The Truth is Not Enough

“If I added a zero to this number, would the sentence containing it mean something different to me? If the answer is ‘no’” maybe the number has no business being in the sentence in the first place.”
- Randall Monroe

So, there are a ton of ways that statistics can be misused, but despite all the newfound attention paid to “fake news”, I want to focus on a way I think that true statistics are misused today: when they’re claimed to be evidence, but are


Bayes’ Theorem: The Root of All Reasoning

Bayes theorem in particular (and probability theory in general) offers the optimal way to reason under uncertainty. It is the “root of all reasoning” in the sense that an ideal reasoner would always change their beliefs according to these principles.

There are already lots of tutorials on Bayes Theorem on the internet. Some are formal encyclopedic articles, while others are youtube videos; some are quite brief introductions, while others cont


Campus Culture: Why Can’t We All Get Along?

[Content Warning: social justice]

I’ve been reflecting about political correctness, content warnings, safe spaces, and free academic discourse recently. These are topics that tend to be difficult to analyze statistically, making them particularly difficult for me to have what I consider an informed opinion. However, I feel like I do have something to contribute. I should note that what I say is simply my impression; individuals experience may va


Summary of Exercise Research

  1. Cardio
  2. Anaerobic Exercise
  3. Stretching
  4. Sitting
  5. Works Cited



Exercise aids in longevity for the first several hundred calories each week. After this, it’s difficult to determine whether exercise is better than a calorie-equivalent dieting. So, assuming you want to minimize exercise without sacrificing longevity, it probably makes sense to do aerobic exercise for somewhere around 75 minutes a week – just as the federal government recommends.


The Rat Race Explained: Income as an Externality

[Content Warnings: suicide]


A study by the Federal Reserve found that, after controlling for various factors (including family income), county income was positively correlated with suicide rates [39]. Recall that income actually correlate with lower suicide risk, so it’s peculiar that the average income of the county you live in actually positively correlates with suicide risk. If we interpret this as causation, this implies a 10% gain in county income causes a 3.2% increase risk in suicide for a family whose income doesn’t rise.


Nudging People Towards Health

Note: I’m trying a new citation format of my own design. By default, I will continue to cite my sources via regular links, but now when I’m citing an academic article, I’ll cite it as a number in square brackets. The number will refer to the number of citations that article has on Google Scholar. This should hopefully give you at least some evidence that I’m not cherry-picking my sources.

Operational Definitions


Gun Control: An Extensive Analysis

[Content Warnings: suicide, homicide, gun violence]

Gun Violence

First, some background.

Guns were used in about 69% homicides in 2013. However, this is not particularly strong evidence that we should have stricter gun control regulations. To determine the extent to which we should regulate guns, we have to look at the empirical effects of gun control.


Demographic Utility Comparison and Suicide

[Content Warning: suicide, rape, LGBT, economic inequality]


First of all, if you are contemplating suicide, please contact the national suicide prevention lifeline at 1-800-273-8255. Most people who survive attempting suicide are glad they survived.

Some people might want to take some of the conclusions I reach later to suggest that, perhaps, one group is somehow “worth less” than another group. However, this conclusion is really not accurate.


Meta-Analysis of the Impact of Fiscal Policies on Long-Run Growth

March 2003
261 citations

Peter Nijkamp
Jacques Poot

original article

This is a boring summary of a study. The "Detailed Summary" section aims at summarizing precisely what the study's authors said with no additions on my part. The main benefit is that this post is an order of magnitude more concise than the original.

High-Level Summary


Political Beliefs PCA


Nearly a year ago, I stumbled across a dataset of thousands of people’s answers to 63 political questions. I was pretty sure it was from Political Compass, but this seems contradicted by two facts: 1. I can’t find the dataset again 2. Political Compass states, It is important to us — and most of our respondents — that the test remains anonymous, and purely for personal information. If we were to log anyone's results, those results would have to be given voluntarily. This would mean that our sample would be self-selected, and therefore not statistically valid. which certainly seems to imply that they don’t collect (let alone disseminate) such data…


Should You Vote?


Imagine there were $n$ people who each had a 50-50 chance of voting “yes” and “no”. For sufficiently large numbers of people (e.g. above 30), the probability of a specific person “swinging the election” is given (approximately) by

$$\sqrt{\frac{2}{\pi n}}$$

For instance, for 100 people the probability is roughly 1 in 13. For 1,000,000 people, the probability is about 1 in 1253.


Stats and Chess

I’m not great at chess – by which I mean that I’m almost certainly below the average ranked player (I’m not even ranked so I’m not sure on the truth of this point). However, I think this analysis I did is really interesting, so here it is.

Gathering Data

A quick note before I begin. In chess game theory, we distinguish between a move and a ply. A move is when both players complete an action. A ply is when a single player completes an action. Thus, in chess, there are always two plies per move.


Conservative Moral Extensions

Conservative Extensions

Before I get to morality, I need to lay some groundwork.

Let’s start with what “theory” means in formal logic. A theory is just a set of axioms (assumptions) we use as a starting point for reasoning. Anything we prove from these axioms is called a theorem.

If I have some theory $T_1$, then I can extend it by adding some axioms to create a new theory: $T_2$.


Marxism and The Great Divergence

The Great Divergence refers to the ever growing levels of income inequality in the United States. In this post, we’re going to look at the extent of this divergence and possible capitalist-based causes. I expect this to be the first in a (non-consecutive) series of posts


First, let’s see how we know there is a divergence.

One of the most popular measures of income inequality is the Gini index. According to the Census Bureau, this has increased steadily since the late 1960s.


Economic Flows

I made the above chart using data painstakingly collected from the Bureau of Economic Analysis.

Each arrow's width is proportional to the size of the flow in 2014. Because of this, flows smaller than about $150 billion aren't shown.

One of the things this chart reveals is just how much of what companies produce gets sold to other companies so that they can produce their products. For instance, Ford couldn't produce cars without buying steel from somewhere else.



Echo Chambers

An echo chamber is when people of the same beliefs get together and tell each other that they’re right. As I’ve mentioned, the question is not whether echo chambers exist, but to what extent they exist.

Do They Exist

Anecdotally, I suspect most of you who are on Facebook have seen links that show you all your friends who “liked" Donald Trump’s facebook page. Inevitably, immediately beneath there are a string of comments where people claim that none of their friends have “liked” Trump.


Just Another Blog

The principle of this blog is curiosity.

Lot's of lip-service is payed to curiosity, but it seems to most people don't actually seek out evidence on which to base their beliefs.

Take, for instance the belief most people have, that women make 70 cents for every dollar men make. Reading just the first three paragraphs of the relevant wikipedia page demonstrates that this is false, as the ratio between the sexes' median weekly income of full-time works is 0.82, not 0.70