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Old December 12 2011, 03:54 AM   #91
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Re: Mythbusters cannonball hits Dublin home and minivan

Lonemagpie wrote: View Post
I'm glad it's not a British show - it'd be axed for that, even though, y'know, it's a bomb range, where dangerous shit is pretty much the expected norm...
The three stooges in Top Gear driving homemade caravans in traffic seemed pretty iffy, Jeremy's block-of-flats on a Citroën in particular.
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Old December 12 2011, 08:31 PM   #92
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Re: Mythbusters cannonball hits Dublin home and minivan

snowman1701 wrote: View Post
^Based on the last article posted, we have at least one person involved with this making semi-veiled lawsuit threats. I'm guessing they aren't particularly interested in seeing this incident end up on their show.
Yes, as I already said, I am aware of the facts of the case. I'm just saying that it would be nice if things were different.


Trekker4747 wrote: View Post
Christopher wrote: View Post
I'm not sure about that. I think the minivan owner did say that his kids were in the minivan a few moments earlier; but if the cannonball had been fired earlier, the odds are that the wind would've been different or it would've bounced differently and thus followed a different trajectory anyway.
Ehhhh,,,, maybe. But I think it's just as likely the cannonball would have followed the same trajectory, or to make the point I was trying to make more dramatic sounding imagine the van arriving a few minutes later.
First off, given how much air the cannonball flew through, I'd say it's extremely unlikely it would've followed the exact same trajectory unless the air had been absolutely still throughout the entire path. And since it reportedly shot across a busy road, there would've been a lot of wind from the traffic, and the different traffic patterns at a different moment would've probably made a difference in the wind currents.

Second, if we're considering the postulate that the moment of firing, the arrival of the van, or any other factor was different, we can't exclude the possibility that other factors were different as well, and indeed they would've had to be. Given the incredible fluke of the cannonball misfiring and bouncing off the hill the way it did, if any variable were altered, it probably wouldn't have happened at all, or would've happened very differently. This wasn't a predictable event that could be repeated, but an exceptional concatenation of circumstances. So it isn't really meaningful to postulate the same event happening a moment earlier or later. It only happened because of the circumstances that came together at that exact moment.

Most importantly, being "dramatic" is not something we should aspire to if we want to understand the facts of the case. Drama generally entails exaggeration of facts and distortion of probabilities. It's certainly "dramatic" to say that the cannonball "almost" hit someone, but it's more accurate and truthful to say that the probability of it hitting someone was quite low. Certainly it would've been awful if someone had been hit, and certainly it's important to take precautions to minimize that risk, but what actually happened -- only property being hurt and not people -- was the most probable outcome, given the facts on hand.


The point being that the cannonball accident here very nearly was fatal because any number of variables could've cause some serious injury. If the people in the apartment had been up and walking around, if the van had gotten home later, if someone was walking down the street.
And that's a misunderstanding of probability, putting "drama" above accuracy. If I get a 9, 10, jack, queen, and 3, then I could say that I "very nearly" got a king-high straight, but that doesn't remotely mean I was more likely to get a straight than a losing hand. Close doesn't count. There are a lot of combinations of cards that are "close" to a winning hand, but they're still losing hands. And the fact that there are so many "near misses" makes a near miss much more probable than a winning hand. So saying I "very nearly" won may have emotional resonance, may feel like a truth, but it's factually misleading.

To make another analogy, let's go back to my high school days and my extremely inadequate sporting skills. I recall a day when we had unstructured time in gym class and I tried picking up a basketball and tossing it toward the hoop. I got "very near" the hoop dozens of times, but I don't think I sank the ball at all -- maybe once in dozens of tries. Because it's relatively easy to get "very near" a small target, but a lot harder to hit it exactly. The probability of getting "very near" is much higher than the probability of a hit. So calling something "very near" is misleading in terms of the actual probabilities involved. There's a reason why close only counts in horseshoes.

Yes, there are countless variables that could've happened differently, but that's exactly why the probability of anyone being hit was so low. Sure, I could say that "if" I'd been dealt a king instead of a 3, I would've won the hand. But that "if" is just one possibility out of many. There were a whole lot of other cards I could've been dealt that wouldn't have changed the outcome at all. So selecting for those few possibilities that would've brought about the outcome you're proposing and ignoring all the many, many more possibilities that would not have done so is misrepresenting the probabilities.

What we're talking about here is an unaimed projectile and a finite number of targets in a very large volume. It should be self-evident that if those targets are moving rather than standing still, it makes it even less likely that they'd be hit. Because it introduces even more possible permutations into the calculation, so that finite number of permutations resulting in injury becomes an even smaller percentage of the total.

So you're right that there are multiple variables that could've been different, but you're drawing exactly the wrong conclusion from that fact. The more variables that are involved, the lower the probability of someone being hurt.

