## Fair Asymmetric Dice, getting there

Ever since my son and I worked on whether different types of 20-sided dice were fair I’ve been thinking about whether there might be some oddly shaped dice that could still be fair.  I’ve watched these three numberphile videos and I’ve looked at these dice. All of which seems to suggest that if you have identically shaped sides, you’re in business. But I’ve still been wondering about other weird shapes.

So I’ve decided to see if I can search for some. This post lays down things I’ve discovered as I’ve geared up to a huge optimization run [SPOILER: I haven’t run it yet]. Here’s the list:

1. There is an angle you can drop a stick (without rotating) so that it’ll hit twice and bounce right back up without rotating.
2. Figuring out the correct response to a rigid body bounce on a hard surface was more complicated than I’d thought it would be.
3. Using Mathematica’s ConvexHullMesh was a cool way to make random multi-sided dice.
4. Getting Mathematica to use “WhenEvent” to determine impacts and then implement point 2 above was frustratingly difficult.
5. Doing bounces like I have in the past (treating the ground as a stiff half-spring) works well and lets me do some energy loss mechanisms that I couldn’t figure out in point 4 above.
6. Soft versus hard surfaces affect the roll (defined as the side that ends up down).
7. My kids have helped me a ton:
1. They think adding in translations in addition to rotations and bounces is important. I’m not sold, but it makes for cool animations.
2. They think hard surfaces look better.
3. They think most of the energy loss happens at the bounces (my first approach was to use a lot of air resistance and have the bounces be pure – especially when doing point 4 above).
8. Determining which side is “down” was trickier than I thought – though I’m open to other suggestions.
9. Ultimately I’d like to get feedback on the assumptions I’m building in so that when I run the optimization I can trust the results.

Given that it’s late on a Sunday night, I think I’ll just show some of my results (graphics and animations below) and see what sorts of questions folks have:

Rebound velocity of stick: This shows the rebound velocity of the center of mass of a stick that has symmetric masses on it. (think —0—-0— or 0———–0 or -0———-0- etc) where the position of the masses as measured from the center is the x-axis. Note that where the velocity crosses zero is the point where the stick would only rotate after the first bounce and therefore the motion would be totally symmetric (it would ultimately bounce right back up with the opposite angle with respect to the horizontal but without any rotational energy).

This shows a dumb mistake I was making: I was assuming that the center of mass of a polygon was equal to the center of mass of the vertices. As you can see below, that’s true for triangles but not for other polygons (COM_reg means center of mass of the region whereas COM_pts is the center of mass of the vertices).

Success bouncing a 2D shape. After finally giving up on the WhenEvent approach in Mathematica, I just said that any vertex that goes below the ground needs to experience an upward constand force. The horizontal line is the original height of the center of mass.

Showing that you really do get different rolls with a triangle. Note that now I’ve added in some friction.

Histogram of 100 rolls for that triangle. You can tell than 100 rolls isn’t good enough since surely eventually side 2 should land more often.

A 4-sided shape and accompanying histogram after 1000 rolls (note that each roll takes 0.5 seconds).

Combing through the data I found one of the rare ones where it lands on side 1:

Ok, I got 3D bouncing working!

And I can do lots of sides!

Here’s a 16-sider with some nice color added.

Here’s a 6-sider comparison showing a soft (top) and hard (bottom) floor. Note the difference in the ultimate side that ends up down.

Here’s a plot of the side that’s down as a function of time for the animation above. The blue curve is the soft surface and the red curve is the hard surface.

Ok, so I know I haven’t put much detail in yet, but I wanted to at least get down some of what I’ve been working on. The next step is to check some of my assumptions with you fine readers and then to go ahead and do some long optimization runs. I was thinking of doing a genetic algorithm, but then I’d need a ton of runs (keeping in mind, of course, that each roll takes a while (0.5 seconds in 2D, 2 seconds in 3D).

So some questions for you:

1. 2D is way faster, is it worth my time to explore it?
2. I do friction in the following way (does it bother you?):
1. if it’s not in contact with the floor, there’s no energy loss
2. If it’s in contact with the floor, there’s a contribution to the force that’s proportional to the velocity for those variables related to the vertex that’s in the floor.
3. Note that means I’m not doing sliding friction but rather viscous friction.
3. By adding in translation, I have 2 more variables to keep track of (I’m already doing z(t) of the center of mass and the 3 Euler rotation angles). Worth it?
4. Doing a 1-d minimization would be much faster than something like a genetic algorithm. What would that variable be for, say, a 6 sided die?
5. What do you mean by a fair die? How much variation after, say, 1000 rolls is small enough for you? I’ve asked my kids what it would take for them to be suspicious of any dice they own (big D&D players) and they’ve got some interesting opinions.

