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‘The Proof of Innocence’: Read the Math Problem That Got One Man Out of a Traffic Ticket

Apr. 16, 2012 11:04am
Physicist Uses Mathematical Proof to Get Out of Traffic Ticket

(Photo:Misteraitch/Flickr)

Remember when you used to gripe about doing mathematical proofs in high school arguing a lack of real-life applications for it to be worth your while? Well, here’s how one man got off the hook for traffic ticket he received by using a math problem.

University of California-San Diego physicist Dmitri Krioukov was pulled over and issued a ticket for running a stop sign. While many wouldn’t go through the hassle of actually fighting this ticket in court, Krioukov is an exception — and he came prepared. io9 reports that he presented a mathematical paper to prove his innocence, aptly named “The Proof of Innocence,” and convinced the judge of his case.

Here’s the paper’s abstract:

We show that if a car stops at a stop sign, an observer, e.g., a police officer, located at a certain distance perpendicular to the car trajectory, must have an illusion that the car does not stop, if the following three conditions are satisfied: (1) the observer measures not the linear but angular speed of the car; (2) the car decelerates and subsequently accelerates relatively fast; and (3) there is a short-time obstruction of the observer’s view of the car by an external object, e.g., another car, at the moment when both cars are near the stop sign.

Krioukov further explains the detailed difference between linear and angular speed and how knowledge of such is crucial to making his case. He writes:

It is widely known that an observer measuring the speed of an object passing by, measures not its actual linear velocity by the angular one. For example, if we stay not far away from a railroad, watching a train approaching us from far away at a constant speed, we first perceive the train not moving at all, when it is really far, but when the train comes closer, it appears to us moving faster and faster, and when it actually passes us, its visual speed is maximized.

This observation is the first building block of our proof of innocence. To make this proof rigorous, we first consider the relationship between the linear and angular speeds of an object in the toy example where the object moves at a constant linear speed. We then proceed to analyzing a picture reflecting what really happened in the considered case, that is, the case where the linear speed of an object is not constant, but what is constant instead is the deceleration and subsequent acceleration of the object coming to a complete stop at a point located closest to the observer on the object’s linear trajectory. Finally, in the last section, we consider what happens if at that critical moment the observer’s view is briefly obstructed by another external object.

After a series of graphs and equations to prove his point, Krioukov concludes that “[Officer] O’s perception of reality did not properly reflect reality.” Krioukov writes that because his car was moving in a constant linear deceleration, came to a complete stop and then accelerated at the same speed, it appeared to not have stopped.

Physicist Uses Mathematical Proof to Get Out of Traffic Ticket

This figure from Krioukov's proof shows how the officer may have mistook the car running a stop sign. (Image: The Proof of Innocence/Dmitri Krioukov)

There are no hard feelings though. Krioukov writes in his paper several reasons why Officer O’s mistake was “fully justified,” including the fact that the officer was not measuring linear speed but was estimating via visual angular speed; the linear deceleration and acceleration of the car were relatively high; and another car had briefly obstructed the officer’s view.

Suffice to say, the court took Krioukov’s word — and mathematical proof — for it. Still, the local NBC affiliate (via Gizmodo) reports Krioukov saying not everyone should try to be as cheeky as he had been to get out of traffic violations. He said the situation surrounding the events that happened lined up perfectly for him to make his case.

So, did he really stop? NBC asked Krioukov this question and with a smile he replied, “Of course I did.”

Note: This story has been updated from its original posting to reflect that Krioukov is a professor at UC San Diego not UC-Davis as we mistakenly reported earlier. Thanks Blaze reader Dennis R. for pointing this out. 

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Comments (129)

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  • OldVet
    Posted on April 16, 2012 at 12:28pm

    He obviously wasn’t driving in south Chicago. If he had been, the Officer would validate the ticket by saying that no one checked his doors at the stop sign, therefore he had not come to a full and complete stop.

    Report this comment

    OldVet  
    • jzs
      Posted on April 16, 2012 at 2:09pm

      So he’s saying that at the moment he was stopped, and his angular velocity was zero, another car was blocking the officer’s view. That defence really doesn’t require any math.

