Aumann's Agreement Theorem

Aumann's agreement theorem, roughly speaking, says that two agents acting rationally (in a certain precise sense) and with common knowledge of each other's beliefs cannot agree to disagree. More specifically, if two people are genuine Bayesians, share common priors, and have common knowledge of each other's current probability assignments, then they must have equal probability assignments.
- Less Wrong Wiki


Whenever someone says "well we'll just have to agree to disagree", the parties involved in the disagreement have failed at presenting their cases. It means that all parties, or maybe just one, are ignorant of some piece of information the other is implicitly using.

This happens a lot, unfortunately. The more your argument depends on, the harder it becomes to actually argue. From a distance such arguments look like a series of each person moving the goal posts of the argument, when in reality they're just trying to get across more prior information the other(s) don't have access to.

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40 + 40 x 0 + 1= ?

Short answer: 41

Long answer part 1: is this to be solved by parsing or by algebra? If it's to be solved by parsing, we need a set of parsing rules, in other words a convention. Grade school teaches things like BEDMAS/PEMDAS, but that's a fairly complex rule operating on groups. Instead let's go with one particular way of computer program parsing that is easy for a beginner programmer to write. The general algorithm goes like this:

Read the first number until the operator is found. Create a tree leaf containing the operator, with a left branch containing the first number read, and a right branch being empty. Read the next symbol: if it's a parenthesis, start over but with the right branch becoming a new "leaf" to hold the next operator. If it's another number, put it into the right branch. Now simplify by applying the leaf operator to both its branches, and storing the result inside the leaf and clipping the branches. Read the next symbol, if it's an operator create a leaf with a left branch containing the resulting value previously computed and a right branch containing nothing... repeat.

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Furcadia is Dead

Furcadia is dead. And it's been dead for a long time, at least 4 years. Look at their statistics on the front page. This game has been around since the start of 1997. I spent at least 3 years in it. It helped improve my writing and imagination, it helped me meet my best friend and others I still talk to frequently, it was a nice, creative form of entertainment that ascended beyond mere point-and-click first-person-shooters.

And yet:
135162 characters connected this month
Max players ever: 4640

I'm going to make a lot of assumptions and guesses, based on things I've heard, read, and experienced. I wouldn't put 95% certainty on any of them but I'd be surprised if I was really far off the mark. This is why I classified this post as a rant and blog fodder.

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Notes from Probability Theory Chapter 1

Probability Theory: The Logic of Science, by the great E.T. Jaynes, has been in my reading queue for quite some time now. Unfortunately for me it's a dense book after the first few chapters, so I've kind of plateaued around chapter 3 while reading from a bunch of other sources.

I've found that my brain is like boiling soup, in a sense, with different things coming up to my attention almost randomly but the important ones usually coming up just-in-time. So now a Jaynes bubble has reappeared and I'm going to review what I've read! If you're interested I highly recommend the actual book, since I'm here going to be sometimes more verbose, sometimes less, sometimes tangential, and always less organized than Jaynes; leave your email in the comment form and I'll send you a PDF copy if you want.

Chapter one begins with this thought-provoking quote:
The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man’s mind.
James Clerk Maxwell (1850)

1.1 - Deductive and Plausible (Inductive) Reasoning (Inference)

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Forms of atheism and death tolls

A common debate amongst atheists and theists: who is responsible for more deaths? Related: was Hitler an atheist or a Christian? It doesn't matter since Stalin killed more and atheists suck! A common response to that last bit: Stalin also believed the Earth rotated around the Sun; Sun-centric people are evil!

There are two major mistakes in that short characterization. (Click while viewing the full post for the singular points.) The first is a relevance error, the second is a category error. First: does it matter who is responsible for more deaths? 1.8 people still die every single second. (http://www.census.gov/population/international/data/idb/worldvitalevents.php) The better question, to me, seems: are atheists or theists more likely to reduce this atrocious death rate? The fact is, about every 2.75 years or so, we lose an equivalent to all those lost directly due to the major conflicts of the 20th century. (http://necrometrics.com/20c5m.htm) Most of those deaths in the 2.75 years are due to disease, and the "old age"-specific disease is largely the family of cardiovascular ones. This indicates that whoever can cure or stop these diseases (and old age) can do a lot for reducing the death rate.

That question's answer isn't so clear-cut, because the simpler form is more of the typical science vs. religion issue and I think most people can agree how that's gone (in science's favor if you're wondering). The confounding variable there is that doing science that is beneficial to humanity doesn't require one be an atheist. One may work incredibly hard on some HIV drug, motivated by religious concerns while using techniques that, if applied to one's own belief system, may destroy it.

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Playing with Morton Numbers

Dimensionality is a lie... okay, it's more of an interpretation.

If you have a set of integers such that you can construct coordinate pairs (x,y) (such as the locations of the pixels on your screen), this set of pairs is said to have two dimensions. But there's no reason it can't have three: the third dimension is just always 0! (x, y, 0). And so on for any upper dimension.

What about scaling it down to 1 dimension though? Is that even possible? Turns out, yes, and it's pretty easy. Just convert each x and y to base 2, and interleave the bits such that all of x's bits are in even positions and y's bits are in odd positions. We call the resulting binary number a Morton Number.

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I wish Python had macros, but it's okay

I love Python, I just wish it had macros so I didn't always have to use eval/exec and friends. I'm not even asking for Lisp macros! C macros would be enough. (Though I guess it's not too hard to wire Python up to use the C preprocessor or something similar.) Yet as I'll show, Python's nice enough that for most cases it can get by just fine. Look at this:

#define Q(x) ((#x)[0])

#define CH(N) if (ch == Q(N)) GPIO_WriteBit(GPIO7, GPIO_Pin_##N , GPIO_ReadBit(GPIO7, GPIO_Pin_##N ) == Bit_RESET ? Bit_SET : Bit_RESET)

      CH(0);CH(1);CH(2);CH(3);CH(4);CH(5);CH(6);CH(7);

expands to (pretty printed):

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