, what is the point?
Four
In this game, it is full of randomness and emergence.
The initial pattern will continue to change, these changes are often unexpected:
Sometimes, the seemingly complex initial pattern will disappear after many rounds, or extinction.
extinction
Sometimes, a stable state is formed.
Still life
Some cells have a very stable distribution. No matter how many generations you run, they will always maintain the same shape without change. These distributions are called still life. For example, the following forms.
oscillator
Sometimes, an oscillating state will be formed, repeatedly switching between different patterns, this type is called an oscillator.
Mobile oscillation state
Sometimes, a “moving oscillation state” is formed.
For example, the “spaceship” below, this pattern can move around in the checkered world.
Glider
For example, the following picture is a sustainable breeding model in the game of life: “Gaussian machine guns” continuously manufacture “gliders.”
Five
In Conway’s “Life Game”, the initial state is random and simple, seemingly disordered, but under extremely simple rules, the cells will gradually evolve a variety of exquisite and tangible structures.
After “evolution”, some are dead, some are still, some are moving like life, these structures often haveVery good symmetry, and each generation is changing shape, and can even jump into another level of evolution.
The meaning of “life game” is to verify the universe view of some scientists, namely:
The simplest logic rules can produce complex and interesting activities.
Conway’s “game of life” comes from von Neumann’s idea of the evolution of the machine:
Cellular automata.
Cellular automata is a powerful method for simulating complex phenomena including self-organizing structures, also known as cellular automata.
The basic idea of the cellular automaton model is:
Many complex structures and processes in nature are ultimately caused by simple interactions of a large number of basic building blocks.
The cellular automaton mainly studies the theoretical models of small computers or components connected in a neighborhood connection to form larger, parallel-working computers or components.
It is divided into fixed value type, periodic type, chaotic type and complex type.
Von Neumann ’s original intention in designing cellular automata was:
Provide a simplified theory for natural self-replication and biological development.
Maybe physicists are at the upstream of the scientific contempt chain. At that time, not only von Neumann, Schrodinger also wrote “What is Life”, to understand the essence of life from the perspective of quantum physics .
In that legendary crossover speech, Schrodinger magically predicted:
If each biomolecule is determined by a word composed of 1 to 25 letters, and the word is composed of 5 different letters, there will be 372,529,029,841,191,405 possible different combinations-this is far beyond any organism The number of molecular types currently known in.
Schrodinger further concluded:
“Mini passwords should correspond to a highly complex and precise development blueprint, and may somehow contain procedures that make passwords work, which is no longer unimaginable.”
Later, the three scientists who won the Nobel Prize for revealing the structure of DNA all claimed that “What is Life” played an important role on their way to the double helix.
Let’s go back to “Life Game” and “Cellular Automata”.
The greatest reflection of cellular automata on biological phenomena lies in:
The origin of life is more like a phase change, while evolution is like a struggle between order and chaos.
Xu Hanyi wrote in an article in “Global Science”:
Von Neumann ’s followers feel that it has extraordinary significance for the interpretation of life.
In this context, Conway proposed the best sample of cellular automata in 1970-the game of life.
The documentary “The Great Design of Stephen Hawking” is introduced as follows:
“Simple rules like life games can create highly complex features, and wisdom may even be born from it.
This game requires millions of squares, but it ’s not surprising that we have hundreds of billions of cells in our brains. “
In other words, the metaphor of “life game” is that the world we are in, the birth of life, and the formation of wisdom may also be the result of some kind of “life game”.
Six
So, are there designers in this world?
From the “Glider” pattern in the “Life Game”, we seem to be able to say: “Design” and “Organization” will appear spontaneously without a designer.
However, the “glider” above was formed under Conway’s three rules.
So, can it be said that the creator designed this world, using extremely simple rules, and then adding randomness?
Furthermore, is the checkerboard similar to the “game of life” happening, is it the space-time structure of the universe?
Interestingly, people found that the moving patterns in the “Life Game” also have their own insurmountable “speed of light”.
