Towards the end of my PhD, I became an expert on black holes and was given the opportunity to work as a postdoctoral researcher in Hawking's research group at the University of Cambridge.
This was my first step as a theoretical physicist studying gravity.
But as graduation approached, I began to doubt whether this was really what I wanted to do.
Above all, the problem was that what I was going to do had nothing to do with people's well-being or happiness.
Moreover, I learned that there are very few physicists in the world who are truly interested in the details of my research.
--- From the "Preface"

Uncertainty is the essence of life.
The word itself doesn't sound very pleasant, but our lives are full of uncertainties.
No one knows if they will have a car accident next week or win the lottery and change their fate.
The further ahead you look, the greater the uncertainty.
What if another global financial crisis strikes in a few years, destroying all my investments? Or a global pandemic, the outbreak of World War III, or a drastic climate change? No matter how hard you look at it, nothing is certain.
But what kind of lives would we lead if we had the ability to accurately predict the future? Even if we could foresee what the future holds, would we still remain a creative and vibrant species?
--- From "Entering"

To conclude, there is no need to worry about the Earth being deviated from its orbit.
A team of researchers at Princeton University ran numerous simulations using an ensemble of different initial conditions, and never once did they reproduce the dire scenario of Earth leaving the solar system in the next few billion years.
That means the odds of Earth leaving the solar system are close to zero (though not completely zero!). Worryingly, however, this ensemble prediction suggests that in billions of years, Mercury's orbit will begin to drift slightly, giving it about a 1 percent chance of colliding with Venus.


Here we need to pay attention to the word nonlinear.
In general, a physical system in which input and output are not directly proportional is called a nonlinear system.
A close example is the relationship between lottery winnings and the level of joy.
If you won a million won lottery ticket, you would jump for joy.
But would winning 2 million won make you twice as happy? Sure, you'd be happier than if you'd won 1 million won, but the joy wouldn't be doubled.
Even if you win 10 million won in the super lottery, you won't be 10 times happier. (If you're incredibly rich, imagine converting 1 million won into 10 billion won.) This is the characteristic of nonlinear systems.

--- From "Chapter 1: Chaos Existing Everywhere"

The dimensions of the weather state space are truly beyond imagination.
Considering all the eddies that occur in the atmosphere, the space of weather states is larger than anything that can be represented on a computer.
It is impossible to express it, not to mention the supercomputers that currently exist, or even if a super-supercomputer appears in the future.
The state space of currently used weather forecast models easily exceeds 1 billion dimensions.
Of course, this can be processed to a supercomputer, but it is nothing compared to the dimensionality of the actual state space that weather can have.

The reason that future uncertainty varies greatly depending on the position of the initial uncertainty ring (small circle) is because the equations describing the system are nonlinear.
This characteristic can explain why large-scale events, such as the hurricane of October 1987 or the financial crisis of 2008, occur.
However, using an ensemble system, it is possible to issue advance warning when the system is moving into an unstable state where 'dramatic events may occur, but are not necessarily'.

--- From "Chapter 2: Chaos Geometry"

Experts in the 1950s believed that the atmosphere was so volatile and had vortices of varying sizes everywhere that it was impossible to predict.
Lorenz also said that the degrees of freedom of the atmosphere are only three, making it difficult to predict.
Both are correct.
In 1963, Lorenz concluded that models with three variables were too chaotic to be predictable, and in 1969 he proved that physical systems with many variables (large and small eddies) were more difficult to predict than systems with fewer variables.
However, the real reason why it is difficult to predict the state of the atmosphere lies in the latter, not the former.

--- From "Chapter 3: Noise, Million Dollar Butterflies"

Is the nature of uncertainty epistemological or ontological? If it's epistemological, quantum uncertainty means "physical systems are precisely defined, but our knowledge of them is incomplete." If it's ontological, it means "uncertainty is inherent in nature, whether we care about it or not."
Most physicists believe that quantum uncertainty is an ontological property (for reasons we will discuss later). Since the world we call reality is made up of innumerable quantum particles, this means that reality itself (which we take for granted) is uncertain.
--- From "Chapter 4 Quantum Uncertainty: The Lost Truth?"

