One die to rule them all

For a number of years I’ve been working on finding ways to turn what looks like an unfair die to a fair one (see these posts). Recently I’ve made a lot of progress. This post shows how I’ve turned a 36-sided unfair die into a fair 3-, 4-, 5-, 6-, 7-, 8-, 9-, or 11-sided die.

The two big accomplishments since the last post were to 1) roll an unfair 36-sided die 100,000 times, and 2) figure out how to optimize contiguous groupings of sides to make the fair dice I alluded to above.

The original die

I’m not quite sure why I decided to settle on a 36 sided die, but I did I guess. I knew that each roll would take a few seconds and I knew I needed some good statistics. I have access to a VDI machine at work that can run all night long so I finally got around to leveraging that and getting some decent statistics on the rolls for the die (100,000 rolls that took 5 days of continuous calculations!):

Comparison of actual rolls (red dots), area of sides (orange line), solid angle that side subtends (green), and volume of the die that the side projected to the center adds up to (blue). Note how the y-axis doesn’t go down to zero.

A number of interesting things are represented in that graph. First, you can tell that the die is unfair because the red dots aren’t flat. The minimum probability is ~0.021 and the max is 0.035, or 67% bigger. The three other curves are all pretty similar, and certainly all 4 curves are correlated. But it’s interesting that in my conversations with folks over the last few years I’ve run into people (and web sites) that would claim that side area, side solid angle, or side volume (really the volume of the chunk from the center projected out to a side which is also proportional to the mass of that chunk) should accurately predict the probability. It’s interesting that none do!

Evolving dice

Ok, next came the challenge of finding contiguous groupings of sides that would yield (nearly) identical probabilities. I thought I had figured out how to find random groupings as shown in this image for a random die I used in my last post:

9 different ways to break up the same random die into contiguous regions

The trick to do that was the Mathematatica command “FindGraphPartition” where the graph in question has the faces as the nodes and connections exist between faces that touch. That command finds regions that are connected, trying to keep regions with strong connections together. It does that by looking at the edge weight between them (higher number means they’re “more connected”). So I just fed that function the graph of my polyhedron with random (positive) numbers for the edge weights (for a 36-sided die there are 54 edges).

So I could run that random weighting over and over again to try to find regions that just happened to be fair. This is hit-or-miss, of course, so I thought I’d try to make a genetic algorithm work.

A genetic algorithm, or really any of the evolutionary programming types, work really well when you have a huge parameter space (54 different parameters, in this case, that can each be any real positive number) and lots of potential local minima. What I wanted to do was to use the 54 parameters as continuous variables and to let the genetic algorithm test random “parents”, rank them, throw away the bottom half of the population, and then repopulate that bottom half with “children” made from the remaining parents. I pair two parents up, take the first, say, 20 parameters from one and the last 34 parameters from the other and vice versa to make two kids. Then I “mutate” some of the kids “genes” by adding a random number to one or more of the parameters. Then I run them through the fitness test and the next generation repeats.

In this case the fitness test I used was the max probability (of one of the contiguous groupings) minus the min probability. I got the probabilities by adding the side probabilities involved in each contiguous region. Those I got from the 100,000 rolls that I did earlier. If the max-min goes to zero, then all the probabilities are equal and I’ve got a perfectly fair die. That never seems to happen, but after 1000 generations I tended to get decent results

Before talking about what I mean by “decent” here’s a pic of my fairest 5 sided die followed by a panorama of all my dice so far (again, they’re all made up of the same 36-sided die, just with different groupings of sides painted)

5 “sided” die made from a 36-sided unfair die
top row: 3-, 4-, 5-, and 6-sided fair dice
bottom row: 7-, 8-, 9-, and 11-sided fair dice
For all the die is shown on the bottom and the sides are broken out.

What is “decent” or close-enough to fair?

Since none of the genetic algorithm runs ever ended with a fitness of zero, none of the dice in the image above are strictly fair. But what’s fair enough? My kids and I decided that no one would really notice if after a few hundred rolls it seemed like the sides were roughly fair. That can be quantized a lot better, of course, but that’s the gist of what I did here.

Lets say you rolled a fair 7-sided die a bunch of times. What would the histogram of the rolls look like? If you rolled it an infinite number of times every side would come up 1/7th of the time. But you’re not going to roll it that often. If you only roll it 100 times, you might expect each side to be rolled 14 times with two of them being rolled 15 times. But you don’t usually find that. Instead you get more variability that you expect (or at least than some of us would expect). Counting statistics (or Poisson distributions if you like) would suggest that the typical variation after 100 rolls for each side would be the square root of 100 divided by 7 or roughly 3.8. In other words, most of the time the sides would be off from the expected 14 by 3 or 4 (either high or low – obviously the sum of the sides would be 100 still).

Ok, so what if you are suspicious that it’s not fair? Well, you can roll it a bunch of times and check the result against what the fair statistics would suggest. If you do it 100 times and you get a bunch of results within 3 or 4 of 14 you’d have to admit that it still seems fair. Of course if you’re patient you could roll it 1000 times. Then you’d expect each die to roll 142 or 143 with a typical spread of 12. Don’t freak out that 12 is bigger than 3 or 4. What really matters is the relative spread. 12 divided by 142 is smaller than 3 or 4 divided by 14.

So what I did was look to see how many rolls you’d have to roll my not-quite-fair dice to see results that start to look suspicious. The very worst of my dice would need over 500 rolls for that to happen. I guess I think that’s “good enough.”

Of course there are much more formal ways to do this. Mathematica provides DistributionFitTest for just this purpose. You can use it by providing a set of rolls of a die and ask the chance that the rolls came from a perfect die. It returns a p-value that can be interpreted as exactly that chance. Of course every 1000 rolls is different, so if you rerun the command with a different set of rolls you get a different p-value. That’s why what I’ve got below are histograms for each die where I rolled 1000 rolls 1000 times each. The x-axis is the p-value it found and the y-axis is the probability.

p-value histograms for each die with 1000 rolls

Note that doing the same thing with perfect rolls yield a graph similar to the 7-sided curve. Really the only one that’s not great on this scale is the 11-sided die. Note also that if I do this for an un-optimized contiguous side set you nearly always get a p-value less that 5%. This shows that I really needed that genetic algorithm.

