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Estimate of the Situation

This is guest post by Liam McDaid, Astronomy Coordinator and Professor of Astronomy at Sacramento City College. He is also a Senior Scientist at Skeptic Magazine. This guest post is the first to result from my effort to get more education (e.g., Astro101) and public outreach content on AstroBetter and it focuses on the application of estimation in the Astro101 classroom. I also think there are lessons to learn here that are applicable to mentoring research students. How often do we ask our students to estimate the results before doing the calculation/data reduction? Or maybe ask them to draw what they expect the plot to look like before generating it. What are the order-of-magnitude estimates that we should expect our budding Astro PhDs to be able to perform? It’s something that most of us are aware that we need to know how to do, but are we actually teaching the skill to our undergraduate and graduate students?

One of the things we hear about students (particularly in the US) is their terror of math. The fear of math is oddly selective. The same students who hate/fear math are the ones who balance their checkbook each week and know their grade in class to four significant figures. Clearly, they can do arithmetic when it’s important to them. Over the summer, I read an interesting book called How to Measure Anything, by Douglas Hubbard (it does indeed show how to measure anything). I realized that a big key to the problem of students and math lay within. For whatever reasons, most people don’t know the value of information they have an interest in. For example, if a piece of info would save your company $5 million, how much should you pay for it? How do you quantify the value of a piece of information? Clearly this is an important task for a company, yet few know how to do it.

The solution is to get people to start estimating. I don’t mean solving problems, I mean getting them to create rough estimates of something. The endgame is to make people into what Hubbard calls “calibrated estimators”. For example, if you ask your students when the Roman Emperor Domitian died, it is unlikely that they will know. But they can estimate, can’t they? They may know that the Roman Empire was on top from about 150 ce to 300 ce (roughly). The fact Domitian was an emperor means he likely lived and died in that range. In astronomy, a couple of examples could involve:

- How long is the Moon’s sidereal period? (This only works before students learn the value). It’s interesting to see what the upper limits for this one are –-longer than a year is not unheard of.

- What is the photospheric temperature of the Sun? This works as a good order-of-magnitude exercise to see if students think of it in terms of thousands or millions of degrees. Since dealing with the Sun involves both temperature scales, confusion is common. To make things a bit more concrete, you can frame it around controlled nuclear fusion. We don’t have it, so which temperatures are more likely involved?

- How far away are the stars we see in the sky? There is no single answer but one of the most luminous stars easily visible to the eye (Deneb) is only about 1500 ly away. So the range would have an upper bound of a few thousand ly, or 1 kpc if you have been habituating your students with those units.

- Fermi’s paradox. Aside from being ultra-sexy content, it lets students hammer out estimates for how long we should wait for the aliens to contact us.

This is guest post by Liam McDaid, Astronomy Coordinator and Professor of Astronomy at Sacramento City College. He is also a Senior Scientist at Skeptic Magazine. This guest post is the first to result from my effort to get more education (e.g., Astro101) and public outreach content on AstroBetter and it focuses on the application of estimation in the Astro101 classroom. I also think there are lessons to learn here that are applicable to mentoring research students. How often do we ask our students to estimate the results before doing the calculation/data reduction? Or maybe ask them to draw what they expect the plot to look like before generating it. What are the order-of-magnitude estimates that we should expect our budding Astro PhDs to be able to perform? It’s something that most of us are aware that we need to know how to do, but are we actually teaching the skill to our undergraduate and graduate students?

One of the things we hear about students (particularly in the US) is their terror of math. The fear of math is oddly selective. The same students who hate/fear math are the ones who balance their checkbook each week and know their grade in class to four significant figures. Clearly, they can do arithmetic when it’s important to them. Over the summer, I read an interesting book called How to Measure Anything, by Douglas Hubbard (it does indeed show how to measure anything). I realized that a big key to the problem of students and math lay within. For whatever reasons, most people don’t know the value of information they have an interest in. For example, if a piece of info would save your company $5 million, how much should you pay for it? How do you quantify the value of a piece of information? Clearly this is an important task for a company, yet few know how to do it.

The solution is to get people to start estimating. I don’t mean solving problems, I mean getting them to create rough estimates of something. The endgame is to make people into what Hubbard calls “calibrated estimators”. For example, if you ask your students when the Roman Emperor Domitian died, it is unlikely that they will know. But they can estimate, can’t they? They may know that the Roman Empire was on top from about 150 ce to 300 ce (roughly). The fact Domitian was an emperor means he likely lived and died in that range. In astronomy, a couple of examples could involve:

- How long is the Moon’s sidereal period? (This only works before students learn the value). It’s interesting to see what the upper limits for this one are –-longer than a year is not unheard of.

- What is the photospheric temperature of the Sun? This works as a good order-of-magnitude exercise to see if students think of it in terms of thousands or millions of degrees. Since dealing with the Sun involves both temperature scales, confusion is common. To make things a bit more concrete, you can frame it around controlled nuclear fusion. We don’t have it, so which temperatures are more likely involved?

- How far away are the stars we see in the sky? There is no single answer but one of the most luminous stars easily visible to the eye (Deneb) is only about 1500 ly away. So the range would have an upper bound of a few thousand ly, or 1 kpc if you have been habituating your students with those units.

- Fermi’s paradox. Aside from being ultra-sexy content, it lets students hammer out estimates for how long we should wait for the aliens to contact us.

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