Magic numbers: Society and what is "normal"

I was involved in a thread once upon a time and got trolled (expected if you talk about anything of significance -- and sometimes even if you are just talking about the weather). This was a thread talking about one of society's "magic numbers".

These are part of a group of numbers which we use based on statistical information. As Mark Twain once said (he said that the British Prime Minister Disraeli said it first): "There are three kinds of lies: lies, damned lies, and statistics."

For example, in current society a number called the Body Mass Index (BMI) is used to determine whether you are overweight, underweight, or in a "good range". This number is a ratio of height to weight and provides reasonable results for 80 to 85% of the population. For the other 15% to 20% of the population, the number just doesn't work well. If you are an athlete (or work out a lot and have more muscle) it doesn't work well. If you are a total couch potato with almost no muscle it will actually give you a better result than you "deserve". If you truly do have "thick bones" you will be at a disadvantage. This doesn't matter that much except if people are basing other things on that number -- insurance companies and computerized social services for example.

Why do we use this "magic number"? It is quick. It is easy. It is cheap compared to other, more accurate methods of body fat percentage calculations. However, even if one used a more accurate measure than that of the BMI, it would STILL not be accurate for everyone because there is no "one body shape fits all". For some, to hit that "ideal", one part of their body would have to be UNDER-weight in order for the average to be correct.

There are other "magic numbers" used. The "age of consent" is a magic number which, in more technical society, indicates that a child has become an adult. They are able to sign contracts, do things without permission from parents or guardians, get married and so forth. This magic number ranges from 13 in Japan to 21 in Bahrain. In some non-technical societies, it depends on the age when menarche sets in for women and "rites of passage" for men.

Many people get the direction of "age of consent" backwards -- thinking that a higher age of consent protects the child more from society. In reality, the family, church, or government usually have many options to do what they want with children at the age they think is right. The "age of consent" is what gives people the right to control, for themselves, decisions that affect their lives.

These numbers are set for two principal reasons. One is to prevent abuse of others by pushing them into activities (such as marriage or other things) before they can really make good decisions for themselves. The other is to determine an "age of emotional and mental maturity" which is taken to be an indication that they can make good decisions.

This type of magic number is determined almost solely by societal norms. It is usually lower in agricultural societies and higher in societies that require a longer period of education and social adjustment. It is also higher in societies where familial, and religious, control of women is greater. But, as is true with the BMI, it is (at best) a statistical reflection. Some will not be ready at age 30 to properly make decisions for themselves. Some might be ready at a very young age. There have been no psychological studies and are unlikely to be such.

Even the "age of consent" is not for everything. There are separate "magic numbers" for voting, being drafted for war, being able to drive, being able to work full-time, for purchasing and using legal drugs, and so forth. In many instances, the society would like to prohibit the activity but do not have sufficient backing from the populace to do such. Therefore, they set an age which most of society agrees is appropriate.

In all of these areas (and more), the "magic number" is sometimes determined by a statistical averaging and sometimes determined by societal norms. It is rare that the number is backed up by thorough, and consistent, studies -- which is why it is "magic".

What other "magic numbers" are you aware of within society? Do you know of any that have a researched background reason? Others that do not have such a background?

Driving and Physics : the laws of the road that cannot be broken

   There are two sets of laws involved with driving a car. The first set is made from the human-made laws which are a set of etiquette laws of how people can share the roads and passageways while driving 700+ kilogram vehicles. The other, underlying, laws are associated with the laws of physics. The first set can make interacting with other vehicles, and their drivers, more predictable -- and generate income for the various cities in which you drive. The second set -- unlike the situation for the Coyote or Bugs Bunny in Looney Tunes -- cannot be broken and determine what will happen when your car interacts with other physical objects.

   The first topic that I'll mention is that of relative velocities. If you are driving 30 mph (or 50 kph, if you prefer) and you run into a wall, there is 30 mph (squared times half your mass) amount of force with which you hit the wall. This is called kinetic energy. If you run into something coming towards you (such as another car) at 30 mph, the amount of energy is quadrupled and it is as if you hit a wall at 60 mph. (Note that hitting a wall at 60 mph does more than four times the amount of damage as 30 mph.)

   If two cars are going in the same direction then the collision energy is subtracted. If you are driving at 60 mph along a road and someone driving at 65 mph bumps into you then it is the same as if they drove into a wall at 5 mph. Not very noticeable unless that bump makes you lose control and you use your 60 mph kinetic energy to run into a tree.

   This is the principle behind merging. The idea is that you drive your car such that you are driving at approximately the same speed as other cars by the time you leave the on-ramp to the highway. You speed up a little and safely merge ahead of a car. You slow down a little and safely merge behind a car (preferable). If you are going 30 mph while all the other cars are going 60 mph it makes it much difficult for you, and for all the other cars, to merge safely.

   This leads to the next topic -- "tailgating". This is where you are traveling at a speed such that it is not possible to stop without colliding into the car ahead of you if they abruptly stop. My old traffic books indicated one car length per 10 mph -- so, around 90 feet for travelling at 60 mph. I routinely see people driving with a single car length between cars while driving 60 mph. This situation is very dangerous for two reasons -- if the car ahead abruptly stops, you have converted a 5 mph bump into a 60 mph crash into a wall. The second reason is that it makes it very difficult to merge. The merging car cannot safely go ahead, or behind, other cars on the highway if there is no room.

   Tailgating is directly involved with another law of Physics called inertia. This is Isaac Newton's "First Law of Motion". It says that if something is at rest it will want to stay at rest (difficult to start moving) and if it is in motion it will be difficult to stop and will continue at the same speed and direction unless outside forces change it.

   So, let's apply this law of inertia to tailgating. Stopping distance involves the factors of "reaction time" and physical stopping time. Reaction time varies between people. In general, women have better reaction times than men and, in general, younger people have better reaction times than older people. However, reaction time can never be zero as it takes time for the outside signal to reach your eye (you see a brake light) and your brain to process the signal to start a reaction (stepping on the brake).

   This is why it is impossible to stop if you are tailgating someone and they abruptly stop no matter how good are your reflexes. IF you both started stopping at exactly the same time AND both had the same tires and same braking systems on your cars THEN tailgating could be safe. Those factors are not true.

   This leads into the final topic for this blog. Driving in weather. Weather affects a lot of factors. It can make visibility easier or harder -- which affects reaction time. It can make the traction of the tires on the road better or worse -- which affects physical stopping time. Results from relative velocities remain the same but the outside aspects which makes a difference in how, when, and why have changed.

   So, if you drive on a snowy, icy road you have increased reaction time, physical stopping time and the principles of inertia make it more difficult for you to either turn or stop without the car wanting to continue in the same direction and speed.

   In the end, the laws of physics will exist and they won't change so merge properly, don't tailgate, and allow for changes in road conditions for judging safe driving.

[formula for kinetic energy corrected due to the sharp eye of Dave Albay-Yenney]