Next steps

I’d love to 3D print my 36-sided die a few times and paint the sides. I bet I’d find some D&D folks interested in buying them.

I’d also like to figure out why I can’t do 10-sided. Mathematica crashes every time I run the genetic algorithm. I really can’t figure out what’s going on.

I’d love to figure out if you could predict the side probabilities from some physical measure of the die. Obviously side area, side volume, and side solid angle don’t do it, but maybe some other measure does. One thing I’ll try checking is looking at the effective depth of the potential energy dip for each side. What I mean is: to topple from one side to a neighbor, you have to make the die go up on an edge. This has a gravitational potential energy cost. Each side is a triangle and so you could get three measures of that for each side. Wouldn’t it be cool if the actual rolling probabilities tracked with that measure! Then I wouldn’t have to spend a week calculating those probabilities and I could really do some fun stuff.

Your thoughts?

Here are some starters for you

  • I think this is really cool. What I especially liked was . . .
  • This is really dumb. Here’s why . . .
  • Why do you call it a “fitness function” when you’re clearly minimizing. Try calling it a cost function, jerk.
  • I ran FindGraphPartition and occasionally got partitions that aren’t contiguous! What sort of magic did you do to fix that? (answer: updated the fitness function to make sure those got huge costs – used ConnectedGraphQ on a graph subset)
  • If you can’t make perfect dice, I’d never pay for them. You should say that more clearly at the top of this dumb post
  • Why do you bother with contiguous groupings? Couldn’t you just use random groupings and print them with the appropriate number in each triangle? (answer: I do get better p-value results this way, but my kids think contiguous is cooler)
  • I think you’ve succumbed to p-value abuse. You clearly run it over and over again until you get what you want. Hence the histograms.
  • I think you idea about the potential energy measure of a side has merit. Here’s what I’d do . . .
  • I think I know a different physical measure that will predict the probabilities. Here’s what it is . . .
  • There is no physical measure that will work. You’ve got to really roll them. I think you should pick a random shape, 3D print it, roll it 100,000 times yourself, look at the probabilities, then make a tiny change and repeat.
  • I don’t think a genetic algorithm was the best choice here. Instead I would . . .
  • All the Mathematica advertising gets old. I’m pretty sure I could do all this with my TI-84.
Posted in fun, mathematica, physics, research | 4 Comments

Lifelong computational skills

I’m frantically putting together my syllabus for our brand new Computational Data Science intro course (this comes after a programming course) and I realized that I’m not using one of my favorite syllabus planning tools: this blog!

This course was proposed and is listed in the bulletin thusly:

Title: CDS 1020 Introduction to Computational Data Science

Goals: To continue the study of computational techniques using Python, with an emphasis on applications in data science and analysis.

Content: This is a continuation of CDS 1010, applying algorithmic thinking to applications in data analysis. Topics include data mining, data visualization, web-scraping.

Prerequisite: CDS 1010

I’m really excited to teach this course, especially as it’s been a year and a half since teaching an in-person class (I teach one class per year in the dean’s office and last year I taught a fully-online course). However, I’m feeling the pressure to make sure this is a strong course and I have some things I’m grappling with right now. This post is trying to put my thoughts and questions down around the idea of skills/approaches/ways of thinking that I want my students to really own after this class.

Cool now versus later

As I’m looking at all kinds of cool ways to show students the power of computational approaches to data collection, analysis, communication, and use in decision making or story telling, I’m trying to think about what it takes for students to use those tools beyond my class. For example, while there’s lots of tutorials (like this cool one about Natural Language Processing in python) I’m sure I can help my students get running while they’re in the course with me, I’m not sure they’ll feel like they could really use that tool without my scaffolding handy. Instead, possibly I should focus on skills or approaches that would better empower my students, even if they’re not as powerful.

The nltk library for python is very powerful and doing some work with it during my course would likely cause students to appreciate its power as it helps them do cool projects. However, I’m nervous that the learning curve associated with it might make them not want to reuse it on their own time after my course. Of course the students that really dive in to our new Computational Data Science major might, but I’m not sure they’re my target audience for this first time through.

In my physics teaching, this reminds me of our work trying to get students to do automated data collection and experimental control using first LabVIEW (yes, that’s how it’s spelled) and later arduino. I was a huge LabVIEW user all through grad school and we had a mini-site license when I first started here. In our Modern Physics lab we taught the students how to use it and got them to do some interesting things in that course. However, we started to notice that students were not reaching for that particular tool the next year in our Advanced Lab. In that lab they design and execute their own team-based year-long projects, often based on ideas they’d find in the American Journal of Physics. We would hear things like “oh we’ll just manually record that data because it’s too hard to get the LabVIEW stuff working” or “I don’t remember how to install all the right things to get LabVIEW working so we’re not going to bother.” Later we switched the modern physics lab over to arduino, in the process reducing the complexity of the things they were interfacing with. Suddenly nearly all the projects in Advanced Lab were at least brainstorming ways they could get the arduino ecosystem to help them. So my lesson from that was that a slightly inferior tool set that has less logistical on ramps led to students using it more in the places we were hoping for.

Types of things I’m considering

Here’s a short list of the types of things I’m talking about and that I’m trying to make decisions about:

Tough on-rampEasy on-ramp
nltkregex (possibly starting with simple spreadsheet commands)
twitter apicopying and pasting from twitter search (and then some sort of analysis)
list comprehensionsfor loops
setting up local databases and using python to manage and analyzeUsing simple spreadsheets and perhaps google apps script to manage and analyze
Things I’m thinking about

Certainly I would choose the tough on-ramps if I knew for sure my students would be majors and would have someone like me around to both help them use the tools and cajole them to consider them when they’re doing complex projects.

For students who might not be majors and who I would hope would use computational approaches to decision making and story telling in the future, I might choose the easier on-ramps, even though in nearly every case above it’ll be limiting.

My guess is I’ll oscillate between those columns as the semester goes along.

