How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg

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The Essence

Being wrong a lot less of the time means understanding that mathematics holds the secrets of navigating a world ruled by probabilities. Common sense tends to lie beyond the mathematical traps that day-to-day life lays. Such as falsely assuming linearity when the rate of change may not remain the same. Numbers may not always be what they seem to be, and it is our duty to apply the principles of mathematics to unveil the conventional approach to life as inherently flawed. How not to be wrong takes what math has learned about the world, and makes it palatable enough to avoid being mathematical bested by our lives (or at least understand when we are).

How Not to Be Wrong Journal Entry Notes:

This is my book summary of How Not to Be Wrong. My notes are a reflection of the journal write up above. Written informally, the notes contain a mesh and mix of quotes and my own thoughts on the book. Sometimes, to my own fault, quotes are interlaced with my own words. Though rest assured, I am not attempting to take any credit for the main ideas below. The Journal write up includes important messages and crucial passages from the book.

• Mathematics is the study of things that come out a certain way because there is no other way that they could possibly be.
• The extension of common sense by other means.
• Avoid thoughtless linear extrapolation: Not every curve is a line.
• Twice a tiny number is a tiny number: Risk ratios applied to small numbers in probability can easily mislead us.
• A mathematician is always asking: What assumptions are you making, are they justified?
• Nonlinear thinking means which way you should go depends upon where you already are.
• Diving one number by another is mere computation; figuring out what you should divide by what is mathematics.
• When you’re testing a mathematical method, try computing the same thing several different answers, something is wrong with your method.
• Math is like meditation, it puts you in direct contact with the universe, which is bigger than you, was here before you, and will be here after you.
• A basic rule of mathematical life: If the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe does not object.
• “P-Hacking”: Due to our publish or die culture, the science community runs a survivorship bias on themselves ‘To live or die by the .05’. We need statically insignificant data, the value is purely arbitrary and prompts dishonesty and elaborate verbal twists in our to be considered for publication.
• The significant test is the detective, not the judge.
• A significant test in an instrument, like a telescope.
• What is improbable is probable.

• Expected Value = Average value would be a better name.
• Almost any condition in life that involves random fluctuations in time is potentially subject to the regression effect.
• Uncorrelated doesn’t mean unrelated; not relationships are linear. Certain mathematical tools only pick up certain relationships, not all phenomena.
• The Baltimore Stockbroker = Survivorship bias
• Proving by day & Disproving by night. Put pressure on all of your beliefs. This will deepen your understanding of why you believe what you do, and how does it weigh up against the evidence.
• If gambling is exciting, you’re doing it wrong.
• Genius is a thing that happens. Not a kind of person. It is something that is hard won and the cumulative achievement of years, even centuries of progress.
• In a Bayesian framework, how much you believe something after you see the evidence depends not just on what the evidence shows, but how much you believed it to begin with (the Base Rates).
• Our priors are not flat, but spiky.
• Variance, a measure of how widely spread out the possible outcomes are, and how likely one is to encounter the extreme on either end is one of the main challenges to managing money.
• Wrongness is like original sin. We are born to it and it remains always with us, and constant vigilance is necessary if we mean to restrict its sphere of influence over our actions.
• Miss more planes! Save your Utils, by eliminating all risk you are carrying the extra cost for the small statistically risk.
• Orthogonal: As far as correlation goes, they are not related. Zero
• Law of Large Numbers: The more coins you flip the less likely you are to get more than 50%. Understand the results of an experiment tend to settle down to a fixed average once the experiment is repeated again and again.
• Ergodicity: “Suppose you want to buy a pair of shoes and you live in a house that has a shoe store. There are two different strategies: one is that you go to the store in your house every day to check out the shoes and eventually you find the best pair; another is to take your car and to spend a whole day searching for footwear all over town to find a place where they have the best shoes and you buy them immediately. The system is ergodic if the result of these two strategies is the same”
• Smaller populations are inherently more variable.

If you liked what you saw. Here are 3 titles that I recommend based on what was discussed in How Not to Be Wrong.

1. Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Nicholas Taleb
2. Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian
3. The Signal and the Noise: Why So Many Predictions Fail-but Some Don’t by Nate Silver

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