Physics majors practice presentations

For years we’ve been working to give our physics majors opportunities to improve their presentation skills. We do a lot of oral exams but we also want our students to do well in more formal settings. We have a junior/senior seminar that the students take for 4 semesters, and they have to present in three of them. For their first one (fall of their junior year typically) we don’t want them to stress out over physics content so, assuming they don’t have a research project to report on, we tell them to give us a short presentation on a general physics concept that they understand well. This post is my thinking on how to improve that.

Typically students pick something like a projectile problem and they present it kind of like a mix between an oral exam and a mock teaching situation. The former is weird because it’s usually a really easy problem (for juniors) and the latter is problematic because that kind of presentation tends not to be how we’d choose to teach the material (no interactivity, for example). Normally we end with some token physics criticism/question but them concentrate on suggestions for how they could present better.

My biggest problem with this setup is how fake it is. It’s not the type of presentation they’ll likely be giving in the future. Then they’d much more likely be talking about a data-driven decision or conclusion they’ve reached. They likely wouldn’t be defending their understanding of a simple concept and they certainly shouldn’t be teaching like that (mostly dark room, only one person talking, etc).

So my current idea is to have them still have a pretty safe and easy thing to prepare but to have it be much more in the spirit of the types of presentations we’d like to see from them. I thought it might be cool if they could present their data from a lab they’ve already done. It might be a simple lab from general physics or something, so likely none of us would be surprised by the outcome, but they could be asked to approach it as trying to convince someone of the conclusions they’ve drawn. We could then really help them focus on what aspects of the presentation need focus (well done data plots, clear explanation of any theory necessary, etc). We still might make minor physics criticisms or questions but we could focus on the presentation skills we really care about.

I figure we could ask students in their first one or two physics classes to pick the lab write up they are most proud of and we could keep it for them to hand back when their juniors. We could do that early in the semester so they could have time to get their presentations ready.

Your thoughts? Here are some starters for you:

  • I’m in this class and I like this plan a lot, here’s why . . .
  • I’m in this class and this is a stupid plan, here’s why . . .
  • Why not force them to do an actual experiment? You act like it’s only worth 0.5 credits or something.
  • Would this work for the labs that are more along the lines of verification labs (“yep, I get 9.8 m/s/s”)?
  • Why have them pick their best one? Maybe the lab instructor should pick it
  • Maybe you could make sure that no two students do the same lab. Here’s how I’d set that up . . .
  • I like presentations based on ________ better, here’s why . . .
Posted in syllabus creation, teaching | 5 Comments

Wasted 10 minute quiz

These days I do a daily quiz for my students. It’s a problem randomly selected from the three problems assigned last time (unless it’s a review day, then it’s randomly selected from the previous 2 days). These are typically deep, rich problems so the only way you could do them in 10 minutes is to have really worked on them ahead of time. I usually add some twists or turn them inside out but, basically, if they’ve worked on them and really understood the material they should be doable. The problem is there’s a noticeable minority of students who do very poorly on these quizzes. They get bad scores (1’s or 2’s on my 4-point scale) and spend a large amount of the 10 minutes just sitting there with a defeated look on their face. So I’m trying to brainstorm other approaches and would love it if you, kind reader, could chime in.

Learn their lesson

Option one is just do nothing and hope that they learn their lesson eventually. Perhaps enough 1’s and 2’s will get them to realize they really should work harder (or perhaps differently) on these problems.

Because I use a Standards-Based Grading approach they know they can repair their grade by turning something in later so there’s not a lot of pressure to perform in class. Of course many of these students pile up a lot of 1’s and 2’s and tend to fall far enough behind that my two week rule gets them in trouble.

I guess what I’m feeling right now (facing the prospect of (once again) turning in lots of F’s for midterm grades) is that the lessons aren’t being learned.