Your thoughts? Here’s some starters for you:

  • Glad to have you back in the blog-o-sphere, where have you been?
  • This sounds like a fun class, can I sit in?
  • This sounds like a dumb class, can I lobby to have it cancelled?
  • I like the _____ on ramp things and here’s why . . .
  • The LabVIEW/arduino example is great, here’s a similar example from my work . . .
  • The LabVIEW/arduino exaple is dumb and doesn’t apply to this at all, here’s why . . .
  • As usual you couldn’t even bother to google some clear answers to these problems. Here’s several articles you should have read before even writing this drivel: . . .
  • Here’s some things I’d add to your table . . .
  • Wait, are you going to actually teach a python class? No Mathematica? I don’t believe it.
Posted in arduino, programming, syllabus creation, teaching | 8 Comments

Virtual Physics Conference

I’m part of a grant team right now brainstorming a new project, and a part of it is potentially hosting a conference. We kicked around some ideas about it, and as usual in situations like this, we casually talked about what a virtual conference might look like. That got my brain going so I thought I’d get some thoughts down here.

My goal: A virtual conference for physics teachers to be help potentially in the summer of 2020.

Whenever I’m a part of conversations like these, the typical pros and cons list look like this:

  • Pros
    • Cheap (I almost stopped this list here)
    • Flexible
    • Comfortable
    • Wider reaching
  • Cons
    • Not as immersive
    • Missing “hallway conversations”
    • Less connections
    • Less commitment from participants

I’ve been thinking about all of those and I think I’ve thought of at least a beginning of a plan that address all of them. Certainly the pros will still be there, but hopefully it’ll be an experiment worth doing if we can address the cons at least to some degree.

Technology

I’ve used a ton of different technology for doing meetings like these. Back in the glory days of the Global Physics Department we used both Elluminate Live and later Blackboard Collaborate (really the same software, just bought out by Blackboard). Since then I’ve used WebEx, Google Hangouts, and Zoom a ton and I’ve occasionally used others as well. For this experiment, I would mostly want a reliable technology, and the one that I’ve had the most luck with there is Zoom. But below I’ll lay out what I think the needs would be.

Participants at a minimum would need a computer/phone with decent internet speed and speakers. A microphone would be great and a camera would be too, but I think I’d be open to where we’d draw the “necessary” bar.

Speakers would need audio and video and screen sharing capability. It’s possible we could ramp up to something like dual monitors or something but I’m definitely open to suggestions.

Rough outline

My vision is something like this:

  • Parallel sessions
  • ~5 speakers per session
  • 4 sessions blocks in a day
  • A single day

Immersion/Commitment

This is the toughest nut to crack, I think. The longest online conferences I’ve been in were 8 hours long and it was hard to stay focused. So what would it take to get people to stick?

Taking the outline elements from above: Parallel sessions allows people some choice. Certainly at in-person conferences people really appreciate that, especially when a session doesn’t have what you’d thought it was going to have. ~5 speakers per session makes it seem like you could potentially hold all that info in your head at a time and really have a great conversation going. Four session blocks in a day just seems reasonable and one day is a great start for this experiment, at least I think that’s true.

Addressing issues like “my favorite part of conferences are the impromptu conversations that happen between sessions” is something I’ve been thinking about a lot. I think it would be great if we had technology that allowed the following:

  • Every session has a Zoom room (I’ll just use zoom vocabulary here to simplify) with a main speaker at any given time but a running commentary that people can participate in.
  • Questions will be submitted and voted on during each talk so that speakers can answer them in a crowd-prioritized way.
  • Discussion will use software like my “my-turn-now” software that allows for equitable discussions.
  • [This one I don’t know about existing solutions] This one is what I’ve been thinking would help the most with some of the cons above. I call it “hallway conversations.” I want any two-or-more groups to be able to spontaneously spawn a new zoom room. They would get video conferencing, a chat board, and a white board. They could welcome anyone else in who “knocks” and they could choose to be either public “Andy and Super-Cool-Person’s room” or private.
  • Drop in rooms for common topics
  • You’d get a personal recap record of every room you were in along with whatever contact info people in that room were willing to share. You’d also get a chat transcript and any whiteboards.

Imagine sitting in your pajamas with a beer and seeing that people you are excited to meet are in a public room. You knock and they let you in! You then can meet them and either hang at the periphery to just listen or jump right in. Kind of sounds like an in-person conference, doesn’t it? The originators could leave and the room would still exist until there’s not at least two people in it. The personal recap record would really help you maintain any contacts you’ve developed.

My other big idea is meals, specifically lunch. I envision partnering with something like Door Dash to get everyone a meal at the same time. They’d pick their meal at registration (possibly even same day, I suppose) and then it would be delivered to everyone at the same time (yes, I know, there’d be some time zone problems but I think it might be cool enough to convince west coast people to eat at 10). There’d be Zoom rooms for every type of food. You’d be in a video conference with anyone else eating “at the same restaurant” and you could hopefully be involved in some fun conversations (and of course you could still launch a “hallway conversation” if you wanted to).

Cost

This couldn’t be free, as the Zoom cost won’t be zero. But it would surely be cheaper than gas/plane + hotel that a normal conference would have. If we had 5 parallel sessions and 5 speakers in each session and 4 session blocks that’s 100 people. If we charged $100 per person that would be $10,000 which might be enough for the Zoom ideas above. I plan to research this a lot more.

Flipped?

A collaborator of mine shared this white paper from the University of California system that talks about an approach to virtual conferences that sounds a lot like a flipped conference. Speakers record their talks ahead of time and each talk has a discussion board associated with it. I think that’s a cool idea, but I’ve always been unable to get my cognitive energy focused like that ahead of a meeting. The plan above allows you to come in cold (with the exception of your own talk of course) and just let it flow over you dynamically. I’m curious what others think, though.

Your thoughts?

So that’s where I’m at with my brainstorming. Your thoughts? Here are some starters for you:

  • I love this idea, where can I sign up? I just had a couple of thoughts to make it better . . .
  • Um, ever heard of google? This exists and is called . . .
  • If I can’t shake someone’s hand I don’t think it’s a real relationship. How are you going to do that?
  • Love the “hallway conversations” but I think you’d also have to think about . . .
  • $100?! Way too _____. Instead you should . . .
  • I would love to facilitate a session. Can I shoot you some ideas? Who’s on the committee?
  • Could we do a poster session too? I have some ideas about how that could work
  • Door Dash exploits their delivery people. Instead think about partnering with . . .
  • Here’s an interesting way to mix your ideas with the flipped conference ideas . . .
Posted in community, glodal physics department, teaching, technology | 8 Comments

Google Apps Script Physics Problem Database

I tweeted out the other day an opinion about using google apps script (GAS from now on) as a web framework:

That led to some follow up from my awesome tweeps, including a nudge to write this blog post, so here you go.

