Tag: astronomy

Skype, facetime and a growing collection of virtual meeting tools like Blackboard Collaborate are making communication easier, cheaper and “almost like being there” with family, friends and colleagues around the World. Scheduling these conversations makes us acutely aware of the different time zones we live in. “PST”, “EDT”, “UT” are all becoming familiar parts of speech. If you think these time zones originated with the railroads of the British Empire, you’re half right. It was an Empire but not British. Try Roman.

Time zones, recall, divide the Earth in 24 strips, each 15 degrees of longitude wide, with local variations which follow political boundaries between countries. Everyone living within a particular strip sets their clocks to their strip’s specified time. The 24 strips, each differing by 1 hour, stay synchronized with the Sun: the Sun passes over the center of each strip (the prime meridian) at 12 noon every day (except when Daylight Saving Time is activated – then “solar noon” occurs at 1 pm local time.)

Time zones divide Earth into 24 one-hour wide strips. (Image: CIA, Wikimedia Commons)

The origin of the time zones is typically traced to British railroad time around 1847. It was difficult to coordinate the train schedule when each city or town along the railway followed their own, local time. A hypothetical train speeding eastward along the Equator at about 1700 km/h could keep up with the rotation of the Earth and it could pass through every station at 12 noon. Just imagine the confusion:

SirSanfordFlemmingbyBarbieJollota2007HalifaxNovaScotia — Sir Sanford Fleming by Barbie Jollota (CC, Wikimedia Commons)

“When does the train leave Paddington?”
“Noon, sir.”
“And when does it arrive here?”
“Noon, sir.”

The traditional story continues with Sandford Fleming leading the establishment of World-wide time zones in 1879. This, and a long list of accomplishments, led to his knighthood in 1897.

This traditional account of the origin of the time zones omits their true origin, nearly 2000 years earlier during the time of the Roman Empire.

Roman Ruins at Belmonte — Roman Ruins at Castelo Belmonte (Wikimedia Commons CC, image by kjfnjy on flickr)

We’re all familiar with accounts of how the Romans used signal fires to communicate. Roman soldiers manned chains or networks of towers similar to this one at Castelo Belmonte, covering and uncovering the signal fire in a code that relayed information from one tower to the next. However, as pointed out by P. Southern in Signals versus Illumination on Roman Frontiers (1990), the English translation for these towers is “watchtower” or “signal tower”, not “fire tower.” Furthermore, this method of communication was hindered by poor weather. In looking for alternative forms of communication, G.H. Donaldson, in Signaling Communications and the Roman Imperial Army (1988) reports the existence of acoustical horns on some signal towers in Germany.

Roman_soldier_clamantia — A Roman clamantia relaying a message verbally (Wikimedia Commons CC)

In fact, these mouthpieces were used by the Roman clamantia to verbally relay messages from location to location. One by one along the line, soldiers listen for the call from their neighbor and then call out that message in the direction of the next soldier. Though this requires soldiers, more to be more closely space than the watchtowers, this system of communication does not require line-of-sight, works in both the day and night, and still functions in rain and fog. A well-trained team of clamantia could relay messages at nearly the speed of sound.

Soldiers stationed on signal chains running primarily east-west were also tasked with relaying the time of day. Starting at noon on the most eastern end of the chain, one by one, westward along the line, soldiers cried out, “Meridiem!” or “Noon!”. This system of time-keeping proved to be remarkably accurate Italy, the heart of the Roman Empire.

CircumferenceThruRome — The parallel of latitude at latitude θ has radius r = R cos θ (Diagram by me, CC)

This diagram of the Earth shows the Equator and one parallel of latitude in the Northern hemisphere. The radius of the parallel of latitude at latitude θ is r = R cos θ so the circumference of the Earth at latitude t is 2 π r = 2 π R cos θ or (40 000 cos θ) km since the circumference of the Earth is 40 000 km. In the vicinity of Rome at latitude 42 degrees N, the circumference is 40 000 cos (42) = 29 700 km. A hypothetical chain of clamantia strung out along this parallel of latitude, relaying messages westward at the speed of sound, 1225 km/h, would transmit the “Meridiem!” message all the way around the Earth in

(29 700 km) /(1225 km/h) = 24.2 hours,

almost exactly tracking the daily motion of the Sun. The establishment of “prime” clamantia every 1225 km along the east-west chains creates a sequence of time zones, each one hour wide.

As the Roman Empire fell, so did this system of time-keeping, only to be revived 2000 years later when, once again, society found it necessary to keep track of time beyond the outskirts of each village, town and city. And next time, don’t fool yourself with that modern tale of railroads and Sandford Fleming.

Is going over the answers negative reinforcement?

March 4, 2012

Peter Newbury

astro 101 clickers physics teaching 5 Comments

My wife works with people with developmental delays, like autism and fetal alcohol spectrum disorder. Her niche is sexual health. Imagine the hormones of a teenaged boy with the impulse-control of a 5-year-old. She often gets called in when some Grade 6’er starts whippin’ it out – either for the reaction he gets or because he doesn’t realize that’s not what typical Grade 6ers do.

The other day, we were talking about how to change people’s behaviours and she gave me an example of positive, no wait, negative, erm, reinforcement. I’m out of my depth when it comes to psychology so let me remind me (and you) about the difference, in overly-simplified terms I can get my head around. Oh, and when I’ve mentioned I’m writing this post, everyone I’ve spoken to gives a different definition of negative reinforcement, so it’s possible the one below is different than yours…

Positive reinforcement is something that’s added, typically by the person in authority – a parent, teacher, boss – after a person does something good. Like a high-5 by the coach after a good play, for example. That action strengthens the person’s motivation to repeat the behaviour.

