When you get behind the wheel of your car and go for a leisurely drive, you become an estimator of probabilities whether you realize it or not.
Driving down your neighborhood street, you might spy a dog that’s meandering off its leash.
Assuming that you are a conscientious driver (I hope so!), you would right away start to consider the chances or probabilities that the dog might decide to head into the street.
Presumably, you aren’t going to just wildly gauge the odds of the dog doing so, and instead will use some amount of logical reasoning in making your estimation.
For example, you might look to see if the dog is heading away from the street, toward the street, or paralleling the street, plus carefully observe the pace of the pooch.
Meanwhile, you might be considering the speed of your car as it is rolling along, and be judging the timing of when the car could reach the point that the dog might startlingly end-up in your path, assuming that the dog decides to dart out into the street.
Maybe you perchance spot the owner of the dog and realize there’s another possibility involved, namely that the owner might realize that a car is going to potentially jeopardize their beloved pet, and perhaps the owner will call out to the dog to get it to retreat away from the impending danger, urging the canine to scamper away from the curb.
Here’s a twist on top of it all.
You know the dog, having seen it around and petted it from time-to-time.
Is there a chance that the dog will see you, sitting in the driver’s seat, and because of your friendly attachment, it might decide to intentionally come toward the vehicle?
On the other hand, you know that the dog has lived on the block for many years, and never had any incidents with cars, thus, in your mind, you would rate the probability pretty low that the dog will opt to do so now.
Yet, as they say, you never know, this might be the one time that it happens.
Overall, there are seemingly numerous and complex innate probability calculations going on in your noggin about this evolving situation.
Consider this base set of mental machinations and estimations involved:
· What is the probability that the dog will turn toward the street and enter into the roadway (let’s label that as the probability of event E occurring)?
· What is the probability that the dog will do so at a timing that would potentially intersect with your car (let’s label that as the probability of event I occurring)?
· What is the probability that you will realize the dog is ending up in the street and that you will have sufficient time to hit the brakes to avoid ramming into the animal (label this as the probability of event T)?
· What is the probability that your car will respond to your wishes, namely that if you do have to jam down on your brake pedal that the car brakes will work properly and bring the car to a halt (let’s say this is the probability of event H)?
· And so on.
Each of those are specific potential events or occurrences, and each has its own chance or probability of happening, meaning that you’ve somehow got to come up with a semblance of the probabilities associated with the occurrence of I, E, T, and H.
Furthermore, not only are you estimating those distinct or individual probabilities, you are combining them together to guide your actions as the driver of the car (trying to blend or unite together I, E, T, and H, overall), including coping with those events that are independent of each other and those that are dependent upon each other.
Wow, that’s a lot to consider!
Before I proceed with further explanation on the car driving probabilities aspects, let’s all assume that you judged wisely and fortunately avoided the pup, which it turned out became so preoccupied with a nearby fire hydrant that it never did get into the way of your car, thankfully.
The overarching point is that you had to make judgments or assessments that involved probabilities.
Thinking About The Thinking Of Probabilities
Some of you might right away be protesting that you drive a car all the time and never need to mathematically make such arcane calculations.
In other words, you insist that your mind is not somehow identifying a numeric value for the likelihood of an event, nor that you are using some complex formula to combine together the probabilities of numerous potential events as though trying to arrive at an overall probabilistic score.
Maybe you don’t.
Or, maybe you do, and you just don’t realize that you are doing so.
Unlike the probabilities that you might have learned in school, admittedly your mind might not be converting the things you see and do into a numerical description that consists of a probability value between 0 and 1, whereby 0 means the chances are nil of the event occurring and the vaunted value of 1 means it is an absolute certainty.
Furthermore, your thinking processes might not be overtly ascertaining the Merriam-Webster definition of probability, to wit “the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.”
For those of you that have taken a statistics class, you might recall “fondly” the oft taught Bayes’ theorem or rule, named after its author, Thomas Bayes, and his famous formula or algorithm that has to do with conditional probabilities.
Not wanting to stir nightmares of your having taken a mandatory class on stats that maybe didn’t go so well for you, but you might recall that you can figure out the probability of an event A occurring given that event B is true, doing so by multiplying the probability of B given A is true, times the probability of A, and dividing that multiplied result by the probability of B.
Or, something like that (go ahead and look it up, you’ll smile at the refresher, undoubtedly).
Anyway, let’s say that your mind doesn’t use those formalized means to calculate probabilities.