This post will be mostly about how to use GAS as a data-driven, responsive website, with the Physics Problem Database really just the example I put together to show things.

Why GAS?

A data-driven website needs to store and retrieve data. Most of my other projects tend to use mysql databases for that (and PHP (yes, stop laughing and look up Laravel) for the html/interfacing) but that approach can have a pretty big startup cost (mental energy and time, not necessarily money). I certainly know how to spin up a new Laravel site and set up a new mysql database, but I know that’s a huge barrier for folks who want to just build something small-ish.

I’ve been using GAS for a long time now to help automate certain tasks (and you’ll note at that first link that I’ve thought about GAS as a website driver before – the difference in this post is that I don’t bother with the sketchiest part of that post in this new work – namely using the query command in a new sheet all the time). The way it can interact with a spreadsheet is what’s really driving this post. Basically I’m exploring how you might use a spreadsheet instead of a database to really get something up and running.

Benefits?

  • You don’t need a server! Or even a coding environment. I did nearly all of this coding on a chromebook because all you need is a google account and they provide the IDE (integrated development environment), the storage of the “database,” and the hosting of the pages
  • The “database” is a very user friendly environment. What sql would call tables, I just call different sheets. It’s very easy to see, edit, and delete the data in the “database”.
  • Both the server-side and client-side code is javascript. I’m not necessarily praising the language here, though it is fun to code in, but rather mostly praising the fact that you only have to know one thing (plus html, of course).
  • Authentication is basically built in. See below for more on that
  • AJAX (or the ability to update or query the “database” without reloading the whole page) is particularly easy

Drawbacks?

  • It’s not super fast. You’ll see how the physics problem database takes about ~5 seconds to load.
  • The spreadsheet can only get so big. I believe the relevant quota is 5,000,000 cells. I would guess that you could do fine with 1,000 – 10,000 main records.
  • You have to build your own unique ids, whereas sql will normally just do that automatically. You have to do this rather than just finding the row things are on to protect against someone changing the order of the cells in the spreadsheet (deletions, adds, sorting, etc). I suppose if you make it so that you’re the only one who can access the spreadsheet and make a promise to yourself never to change the record order, then you could skip this. This is especially important if you do some one-to-many or many-to-many relationships among the sheets.

Now I’ll shift over to using the Physics Problem Database as context to explain how you can stuff.

Physics Problem Database

Years ago the Global Physics Department put a fair amount of effort into a physics problem database. We thought it would be fun to both build such a thing for teachers to use, especially those doing Standards-Based Grading (who often have to give students new and different problems to try) *and* to help our members learn how to code. While a ton of people were interested, the barriers of learning how to get a database-driven webpage running were tough. So I thought I’d use that idea as context to really push this GAS approach.

For those of you who don’t care about what I have to say below about what I learned in doing this, here’s the direct link to the GAS Physics Problem Database

Goals:

  • Display physics problems that people could use
  • Allow only authenticated uses to be able to add problems
  • Develop a tagging system with a limited number of approved tags

The first thing I did was decide the data structure. After minimal thought, here’s what I came up with:

  • Problems
    • unique id
    • problem
    • user id
    • date
  • Tags
    • unique id
    • tag
    • user (didn’t end up using this)
    • date (didn’t end up using this)
  • Users
    • unique id
    • email
    • name
    • date
  • Problem_tag (this is the Laravel naming convention – it’s what some call a pivot table since this facilitates the many-to-many relationship between problems and tags)
    • unique id (not sure this is necessary)
    • tag id
    • problem id

Next I started by making the page that would just display all the problems. I wanted the display to show the problem and any tags that go with it. I think I meant to show who wrote the problem too, but I don’t think I coded that yet (though it would be super easy to do).

Ok, so how to manage the data? What I decided to do was to just load all the data in all the sheets into a massive javascript object. I actually do this a lot with other GAS projects that I work with. It seems that several hundred rows of data works just fine, so I think this is at least somewhat scaleable (which google insists is spelled wrong, by the way). Here’s the code that does that:

function loadData() {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheets=ss.getSheets();
  var whole={};
  for (i=0; i<sheets.length; i++) {
    var data=sheets[i].getDataRange().getValues();
    // creates object with column headers as keys and column numbers as values:
    var c=grabheaders(data); 
    var list=data[0];
    ob={};
    for (j=1; j<data.length; j++) {
      ob[data[j][c["unique"]]]={};
      for (l=0; l<list.length; l++) {
        ob[data[j][c["unique"]]][list[l]]=data[j][c[list[l]]];
      };
    };
    whole[sheets[i].getName()]=ob;
  };
  return whole;
}

That produces and returns an object called “whole.” It has a key for every tab in the spreadsheet. The value for each key is an object with keys set to the unique ids. The values of those are objects whose keys are the the column headers in that tab. Say you wanted to find the problem associated with a particular problem_tag relationship. You’d get it with whole[“problems”][whole[“problem_tag”][unique-number-you-care-about][“problem id”]]. I know, it’s hard to read, but you can navigate all relationships this way.

