# Has anybody out there even used physics or math to win over any court cases? **URL:** \ **Category:** Factual Questions\ **Created:** [June 29, 2004, 1:27am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641 "2004-06-29T01:27:46Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Dewey\_Finn](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dewey_finn/32/4222_2.png) [@Dewey\_Finn](https://boards.straightdope.com/u/Dewey_Finn)\ **Post date:** [June 29, 2004, 3:37pm UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/21 "2004-06-29T15:37:44Z")
> [@Garnet](#): > > Here’s one from the other side… I once knew someone who worked as a sonographer, and he was called in to serve on a jury for a speeding ticket. And the defendant’s lawyer tried to argue that the presence of large moving objects near the defendant’s car, such as a passing truck, could throw off the radar gun’s reading (!) > > Needless to say, this guy works with waves all day and knew it was a complete fabrication. He explained it to the jury and they voted to convict. Score 1 for fighting ignorance! 🙂 IANAL but this seems wrong to me. The sonographer provided testimony in the jury room without going through the process of being qualified as an expert witness or cross-examined. He should not have done that, whether or not he was correct. And two previous posters here have suggested how he might be incorrect. ---
**Author:** ![Hamlet](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hamlet/32/2818_2.png) [@Hamlet](https://boards.straightdope.com/u/Hamlet)\ **Post date:** [June 29, 2004, 6:45pm UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/22 "2004-06-29T18:45:36Z")
Since there are a plethora of speeding ticket stories in this thread, I’d thought I’d offer a quick glimpse behind the curtain. When I began my prosecution career, I started, as most do, in traffic court in a smallish county. A majority of the tickets that went to trial were speeding tickets, which people think they can beat. A couple of the magistrates I was in front of had what they referred to as the “interesting theory” dismissal where, if a defendant on a non-accident speeding ticket showed up, wasn’t a jerk, didn’t have a horrible driving record and presented a defense that involved physics, higher math, or another “interesting theories” the magistrate would dismiss the ticket. Talking with them after court, they seemed to think if someone went through all the trouble of preparing a defense, they might as well acquit them. It had little or nothing to do with the actual science, but it was amusing none the less. Since that time, I’ve used math, probabilities, and extrapolations in many cases, most notably DNA cases and DUI cases. Jurors seem to put a fair amount of credence into an expert who can make scientific arguments. ---
**Author:** ![Cerowyn](https://avatars.discourse-cdn.com/v4/letter/c/82dd89/32.png) [@Cerowyn](https://boards.straightdope.com/u/Cerowyn)\ **Post date:** [June 29, 2004, 8:24pm UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/23 "2004-06-29T20:24:48Z")
> [@Mathochist](#): > > The main quality of a professional mathematician is not a facility with numbers, but a steadfast dedication to rational thought and attention to detail. > > As such, this is how mathematics (in this more general sense) would have acquitted such a defendant: by pointing out that it is only a crime to run a red light. In Ontario, and at least four other states or provinces in North America that I’m aware of, running an amber light is also worth a ticket, albeit different from running a red light. ---
**Author:** ![Topologist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/topologist/32/3208_2.png) [@Topologist](https://boards.straightdope.com/u/Topologist)\ **Post date:** [June 29, 2004, 10:56pm UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/24 "2004-06-29T22:56:59Z")
> [@Dewey Finn](#): > > IANAL but this seems wrong to me. The sonographer provided testimony in the jury room without going through the process of being qualified as an expert witness or cross-examined. He should not have done that, whether or not he was correct. And two previous posters here have suggested how he might be incorrect. IANAL either, but recently I was interviewed as a potential juror for a vehicular manslaughter case. The lawyers and the judge all seemed quite concerned how I, as a mathematician, would evaluate the expert witness testimony that the case would involve. They said, essentially, that even if I knew that the “expert” was wrong, based on any specialized knowledge I might have, I was to accept the testimony as if it were correct (and certainly not let my fellow jurors in on the error). Ultimately, I did not make it on to that jury. ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [June 29, 2004, 11:32pm UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/25 "2004-06-29T23:32:38Z")
Here in the UK, an amber light means that you should stop if you can do so safely (no emergency stop etc) - if you’re too close then the correct thing to do is go through. ---