For all we know, your mind uses some other approach to deal with probabilities.
Nobody can say for sure.
Our minds are one of the greatest hidden mysteries, locked away in our brain, and within seemingly easy reach, yet remains incredibly inscrutable, despite modern attempts by cognitive scientists, psychology researchers, neuroscientists, and others.
The use of mathematical models such as Bayes’s law is useful nonetheless and appears to capture human behavior, which is exhibited by what we do, regardless of what actually takes place via the neurons in the brain.
Contextual Changes In Probabilistic Thinking
In describing the car driving example about the dog, you might have noticed that I purposely indicated that you were taking a leisurely drive.
Imagine how your mind must be racing with probabilities when you are driving under pressure, such as driving on the freeway, in the rain, on the way to work, and you are late and trying to make up for the lost time by driving aggressively.
What happens to your probability estimations then?
It would appear that drivers might adjust their belief about probabilities, based on the context of the driving situation. Since you are late to work, you might mentally justify going past the speed limit and reduce your personal assessment of the probability of getting into a wreck, simply to rationalize your bad driving behavior.
Or, you might think to yourself that you are normally a careful driver, one that takes little or no chances, so you’ve “earned” the right to drive recklessly, this one time, and are willing to take the chances of getting into a car accident, though you convince yourself the odds are low due to your usually being overall precautious as a driver.
In the United States alone, Americans drive about 3.2 trillion miles per year, which is a lot of miles.
Much of the time, we manage to drive without incident.
This almost seems like a miracle, when you consider that having about 225 million licensed drivers taking to the roads for trillions of miles is bound to be a scary thing. Regrettably, sadly, our driving actions aren’t always incident-free, including that there are about 40,000 deaths annually in the U.S. and around 2.5 million injuries due to car crashes.
Speaking of driving, let’s consider what is taking place to try and develop AI-based true self-driving cars.
True self-driving cars are ones that can drive without the need for a human driver. The AI system is able to drive the car, and never need to ask assistance from a human driver, and nor require that a human driver is at the wheel and ready to take over the vehicle.
Developing an AI system that can be fully autonomous when driving a car is a lot harder than it might seem.
An ongoing debate involves the role of probabilities.
Well, recall that we’ve just discussed that human drivers seem to make use of probabilities, though whether it is a numeric value or some other means of mental consideration is an open question.
Today, we don’t require human drivers to explicitly say what probabilities they are using as they drive a car.
We let your actions speak for your words.
If you remain incident-free, apparently you are doing well at your probability estimations. When you get into a car crash, we question your probability thinking and you can potentially go to jail or suffer financial penalties for your driving results.
Consider these crucial questions about an AI self-driving car:
· When building or developing an AI system, and especially one that drives a car, should the AI have explicitly programmed capabilities at probability estimation, such that we can all open the kimono and discuss what probabilities it is using for making life-or-death driving decisions?
· Or, do we let the AI system have hidden assumptions about the probabilities involved in driving, and for which we as humans might not even know or be able to ferret out those encoded probabilities?
Another facet about self-driving cars involves establishing virtual boundary boxes around detected objects, and estimating the chances or probabilities that those objects might physically encounter the self-driving car (see the link here for my analysis of such aspects).
The advent of Machine Learning (ML) and Deep Learning (DL) is a handy means to aid in the effort toward “programming” AI systems to drive, yet this also generally is taking us down the path of not being able to explain or articulate what kinds of probabilities are associated with the AI driving system under-the-hood.
In a typical use of ML/DL, you collect lots of data and have the ML/DL algorithms do pattern matching, attempting to identify computationally any underlying patterns. The resulting ML/DL can become large and convoluted, reducing the chances of being able to decipher any logical basis for why the mathematical patterns arise.
How does this relate to the probability of driving?
Suppose I collect lots of driving data associated with human drivers and use that as the primary input into an ML/DL.
The ML/DL tries to model the driving behavior, and then the AI system will drive in a similar manner.
If the data collected was based on say aggressive New York City drivers, presumably the AI system would then have a tendency to drive in a similar vein, based upon the patterns of how those drivers tend to cut corners and take heightened risks while driving.
Digging into the ML/DL model might not especially showcase the matter, and only once the AI system is driving a car, would you begin to realize that the AI has adopted those in-your-face driving tactics.