Remind them to ask for help

I could remind them that since the quiz grade doesn’t set in stone that standard’s score, if they feel like they’re likely to get a 1 or a 2 they could try to explain on their quiz what they’re struggling with. When this happens now, admittedly rarely, I tend to either give that person some feedback on their quiz paper, send them a video, or send the whole class a video with some explanation. I think in the smaller classes that I could handle this scaling up a little and I think I’d understand better where the students are at than grading a crappy quiz performance.

I think if I didn’t stay on top of it and continue to give personalized feedback, students would likely stop writing a whole lot and instead continue to use their 10 minutes in class to do other things (with a defeated look on their face).

Show them something else

I was brainstorming with a student who’s in class with me right now about what would work better for him on days when he doesn’t really know how to start the quiz. I asked him about the notion laid out above and he thought that seemed reasonable. Then we started to brainstorm this new notion. Maybe I could give students a choice: either take the quiz or come with me to another room where I’d do some additional instruction on the topic. Maybe that could just be me trying to articulate every thought in my head as I try to do the quiz.

I’m definitely attracted to this if only to avoid looking out and seeing defeated faces. On the down side I feel like this sort of direct instruction 1) makes the students feel like they’re learning, but 2) doesn’t really help their learning. It reminds me of the students who say “I own the solution manual but I don’t use it to do my homework. Instead I love to study from it much more than struggling over any suggested exercises.” I’ve never actually believed students when they say that (not the first part, the second part). I think they look at well solved problems and dutifully nod their heads saying “oh yeah . . . of course . . . yep that’s right” instead of what we want our students to be thinking: “hmmm … not sure… oh wait  … let me try … ooh, now I know!”

I’m also not sure if students would tend to make the right choice (for them) when offered to either take the quiz or come with me. I guess I’m not sure what to think.

Your thoughts? Here are some starters for you:

  • What does “turn them inside out” mean?
  • I like the _____ option but not the ____ option because . . .
  • Why do you do quizzes at all? Instead you should . . .
  • I’m in this class and this post is great because . . .
  • I’m in this class and I hate this post because . . .
  • Wait, how do they use Mathematica during their quizzes?
  • I study from worked examples all the time. Why are you criticizing me?
  • That’s not what I think should be going through students heads when working problems. Instead I’d like to see  . . .
Posted in syllabus creation, teaching, Uncategorized | 11 Comments

Interactive arduino internet-of-things

I’ve written before about my Math and Computational Methods for Physicist course and how we’re doing a cool Arduino-based Internet of Things project. I’ve been brainstorming some new things we might do with that project and I wanted to see if you, dear reader, might have some suggestions/observations/complaints/whatever.

First an update on the database and our prototype. I haven’t added much to the database. Really only a dashboard list for the admin (me) showing the total number of measurements for each machine and when the last measurement was. It turns out that even though I fixed the pretty common wifi freeze with the watchdog approach, it still goes down about twice a week. I’m not really sure what’s up with that. The most recent time it happened I didn’t notice for about a day so when I went to look at it I noticed it was pretty hot. Unplugging it for 10 seconds or so and then replugging it seems to have fixed it for now. Any thoughts on how I can figure out what causes those very intermittent problems would be greatly appreciated. The class has devoted one lab to Arduinos so far and they all got to the point where they were measuring and calibrating temperature and controlling an LED. Pretty good for 90 minutes. We meet again about it this coming week when I’m hoping they’ve all found a “client” that they can program the arduino for.

Using a clock

The first new idea is to deal with client requests that are time-based. Something like “every night at midnight check the XXXX and report” as opposed to what we already have: “every Y minutes do something.” The arduino has a millisecond timer on it, but you can’t trust it to know in absolute terms what time it is. So at first I thought we couldn’t handle those requests. But then I remembered that we have a working wifi card on all of these! I figure we can just have it check the absolute time on some time server somewhere and at most be off by Y minutes. That’ll likely satisfy those sorts of clients (at least I hope so).