**Author:** ![Gadarene](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Gadarene](https://boards.straightdope.com/u/Gadarene)\ **Post date:** [June 30, 2004, 12:26am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/26 "2004-06-30T00:26:50Z")
**CalMeacham:** > [@](#): > > John Allen Paulos, in his book Innumeracy, talks about a court case in which both sides used probability to argue for a client’s innocence or guilt. The prosecution calculated that the chances of anyone matching the description given were one in a million. The defence showed that, even if you accepted those numbers, in a city the size of LA, there were still plenty of people who ought to meet the criteria, on the basis of staistics alone. In case anyone’s interested, the case referred to above is _People v. Collins_, 68 Cal. 2d 319 (1968). Here are some excerpts: > [@](#): > > As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment. > [@](#): > > In an apparent attempt to bolster the identifications, the prosecutor called an instructor of mathematics at a state college. Through this witness he sought to establish that, assuming the robbery was committed by a Caucasian woman with a blond ponytail who left the scene accompanied by a Negro with a beard and mustache, there was an overwhelming probability that the crime was committed by any couple answering such distinctive characteristics. The witness testified, in substance, to the “product rule,” which states that the probability of the joint occurrence of a number of mutually independent events is equal to the product of the individual probabilities that each of the events will occur. Without presenting any statistical evidence whatsoever in support of the probabilities for the factors selected, the prosecutor then proceeded to have the witness assume probability factors for the various characteristics which he deemed to be shared by the guilty couple and all other couples answering to such distinctive characteristics. > > Applying the product rule to his own factors the prosecutor arrived at a probability that there was but one chance in 12 million that any couple possessed the distinctive characteristics of the defendants. Accordingly, under this theory, it was to be inferred that there could be but one chance in 12 million that defendants were innocent and that another equally distinctive couple actually committed the robbery. Expanding on what he had thus purported to suggest as a hypothesis, the prosecutor offered the completely unfounded and improper testimonial assertion that, in his opinion, the factors he had assigned were “conservative estimates” and that, in reality, “the chances of anyone else besides these defendants being there, . . . having every similarity, . . . is something like one in a billion.” > [@](#): > > As we shall explain, the prosecution’s introduction and use of mathematical probability statistics injected two fundamental prejudicial errors into the case: (1) The testimony itself lacked an adequate foundation both in evidence and in statistical theory; and (2) the testimony and the manner in which the prosecution used it distracted the jury from its proper and requisite function of weighing the evidence on the issue of guilt, encouraged the jurors to rely upon an engaging but logically irrelevant expert demonstration, foreclosed the possibility of an effective defense by an attorney apparently unschooled in mathematical refinements, and placed the jurors and defense counsel at a disadvantage in sifting relevant fact from inapplicable theory. > [@](#): > > As we have indicated, the specific technique presented through the mathematician’s testimony and advanced by the prosecutor to measure the probabilities in question suffered from two basic and pervasive defects – an inadequate evidentiary foundation and an inadequate proof of statistical independence. First, as to the foundational requirement, we find the record devoid of any evidence relating to any of the six individual probability factors used by the prosecutor and ascribed by him to the six characteristics as we have set them out in footnote 10, ante. To put it another way, the prosecution produced no evidence whatsoever showing, or from which it could be in any way inferred, that only one out of every ten cars which might have been at the scene of the robbery was partly yellow, that only one out of every four men who might have been there wore a mustache, that only one out of every ten girls who might have been there wore a ponytail, or that any of the other individual probability factors listed were even roughly accurate. > > We seriously doubt that such evidence could ever be compiled since no statistician could possibly determine after the fact which cars, or which individuals, “might” have been present at the scene of the robbery; certainly there is no reason to suppose that the human and automotive populations of San Pedro, California, include all potential culprits – or, conversely, that all members of these populations are proper candidates for inclusion. Thus the sample from which the relevant probabilities would have to be derived is itself undeterminable. Great stuff. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 30, 2004, 12:46am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/27 "2004-06-30T00:46:16Z")
> [@Topologist](#): > > IANAL either, but recently I was interviewed as a potential juror for a vehicular manslaughter case. The lawyers and the judge all seemed quite concerned how I, as a mathematician, would evaluate the expert witness testimony that the case would involve. They said, essentially, that even if I knew that the “expert” was wrong, based on any specialized knowledge I might have, I was to accept the testimony as if it were correct (and certainly not let my fellow jurors in on the error). Ultimately, I did not make it on to that jury. You’re kidding. Yet another perk! Screw the lousy pay, I can get outta jury duty 'cause I think too much! ---
**Author:** ![jackelope](https://avatars.discourse-cdn.com/v4/letter/j/a6a055/32.png) [@jackelope](https://boards.straightdope.com/u/jackelope)\ **Post date:** [June 30, 2004, 1:27am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/28 "2004-06-30T01:27:31Z")
Years ago, I wrote a short story in which the protagonist used the Mean Value Theorem to get a traffic ticket dismissed. Looks like I wasn’t as original as I thought. ---