Negative reinforcement strengths the unwanted behaviour. Your kid is having a fit because she doesn’t want to clean her room. Suppose you say, “Okay, I understand you don’t want to do it. Why don’t you watch TV for half an hour, calm down, and then clean your room….” It reinforces the undesired behaviour.

Every source I googled made sure to point out negative reinforcement is not the same as punishment. Getting grounded because you haven’t cleaned your room is not negative reinforcement.

(Geez, this is subtle. I can imagine some amazing clicker questions about positive reinforcement, negative reinforcement and punishment. [Update March 19, 2012: A couple of days after I wrote this post, Derek Bruff wrote about a clicker workshop he gave, including some pos/neg reinforcement clicker questions created by one of the participants.] Okay, back to the conversation with my wife.)

Scene 1: Grade 6 classroom

There’s this boy, let’s call him John. John like to strip his clothes off at school. Like in the middle of class. His teacher intervenes. Frustrated with John’s continual stripping, the school decides they have no choice but to send John home when he strips, punishing him for his behaviour. But here’s the thing – John might have a developmental delay but he knows what’s what: he doesn’t like school. He strips so he can get sent home. In fact, John has started stripping on the school bus on the way to school so he doesn’t even have to go through the charade of going to class. Sending John home, which the staff feel is punishment for his behaviour, is, in fact, a reward for John. What they think is punishment is, in fact, negative reinforcement for John.

“So what are they supposed to do?” I asked her.

They shouldn’t send John home. And they shouldn’t praise him for keeping his clothes on. Instead, throughout the days when John is at school, the teachers should say, “We’re so glad you’re here with us today, John!” That’s positive reinforcement, something added to John’s school day that strengthens the good behaviour of keeping his clothes on.

What I’ve left out is what to do during the difficult transition time between he continually rips off his clothes and when he keeps them on. The teacher needs to intervene somehow. Calling my wife is a good start!

Scene 2: University physics lecture hall

The physics instructor has realized that his traditional, “all lecture, all the time” style of teaching does not promote learning like he wants. He’s decided to make the class more student-centered. He gives 10-15 minute mini-lectures and then hands out worksheets which are supposed to guide and scaffold the students through the next stage of the development of the concept. The problem is, the students don’t do the worksheets. They just sit there, staring at the empty spaces on the page or desperately scribbling down formulas like I described here, biding their time, because they know he’ll be going over the answers in a few minutes. Sure enough, after a while, he goes over the answer to Question 1. The students madly scribble down his solution or, increasingly, grab their phones and start snapping pictures.

He’s not punishing them for not doing the worksheets (“Why have you not answered the questions!? You will all Remain. In. This. Classroom. Until I see some work!”) Rather, he’s reinforcing their behaviour of not doing the worksheet. They get what they want (the answers) and he thinks he’s helping. This seems to be an example of negative reinforcement, at least according to the definition I posited earlier.

“So what is he supposed to do?”

Good question.

Let’s look at this top down: What do the students need to get out of the activity? They need feedback on their answers in a timely manner. “Timely” because feedback a month later when they fail the exam is too late. One way to give them feedback is to go over the answers so they can check. That’s not the model used by the significant portion of the astronomy education community who use the Lecture Tutorials worksheets. Instructors do not go over the answers. Instead, the worksheets have built-in feedback and most instructors follow the worksheets with a sequence of peer instruction questions. If you get those questions correct, you know you’re okay on the worksheet. If you don’t get the questions correct, your peers will straighten you out. At the very least, you’ll know which concepts you didn’t get and can talk to the prof or TAs about them. More positive reinforcement comes when you ace those identical or “identical except some parameters changed” questions on the exam.

I’d love to create a sequence of clicker questions to follow the worksheets in this physics class but that’s not the simplest alternative because it requires the instructor to be agile with worksheets AND with peer instruction. One thing at a time…

What about this? The instructor watches the students doing the worksheet questions, monitoring their progress. If everyone is getting along just fine, don’t stop them. When it looks like students are stuck, and individual attention by the instructor or TA can’t handle the widespread confusion, intervene with a class-wide discussion. Don’t begin with, “I’m so happy you answered Questions 1 and 2 by yourselves!” (“John, I’m so glad you kept your pants on today!”) Instead, work together to get past the sticking point. Get the students to contribute to the solution, using the work they’ve already done to chip away at the problem. A pat on the back or a high-5 for a good tidbit of problem solving. The students are praised and rewarded for the work they’ve done, even if it’s not complete. That’s positive reinforcement for good behaviour, right?

(Unless that’s an example of “intermittent” negative reinforcement which, according to my wife, is even stronger than continuous.)

Yes, there will be difficult transition period, when students are not solving the problems and the instructor is not going over all the answers. Sorry, tough it out.

What if the students were never allowed to get into the habit of not doing the questions? What if, from Worksheet 1 on Day 1, this collaborative solution approach was the way it’s done. Ahh, now that would be something, wouldn’t it?

Alright, I’m not exactly sure where I’m at. I know the current method of going over the answers isn’t working. And that if we make changes, there will be a difficult period of transition. I like the collaborative problem solving approach — I’ve seen it happen in a physics class of about 30, where the agile instructor knew everyone’s name and kept track (in his head) of who hadn’t contributed yet, calling on them for input.

One other thing I know: I should learn some more psychology.

Image: RaaksBeton2 by Dan Kamminga on flickr CC. In my mind, it shows people working together to reinforce what they’re building.

Time zones are much older than you think

Is going over the answers negative reinforcement?

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