Already a few potential clients have asked for things like “every time the door opens measure XXX and report.” If they can handle a resolution of Y minutes, then we’re all set. Otherwise we’ll have to use the built-in interrupt stuff for arduinos. Then if the door opens an interrupt will be thrown and we’ll execute the whole “measure XXX and hook up to the internet” code.

Make a measurement if we say so

This is the one that I would really like some advice on. Some students and I were brainstorming how we might communicate to the arduino to make a measurement. Really this would be an extension of the “using a clock” idea above. We’re thinking of updating the database web site so that the owner of the machine (which is currently defined as the person who most recently updated the code for that machine) could update a page with something like “yes” or “no” returned so that the machine would check that page first (every Y minutes, say) before deciding whether to do anything else. We could, of course, get more complicated with various messages triggering lots of different responses from the machine. The limit would be the storage on the arduino (20 totally different codes stored might not be possible, for example) but I think we can still do some cool stuff.

I guess my question is: is this the right way to go about it? I read a lot about making the arduino basically a web page server so that you can go to it and ask for things. That’s the bulk of the pages you get if you search for “arduino internet of things” so I know it’s pretty popular. My problem is that it seems like it’s asking the arduino to do quite a lot, and essentially be fully on (as opposed to a boring “pause” loop) all the time. I figure this approach saves a lot of that, but maybe I’m missing something.

So, we’d love your help. If you have any ideas/hare-brained-schemes/concerns/anecdotes/love-letters-to-mathematica let us know in the comments below. Here are some starters for you:

  • I’m in this class and I’m really excited about this project. What Andy forgot to add was . . .
  • I’m in this class and I hate it. What I’d love is if someone made it clear to Andy that this is a dumb project so we don’t have to do it.
  • I’m in the HUWebApps group that Andy talked about here and I think this could be some fun work for us. One thought I had was . . .
  • I think these new ideas are really cool. One thing I’d be a little worried about is . . .
  • I think that some of these ideas are really bad, damage-people-for-life bad! Here’s a better way to go about it . . .
  • I’ve done some similar work <snark>thanks for linking to me</snark> and I’d suggest you read this, this, and this.
  • I run my arduino as a web server and it works great! You should really switch because . . .
  • I run my arduino as a web server and it sucks! I’m thinking of switching to how you do it, can I use your database?
Posted in arduino, HUWebApps | 6 Comments

Web apps workgroup

We’ve been thinking a lot lately about finding new ways to give our students more computer programming skills. We don’t have a computer science major but are willing to do certificate/minor-type things that will help students succeed in their chosen major. One thought I had was to introduce students to web programming (scripting with PHP and database backend with MySQL because that’s what I know) but I’m not sure how to pitch that class (and at what level). Instead I thought I might just try to develop a club/group on campus that develops web apps to see where the sweet spot is.

Web vs mobile apps

This article helped me clarify my thoughts about why web and not mobile apps. Honestly, for me, it’s a learning curve thing, since I know how to do web stuff (I’ve written my own LMS, a course schedule web site for my institution, a site for concept tests/quizzes, a jeopardy quiz site, and an Arduino Internet of Things site (which I wrote about in my last post)). Also it seems that you don’t have to make a choice between apple and android if you go with web apps. However, I think we’ll concentrate on things that’ll work well on mobile browsers just to keep that audience in mind. It helps that Twitter Bootstrap is mobile-first.


The hope would be that we could develop something that people need. I wrote about something that I’d like a while ago so maybe we’d just start with that one (it’s a site where students could upload photos that would be added to an ongoing slideshow that would be projected). I’d love it if we could respond to the needs of the community to make things that are useful (and teach students some useful coding skills).


We would use github and trello to keep organized. Github would allow us to has a core of working code along with branches where new features are developed. Github would also let new people join in pretty easily, though a working project might be intimidating to some. At first at least we’d be coding in the Laravel PHP framework. Participants would need a development machine that could run Laravel/php along with mysql. Installing xampp would do the trick, along with composer to easily handle various code dependencies. Once they have those working (really it only takes about 10 minutes to get all that working on a windows machine) they would just pull down the githup repository they’d like to work on and they’re in business. Really the notion of handling code with others using git is a useful skill.