How do you send that to be parsed in the html document? First note that all GAS projects can be made up of javascript documents and html documents. They’re all actually stored in the single script document. I use templated html where you can intersperse <? useful server-side javascript ?> into your html. So the table for the problems is done with this code (ugh, the html syntax highligher is failing on all of the “>” characters, replacing them with &gt – sorry about that):

<table class="table table-striped">
     <thead>
      <tr>
       <th>Problem</th>
       <th>tags</th>
      </tr>
     </thead>
     <tbody>
      <? Object.keys(data["problems"]).forEach(function(key) { ?>

       <tr>
        <td><?= data["problems"][key]["problem"]?></td>
        <td><?!= findTags2(key,data) ?> </td>
       </tr>
      <? }) ?>
     </tbody>
    </table>

The “forEach” part is going through all of the problems in the problems object (also note that I’m passing “whole” as “data” – don’t ask why.) Then each one adds a row to the table, displaying the text of the table with data[“problems”][key][“problem”]. Then it runs a function (on the server, before the page is rendered) called findTags2 that accepts the key (unique id for the problem) and the full data object and then returns a list of hyperlinked tags that, when clicked, show a page with just problems with that tag. That page does that filter by doing the “loadData” above and then deleting any elements that aren’t connected to that tag before sending data to a very similar html page. Note that to add in the creater of the problem I would just add something like <td><? data[“users”][data[“problems”][key][“user id”]][“name”] ?></td>

The only other thing the page does right now is allow authenticated users to add problems. That page is given all the tags and grabs the user’s email (you have to be logged into a google account to use the page). There’s a simple text entry box for the problem and the user can then select any appropriate tags. When they hit submit there’s an AJAX call to update the spreadsheet. All that means is that the page doesn’t have to reload to do it. The data is sent to the server, it updates the spreadsheet (in several ways – see below) and then returns a note saying it was successful. That updates some text on the page. It all takes about a second. The spreadsheet updates are:

  • Put the problem into the “problems” tab. For that you can use the “append row” method in Google’s SpreadsheetApp. For the unique id I just use the number of milliseconds since January 1, 1970, making the assumption that I won’t run the script twice in the same millisecond.
  • Then the “problem_tag” tab is updated, with a new row for every tag that was checked by the user. This is where I use the unique id for the problem (the unique id for each tag is embedded in the form to allow them to be passed to the server correctly).

The authentication is super easy if you’re doing this in a google-school domain. Basically you set the script to run as you (the developer) and use the users tag to check to see if the user email (that google provides for any user visiting the page) is in your approved list. That way you’re letting google do all the authentication (they have to be in your domain) and you can only allow those who are in your users tab to be able to even access the page.

Unfortunately the authentication is a little harder for normal consumer google accounts, but still doable. Unfortunately the command that returns the visitors email only works if you allow the scripts to be run as the person visiting the page. That means they need access to the spreadsheet, something you don’t have to do in the domain version. What’s cool, though, is that you can just give the whole world “view” access and this script will still work. What you have to do in addition to updating the “users” tab is to give those people “edit” access to the spreadsheet. Then everything works!

When users visit the page for the first time they have to go through a permissions check. Basically google checks your script to see what things you’re doing and makes sure the user is ok with that. The first time I did what’s described above for my consumer google account I noticed that the permission warning said that the script would have the ability to view, edit, and delete any of my drive files. Now I know I’m a trustworthy guy, but I figured even my friends would have a problem with that. Luckily I found this page that made it clear you can limit the access to just the associated spreadsheet, something I already was doing by giving them “view” access! Problem solved.

So, I think I’ve got a roughly-working beta version up and running. Please let me know your thoughts. Here are some starters for you:

  • I like this, especially how I could develop a web page typing a new line on every computer I stumble onto without having to load a full development environment.
  • I hate this: I need to do all my coding on my own local machine before even thinking about putting it up on the web. It’s too bad there’s no way to do that with GAS.
  • I like this but I’m nervous about whether it would scale. Why haven’t you just pasted in a bunch of nonsense problems to see when it breaks?
  • I got a “you’re not authorized” message when I tried to hack in and load a bunch of crap into your crappy database. Can you please give me access?
  • Your tag choices are dumb. Instead I think you should use . . .
  • I think you didn’t need to bother with restricting the permissions scope to just the one spreadsheet. I trust you!
  • If I’m at a google school can I build something that people outside of my domain could use?
  • Can users select problems and save them? Print them? LaTeX them?
  • What happens if you share the script with someone? Can they collaboratively edit? At the same time?
  • I’ve been laughing so hard at the fact that you sometimes code in PHP that I haven’t been able to digest the rest. Can you make it a flash video and put in on your myspace page?
  • I think it’s dumb to load the whole spreadsheet into memory. Just load in all the unique numbers and the rows they’re on and load stuff when you need it!
  • I just tried to email you about this at your job and got an away message saying you’re on vacation. You do this crap for fun?!
  • I see you have LaTeX in one of the problems. Are you just using MathJax?
Posted in HUWebApps, physics problem db, programming | 6 Comments

Shooting circuits

I’ve posted before about how I struggle teaching complex circuits (really just circuits that contain batteries and resistors in ways that can’t be analyzed with parallel and series tricks). There you’ll read about how I find that if I just give my students one of the unknowns for free it allows them to show me how well they understand the basic principles of circuits without getting bogged down in the math of, for example, five equations and five unknowns.

I’ve shared the ideas from that post a bunch and occasionally I get feedback that it robs students the ability to actually solve the circuits from scratch, since I’m giving them one of the unknowns for free. This post is about thoughts I’ve had about that, including some more substance to my ideas at the end of that post about guessing and checking.

Bridge circuit

The gateway drug that demonstrates the need of tools beyond series and parallel tricks is the bridge circuit:

Typical bridge circuit

The problem with this circuit is that you can’t model the resistors as a combination of series and parallel elements. Go ahead, try, I’ll wait!

… nope R1 and R2 are not a parallel pair

… nope R1 and R4 are not a series pair

… etc

Ok, now that you’re on board with that, the question is how to analyze such a circuit using the basic principles that went into developing the series and parallel tricks, namely that current flowing into a node flows back out again (conservation of charge or “no piling up!”), batteries raise the voltage from one side to the other by the EMF of the battery, and resistors reduce the voltage from one side to the other in a way that’s proportional to the current flowing through them (and the proportionality constant is conveniently named “resistance”).

Other answers to that question include:

  • Kirchhoff’s laws (do a bunch of loops and a bunch of nodes and hope you have the right mix that enables a successful linear algebra solution)
  • Mesh approaches that are really the same thing, with just a little different focus
  • Go in the lab and measure everything

My answer, as noted in that last post (it was 5 years ago!), is to make a guess for one of the currents and then follow through the ramifications of that guess until you reach a discrepancy. For the circuit above, for example, I would (note that when I say “voltage” I actually mean the voltage difference between that point and the bottom of the battery):

  • Start by making a guess for the current through R1
  • That enables me to calculate the voltage at the left node
  • That enables me to calculate the current through R4
  • Those two currents enable me to calculate the current through R3.
  • That enables me to calculate the voltage at the right node
  • That enables me to calculate the current through R2 (because I know the voltage drop across it
  • HERE COMES THE COOL PART
  • That enables me two ways to calculate the current through R5:
    • One way is to consider the voltage drop across it (which we know) and then determine the current
    • The other is to use the current flowing into the right node and make sure nothing piles up

Unless you make a lucky guess, those two calculations will not be the same. I’m calling their difference a “discrepancy”.