So, can you help? Here are some starters for you:

• I’m in this class and . . . wait . . . nevermind
• Seriously, you haven’t posted since February and this is all you can come up with??!!
• I think this is cool. I think you should . . .
• I think this is dumb, I think you should . . .
• Once again that promise to switch to python wasn’t worth the breath it took to say it, I see.
• Here’s my address where you can send your new 3D printed dice to me.
• Even 1000 roles isn’t enough. This will never be done to my satisfaction.
• What about dice where a few sides almost never come up but the rest have near equal probability?
• Without even looking at your code I know what your WhenEvent problem is. Here’s how to fix it . . .
• I would have thought it would be obvious that a rigid body should bounce off an infinitely massive floor such that the local velocity of the part that hits the ground reverses its z-component and that there’s only one solution for the speed of the center of mass and the rate of change of the Euler angles that both conserves kinetic energy and correctly accounts for the expected change in angular momentum!
• I don’t understand why you say it’s hard to figure out which side is down. Just look at it!
Posted in fun, mathematica, physics | 5 Comments

## Critical Disagreement

I’m just wrapping up my time spent at a really great conference that’s all about the First-Year Experience for students in college. I’ve got lots of thoughts running through my head, including lots of cool ideas for a large part of my job: director of my university’s First Year Seminar program. This post is about just one of those.

I was in a pre-conference workshop that was about critical thinking. This is a hot topic in higher ed, especially ever since “Academically Adrift” was published, indicating research that many college student’s critical thinking skills actually got worse during their college years. Someone mentioned something that really has me thinking:

Students struggle to understand how two people who are both thinking critically can come to different conclusions.

Not surprisingly a few people in the workshop muttered about politics in the US to give a bunch of examples. For me, though, I realized that my main discipline doesn’t really suffer from this problem. If there’s a disagreement between two physicists, it usually means there’s just not enough evidence in yet. The two can be arguing about which theory best describes reality, but if they’re really arguing, it’s usually because both of their theories match all the available data. The reason they don’t fully agree is that the two theories make predictions about things that haven’t been detected yet.

This actually was a large part of my masters work. I was in a group that was really trying to understand how ultrashort pulse lasers work. [brief aside: These are lasers that blink. They’re only “on” for 0.0000000000001 s, then they wait for a few microseconds before they repeat.] My group had one theory, and another prominent group had another to describe exactly how these lasers developed the intense electric fields involved. The problem was that the standard measurement that people were able to do at the time did not distinguish the two theories. It was interesting to go to conferences and be involved in what felt like heated debates. But really they were just hopeful debates. Both sides wanted to be right, but both realized that at most only one of them was. My masters thesis was all about the development of a new measurement technique that could clearly distinguish the two theories.

So that really has me thinking. Does this approach to natural science distinguish how it employs “critical thinking” from other disciplines? I’ve begun to explore the political arguments I’ve been involved in, especially those where I feel like both sides are “thinking critically.” We have access to the same facts, but we feel that the best moves for the future are nearly diametrically opposed. It seems to me this happens for at least two reasons:

1. We disagree on base assumptions about something.
2. We prioritize particular future events differently.

I’ve been a participant in arguments that have fizzled because both parties have realized that either 1 or 2 above is what’s happening. That fizzle takes the form of “oh, well then I guess we just disagree then” or “well, then you’re just an uncaring SOB, I guess.”

In physics, the arguments come to an end when new data comes to light. People can be disappointed that their theory wasn’t right, but they don’t kick themselves for being wrong. Their theory matched the data that was known. They just bet wrong. Moving forward they’re happy to use the correct theory.

One interesting physics example is how to interpret quantum mechanics. There’s tons of disagreement about what’s real, what a measurement does, how many universes there are, etc. However, to participate in the argument, you have to back a theory that matches all the data. When pseudoscience folks try to join or say things like “well anything goes”, they’re usually pretty easily shot down when their theories are shown to not match particular measurements. The argument is really about what reality is, not how to make calculations or predictions.