**Author:** ![caphis](https://avatars.discourse-cdn.com/v4/letter/c/e19adc/32.png) [@caphis](https://boards.straightdope.com/u/caphis)\ **Post date:** [June 30, 2004, 1:35am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/29 "2004-06-30T01:35:51Z")
> [@jackelope](#): > > Years ago, I wrote a short story in which the protagonist used the Mean Value Theorem to get a traffic ticket dismissed. Looks like I wasn’t as original as I thought. A friend of mine used that once; he got his timestamps from toll booths. If I recall correctly, an officer had wrongly accused him of speeding, and my friend basically proved that in order for him to be travelling at the speed the officer cited, he would’ve had to also park on the road for no less than 3 minutes, or something like that. It worked. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 30, 2004, 1:37am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/30 "2004-06-30T01:37:52Z")
> [@jackelope](#): > > Years ago, I wrote a short story in which the protagonist used the Mean Value Theorem to get a traffic ticket dismissed. Looks like I wasn’t as original as I thought. This I want to hear. The only context for the (differential) mean-value theorem that comes to mind is considering position as a function of time. In this case, all the theorem says is that there exists a time where you were going a certain speed (as specified by the theorem). This is ususally brought up as an idea for proving speeding violations for, say, travellers on a turnpike where the distance between booths is known in advance and making time measurements on a stamped ticket can sometimes establish that _at some point_ the driver was speeding. I don’t see how it can be used to get a ticket _dismissed_ though. Along a linear path you could only manage to invoke this theorem to prove you _weren’t_ speeding if you could somehow bound your speed from below. I don’t think you could do it at all if there’s any possibility of looping back on your own path. So, did your character prove he never went below a certain speed along a linear path? Is there another context in which you invoke the theorem? Were you just confused about what the theorem actually says? ---
**Author:** ![Dewey\_Finn](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dewey_finn/32/4222_2.png) [@Dewey\_Finn](https://boards.straightdope.com/u/Dewey_Finn)\ **Post date:** [June 30, 2004, 2:04am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/31 "2004-06-30T02:04:02Z")
> [@Garnet](#): > > Here’s one from the other side… I once knew someone who worked as a sonographer, and he was called in to serve on a jury for a speeding ticket. A jury trial for a speeding offense? I’ve never heard of such a thing. ---
**Author:** ![jackelope](https://avatars.discourse-cdn.com/v4/letter/j/a6a055/32.png) [@jackelope](https://boards.straightdope.com/u/jackelope)\ **Post date:** [June 30, 2004, 2:15am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/32 "2004-06-30T02:15:06Z")
> [@Mathochist](#): > > This I want to hear. The only context for the (differential) mean-value theorem that comes to mind is considering position as a function of time. In this case, all the theorem says is that there exists a time where you were going a certain speed (as specified by the theorem). Right, I didn’t say it was a speeding ticket. In the story, it was a ticket for running a stop sign when the guy had rolled up on a hill, rolled back a few inches (it was a manual transmission), then proceeded. He got the ticket because the cop didn’t think this counted as hitting a _complete_ stop, but established in court that if he’d rolled slightly backward before proceeding, then he must have passed through the same point twice. His average speed between those two moments would have been zero, and therefore there was at least one moment at which his speed was zero. I.e., a stop. Hey, I didn’t say it was a _good_ story. I was about 18 or so and had just learned what the Mean Value Theorem is. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 30, 2004, 2:22am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/33 "2004-06-30T02:22:17Z")
> [@jackelope](#): > > Right, I didn’t say it was a speeding ticket. In the story, it was a ticket for running a stop sign when the guy had rolled up on a hill, rolled back a few inches (it was a manual transmission), then proceeded. He got the ticket because the cop didn’t think this counted as hitting a _complete_ stop, but established in court that if he’d rolled slightly backward before proceeding, then he must have passed through the same point twice. His average speed between those two moments would have been zero, and therefore there was at least one moment at which his speed was zero. I.e., a stop. Ah. Mistaken as I may be in many jurisdictions about yellow lights, I’m sure that the laws regarding stop signs specify a “full and complete stop”, which is usually defined as a certain length of time at rest, rather than as a single point of time at rest. ---
**Author:** ![caphis](https://avatars.discourse-cdn.com/v4/letter/c/e19adc/32.png) [@caphis](https://boards.straightdope.com/u/caphis)\ **Post date:** [June 30, 2004, 2:37am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/34 "2004-06-30T02:37:00Z")
> [@Mathochist](#): > > Ah. Mistaken as I may be in many jurisdictions about yellow lights, I’m sure that the laws regarding stop signs specify a “full and complete stop”, which is usually defined as a certain length of time at rest, rather than as a single point of time at rest. Not to be anal, and IANAL, but if he rolled up to the sign, then rolled backward, then there was a point where his speed was, indeed, zero. Whether it be at the transition point from rolling forward to rolling backward, he hit 0 at some point in time. I’ve never seen the length of time one must spend at a stop sign specified in any lawbooks, so it follows that 1 second could count as full and complete. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 30, 2004, 2:57am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/35 "2004-06-30T02:57:51Z")