      Report this comment

      jzs  
    • 13th Imam
      Posted on April 16, 2012 at 3:27pm

      He also helped Barry write Obamacare. Even if the dopes that voted for it, couldn’t comprehend this mumbo-jumbo, they would claim to understand it, as they are experts at everything. Barry is the same way. He knows everything about everything, specially economics. And the Constitution.And the Fluke Condom Curve.

      Report this comment

      13th Imam  
    • Hollywood
      Posted on April 16, 2012 at 4:00pm

      Nah. In Chi town the Cop would have taken 50 bucks cash, to settle the matter!

      Report this comment

      Hollywood  
    • JimCDew
      Posted on April 16, 2012 at 4:13pm

      “So, did he really stop? NBC asked Krioukov this question and with a smile he replied,’Of course I did.’â€(Relatively speaking)

      Report this comment

      JimCDew  
    • mcFirst
      Posted on April 16, 2012 at 4:35pm

      or if person was related to any city official they would have certainly have stopped.

      Report this comment

      mcFirst  
    • Ranubis
      Posted on April 16, 2012 at 5:21pm

      If you can’t dazzle them with brilliance, then baffle them with bull s#!t

      Report this comment

      Ranubis  
    • carlschulz
      Posted on April 16, 2012 at 9:31pm

      I grew up in Illinois and we were taught in driver’s ed that you were required to be stopped for at least 3 seconds to be a “legal” stop.

      Report this comment

      carlschulz  
    • READRIGHTHERE
      Posted on April 16, 2012 at 10:11pm

      @charles

      Here in Utah I have an acquaintence who was actually issued a ticket for failing the three second rule. When I count to three it makes me laugh at how rediculous the law is. As if the time of the stop guarantees my awareness!

      Report this comment

      READRIGHTHERE  
    • earthbonz
      Posted on April 16, 2012 at 10:28pm

      JZS….got me laughing.

      Report this comment

      earthbonz  
    • jzs
      Posted on April 16, 2012 at 11:19pm

      earthbonz, thanks. My opinion is that he rolled through the stop sign, like 99.9% of the rest of us do when there is no oncoming traffic. My statistical point of view is that it is unlikely in the extreme that the guy actually came to a dead stop as the law requires, because virtually nobody does that when there are no cars coming. And, seriously, why would anyone do that? If you are an alert, responsible driver, stopping completely at an intersection when no one is coming serves no purpose.

      Just the same, if this case promotes an understanding of math with even a single person, I’m for it.

      Report this comment

      jzs  
  • JimCarriesA1911
    Posted on April 16, 2012 at 12:25pm

    Bazinga

    Report this comment

    JimCarriesA1911  
  • MittensKittens
    Posted on April 16, 2012 at 12:06pm

    I can imagine when he brought this to court there were quite a few blank stares…no wonder he got off…baffle them with b*llsh*t

    Report this comment

    MittensKittens  
    • GiveUsJustice
      Posted on April 16, 2012 at 2:18pm

      I wouldn’t say so. I think this makes total sense. I wouldn’t bring all the fancy graphs though.

      If an officer isn’t to the side of you, how can he tell you came to a complete stop? It’s nearly impossible without some other outside object right in front of you to gauge that.

      Report this comment

      GiveUsJustice  
    • 4xeverything
      Posted on April 16, 2012 at 2:45pm

      Like a stop sign?

      Report this comment

      4xeverything  
  • LeadNotFollow
    Posted on April 16, 2012 at 11:59am

    …
    Many years ago, I was riding with my Mom, when she was ticketed for not coming to a “FULL” stop at a stop sign.

    The officer said, that a “full” stop is when you stop the vehicle, the vehicle tilts quickly to the front, then tilts quickly back to the rear (lunge forward, then back).

    He said her car only lunged forward, that she did not wait long enough for the car to rock to the rear before she proceeded to go through the stop sign. She didn’t fight the ticket. She paid it.

    From that day on, I’ve paid attention to vehicles stopping at stop signs. At least ninety percent of drivers do not come to a “full” stop, unless there is a vehicle coming and they have to fully stop and wait for the other vehicle to pass.

    Report this comment

    LeadNotFollow  
    • grimmy
      Posted on April 16, 2012 at 12:37pm

      @Lead.
      I can take my F 250 crew cab p/u and come to a complete stop,and never have the veh. “lunge” to the rear.