And let's also consider how precedent factors into a probabilistic analysis. The Mythbusters misfiring a cannonball that bounced into a residential neighborhood is something that happened once and almost certainly never will again. Meteorite impacts, on the other hand, happen approximately 500 times a year, every year, throughout human history. And yet there are only two documented cases of meteorite impacts causing injury, zero cases of fatality. So no, it's really not all that amazing that nobody was hurt. It may feel that way, but a scientific appraisal shows that, as usual, our feelings aren't the best guide for understanding objective reality.


Psion wrote: View Post
I don't unconditionally accept the statement that kids had been in the car moments earlier. A lot of people are prone to exaggeration. "Moments earlier" might have been as much as an hour earlier prior to an urge to dramatize the danger of the scenario.
Also a good point, and another reason why being "dramatic" is not a good way to get at the facts of the matter.


This is not to say that I don't understand or sympathize with the feelings of the people involved. I know I'd be spooked if it had happened to me, no matter what reason tells me. And of course improbable things do sometimes happen, and if someone actually had been hurt by this or worse, it would've been terrible and tragic. But that's all the more reason we should be glad that probability was in favor of nobody getting hurt. Probability worked in everyone's favor this time, so we should respect and appreciate probability instead of misrepresenting it for the sake of being "dramatic" and stirring up fears.
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Old December 12 2011, 09:26 PM   #93
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Re: Mythbusters cannonball hits Dublin home and minivan

Christopher wrote: View Post
'....
:facepalm:
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Old December 13 2011, 06:39 AM   #94
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Re: Mythbusters cannonball hits Dublin home and minivan

Trekker4747 wrote: View Post
Christopher wrote: View Post
'....
:facepalm:


...

But allow me to elaborate!

I think Christopher's on the right track in trying to look at this objectively and doing a scientific appraisal.

Dublin California has, according to the 2010 census, a population density of 1,192.3 citizens per square kilometer. Thus, there are 0.0011923 people per square meter in Dublin.

The cannonball flew about a kilometer before coming to a rest inside a parked van. However, only about 440 meters of that path actually took it through a residential area. The other 560 meters were within the bomb range.

Assuming a roughly straight trajectory, and rounding up to account for bounces, let's assume the projectile traveled through 500 meters of residential space before stopping. Very crudely, that indicates a 59.6% chance of the cannonball moving through at least one occupied square meter during its run (500 meters x 0.0011923 people per square meter). Let's round that up to dispense with any assumed precision in these calculations: a 60% chance of the projectile intersecting with an occupied space.

Sounds bad, doesn't it? But! A cannonball of that mass is only about 20 centimeters in diameter. And you could probably fit four people within a square meter. 0.2 x 0.25 = a 5% chance of a cannonball actually hitting a person in an occupied square meter. I think that looks low, so I'm going to err on the side of caution and double those odds. A 10% chance of a hit.

So, we now have 60% chance of hitting an occupied space [times] a 10% chance of actually hitting a person in that space [equals] a 6% chance of a person actually getting hit by a rogue cannonball.

But wait! There's more!

Remember, this happened at a time of the day when, according to the reports, most people were at work. Let's assume half the residents in the area weren't at home. That means there's a 3% chance that a single shot along that trajectory would actually hit someone.

Now my calculations here are very, very crude, but they're a start. I welcome refinement to my methodology, but so far, the numbers show that Christopher's right.
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Old December 13 2011, 03:12 PM   #95
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Re: Mythbusters cannonball hits Dublin home and minivan

^Thank you. Really, isn't that what Mythbusters is all about? It's about turning any situation -- including surprising, even catastrophic failure -- into a learning experience. It's about taking events that affect us emotionally or viscerally -- "myths" -- and applying critical thinking to them, questioning our emotional reactions and testing them with science to determine whether they're valid. Here, the myth, the "dramatic," visceral take on a scary event, is "It's a miracle nobody was killed." But putting that myth to the test reveals that it's pretty much busted. And so instead of being scared and upset by this event, we turn it into a learning experience and are reassured. Knowledge is the best antidote to fear.

As for your analysis, I'm not sure we should go by square meters, since we're talking about a volume here and it should be cubic meters. We need to take the vertical space into account as well. Since we're dealing with houses 2-3 stories high, and maybe some variation in terrain height, we may be dealing with a vertical component on the order of 10 meters, to keep it simple. So if it's roughly 0.0012 people per square meter, it becomes 0.00012 people per cubic meter. Now, if we accept your figure of 500 meters for the length of the cannonball's path, multiplied by the cross-sectional area of the cannonball (pi x (0.1m)^2 = 0.0314 m^2), then the volume the cannonball's path carved out through the neighborhood adds up to only about 15.7 cubic meters. That comes out to only about a 0.19% chance of a person occupying that path, i.e. of a person being hit.

