This was supposed to be the post analyzing the survey results.Then I thought: if I’m writing that, I may as well show examples of some basic Bayesian analysis, like using likelihood ratios. And if I’m doing analysis, I may as well give some more background on data science and also show how the results depend on assumptions. And if the results depend on assumptions, I may as well fit a full consequential model with continuous interdependent parameters and the appropriate prior.
Bottom line: I spent the week reading a textbook on data analysis and didn’t write anything. Instead, this short post is a sequel to Conned, part of an emerging series tentatively called “what it’s like being a crazy person who nitpicks random numbers he sees”.
So, a crazy person walks into a new poke restaurant. First, he notices that this restaurant, like the last 7 poke restaurants he went to, isn’t called Pokestop. This is puzzling, because the perfect name for a poke restaurant exists, and it’s Pokestop.
Then, the crazy person notices a Number:
200,000! That’s even more than the number of trees we could save by paying our electricity bills online!
The crazy person flips the menu, and gets so caught up in the math that he somehow orders a grotesque monstrosity made of surimi (I learned that it’s just a fancy word for imitation crab sticks), mango, seaweed, and Hawaiian salt (I learned that it’s just a fancy word for salt).
As the astonished cook reaches for the salted mango, the crazy person starts doing mental math.
200,000 combinations and we have 6 categories, so the average number of items in each category must be the 6th root of 200,000, or the cube root of the square root of 200,000. The square root of every even power of 10 is easy, i.e. √10,000 = 100. We’ll break 200,000 into 10,000*20. 20 is between 16 and 25 so the square root of 20 is ~4.5. This means that √200,000 ≈ 100*4.5 = 450. OK, I need the cube root of 450. Do I remember any cubes? 103=1,000, that’s too much. 83=29=512, bingo! The sixth root of 200,000 is the cube root of 450 is just below 8, so there should be 7-8 combinations on (geometric) average in each category. (The actual answer turns out to be 7.65).
That’s how I do math quickly in my head. I remember a few basic facts (like powers of 2 up to 1,024) and a few basic rules (like ( a m ) n = a mn). I can get an approximate answer in my head to almost any calculation including roots, logarithms and exponents faster than I can pull out my phone. I taught a workshop training my MBA classmates to do this before consulting interviews. One Chinese girl was so impressed by this workshop that she dated me for a month even though she’s a straight 10 and I’m a 6.5 if I get a good haircut.
Anyway, back to poke: 200,000 options is obviously way too low. The average number is close to 7 or 8, but several of the categories allow you to pick more than one item. For example, you can create 16 combinations of toppings by choosing to include or exclude any of the four toppings available. As for add-ins, being able to pick 6 out of 13 involves the combination function, and the combination function has factorials in it so you know it means business. By the time my bowl was done, I estimated that Koshe Poke are underselling themselves by at least two orders of magnitude. It turns out they’re off by a factor of 3,500:
710 million! You can try a different combination of poke each day without repeating yourself for almost 2 million years. Sometime around 1,509,464 AD, you’ll stumble upon a combination as horrible as surimi-mango-salt-seaweed and you’ll finally understand what it’s like to be me, a crazy person living in a world of crazy numbers.