Here’s the short version.
Let’s take ringing bells in a church as an example.
A permutation is an ordering of the bells. You’re figuring out the best order to ring your bells, one at a time.
A combination is the choice of bells. You’re choosing the bells that you’re going to ring.
If you have too many bells, you first choose them, and then order them. This is expressed, mathematically, by the familiar identity:
(n P r) = (n C r) * r! It says that the way to order
r items out of
n is to first choose
r items out of
n, and then order the
r items (
Have you ever had your boss pass their mistakes on to you?
Well, Bob the Boss does. At a critical meeting, Bob asks his team for suggestions on how to fix things. Alice shares an interesting idea, and Bob takes it to upper management. However, it ends up making things worse. Tough luck. Bob then redirects all the blowback to Alice. “Look what you made me do, Alice! Fix it, it’s on you now”.
Bob is playing a game of “Look What You Made Me Do”. He’s setting things up so the blame never lands on him. He’s vindicating himself.
If you can relate to this game, you’re not alone. …
Consider a team of engineers that’s building a feature API for Snapchat. Let’s call them Ovah’s team. They’re facing two big questions: how do they build it, and how long will it take?
If they can’t figure out how to build it, the feature is dead already. If they take too long to build it, the feature is as good as dead — Instagram would copy it before they’ve built it.
This post contains four different perspectives that look at the two problems. As you read through the perspectives, notice the tension in the examples. Both problems are vastly different, and some perspectives are better for one problem, and worse for another problem. …
Most people don’t practice taking ideas seriously. I think it’s because most people don’t know how to. I didn’t either, until I stumbled upon an implication.
For example, what would it mean to take compounding seriously?
Ugh. I can feel your aversion. You’ve already heard so much about compounding, how it works, how it’s the eight wonder of the world, etc. etc.
But, familiarity is not the same as taking it seriously.
Say you start with $100, and every year, make 10% more. This compounds, since the extra money is a function of how much you already have. The more you have, the more you get. …
Meet Mason. He’s an average American 40-year-old: 5 foot 10 inches tall and earning $47,000 per year before tax.
How often would you expect to meet someone who earns 10x as much as Mason?
And now, how often would you expect to meet someone who is 10x as tall as Mason?
Your answers to the two questions above are different, because the distribution of data is different. In some cases, 10x above average is common. While in others, it’s not common at all.
Today, we’re interested in normal distributions. They are represented by a bell curve shape, with a peak in the middle that tapers towards each edge. …
In 2018, I started working at Bloomberg. Things have changed a lot since then. I’m not the most junior member in the company anymore and I’ve mentored quite a few new engineers, which has been amazing. It helped me observe how others differ from me, absorb their best practices, and figure out things I’ve unconsciously been doing pretty well.
Yearly work reviews are a good way to condense these lessons I’ve learned. They’re valuable for pattern matching, too. Only when I zoom out do certain patterns become visible. I can then start tracking these patterns consciously. The broad theme for this year is zooming out and challenging the boundaries. It’s also about zooming in and adding nuance to the sections from last year. …
Have you ever noticed how you can be fuming with anger one second and absolutely calm the next?
A bad driver cuts you off on the highway, and you’re raging. A moment later, you notice him pull into the hospital and your anger melts away. “Yeah, maybe he has a patient in the car with him. Or, maybe someone close is dying. I guess he’s not so bad after all.”
An obscure rule from probability theory called Bayes Theorem explains this very well. This 9,000-word blog post is a complete introduction to Bayes Theorem and how to put it to practice. In short, Bayes Theorem is a framework for critical thinking. …
Rationality is the art and science of two things:
If you win when you’re happy in your relationships, then that’s where rationality shall take you.
If you win when you’re a billionaire, then that’s where rationality shall take you.
Of course, it isn’t magic. Outcomes aren’t assured. To a rationalist, the world is probabilistic: Rationality aims to increase the probability of you winning.
It’s not just about using statistics and math to solve every problem. Neither is it about becoming a robot and having no emotions “interfere” with decision making. …
I had one goal: build a spaced repetition app I myself would like to use.
I’ve tried Anki, and I don’t like it. It’s too slow: it takes several seconds to get to the screen where you can start revising cards.
When I’m standing in a queue waiting for a meal, if it takes more than a second to open the damn app, I’m not going to use it. Revising cards should be easy and frictionless.
Or, that was the idea, anyway.
Spaced Repetition is a learning technique where you revise things based on how often you forget them. The best time to revise something is right before you forget it. …