Here are three minutes of a Harvard graduation ceremony and the relevant program. My cousin Adarsh is graduating and his name is quite a ways down.
I’d like to take a nap but I’ll set a timer first so I won’t sleep through my cousin’s walk across the stage.
What time should I set the timer for?
Tell us the time and your method in the comments. The winner is whoever comes closest to the time my cousin walks across the stage, without going over.
JonathanJune 28, 2015 - 7:14 pm -
He’ll walk across in about 18 minutes. But since you’ll want to get the camera ready, you set the timer for 15 minutes.
5-6 seconds per name, 70 people per page, that makes him about person 170.
JonathanJune 28, 2015 - 7:16 pm -
Argh, I meant he’s about person 150.
Kyle PearceJune 28, 2015 - 7:18 pm -
Cool video and awesome question.
My guess on Twitter was 22 minutes. Here’s my thinking:
It took about 15 seconds to get going, which over time isn’t a huge deal unless I could find a very accurate rate of change.
It took about 8-10 seconds or so to pass between handshakes early on. Then, a long name came out and stretched it beyond 10 seconds. I was thinking as well that some folks may have some special awards/recognition along the way, so that could hold up a few of the handshakes here and there. I decided to go with 12 seconds, on average, between each handshake. Although now I realize I failed to account for the fact that the speaker may get faster once she gets into a groove (or slower, if she’s as bored as Dan??).
For the number of people, I sort of eyeballed and paused the video for the first visible portion of the list and skip counted to the best of my ability. I came up with 90 names (however, I’m pretty confident that is inaccurate).
So, my thinking was:
90 people x 12 seconds = 1080 seconds / 60 seconds in a min
= 18 minutes
Then, I added a couple minutes *thinking* I may have not counted enough people in the list AND I also thought… man, 18 minutes doesn’t really seem that long…
Whew. After some thought, I’m probably way off!
Ray O'BrienJune 28, 2015 - 7:26 pm -
Hmmm. 160 or so people. Maybe 7 people per minute, since some names are longer. 70 names 10 minutes, 140 names 20 minutes. 20 more names 3.5 minutes. 23.5 minutes total.
Mark ChubbJune 28, 2015 - 8:13 pm -
Here are a few of the things I considered…
The video shows 33 names being called in 3:42. However, the video started about 12 seconds in to the footage. That means 33 names in 210 seconds. Or just over 6 seconds per person (6.36 seconds).
Your cousin is listed as the 156th graduate on the list (if I counted correctly). So he should be finished shaking hands and the next name being called in about 992.7 seconds if that rate continues (or 16minutes, 32 seconds) starting from the first name.
However, the actual time between names differs based on syllables, number of middle names/ surnames/ hyphenated names…, and the speaker’s endurance (talking for 15+minutes can be exhausting!).
As I consider her pace I decided to rewatch the video and count the number of handshakes each minute…
First minute(until 1:12 on vid) =7
Second minute = 9
Third minute = 11
I don’t believe she will continue to go faster, but I do imagine she started off slower and found a comfortable pace.
If she can hold pace for 11 people a minute the time will be closer to the 14 minute mark. (11x 14 =154). But he is the 156th name
So for my final estimation, I suggest you set your alarm 14 minutes into the ceremony. That should give you a chance to watch 1 person and then your cousin.
Can’t wait to see Act 3:)
Mardalee BurwitzJune 28, 2015 - 8:31 pm -
I see your cousin at the 156th graduate. Skipping to the end of the video, I found Mr. Corvalan at about 3 1/2 mintes. being 32nd in line, at 210 seconds, that ends up around 6.56 sec per person. Seeing your cousin as the 156th in line (I believe)… I multiplied this number by 7 sec and then divided by 60 to get into minutes. This works out to be 18.2 minutes. However, I believe the speaker, may have needed a swig of water, so I am adding an extra 1minute on to this for drink time. Total: 19.2 minutes.
KNOW: seconds, list of names, school name, can stop video to count students…
Need to KNOW: how many names per minute, proprotional or non-proportional, would a graph help solve this, extra time for special recognition or pauses (need for water, or a coughing attack) ….
And congratulations to your cousin!
Julie WrightJune 28, 2015 - 9:41 pm -
I’m guessing 11 minutes from the end of this video (after Virginia C). (Presumably your nap didn’t start while you were videotaping. But you can call my time 14:40 if you’re counting from the beginning of the video.)
