Action at a Distance

Oddly, the very first person in line won the Saturn, or beating the odds while waiting in line

Yesterday my wife, brother-in-law, and I were at the mall, watching some radio station give away a Saturn sedan. The authorities had a bucket with 70 keys in it, one of which was the key to the Saturn. There were about 70 people lined up to try their hand at picking a key and starting the car. Whoever picked the working key would win the car.

Strangely, the very first person in line--an older lady with black hair--picked the working key. The odds of this happening are quite low--about 1 in 70 I'd say, but it got my brother-in-law and I thinking about the set-up of the key drawing and the probability of winning. We wondered where in the line of 70 one should stand to maximize their odds of drawing the correct key. Since each key that didn't work would be removed from the bucket for the next contestant's pick, your odds of drawing the winning key go up as the total pool of keys decreases in number. The first person has a 1/70 chance, but that increases to 1/69 for the next person, and so on down the line to the last person who has a 100% chance of picking the right key. Unless someone else picks the winning key before them, and that's where the rub lies. Although your selection pool decreases the farther back in line you are, thereby working to increase your odds of picking the winning key, it is also the case that the odds of someone else picking it first go up the farther back in line you are.

Our questions are:

(1) Are these two factors inversely related, thereby making no difference regardless of where one stands in line, or are they not, thereby creating a position of maximal chance for success for some position in line?

(2) If the two factors previously mentioned are not inversely related, then how does one go about figuring out which position in a drawing line of the type described has the best odds of winning, for any line of length n?

I'll keep trying to sort this out, but if anyone out there either knows how to solve this or has some good ideas, I'd appreciate hearing them.

The Authorities refuse to believe in the supernatural

Last week I posted a CNN article noting that UFOs had been sighted by Mexican Airforce pilots. However, it didn't take the unbelievers long to explain away the sighting.

UFOs are, I think, an interesting subject. Probably, most of what is written is sensational and highly fictional, but it seems that people really do occassionally witness odd phenomena that doesn't appear to be explicable by recourse to ordinary channels of interpretation. I know two people, both of whom I believe to be credible, that have seen what they describe as UFOs.

The explanations I have heard for UFOs are as follows:

1. Alien aircraft
2. Experimental government aircraft
3. Rare weather phenomena
4. Demonic aircraft

I don't give any credence to 1 or 2, because I don't believe in aliens (they simply have no place in my conceptual framework), and because I don't believe the government is sufficiently competent to develop any sort of aircraft capable of the standard UFO flight abilities (i.e., rapid reversals of direction, dissappearance/reappearance, etc.) while keeping said development fully confidential.

Much more likely is 3. As in the above mentioned case, this explanation seems to make sense. My father has a book describing the many possible types of weather phenomena, and there are numerous events that I have never seen, such that should I see them, I would find them highly unusual.

4 is kind of weird. I heard a fairly disreputible but interesting speaker (Kent Hovind) say that UFOs could be means of Satanic/demonic transportation. His rationale went something like this: (a) demons exist because the Bible says so, (b) unlike God, Satan and his angels cannot be everywhere at the same time, (c) because they're not omnipresent, the demonic entities have to travel from one location to another, (d) they could use some sort of air/space craft to travel around, (e) these aircraft could be the basis of many UFO sightings.

Strange. Strange, but interesting.

UFO sighting backed by Mexican airforce

I knew it!

Two Years Later, or Making Sense of Donnie Darko: The Redundant Engine Paradox explained

I originally saw Donnie Darko off Matt Allison's recommendation, and since then have introduced numerous people to the joys therein. However, neither I nor any of those I've seen Donnie Darko with have been able to explain the movie in a way that MAKES SENSE! I sat through several post-viewing bull sessions last year, but no one seemed to be able to come up with a logical explanation fo the plot. I wanted to post the following to perhaps encourage others who know or believe they know how to adequately explain the plot to do so.

Recently, a friend of mine sent me the supposed contents of the fateful "The Philosophy of Time Travel" book that came into Donnie's possession (I think these may have also been in the extras on the DVD version of DD, but here's the source website). I wanted to respond to the contents here. The Philosophy of Time Travel (POTT) is hugely succesful in both explaining the movie, and supporting my own interpretation of the movie in a self-satisfying way.

Prior to reading the POTT copy my friend sent me, I would have said the biggest loose ends in the movie (those ends that prevented the plot from making logical sense), were these:

1. We sort of realize that Donnie has to fix the loose ends in the tangent universe in which he's trapped, so we guess that he realizes that the jet engine that nearly killed him when the whole thing started comes from the plane on which his mom and sister are riding in. The loose end for us is: How does Donnie cause the plane to fly near enough to the black hole to for the engine to break off and go back in time? The book provides an explanation for this is noting that the Living Receiver often has super powers. Remember Donnie sticking the axe into the bronze statue's head? Remember what he says when Gretchen tells him that his name sounds like a super hero or something? POTT clears this up.

2. What POTT doesn't clear up is WHY THE FRICK THE JET ENGINE COMES THROUGH THE ROOF AGAIN AT THE END OF THE MOVIE?!!!?! It's like the director wanted to present this difficult yet coherent plotline about time travel, then, after making everything work out just right, for absolutely no reason, tosses in a totally random and logically destructive plot device that kills the protagonist! POTT is, as far as I can tell, no help at all on this point.

My theory is that Donnie Darko can make coherent sense--but only apart from the redundant jet engine. The redundant jet engine is the paradox-maker. I propose that an account of the movie that can incorporate and explain the redundant engine will make the whole film make sense. In fact, the Redundant Engine Paradox (henceforth REP) is the key to whole film. If you can explain the REP, then you can explain everything. I believe have identified the necessary conditions for the coherence of Donnie Darko, without supplying the answer myself.

Just kidding--here is my initial attempt at solving REP: