Symmetry Breaking: Destiny is Just Cooled Coincidence

The conceptual tool introduced in this lecture might be one of the most powerful weapons complexity science has bestowed upon us.

You’ve surely seen photos of the night sky taken by space telescopes: countless stars densely packed across the frame, their positions appearing entirely random. You might think that with galaxies so haphazardly arranged, moving a few here or there probably wouldn’t make much difference.

But the truth is, you can’t move them. Each tiny speck of light in those photos isn’t a star, but a galaxy; a millimeter on the photo represents hundreds of millions of light-years. The energy required to ‘slightly shift’ a galaxy is simply not permitted by nature. Galaxies do move, but that photo won’t show any visible change for thousands of years. What you’re facing is an indestructible fait accompli.

But why are those galaxies positioned this way? They must have an origin, right?

The answer comes from contingency. In the early universe, matter-energy density was nearly uniform, overlaid with only extremely tiny quantum fluctuations—a slightly denser spot here, a slightly sparser spot there, and this ‘slight’ difference amounted to one part in a hundred thousand. Yet, it was precisely these minuscule differences that led to a distribution of matter in the later universe where there was a little more in one place and a little less in another. Under the influence of gravity, that matter slowly evolved into galaxies, ultimately forming the universe we see today.

The distribution pattern of these galaxies today—where starlight clusters and where vast emptiness prevails—is merely the amplified effect of those random jitters from back then.

This process, where ‘anything is possible’ transforms into ‘only one possibility, and an indestructible one at that,’ has a specialized term in physics: ‘symmetry breaking’.

Imagine balancing a pencil on its tip on a table. All directions around it are perfectly equivalent—the laws of physics favor no particular direction; this is symmetry. However, the pencil cannot stand forever; perhaps due to a momentary air disturbance, or a subtle texture on the table, or some tiny, almost imperceptible chance factor, it will eventually fall. And once it falls, it can only fall in a specific direction, never returning to its initial symmetric state. This is symmetry breaking.

The equations are symmetric, but the outcome is broken.

Chaos is symmetric; its initial unfolding is broken. From this, all things unfold.

In 1972, Philip Anderson, a physicist at Bell Labs—who later won the Nobel Prize in Physics—published an article in Science titled ‘More Is Different’ [1]. He mused that the laws governing the macroscopic world cannot be simply derived from microscopic equations, and that ‘broken symmetry’ is precisely the key to understanding why new orders can emerge layer by layer in the world.

What I want to say is that this key can not only explain the mysteries of the cosmos but also illuminate your own circumstances. Simply put—

Destiny is merely cooled coincidence.

The Cooling Universe and Contingent Choices #

Let’s first look at the evolution of the universe. The history of the universe is a history of cooling down, and each drop in temperature has forced the universe to make a choice.

According to Alan Guth’s ‘inflationary theory’ [2,3], proposed in 1981, after its birth, the universe underwent a cosmic inflation—an super-explosive expansion of space itself—in far less than a second. This stretched the fleeting quantum fluctuations of the microscopic world all at once to a macroscopic scale, ‘freezing’ them into the blueprint for the universe’s density distribution. For the subsequent tens of billions of years, gravity has merely been ‘constructing’ according to this blueprint.

Next, approximately one trillionth of a second after its birth, when the temperature dropped to the order of quadrillions of degrees, symmetry breaking occurred for forces and mass. Before then, electromagnetic and weak interactions were still a single force, and the particles mediating forces and composing matter had no mass. After this, the Higgs field pervading the entire universe could no longer ‘sustain itself,’ akin to the pencil on the table randomly falling in one direction. The electromagnetic and weak forces separated, and particles like electrons and quarks consequently gained mass. This is ’electroweak symmetry breaking’.

Next came the asymmetry of matter-antimatter particles. Logically, the Big Bang should have produced strictly equal amounts of matter and antimatter. When matter and antimatter meet, they annihilate, turning into light. If the universe had strictly adhered to this symmetry, its fate would have been nothing but pure light.

But for some unknown reason, a tiny remnant appeared in the ‘accounts’ of that time: for roughly every billion antimatter particles, there was one billion and one matter particles.

Consequently, when annihilation duly arrived, after a billion pairs mutually destroyed each other, there was always one matter particle left over.

It is precisely this one-billionth remnant that constitutes all the ordinary matter in the universe today—including you and me.

Where did this remnant come from? Where exactly were the laws of physics asymmetric? Over the years, physicists have found some clues but have not yet fully resolved this issue [4,5].

All three of these symmetry breaking events occurred within the first second after the Big Bang. We are fortunate that the universe is a product of ‘imperfection’.