My method: As an embittered W, I am aware that there is lots of ponderous gravity for A’s and B’s, then everybody gets bored and speeds things up. (OR NAPS. Ahem.)
It definitely seemed like the name-reader got faster toward the end of the video, in fact, fast enough that I doubted she would speed up any more. So I counted how many names she read in the last 30 seconds, and it was between 5 and 6… so let’s say a rate of 11 per minute.
There are 122 people before your cousin and after Virginia C., so it will take about 11 minutes to read their names. It would probably be a bit more, but I’m increasing the chances of not going over.
Michael WeingardenJune 28, 2015 - 9:55 pm -
Love it! I did the same thing during the graduation ceremony at my high school a couple of weeks ago. We had an extremely large graduating class, the sun was beaming down onto the faces of faculty (including me), there were dozens of valedictorians and bathrooms were an uncountable number of steps away. So, after they started reading the names, I did a bit of measuring and then a bit of math and predicted the time that the name calling would end. It was so nice to have some idea when we would be seeing the light at the end of the tunnel. My bladder certainly appreciated it.
I was so proud of myself for “discovering” a great, real-world application. I also have a video of the names being called for some arbitrary length of time and I saved the program as well. I am a bit envious that you published your experience first!
JoshJune 28, 2015 - 11:50 pm -
So far, there is a consensus method:
– measure the time for a sample of names
– calculate an average time per name
– multiply by the number of names remaining before cousin
Instinctively, I would use this method as well.
As far as I see, no one has spoken to the point about how to figure out how many names remain between now and cousin’s name.
Here are two other methods, based on different fundamental units than the time per individual graduate:
(1) by syllable. This model assumes the time taken for each individual is a + b s where:
– a is a fixed time per person for walking across the stage/shaking hands/etc
– b is a time to pronounce each syllable of a name
– s is the number of syllables (varies by person)
To estimate this model, we need to take a couple of different snapshots where our data set would have entries of the form:
(time, person #, cumulative syllables read)
Given this model, we then need to know the remaining people and syllables to be read before the cousin.
Note: not only does this approach take more data, it seems practically unreasonable because it will be impossible to predict how many syllables will be read in each name (the reader doesn’t read everything that is printed in the program).
(2) by column of names in the program.
between 0:05 and 3:27 (3min22seconds) the reader covers roughly 80% of a column. From that point, there are slightly more than 3 columns of names prior to the cousin. That gives us an estimate of the video clock time of
3:27 + 3:22/.8 * 3=107 + 6060/8 = 864 seconds=14:24
This approach takes the least effort, I’ll go with that estimate.
DrewJune 29, 2015 - 4:20 am -
Short and sweet – I counted 29 people in 3 minutes (I hope I didn’t lose track), so calling it 10 people per minute rounds in a safe direction. About 150 people down the program, so it’ll happen in like 15 minutes. Set the alarm for like 14 minutes.
If you’re really going to nap, the calculation needs to be quick!
ScottJune 29, 2015 - 5:03 am -
Lazy so I only watched the first part of the name calling. She rattled off four names as I watched the clock in about 28 seconds. Call it 7 seconds per name because I like unit rates and integers (and, as mentioned, am lazy). Name lengths I listened to from the program seemed to be a fairly representative sample but maybe a bit short. Appears to be about 150 names prior to your cousins. 150 x 7 = 1050 seconds. 1050 / 60 = 17.5. Add the bit of time prior to starting and a few seconds for a switch in readers as tends to be customary in larger groups like this and your at 18 minutes on the clock when your cousins name is read. 18:01 if we’re playing Price Is Right rules. ;)
SadlerJune 29, 2015 - 7:30 am -
Sampled 2nd and 3rd minutes and took the average. Counted names in one column 39 and multiplied by 4 = 156. Cousin’s position on last page and space taken by title cancel each other.
Divide 156/Average (11) = 14’10” but given that it is better to wake 10 seconds early than miss it, I would submit 14 minutes.
Leigh NataroJune 29, 2015 - 7:34 am -
The first minute was about 8 people, but the pace picked up to reading 10 name per minute after that. Your cousin is the 156th name on the list. So…about 15 min 30 seconds into the reading of names you will hear your cousin’s name. Assuming you don’t start the timer until after 3 minutes have elapsed, I would set your timer for 12 min. This would give you time to rub the sleep out of your eyes, find the program thT is now on the floor and focus your phone to get a good picture for posting on Instagram.