Now, what are the odds of that person being fatally hit? Let's call that the odds of hitting the head and central torso, basically... just ballpark, maybe a third of the body's volume? That makes the odds of fatality something like 0.06%. Other contributing factors like shock, blood loss, shrapnel, etc. could raise the odds a bit, so let's say 0.1% as a very rough figure. That's around one chance in a thousand.
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Old December 13 2011, 03:39 PM   #96
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Re: Mythbusters cannonball hits Dublin home and minivan

I had deliberately left the third dimension out because I wasn't sure how far or how high the ball had bounced, and keeping it on a flat grid simplified matters. But you're absolutely right to include it, refining both the methodology and numbers.

There's a paper in here somewhere!

Really, isn't that what Mythbusters is all about? It's about turning any situation -- including surprising, even catastrophic failure -- into a learning experience. It's about taking events that affect us emotionally or viscerally -- "myths" -- and applying critical thinking to them, questioning our emotional reactions and testing them with science to determine whether they're valid. Here, the myth, the "dramatic," visceral take on a scary event, is "It's a miracle nobody was killed." But putting that myth to the test reveals that it's pretty much busted. And so instead of being scared and upset by this event, we turn it into a learning experience and are reassured. Knowledge is the best antidote to fear.
So ... which one of us gets the beanie and Cthuloid lip hair?
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Old December 13 2011, 03:55 PM   #97
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Re: Mythbusters cannonball hits Dublin home and minivan

Oh, wait a minute, I made a mistake. I forgot to include your correction for the time of day, the fact that a lot of people weren't home in the middle of the afternoon. Using your estimate, that would halve the probability of injury to 0.09% and of fatality to less than 0.05%. (Probably much less. It would be informative to find some kind of survey of cannonball injuries and the rate of survival therefrom, but most cannonball injuries probably occurred before modern medicine and so we'd have to distinguish between fatalities due to the impact and fatalities due to infection or inept amputations.)
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Old December 13 2011, 04:59 PM   #98
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Re: Mythbusters cannonball hits Dublin home and minivan

Sigh.

My underlining point remains unchanged. Yes there's a large number of variables here, yes any one of those variables changing would change all of the other variables which would change other variables which would make everything different.

Thank-you Drs. Malcolm, I get the Chaos Theory idea.

Still this could have been fatal if various human elements had been different. If in the exact same conditions this occurred in someone had been walking on that path they would have gotten hit by this cannonball and killed.

If someone had been awake in the home(s) ans standing in the right place at the right time they would have been killed. If the guy with the van had gotten home whatever length of time later he would have been killed.

This wasn't fatal, sure, and the likelihood it could have been is very, very slim, yes given the physics, population density and everything else involved was slim.

My point remains, it could have been if the various human elements we know about were different.
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Old December 13 2011, 05:46 PM   #99
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Re: Mythbusters cannonball hits Dublin home and minivan

It could be fatal to get in your car and drive it down the expressway. It could be fatal to fly an airplane. Propane storage facilities sometimes blow up, threatening nearby civilians. Risks have to be considered in the context of their likelihood to cause harm.

We're not proposing that cannon enthusiasts start unleashing fusillades of artillery fire into residential neighborhoods -- at least I'm not, and Christopher strikes me as a fairly responsible fellow in that regard -- but this hand-wringing over what could have gone wrong seems to border on hysteria. The fact that no one was injured by this rogue projectile as it careened through a neighborhood pretty well illustrates that the math we're doing is right: it wasn't a fluke that no one was injured ... it was much more likely the cannon ball would pass through the area without doing anything more than a little structural damage. It would have been a fluke if someone were injured.

Generally, the outcome of any single event is the most likely outcome of that kind of event.
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Old December 13 2011, 05:53 PM   #100
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Re: Mythbusters cannonball hits Dublin home and minivan

Why isn't it a fluke that no one was injured? True, we can do the math until we're blue in the face, but how easy could it be to predict who is going to be there? You don't know who lives in the area, you don't know what their jobs are, you don't know when they're likely to be home.
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Old December 13 2011, 06:33 PM   #101
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Re: Mythbusters cannonball hits Dublin home and minivan

Mr. Laser Beam wrote: View Post
Why isn't it a fluke that no one was injured? True, we can do the math until we're blue in the face, but how easy could it be to predict who is going to be there? You don't know who lives in the area, you don't know what their jobs are, you don't know when they're likely to be home.
The population density of the region is an established fact (see my first post). Reports indicated that fewer people were home in the afternoon ... it's a simple inference from the fact that it's a residential neighborhood that the population density of the neighborhood would fall during working hours, thus reducing the chance of a hit. Even if you disagree with that inference, and I'm not sure how you could logically support such a position, there is still only a 0.19% chance that a cannonball fired along that path would actually hit someone.

