By the Numbers

I presume most people recognize that there is a vague connection between statistics and probability, but, having taken a course in probability theory, I'd be willing to bet the farm that very few people realize the full breadth of intimacy between the two. This is true in particular because despite having studied both, I'd count myself as one amongst the naive. From the outset probability is simply difficult, and often counter-intuitive. Not only does probability proceed in ways contrary to our intuition, it does so in such an amazingly tricky way! Maybe it is a function of how easy it starts out: given a typical six sided die, most everyone knows that the chance of guessing which number comes up is one in six. Easy enough, you pick one side out of a total 6, so the probability is 1/6. The common understanding of probability stops there, for the simple reason that any situation even marginally more complicated than that becomes remarkably more logically and mathematically sophisticated. Suppose I'm flipping a coin and you're guessing the results. For some reason you're having terrible luck and you've guessed wrong 10 times in a row, what's the probability that you guess the next flip wrong as well? Think about it for a minute and when you've logically arrived at what must certainly be the answer, highlight the following space for the answer:  1/2

Next, try to logically deduce the probability of guessing incorrectly for 10 coin flips in a row. Answer:   1/1024

It only gets so much worse from there, to the extent that I'm really not confident I could present the correct answers myself! Even admitting that I can't help but try for one more. Assume that 4 out of 5 people prefer Crelm toothpaste. What's the probability that from a selection of 5 people 4 of them prefer Crelm? Answer (I think): 256/625

The important notion here is that a probability says something both nebulous and concrete about reality. If a truly random die is thrown 6 million times, in all likelihood each number will have come up about 1 million times. If 4 out of 5 people really do prefer Crelm, then the chance that a randomly selected person prefers Crelm is 4/5 or 80%. As much as we all like to think that the statistics don't apply to us (because we're special), if the statistics are accurate there's no way to escape them. Most of the time this is a banal statement, as when referring to whether or not you prefer Crelm--either way it's not exactly a big deal. But then... there are the other statistics. "Around 50% of US marriages end in divorce" can be a pretty hard pill to swallow for a couple walking down the aisle. I have reason to believe the number of couples who'd figure they end up on the successful half of that statistic while exchanging vows is much higher than 50%--clearly if they thought it wasn't going to last they'd probably not be entering the commitment in the first place. Similarly, doubting the success of the marriage from the outset probably isn't going to increase the chance of a favorable outcome. What's left is an awkward position, objectively maybe the best one can think is that at least the odds aren't as bad as they could be, better than any casino game. However marriage is a particularly special case for a number of reasons, the primary one being the shift in locus of control which is applicable to all interpersonal relationships; though a bit less severe, anyone who's been dismayed by the lack of a second date (etc.) knows the score. To be fair the actual divorce rate changes based on many factors, where 50% is just the overall rate. The lowest divorce rates are found in each of the following categories: first marriage, atheist or agnostic, age 30 or older, residing in the Northeast and no cohabitation prior to marriage.

Uncontrollable statistics naturally lead to other more personally manageable probabilities. For instance, 28% of car accidents in the US happen while at least one of the drivers is using a cell phone. This is the part where I reiterate: we love to think we're special and that the statistics don't apply to us, but it just doesn't work that way. We are all special, I'm fully on board with that, but that doesn't grant any of us statistical immunity. Using a cell phone while driving (even with a hands-free headset) substantially increases the chance that you will be in a car accident, which could result in your death, or, arguably worse, the death of another/others with the accrual of manslaughter charges and the lifelong burden of knowing that you've killed someone. It's very simple: while the car is in gear, your phone doesn't exist. There are absolutely no excuses.

Demonstration of feasibility

I'm a bit too busy to give the normal glyphic flood, but as proof following my plea for autonomous vehicles this demanded mention. The Center for Automotive Research at Stanford (CARS) is planning to send an autonomous Audi up Pikes Peak at race speeds. Pikes Peak is a mountain road used as a rally stage, with surfaces varying from packed dirt to loose gravel. Actually an autonomous car has finished the course previously, but "only" at an average 25 mph. There is some reason to suspect the Stanford team will succeed in their intent, as they won DARPAs Grand Challenge and took 2nd place in their Urban Challenge; the car can at least drive 120 mph across the salt flats. I cannot wait to hear the results!

Nissan Succumbs to Logic

Making the rounds on the web is a new Nissan Land Glider concept vehicle. My opinion is that this represents the first indication of a correct step towards a sustainable near-range vehicular platform from a major automobile manufacturer. Included with all the sites discussing it are a few pictures and the following video (which has a very interesting choice of music with what I'm quite certain is the avant-ambient work of Steve Roach):



Get more after the jump!