In short, should AI-based self-driving cars be able to exist and drive on our public roadways even if we can’t discern their internal probabilities aspects, allowing them to be opaque or impervious as we allow for the hidden mysteries of what’s going on in human minds of drivers, or should we instead insist that the AI systems have to be opened up and reveal explicitly those matters?
Time will tell and so will the public and regulators, depending upon how the AI self-driving car adoptions proceed.
Social Distancing and Probabilities
Recently, we’ve all suddenly become a lot more conscious about probabilities, though not in the context of driving.
To avoid potentially getting infected and to try and curtail or mitigate the rapid spread of the COVID-19 virus, social distancing has become a key tool toward fighting the pandemic.
You might be puzzled about the role of probabilities since it doesn’t seem to be an explicit discussion topic when it comes to social distancing.
Well, once again, whether you know it or not, you are indeed making use of probabilities, albeit not necessarily in a formalized mathematical way and instead perhaps in a more instinctive and intuitive manner.
Let’s see how.
The rule-of-thumb about contact with others involves remaining at least six feet away.
This is really a physical distancing aspect, rather than a “social” distancing aspect, and some wish that the phrase hadn’t become known as social distancing versus say physical distancing. They mention this facet since you can still presumably be sociable in our society, and do so with an added physical distance involved, rather than the sour implication of somehow becoming “anti-social” via distancing yourself from other humans.
In any case, the basis for keeping six feet away from others is due to the attempt to avoid getting the virus on you.
· If a person has the virus and they physically touch you, there’s a chance or probability that they might transfer the virus to you.
· If a person has the virus and coughs or sneezes, there’s a chance or probability that the virus now is in the air, and it could land on you.
To try and avoid getting touched by a person that has the virus, you prudently want to stay away from the person, and though you could potentially get within a closer distance and avoid being touched per se, there are the chances too of the airborne form of physical contact, so it makes sense to remain far enough away from the person that the odds of the airborne contact are lessened too.
As a result, society has collectively agreed on a distance of six feet.
It’s an easy rule to remember.
Some though misinterpret the rule.
They think it somehow gives them a kind of ironclad guarantee or absolute certainty.
It’s more of a rule-of-thumb based on probabilities.
The probability of not physically touching a person that has the virus and that is six feet away from you is considered better than if you were within six feet, and the same is said of the airborne transmission, namely that by staying six feet away you are lowering your probability of having an airborne release of the virus be able to land on you.
Similar to when thinking about a self-driving car or even a human that’s driving a car, there are various potential events or occurrences that you are assigning a probability toward when practicing social distancing, such as:
· Probability that a person near you has the virus (let’s label this as probability V).
· Probability that the person will make contact with you via touch or via the transmission of their airborne release (let’s label this as probability R).
· Probability that once the virus has landed on you that you will contract an infection from the virus (label this as probability C).
· Probability that upon contracting the infection that it will engage your body and cause substantive harm to you (label this as probability Y).
· And so on.
In the case of probability V, we are right now all adopting the perspective that we must assume that V is high for everyone around us, even though we might not know whether that’s really the case or not (this has especially become a concern upon the realization that people can have the virus and yet are not displaying any obvious indication, i.e., they can be asymptomatic).
Those college students that seemed to be frolicking in the sun during a Florida spring break, despite the pandemic, could be said to have been underestimating the probabilities involved in this matter (though, some might argue they weren’t considering the probabilities altogether or were ill-informed about the probabilities).
If someone falsely believes that Y is near zero, in other words, those that think they are invulnerable and cannot be harmed, the other probabilities of V, R, and C, don’t especially matter to them.
Taking precautions such as wearing a mask or face covering are intended to reduce the probability of C, meaning that by putting on a shield or some other precautionary artifact, you are attempting to cut down the chances of C occurring.
For people that go for a stroll or wander around where other people are, they are inextricably going to be mentally coping with probabilities as it pertains to social distancing, whether they realize they are doing so or not. Similar somewhat to the act of driving a car, the situation of the moment will cause you to adjust your perceived probabilities associated with V, R, C, and Y.
Social distancing is a probabilistic based approach.
People are continuously estimating the probabilities associated with encountering other people and having to adjust often on-the-fly as to the perceived risks involved.
When discussing probabilities, it is important to also realize that it is not just the events to consider, but also the consequences or severity of the event itself, assuming that the event does occur.
Events that entail life-or-death consequences require that we be even better at our probability estimations, and the more that people are aware of the matter, hopefully, the more prudent they will be.