Trello is an awesome way for a group to keep track of what there is to do, who’s doing what, and what’s done. I used it to great effect this summer with my research students (here’s our public list).

Once students have got a cool feature working on their local machines I would just have to merge the repository and pull it down to the development machine (for now it’ll be physics.hamline .edu which is where all the examples above are hosted – eventually I would hope to get something like or something). That way I’d be the only one dealing with the production machine and any headaches that come with getting it working right. I really like how github would help with that (and how students can see the working code on their development machines without having to wait for me to get it up for the whole world).


I think it’ll be fun to work with students who are developing these types of skills. I think I’d be a little hands-off with dictating what we work on and how, but I’d probably stick to Laravel, Test Driven-Development, and mysql. If someone comes along with skills to get other approaches working, then sure! I got all excited about Meteor a few months ago but getting it to work on a server with ease of community-based updates was a big hassle (for me). So Laravel/PHP/MYSQL for us for now. I think that students who really put some effort into this will be able to easily sell their scripting and collaboration skills with some production code to show off.

What’s missing?

So what do you think. This is really just a 2-day-old brainstorm for the moment. I’d love some help moving this project forward. Here are some starters for you:

  • I love this. What I’d add is . . .
  • I hate this. Instead you should . . .
  • PHP?!??!! Why in the world would you expose students to that crappy approach? I’ve never heard of Laravel but I bet it’s a piece of crap built with crap.
  • Why not Django? I suppose you’re too scared to ask your ITS to add yet another module to Apache, huh?
  • Why not Meteor hosted on Galaxy? What are you, cheap?
  • Ooh I’ve got some great ideas for apps. Where would I send them?
  • Ooh I’d love to work on this. When are our meetings?
  • I don’t understand. I love the apps on my (fill in a brand of phone here). Why don’t you just develop more of those?
  • The photo/slideshow app you’re looking for exists. It’s called . . .
  • This sounds like a better class than a club/group. I think it should be called . . .
  • This should never be a class. Keeping it separate from students courses is smart.
Posted in technology | 3 Comments

Arduino internet of things

This summer several colleagues and I had some seed money to brainstorm ways to put more sustainability ideas into our curriculum (physics, chemistry, and math was represented). One of the projects we decided to flesh out is having students develop arduino hardware and software to collect data about our campus that would help with energy management. We followed some online tutorials  though we decided to have the arduino simply send its data to a web page every 5 minutes instead of having it act as a server that you could go to with your browser. The idea is that the arduino will record its probe data every 5 minutes (say), hook up to the internet, and send the data to a simple url like cooldatabasesite/probe1=X&probe2=Y. We did the initial testing with a Wolfram Data Drop but later decided to just make our own database to collect the information. I wanted to write this to get the gist of the project down and to possibly see if our database could be of use to others.


With some more internal funds we now have enough Arduino Uno’s, CC3000 wifi boards, and DHT 22 temperature/humidity probes for my whole class this fall (13 students). The total cost was something like $1200.

Arduino code

I based the code on two examples that come once you download the cc3000 library from Adafruit. The “build test” example checks the functionality of the board, and, importantly for how we wanted use it, sends the MAC address of the board back along the serial line to the computer. Then the “web client” example is what I made slight adjustments to in order to get it to work with our database. Really you’re just having it connect to a simple web page (with a GET request) and then having it read the result and then shut down. There’s a lot of code to help with connecting to the wifi but it’s pretty straightforward. At my institution the main wifi signal uses WPA2-EAP (I think) for security (the kind where you put in a username and password in the wifi configuration on your computer as opposed to the kind where you put your username and password into a browser page) and the cc3000 can’t handle that. I thought we were out of luck but one forum I read suggested seeing if my ITS department would be willing to just store the MAC address of the boards and allow them on the network without all the certification stuff. It turns out they were willing to do that! It’s on the “guest” wifi signal as opposed to the main one but it seems to work great. (Note the comment above about being able to have the arduino print out the MAC address with the initial test).

