Show don't tell

I suspect we do a better job teaching children than adults, and much of that has to do with trying harder to explain things visually, in the most intuitive, simple way possible, to children. As we grow older, we start stacking on level after level of abstraction, losing more and more students along the way.

Even language is an abstraction, and while I enjoy writing, the ratio that a picture is worth a thousand words is a cliche that describes a very real ratio. As someone I chatted with noted this week, we have an actual way of quantifying the relative value of video versus images versus words: the CPMs that advertisers are willing to pay for video ads versus display ads versus text ads. My early years at Hulu, it was unbelievable how high and rock solid our video ad rates were compared to other ad formats on the market. All the recent pivots to video are surprising only for how late they're coming for many; trying to run a business off of text and display ad revenues is life with poverty unit economics.

This is not to say video is always better. As a format, it's harder for many to master, and like many, I often roll my eyes when sent a link to a video without a transcript. It's not because I don't believe video is a more accessible, democratic, and moving medium. It's just that a lot of instructional video would be just as information rich and more quickly scanned for its key messages if transcribed into text. Many a media site will struggle with pivoting to video unless they understand the format at the same level they do text and photos.

Video at its best is much more than a camera pointed at a person speaking. Now, granted, some speakers are immensely gifted orators, and so a TED talk may have more impact when watched rather than read. However, the average MOOC video, to take one example, is dull beyond words.

Video as a medium still has enormous potential, especially for education. In the trough of disillusion for MOOCs, I expect we'll see something rise from the ashes that finally unlocks video's potential as a communications medium. We've done a solid job with that format as a narrative storytelling device, and that's partially because the revenue in Hollywood supports an immense talent development infrastructure. Education might be able to provide that level of financial incentive if global distribution through the internet allows for aggregation of larger scale audiences.

One of the core challenges of education, as with disciplines like fitness and diet, is motivation. That is another area where video shines. David Foster Wallace warned of the addictive nature of video in Infinite Jest, and the fact that the average American still watches something like four to five hours of TV a day, despite the wealth of alternatives in this age, is an astonishing testament to the enduring pull of filmed entertainment.

As with anything, the seductive nature of moving images is merely a tool, inheriting its positive or negative valence from its uses. When it comes to teaching abstract concepts, I prefer good visuals over clear text almost every time if given the choice. Our brains are just wired for visual input in a way they aren't for abstractions like language, which explains many phenomenon, like why memory champions translate numbers and alphabet characters into images, and why they remember long sequences like digits of pi by placing such images into memory palaces, essentially visual hard drives.

One could try to explain the principles of potential and kinetic energy, for example, with a series of mathematical formulas, in a long essay. Or one could watch the following video.

Here's the video of the full routine by Joann Bourgeois, performed in San Sebastian. Just gorgeous.

This is what I wish Cirque du Soleil would be every time someone drags me to one of their shows.

The game theory of the toilet seat problem

By toilet seat problem I refer to the problem of a couple living together, one man and one woman, sharing one toilet. To be more mathematically specific:

For Marsha the seat position transfer cost is 0 since all operations are performed with the seat in the down position. For John the cost is greater than 0 since seat position transfers must be performed.
 
Let p be the probability that John will perform a #1 operation vs a #2 operation. Assume that John optimizes his seat position transfer cost (see remark 3 below.) Then it is easy to determine that John’s average cost of seat position transfer per toilet opeation is
 
B = 2p(1-p)C
 
where B is the bachelor cost of toilet seat position transfers per toilet operation.
 
Now let us consider the scenario where John and Marsha cohabit and both use the same toilet. In our analysis we shall assume that John and Marsha perform toilet operations with the same frequency (see remark 4 below) and that the order in which they perform them is random. They discover to their mutual displeasure that their cohabitation adversely alters the toilet seat position transfer cost function for each of them. What is more there is an inherent conflict of interest.
 

This is one of the more rigorous game theory considerations of the toilet seat problem I've read. The solution proposed at the end seems sensible enough.

Let's not allow our current technological constraints and limited imagination confine our solution set, however. I propose a different, even more ideal solution.

We develop a toilet seat that is in communication with the Apple Watch worn by both the man and the woman. When the woman walks into the bathroom, her Apple Watch authenticates itself to the toilet seat which then automatically lowers itself. Meanwhile, when the man walks in, the toilet seat remains in whatever position it's in, per the widely accepted bachelor toilet seat strategy. One could try to further optimize for the man by learning, Nest-style, the general pattern of #1 and #2 operations and caching the last 24 to 48 hours worth of such operations, but the added complexity may only capture a slight marginal decrease in cost to him.

There is yet another solution, brought to mind by episode 4 of season 4 of Curb Your Enthusiasm, in which Larry David admits to peeing sitting down. Optimal for her, and, David claims, good for him as well.

“If I pee twenty times in a day I can get through the whole New York Times, for god's sake!”

That's two posts today that mention bathroom operations. My mind is really in the toilet.

Bayes's Theorem

This is from 2012 but is still a great overview of Bayes's Theorem which really doesn't age.

Bayes’s theorem wasn’t actually formulated by Thomas Bayes. Instead it was developed by the French mathematician and astronomer Pierre-Simon Laplace. 

Laplace believed in scientific determinism — given the location of every particle in the universe and enough computing power we could predict the universe perfectly. However it was the disconnect between the perfection of nature and our human imperfections in measuring and understanding it that led to Laplace’s involvement in a theory based on probabilism.

Laplace was frustrated at the time by astronomical observations that appeared to show anomalies in the orbits of Jupiter and Saturn — they seemed to predict that Jupiter would crash into the sun while Saturn would drift off into outer space. These prediction were, of course, quite wrong and Laplace devoted much of his life to developing much more accurate measurements of these planets’ orbits. The improvements that Laplace made relied on probabilistic inferences in lieu of exacting measurements, since instruments like the telescope were still very crude at the time. Laplace came to view probability as a waypoint between ignorance and knowledge. It seemed obvious to him that a more thorough understanding of probability was essential to scientific progress.

The Bayesian approach to probability is simple: take the odds of something happening, and adjust for new information. This, of course, is most useful in the cases where you have strong prior knowledge. If your initial probability is off the Bayesian approach is much less helpful.

Includes a link to Eliezer Yudkowsky's intuitive explanation of the theorem and this Quora response to the question “What does it mean when a girl smiles at you every time she sees you?” which are both excellent.

A Bayesian approach to life is a sensible one, but the human mind isn't optimized to apply the theory accurately except at the broadest of levels (most people's intuition is way off when it comes to the mammogram example used in both the overview and the Yudkowsky piece linked above). This can be particularly problematic when it comes to our judgments of other people; we overweight new information without considering the prior odds. This is exacerbated by the internet, where we are prone to judge others on the select few pieces of content they choose to post for public consumption.

Mathematics of why hipsters all dress the same

Here comes the crucial twist. In all of the examples so far, we assumed that everyone had instant knowledge of what everyone else was wearing. People knew exactly what the mainstream trend was. But in reality, there are always delays. It takes time for a signal to propagate across a brain; likewise it takes time for hipsters to read Complex or Pitchfork or whatever in order to figure out how to be contrarian.

So Touboul included a delay into the model. People would base their decisions not on the current state of affairs, but on the state of affairs some number of turns prior.

What Touboul noticed is that if you increase the delay factor past a certain point, something amazing happens. Out of what appears to be random noise, a pattern emerges. All of the hipsters start to synchronize, and they start to oscillate in unison.

This mathematician must be an early frontrunner for the Nobel Prize.

In all seriousness, though, the model has a certain explanatory elegance, akin to Schelling's Segregation Model.