Richardson's dream was finally realized after World War II with the advent of the first electronic digital computers.
After that, John von Neumann, a genius mathematician and physicist at Princeton University, organized a research team led by meteorologist Jul Charney and began developing a full-scale weather forecasting system.
Such models are based on physical laws such as the Navier-Stokes equations.
To distinguish them from the earlier models proposed by Fitzroy, Blandford, and Walker (also called data-driven models, models based on experience and statistics), we will call them physics-based models.
To run their physics-based model, Charney's research team used a "programmable electronic digital computer," known as the ENIAC, the first known computer.

How can we inject probabilistic concepts into models based on determinism? There are ways.
We can introduce the Monte Carlo calculation method developed by Reese a few years ago.
However, instead of taking the average of the forecasts like in Reese's, we need to predict the probability that various weather patterns will appear from the ensemble members.
In 1985, Murphy and I successfully built the world's first ensemble forecasting system based on a physics-based model.
--- From "Chapter 5 Two Roads to Monte Carlo"

Simply put, to accurately understand the impact of climate change on us, we need to accurately understand the level of uncertainty in the information provided.
How can we achieve this task? The ensemble technique used in weather forecasting in Chapter 5 is a classic method for assessing uncertainty.
In fact, we can never scientifically understand climate change without knowing the three functions of the ensemble.
The three functions I just mentioned are, first, estimating the uncertain feedback effects of climate science, second, evaluating the effectiveness of policies designed to address climate change, and third, distinguishing between naturally occurring and human-induced chaos.

It is a clear fact that the chaos world never takes the same path twice.
Therefore, we cannot be 100 percent sure that actual weather phenomena are caused by carbon emissions.
But that's not the point.
What's important is that the probability of the aforementioned disasters occurring due to climate change has increased by a factor of 100, from once in 1,000 years to once in 10 years.
Using these statistics, we can identify areas that need urgent improvement, such as strengthening forest management laws or building flood defense facilities.

--- From Chapter 6, “Climate Change: A Catastrophe or Just a Small Change”

British politicians have insisted that science should be followed as closely as possible when dealing with the pandemic.
But as with climate change, science itself doesn't advocate for any particular policy.
When we want to reduce the risks of climate change, climate science only recommends that reducing carbon emissions is beneficial, but does not mandate that we must reduce carbon emissions.
It is not science but humans who consider this to be an obligation.
Likewise, when trying to prevent a situation where medical services are paralyzed, scientific theories related to the coronavirus only recommend that "reducing interpersonal contact is advantageous," but do not mandate that "interpersonal contact must be completely eliminated."
This too can have different weights depending on human judgment.


As with climate change, it's experts who provide the information, and politicians who then decide on policies (strengthening or relaxing social distancing measures, border closures, etc.).
Of course, the more uncertain the prediction, the more difficult it will be to make policy decisions. However, it is not the duty of a scientist to make predictions that are easy to make policy decisions but have low reliability.
If that policy fails, politicians will look for scapegoats among scientists.
--- From "Chapter 7 Pandemic: Between Viruses and Politicians"

Good models are needed to quantify the predictability of the economy.
But what constitutes a "good economic model"? In 2008, after discussions with several economists, French economist Xavier Gabe and his colleagues published a paper titled "Seven Properties of a Good Model."
The items they ultimately proposed were simplicity, manageability, conceptual insight, generalizability, falsifiability, agreement with experience, and predictive accuracy.
However, many economists are said to have accepted only the first four items and reacted somewhat negatively to the remaining three.
I couldn't understand economists.
If I were to ask my fellow meteorologists what makes a good model for weather forecasting and what makes a bad model, the obvious answer would be, "If it's accurate, it's a good model; if it's inaccurate, it's a bad model."
One might question the criteria for judging the accuracy of weather forecasts (e.g., whether they are better at predicting normal weather versus extreme weather), but these are merely details.
In other words, the items that economists scored lowest on (falsifiability, consistency with experience, and forecast accuracy) were scored highest by meteorologists, and vice versa.
Moreover, I have never met a single meteorologist who listed 'simplicity' as a requirement for a weather forecast.

--- From "Chapter 8 Financial Collapse: What if Meteorologists Could Predict the Economy?"

