"The Story of Probability, From Dice to the Heart of Artificial Intelligence"
Random walk, Bayes, information entropy, quantum mechanics
Understanding artificial intelligence

It's easy to believe that artificial intelligence is a being that calculates everything precisely.
However, Dr. Zhang Tianlong, the author of this book, does not subscribe to this belief.
This book compellingly demonstrates that the true workings of the artificial intelligence that dominates our daily lives are surprisingly rooted in the mathematical concept of probability.
The author received a Ph.D. in theoretical physics from the University of Texas at Austin, and is a science writer who has taught science for a long time at the University of Science and Technology of China, where he has conveyed cutting-edge topics such as quantum mechanics, cosmology, and artificial intelligence to the general public in an easy and interesting way.
Her writing is renowned for its ability to interpret the rigorous language of science in a story-like, entertaining way.

This book begins with a simple question.
“How can we predict what number will come up when we roll a die?” And the story soon expands to Bernoulli’s law, Bayesian inference, Markov chains, and information entropy.
Next, we will gradually unravel how these concepts are connected to AlphaGo, ChatGPT, recommendation algorithms, and language generation models.
In particular, interesting probability problems and thought experiments such as the 'rat and poison problem' and 'Bayes' billiard table' provide readers with a sense of immersion as if they are experiencing mathematical concepts with their whole body.
When readers reach the conclusion that “AI does not know the right answer, but rather predicts plausible answers probabilistically,” they will finally understand the power of probability.

As scientific civilization becomes more precise, probability becomes more important.
In a reality where we cannot know all the data, we have to choose the 'most plausible' among the possible ones.
The basis for that judgment is probability.
Interpreting the world through probability and finding order in uncertainty.
"Mathematical Everyday Life Seen Through Probability" explores the world of probability without complex formulas, and through real-life examples, clearly shows the principles within which the era we live operates.
For everyone living in uncertain times, this book will serve as an intellectual compass.

Dice have been used in gambling since ancient times, and it appears that humans have been using them for 5,000 years.
Although the Egyptians were the first to invent dice, similar items that were independently invented by several other ancient civilizations appear in the history of the world.
But even though humans have been playing with dice for thousands of years, shaking and throwing them, that doesn't mean we've fully grasped the profound mathematical secrets hidden within them.


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Although the definition of 'probability' may seem easy to understand and accessible to everyone, we should not overlook the fact that the results of probability calculations often contradict our intuition.
This is because it is difficult to explain even with probability theory, and paradoxes that seem plausible but are not true exist everywhere.
However, that doesn't mean you should blindly trust your intuition.
Our brains can create errors and blind spots.


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In 2001, Enron, the largest energy trading company in the United States, declared bankruptcy, and news broke that the company's top executives were accused of falsifying accounts.
Enron's top executives manipulated financial data, causing their published earnings per share data for 2000-2001 to not conform to Benford's Law.
Benford's law can also be used to analyze the stock market or monitor election manipulation.

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The wonder of the central limit theorem cannot be denied.
Under certain conditions, when random variables generated from various types of probability distributions are combined, the overall effect follows a normal distribution.
This is particularly useful in statistical experiments, because real biological or physical stochastic processes do not arise from a single cause, but are influenced by many random factors.


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While frequentists seek to explain the nature of things, Bayesians focus on explaining how an observer's state of knowledge is updated after a new observation occurs.
This can be seen as a difference in worldview affecting a difference in method.
For example, in the process of coin tossing, the frequentist school emphasizes 'multiple trials', while the Bayesian school emphasizes exploring ways to update the 'outcome of the trial'.


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The winner's process is an extreme process of a random walk.
In general, a random walk is a process of moving one grid at a time within a grid space, and if the distance between grid points is ??, then the Wiener process is the limit of the random walk process when ?? approaches 0.


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Maxwell initially studied the dynamical theory of gases and maintained the view that 'the absolute temperature of a gas is a measure of the kinetic energy of its particles', but at a constant temperature ?? he believed that the kinetic energy of all molecules was not a single fixed value but followed the law of statistical distribution, that is, a distribution curve.
The velocity of individual particles continually changes due to collisions with other particles, but in the case of a large number of particles, the proportion of particles within a particular velocity range remains almost constant.


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1928 RVH
Harley RVH
Harley once suggested that information be expressed in terms of ??log??.
In 1949, Wiener, the founder of cybernetics, introduced the concept of quantitative information to thermodynamics.
In 1948, Shannon viewed information as a concept that describes the uncertainty of the state of motion or existence of an object, and derived a formula for the amount of information by extending Halley's formula to cases where each probability ???? is different.
In this way, he gave birth to information theory for us, defined the scientific meaning of 'information', and became the 'father of information'.


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In the case of a human relationship network, each individual can be considered a vertex in the graph.
For example, the relationships between people, whether they know each other or not, are represented by edges connecting the vertices of the graph.
Using a 'graph' as ​​a network model is not the only way, and its choice depends on the subject of research.
For example, a human relationship network may have individuals or groups as vertices.


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To better understand the role of convolution, we can compare it to the Fourier analysis of an audio signal.
Sound signals exhibit very complex curves in the time domain, and a large amount of data is required to represent them.
If converted to the frequency domain through Fourier, it can be displayed with only a small amount of spectrum, fundamental frequency, and a few harmonic overtone data.
In other words, Fourier analysis can effectively extract and store the main components in a sound signal and reduce the number of dimensions describing the data.

--- From the text