Blogtrek

Blogtrek

2004/11/20

Halloween 2004

This year's Halloween had a few unusual features. The first is that the first trick-or-treaters (3 of them) came at 17:41 (5:41 pm), beating the previous record of 17:48, and were followed only a few minutes later by another group of 3 trick-or-treaters. So they started coming early. There were fewer of them this year, 54 compared to last year's 70. I have come up with a combined graph of these trick-or-treaters, and they indicate two peaks over the past 8 years of trick-or-treaters. One of these is at 18:22 and another is at 19:27. Apparently they like to come during dinner time. One interesting characteristic of this year's trick-or-treaters: an abnormally large number of them were adolescent males, between 11 and 16 years old. I don't know why this age group wants to go around trick-or-treating, unless they are out roving around getting their kicks or something. Or maybe these kids just don't want to grow up. Numbers of trick-or-treaters have definitely gone down since 2001, the year of Planeattack. Apparently people are more afraid and security-conscious and the result is fewer trick-or-treaters. Maybe they go to organized Halloween parties instead. It doesn't matter. It's just a tradition.

2004/11/17

K-Mart and Sears

It came as a blockbuster early today. K-Mart and Sears were going to merge. No, actually, little old nearly bankrupt K-Mart was going to buy Goliath Sears. This really seemed weird. But the two companies apparently complement each other. The new corporation will have K-Mart's real estate in places away from malls and Sears' tradition of quality. They are going to call the company Sears Holdings. Holdings? That seems trite to me. Is the CEO of Sears going to pick up and hold the CEO of K-Mart?

I think they deserve a better name than that. One immediate idea is K-Sears, but that seems too ordinary. Perhaps S-Mart would be better because that would be smart. S-mart, don't you get it? Shop Smart at S-Mart! But maybe that seems too much like PetSmart. Or how about K-Sears? Or K-Mart, Roebuck and Co.? Or K-Mart, Sears, Roebuck and Co.? Or maybe KSR corporation? Uh-uh. That is getting a little hackneyed again. How about Mart-K-Sears, as in The Three Mart-K-Sears? Or maybe Mouse-K-Sears? Em-Aye-Cee, Kay-Ee-Wye… Uh-oh. I see another merger coming.

But if not the name, maybe this merger will come with interesting subnames. For example, K-Mart sells Martha Stewart products, and Sears recently purchased Land's End. So combine these two together and the result is Martha's End. Or maybe we will fix our houses with Martha Stewart Craftsman tools or wash our clothes in our Martha Kenmore washer. Or maybe call the store K'Mart in honor of Apostrophe, one of Sear's product lines. Or how about the Sears Tower? Paint that blue and get The Blue Tower, or the Blue Light Tower. That won't work. The tallest building in the US is the Great Tower of Chicago, not the Sears Tower, because Sears no longer owns it, and so Sears can't paint it blue.

Of course none of this will happen. We will go to our Sears and K-Marts as always, although we may see Craftsman Tools in K-Mart or Martha Stewart products in Sears, and we may see a host of Sears outside the malls. But remember that a titanic merger occurred today between two retail giants. Let's hope that's titanic as in colossal instead of as in blub, blub, blub.

2004/11/16

Flipping Digits

Yesterday my van's mileage was 99982 or something. I drove to work, and then when I went out to go home at night, the van's odometer stared me in the face with 100000. Yes, the van's odometer flipped from 9s to 0s, and the reading added a digit. I have seen the flip occur on a couple of other cars that I have owned.

Flipping digits happen because of our system of enumeration. Before the flip, everything was at 9s because 9 is the greatest digit, one less than ten. It is one less than the base. When that happens all that has been built up to that point gets cashed in for the raise of a digit on the left, or in this case, an additional digit. In a sense, it is a moment of achievement.

In 2003 I achieved three different Toastmasters awards, namely an Advanced Toastmasters Bronze (ATM-B), a Competent Leader (CL) award, and a Competent Toastmaster (CTM) award. This happened because I had two or three manuals each with about two or three speeches to do. I completed all of these that year, and like the 9s on the odometer, I flipped a huge collection of achievements.

Now I am at all zeroes, trying to start all over again. That is what life is all about. Reach an achievement or group of achievements, then start all over again on your next journey. When was the last time you flipped zeroes in your life?

2004/11/14

Sitting Next to your Preferred One

I recently came up with an interesting mathematical puzzle today. It is based on some of these conventions and dinner parties that I go to. The problem is this. There is a big banquet at the end of the convention. There is a special someone that you want to sit next to. Perhaps you're in love with this person. Perhaps this person has the key to your next job. Perhaps this person is simply someone you like to sit next to. We will call this person Connie (for "convention").

Most typical banquets feature some 10-20 tables seating 10 each, for a total of 100-200 banqueters. You know that Connie is going to appear at this banquet. So when do you sit down? You don't want to be the first to sit down, as then you have no control over who sits next to you. It's whoever wants to sit next to you, and that might not be Connie. You don't want to be the last person, either. Then there will only one seat left, and that is then yours, and you have no control over who is sitting there either.

The optimal solution is to sit somewhere in the middle, but where? I will measure this by the percentage of people who have seated by the time you choose your seat.

To illustrate this problem, I will assume that everyone is seated in one big circle instead, arbitrarily large. Then you want to get into one of the two seats next to Connie. Suppose you choose time x to sit down. Then the probability is x that Connie is already seated. In that case, the probability that you can sit next to her is 1-x2, as x2 is the probability that both seats are occupied (for an infinite circle - for a finite set, replacement needs to be taken into account). So this makes a term x(1-x2). In the 1-x chance that Connie is not seated, the probability is near zero that she will sit next to you (unless she is attracted to you, in which case it is certain she will sit next to you, but I am not assuming that is the case; also this assumes an infinite circle or strip of seats). Therefore the probability of getting a seat next to her is x(1-x2). The method here is to differentiate and set equal to zero, and solve for x. When you do that, you get the optimal x to be the square root of 1/3, which is about 0.577. So this mean you will wait until 57% of the people are seated, then you will go in and sit down.

This would make for an interesting problem to work out. I have assumed an infinite strip, but what happens in finite cases? The size of the tables makes a difference; if there are 10 to a table, then Connie can sit anywhere at that table and you can still get to her table. Some seats may be more valuable than others; e.g., next to her rather than across the table from her. And what if you want to sit next to a group of people, and what if the people them cluster into groups or cliques? And once someone works out all those cases, are they prepared to use it at a real banquet?

Stay tuned.