So what do you think? Here are some starters for you:

• This is interesting. Here’s an argument that happens in my field  . . .
• Have you ever heard of reading?! Here are 10 things you should read before blathering on like this  . . .
• I think you’re not being entirely honest here. After reading your paper I see that your new technique vindicated your group’s theory. Seems fishy to me.
• I remember when FROG was invented. It opened up so many new ways to think about our ultrashort lasers, thanks!
• If someone disagrees with me, it’s clearly because they’re not thinking critically.
• Quantum mechanics is just a spherical-earth conspiracy.
• What arguments do you see your students having in lab?
• Are you saying that if disagreement lingers the participants aren’t thinking critically?
• I wrote “Academically Adrift” and now I think I should go and write a whole new chapter about how the critical thinking abilities of bloggers goes downhill.
Posted in dean, physics, teaching | 2 Comments

## No connections

Driving home today I heard a great story on NPR. I liked it so much that I thought I’d put it here to remind myself about it. I might have forgotten some of the details, but I think I still remember the gist.

### Teachers without their PLCs

Principals have been realizing lately how hard it is to get their teachers to do good work. Too many of them have been spending time talking to each other to find better ways to teach. That takes away from the time that they could be interacting with their students. Now a few schools around the country have started to use a new approach: locking each teacher away from all others.

When the teachers get to school, they can be seen smiling and chatting with their friends in the parking lot. But when they get to the school, they’re met with a phalanx of administrators just inside the door who put all the teachers in bags and cart them off to their classrooms where they’re locked in. At the end of the day they are brought back out, and only then are they able to interact with their co-workers.

“It really sucks because it’s usually so great to get good ideas from people in similar situations that I can incorporate into my teaching,” said one teacher, clearly pining for her friends. Another added “I can’t believe that they’re painting us all with the same brush, assuming that all we want to do it talk with our friends instead of teaching. That’s not fair. I love to teach!”

But the principals have come to understand that any sort of access to professional development that might bring in new ideas can only take away from the tried and true approaches to working with students. While their teachers are complaining, the principals are sure this is the right approach.

Some brave teachers have pointed out that the lack of access to their professional coworkers has changed their behavior. Now if they can’t figure out how to work with a student, they just keep trying other things that they come up with off the top of their head. “Before I would find a friend at lunch to brainstorm ways to help, but now I have way more time to really focus on the problem.”

The bag and lock technology is being pioneered by BeAlone, whose founder realized just how bad things were when he asked how his daughter was doing in school and only got a response after the teacher checked in with all his daughter’s teachers. “I couldn’t believe how long that took! I just wanted to know if she was getting an A+, not whether she was developing lifelong learning strategies.” The company’s clients also include comedians and musicians who like to make sure their audience is only listening to them. The cost is $200 per bag or schools can rent them for$30 per teacher for the school year.

Your thoughts? Here are some starters for you

• That’s weird, I listened to NPR on the way home today and I didn’t hear that story.
• Wait, I feel like you’re being sarcastic, but I can’t put my finger on it.
• You forgot about my favorite part: …
• This is dumb. Principals who do this just don’t realize how creative teachers can be when they can work together.
• This is great. I think we should seek to have this in all schools!
Posted in fun, teaching, technology | 1 Comment

## Mass changing orbits

A few weeks ago my good friend John Burk posted some intriguing questions about what happens to planetary orbits as the sun loses mass (all that heat has to come from somewhere!). I’ve been thinking about it ever since and finally got around to doing some modeling to see if I could answer any of the questions.

My first thought was to see if there were ways to simplify the differential equation solving approach. What John was doing was the full 3D version assuming the sun’s mass stays significantly above the mass of the planet. So he’s already doing some simplifications because he’s not bothering with the center of mass frame. I think he’s right to do that because after a page or so of notes, I’ve realized that the center of mass frame gets pretty ugly when one of the participants is losing mass.

So what else can be simplified? The great thing about central force problems is that you can reduce it all the way down from six variable to one (in fact that’s one of my standards when I teach Theoretical Mechanics):

1. Each of the two masses has 3 variables (x, y, and z) so you start with six.
2. The center of mass approach lets you model the problem as a fictitious mass (=m1m2/(m1+m2)) that’s the same distance from a fictitious force center as the two actual masses are from each other. Now you’re down to three.
3. If it’s a central force, the angular momentum is conserved. That means the fictitious particle has to stay in a plane. Now you’re down to two variables.
4. If the angular momentum is conserved, you can treat the rotational part of the kinetic energy as an effective potential energy, leaving only the radius variable. Now you’re down to one.