      Report this comment

      grimmy  
    • drphil69
      Posted on April 16, 2012 at 2:53pm

      It will only lunge if you are hard on the brakes. I coast nearly to a stop, so no lunge forward or back.

      Report this comment

      drphil69  
    • 13th Imam
      Posted on April 16, 2012 at 3:30pm

      Those at PMSNBC Lunge Forward,, but to the left

      Report this comment

      13th Imam  
    • Wornout
      Posted on April 16, 2012 at 3:31pm

      I feel sorry for your brakes. My car never “lunges” to a stop or to accelerate. It wastes gas and brakes and is uncomfortable for passengers. The cop was wrong. A full stop means the wheels stop turning, count to 3 if you need to to feel safe, but this cop’s definition would not hold up in court.

      Report this comment

      Wornout  
    • Brooke Lorren
      Posted on April 16, 2012 at 3:31pm

      I can come to a full stop without having my vehicle go backwards, if my car decelerates slowly enough.

      My car could sit there for a few minutes or more… if I wasn’t at a full stop, then the car would eventually move, I would suppose.

      Report this comment

      Brooke Lorren  
    • SgtB
      Posted on April 16, 2012 at 4:20pm

      Who cares if your car comes to a complete and total stop? Really, the purpose of any road sign or rule is to ensure safety of the citizens travelling on the road. If you roll to a 4-way intersection with a clear view and you clearly see that no cars, bikes, or pedestrians of any kind are approaching the intersection, then why can you not roll through it without having come to a “complete” stop? The only time that I completely stop is when there is competing traffica and the complete stop is the judge of who got there first and who will subsequently go through first. Of course, I live in Oklahoma though and in tie situations or even just close, the other driver and myself end up in a kindness battle royale each encouraging the other to go through first.

      The reason and original intent of any law is to keep people safe. If the enforcement of a law does nothing to increase safety, then it is wasteful and fraudulent IMO.

      Report this comment

      SgtB  
  • RJJinGadsden
    Posted on April 16, 2012 at 11:56am

    If observing an intersection for this purpose always aim cruiser so that dash cam gives you video evidence.

    Report this comment

    RJJinGadsden  
  • cemerius
    Posted on April 16, 2012 at 11:54am

    Uh Oh!! This man’s life is in danger now!! He broke the lawyer’s secret code of “If you can’t dazzle them with brilliance, baffle them with BS”!!!

    Report this comment

    cemerius  
  • clemV
    Posted on April 16, 2012 at 11:43am

    Who cares about this? Wake up and demand real news, people! Rampant voter fraud in the Maine Caucus and beyond. Check this out: http://www.youtube.com/watch?v=QApII_DbDik

    Report this comment

    clemV  
    • Ming The Merciless
      Posted on April 16, 2012 at 12:03pm

      They don’t want you to know the real news out there – they’ll ‘entertain’ you with these types of ‘non-news’ stories to get you off the path. Glenn, Pat and Stu will ‘feed’ you the news – listen to them and vote for the guy they’re voting for.

      As for me – Ron Paul 2012 or no one!

      http://www.dailypaul.com

      Report this comment

      Ming The Merciless  
    • Bombgod1
      Posted on April 16, 2012 at 12:28pm

      Sometimes it’s good to escape the realities of life, and to just sit back and enjoy a light hearted story.

      The bad things are still out there, the black helicopters are still coming from you, the voices are still yelling at you, no matter how hard you try your still living in your mom’s basement and if you’re lucky you will have 100 face book friends by next week.

      Life is too short to dance with ugly women.

      Report this comment

      Bombgod1  
    • LostInTheSpin
      Posted on April 16, 2012 at 12:33pm

      I see that crap every single day…good to lighten up and be entertained every once in a while. If you don’t like articles like this…THEN DON”T READ THEM!

      Report this comment

      LostInTheSpin  
    • AmazingGrace8
      Posted on April 16, 2012 at 1:04pm

      This guy sounds like a boyfriend I had in the 60′s. He was a Physics Major (I attended a universary for awhile & not my bag & went to business school) but I found him to be very entertaining & he would come up with this kind of physics problem. I have never had a ticket/moving violation in my 50 yrs of driving..knock on wood…but use to be, a rolling-stop was called a California Stop. I am a very law-abiding citizen and I don’t want any trouble so when I do stop at a sign, I count 1-5 and then start up. Yeh, I know, hey lady get a life. Just doing my thing, man. Don’t want any trouble but if you are looking for trouble, I will respond. Have a great day!

