I can’t be the only person afflicted with these sidebar ads. The series is notable for taking guys who have at most 7% body fat and then Hulking them out even further through some form of isometrics or meditation or whatever. They doubled down on whatever game they’re running, though, with this particular before/after set. You have to imagine it animating back and forth between the two:

The deceit here is vaguely mathematical so I asked my first class of students, “What is it selling and how does it try to sell it?” Most identified the product as some kind of weight loss formula and/or protein shake. No one identified the deceit.

So I asked my next class, “What is it selling and how does it lie?” Many suggested we were looking at two different people here, which I said was false (with about 99% certainty). One student thought the ears were the giveaway, which is true, though not the giveaway he thought they were.

I guess I’m curious a) if you notice the deceit and b) if there’s any way to translate that deceit into an actionable math unit?

Update: Yeah, it’s the distortion, which is about 17% too wide in the first image and 17% too tall in the second image. Should it worry me that none of my students caught it?

Here are my estimations of the undistorted images.

Graph: effectiveness of ad v. percent distortion.

[Update: Holy cow. They fixed the proportions in the latest ad buy.]

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

1. #### Jon

October 19, 2009 - 3:09 pm -

I’ll take a wild stab to say the deceit has to do with the “four weeks” promise–if you worked out two days a week for twelve weeks, it’d be the same as working out seven days a week for four weeks. Then again, I could be pulling things out of thin air!

2. #### Jon

October 19, 2009 - 3:10 pm -

That or stretched proportion of the picture–which now that I have posted what I did above seems to make much, much, much more sense.

3. #### Rich

October 19, 2009 - 3:17 pm -

Well, my belly button may be falling too, but it’s not because I’m getting MORE buff. Gosh, this guy’s navel seems to be a good 10″ lower after the four-week transformation. Either that, or he got stretched on the Silly Putty machine.

Of course, it might help if we had full body photos to confirm that he is still the same height as he was before the weight loss regime.

4. #### mathmom

October 19, 2009 - 4:07 pm -

His head got narrower too! Definitely changed the proportions on those photos.

5. #### GP

October 19, 2009 - 5:57 pm -

Before I even started reading the text I noticed that the one on the right has a much longer torso. As for an actionable math unit… percent change in shoulder width to torso length ratio or something?

6. #### Kate

October 19, 2009 - 6:43 pm -

The math problem here may be found in the percent of change in the body proportions from picture one to picture two. Using photo editing programs such as iphoto students can take pictures and recreate the dimensions and change ratios.
Also, their are significantly more tattoos one the man in picture two. How many hours of tattooing…how long for healing, color fade…I am certainly not a tattoo expert but the color on picture one looks deeper than on picture two- where more work has been done…..wouldn’t the newer work be deeper colors?
The eyes are hard to see in photo 2 but the triangle dimensions from eyes to tip of the nose would not change- unless there is some tampering.

7. #### Jimmy

October 19, 2009 - 6:51 pm -

How about that it is not “Free” to find out what his secret is, yet the advertisement is stressing the importance of the word “free” to susceptible customers believing that it won’t cost them anything. How that can be related to math, that will need further thought.

8. #### Britt

October 19, 2009 - 7:04 pm -

A) I will have to agree with the stretching of the image as the deceit, at least the primary deceit.
B) I was trying to not over think it, but my 5th grade teacher brain was enjoying the challenge of an actionable lesson for a high school classroom. The only reasonable topic I could think of would be to encourage the discussion toward y-intercept, slope, or some other graphing concept that could be applied to compare the two pictures. I am pretty sure that if we found a couple of points on his body that shouldn’t change with weight loss (ear to mouth or waist to shoulder) and established the slope of that line, we would quickly find some inaccuracies between the two pictures.

But like I said – I hope I didn’t over think it. Thanks for the question. I’m working on demanding similar cognitive engagement for my 5th graders…it is a challenge (for me anyway).

9. #### Jim Duffy

October 20, 2009 - 5:55 am -

Hi Dan,
I had students take the ad and copy it into geogebra. They could then measure what should be fixed (nose to navel, width between eyes) and get interesting ratios to work with. Thanks for the lesson in math and ethics at the same time. It makes the students think!
Jim

10. #### Maria Droujkova

October 21, 2009 - 8:19 am -

There are two relevant reference. The first is a blog I love, called Photoshop Disasters, that collects distortions of this sort and other, well, Photoshop disasters: http://photoshopdisasters.blogspot.com/ The kids I regularly email this stuff report developing a keener eye for broken ratios.

The second is TinEye, which you can use to search for similar images, though it does not find any in this case: http://tineye.com/ I use it to investigate Photoshop shenanigans.

11. #### Anonymous

October 21, 2009 - 6:25 pm -

Also, the four weeks seems suspect – look at the tattoos on the arms. Those take time to heal and it’s not recommended to tattoo too much skin at once. The beard too – but growing one like that in four weeks is doable, if your beard thrives.

12. #### gurgle

October 22, 2009 - 7:10 am -

Good point by anon above, although I think the beard is a reasonable 4 weeks growth. One other factor that other’s haven’t noticed is the ability to relax the ab muscles and let the stomach pop out – it can make you look a lot fatter than you actually are!