The Monty Hall Problem, Bayes Theorem, and a fault in Numberphile

I watch a lot of educational videos on YouTube, in particular the awesome channel Numberphile.  I recently saw their video on the Monty Hall Problem, and was kind of disappointed at what seemed to be a rather pointless calculation that didn't really show the result, and instead showed something that was already kind of obvious.

The video can be found here and explains everything, but let me explain it again for completeness.

The Monty Hall Problem is a classic apparent paradox in probability, named after gameshow host Monty Hall from Let's Make a Deal.  In the show, the contestants are shown three doors and told behind one of the doors is a brand new car.  Behind the other two doors are "worthless" prizes; anything works, but traditionally the problem says the other two doors hold goats.  The player gets to pick any of the three doors, and whatever is behind the door is what they win.  If they pick right they get a car, otherwise they get a goat.

To add tension, after the contestant picks, Monty Hall would walk to another door, a door that the player did not pick, and show them what was behind it.  And look!  It's a goat!  The car is still out there!

In the Monty Hall Problem (not necessarily the show), Monty then asks if the contestant would like to change their mind.

The question is, what is the probability of the player guessing correctly if they swap their pick?

Richard Feynman and the Message of Christmas

I often come across as a Grinch during Christmas.  It isn't that I don't like the holiday, it's that I find the actual celebration of the holiday so small compared to the actual ancient reason for celebrating.

The phenomenon of Christmas, as it exists today amongst moderns,  is largely a commercial platform to sell you movies, toys, electronics, and honey baked hams.  We sing about snow and various foodstuffs eaten and herd animals, we share some presents, spoil our children, and eat a lot of food.

To most modern people, this is what it's about.  Its about time with family and the magic of Santa and having fun singing Christmas songs.

I don't think modern people really understand Christmas.  I don't think they get it.

To explain Christmas, then, let me begin with a quote by Richard Feynman (from this video interview):

I can’t believe the special stories that have been made up about our relationship to the universe at large. They seem to be… too simple to conn- too local, too provincial! The Earth! He came to the Earth! One of the aspects of God came to the Earth mind, you. Look at what’s out there! It isn’t in proportion.

Richard Feynman gets Christmas.  In his own way, as a nonreligious Jew, Feynman understands the celebration of Christ's birth better than most people alive today.

Alternative to the d20 System

Early D&D used to be a mishmash of various different rules. Roll this die for this, that die for that, look on a table for this other thing. Thieves rolled a percentile die (two d10s with one treated as the "tens" place) and compared to a table on thieves skills; fighters rolled a d20 and looked up their result on a table organized by their level and the targets AC; later fighters rolled a d20 and compared THAC0 and AC to the result; some traps you rolled a d6 and found it on a 1, some doors you rolled a d8 and forced it open on a 1, some checks you rolled a d20 and tried to get under your ability score like STR.

It was kind of a crazy, scattered mess.

Advanced Berenst#in Bears Theory - Complex Euclidean Space

I wrote a blog post several years ago about the Berenst#in Bears that, somehow, against all odds, managed to get picked up on the internet.  It's been posted on Reddit and other outlets several times, and accounts for about 95% of all traffic to my blog.

The post is of course intended to be silly, but part of the silliness is that hidden inside this ridiculous proposition of universes merging over children book names is a very mathematically complicated thesis about the nature of space and time.

I don't think I did a very good job explaining what that thesis is, because I often see my blog being referenced as claiming either time travel, the many-worlds hypothesis, or something else about quantum mechanics are responsible for us finding ourselves in this piteous state of being in the wrong universe with the wrong cartoon bears.

In this post, my goal is to outline what exactly it is that I was "claiming," so that if the story gets picked up again (unlikely now that more major outlets have picked it up), maybe people can actually at least summarize what I'm saying correctly.

TL;DR the theory is about changing the geometry of spacetime by allowing all four dimensions to be general complex numbers.

Let me start with what the theory is not.

A Rule for Shields from Descending Armor Class, Applied to Ascending Armor Class

I've been playing 'D&D 'ever since I was a young boy and found my dad's Dungeon Master's Guide on his bookshelf (the original, by Gygax).  I was still too young to understand a lot of it (Gygax opens with a discussion of uniform vs binomial probability distributions...), but I spent hours of days flipping through the pages, looking at the pictures and reading the descriptions of a fantastic world.  It inspired me to make my own games about exploring through planned dungeons with friends and having them use ability scores to get through.

By the time I was old enough to try to really figure out the rules, version 3.0 was out, which made a lot of changes.  One of the biggest was replacing the original Descending AC and THAC0 system with the slightly more intuitive Ascending AC system.  This system always just made sense to me, whereas DAC and THAC0 always seemed weird and complicated.  I never understood how DAC worked, and never really saw a good explanation of it, and so just never used it.  It was only recently, when getting into old school tabletop RPGs, that I decided to look up an explanation of how DAC and THAC0 used to work.

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Update: I think I figured it out.  Comments should work better now.

From my phone I can comment.  From my computer, I'm only able to  comment if I use a separate page for  comments.

The Baker and the Beast

I have an idea for a movie.  It's a moving tale of passion and vocation.  I've pitched it to my wife and a few friends, and all agree, it's pretty brilliant.

Since it infringes on all kinds of Disney copyright, and since the premise is kind of ridiculous, it will never actually be made into a movie.  So I figured I'd just pitch it here.

The genesis.

So, I hate pop music.