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The Drunkard's Walk: How Randomness Rules Our Lives is a 2008 popular science book by American physicist and author Leonard Mlodinow, which became a New York Times bestseller and a New York Times notable book.
- Leonard Mlodinow
- United States
- 2008
- English
- Starter Calculations
- Deriving A Formula
- Solving For P1, The Probability of Eventual Doom
- What Does This Mean to Us?
- The Most Surprising Result
Let’s get a feel for how these probabilities play out by crunching some numbers. Imagine the drunk man is standing at 1 on a number line. At zero he falls off the cliff. Each number increasing from 0 represents how many steps he is from the cliff. Let’s visualize the walk in a chart of probabilities. The man starts 1 step away from the cliff with a...
This problem is only one of many variations. The probabilities 1/3 and 2/3 might as well have been any other probabilities summing to 1. Now that we have an idea of how it works, let’s generalize the problem. Let the probability of stepping right be some value p and the probability of stepping left be 1 – p (since 1 – p + p = 1) where p is between ...
Now we have a quadratic to solve. All these p’s are a little confusing, so I’ll temporarily let P1=x to make the equation look more familiar to us. A little rearranging and we have the standard form of a quadratic: Whenp=0, P1=x=1. This makes sense. When the probability of moving right is zero, we have a 100% chance of falling off the cliff. When p...
This means that we should model this problem with a piecewise function, where values for p less than 1/2 are modeled by x=1, values larger than 1/2 are modeled by (1 – p)/p, and p=1/2 can be modeled by either equation since they both yield x=1.
In fact, if his probability of stepping away from the cliff is less than or equal to 1/2, our function defaults to the P1=x=1 solution. Meaning that even at a 1/2 chance of stepping in either direction he is guaranteed to eventually fall off the cliff! There is no escaping it. Turns out that being drunk and standing near a cliff is a mathematically...
In mathematics, a random walk, sometimes known as a drunkard's walk, is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line Z {\displaystyle \mathbb {Z} } which starts at 0, and at each ...
El libro se llama, en su versión original, "The Drunkard's Walk: How Randomness Rules Our Lives". La versión en español de la obra está dividida en 10 capítulos y 228 páginas.
drunkard’s walk. mathematics. Learn about this topic in these articles: random walk problems. A typical example is the drunkard’s walk, in which a point beginning at the origin of the Euclidean plane moves a distance of one unit for each unit of time, the direction of motion, however, being random at each step.
The Drunkard’s Walk will challenge everything you think you know about how the world works as Mlodinow argues passionately about the randomness of the world Buy this book at Amazon, Barnes and Noble, IndieBound, or iBooks.
8 de jun. de 2008 · But as Leonard Mlodinow explains in “The Drunkard’s Walk: How Randomness Rules Our Lives,” there are, in fact, four possible outcomes: heads-heads, heads-tails, tails-heads and tails-tails....