Old cars are not safer!

Here's another common misconception ready to be exposed: old cars aren't safer. By older cars it is typically meant late 60's and prior, and the thought goes that because they are heavier, they are safer. This is absolutely false, weight doesn't matter in vehicle safety; what really matters is the ability of the frame to absorb impact while maintaining structural integrity of the passenger space. The safety of a vehicle accident is very simple physics: by spreading an impact over time and distance the force of impact is also minimized. This matches our intuitive understanding, just imagine dropping an egg from 10 feet. If the egg hits concrete, it breaks--it goes from speed to stopped instantaneously. If the egg hits 5 feet of padding, it will be fine--it will slowly go from speed to stopped over time and distance, as the padding absorbs energy from the moving egg. The "padding" in a car accident is mainly of one form, the crumpling of steel. Of course this is all moot if the passenger cabin is compromised, as our soft, fragile bodies are no match for hard things moving at high speeds, and that's the rub; no matter how much energy is absorbed, if the engine block ends up in the driver's seat or the vehicle explodes, there is little hope of walking away from the accident. Excluding air bags, seat belts, and other obvious safety features, modern cars still have the advantage because they are designed to crumple up to the cabin, which is in turn designed to be as rigid as possible. As far as I know, older cars weren't designed with any energy absorption in consideration, and thus a double edged sword: if the car doesn't crumple at all, no energy is absorbed and it is like an egg hitting concrete; if the car does crumple, it will most likely continue to crumple well past the engine bay and into the cabin, rendering all energy absorption for naught. And now, for the demonstration:



The cars collided each moving at around 40 mph. As is usual for the Internet, a number of people (I think it's safe to assume they are classic car enthusiasts) have stepped forward challenging the veracity of the video, suggesting that the chosen car was not representative. As in any scientific pursuit, contentions are often valid and desired, and the responsible scientist will acknowledge, explore, and respond to any valid concerns. I found this on Consumerist, where amongst the comments arose criticism (from user Nighthawke) as follows: the appearance of reddish dust that may indicate the presence of structure-compromising rust; the lack of seat belts used in the test vehicle (which were available as a dealer option); The expense of an unsafe frame for the aesthetics of the curved front pillar specific to Bell-Airs; Finally, the frontal offset test is unfair because the skinny engine didn't have the opportunity to absorb energy.

The responses are easy, as only the first point is really valid. The IIHS, which conducted the test, assured that the "rust" was just accumulated dirt and the car appeared structurally sound. For the final 3: the optional seat belts were lap belts only, and almost certainly wouldn't have made a modicum of difference; perhaps the Bell-Air has uncommonly poor structural integrity (I'm not sure, but I know of other classic cars with the same pillar shape), but the whole point is to show that collision safety design has improved tremendously and no other modern American car has performed anywhere near as bad as this Bell-Air; Last but not least, life isn't fair and the frontal offset test is one of a scant few standard tests that all cars undergo. Likewise, it's an important test for how common this type of accident is; James Dean died in a frontal offset collision. Frontal offsets have a particular propensity to cause extensive damage--the energy of the collision is focused on a smaller portion of the vehicle, thus causing more damage. In fact, in terms of energy absorption, a direct, in-line/"head to head" collision is safer! Clearly our intuition begins to fail us at this point, our instinct even more so; two people destined for a head on collision will swerve, unfortunately magnifying the danger of the impact be reducing the surface area of the collision. Nonetheless, this idea of applying a force over increased surface area is one that is often understood (or at least utilized) by people using snowshoes. This same principle is what allows people to lay on a bed of nails.

At least we have some kind of standards! Check out other poorly fairing vehicles here and here. In closing, I want to point out that heavy modern cars aren't safer either--in fact many large vehicles (trucks, SUVs) fare worse in passenger protection than smaller vehicles for a few fairly obvious reasons. Also, it's a matter of perspective: presume large vehicles are safer for the occupants, what about the people in any smaller car that may be hit? You'll probably walk away from your Suburban with a few scratches, but how will you feel about having possibly killed several or all of the people in that Yaris? The truth is, large vehicles aren't safer, they're more dangerous for everyone. The only reason huge cars can be viewed as safe is because there are other huge cars out there, and that's just an unsustainable and foolish perspective--keep it going and before long we're all driving monster trucks. Unfortunately even that won't help just as our huge SUVs haven't helped because more and more people will be getting injured in single-vehicle rollovers.

Certainly cars have gotten a lot safer, but as long as they are being driven by people, they will never be safe enough.