April 19, 2012

More on the braking, sneezing physicist in a car

For some reason, the story of the physicist who used science to get out of a traffic ticket has continued to hold my attention.

In my last post, I made some quick calculations based on the claims implied in the paper. My calculations showed that if the car was slowing down at the claimed rate of 10 m/s2 then the car would have been traveling at least 223 miles per hour at the low end of the range indicated on the graph. A careful reading of the paper reveals that the author does not reveal what speed he was going before inadvertently applying the brakes while sneezing.

I've never really thought much about the observed angular speed of an object passing in front of you at high velocities.  I can remember being on train platforms and watching a train approaching in the distance and being amazed at how it appeared to be going slow when it was far away, but as it passed it seemed to be going really fast.  I don't find anything wrong with the theory presented in the first part of the paper.

I do have issues with the values of the velocities purported in the paper (as I already mentioned) and the values of the accelerations (as I mentioned in the last post). So, I wanted to see what the author's graphs might look like with more realistic values for velocity and acceleration.

The first graph I made is a graph comparing what the author claimed: constant deceleration of 10 m/s2 for 10 seconds followed by 10 seconds of acceleration at 10 m/s2.  Then I made a graph of a car going at a constant velocity of 10 m/s (22 mph) for 9 seconds, slowing down at 10 m/s2, stopping for an instant, speeding up for 1 second  at 10 m/s2, and finally continuing on at 10 m/s for another 9 seconds.  Here are the two graphs superimposed on each other:

The graphs are remarkably similar, which is at first somewhat surprising, but can easily be explained. Two things that you should note from this graph: 
  1. The observed angular speeds are initially higher for the more realistic case. 
  2. The deceleration portion of the realistic case exactly overlaps the author's model.
The first point can be explained due to the fact that the car is actually much closer to the stop sign at t = -10 s in the more realistic case.  The second point is exactly what we would expect to see since both cases used the same accelerations during the time interval from t = -1 s to t = 1 s.  For the physics and math nerds reading this (and if you're not a physics or math nerd, bravo to you for reading this!) I wanted to check my method of calculating the angular speed versus Krioukov's method.  I used an approximation of angular speed by calculating  the change in angular speed between small time intervals.  With a small enough time interval, the approximation should be good enough, and it was good, since the two graphs overlapped.

Since my method was sound, I modeled a more realistic scenario for braking and accelerating: First the car approaches at constant speed of 10 m/s.  The car brakes at a maximum safe negative acceleration such that it comes to rest at t = 0 s. Immediately the car accelerates at the maximum acceleration for a Toyota Yaris until it reaches a speed of 10 m/s at which point it stops accelerating.

I used a coefficient of friction between the rubber tires and the road of 0.8.  With an initial velocity of 10 m/s, I was able to calculate the highest acceleration that would safely bring the car to a stop.  I found the acceleration to be 7.8 10 m/s2, which was not far from the estimate of 10 10 m/s2 in the original paper.  But the quickest time for a Yaris to go from 0 to 60 miles per hour I could find was 9 seconds. This corresponds to an acceleration of 3 m/s2, which is far less.  Combining these parameters into my model and comparing with Krioukov looks like this:

Using more realistic accelerations, the graph looks significantly different than the case presented in the paper.

But, I don't really care about the physics reported in the author's paper.  I believe that Krioukov wrote the paper as a harmless April Fool's Day prank (just like the 100 m telescope paper and the magnitude of the Tooth Fairy paper) hoping only to give other physicists and readers of arxiv a good laugh.

But shouldn't news bloggers do a bit more checking first? It seems wrong to just blindly accept whatever a scientist says without even questioning it. That doesn't seem scientific at all. On the other hand, whoever is running the twitter account for AAPT also seemed to be willing to accept that

Do the ends justify the means here?  Assuming the paper is a prank, then is it okay that the nonscientific public not realize that it is a farce? I'm a big fan of clever scientific play such as this, so at the end of the day, I don't really care that this stunt was pulled.

What I care about is the issue of how science is being reported to the non-scientists.  We should be able to rely on science journalists (and journalists, in general) to do some basic fact-checking to see if the story checks out.  The back of the envelope calculations I made for velocities and acceleration don't require anything more than high school physics, so they aren't out of the reach of journalists, yet countless journalists made light of the mathematics used in the paper.

More disturbing to me is I see no evidence that even non-scientific facts were checked.  Here are some questions I would be asking if I was a journalist:
  • When was the citation issued?  Can I see a copy of it?
  • When was the court date? Who was the judge? Can I get a copy of any court records?
  • What is the maximum fine (including fees) for running a stop sign in California?
Again, I don't really think there is any harm done by this story, if we can all learn something from it. I've learned that stories about the little guy beating the long arm of law are popular, even if they don't make much sense.  I've learned that some journalists do even less investigative work than I previously thought. Most importantly, I guess I've learned that we have a long way to go before we see a scientifically literate news media.


Hyperspace said...

Hello Drew,

My name is Brian Jacobsmeyer, and I'm the author of the original Physics Central blog post on Dmitri Krioukov's paper and traffic ticket.