      Report this comment

      AmazingGrace8  
  • DagneyT
    Posted on April 16, 2012 at 11:37am

    I got out of a ticket thanks to my bumper sticker, “If guns kill people, do pencils misspell words?”

    Report this comment

    DagneyT  
  • tzion
    Posted on April 16, 2012 at 11:35am

    WOW! And strangely enough I actually understood that. Weird but strangely enough it works.

    Report this comment

    tzion  
  • BlackCrow
    Posted on April 16, 2012 at 11:32am

    I beat a speeding ticket buy proving the officer operating the radar gun has no indication of just what object’s velocity the radar is measuring. The cop insisted that he had 40 hours training in radar and that was sufficient to make him an expert in radar. I then produced transcripts showing 3000 classroom a journeyman’s course and 20 years experience doing nothing but radar repair and operation. Case dismissed.

    Report this comment

    BlackCrow  
    • RJJinGadsden
      Posted on April 16, 2012 at 12:00pm

      I had a friend in Florida do the same thing. Except he was the cop and a former Marine Aircraft Radar Technician. Ate the lawyer alive to the point that it was actually funny. I got to see the video afterwards.

      Report this comment

      RJJinGadsden  
    • supermansdad
      Posted on April 16, 2012 at 1:28pm

      Only proves 2 things.
      1: The judge didnt know what he was talking about. Case law has repeatedly proven officers do NOT need to know the inner workings of the radar, only be familar with the operations of the unit and how to do a tuning fork test.
      2: Officer was dumb enough to call himself an expert when it is not required.

      Won out of stupidity not because you were or were not speeding. Congrats either way. Makes us do a better job of properly articulating the case and only issuing the citation when warranted.

      Report this comment

      supermansdad  
  • spfoam1
    Posted on April 16, 2012 at 11:30am

    If I had come up with something like that they would have tazed me in the court room and drag me off into a cell.

    Report this comment

    spfoam1  
  • youdidthis
    Posted on April 16, 2012 at 11:28am

    no victim,
    no crime…fluke the bs laws.

    dam tired of these quota driven so called police.

    quota’s for tickets , misdemeanors and felonies…time to end the bs.

    Report this comment

    youdidthis  
  • Rowgue
    Posted on April 16, 2012 at 11:26am

    There isn’t anything there that proves his innocence. He offered up a questionably valid theory as to how somebody might accidentally think somebody ran a stop sign when they really didn’t. What he didn’t do was illustrate how that theory applies to his case specifically. This is just a judge that got tired of hearing a BS artist talk, and dismissed the case so he didn’t have to listen to him anymore.

    Report this comment

    Rowgue  
    • disque-0-duc
      Posted on April 16, 2012 at 12:24pm

      yeah, but it worked and that was the goal of the defendant.

      Report this comment

      disque-0-duc  
    • romaddan
      Posted on April 16, 2012 at 12:50pm

      @ROWGUE, Do not ever forget that our laws are NOT for us to PROVE our innocence, BUT for the government to PROVE our guilt – The defendant in this case caused enough doubt for the judge to throw it out. The government could not PROVE him guilty… Good on him.

      Report this comment

      romaddan  
    • ThorLoser
      Posted on April 16, 2012 at 12:56pm

      You do not have to prove that you are innocent. They have to prove that you are guilty. Those are two completely different things. All you have to do, as a defendant is to give at least one other alternative possibility which will make something (in this case, observations) possible. Once there are two possibilities, since there is a presumption of innocence, you cannot be found guilty (unless they can prove that the alternative possibility is not actually possible in this case).

      Report this comment

      ThorLoser  
    • Rowgue
      Posted on April 16, 2012 at 8:55pm

      You have a severely perveted idea of how the law works. The burden is to prove guilt beyond a reasonable doubt. Not absolutely or with 100% certainty. The requirement is simply to present a case where any reasonable person can see that they are most likely guilty of the violation.

