Have you ever wondered why the whole is greater than the sum of its parts?

Yang Mingzhe

If there is a cake like this on the table in front of you, you will probably want to eat it, but wait, why do you want to eat it? You may say, because I am hungry, because it looks delicious. But if you continue to dig deeper, you will encounter a mystery that surprises scientists.

The progress of science over the past thousands of years has made us discover that everything can be broken down into pieces. Once you have broken down a system, you will understand it. But something as simple as eating cake is difficult to do. The idea that controls my behavior must come from the brain, and the brain can be broken down into neurons. But if you ask all the neurons, no neuron will tell you the complete message "I want to eat cake". Neurons that look ordinary can actually form such a complex and exquisite organ as the human brain when gathered together. This is emergence .

Emergence: Why the whole is greater than the sum of its parts

Emergence is a very common phenomenon. You don't eat cake every day, but you definitely drink water every day. When the temperature is high, each water molecule moves around freely and twists and turns. At this time, if you look at this ball of water vapor, it is the same whether you look up, down, left or right. It can be said to be completely symmetrical . When the temperature drops, the water molecules have to line up and form a tight lattice, which is ice. At this time, if you switch to different observation angles, the arrangement structure of water molecules seen in different directions is different. The symmetry is destroyed. This phenomenon is called spontaneous symmetry breaking by physicists.

What does this have to do with emergence? In fact, a physicist named PW Anderson believed that symmetry breaking is the basis of emergence . In 1972, he published a famous article in Science magazine called "More is different". These three short words have a sense of simplicity. It translates to " more is different ". Simply put, it is different when there are more. So the question is, how can it be different when there are more? An orange is an orange, but if two oranges are put together, it is no longer a fruit?

In fact, no matter how many oranges there are, we would not expect any magical phenomenon of quantitative change leading to qualitative change. But if you replace oranges with ants, the situation is quite different. A single ant is stupid, but a group of ants together can spontaneously form an ant colony. They build winding and complex anthills, develop division of labor, and develop agriculture and animal husbandry - some ants maintain fungus farms, some take care of aphid pastures, and so on. So why do ant colonies do these things? You can't get a clear answer if you ask a single ant, just as your neurons don't understand the concept of cake. But a large group of ants communicate with each other through pheromones, which can achieve the effect that the whole is greater than the sum of its parts, and a high degree of intelligence emerges.

The difference between a pile of oranges and a pile of ants shows us that "big" and "many" do not necessarily lead to emergence. In fact, we need to set a boundary for the description of emergence to see under what conditions emergence will occur.

When does emergence occur?

【1. Divide the scale】

First, we need to distinguish descriptions at different scales . For example, when I say that water freezes into ice, I am describing a macroscopic change, and when I describe the changes of individual water molecules, I am describing it at the microscopic scale. Any number of things can be described in this way, and there is nothing strange about it.

[2. New causes and effects emerge]

Next, we will focus on some special systems. Some of their results on the macroscopic scale cannot be reduced to the microscopic level to find reasons to explain because of broken symmetry. So we have to find a new "cause" on the macroscopic scale to explain the macroscopic "effect". The reason for the new cause is that we treat a system as a whole.

For example, for water waves, we know that water waves are composed of water molecules, but how would you describe such a phenomenon? Would you say "a water wave propagates from left to right" or "a water molecule vibrates up and down, driving the surrounding water molecules to vibrate, thus causing a phase difference between water molecules in different spaces"? Obviously, it is simpler to view the water wave as a whole, or the causality is more obvious. Today, different disciplines have chosen a scale with the strongest causality to study the issues they are concerned about.

3. Choose the most causal scale

Combining the above three steps, including the division of scales , the emergence of new causalities, and the selection of the strongest causalities , we have the prototype of a theory called causal emergence. This theory was proposed by a neuroscientist named Erik Hoel in 2013 and is currently one of the more mainstream theories for defining and quantifying emergence. It should be pointed out that emergence is now more of a description of some phenomena, and it is very inconsistent. The theory of causal emergence is not a universally accepted theory, but a method to try to quantify emergence. There are many theories in this regard, so I will not go into details here.

At this point, we can shout the slogan "More is different", because the whole is indeed not equal to the sum of the parts. The things studied by chemists, biologists and even sociologists cannot be explained by the most basic physics. It can be said that it is precisely because of the emergence phenomenon that we need to derive many disciplines to study the same real world from different scales.

In short, the emergence of such a magical phenomenon makes our world not boring. From the origin of life to your understanding of the central idea of ​​an article, from the flexible and orderly flock of birds to the "I" in this video, understanding emergence will give you a layer of wisdom in looking at the world. Please note that the "I" in your eyes at this moment is not a person, but a combination of pixels.

This article is a work supported by Science Popularization China Starry Sky Project

Author: Yang Mingzhe

Reviewer: Zhang Jiang, Professor of School of Systems Science, Beijing Normal University

Produced by: China Association for Science and Technology Department of Science Popularization

Producer: China Science and Technology Press Co., Ltd., Beijing Zhongke Xinghe Culture Media Co., Ltd.