So what now? Well, as I stated in the last post, do all that again with a different guess and find out how the discrepancy changes. Since it’s a linear circuit, you then “just” need to extrapolate from those two data points to find out what guess would yield a zero discrepancy.

When I wrote about this 5 years ago, I gave a nod to the fact that it’s a lot of work to do all that. But now that I’ve actually tried it a few times, it really isn’t! The first pass is when you establish the relationships, and the second is easy if you use a tool like a spreadsheet. It also turns out that if your first guess is zero and your second guess is one the extrapolation is really easy as well.

What I mean by that last point is that if d0 and d1 represent the two discrepancies for a guess of zero and one respectively, the correct current is simply d0/(d0-d1).

Here’s an example. Let’s say that R1=1 ohm, R2 = 2 ohm etc and that V=10. Here’s the first pass assuming the current through R1 (labeled I1) = 0:

  • I1=0
  • Vleft=10
  • I4=10/4=2.5 down
  • I3= 2.5 left
  • Vright= 10+2.5*3 = 17.5
  • I2=(17.5-10)/2=3.75 up
  • I5a=17.5/5=3.5 down
  • I5b=6.25 up

So d1=6.25 – (-3.5)=9.75 (also note that Vright gives you a clue this is a bad guess since you wouldn’t expect any part of the circuit to have a voltage higher than the battery)

Here’s the second pass with I1=1:

  • I1=1
  • Vleft=10-1*1=9
  • I4=9/4=2.25 down
  • I3=2.25-1=1.25 left
  • Vright=9+1.25*3=12.75
  • I2=(12.75-10)/2=1.375 up
  • I5a=12.75/5=2.55 down
  • 15b=1.25+1.375=2.625 up

So d2=2.625-(-2.55)=5.175. Getting better.

That means that the correct current through R1 is 9.75/(9.75-5.175)=2.13 amps.

Yes, that seems to have gotten ugly, I admit. But repeating identical calculations is what spreadsheets are built for. Here’s one I built for this problem (note that I decided down or right would be considered positive):

Cells B2:D9 have the formulas indicated in column A. The yellow cell has the formula B9/(B9-C9)

Note the zero discrepancy in cell D9! Hmm, I wonder if certain people in my life will read that last sentence and let me have it.

So now I’m starting to think this method has some merit. We’re always talking about the value of spreadsheets in physics teaching (usually lab, but still) and now with this approach you’ve really only got to see what students do for the formulas in column B to see if they get the physics!

Not only would you look at their formulas, but the order they go through the circuit is important and makes me feel that this approach is closer to “problem solving” than “exercise” that Ken Heller is always pestering me about. What I mean is that in the usual Kirchhoff procedure students are given an excellent algorithm that has simple choices involved: What loops and nodes should I do? What direction should I go around the loops? Contrast that with carefully seeing what new piece of information you can discern from the previous step as is needed in this method. I think it involves more decision making. It also has some great teachable moments like above when I pointed out a voltage that was higher than physically possible.

Why I call it shooting circuits

I was sharing this approach with a colleague yesterday and she said it reminded her of the shooting method for solving second order differential equations. Here’s an example of how I use that to solve for the quantum states of a hydrogen atom. In that method you start with a guess of the wavefunction at one side of a quantum well and then look to see how it screws up on the other side. Then you make an adjustment to your guess and try to extrapolate the results so that it doesn’t screw up on the other side.

So this is a lot like that. What the heck, we’ll call it shooting circuits!

Series/parallel comparison

Consider this incredibly common circuit:

A typical circuit used to apply series and parallel tricks

First let’s consider the work necessary to calculate the current through all the resistors:

  • Combine R2 and R3 into Req1
  • Combine R1 and Req1 into Req2
  • Determine the current through Req2
  • Recognize that the current through R1 and Req1 is that same current
  • Determine the voltage at the node by finding the voltage drop across R1
  • Determine the current through R2 and R3 similarly using the now known voltage drops across them.

It’s interesting that many students think they’re done at step 3 (or possibly 2). They groan when you tell them that they still have to reconstruct the circuit to find all the currents.

Now let’s do it the new way, again using R1=1, R2=2, R3=3 and V = 10:

Similar to the previous spreadsheet but for the series/parallel circuit

So it’s 4 different statements of physics (A2:A5) and we’re done! All four of those statements demonstrate the student’s mastery of either Ohm’s law for a resistor or the node law. But remember that the order is interesting too! Can you do it in a different order? Does it work if you choose to make your guess for one of the other currents? Give it a try!

Pitfalls

I’ve been playing with this quite a bit and haven’t really found many pitfalls. One minor one involves the most basic parallel circuit (one battery, 2 parallel resistors). If you guess the current through one of the resistors you immediately get a discrepancy regarding the voltage drop across that resistor. That’s cool, as then you can apply the method, but you learn nothing about the other resistor! So then you’d have to repeat for that one, I guess. I think that means that a complex circuit that basically has two parallel parts might suffer from that problem.

Your thoughts?

Here are some starters for you:

  • I like this method, but would it work for . . . ?
  • I think this method sucks and here’s why . . .
  • What’s wrong with ending a sentence with a number and then an exclamation point?
  • What circuit drawing software do you use? They really look great!
  • Mathematicians would call this method . . .
  • Can you tell me more about how you can assume the discrepancy is a linear function of the original guess?
  • Of course you can describe a bridge circuit as series and parallel! Here’s how . . .
  • Seriously, you want students to do their homework with a spreadsheet!? You’re an idiot
  • I’m not sure I understand your pitfall situation. Can you describe it better?
  • Here are 7 more pitfalls I thought of within 10 seconds of reading this:
  • I clicked through to the old post (which you oddly called your last post – what the heck?) and gave up on you when I saw you hate Kirchhoff’s loop law!
  • Would this work for the “you have a cube made of resistors . . .” problem? I hate that problem.
Posted in general physics, physics | 8 Comments

App for facilitating calling on people

“Two posts in one day?” you ask? Yep, I’ve kind of forgotten how useful it is to organize my thoughts here and to get such useful feedback from you awesome folks.

