Defeating uncertainty with certainty is the essence of “Being an Enemy with Heaven.”

One side insists that the best decisions are based on constraints and data dictated by past patterns; the other side is based on a more subjective belief in an uncertain future.

This is a conflict that has never been resolved.

Bayes' theorem focuses on the common situation when we make reasonable intuitive judgments about the probability of some event, but also want to understand how to adjust our previous judgments when the event actually occurs.

Simply put, the law of large numbers means that the difference between the observed value of a sample and its true value will disappear as the number of observed samples increases.

"If human nature has no interest in trying luck, people will not carry out too many investment activities just relying on calm calculations." Time is the decisive factor in gambling.

Risk and time are two opposite sides of the same coin, because if there was no tomorrow there would be no risk.

Time changes risk, and the nature of risk is shaped by the extent of time.

The greater the uncertainty about the outcome, the greater the value of delaying action.

The gambling Greeks didn't invent probability. Why?

Because for the Greeks, reality was only those things that could be verified by logic and axioms, and their insistence on evidence completely opposed reality to empirical experiments alone.

The Greeks believed that there was a strict line between reality and possibility, and they could not imagine any form of physical structure or coordination in the everyday chaos of nature.

Modern methods of dealing with uncertainty start with measurement and use chance and probability.

First and foremost are the numbers.

The Fibonacci Sequence is much more than just a pastime.

Divide any number in the Fibonacci sequence by the number after it. The result after the number 3 is always 0.625, and the result after the number 89 is always 0.618; the larger the number, the more decimal places.

Dividing any number after the number 2 by the number before it will always result in 1.6, and after 144 the result will always be 1.618.

The Greeks knew this ratio, they called it the "golden section."

Form is independent of growth.

The unique quality of the Greek spirit is their insistence on proof.

They care more about the "why" than the "what."

Central to the Hindu-Arabic numeral system is the invention of zero.

If there is no logical conclusion, no matter how far the thought goes, it will stop.

The idea of ??risk management emerges only when people think they have reached a certain level of liberation.

Chapter 3: Promotion of double-entry accounting.

The most likely reason is that the Greeks were not interested in doing experiments, they were only concerned with theory and proof.

They apparently never considered that replicating a phenomenon would be sufficient to confirm a hypothesis.

This is probably because they believe that daily affairs are step-by-step and there is no regularity.

Accuracy is something God is responsible for.

Probability always has two meanings, one represents the future and the other describes the past; one is about our opinions and the other is about the facts we know.

The Book of Chance, written by Cardano during the Renaissance, is the first known book on the measurement of risk.

Three Frenchmen, Pascal Fermat and Mason Chevalier.

Pascal and Fermat created the first theory of probability.

This theory uses actual numbers to measure probabilities, which is completely different from the previous decisions based on credibility.

Fermat and Pascal's solution of allocating chips has long been used to pay for social benefits and is the cornerstone of modern insurance and other forms of risk management.

Decisions should be related to how much we desire a particular outcome and to how much we believe in the probability of that outcome.

The power of our desire for something, that is, utility.

Utility is about to become central to all theories of decision-making and risk-taking.

Pascal and Fermat held the key to using classification methods to calculate the probabilities of future events.

Chapter 5: The use of sampling methods and probability calculations in the second half of the 17th century. These two methods are the basic materials for all risk management methods, covering risk management methods from insurance and environmental risk measurement to the design of extremely complex derivative products.

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Grant and Petty were the co-founders of statistics.

Sampling, averages, and what is considered routine form the framework of statistical analysis and enable information to serve in decision-making and influence our confidence in the likelihood of future events.

Halley made accurate estimates of the total population based on death and birth figures.

The next step is to design a table based on the age distribution.

This table can be used to calculate insurance prices for different age groups.

Also in the second half of the 17th century, the modern insurance industry sprouted.

Transform the identification of mathematical probabilities relevant to decisions into estimates of the probabilities of uncertain events.

Instead of just collecting raw data, decide what can be done with it.

The way knowledge has advanced at this point is more surprising than meets the eye.