“The Improbability Principle is not a single equation, such as Einstein’s famous E = mc², but a collection of strands which intertwine, braiding together and amplifying each other, to form a rope connecting events, incidents, and outcomes. The main strands are the law of inevitability, the law of truly large numbers, the law of selection, the law of the probability lever, and the law of near enough. Any one of these strands is sufficient, by itself, to produce something apparently highly improbable – a multiple lottery winner, a financial crash, a precognitive dream. But it’s when they combine and work together that their real power takes hold.” (The Improbability Principle – p235)
Author: David J. Hand
Publisher: Scientific American
Publication Date: 2014
Origin: I saw The Improbability Principle during a trip to Starbucks/Chapters…and it looked interesting. I like math, and I don’t like misconceptions, so if this uses the former to address the latter, then great!
Summary: In The Improbability Principle, David Hand explains why supposedly unlikely events (like the time an earwig fell off a ceiling and landed directly in my ear!) and seemingly miraculous coincidences are actually inevitable and, in fact, commonplace. This reality results from five related strands or laws, that work together:
- The Law of Inevitability
- The Law of Truly Large Numbers
- The Law of Selection
- The Law of the Probability Lever
- The Law of Near Enough
Throughout the book (and at the website), Hand provides all sorts of historical examples, many of which might be familiar to you. With his laws, he thoroughly debunks the mythology surrounding these events.
My Take: While I feel like I’m being a bit unfair, I found The Improbability Principle to be a bit light. I don’t know how this would be addressed without making it so dense that it puts off readers, but I kept getting excited only to be underwhelmed. Nevertheless, the book does well to explain why seemingly remarkable things happen all the time.
For those of you who get annoyed at hyperbole and misunderstanding, The Improbability Principle gives you a good framework with which to respond to outlandish claims and headlines; for those who are constantly amazed at the divine coincidences that fill your life, you might look at things a bit differently after reading it (there’s still reason to see things as wondrous, though, as the universe truly is exactly that…it’s just that the wonder doesn’t need to be ascribed to anything divine).
Read This Book If: You want to understand why seemingly unlikely things happen all the time.
Notes and Quotes:
- p6 gives a good introduction: “The answers to all these questions hinge on what I call the Improbability Principle. This asserts that extremely improbable events are commonplace. It’s a consequence of a collection of more fundamental laws, which all tie together to lead inevitably and inexorably to the occurrence of such extraordinarily unlikely events. These laws, this principle, tell us that the universe is in fact constructed so that these coincidences are unavoidable: the extraordinarily unlikely must happen; events of vanishingly small probability will occur. The Improbability Principle resolves the apparent contradiction between the sheer unlikeliness of such events, and the fact that they nevertheless keep happening.”
- Science, baby! This called to mind Carl Sagan‘s The Demon-Haunted World, p6-7: “But explanations which have not been or cannot be tested can have no real force: they are simply anecdotes, or stories, with the same status as a child’s bedtime tale about Santa Claus or the tooth fairy. They serve the purpose of reassuring or placating those who are unwilling or unable to make the effort to dig deeper, but they don’t lead to understanding.”
- Interesting how the shift from polytheism to monotheism had an impact, p27: “From a human perspective, the possibility of indeterminate, change, and contingent events was lost with the rise of monotheism. It meant all events were predetermined. When there were many gods, people could attribute inexplicable events to one god disrupting the plans of another. But when there’s only one God, who sees and controls everything, there seems to be no scope for chance and for luck. If we believe there’s a single intelligence directing the universe, we ascribe events to chance only because we don’t know their cause. Chance is then a matter of ignorance of fundamental cause rather than a fundamental cause in and of itself.”
“When there were many gods, people could attribute inexplicable events to one god disrupting the plans of another. But when there’s only one God, who sees and controls everything, there seems to be no scope for chance and for luck.”
- Here’s a good quote from Edward Lorenz, one of the founders of chaos theory, on p47: “Chaos: when the present determines the future, but the approximate present does not approximately determine the future.”
- Neato! I’d never heard of this crazy math thing before. I don’t remotely understand it, but find the existence and links to number theory interesting nonetheless. Math is friggin’ crazy and beautiful.
- A short explanation, p114: “The law of truly large numbers says that if there are enough opportunities for an event to happen, then we should expect it to happen, even if the probability that it will happen on any particular occasion is tiny. Furthermore, as in the birthday problem, often the number of opportunities is far greater than at first meets the eye, so that the impact of the law can be unexpected and deceptive.” (incidentally, the math behind the birthday problem has all sorts of real-world applications, for instance in computer security)
And here I will take a brief interlude, to relay this snippet of The Big Bang Theory (s1e4):
Penny (popping her head round): Hi, hey. I’m running out to the market, do you guys need anything?
Sheldon: Oh, well this would be one of those circumstances that people unfamiliar with the law of large numbers would call a coincidence.
Penny: I’m sorry?
Sheldon: I need eggs.
- p147 and surrounding explain the ridiculousness around so-called unpredictable financial collapses, and got me thinking about Taleb and The Black Swan. Guess what, finance folks – if you have a 25-standard-deviation event, then your models are laughably broken.
- p149 introduces the Cauchy distribution, which I don’t recall in any detail from my probability courses, but which apparently (upon checking the textbook index) is in there, but barely (literally, two lines and a formula). From my subsequent reading, it seems pretty damned important. In a nutshell: at a glance, it looks similar to a normal/Guassian distribution, but has immensely higher probabilities away from the mean. So in practice, people look at some stats and go “That’s a bell curve” and then make all sorts of well-behaved assumptions. Then Mr. Cauchy rears his head and you get 25 sigma events. From p150, “Under one assumption (i.e., Gaussian), the event is so improbable that you’d not expect it to happen in the entire history of the universe. Under the other, almost imperceptibly different assumption (i.e., Cauchy), you might expect to see it happen every day.”
“Under one assumption (i.e., Gaussian), the event is so improbable that you’d not expect it to happen in the entire history of the universe. Under the other, almost imperceptibly different assumption (i.e., Cauchy), you might expect to see it happen every day.”
- There’s a great table on p150 that puts the previous quote into numerical terms, and shows the probabilities of 5-, 10-, 20, and 30- sigma events happening with a normal distribution and with a Cauchy distribution.
- Here’s one for the memory bank, from p164: “I’d rather be vaguely right than precisely wrong.” – John Maynard Keynes
- And another, p175: “I wouldn’t have seen it if I didn’t believe it.” – Marshall McLuhan
- p198 mentions a book that I read a few years ago, The Drunkard’s Walk by Leonard Mlodinow. This particular reference is about how things that are seemingly obvious in retrospect really were impossible to predict as they unfolded. While I’m on the subject of other books that are mentioned, this is yet another one that talks about Daniel Kahneman and Amos Tversky. Seriously, these guys are in everything.
- p235 sums things up nicely: “The Improbability Principle is not a single equation, such as Einstein’s famous E = mc², but a collection of strands which intertwine, braiding together and amplifying each other, to form a rope connecting events, incidents, and outcomes. The main strands are the law of inevitability, the law of truly large numbers, the law of selection, the law of the probability lever, and the law of near enough. Any one of these strands is sufficient, by itself, to produce something apparently highly improbable – a multiple lottery winner, a financial crash, a precognitive dream. But it’s when they combine and work together that their real power takes hold.”