This is a bit of a new experiment: rather than adding new content directly to pages, I write bloglike posts that (besides being archived as blogging) get transferred to the appropriate Wiki pages. Here's hoping.
2013-12-04: The Introduction to a Merit Brief in the Case of the Bayesian Clocks
For those of you who don't read Zhurnaly's blog, a brief summary of the Adventure of the Bayesian Clocks: during a car ride, two clocks -- henceforth referred to as "dashboard" and "watch", although I suspect the latter chronometer may have been a smartphone -- were observed simultaneously to show the same time in hours and minutes (neither showed seconds). The question was then asked: given this observation, what could be deduced about the difference in time between these two clocks?
In submitting this (metaphorical) brief, I shall cleave to the specified principle of Bayesian reasoning. I shall not provide a full tutorial on the principles of this approach -- such can be found in a number of places online, such as Eliezer Yudkowsky's "An Intuitive Explanation of Bayes' Theorem" -- but to summarize in broad strokes:
- The Bayesian agent is charged with dividing the world into a set of hypotheses, exactly one of which will correspond to reality, and assessing -- based on what knowledge this agent has access to -- the probability of each.
- Each hypothesis in turn is responsible for describing the possible future observations of the Bayesian agent and assigning probabilities to these observations. These are the conditional probabilities: how likely an observation is given a hypothesis.
- Upon making each actual observation, the Bayesian must take the prior probabilities -- i.e. the probabilities assigned to the hypotheses before making the observation -- and update them -- i.e. adjust them up and down based on how accurately or inaccurately they predicted what was observed -- to produce posterior probabilities -- i.e. the probabilities assigned to the hypotheses after taking the observation into account. This step is carried out using Bayes' rule:
- First, determine from the prior probabilities the prior probability of the actual observation. To do this, multiply the probability of the first hypothesis by the conditional probability it gave for the observation, then add to it the probability of the second hypothesis multiplied by its conditional probability for the observation, and continue adding these probabilities until you have summed the contributions of all hypotheses.
- Second, for each hypothesis, take the probability assigned to the observation and divide by the aforementioned prior probability of the observation. Multiply this number by the prior probability of the hypothesis. This number is the posterior probability of the hypothesis.
Thus, for this problem, I will:
- Suggest a sequence of possible prior probability distributions for:
- The actual time of day at the time of observation.
- The error from the actual time of day of the dashboard at the time of observation.
- The error from the actual time of day of the watch at the time of observation.
- Using a square bracket to indicate inclusion and parenthesis to indicate exclusion of the endpoint, these will be probability distributions within the ranges [0,1440), [-720, 720), and [-720, 720), respectively, with all numbers measuring in minutes. Each of these probability distributions will be assumed to be independent.
- As a simplification, I will assume that the observation of dashboard time and watch time were both infallible. In other words, I assume that the conditional probability of observing an integer minute time n on either clock is equal to 1 when the clock time falls in the range [n,n+1) and 0 otherwise.
- For each such prior, I shall calculate:
- The posterior probability distribution for the difference between the dashboard error and the watch error.
- The mean, median, and modes of said distribution.
From these calculations, I intend not only to resolve not only the question asked, but several others that might occur to an intelligent person.
2013-07-15: X-COM again
During the post-game discussion after D&D yesterday, we were having a conversation about games in which the events outside of battle and the events inside of battle had a close interaction -- a strange loop, to (ab)use Douglas Hofstadter's phrase -- and it reminded me of one of the greatest games ever: X-COM: UFO Defense.
I love that game. I never played it very far. And for both these reasons, I want to do a Let's-Play-style playthrough -- and use this Wiki to do it.
So I will. Watch this site -- this could be good.
2013-07-03: A kind moment
Today, after I left my psychiatric appointment (having had to confess that I had not stayed on top of taking the medication that was supposed to help me stay on top of things), I was just across the street from the bus stop when I saw the bus I wanted to catch rolling down the hill. The light was against me. I decided to run for it, trying to outpace the bus sufficiently to catch it at a later stop.
Two things: first, I have not been keeping up my physical fitness properly; and second, none of the lights were with me. I made it three long blocks before realizing I hadn't a chance of catching it ... and then I noticed that I would have to cross three ways to get to the corner where I hoped to intercept it anyway.
Speaking of crossing three ways, I had to hustle not to miss the light for the first crossing. I then crossed the second way after it changed, and crouched for a moment in the light rain to catch my breath and rub my eyes.
It was at that point that a driver -- seeing me on the street corner there -- rolled down her window and asked if I was all right. I can't imagine she had any idea who I was or why I was there, she had her own thing going on, but she wanted to know that I would be okay. I reassured her that I was merely out of breath from running for a bus, and threw her a thumbs-up when the light changed and I could cross.
People are nice.
2013-06-28: The Grammar Metaphor in Since feeling is first
In the e. e. cummings poem called "Since feeling is first" (Writer's Almanac link), there's what I think is a running metaphor of grammar for existence, mentioned in the first stanza ("who pays any attention/to the syntax of things") and the last two lines ("for life's not a paragraph//And death i think is no parenthesis"). I think to a large extent what e. e. cummings is doing with this poem is denying this metaphor and its implications, so I want to figure out exactly what this thing is that he is opposed to.
First, I don't believe this is supposed to be a figment of his imagination that he is rejecting -- I think this is an actual opinion that these people "who [pay] attention to the syntax of things" hold.
Second: I think the contrast between life being a paragraph and death a parenthesis (presumably a close-parenthesis) is crucial. To make an HTML metaphor, a paragraph is a block-level element and a parenthetical is an inline element -- parentheses occur within paragraphs. (Okay, so there have been some really long parentheticals, but general rule.) To say that life is a paragraph and death is a parenthesis -- as the syntax-of-things people do -- says many things, but most crucially that what ends in death is only an aside, not the main story.
If life is a paragraph and death is a parenthesis, then the end of our individual lives is something to look forward to -- a return to the main line of narrative.
If life is a paragraph and death is a parenthesis, then the events of our individual lives are unimportant -- amusing, possibly relevant as illustrative of a broader point, but not essential.
If life is a paragraph and death is a parenthesis, then our individual lives are isolated things, independent, only associated with each other by existing within the same narrative.
If life is a paragraph ... but life is not a paragraph. Death, I agree, is no parenthesis. Dying is the end, an end that we rightly despise, of something important ... and important to more than just ourselves, for we are for each other.