I'd like to thank you for your thorough analysis of this story, especially your investigation of the original paper's mathematical details. When Krioukov told me that he wanted readers to find the flaw in his argument, this is exactly the kind of analysis that I hoped to see!

Also, I wanted to address some of your concerns about the fact checking conducted for this story.

First, in regards to the scientific fact checking, part of the purpose of my post was to encourage our readers to critically look at the paper and evaluate it for themselves. That's why I presented his paper's argument and included the final quote from Krioukov asking the readers to look for a flaw. You may disagree, but I think revealing the mathematical flaws in the original post may have stymied the analyses that you and others have done. I think it was important that these were done after the fact because they generated more discussion about the physics involved.

Secondly, I will admit that more fact checking of the non-scientific facts could have been done. But verifying some of the questions you listed may be more difficult than most think. When I talked to Krioukov, he mentioned that the traffic ticket was issued last summer, but I did not include that information in my post. Perhaps I should have.

Ideally, I wanted to verify that information independently, but finding court documents for traffic tickets can be difficult. As the San Diego county court states on its website:

"These files are not available on-line. (emphasis from the original webpage)

Be aware, these records are stored at the court facility only for a short time before being housed at an off-site location. It could take several days to retrieve the records and there will be a fee charged for retrieving the record if it is in storage."

When Krioukov spoke with me over the phone, he detailed facts about the court case to me. I made a judgment of the veracity of his statements and decided to write the post. I think that my post reflected an air of skepticism, and I never anticipated that this story would become so popular.

I want to emphasize that there are science journalists who are making an effort to accurately portray science. In the end, this wasn't a hoax; the paper was presented in court; and I think the story was a great way to pique people's interest in physics.

Andrew said...

Hi Brian,

Thanks for the comments. I hope I didn't sound too antagonistic towards the Physics Central blog post (or you for that matter.) I was really directing my comments towards the news outlets (including radio, TV and newspaper) that read your post, reworded it and didn't apply any investigation at all.

Like I said in one of my posts, I love great science jokes and pranks. A well-done prank does raise interest in science, which I think was clear here.

I was able to discern the skepticism in your post, but I thought it was interesting that the majority of the commenters on that post didn't seem terribly skeptical of the science. I saw more arguments about what it means to stop at a stop sign than I saw critical analysis of the physics. I see that as a sign that we as a physics community still have a long way to go to communicate that not all the science that is done is impossible for the non-scientist to understand.

I do enjoy the Physics Central blog. Keep up the great work!

warren said...

There was a similar (tongue-in-cheek) story in the early 1900's where a similar citation was issued to a physicist for running a red light. The story goes that during the court hearing, the physicist gave, as an excuse, a brilliant lecture on relativistic Doppler effect, which caused the red light to appear greenish. The judge accepted the argument, recanted the red light ticket and instead issued the physicist a (huge) fine for speeding.

Nicolás said...

Hello Andrew.

I wrote to Dr. Krioukov telling why I think this is a joke and also looking for a confirmation, but he didn't answer. (?)

This is what I wrote:

(Before you start to read, please excuse me for my bad english, I'm learning)

Dr. Krioukov: I'm writting you because of the article you send to ArXiv in April 1º. Well the thing is that, although all derivations in the article are right, the argument isn't right:

One reason for this is that the first condition in your argument is false. First I was surprised that you didn't add any reference for this statement, so I looked in journals of psichology and obviously didn't found anything. Then I realised that i was never going to find it, because it doesn't exist: In equation 7, for instance, if r0 goes smaller then perceived velocity goes smaller, and vanish when r0=0 (taking the limit). This means that an observer is not capable of perceive the velocity of a car that is going to run over him, which is absurd. Also, in the case of a car moving with constant velocity that accelerates in a given instant, the complete curve of perceived velocity isn't continuous (for example: for an acceleration of 10m.s⁻² between t=0 and t=1 followed by uniform motion of 10m.s⁻¹, in t=1 curve of accelerated motion gives 0,8rad.s⁻¹ but curve of uniform motion gives 0,5rad.s⁻¹), which is absurd. Equations fail to represent what a person sees, so first condition is false.

Other reason is that the blue solid curve in FIG. 5 is the same that the blue solid curve in FIG.3, that shows velocity perceived of a car with constant linear deceleration of 10m.s⁻² followed of an acceleration of 10m.s⁻². Well, if curve extends from -10s to +10s that means that Yaris can go at 360km/h, and also means that you can sneeze for 10s... I don't think a human been can be so sick :D .

Also (and this is the most important thing to me) your argument depends on comparation of velocity curves as functions of time, but this is not what an observer perceives directly. Observer perceives directly the trajectory of the car, so it is irrelevant if the velocity curves are similar for a car at uniform motion and a car at accelerated motion, if the corresponding trajectories are different.

¿Why am I writting to you? Because I'm trying to explain to a friend why this is an April Fools Day prank, but he refuses to understand it. I think that if he sees your response confirming that this is a prank, then he will open his mind and will be able to understand what i'm trying to explain.

I appreciate your time and hope you can answer soon.

Best regards.

Your post is the first I see that shows the argument in that paper isn't right. I'm starting to think this was not really a joke :S