Loading the Dice: Show and Tell

I’ve been using a set of four six-sided dice to generate random numbers for one of my classes this year, generally to establish a presentation order or things like that. We’ve had a number of students getting the same number and so we have to have roll-offs. Now in this case, the most common number rolled so far has been in the range of 17-19 but we have only generated about 18-20 rolls so, while that’s a little high, it’s not high enough to arouse suspicion.

Today we rolled again, and one student wasn’t quite there yet so I did it with the rest of the class. Once again, 18 showed up a bit. This time I asked the class about it. Did that seem suspicious? Then I asked them to look at the dice.

Oh.

Only two of the dice are actually standard dice. One has the number five on every face. One has three sixes and three twos. The students have seen these dice numerous times and have never actually examined them – of course, I didn’t leave them lying around for them to examine but, despite one or two starting to think “Hey, that’s a bit weird”, nobody ever twigged to the loading.

All of the dice in this picture are loaded through weight manipulation, rather than dot alteration. You can buy them for just about any purpose. Ah, Internet!

Having exposed this trick, to some amusement, the last student knocked on the door and I picked up the dice. He was then asked to roll for his position, with the rest of the class staying quiet. (Well, smirking.) He rolled something in 17-19, I forget what, and I wrote that up on the board. Then I asked him if it seemed high to him? On reflection, he said that these numbers all seemed pretty high, especially as the theoretical maximum was 24. I then asked if he’d like to inspect the dice.

He then did so, as I passed him the dice one at a time, and storing the inspected dice in my other hand. (Of course, as he peered at each die to see if it was altered, I quickly swapped one of the ‘real’ dice back into the position in my hand and, as the rest of the class watched and kept admirably quiet, I then forced a real die onto him. Magic is all about misdirection, after all.)

So, having inspected all of them, he was convinced that they were normal. I then plonked them down on the table and asked him to inspect them, to make sure. He lined them up, looked across the top face and, then, looked at the side. Light dawned. Loudly! What, of course, was so startling to him was that he had just inspected the dice and now they weren’t normal.

What was my point?

My students have just completed a project on data visualisation where they provided a static representation of a dataset. There is a main point to present, supported by static analysis and graphs, but the poster is fundamentally explanatory. The only room for exploration is provided by the poster producer and the reader is bound by the inherent limitations in what the producer has made available. Much as with our discussions of fallacies in argument from a recent tutorial, if information is presented poorly or you don’t get enough to go on, you can’t make a good decision.

Enter, the dice.

Because I deliberately kept the students away from them and never made a fuss about them, they assumed that they were normal dice. While the results were high, and suspicion was starting to creep in, I never gave them enough space to explore the dice and discern their true nature. Even today, while handing them to a student to inspect, I controlled the exploration and, by cherry picking and misdirection, managed to convey a false impression.

Now my students are moving into dynamic visualisation and they must prepare for sharing data in a way that can be explored by other people. While the students have a lot of control over who this exploration takes place, they must prepare for people’s inquisitiveness, their desire to assemble evidence and their tendency to want to try everything. They can’t rely upon hiding difficult pieces of data in their representation and they must be ready for users who want to keep exploring through the data in ways that weren’t originally foreseen. Now, in exploratory mode, they must prepare for people who want to try to collect enough evidence to determine if something is true or not, and to be able to interrogate the dataset accordingly.

Now I’m not saying that I believe that their static posters were produced badly, and I did require references to support statements, but the view presented was heavily controlled. They’ve now seen, in a simple analogue, how powerful that can be. Now, it’s time to break out of that mindset and create something that can be freely explored, letting their design guide the user to construct new things rather than to lead them down a particular path.

I can only hope that they’re exceed by this because I certainly am!!