### TCP Shorts: Existence Proofs

An existence proof is simply a proof that shows a particular kind of object exists, or can exist. Why is that interesting? Because if you're in the early days of gathering data about something and you never observe the thing actually happening, it's very hard to tell if it's a ... Read more »

### Orders of Magnitude

Imagine you're building yourself a new house, from scratch, and you're trying to guess how many bricks you'll need. You can't be sure in advance what the exact number will be, but you can try to calculate within the right ballpark: will it be thousands? Tens of thousands? Hundreds of ... Read more »

### Irrational Numbers

Disclaimer: Some of the terms defined below are defined differently elsewhere. The differences are mostly semantical and it’s easier to only focus on the most useful definition for each, so that is what we will do. When we learn numbers, we first learn the counting or natural numbers, that ... Read more »

### Prime Numbers

Walls have bricks, elements have atoms, organisms have cells, and a bowl of Lucky Charms has little fake marshmallows. Walls, elements, organisms, and Lucky Charms all break down into smallest indivisible units. Although a single brick or Lucky Charm is not particularly fortifying or filling, they are the irreducible pieces. ... Read more »

### Combinatorics: Permutations

Even though counting is the first mathematical concept almost every kid learns, somehow a significant portion of cutting edge math research relates to questions that basically boil down to counting. Mathematicians call this field combinatorics, which is essentially a term for all the problems that start with the words "how ... Read more »

### Convergence

Imagine you’re running a 10K. Now imagine you’re running a 10K and you had a three-egg omelette, raisin toast, grits, and a side of hash browns for breakfast. You make it through the first 5 kilometers in 30 minutes and then your stomach starts to fight back. You ... Read more »

### Metric Spaces

Even in everyday life, the question “What’s the distance between Point A and Point B?” is ambiguous. The standard definition of distance is the length of a straight line segment with one end at A and the other at B. But, if you ask me how far it is ... Read more »

### Game Theory: Strategy and Backward Induction

Let’s play a game. I’ll let you go first which I promise will let you win… if you play just right. The game is called 50 and the goal is to say the number 50 first. Before you shout it out like a smart ass, I should clarify ... Read more »

### Understanding Binary

Imagine you have a bunch of pet blobs. You keep your pet blobs in a little row on your desk. They look like this: Now, obviously all of your blobs are special in their own sweet way, but it isn’t hard to notice that one of them (the pink ... Read more »

### Categories

Get monthly email updates with the best from The Concepts Project. No spam, ever.

Get in touch, we'd love to hear from you: theconceptsproject@gmail.com

### Greatest Hits

Thinking At The Margin: what to do when you drop your piggy bank in the middle of the forest.

Strategy and Backward Induction: how to win a week of lunches from your unsuspecting colleagues.

What is Multiple Imputation?: when statisticians turn into detectives.

On Shuttle Drivers, Chocolate and NP Completeness: a deliciously difficult problem in computer science.

Rest and Digest vs Fight or Flight: how your body (and medications) help with fighting tigers.

### Sites we like

William Shaw, writing about Politics, Theatre, Sci-fi… Mainly Sci-fi.

Better Explained, for maths explanations that click.

Science Non Fiction, a graduate student perspective on science in the news and in our lives.

Clearer Thinking, learn to think more clearly and make better decisions.

EconScribe.org, working to improve the quality of research communications.

Jess Whittlestone, a blog about decision making and behavioural science.