Thus, no injuries is hardly a fluke.
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Old December 13 2011, 07:45 PM   #102
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Re: Mythbusters cannonball hits Dublin home and minivan

Don't misunderstand what Psion and I are saying. Of course any potential risk to life and limb is something that should be taken seriously. The odds of, say, two planes colliding in flight may be low, but even with a low probability, the consequences are grave enough that we employ radar and air traffic control and all possible precautions to get the risk as low as we possibly can. And of course the Mythbusters always take precautions to ensure the safety of anyone that they realistically expect could be endangered by a test with explosives or projectile weapons, because that's just common sense.

But there's a difference between responsible management of a risk and irresponsible sensationalizing of a risk. It is sensationalist and wrong to say "It's a miracle nobody was killed." That's putting emotional reflex ahead of the facts. There was a genuine risk of injury in this unfortunate incident, but risk is cause for reasonable caution, not hysterical panic. Stirring up unjustified fears is not a constructive reaction here. Both our calculations and just plain common sense should agree that the odds of an unaimed projectile hitting someone a kilometer away are very low. Certainly they're significant enough that every reasonable precaution should be taken not to fire unaimed projectiles through populated areas, and nobody can validly deny that the Mythbusters took every reasonable precaution. This was a one-in-a-million fluke and should not be taken to reflect negatively on their caution or responsibility, let alone on that of Sgt. Nelson and the staff of the Alameda bomb range. Certainly we should breathe a sigh of relief that that one-in-a-thousand event of someone being seriously injured or killed didn't happen. It could've happened, and it's great that it didn't. But it's just plain wrong to talk about it as though it were likely to happen. That's like getting off a plane and saying it's a miracle you didn't crash. Plane crashes do happen, and they're terrible when they do, and it's certainly worth guarding against them, but that doesn't mean they're more likely than the alternative.
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Old December 13 2011, 08:04 PM   #103
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Re: Mythbusters cannonball hits Dublin home and minivan

And I did not mean, nor do I think I did, to imply that the Mythbusters, Discover, the bomb range or anyone acted poorly in this case.
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Old December 13 2011, 08:09 PM   #104
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Re: Mythbusters cannonball hits Dublin home and minivan

Trekker4747 wrote: View Post
And I did not mean, nor do I think I did, to imply that the Mythbusters, Discover, the bomb range or anyone acted poorly in this case.
I think we're all in agreement on that. The Mythbusters team did a great job addressing the mistake. My only disappointment is that they're not going to take advantage of it to present a "learning opportunity" episode covering this and other Mythbusters accidents.

We're just debating the value of statements like "lucky no one was hurt" at this point. And it's a fun, interesting debate so far.
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Old December 13 2011, 09:37 PM   #105
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Re: Mythbusters cannonball hits Dublin home and minivan

Psion wrote: View Post
I think we're all in agreement on that. The Mythbusters team did a great job addressing the mistake. My only disappointment is that they're not going to take advantage of it to present a "learning opportunity" episode covering this and other Mythbusters accidents.
Right, because a key part of science is being able to learn from failures, or at least from things that don't go the way you expected.

What started this for me was the discussion of responsibility. It's certainly responsible for the Mythbusters to respect the families' wishes if they prefer not to have this footage used, but I think that if the families were receptive, then using this as an opportunity to teach some science (and some statistics) would also be a responsible way of dealing with it, because the intent would be constructive rather than exploitative.


We're just debating the value of statements like "lucky no one was hurt" at this point. And it's a fun, interesting debate so far.
Maybe the issue is how we define "lucky." I think when people generally say things like that, what they mean is "It's a relief nobody was hurt," and I certainly can't argue with that. But it should be understand that it's not a great surprise that nobody was hurt, because that was the most likely outcome. It's hard enough to hit targets you're deliberately aiming for. This rogue cannonball was an incredible fluke event to begin with; if it had hit someone purely by random chance, that would've been an even more incredible fluke. It would be whatever the evil equivalent of a miracle is.

Hmm. Does it say something about our cultural perception of the probability of good vs. bad events that we have a word for "extremely unlikely positive event caused by divine intervention" -- namely "miracle" -- but don't have an equivalent word for "extremely unlikely negative event caused by demonic intervention"? Do we just take it for granted that surprisingly bad events are likely to happen without needing special explanation, whereas surprisingly good events are so unlikely that they require divine intervention? That kind of "expect the worst" mentality might be related to the same kind of thinking that prompts the "It's amazing nobody was killed" reaction here.

Of course, I'm as human as anyone and I'm certainly not immune to overreacting to the threat of low-probability negative outcomes. It's why I avoided flying for many years. (These days I'm okay with flying per se, but I have issues with the cost and the x-ray exposure from airport scanners. Although the latter is arguably a low-probability risk too.)
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