I’ve been working on a new web app and I’m looking for ideas for how to improve it. It’s called “My Turn Now” and it helps people “raise their hands” in a discussion in a way that allows the facilitator(s) to equitably lead the discussion. The name comes from the phrase my middle kid used to say (imagine a really cute 5-year-old voice when saying it) when they wanted a chance to try something.

The problem it addresses

I was actually inspired to write it when I took over facilitating a standing committee of faculty. It only had 8-10 people on it but it was clear that a few were frustrated at how they were occasionally being ignored or talked over. I wanted the ability for me to better keep track of who wanted to contribute and to do it as equitably as possible.

It was inspired by the “raise hand” feature of so many online web conferences, most notably Elluminate Live back in its heyday. If participants hit the button the facilitator (and the rest of the “room”!) were shown the chronological list of the raised hands.

How it works

The facilitator begins a meeting and sends around a link to all participants. They’re shown a window with two buttons side-by-side. One is for “new topic”s and one is for “follow up” questions. Underneath each is a live chronological queue of each type of question, showing the name of each person who has raised their hand and how long ago they did it. Here’s a dummy example (note that this one spanned multiple days).

Example of what a user (non-facilitator) sees

This is a screenshot of user sdfdsfsd. That’s why only that “raised hand” has buttons next to it. Each user can unraise their hand or transfer their question over to the other queue.

The facilitator has a similar view but with buttons next to each that allow it to “call on” the person. Really that just removes it from everyone’s screen.

As a facilitator you can watch both queues and decide how long to let the current topic go while also watching to see how many people want to contribute.

At the end of the class/meeting/whatever, the facilitator can get a report about the discussion. Here’s an example from the first meeting I used it in a couple years ago:

Chart available to facilitator(s) after a discussion

The small text in the middle explains how to read the colorful chart. A quick impression is that this meeting spent most of its time following up a single idea because everything went blue for most of the meeting.

The chart at the top can be useful in seeing what kind of contribution each person made. It can also help you get a sense of the experience each contributor had.

Programming logistics (skip if you don’t care)

The database schema for this app is pretty straightforward. I store meeting details in one table, and hand raises in another, updating whether its a new topic or follow up and whether its been called on. The “created_at” and “updated_at” are automatically updated so the date chart above is pretty easy.

The chart uses the fantastic Google Charts API. I love using that. You just have to get your data in the right format and it just works.

The hard part was finding a way to push the data to all the participants in real time. I have played around a little with Meteor which is really good at that, but I could never get my local server working right. Luckily I dug a little in the Laravel/PHP world and stumbled on Pusher. It does all the dirty work of the crazy realtime crap, leaving me with just managing the data. Note that the free version of Pusher has a cap of 100 simultaneous connections so if I really want to extend the use of this I’ll have to start paying some money. I’d only do that if it’s worth it, of course.

What excites me about it

I know I’m not great at calling on people equitably. I also know that when I’m best at that, I’m not great at actually following the discussion. I think this could be a great tool for folks to diagnose issues with how they (or possibly their student discussion leaders?) facilitate conversations.

Feedback I’ve received has been interesting. I’ll get to the negative stuff below, but one major positive is that people love getting to know the names of people. I did it in a group of 20 or so faculty and I got exactly that feedback. It was interesting because I just assumed they all knew each other.

I think the chart/roundup could be really useful in diagnosing lots of things:

  • How much did everyone contribute?
  • Who has to wait the longest on average?
  • Are there patterns to who I call on?
  • Do I spend too long on single topics?

I also think that having everyone see just who and how many are interested in participating can help people self-regulate their own contributions.

If someone is way down the “new topic” queue but realizes their point meshes with the current conversation topic, they can hit “transfer” and likely move way up because that queue might be shorter. Similarly if the current topic goes away from your follow up, you can shift over to the new topic queue.

Problems

Other, shall we say less-positive, feedback is mostly about how unnatural it feels. People really like to 1) just start talking and/or 2) physically raise their hands, often while using body language to indicate the relevance of their particular contribution.

There were a lot of technical problems with version 1.0 (small buttons, hard to see, duplicate names, etc) but I’ve mostly cleared those up with version 2.0. I’m not really as worried about those I guess.

What’s next?

So now I need help.

  • Is this something I should encourage others to use?
  • What are the best test cases for it?
  • What are the major assumptions I’ve build in that I might be blind to?
  • What student populations might be helped? hurt?
  • What should be added? Subtracted?

Here are some starters for you:

  • I think this is cool! Can I use it? I’m excited to use it in . . .
  • I can’t believe you ripped off my idea. Ever heard of Google? Use it, jerk.
  • I like the chart, especially the part that . . .
  • I hate the chart. Instead you should . . .
  • I checked out Meteor and Pusher. They suck. Instead you should . . .
  • Why don’t you just write an iOS app?
  • Why don’t you just write an Android app?
  • This assumes students have smart phones. You need to stop assuming people have those.
  • Wait, you program in PHP. Last post I’m ever going to read of yours, goodbye.
  • Why don’t you write this in Mathematica?
Posted in programming, teaching | 3 Comments

Talking to parents of admitted students

One of the roles I have in the dean’s office is to talk to parents at admissions events. This week I talked with three different groups of parents of admitted students the day before their students registered for the fall. I wanted to take some time to get down some of the things we talked about.

Helicopter versus snowplow parents

Right at the beginning I talk about my view of helpful parents for college students. As the director of the First Year Seminar I think a lot about this, and one of the great things about working in the dean’s office is getting to know the awesome work that my colleagues in Student Affairs (like the Dean of Students) do. They’re the ones who have really taught me to value the supportive role that parents can play.