Something perfect should be absolutely symmetric, but absolute symmetry would mean nothing at all. Impartial annihilation would leave no matter, a Higgs field that didn’t ’take a stand’ couldn’t impart mass to particles, and a perfectly uniform universe couldn’t give birth to galaxies.

Therefore, symmetry breaking is not a flaw in the world. It is the generative mechanism of the world.

Cooling and Solidification in the Human World #

The freezing of fluctuations, the Higgs field ’taking sides’, and matter-antimatter annihilation are three distinct physical processes, yet they share a commonality: they allow a tiny, accidental difference to be selected, amplified, and ultimately preserved permanently. So it is in nature, and so it is in human affairs.

Human society also experiences moments of symmetry: several forces temporarily achieving equilibrium, multiple factions potentially emerging victorious, several standards appearing reasonable, multiple futures seeming plausible—anything is possible. In this high-temperature state, a tiny disturbance can lead to immense changes. Society at that time is like freshly blown glass, soft and malleable; a mere breath can make it bend into an arc…

But it will quickly cool and set. By then, even if you strike it with a hammer, there are only two outcomes: either it remains utterly unmoved, or it shatters into a million pieces—in any case, you won’t get the shape you want.

In 1947, the British finally decided to withdraw from India. The Indian National Congress intended to unify all of India, while the Muslim League insisted on establishing a separate Pakistan. So Britain proposed the partition plan for India and Pakistan [6]. But where exactly should the boundary line be drawn? With both sides in fierce disagreement, the British government simply entrusted this task to a London lawyer at the time, Cyril Radcliffe.

Radcliffe only traveled to India for the first time after receiving the assignment. However, he did not personally visit the areas where the boundaries needed to be drawn but merely participated in committee work. He made his decisions in Delhi, based on maps, census reports, and some hearing materials.

If a discerning person at the time could have invited Radcliffe for a meal and thoroughly explained the religious beliefs and historical context of both sides, surely the situation today would be much better… Yet, the outcome was that a person completely unfamiliar with the land casually drew a line, thereby performing a ‘geographical surgery’ on India and Pakistan.

Subsequently, tens of millions of people fled from one side of the border to the other, followed by mass killings, and then the ongoing India-Pakistan conflict. Radcliffe’s line back then was clearly not well-drawn, yet attempting to redraw it now is almost impossible.

Changing the same thing is effortless when it’s hot, but as difficult as moving galaxies once it has cooled.

Establishing Legacies: Seizing Windows of Historical Opportunity #

Therefore, to establish a legacy that benefits future generations, mere intelligence and talent are insufficient; one must seize the window of opportunity.

For instance, in a country as vast as China, with people living so far apart from south to north, west to east, all using the same written language—don’t you think this is a miracle? It was during the moment when Qin Shi Huang had just unified the realm, and warfare had just melted down the old order completely, that Li Si seized this opportunity and standardized the written language based on Qin seal script [7].

Looking back at Chinese history, there might have been only this one window of opportunity to achieve such a feat.

Originally, the written characters of the various states all originated from the Shang and Zhou traditions but had long since diverged, each with its own writing style [8]. Fortunately, at that time, none of the states had yet cultivated centuries of classics, mature official documents, or a large scholarly class, so their sense of identity with their specific scripts was not deeply ingrained. This allowed Li Si to ‘flatten’ these differences with a single decree. If Li Si had not acted back then, allowing local languages and scripts to continue evolving independently, China would have become like Europe—where even Latin couldn’t enforce uniformity, eventually leading to Romance languages like French, Italian, and Spanish diverging from Latin, and Germanic languages like English and German having separate origins, all developing mature cultures, making unification for later generations incredibly difficult.

Malleability is not a function of power, but of temperature.

I could list more such foundational moments: as long as the system remains in a ‘high-temperature’ state, you can make your choices the default settings for future generations.

When the position of American President was still a blank slate, Washington voluntarily stepped down after serving two terms, and from then on, the notion of ’the president is not a king’ became customary. All presidents for the next 140-plus years limited their terms to two or fewer, until Franklin D. Roosevelt broke the precedent… but eventually, this custom was codified into the Constitution.

When the operating system for personal computers was still undefined, Bill Gates did not sell DOS outright to IBM but retained the right to license it to other manufacturers. Subsequently, compatible machines, software, and users all coalesced around MS-DOS, and Microsoft thereby occupied the ’toll booth’ of the entire PC world.

When the World Wide Web was still just an internal information-sharing project at CERN (European Organization for Nuclear Research), CERN placed its core software in the public domain in 1993. Consequently, browsers, servers, and webpages were able to grow together around open protocols.