“Life Game” presents us with “emerging complexity” and “self-organizing system” in a very simple and visual way, coupled with computer simulation evolution.
Is this complex world “emerging” from a few extremely simple rules?
For example, the shell grows one layer of cells at a time (similar to nails), and the growth process is a one-dimensional cellular automaton.
Photo: Meinhardt, H. (1995). The Algorithmic Beauty of Sea Shells. Springer Verlag. pp.179
Some people say that the “ultimate algorithm” in this world may not have many lines of code.
Or as in my “Algorithm of Life”, I also tried to use physics and probability to explore the “alchemy” of the secular world and found the “simple rules” behind the uncertain world.
(For more information, please click “ Seven
The cellular automaton behind life games has been widely used in geography, economics, computer science and other fields.
In my opinion, in the business field, those powerful companies and business models are also the result of the randomness of cellular automata.
Especially in the field of information industry.
I remember when Weibo first appeared, many people were extremely confused: what is this stuff? It’s too ridiculously simple.
Indeed, the original manuscript of Weibo’s ancestor Twitter in 2000 was as follows:
Let’s talk about the popular vibrato now, its product predecessor, musical.ly, is also simply outrageous.
Of course, the success of Douyin depends on the powerful algorithm and operation of byte beat.
Using a less precise analogy, the so-called successful company or business model is like the “oscillating state of movement” in the “game of life”, and it can also evolve twice.
Although this piece is interesting and practical, I am too lazy to start writing.
I am n times starting a business and often torture myself like this:
1. What is the simple prototype of the company?
2. What is the play method (that is, the rules) that can be copied on a large scale?
3. Where is the stage and boundary of the square grid?
4. What kind of vitality will emerge from the company and how will it evolve?
Eight
In September 1944, Schrödinger wrote in Dublin:
The relentless pursuit of unified and universal knowledge is the best quality we have inherited from our predecessors.
I hope you have read the previous texts and do n’t simply sigh. Is n’t this what our ancestors said “two lives, two lives, three lives, and three things in all life”?
Knowing and understanding are two different things.
The “smart” summary and the “stupid” exploration are two different things.
I also hope you can understand that no matter how much I like to use money and secular success as a metaphor when I write “Lonely Brain” and “Life Algorithm”, I am not trying to wrap “success” with science and formulas.
I am using statistical mechanics to play a game called “Alchemy in Life”. The game points to exploration, and life is background music.
The “simple application” and “shallow analogy” between natural and social sciences are difficult and meaningless.
The only value may be a little inspiration.
Wikipedia says that in 2004, Simon-B-Cochin, another scientist at Conway and Princeton, proved the free will theorem, which is a special version of the principle of “no hidden variables” in quantum mechanics.
The theorem states:
Under certain conditions, if the experimenter is free to decide what amount to measure in a particular experiment, then the elementary particles must freely choose their rotation, so that the measurement results conform to the laws of physics.
In Conway ’s slightly exaggerated language, it is:
If the experimenter has free will, so are the elementary particles.
So, will scientific research revive the omniscient Laplace beast?
Does Conway’s random-based games reveal “determinism”?
Will endless exploration destroy human nature and lead to a complete void?
I’m not worried about this at all.
Just like Feynman is a firm reductionHe is also an outstanding quantum physicist and probabilistic thinker.
Complexity and simplicity, randomness and decision, reversible and irreversible, free will and Laplace beast, behind these oppositions, there may be the same “cellular automaton” that constructs the “life game between universes” “.
As Goethe said:
Existence is eternal; because there are many laws that protect the treasures of life; and the universe draws beauty from these treasures.
Last
Let’s miss John Conway, the designer of “Life Game”.
Even after many years, when people think of him, they will still remember those fun things.
For example, he is completely addicted to mathematics and games, and his office is so messed up that he ca n’t stand it anymore. He will cutely find his name in the index behind the newly published mathematics book to satisfy vanity. ….
He reminds us that this world is still interesting.
In this messy time, please allow me to change one of Conway ’s advices:
Ignore the idiots! In this interesting universe, have fun.