So you load the cc3000 library, run the “build test,” grab the MAC address, send it to ITS, then run a doctored version of “web client” with the appropriate wifi settings and the correct url for the database (and collecting the appropriate probe data).

One major headache that happened was the arduino would hang every few hours or so. It gets stuck in a loop and won’t do anything. Hitting the reset button fixes it, but that’s a pain for a machine placed somewhere on campus. Luckily there’s a very cool “watchdog” library for arduino that allows you to program the machine to reset if it goes into an infinite loop. Unfortunately the longest you can have it do something before it’s decided that it’s stuck is 8 seconds using the default watchdog approach. That sucks because the whole “connect to the wifi, send the info, parse the result” takes something like 24 seconds. Luckily, I found a very cool work around that allows you to multiply that 8 seconds by any integer you’d like. It uses interrupts on the watchdog and is very slick. Check it out. So now if it hangs in the wifi hookup process, it just resets itself and continues right along. If I look at my data I see usually one or two gaps of 6 minutes instead of 5 minutes between my data points every day. Not too bad.


I wanted to build a pretty flexible database for all this data. I wanted authorized uses to be able to add new machines (register the MAC address), attach probes to it (so the system could make sure that the type of data submitted was of the right sort), and describe the location it’s in. I also wanted to have a place to store the arduino code on the machine so that people could check it to understand any calibration issues. I’ve got nearly everything done:

  • Admin section
    • Approve uses
    • Edit machines (location, attached probes)
    • Add/edit probes (what’s available to be attached to machines)
  • Add machine
    • submit MAC address (right now the format is just decimal without colons but possibly changeable)
    • attach probes
    • put in location
      • short name
      • description
      • GPS coordinate (I haven’t standardized these yet but I think it should be possible)
  • Accept measurements
    • …./measurement?macaddress=XXXX&p[Y]=y&p[Z]=z&…
      • where Y and Z are ids of the probes in the system
  • Display data
    • You see a list of locations
    • Then see a list of available measurements
    • Then see a plotly.js-driven interactive plot of the data
    • below which is a list of downloadable formats
      • json
      • html table
      • excel
      • csv

This was the first time I programmed an application using Test Driven Development and I really liked it. I now have a suite of tests (over 50) that test every aspect of the application. That way if I make a change I’ll know if I’ve screwed something else up. Basically it’s a way to test all your web pages and user-clickable events to make sure they’re all still working. In the old days I’d just make a change, make sure the new thing I was working on was working and only find out days later that I screwed something else up. Very cool.

You can see the working database here.

I’m pretty excited about what we can do with that. We can have machines all over campus submitting data that we can really put to use. I’m also excited because I think I could easily handle other people’s data as well. If you’ve got a wifi-enabled arduino, just register on the site (and maybe send me a message), I can approve you and decide if you should be an admin or what and then you’d have access to your data. Alternatively people could feel free to fork my application and just host it on their own server.

By the way, there’s also a Plotly approach having arduino stream data to a graph if that’s all you’re interested in.


In the old days I’d just make up some dumb thing for my students to work on when learning how to work with an Arduino (make a working stoplight circuit, move a motor at a speed determined by the temperature, etc). What I’m excited about with this project is that they’ll be learning many of the same skills while adding to a larger university-wide project that other people care about. I hope that helps motivate them.

Working with my math colleague has been fun because he has his students deal with data sets in his statistics courses. Now he’s excited to use this data instead with really very little change to the learning outcomes. Again motivating the students to come up with hypotheses that could be tested using our data should be easier with this.

The other thing I’m excited to do in this upcoming class is to encourage the students to engage with community members. My hope is to identify several potential “clients” that they can go talk to and figure out what kind of data they want logged and why. It’s a math methods class for physics majors so maybe they can do some modeling of the system being measured. Not sure about that (though simple heat flow should be pretty easy) but it’s certainly possible.