You can model the complex 6-dimensional problem as a single (reduced) mass experiencing a potential energy function given by:

$U_\text{effective}=U_\text{actual}+\frac{l^2}{2 \mu r^2}$

where $\mu$ is the reduced mass and U is the potential energy that is only a function of r. To get the force this fictitious one dimensional particle feels, you just need to take a derivative (and add a negative sign).

So I gave it a try. The first thing I did was try to see how far into the future I could integrate using Mathematica. It turns out I could go quite a ways! Here’s a plot of the radius as a function of time.

As you can see, I was able to go out several billion seconds of integration time. This turned out to be around a billion “years” given the simple parameters I chose. If the radius grows, we expect the years to take longer. Here’s a plot of the instantaneous “year time” over the simulation:

as expected!

So it seems that a very slow loss of the sun’s mass would just slowly increase both the circle radius and the year time of the planet.

Another question that John asked was whether there might be an analytical solution to this. I quickly tried DSolve instead of NDSolve in Mathematica and got no joy (I wasn’t overly hopeful). I did ask a good friend of mine who’s a real expert in differential equations whether he knew of a particular decay function I could use that might have an analytical solution. He couldn’t think of one, but did point out that if you had the mass changes be discrete you could “easily” build up the solution since in between the mass changes you’ve got a simple inverse square law orbit that does have an analytical solution.

What he means is that if you start with, say, a circular orbit, you can predict exactly where the planet will be and what direction it’s traveling (and what speed) when the first mass change happens. When it does, you now have initial conditions for a slightly different inverse square law problem. Because the sun has lost mass, it doesn’t pull as hard as before so the circular orbit becomes an ellipse. That ellipse is fully analytical and you can figure out everything you need to know about the planet at the next mass drop. Repeat this to your hearts content and you’ve got a piecewise analytical solution.

This sounded intriguing, but I started to wonder what the physical differences would be between the two approaches. I figured I could check on a relatively small time scale and look for differences. So I coded up both a continuous and a discrete mass loss model, where they connect with each other after each mass loss. Here’s a plot of both mass loss functions:

Here’s the animated result (the blue dots are the points of the mass change for the discrete (blue) model:

As you can see, there’s a pretty noticeable difference in the orbits. Admittedly this is only because the mass jumps are pretty big, but it still makes me nervous.

Here’s a plot of the radius function for both:

Note how the continuous one seems to never get any close to the sun while the blue one is clearly showing more of an elliptical motion (it gets closer and further from the sun during every orbit). To see that more clearly, here’s a plot of r'[t] or the rate of change of the radius:

It sure looks like the orange line doesn’t go negative (indicating the planet never gets closer to the sun). Here’s a zoom in of the orange one to see it better:

Yep, never negative!

Your thoughts? Here are some starters for you

• This is cool, but I’d like to hear more about . . .
• It looks like you were doing a Hamiltonian approach in your notes. I thought you hated the Hamiltonian approach!
• You do know that the perturbations due to Jupiter alone would totally wash out these small effects, right?
• As soon as I saw that you don’t bother to label your axes, I stopped reading. Thanks for saving me some time.
• I thought you said you were going to try to do everything in python from now on? Liar!
• Why didn’t you set up your constants so that a year takes a year? Seems obvious to me.
• Can you share your code?
• How well do your students do on the 6->3->2->1 standard?
• In the piecewise analytical approach, could you look at the solution when the gap time between mass changes goes to the limit of zero?
Posted in general physics, mathematica, physics | 2 Comments

## What are integers

This morning over the breakfast table my family had a great conversation about integers It started when my youngest, L (5th grade), talked about his math test tomorrow. He said the whole chapter was easy and that he wasn’t worried about it. I asked what kind of questions would be on the test, and he said that it would be things like “identify the integer in the following statement: it is -20 degrees C outside.” I’m sure the test will have more than that on it, by the way, but that launched us into some fun conversation about integers.

I asked him if he thought there was an infinite number of cells in the human body. That launched us into talking about all of these:

• Air molecules on earth
• houses
• homes
• books
• gallons of milk
• cups in the world
• heaps of sand

Some were easy: houses, gallons of milk, cups. Some got us really talking, especially “books” as we started to interpret those as fiction books.