Here are my definitions:

  • Helicopter parents
    • Emotionally supportive
    • Help students understand the nature of the choices students have
    • Ultimately help students make decisions
  • Snowplow parents
    • Clear the path of anything in the way
    • Determine the direction of the path
    • Make decisions for the students

I recognize there’s a lot of nuance and gaps in those definitions, but they get me pretty far when talking with (mostly nodding) parents. Some people like “lawn mower parents” in place of “snowplow parents” but, coming from Minnesota, I really think about those times when you’ve gotten a foot of snow and only have time for a quick path. You define not only where you are going to walk, but where your mail carrier is going to walk, where your kids are going to walk, and even where the pets are going to walk. My colleague rightly points out, however, that snow plows often follow defined paths whereas lawn mowers can create very strange but well-defined paths. Regardless, the big deal is who makes the decisions.

As I talk about various signs of success that parents can watch for, I like to contrast how a helicopter vs snowplow parent might respond. If the student asks for help in deciding what to register for, the snowplow parent might say “you did well in biology 3 years ago, you should register for that” while a helicopter parent might ask “why did you do so well in biology 3 years ago?”

What problems do you enjoy solving?

Students at this point in their life are innundated with questions like:

  • What are you passionate about?
  • What do you care about?
  • What are you good at?

Those questions and others like them start to morph into “what are you going to major in?” While I find that question to be a part of interesting and useful conversations, I’ve started to use a different one: What problems do you enjoy solving?

Another way of asking that is to encourage students to reflect on times when they’ve looked up and been astounded to see it’s after midnight. What were they working on? Why were they so focused? Did they enjoy it?

What’s particularly interesting is how that question contrasts with the 3 above. A student might be passionate or care about something but not enjoy the work it takes to follow those passions. The simple example I use is “world peace.” People can be passionate about that, but many don’t enjoy the work it takes to achieve it. And the “are you good at it” one is particularly significant: If you know of problems that you enjoy solving, higher ed is a fantastic place to get better at doing it. Getting better then leads you to even more interesting problems! It’s not like we get you to the point where you’re awesome at something and everything is easy from that point on. How boring!

Parents can be awesome at helping students answer the question, which can then help them make all kinds of academic decisions. It can also help with the mid-October phone call that goes like this:

  • “How are things going?”
  • “Ugh, I’ve got 20 more calculus problems to do tonight.”
  • “Shoot that stinks”
    • This part is important. I learned a great parenting lesson from my sister-in-law: deal with your kid’s emotions first, then the logistics of the problem. It only has to take 10 seconds.
  • “Is this getting you any better solving problems that you enjoy solving?”

Ok, I know, it wouldn’t happen quite like that. But something close to it could happen.

Multiple doors

I also talk with parents about the delicate balance students have to achieve in keeping some doors open, shutting some, and diving through others. “What kind of problems do you enjoy solving” can be helpful with that, but I know the paralysis of wanting to keep everything open. It’s important to recognize that you have to dive through at least one and find whole new sets of doors. But if things go south and you have to back up again, are those other doors rusted shut?

My best piece of advice is to change the paradigm. Change them to windows, prop some open, whatever. Think about, for example, non-academic ways to explore those other pastures. At my institution you can take 4 classes, play in the Jazz Ensemble, play a sport, and volunteer at the elementary school across the street all at the same time. What can those non-academic experiences do to help you understand your door environment?

SEEC

I’ve written a little about the SEEC paradigm before, but I’ve found that it really helps when talking to both students and parents. Quickly, students should:

  • SEE that all ideas are connected
  • EXPLORE those connections
  • EVALUATE those connections
  • CONTRIBUTE new connections and ideas

Encouraging parents to talk to their students about this paradigm is useful, I think. Every course they take should add to the student’s “lenses” to look at the world. Every new lens helps you SEE whole new connections for an idea. Seeing them is always the first step to EXPLORING, EVALUATING, and, most importantly, CONTRIBUTING. Is that calculus homework going to help you SEEC knowledge?

It’s fun to talk to parents about what to watch for by Thanksgiving in the fall. Have they CONTRIBUTED a new idea? They should have. Either in a discussion or a paper or even a homework assignment. Certainly they should be CONTRIBUTING “big” ideas by the time they’re ready to graduate, but even in that first semester they can do it. But they have to S-E-E first, and that’s what our curriculum is all about (FYSEM, General Education, and Majors all do that).

Signs of success

Here are a few of the “signs of success” I encourage parents to watch for:

  • Being able to articulate what they’re up to using the SEEC paradigm
  • They should have had at least one personal conversation with every instructor they have by Thanksgiving. Typically at my institution the biggest class they’ll have is around 40 and I know my colleagues can handle this.
  • Are they owning their education? Do they turn the lights on in the classroom or wait for the instructor to do it. Are they EXPLORING cool connections that a new lens they’ve developed lets them?
  • They should average a new faculty or staff member name on their “forever list” every year.
    • “forever list” is my shorthand for that list of people you keep contact with. It’s your holiday card list, or the list of people you’d consider inviting to your wedding. I encourage parents to ask students if they’ve added one to the list around April of their first year. They really should be making that strong of a connection with a faculty or staff person every year. Admittedly Facebook has changed this equation a little, but mostly people get what I mean when I say this.

In addition to those signs, it’s helpful to talk to parents about the W curve. It’s a plot of how settled/happy/adjusted students are at college in their first term and it looks like a ‘W’.

Your ideas?

Thoughts to add or subtract? Here are some starters for you:

  • Thanks for this, it really helps me. What especially resonated was . . .
  • What a waste of time. I could have written this myself, but I would have changed . . .
  • Helicopter parents are the bane of my existence. Why are you praising them. Please take this post down.
  • Here’s a few more descriptions that can fill out your parent spectrum . . .
  • What did that last commenter mean by “parent spectrum”?
  • I think “follow your passion” is a much better way to talk to students and here’s why . . .
  • I think “follow your passion” has harmed some students. I’m not sure I like your approach any better but that last commenter was a little over the top so I just stopped by to say thanks for giving me something to think about.
  • I liked what you said about balancing open doors. Here’s what’s helped me with that . . .
  • Students should know the one door they want to go through before enrolling. It makes things much easier.
  • I think it should be SEECC with the second C being “communicate”
  • SEECC is really hard to pronounce. What was that last commenter thinking?
  • I like your “signs of success.” Here’s a few that I use as well.
  • Your “signs of success” are way off the mark. Instead you should use . . .

Posted in dean | 4 Comments