So I’m pretty excited. Your thoughts? Here are some starters for you:

  • This is great! Something else you could do is . . .
  • This is dumb. Haven’t you seen . . .
  • Why didn’t you post your Arduino code here?! It’s almost as if you’re typing this on a chromebook at home because you left your development computer at work.
  • Wait, let me get this straight: you abandoned a solution based on a Wolfram product? Who are you and what happened to SuperFly?
  • It seems like you’re doing application testing, not unit testing. Did you do any unit testing?
  • What code do you use for the database? (It’s a Laravel/PHP/MySQL stack – I really like coding in the Laravel framework)
  • Why don’t you use a Raspberry Pi for this?
  • Wait, 15 machines every 5 minutes is 3 million data points per year. Can your system handle that and expand beyond it?
  • Could you have a machine take rapid data over a short period and then repeat that daily?
  • Why are you so inconsistent with your capitalization of aRdUiNo?
  • Why are you doing all of this in a math methods class (the actual name is Mathematical and Computational Methods for Physicists)
Posted in arduino, community, lab, technology | 5 Comments

Teaching driving is depressing

My son is learning to drive. I’m past the “oh crap” stage and the “but just . . .!” stage and squarely into the “it’s going . . . ok” stage. He takes his test next month and I’m pretty confident he’ll do fine. Here’s the thing, though: I suck at teaching someone to be a good driver. No, this isn’t a post about how you can’t teach your own kids anything, though that’s often true with mine 🙂 It’s about realizing just how I got good at driving and how hard it is to teach that in just a few months.

My partner and I talk a lot about how our son is learning. We think he does a great job with some things and just an ok job at others. We’ve been with him in stressful situations and we’ve all made it through (even the car!). But as we reflect on what we would have done in those situations we start to realize just how much better we are as drivers than he is, or that he will be even after another few months of intensive training. We’ve had (cough cough) 30 years of practice, and now we’d say we’re pretty good at it.

What I’m depressed about is the realization that years of experience (or 10,000 hours, if you prefer) can’t be taught. I’m pretty sure that my son will become a great driver, but I don’t think there’s anything I could do to help that along very fast. I’m depressed because my profession is teaching physics, and all I ever get is four years with a student. For most of my students all I ever get is one semester. Trying to teach “physics maturity” (to borrow and slightly change a phrase from my mathematics buddies) in a semester is really hard. Maybe impossible. If I knew my students were going to go off and continue to think about physics and practice physics and model things like crazy throughout their life, I suppose I could take solace that they’d eventually become the experts I want them to be. But the students that do that are in a minority so small that it’s probably not worth it to count them.

I’m realizing that all I can do is set the table for them. I can try to make a course experience that gives them some tools and gives them glimpses of others. Just as I can’t make my son a great driver in just a few months, I can’t make an expert in physics in one course.

So I’m depressed, but super excited to be heading off to the AAPT conference today so I can get the usual pick-me-up that I get from all my friends there. Who knows, maybe when I get back I’ll have a post with a title like “Teaching physics is the greatest thing you can do” or something like that.

Your thoughts? Here are some starters for you:

  • Thanks for this. I’ve been thinking along similar lines . . .
  • This is dumb. Physics and driving teaching are nothing alike. What you should compare is . . .
  • You say “depressed” but you don’t really mean that. It’s a disservice to those who really do suffer from depression (sorry about that).
  • I taught my child to drive and in the process learned a ton from them. Things have really changed!
  • All that matters is that they know where the brake pedal is. Everything else is fluff.
  • Wait, you’re going to AAPT? Want to catch a meal?
Posted in teaching, Uncategorized | 5 Comments

Help us crowd-source our drums!