As I mentioned in Chapter 8, around the time I was finishing this book, Russia invaded Ukraine.
This was predicted by a forecasting system that runs every few months, mainly because Russian forces had been concentrating on the border for several months before the invasion.
But even beyond this, Richardson's conflict conditions had already been met.
For example, the fact that Russia and Ukraine have shared a border for many years, the Russian president's persistent dissatisfaction with Ukraine since the collapse of the Soviet Union, and the comprehensive buildup of Russia's military in recent years are all evidence of a deepening conflict.
In fact, Ukraine had been classified as a conflict risk zone in Guo's conflict model for several years before the war broke out.
--- From "Chapter 9 Fatal Conflict: The Physics of War, Conflict, and Survival"

Ensemble forecasting can help you make much more discerning decisions about when to take action.
Relief agencies and aid organizations call preemptive action the act of determining who to target for relief before a disaster strikes.
Just as my friend decided whether to rent a tent based on a critical probability, relief organizations predetermine a critical probability based on an estimate of the cost-loss ratio and take preventive measures when the probability of a disaster is greater than this value.


Climate change can be considered from a similar perspective.
Does burning fossil fuels increase atmospheric carbon dioxide levels? Science tells us the answer is yes.
Is carbon dioxide a greenhouse gas? This too is scientifically confirmed as a "yes."
Will continued greenhouse gas emissions lead to dangerous climate change? Science is never a "yes man," but this answer is a clear "yes."
The atmosphere seems to be getting more and more gloomy.
So, should we reduce greenhouse gas emissions as soon as possible? Science suddenly adopts an agnostic stance on this crucial question.
Environmentalists who insist on listening to science seem to have overlooked this point.
German physicist Sabine Hosenfelder metaphorically explained the way science communicates its message (she was no doubt inspired by the antics of drunken Germans on railway bridges): Science does not warn us not to urinate on high-voltage power lines.
It just tells us that urine is a good conductor.
--- From "Chapter 10: Make a Decision, Make a Decision!: How Science Conveys its Message"

“The smaller the better.” This is one of the core philosophies that has underpinned theoretical physics throughout the 20th and 21st centuries, sometimes referred to as methodological reductionism.
Even now, particle physicists have installed a giant particle accelerator under Lake Geneva in Switzerland and are colliding particles with enormous energies to explore the ultra-small realm.
Because I believe that the smaller the subject of inquiry, the deeper the understanding of nature becomes.
However, I believe that methodological reductionism is a flawed philosophy and that physics is headed in the wrong direction because of it.
--- From Chapter 11, Quantum Uncertainty: Reality Rediscovered?

Couldn't we glean a hint from the eureka moments of renowned scientists? Their creativity, their groundbreaking breakthroughs, stemmed from the subtle interplay between these two modes.
There are clear limits to the creativity that can be expressed in full-power mode.
The decisive eureka moments often come in low-power mode, perhaps because the brain is more sensitive to noise in this mode.
When you have to make a difficult and important decision, you should list all the pros and cons of each decision and then think about it carefully for several days.
This is the lesson that the Eureka moment teaches us.
Another good way is to build an ensemble of all possible futures resulting from individual decisions.
There is no need to bother calculating the probability of every ensemble member individually.
It is enough to simply establish a 'storyline' for each ensemble member to draw.
In climate science, too, when calculating probabilities is difficult, establishing the "most plausible storyline" for each ensemble member is emerging as an important issue.
--- From "Chapter 12: Our Brains Full of Noise"

As someone who has resisted family encouragement to go to church since childhood, I tend to think of the universal immutable set as an alternative to religion whenever I find myself thinking metaphysically.
The points in each set are things that once existed in the past, things that exist now, things that will exist in the future, things that could have existed in the past, things that might exist now, and things that might exist in the future.
This set is truly the collection of all possible things and is an omniscient structure.
Although we cannot distinguish what is real due to the constraints of algorithmic undecidability, these points know precisely which states in the state space of the universe are physically real and which are not.
Additionally, invariant sets are timeless entities and are not subject to time constraints.
So, can an invariant set hear our prayers? In a sense, the answer is yes, since prayers containing our hopes and wishes are part of the self-referential process discussed earlier in this chapter—the process that holds us morally accountable.

--- From "Chapter 13 Free Will, Consciousness, and God"