Here are some of the thoughts that occurred to us as we argued around the table:

• If you don’t know where the end is, you can’t say you’re halfway done.
• Once it’s done, there’s a halfway point if you count pages or words, but half a story or half a plot is harder.
• We talked a lot about how the Harry Pottter books cram a lot in the last 100 pages or so, for example
• If you have a heap of sand and take a grain out, it’s still a heap. If you repeat, at some point it’s no longer a heap, but it’s never a fractional heap.
• So maybe integers are used for things that can’t be split up? If you can split them up, you should use reals or decimals or rationals or something.
• My partner is a writer and she talks about how many of her writing friends are heavy outliners. They know where the half-way point of their story is.
• Houses are measured with real numbers, but homes are like heaps: they’re a home until they’re not. Half a home doesn’t make sense.
• Human cells are interesting. They “divide” to reproduce, but my argument was that right up until it actually splits, it’s one cell, and once it splits, it’s two.

I’ve been thinking about this all day. I’m coming around to the notion that we often say something is integral (or is counted by integers) when really we should use real numbers and admit that it just works out that they’re often things like 2.00000 . . . etc (like houses, or gallons of milk, or cups, but not homes, books (maybe?), and air molecules). I think we use rational things (fractions) when maybe we shouldn’t. Maybe when someone says they’re halfway done with a story they’re really saying they are still at zero stories but will soon be at 1 story. They might be measuring time, or words, or pages, but that’s a proxy, using things that can’t be measured with integers.

One interesting thing was the different approaches of my kids. L was interested but admitted he was confused at times (now we’re a little nervous about tomorrow’s test – I joked that I should send this post to his teacher). C (10th grade) really felt that if you couldn’t clearly see the end of something, figuring out fractions didn’t make sense. A half gallon makes sense because we know what a full gallon looks like, but a half story is tough to make sense of. B (12th grade) felt that you can convince yourself that you have less than 1 of lots of things (like books), but even if you can’t figure out what the fraction actually is, if there’s a way to think about it being less than one, you can’t say it’s described by integers. Mostly that argument was on the book side, not air molecules or hairs on your head.

Overall it was a fun conversation. I love seeing the #tmwyk hashtag on twitter (talk math with your kids) but it’s often hit or miss with my own kids. This was fun mostly (I think) because I was really trying to wrap my own brain around it, and not just trying to teach them something.

So what do you think? Here are some starters for you:

• This is great. I think another great thing to talk about to see if it’s integral is . . .
• Why don’t you use the word “quantized” for this? What, are you scared of physics or something?
• This is dumb, everything is countable and split-able. I can’t believe I even read half of this post.
• #tmwyk can work great even if you’re “just” teaching them something, here’s 7.5 examples . . .
• What did you have for breakfast?
• I’m a fiction author and I’m really bothered by what you say. I often take 3/4 of one book and put it together with 1/4 of another to get a new book I can publish.
Posted in math, parenting | 4 Comments

## Snow wave

If you click through you’ll see lots of great ideas. I’m not sure what the right answer is, so feel free to weigh in below in the comments.

What actually made me decide to blog about it was that I realized that I asked the wrong question. I really wanted to know what would cause the repetitive pattern, so I think really I was thinking about what would cause the frequency of the wave.

Now, I think everyone who replied on twitter recognized one of the fundamental relationships about waves when answering my question:

$\text{wavelength}=\frac{\text{speed}}{\text{frequency}}$

and really just jumped to physical descriptions of what might cause that frequency. In other words, they realized that the car was moving and basically leaving behind a trail of snow blasts at a particular frequency. Spatially that all works together to leave a record with a measurable wavelength.

As I thought about both my question and the answers throughout the day, it hit me that it’s one of those things that might lose students, especially early on before they’ve really internalized the relationship above. If you ask students to engage with the image or even the Hyundai commercial it comes from, they’ll engage and come up with all kinds of interesting questions, it seems to me. But if you ask about the wavelength like I did, it might shut them down, because then they’re not going with their gut and instead are trying to remember the relationship between wavelength and frequency (or possibly period).

I guess what I’m saying is that I knew my audience and I figured I could ask the question any way I wanted to. And it worked! But as I think about using this in class, I think I would have to be more careful. I think that’s a cautionary tale for me. It reminds me of times I’ll ask about something I think they’ll have experience with, or maybe some cool insights about, but I’ll ask it using vocabulary that’s still too new for them. I think instead I should just show them something and ask “what do you see?” or “what do you think is going on here?” or “Is there anything interesting going on?”

Your thoughts? Here are some starters for you:

• This is interesting. It reminds me of . . .
• This is really dumb. What you should have asked instead was . . .
• This is really cool. I think I’m going to buy a Hyundai now.
• This is really a waste of my time. I already have a car.
• Why didn’t you post a link to the video instead of a crappy screen grab you clearly took while pausing the tv during a really exciting Manchester Derby?
• I was the driver in this commercial and here’s what actually caused that . . .
• I was the camera person in this commercial and here’s why the driver really doesn’t understand physics.
• Here’s my crazy explanation for that snow pattern.
• It’s not a wave, you should stop saying that.