In 1997, Apple Inc. was on the verge of bankruptcy. Capitalizing on the near-collapse of the entire organization, Steve Jobs drastically cut 70% of the product roadmap in one go, re-concentrating resources. The subsequent success of the iMac, iPod, and iPhone began precisely with this restructuring, accomplished within a few weeks.

Before symmetry breaking, the situation is like a coin standing on its edge; after symmetry breaking, historians begin to explain ‘why it inevitably’ fell to one side—yet complexity science reminds us that it might have been merely an accidental fall.

But once the situation begins to tip to one side, positive feedback will increasingly lock in this contingency: the more people accept it, the more compelling the reasons for its acceptance become—economists call this ‘path dependence’ [9].

Pioneers ‘have reasons for whatever they do.’ Most people, however, only remember they have opinions about the shape of the glass after it has completely cooled.

Seizing the ‘Hot Moment’ for Personal Destiny #

You might ask, what does this have to do with me, an ordinary person? The answer is: the more you wish to change your destiny, the more you must be able to seize ‘hot situations’.

Actually, ‘hotter’ isn’t always better. If the glass remains perpetually hot, your actions are merely noise. The true window of opportunity is when the situation is ‘about to cool but not yet cooled’: possibilities have begun to converge but haven’t yet converged to just one—just as we mentioned earlier in discussing making money, the ‘opportunity window’ theory states: an opportunity window opens when a dominant category emerges and closes when a dominant design appears.

Here, let’s briefly summarize the ‘mindset’ for leveraging symmetry breaking, which comes from research on ‘critical phenomena’ [10]. There are three main points—

First, observe the system’s ‘plasticity’. A hot system must have more than one future option still available.

If a field has only one recognized winner and one accepted approach, then it has already ‘cooled’. However, if three or four interpretations all make sense, and no one dares to declare which is the standard; if technological paths are not yet fixed, if the industry has not yet formed a professional title system, if organizations have not yet established processes, and if no recognized ‘viral formula’ has appeared on platforms, then it is still within the ‘window of opportunity’.

A key characteristic of ‘about to cool but not yet cooled’ is that people no longer make independent judgments but instead inquire about ‘how others are choosing’: ‘Let’s wait and see what the big players do,’ ‘Let’s see how the leaders express themselves’—people are awaiting ‘common knowledge’.

Second, using a physics term, look for an ‘order parameter’: that quantity which can compress countless local choices into a single macroscopic direction.

The net magnetization direction of a magnet, the proportion of an industry adopting the same standard, the number of key figures in a circle who publicly acknowledge the same designation—these are all order parameters.

When two technological routes compete, it can be measured by subtracting the proportion adopting B from the proportion adopting A: if the difference is close to zero, it means the system has not yet ’taken sides’; but once the difference consistently leans to one side, it indicates that symmetry breaking is occurring. Once the order parameter consistently shifts, a large number of previously independent choices within the system will begin to rearrange themselves around it.

Third, seek ’lock-in potential’. When you finally make your move, ensure that your small step can be ‘remembered’ by the system.

Small actions usually have little effect, because stable systems have a strong capacity to absorb things; minor incidents, small articles, petty disputes quickly fade away silently. However, in systems approaching symmetry breaking, small matters resonate repeatedly and linger—for example, an article is circulated again and again, a small demo causes anxiety throughout an entire industry, a routine meeting is privately discussed for weeks. All of this indicates that the system is looking for an outlet…

Applying ‘Symmetry Breaking’ in Life #

Let’s look at a few application scenarios in daily life.

One scenario is when a new tool is first introduced to a company. The boss announces ‘full embrace of AI,’ but internally there are no processes, no templates, no one knows how to use it, and everyone is watching and inquiring—this is plasticity. And ‘which set of usages is becoming standard practice’ is the order parameter. If you quietly create a reproducible ‘Skill’ to share with colleagues, and even introduce it into internal tutorials, symmetry breaking has already occurred. When people start asking, ‘Shouldn’t this be done your way?’, you become the molder of the system.

Another scenario is your first three months on a new job. At this point, no one knows who you are, and you can actively decide how others ’typecast’ you. First impressions last a long time. So, in these first three months, pick one or two high-visibility small tasks and do them exceptionally well, so that the first time people think of you, a clear label comes to mind, like ‘This person can explain complex problems clearly’.

Consider, for example, the first round of negotiations. The prices, responsibilities, and boundaries expressed in the first round become anchor points. Therefore, don’t wait for the other party to ‘set the agenda’; you should break the symmetry first. For instance, right from the start, provide a summarized one-pager: clearly defining objectives, division of labor, deliverables, timelines, and what is not included, then invite the other party to respond, confirm, and reference it.