My students have been working hard this summer on a project I’ve talked about before. Here’s the gist:

  • Normal drums aren’t melodic. They have resonant frequencies but they aren’t in a pattern that we think sounds good. That’s why they’re used for percussion.
  • If you explore different shapes you can move the resonant frequencies quite a bit. We’re interested in finding cool shapes that might sound melodic.
  • If we can find a shape using simulation, we can then print it using a 3D printer

That sounds cool and all, but the details are proving to be tough. I’d like to brag a little about what we’ve been up to in this post (mostly so there’s a good record of it somewhere), but if you’re wondering about the title of this post, just go here where there’s a little explanation for what we need for you. Read on for more details.

Calculating resonant frequencies

This is actually the easy part. If you know the shape of the drum head you’re interested in (and can describe it mathematically — see below for that hassle) you just need a single command in Mathematica:

{frequencies, functions}=NDEigensystem[{-Laplacian[f[x, y], {x,y}],
    DirichletCondition[f[x,y], True]}, {f}, {x,y} \Element region, {10}]

where “region” is your mathematical description of the shape of the drum head. This command uses a Finite Element approach and returns the 10 lowest eigen frequencies. Note that you have to take the square root of the frequencies you get from this command to get the audio frequencies.

Here’s a sample of listening to various frequencies on a slowly changing shape:

Describing shapes

Simple shapes are easy: a circle? Disk[], a rectangle? ImplicitRegion[-1<=x<=1 && -2<=y<=2, {x,y}]. But what about crazy shapes? And what about shapes that Mathematica can programmatically shift around while it hunts for cool shapes that produce cool spectra?

What we’ve decided to do is to use control points around the edge that Mathematica can make slight adjustments to. When it does, it redraws a smooth, closed curve that includes all the points and it then uses a cool command that turns that border into a region:

region = BoundaryMeshRegion[controlpoints, Line[{1,2,3,4,6,1}]]

The problem is that you have to make sure that the control points are in the right order around the border (say, clockwise, for example). Luckily it turns out that the traveling salesperson problem comes to the rescue here. If you want to find the shortest path visiting all the points in a plane (and returning to the first one), that path will not cross itself and hence will be a proper region border. So:

fst = FindShortestTour[points];

comes to the rescue. So Mathematica does this:

  1. takes some random points in the  plane
  2. Find the shortest path around them
  3. Use BoundaryMeshRegion to make that border a region
  4. calculate the frequencies for that shape
  5. decide what small adjustments to make (see below).
  6. Make those adjustments to the locations of the control points (first described in (1) above)
  7. repeat 2 – 7 until a cool shape is found

Decide on adjustments

Ok, so let’s say you have six control points. Each one is an x and y value so you have a 12-dimensional optimization problem. What could we use? We’ve decided to use Mathematica’s implementation of an evolutionary algorithm (or genetic algorithm). Really it’s the same thing I was using when trying to see if Mathematica could learn to race around corners. Evolutionary approaches work well where there’s a humongous parameter space and you don’t really know any other way to explore it other than brute force.

The big problem (yes, I’m getting to the title of this post, hold your horses) is that a set of frequencies from a drum head (the result of step 4 above) needs to be converted to a single number that can be used to rank various drum heads in the evolutionary algorithm.

Single number

Ok, so we realized that we needed to be able to look at a spectrum from a drum head and rate it on the scale of “is it melodic?” We thought of some interesting approaches. Mostly they centered around measuring how close the frequency spectrum is to an evenly spaced one (which is what a stringed instrument gives you). We ran into lots of potential problems, though, not least was that orchestra chimes have a “missing fundamental” and still sound good.

We also realized that maybe we could handle mostly evenly spaced frequencies if we could determine where to thump the drum head to kill the offending non-evenly-spaced ones.

Thump predictions

Ok, so now we had to go back to Mathematica to determine where on a particular drum head you could thump it to control the relative amplitudes of the various frequencies (think about how a stringed instrument sounds very different depending on where you hit it.