Posted in physics, teaching, Uncategorized | 7 Comments

## Crowd-prioritized questions for speakers

This past week I tried an experiment during a major speaking engagement on my campus. This was our annual “Commitment to Community” address by the fabulous Kemba Smith. We had her on campus for a day and she interacted with our students in lots of ways, culminating in a major presentation to the campus in the evening.

In my role as director of the first year seminar I was involved in some of the planning (I need to be clear here and heap praise on the C2C team – they did all the work and deserve all the credit for the great day). Specifically I was involved with planning how the overflow room should work. We hold the event in a neighboring church that can only seat something like 500. We like to have a satellite location that can simulcast the event. In early planning, I expressed how it would be interesting to do something different in that room. I thought it would be great to brainstorm activities people could do, while listening, that could raise the engagement of the audience. What we decided on was to crowd-source the prioritization of the questions we’d ask.

### What we planned

We thought it would be great to encourage the audience (only in the satellite room) to use internet-connected devices to submit and vote on potential questions for the speaker.

We picked the Q&A feature of Google Slides to do this. We made a simple one-page Google Slides document and turned on Q&A when the event started. We made sure the url was clearly displayed in the room.

I invited the first year seminar faculty to bring their classes, with a limit of 3 classes, and talked to a few other faculty about it as well.

We told people we’d be the first three questions asked in the church since I promised to text our questions to a plant (from the C2C committee) in the church.

### What happened

Only two faculty brought their first year seminars (the rest went to the church). When I asked people how they made that decision I heard lots of interesting things:

• “I really want my students to be there to hear Kemba”
• “I’m not sure my students will have the focus you’re looking for”
• “Sounds cool but I really want to be in the church”
• “I’d love to because I’m always squished in the church”
• “That’s an interesting experiment”

In addition a few other faculty and students came. All together we had over 80 people there.

We passed out cards explaining what we were doing, because I figured if anyone came late I wouldn’t be able to explain it myself. Many were there early and we verified the technology worked with everyone’s cell phone.

We only had a handful of submitted questions, the highest rated of which only got six votes.

I submitted the questions a little early (we had a 2-minute delay that I didn’t want to miss). The question ranking changed a little after I submitted them, but the top three remained the top three. In the church all our questions were asked, but not all at once at the beginning of the Q&A session.

### Analysis

I was a little disappointed at the lack of engagement with the technology, but quite happy with the respectful and attentive attitude in the room. I’ve spoken with some about why there weren’t so many questions submitted and a few suggested that a lot of Kemba’s presentation was personal narrative, and that’s sometimes hard to question.

I think our questions were good. They certainly weren’t the horror stories you sometimes see at Q&A sessions for big speakers. You know what I’m talking about:

• “Thank you for your talk. I agree that _____ and let me tell you my whole life story before getting to my actual question.”
• “I came in late, could you please say everything you said at the beginning again?”
• “I have told you before that I disagree with you about point ____ and I’m going to walk you through every conversation we’ve ever had right now.”
• “Do you know ____ who says the same stuff as you but better?”

I had a question voted down. What’s fascinating about that is my emotional reaction. I would have thought I’d be disappointed about that. But it was interesting that I was relieved! I realized that I might have asked it if there were no crowd-sourcing and I might only hear after the event how dumb a question it was. In this case I don’t think people thought it was dumb, but they clearly thought other questions were more worth their time, and I think that’s great!

One interesting feature of this experiment was that the speaker couldn’t see how the voting and “leader board” evolved during her presentation. I think that’s likely a good thing, as it can be very distracting. In our implementation I did not project the leader board, but it was on everyone’s phone.

I think I’d like to do a little more experimentation with this. I think it could help with student engagement and I think it could really make the Q&A sessions more worthwhile.

Your thoughts? Here are some starters for you:

• This is cool! You could also think about doing . . .
• This is dumb! Instead you should have  . . .
• I thought you used to love Google Moderator, why didn’t you use that?
• I think you didn’t get too many submitted questions because . . .
• I think you didn’t get too many votes because . . .
• I’m personally hurt by your examples of horror shows in Q&A sessions. I love all of those examples you describe!
• Here’s another to add to your horror show list . . .