Another example is the beginning of a relationship. Who manages money between spouses, how arguments are conducted, where the boundaries for each other’s parents lie—these rules quietly solidify during the first year or two of coexistence. Once this opportune moment passes, the patterns become default settings, and any subsequent changes can only be achieved through ‘making a scene’.

The same applies to children. Every child is ‘symmetric’ at birth, and each time a label is applied, a symmetry breaking occurs. ‘I am bad at math,’ ‘I am someone who can perform on stage’—once these identities freeze, they will in turn dictate their behavior for decades to come.

There’s also a special kind of window: crisis. Unemployment, illness, project collapse, relationship breakdowns—while these are undoubtedly bad news, they are also moments when the situation reverts to symmetry. Those structures you normally can’t change—where you live, who you associate with, how you work, how you live—all become loose at this moment. Crisis temporarily ‘discounts’ the cost of change. While everything is still in a fragmented state, reassemble a better future.

In summary, this ‘mindset’ can be summarized as: Name → Model → Publicize → Solidify. That is, give a name to what doesn’t yet have one, provide a reference model for what lacks a standard, make it public so that ‘others know that others also know it,’ and then embed it into schedules, templates, contracts, or manuals.

To use the theory of ’emergence’ from the previous lecture, this is about letting new order be born through you, but live independently of you.

Infinite Possibilities and a Cooled Life #

People often say the future holds infinite possibilities. However, in reality, only the future of young people holds infinite possibilities. Every step of your growth is a choice, every choice is a symmetry breaking, and every symmetry breaking is a solidification.

Your identity will become fixed, your path will be ’locked in,’ your social relationships will solidify, and your life will cool down. That would be too dull, which is why protagonists in works of literature and art are almost always young people.

‘Choice outweighs effort’ is certainly true, but we don’t always have the right to choose. When the window is open, a small action can rewrite the course of many years to come; but when the window closes, what you perceive as choice is merely striking a pose.

After Cao Can succeeded Xiao He as prime minister in the early Han Dynasty, he spent his days drinking and changed nothing. When Emperor Hui questioned him about his approach as prime minister, Cao Can retorted, ‘In terms of ability, can Your Majesty compare to Emperor Gao, or I to Xiao He?’ The subtext was that the system was ‘hot’ in their time, but had ‘cooled down’ by the time it reached their hands [11].

Of course, the good news is that you will still encounter other moments of symmetry breaking.

Destiny is not unchangeable, but it is also not always changeable. ‘Accepting fate’ means recognizing what has ‘cooled down’; ‘defying fate’ means keeping an eye on situations that are still ‘hot’.

A gatha praises thus:

A speck of dust stirs the eternal galaxy, When kalpic ashes are fully reckoned, this person remains. Speak not of how long heaven and earth have been formed, Still, there is glazed glass, carrying the warmth of fire.

注释

[1] Anderson, P. W. “More Is Different: Broken Symmetry and the Nature of the Hierarchical Structure of Science.” Science 177, no. 4047 (1972): 393–396. https://doi.org/10.1126/science.177.4047.393

[2] Guth, Alan H. “Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems.” Physical Review D 23, no. 2 (1981): 347–356.

[3] Guth, Alan H., and So-Young Pi. “Fluctuations in the New Inflationary Universe.” Physical Review Letters 49 (1982): 1110–1113.

[4] Sakharov, A. D. “Violation of CP Invariance, C Asymmetry, and Baryon Asymmetry of the Universe.” JETP Letters 5 (1967): 24–27.

[5] Christenson, J. H., J. W. Cronin, V. L. Fitch, and R. Turlay. “Evidence for the 2π Decay of the K₂⁰ Meson.” Physical Review Letters 13 (1964): 138–140.

[6] Khan, Yasmin. The Great Partition: The Making of India and Pakistan. New Haven: Yale University Press, 2007.

[7] 《史记·秦始皇本纪》：“一法度衡石丈尺，车同轨，书同文字。”

[8] 许慎：《说文解字·叙》。“言语异声，文字异形”与“（李斯）罢其不与秦文合者”皆出于此。

[9] Arthur, W. Brian. “Competing Technologies, Increasing Returns, and Lock-In by Historical Events.” The Economic Journal 99, no. 394 (1989): 116–131.

[10] Scheffer, Marten, Jordi Bascompte, William A. Brock, Victor Brovkin, Stephen R. Carpenter, Vasilis Dakos, Hermann Held, Egbert H. van Nes, Max Rietkerk, and George Sugihara. “Early-Warning Signals for Critical Transitions.” Nature 461, no. 7260 (2009): 53–59. https://doi.org/10.1038/nature08227

[11] 《史记·曹相国世家》。