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What is the flaw with his argument?

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Ok, there is a story about a California physics prof who is able to get out of a traffic ticket by submitting an essay to the judge.

He wasn't fined as the judge couldn't argue with his defense, however there is a fatal flaw in his plan that even he himself does not recognize.

What is his flaw?

Here is a news article about it:

http://www.thestar.com/news/world/article/1163248--california-physics-prof-beats-traffic-ticket-with-academic-paper

Here's his submitted essay:

http://arxiv.org/pdf/1204.0162v1.pdf

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Posted · Report post

that, even if he actually stopped, it couldn't have been a long enough stop for him to assess the safety of continuing on his way.

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Posted · Report post

that, even if he actually stopped, it couldn't have been a long enough stop for him to assess the safety of continuing on his way.

Not a legal requirement.

Another tidbit:

He actually posted a second article addressing the two most common questions.

The first is the amount of the fine (it is actually about $284 not $400).

The second is the acceleration rate of the Yaris he was driving.

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Posted · Report post

Not a legal requirement.

Another tidbit:

He actually posted a second article addressing the two most common questions.

The first is the amount of the fine (it is actually about $284 not $400).

The second is the acceleration rate of the Yaris he was driving.

It is a legal requirement in my state. I guess California is different.

No. I just checked the California Motor Vehicle Code 21802 about this.

It is a legal requirement even there.

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Posted · Report post

It is a legal requirement in my state. I guess California is different.

No. I just checked the California Motor Vehicle Code 21802 about this.

It is a legal requirement even there.

Really? I thought the only legal requirement was that you come to a complete stop. He can scan the area before coming to his complete stop though.

Either way, I found a major flaw with his argument. I'll post it in a couple days if no one figures it out.

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Posted (edited) · Report post

If the car had stopped, then acceleratde, assuming it's California in the summer, there should be some dust thrown up and clearly visible

Edited by Aaryan
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The author's calculations depend on the fact that the stop sign was located at a point where the officer's line of sight would be perpendicular to the road when he looks at the stop sign. This was never stated as a fact. So, I think the fatal flaw was this unstated assumption.

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The author's calculations depend on the fact that the stop sign was located at a point where the officer's line of sight would be perpendicular to the road when he looks at the stop sign. This was never stated as a fact. So, I think the fatal flaw was this unstated assumption.

it's a decent assumption based on the author's description of the event. The office was on a road perpendicular the road traveled by the car in question. Although the officer himself might have been slightly off of 90 degrees, I'm not sure it would affect things much assuming that r0 from Fig 1 is sufficiently large.

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Posted (edited) · Report post

I'd consider this a case where biology would trump physics.

I'd hypothesize that a seasoned police officer doesn't judge speed based on the angular velocity of his head as it swivels to follow a car. He instead learns how to mentally map his perception of a car into three dimensional space, and can thereby get a reasonably good estimate of its speed (or at least a better one than you would get based purely on angular velocity).

To test this theory, you could have a police officer on a test field with a blindfold that he's allowed to remove for two seconds to estimate the speed of a moving car. He can estimate the speed while the car is far away and traveling more or less toward him (at a low angular velocity), and near him traveling roughly perpendicular to his line of sight (at a high angular velocity). Then use those experimentally measured values as the basis for whether he'd be thrown for a loop by a loss of vision near the stop sign. Use sound-cancelling headphones if you want to take engine noise out of the equation.

Edit:

The final figure in the author's argument shows the officer's perception of angular velocity given an interruption in vision, drawn as a dotted red line that has a plateau at the top. That shape is not the shape produced by an object that's maintaining a constant linear velocity. If the officer were interpreting the car as moving at a constant speed, the dotted line depicting his perception should be the same shape but different amplitude as the solid red line. That is, his misinterpretation would have to put the car as moving several times faster than its actual speed. If an officer can correctly estimate the car's speed regardless of the angle at which he views it, then he would not be fooled if the car has to travel at several times its actual speed while his vision is obscured in order to look like it ran the stop sign. If you have experimental data, you can in principle calculate the probability that he would make such a mistake based on standard deviations of estimated speed.

Edited by plasmid
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Posted · Report post

Much simpler answer

The graphs he shows are plotting angular velocity as a function of time. What the officer really sees is angular position (not velocity) as a function of time - the integral of the plot that's shown. There would be a much more obvious discontinuity in the latter if you were to obscure part of it where the driver comes to a stop.

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Here's what I consider to be the major flaw with his argument.

Directly from his paper:

Unfortunately, it is difficult to measure deceleration or acceleration without special tools,

but we can roughly estimate it as follows. D.K. was badly sick with cold on that day. In fact, he was sneezing while

approaching the stop sign. As a result he involuntary pushed the brakes very hard. Therefore we can assume

that the deceleration was close to maximum possible for a car, which is of the order of 10 m/s2 = 22:36 mph/s.

So, since he braked as quickly as possible for his vehicle, because he was sneezing, then he had absolutely no intention of stopping for the stop sign, or he stopped too early for the line and would have had to inch forward. Generally people slowly brake before a stop sign and a sneeze would've made him stop far in advance.

So we are lead to believe that he either stopped too far in advance of the stop sign, or that there was absolutely no intention to stop for the stop sign.

That was what I considered the major flaw with his argument (I also doubt the ability of the SUV to completely block the officer's view as the SUV should be moving.

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Posted (edited) · Report post

The fatal flaw is that DK’s third factor in his conclusion, “the O's view of C1 was briefly obstructed by another car, C2, around time t = 0“ is wrong. Car, C1, is never fully obstructed because the time for full obstruction is less than time t’, the time to decelerate, stop, and accelerate or “go over its maximum“. Therefore, a portion of C1 was always visible to the officer, who verified correctly that C1 did not stop as required. Case closed and guilty as charged! Figures don’t lie, but liars figure - ignore basic reasoning at own risk.

Edited by LilGreek
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