      Simply presenting an alternative possibility is not sufficient to counter an eyewitness watching you commit the violation. You aren’t automatically found innocent as long as there is another possible explanation. You have to prove that there is reason to believe that other possible explanation might have actually happened rather than the one you’re accused of. That’s reasonable doubt.

      Besides my point was in response to the article, which claims he “proved” his innocence. That isn’t what happened here.

      Report this comment

      Rowgue  
  • Spolic
    Posted on April 16, 2012 at 11:26am

    He was just being “Green.” By rolling the stop sign, he is saving gas and the environment.

    Report this comment

    Spolic  
  • sawbuck
    Posted on April 16, 2012 at 11:26am

    I think the judge (like me)was confused with the equation after the first paragraph .
    But after the obvious example of what a person will do to beat a ticket, coupled with the most original argument the judge has ever seen ,he decided to give the professor a break and threw the ticket out…. Good for him

    Moral to the story…????

    Whoever said “ADVANCED MATH’ doesn’t apply to daily living ..was wrong…!

    Report this comment

    sawbuck  
  • LB
    Posted on April 16, 2012 at 11:25am

    Was that article in English???

    Report this comment

    LB  
  • lukerw
    Posted on April 16, 2012 at 11:24am

    Shedon Cooper… is alive… and at UCD!

    Report this comment

    lukerw  
    • biohazard23
      Posted on April 16, 2012 at 11:33am

      Is it Sheldon or Leonard? If the judge was a woman, then it certainly would not have been Raj, and Howard would have gone to jail just for being Howard.

      Report this comment

       
  • biohazard23
    Posted on April 16, 2012 at 11:24am

    Since when did Sheldon Cooper learn how to drive?

    Report this comment

     
    • lukerw
      Posted on April 16, 2012 at 12:07pm

      He didn’t; he ran the Stop Sign! His math… is Formulamatic… and without varified Variables of the Actual Event as it took place!

      Report this comment

      lukerw  
    • biohazard23
      Posted on April 16, 2012 at 12:14pm

      He must have still been upset after having to drive Penny to the hospital. It must have been traumatic for him. Plus, he missed meeting Stan Lee because of that!

      Report this comment

       
  • vic138
    Posted on April 16, 2012 at 11:22am

    Dork. Cops aren’t all stupid.

    Report this comment

    vic138  
    • Jethro212
      Posted on April 16, 2012 at 11:29am

      Mind you I have some friends that are cops, and they will tell you the following themselves… There are some seriously stupid police officers.

      Report this comment

      Jethro212  
    • marine249
      Posted on April 16, 2012 at 1:14pm

      @ JET

      I am a retried policer officer.

      Mind you, I have some friends who post on the Blaze.
      They tell me that there are some seriously stupid trolls,
      who post here.

      Report this comment

      marine249  
  • spirited
    Posted on April 16, 2012 at 11:22am

    Good for him!

    6^>Count on an officer friendly radar gun next time.

    Report this comment

    spirited  
  • Calm Voice of Reason
    Posted on April 16, 2012 at 11:20am

    Science, for the win.

    Report this comment

    Calm Voice of Reason  
  • DeathRattle
    Posted on April 16, 2012 at 11:19am

    The judge’s decision was somewhere between dazzled with brilliance or baffled by B.S.

    Report this comment

    DeathRattle  
  • liberalescheisskopf
    Posted on April 16, 2012 at 11:17am

    Officers are trained to watch the front wheel. If the wheel came to a stop or continued to roll, aka California stop.

    Report this comment

    liberalescheisskopf  
    • AmazingGrace8
      Posted on April 16, 2012 at 1:11pm

      I am not a police officer but learned to watch the wheels/hubcap of a vehicle that has stopped at a light/stop sign and you are approaching & wondering if the vehicle has not seen you & will pull out from their stop.Little things do mean alot…the people who do not believe that…well, if they were in the jungle, they would be the first to be eaten!

      Report this comment

      AmazingGrace8  
  • greg4fitness
    Posted on April 16, 2012 at 11:17am

    And I bet that judge thought he had heard it all.

    Report this comment

    greg4fitness  
  • Jackie Rogers, Jr.
    Posted on April 16, 2012 at 11:17am

    His argument is obvious.

    Report this comment

    Jackie Rogers, Jr.  
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