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/s
2 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/s
2 for 10 seconds followed by 10 seconds of acceleration at 10 m/s
2. 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/s
2, stopping for an instant, speeding up for 1 second at 10 m/s
2, 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:
- The observed angular speeds are initially higher for the more realistic case.
- 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/s
2, which was not far from the estimate of 10 10 m/s
2 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/s
2, 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.