Here’s an example of how the frequencies from the shape of Minnesota change their relative amplitudes if you thump in the center of every county in Minnesota (note that the find shortest tour command was used to do that):

Luckily the NDEigensystem gives us the resonant shapes for every resonant frequency so finding the relative amplitude for a given thump location (and shape) really just amounts to doing this integral:


where f_i(x,y) is just the ith resonant shape and thump(x,y) is the function that describes the thump shape (and location).

It’s taken us a while to find a good way to do this integral fast, but we’re getting there (right now we’re at one second per frequency per shape).

So now we can look for a good candidate of frequencies and then hope there’s a thump location that’ll shut off the bad ones (fingers crossed!).

Back to single number (Neural networks and you!)

So then we hit on the way we could pull all of this together (we hope). We’ve decided to let the crowd (you!) help us rate a collection of frequencies and relative amplitudes on a scale of 0 – 5 where 0 is like white noise and 5 is a pure tone. We figured that since we’re making drums for people we ought to let people determine the single number that our evolutionary algorithm needs.

One of the researchers in the math department this summer is working on an artificial neural network to recognize handwriting and my students realized that approach could work here. All we need is to train the network on what are good, bad, and medium sounding collections of frequencies and relative amplitudes.

Luckily Mathematica has recently built in some really powerful functions that implement the major algorithms in neural network theory. The one we’re planning on using is “Predict” which just needs a whole bunch of these:

{{216, 456, 786, 890, 1012}, {0.5, 0.3, 0.6, 0.7, 1}}->2

where the first list of numbers is the random frequencies and the second is the relative amplitudes. It then trains on whatever you give it and then it can be used on future untrained ones.

So, we need your help! Please go to our new site and score a few random sounds on our 5 point scale (decimals are welcome). It just takes 1 second per sound and we’d love to just get a ton to train the neural network. Then our workflow will look like this:

  1. set a generation of random control points
  2. find the region for all of them (using FindShortestPath)
  3. find the frequencies for all of them
  4. Check them against the neural network to determine goodness
  5. Make babies with better ones (evolution)
  6. monkey with the thumping (yeah, I know, this part isn’t as clear).

HTML 5 sounds

We started developing the training set using Mathematica to generate sounds. This is pretty easy (just use the Play command) but it was tedius and we weren’t generating enough. This notion of crowdsourcing came from my wonderful students so I decided to give it a try over this holiday weekend.

I knew making a database-driven website wouldn’t be a problem (I rail against Blackboard so much because I finally just wrote my own LMS). But I didn’t know how to generate the sounds. So, I decided to dig into the HTML5 audio standards. It turns out that just a few lines of javascript code will generate a sound with a controllable frequency and amplitude:

oscillator$key = context.createOscillator();
 gainNode$key = context.createGain();
 oscillator$key.frequency.value = $value;
 currentTime = context.currentTime;
 oscillator$key.connect(gainNode$key); // Connect sound source 2 to gain node 2
 gainNode$key.connect(context.destination); // Connect gain node 2 to output
 gainNode$key.gain.value = $amps[$key];
 oscillator$key.stop(currentTime + 1);

where $key is set up as the loop variable (goes from 1 to 5). Feel free to take a look at the html source of our page to see how it all goes together.

So thanks for any help you can give. We really hope we get enough data so that the training is robust.

Thoughts? Here are some starters for you:

  • I love this! Here’s something you could do in addition . . .
  • This is dumb. All of this has been done before and you’re just repeating what someone else did (insert reference here).
  • Why do you do all of this in Mathematica?
  • Are you going to sell these drums?
  • How are you mounting them to keep the tension constant in the crazy shapes?
  • Why don’t you just build tympani?
  • What are you talking about with the “missing fundamental” for orchestra chimes?
  • The web page doesn’t work for me, what’s the deal?
  • Can I have access to the training set?
  • Wait, you wrote your own LMS? That sounds cool, tell us about it!
  • I’m still confused how you’re going to do the thumping in the evolutionary program.
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