Y2K

I recently bought a magazine put out by Popular Science entitled, Mistakes and Hoaxes: 100 Things Science got Wrong. One of the hundred was concerning the Y2K event. It was predicted that on January 1, 2000 computers would go nuts. Apparently computer programmers hadn't accounted for the fact that computers might take the date of 1/1/00 to be January 1, 1900. At least that was the assumption. The disaster that was predicted didn't take place. I don't know if we should label that a mistake or not. I don't recall if anyone said it would happen or that it just could happen. And maybe the work that was done in the months leading up to that date did, in fact, stave off the disaster.

Anyway, according to the same article, we dodged a bullet in 2000, but there is still another computer issue pending. To quote the article, "Many computers still operate on a 32-bit system, referring to the way a computer processor handles information. These systems use a binary code to track time as a running tally of elapsed seconds, beginning on January 1, 1970. at 12:00:00. But a 32-bit system can only handle a value up to 2,147,483,647, which is exactly how many seconds will have elapsed between January 1, 1970 and January 19, 2038. Luckily, programmers have already started updating computers to a larger 64-bit system, hopefully staving off a massive computer shutdown for 292 billion years."

This could lead to a number of great little questions for students to tackle. Such as:

1. Where did they get the number 2,147,483,647 from?
2. Are there really that many seconds between the 1970 and 2038 dates?
3. Would a 64-bit system really translate to 292 billion years?

OK, get to work.

I myself am going to take a dramatic pause here and reexamine this next week to find some answers.

Math Videos

Many math teachers lament the dearth of good math videos. How many Friday afternoons have you thought how great it would be to be a history teacher and just pop in one of thousands of video they have? From some one who has shown "Donald Duck in Mathemagicland" maybe a millions times, the value of a good math video cannot be overstated. I was somewhat surprised to see how many good math related things there are on the PBS website. I literally stumbled on to (via http://www.stumbleupon.com/) a video entitled "The Great Math Mystery". It can be found at http://www.pbs.org/wgbh/nova/physics/great-math-mystery.html. I think it's good. It perhaps tries to do a little too much, but it is a quality video. It shows many good applications in mathematics. It doesn't get into the nitty-gritty of the math, making it showable to pretty much any level of student.  And at 53 minutes, you could probably milk it for two days worth.

Along with other videos, there are also a number of well-written articles. For example one called "Describing Nature with Math" is at http://www.pbs.org/wgbh/nova/physics/describing-nature-math.html. There are quite a few more you can find in their "physics & math" section.

Home Field Advantage

While a lot of people would say that the law of averages would say that flipping a coin means there will be five heads and five tails. Anyone who has flipped coins know this isn't necessarily true. However, things do even out in the long run. In ten flips of the coin, we would not be surprised to get seven heads and three tails. However, we would be quite surpised to flip a thousand times and get seven hundred heads and three hundred tails.

Sometimes the probablilities will sometimes change because circumstances change. We expect coins to fall 50-50 regardless what year we do the flipping. The average life span though has changed through the years.

How about home field advantage for a major league baseball team. Things have certainly changed there. A hundred years ago there were no night games, all the players were white, and spitballs were legal. Fenway Park and Wrigley Field were brand new stadiums. It wouldn't be surprising if home field advantage, if there really is such a thing, didn't change some through the years. Check out the home field winning percentage by decade. (From www.baseballprospectus.com/)

1900-1909     53.3%
1910-1919     54.0%
1920-1929     54.3%
1930-1939     55.3%
1940-1949     54.4%
1950-1959     53.9%
1960-1969     54.0%
1970-1979     53.8%
1980-1989     54.1%
1990-1999     53.5%
2000-2009     54.2%

Maybe even more striking (pun!) is to look at figures rounded to the nearest percentage.

1900-1909     53%
1910-1919     54%
1920-1929     54%
1930-1939     55%
1940-1949     54%
1950-1959     54%
1960-1969     54%
1970-1979     54%
1980-1989     54%
1990-1999     54%
2000-2009     54%

A good intro to this might be to have students share if they think if there is such a thing as home field advantage, what it might be, and would it have changed in the past century.

Coke Rewards

I've collected the codes attached to Coca Cola products for awhile now. I'm about ready to give that up for several reasons. For one, I probably don't need to give up hours recording those codes to finally have enough to get items such as a free t-shirt advertising their company. Anyway, those codes seem longer than they need to be. Here is one I recently used - 5KBMNOMN6FWPFW. There doesn't seem to be a reason for it. I figure the possible combinations are astronomical. There doesn't seem to be anything in particular that would limit the possibilities. For example, I thought maybe the first entry might always be a digit. No, sometimes a digit and sometimes a letter. They do state that the letter O (oh) and the number 0 (zero) are registered the same. This is also true entering the letter I and the number 1.

I had given this some, but not a lot of thought previously. But I read on their website's FAQ section the following:

Why did My Coke Rewards change from 12 digit codes to 14 digit codes? 

Due to the popularity of our program, we’ve made the transition from 12 digit codes to 14 digit codes, to ensure we have a steady supply of codes for you, our loyal members. Please note that 12 digit codes are ineligible effective 8/1/2014.

Really? Twelve are not enough? How many is that anyway? Without knowing of any other limiting factors I assume there are 34 possibilities for the first part of the code. (The 26 letters of the alphabet, the 10 numeric digits, and throwing out the two repeats.) So how many for the 12 digit codes?

                      34x34x34x34x34x34x34x34x34x34x34x34 = 2.386x10^18

I understand there are about 8 billion people on the Earth currently. Dividing those two numbers we see there are enough codes that each person on Earth could have 2,983,000,000 of them. Seems like enough. But apparently there was a need to go to a fourteen digit code. (Since Coke uses the term "digit" to designate both numbers and letters, I will too.)

Students can brush up on their scientific notation a little more by finding the amount of 14 digit codes.
   
                           2.386x10^18 x 34 x 34  = 2.758x10^21

I looked on-line and found that scientists have a rough estimate of grains of sand of all the beaches of the world. There very roughly, 7.5x10^18 grains of sand in the world. Hopefully 14 digits are going to be enough for the Coke folks.