Mathematics Education

Quote: Nareed

Most people don't know what "orders of magnitude" even means. Why don't you say "You're wrong by a factor of one hundred million", for example? That sinks in pretty fast.

The OOM was a petty common term in graduate level mathematics class, but there is a more casual definition of order of magnitude. Casually it often means a factor of 10.

But people should know the distance to the moon, the population of the USA or Mexico, the population of the world much more accurately than by a factor of 10.

Higher level mathematics notation for order of magnitude

Quote: Pacomartin

The OOM was a petty common term in graduate level mathematics class,

My point. How many people take graduate level math?

Quote:

but there is a more casual definition of order of magnitude. Casually it often means a factor of 10.

I learned something along those lines reading science fiction.

Quote:

But people should know the distance to the moon, the population of the USA or Mexico, the population of the world much more accurately than by a factor of 10.

They should also know the difference between science and intellectual trash like "intelligent design," astrology, numerology, phrenology, dianetics, etc. It would even make for a more pleasant world if they did. But they don't.

¿Cuál es el valor de los billetes y monedas por persona que están en circulación por el Banco de México?
(a) MXN$1,700
(b) MXN$7,000
(c) MXN$20,000
(d) MXN$50,000

What is the value of the bills and coins per person that are in circulation by the USA central bank?
(a) US$400
(b) US$4000
(c) US$40000


This is a good order of magnitude question.

San Diego is too spread out and doesn't have enough people going to the airport anyway.
It would be cheaper to give out hotel coupons for FREE taxicab rides to the airport, the hotels and restaurants in the area would get the tourist money and the tourists would get free rides that are probably just as fast on a door to door basis than a short haul bullet train.

Quote: Nareed

They should also know the difference between science and intellectual trash like "intelligent design," astrology, numerology, phrenology, dianetics, etc. It would even make for a more pleasant world if they did. But they don't.

I remember talking to a hippie who was convinced 2000 would be the end of the world. I asked him what happened to commerce when the calendar rolled over from 999 to 1,000 and why would it be any different at 1999 to 2000?

Quote: Pacomartin

The OOM was a petty common term in graduate level mathematics class, but there is a more casual definition of order of magnitude. Casually it often means a factor of 10.

But people should know the distance to the moon, the population of the USA or Mexico, the population of the world much more accurately than by a factor of 10.

Higher level mathematics notation for order of magnitude

Yeah, I'm familiar with OOM too, but my undergraduate education was heavy on engineering or math. Most people don't have our background.

I had no idea how far the moon is from the earth. I just took a guess of 80,000 miles (based on the diameter of the earth). I guess I was within a factor of 10.

But really, again, giving people (especially Americans) too much credit :).

Quote: AcesAndEights

I had no idea how far the moon is from the earth. I just took a guess of 80,000 miles (based on the diameter of the earth). I guess I was within a factor of 10.

That's the one piece of data all habitual science fiction readers know. It takes about a second for light to travel from Earth to the Moon.

Quote: Fleastiff

I remember talking to a hippie who was convinced 2000 would be the end of the world. I asked him what happened to commerce when the calendar rolled over from 999 to 1,000 and why would it be any different at 1999 to 2000?

There was an end of the world movement in the year 999 as well. But the world population was roughly 1/3 billion as opposed to 6 billion in the year 2000. Many people sold their posessions and traveled to the sea to see the end of the world.

Quote: Fleastiff

It would be cheaper to give out hotel coupons for FREE taxicab rides to the airport, the hotels and restaurants in the area would get the tourist money and the tourists would get free rides that are probably just as fast on a door to door basis than a short haul bullet train.

That is true, but Interstate 8 that goes from San Diego to Phoenix must traverse some very steep mountains. At one point the two sides of the highway are run through separate canyons. The road could not handle the increased automobile traffic.

Quote: Fleastiff

San Diego is too spread out and doesn't have enough people going to the airport anyway.

Yes that is true.

But it turns out that only one city, including the densest cities in the world, has a high speed link from city to airport. Shanghai's link is 20 miles in length and only hits top speed for a few minutes. San Diego was talking about a link between 5 and 6 times as long, going from the city to the desert. As I said earlier the construction was heavily subsidized by the German government and was intended as an advertisement in hopes of building the intercity rails in China.

Japan made public the location for it's new airport serving the Tokyo region in 1966 at about 37 miles from downtown Tokyo. The first high speed rail from Tokyo to Osaka opened in 1964 and was greatly improved in 1965. Narita airport finally opened in 1978 when high speed rail was firmly established in Japan. So naturally the possibility of extending the high speed rail link to the new airport was considered but the idea was eventually rejected.

So one of the densest cities in the entire world, with by far the highest rail ridership anywhere has never built a high speed rail link to it's airport. Now don't get me wrong, almost every single person who goes to the airport goes by train (a few by bus), and almost nobody takes a taxi. There are two very good train links, The Narita Express goes 37 miles in about 55 minutes, and the Skyliner goes 32 miles and a billion dollar upgrade to the line in 2010 has reduced the time to 36 minutes. Even if you have the travel budget to take a taxi, it would be insanely expensive to not take the train first to get into the metropolitan area, and then take a taxi to your final destination.

A taxi to Narita will cost you 15,000¥(~$150). The Narita Express is 3000¥ and the Skyliner is ¥2,400. The Express is more expensive even though it is slower because it goes to a more central location, and in addition there are 9 other destinations beyond Tokyo that you can go on to without changing trains. The Skyliner is seldom more efficient for foreigners.

Quote: Pacomartin

What is equally disturbing besides the ability to do simple math, and run the mistake by all the editors, is that nobody thinks that is an incredibly small amount of value for the world's most popular currency. Just on common sense alone, you would think someone would catch the mistake.

I get contacted by journalists all the time about gambling questions. With rare exception, their skill with words comes at the expense of that with math.

2+2=5 for very large values of 2