LiaJune 29, 2015 - 9:45 am -
At the end of your 3:30 video, they had almost made it to the end of the first column of names. They didn’t start calling names until several seconds into the video, but there are a couple of names left in the first column and all of the other columns are a little longer, so say each column takes about 3:30 to read. Your cousin is basically at the top of the 5th column, so there are 3 columns in between. You should set a timer for 10 minutes, 30 seconds so you can stop your timer, recover from your nap, and be ready to watch your cousin without risking missing it.
This is not super precise, but I think this is a situation where the calculation has to be quick to make it worth doing. Otherwise you can’t take a nap at all.
Megan SchmidtJune 29, 2015 - 1:33 pm -
I watched the 3:30 video about three times and came up with about 11 people in the first minute, 9 in the second and 10 in the third. Using approximately 10 people per minute I broke the group down into groups of 10 people. I got 15 groups with 6 left over. This puts Dan’s Cousin at about 15:36. Plus the video started at the :15 mark. So my final answer is 15:51.
Here is a link to my breakdown of groups:
CraigJuly 1, 2015 - 6:06 am -
This method definitely took longer than some of the other estimates. I’m not sure how much nap time you would have left. I created a table in Desmos that used the graduate number as the x-variable and the time in seconds when the graduate’s card was handed to the speaker as the y-variable. I recorded all 33 graduates in the video. Then I used the linear regression tool, assuming the name reading will continue at a semi-constant rate. I was given a slope of 6.1788 and a y-intercept of 12.597. I counted Adarsh as the 156th graduate. Therefore, I guess Adarsh graduates 16 minutes and 16 seconds into the name reading.
Here is a link to my table/graph:
Chuck CollinsJuly 1, 2015 - 11:44 am -
A solution and an observation.
We all agree that we have some pretty noisy data (exactly how many names per minute? and will it be the same the whole time?), so instead of going for the golden ‘one answer’, let’s look at various possible answers. Using @Megan’s data, we have either 9, 10 or 11 names per minute and 156 total people, so we can come up with 3 answers:
9/minute gives 156/9 = 17’33”
10/minute gives 156/10 = 15’36”
11/minute gives 156/11 = 14’10”
(add 15″ for the video time)
Now we can go back to the conditions that Dan has set (1) he need’s to take a nap (so we should maximize his sleep time) and (2) he doesn’t want to miss his cousin’s trip across the stage (so close but over is not good). So you might say, to be safe, take the shortest time: 14’25” on the video. But what if the reader does speed up? Maybe we should look at the results for 12/minute or 13/minute. If Dan absolutely can’t miss, then we might say ‘no nap’, but Dan just finished his PhD so sleep is very valuable, so maybe we’ll allow a 10% chance that he misses the walk just so he can get some extra winks in, and pick something in the middle like 15’51”.
The (long) point is that although “math is great because it only has the once correct answer” (usual reason why a student likes math), when you get ‘real’ and use some data, it no longer makes sense to say that we have the one answer.
(If we had the time and patience, we could produce a time for each person, and look at the possible distributions of overall time with some assumptions about the distribution of times/names, and produce a more complex model, but we’d still end up with what should be a fuzzy answer)
Scott MillerJuly 1, 2015 - 5:29 pm -
I recorded when each graduate handed his or her name card to the reader by stopping the video. Using Desmos I plotted the graduate number versus time after converting the minutes into seconds. After running a linear regression I came up with your cousin being the 157th graduate handing his card to be read at the 16:05 mark. Ardash’s name would be read a second or two after that, say 16:07. You would probably want to set your timer a little earlier so you are fully awake when your cousin’s name is called.
Several assumptions are made in the problem solving. (1) The same name reader is used throughout the graduation. (2) The name reader keeps the same pace. (3) There is no mix up that delays the name reading.
Terrific problem to engage students with.
Here is the link to Graduation Nap https://www.desmos.com/calculator/bljygbqwoa
aga beyJuly 3, 2015 - 12:23 pm -
I took the average of all submissions upthread
Dan MeyerJuly 3, 2015 - 6:50 pm -
Heh. Strong play, there. Answer coming on Monday. Happy fourth everybody, if US holidays are your thing.
Dan MeyerJuly 6, 2015 - 5:17 pm -
Many congrats to Scott & Kyle Pearce for having the closest calculations. Recap posted now.