> [@caphis](#): > > Not to be anal, and IANAL, but if he rolled up to the sign, then rolled backward, then there was a point where his speed was, indeed, zero. Whether it be at the transition point from rolling forward to rolling backward, he hit 0 at some point in time. > > I’ve never seen the length of time one must spend at a stop sign specified in any lawbooks, so it follows that 1 second could count as full and complete. Sure, a full second is usually fine, but that’s much more than is assured by the mean-value theorem. ---
**Author:** ![mmmiiikkkeee](https://avatars.discourse-cdn.com/v4/letter/m/edb3f5/32.png) [@mmmiiikkkeee](https://boards.straightdope.com/u/mmmiiikkkeee)\ **Post date:** [June 30, 2004, 6:45am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/36 "2004-06-30T06:45:03Z")
> [@caphis](#): > > my friend basically proved that in order for him to be travelling at the speed the officer cited, he would’ve had to also park on the road for no less than 3 minutes, or something like that … or perhaps waited 3 minutes behind a few cars in front of him at the toll booth ;). That’s a pretty slim margin of error to argue; I’d feel safer with a 15 minute time lapse. > [@don't ask](#): > > “Who would turn in front of a police car through a red light?” he asked. Plenty of people - I’ve seen it and almost done it myself. When you’re running a yellow you tend to be focused on the light and if anyone _moving_ is going to hit you, not what the make of the _stationary_ car sitting safely stopped across from you is. Tunnel vision comes very easily under such circumstances. ---
**Author:** ![Shade](https://avatars.discourse-cdn.com/v4/letter/s/2bfe46/32.png) [@Shade](https://boards.straightdope.com/u/Shade)\ **Post date:** [June 30, 2004, 10:22am UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/37 "2004-06-30T10:22:56Z")
> [@Mathochist](#): > > Sure, a full second is usually fine, but that’s much more than is assured by the mean-value theorem. I’m guessing it depends what the law means by “full and complete.” For instance, if you came to a literally momentary stop moving forward, it’d be basically indistinguishable from rolling forward. Problem. But if I was the cop or judge, I’d OK it if you rolled backwards two inches - you should be equally able to see that nothing’s coming there as if you’d stopped for that time. We need a lawyer I think. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 30, 2004, 1:10pm UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/38 "2004-06-30T13:10:50Z")
> [@Shade](#): > > I’m guessing it depends what the law means by “full and complete.” For instance, if you came to a literally momentary stop moving forward, it’d be basically indistinguishable from rolling forward. Problem. But if I was the cop or judge, I’d OK it if you rolled backwards two inches - you should be equally able to see that nothing’s coming there as if you’d stopped for that time. We need a lawyer I think. Well that’s my point. I’m not saying that the ticket _shouldn’t_ have been dismissed, but that the single instant guaranteed by the mean-value theorem (and the Newtonian approximation to physics) is not sufficient to invalidate it. ---
**Author:** ![Shade](https://avatars.discourse-cdn.com/v4/letter/s/2bfe46/32.png) [@Shade](https://boards.straightdope.com/u/Shade)\ **Post date:** [June 30, 2004, 1:22pm UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/39 "2004-06-30T13:22:22Z")
True. I agree. Though on re-reading I see in the story the argument Jackelope first said he used was that the _average_ speed was zero, over a back-and-forward path. Which is true, and possibly even reasonable, though I doubt the law defines it quite like that. Also, I think MVT is overkill - IVT would be enough, since he merely claimed it was at the same point twice, and most people would be more amenable to that claim if you _didn’t_ invoke eithe VT. But I could see it being a plausible loophole, depending on how the law was worded - I keep forgetting this was fiction. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 30, 2004, 1:29pm UTC](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641/40 "2004-06-30T13:29:35Z")
> [@Shade](#): > > True. I agree. > > Though on re-reading I see in the story the argument Jackelope first said he used was that the _average_ speed was zero, over a back-and-forward path. Which is true, and possibly even reasonable, though I doubt the law defines it quite like that. Also, I think MVT is overkill - IVT would be enough, since he merely claimed it was at the same point twice, and most people would be more amenable to that claim if you _didn’t_ invoke eithe VT. But I could see it being a plausible loophole, depending on how the law was worded - I keep forgetting this was fiction. The claim about average speed between two points is the precondition for invoking the MVT. Since the average speed is zero, there must be a point in between where the actual speed is zero. I’m not sure how the Intermediate-Value theorem would apply any more directly than the MVT, though. In fact, he _did_ implicitly invoke it to show that he passed through the same point again after rolling back a bit. [Previous page](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641.md?page=1) [Next page](https://boards.straightdope.com/t/has-anybody-out-there-even-used-physics-or-math-to-win-over-any-court-cases/252641.md?page=3)