This New York Times bestseller by American physicist and author Leonard Mlodinow proves how the understanding of chance can allow us to make more informed decisions in our daily lives. In addition, he also proves through the manipulation of statistics and probability the cognitive biases humans have leading to us making irrational decisions under the perception that they are rational. In this review and analysis, I will highlight the key ideas he raised in each chapter.
Chapter 1: Peering through the eye piece of randomness
- When we look at extraodinary accomplishments in sports- or elsewhere- we should keep in mind that extraordinary events can happen without extraodinary causes. Random events often look like nonrandom events and in interpreting human affairs we must be careful not the confuse the two.
Chapter 2: The law of truths and half truths
- If the details we are given fit our mental picture of something, then the more details in a scenario, the more real it seems and hence the more probable we consider it to be- even though any act of adding less-than-certain details to a conjecture makes the conjecture less probable. This inconsistency between the logic of probability and people’s assessments of uncertain events interested Kahneman and Tversky because it can lead to unfair or mistaken assessments in real-life situations.
Chapter 4: Tracking the pathways to success
- Mathematical Expectation (Pascal):
- Weighing the pros and cons of one’s duty to God- if you act piously and God exists, then you gain- eternal happiness- is infinite. If, on the other hand, God does not exist, your loss is small- the sacrifices of piety. To weigh these possible gains and losses, Pascal proposed, you multiply the probability of each possible outcome by its payoff and add them all up, forming a kind of average payoff.
- Hence, the mathematical expectation of your return on piety is one-half infinity (your gain if God exists) minus one-half a small number (your loss if he does not exist). The answer to this will be infinite, thus the expected return on piety is infinitely positive. Therefore every reasonable person should follow the laws of God (Pascal’s Wager- foundation of game theory)
Chapter 5: The dueling laws of large and small numbers
- Zeno’s paradox: suppose a student wishes to step to the door, which is 1m away. But in order to reach the halfway point, she must first arrive halfway to the halfway point. And so on, ad infinitum. Because the sequence goes on forever, she has to traverse an infinite number of finite distances. That, Zeno said, must take an infinite amount of time. Zeno’s conclusion: you can never get anywhere.
- However, the sum instead of approaching infinity, approaches 1 (since distance set is 1m). Zeno’s paradox concerns the amt of time it takes to make the journey, not the distance covered. If she is allowed to move at a constant speed without pausing at Zeno’s imaginary checkpoints- then the time it takes to travel each of Zeno’s intervals is proportional to the distance covered in that interval, since the total distance is finite, as it is the total time- motion is possible.
Chapter 6: False Positives and Positive Fallacies
- Bayes’s theory: the effect on the probability that an event will occur if or given that other events occur
- The fundamental difference between probability and statistics: the former concerns predictions based on fixed probabilities; the latter concerns the inference of those probabilities based on observed data.
Chapter 9: Illusions of patterns and patterns of illusion
- Whenever we have a new idea- instead of searching for ways to prove our ideas wrong, we usually attempt to prove them correct. (Confirmation bias) This presents a major impediment to our ability to break free from the misinterpretation of randomness.
- Eg. When ppl recognize that the sequence consists of increasing even numbers, they seek to confirm their guess instead of attempting to falsify their idea by testing a sequence that includes an odd number.
- As philosopher Francis Bacon put it in 1620,”the human understanding, once it has adopted an opinion, collects any instances that confirm it, and though the contrary instances may be numerous and more weightly, it either does not notice them or else rejects them, in order that this opinion will remain unshaken.” In addition, we also interpret ambiguous evidence in favour of our ideas.
Chapter 10: The Drunkard’s Walk
- Laplace’s Determinism: the idea that the state of the world at the present determines precisely the manner in which the future will unfold.
- Conditions: 1) the laws of nature must dictate a definite future, and we must know those laws. 2) We must have access to the data that completely describe the system of interest, allowing no unforeseen influences. 3) We must have sufficient intelligence or computing power to be able to decide what, given the data about the present, the laws say the future will hold.
- Small differences led to massive changes in the result (Lorenz’s Butterfly effect) When we look back in detail on the major events of our lives, it is not uncommon to be able to identify such seemingly inconsequential random events that led to big changes.
- Determinism in human affairs fails to meet the requirements for predictability alluded to by Laplace due to:
- 1) Society is not governed by definite and fundamental laws in the way physics is. People’s behaviour is not only unpredictable, but as Kahneman and Tversky repeatedly showed, also often irrational.
- 2) Even if we could uncover the laws of human affairs, as Quetelet attempted to do, it is impossible to precisely know or control the circumstances of life.
- 3) Human affairs are so complex that it is doubtful we could carry out the necessary calculations even if we understood the laws and possessed the data. “Chance is a more fundamental conception than causality.” (Nobel laureate Max Born)
- Perrow’s normal accident theory: theory of why, inevitably, things sometimes go wrong, it could also be flipped to explain why, they sometimes go right. In fact, economists like W. Brian Arthur argue that a concurrence of minor factors can even lead companies with no particular edge to come to dominate their competitors. “In the real world,” he wrote, “if several similar-sized firms entered a market together, small fortuitous events- unexpected orders, chance meetings with buyers, managerial whims- would help determine which ones received early sales and, over time, which came to dominate. Economic activity is… [determined] by individual transactions that are too small to forsee, and these small ‘random’ events could [ac]cumulate and become magnified by positive feedbacks over time.”