Common Sense, Knowledge, and Intelligence

A statistician, a mathematician, and a logician are on a train traveling through an unknown country.
The statistician looks out the window and sees a black cow.
He concludes out loud, “The cows in this country must be black.”
The mathematician protests, “You don ‘t know that. All you know is that there is at least one cow in this country that is black”
The logician shakes his head in disagreement and says, “You don ‘t know that either. All you know is that there is at least one cow in this country that is black on one side”

This joke very concisely explains the nature of the rational thinking processes that humans use. The trick is in understanding what each kind of thinking means and when it should be used and more importantly when it should not be used.

Let us take our first thinker, the statistician; he represents the majority of rational human thinking; that which we call common sense. What should we do next? What is everybody else doing? The second question is the kind of question statistics answers. The vast majority of what we do is usually reflected by what the population group that best represents is doing. Disagree; you think you are an individual? Where do you buy clothes? Your food? How do you cook? The answer to these questions is pretty much what everyone else is doing.

You think that those are things that humans are forced to have in common? What shows do you watch? What are your hobbies? What are your opinions? You will find that whatever the answer to these question, many fellow humans share that choice or opinion.

What the statistician has done is inferred from a small piece of information, what the greater body of information is. This is not necessarily a bad thing. It makes life much easier. Why should your choice of clothes be a weighty decision? The only question one need ask, is the general accepted choice (otherwise popularly known as General Body Of Knowledge ; GBOK) the right choice AND is it the right choice for you?

Some are highly resistant to the idea that the people around us have such a strong impact upon us. I assure you that there is really no other way we could make such advancements in civilization and our own personal lives. The vast majority of our knowledge is statistically obtained.

Let us further examine what the statistician sought to do. Essentially, he made a conclusion about the rest of the population by observing one cow. Should he have done this? Well, using our common sense we know that it is quite possible to have cows of many different colours, all inhabiting the same country. The question is how many cows should he have looked at it. All these aspects are explored in the study of statistics.

The romantic way of looking at it, is that statistics measures the quality of truth. Many people feel that truth is an absolute. Truth as an ideal, is an absolute but much of our common everyday truths are not derived from absolutes.

Why is truth so important? Truth is knowledge; when scientists seek knowledge, they are seeking the truth. So how is truth not absolute? Take many of the medical treatments that we use. Let us examine two examples 1) putting a bandage on cut and 2) headache pills.

Looking at the first case, if we are bleeding, putting a bandage on the cut (properly) stops the bleeding. The process by which this works has been for thousands of years; in fact the bandage itself is not necessary BUT it works a lot better with it. When you put pressure on a wound, it restricts the blood flow to that area, letting the undisturbed blood coagulate which seals the wound. We know why this works and we know it works by direct observation BUT this is not always true. Like the mathematician points out that we know that there is at least one black cow in the country, we know that this method works very often. In fact, the method is so reliable, there is an entire bandage industry based upon this method. That being said, there are hemophiliacs on whom very bandages do not work. Also, bandages fail to stop bleeding on severed limbs. Common sense tells us that bandages were never meant for those cases. What we mean by those cases, is that they are outside of the parameters of the solution.

This notion of parameters is very important in rational thought; the idea that a line of thinking only applies in certain cases. In mathematics, it is defined as the domain upon which the function or idea applies.

So what we have found is that even direct solutions do not apply absolutely. Let us examine the second case; the headache pills. Why do we believe they work? The only reason we should believe it works, is that our headache goes away when we take the pills. So do they do that? Personally speaking, my headache has never gone away with taking the pills until I go to sleep. I have not taken headache pills since I was a child; headaches to me are not that bothersome. For others, headaches are a debilitating condition.

Given the huge market for headache pills (it is larger than the market for bandages), how do they ascertain the pills work? This is where statistics shines. The statisticians know (by gathering statistics) how long headaches last. They then do tests of various kinds. One kind is called the double blind test. A group of people, a sample, are gathered; hopefully selected randomly from the population.

Selecting people randomly is not as easy as you think. If you randomly chose people that happen to be walking by a corner downtown at 10:30 am, how many of these people will be farmers; or in the manufacturing industry; or school teachers; or school children. What you will find is that there is a bias built in by your choice of selection. Statisticians work out ways to remove biases from tests. The removal of bias, is one of the purposes of using the double blind test.

So with this randomly selected population; half are given the headache medication and half are given a placebo that they believe is headache medication. No one is told who is getting medication and who is getting the placebo, not examiners nor the test subjects; hence the name double blind. This removes the bias that the subject believes that the pill should work so they are motivated to think their headache has been cured and it removes the bias from the examiner who may chose subjects that are likely to respond well.

The population size has to be large enough so that all the variations in people, headaches, errors in use will be small in comparison to the overall population size. So not only do all the right people have to be included; a sufficient number of them have to be taken as well, to be truly representative of the human population. Now the perfect answer (ie the truth) could only be obtained if we ran both set of pills on every person on the planet numerous times. Obviously, a test of this scale is impossible. The study of statistics measures and defines how large a population, over how many trials will yield results with how much error.

This leads us to the last aspect of statistics that we will examine (for now). Error; what is that supposed to mean? Obviously, we want as little error as possible but by the very definition of sample, we are guaranteed some error. Statistician seek not only to minimize error BUT also to quantify it. The best example of this is when we here poll results. They always report results for example; the figures are accurate within 4% 19 out of 20 times. Ever wonder what that means? Let us say that poll say President Bush ‘s policies are supported by 30% of the population; the figures are accurate within 4% 19 out of 20 times. This means is that if the poll were taken 20 times, 19 of the poll results would be (4% of 30 is 1.2, so 30 minus 1.2 is 28.8 and plus 1.2 is 31.2) would be between 28.8 and 31.2. What about the last result? It would either be less than 28.8 or more than 31.2.

The vast majority of modern knowledge is gained (or more precisely measured) through statistics. We have no other way of measuring it BUT more over there is no better way. Many luddites use this idea to suggest that modern science knows nothing at all. This is where the understanding of mathematics comes to the rescue. NOT to save us from statistics but to save us from the backward way of thinking of the luddite.

The question is how do we KNOW things at all? What does it mean to KNOW something? Some people say they may not know much but they know the sky is blue. Well just look at it. So what about a cloudy day, or night time or New York or London? The correct statement is “Sometimes, somewhere the sky is blue.” What was wrong with the first statement? Well, the parameters were not correct. For the statement, “The sky is blue” to be correct, the sky would have to be blue all of the time in all places. For any such statement to be true, it has to be true for all cases. BUT how many times do we know anything for all cases? Essentially, there would be no point in saying anything at all if we had to examine all cases to be making a statement.

So where is this line drawn? Well the parameters are defined by common sense. When most people say the sky is blue they mean today and wherever they are. They usually do not mean a week from now half way across the world.

What I am saying may sound silly and obvious and these arguments might sound like the kind children make but full grown adults make the same silly arguments.

Case in point, smoking. I can not count, the number of times I have had people tell me that it is not proven that smoking is bad for you. They will say they have had some uncle or aunt who has smoked until they died at a ripe old age of ninety. Well the point is, the studies have never said that all people who smoke will die. They say that those who smoke suffer an increased risk. Sorry, I have to sneak in one more term. Risk, is the likelihood of loss. Be careful here, risk is not the chance of losing; it is the chance of losing something of value. This distinction is important. There is no risk if there is no value attached. At that point all you have is likelihood of an event. In the case of smoking, what is at stake is your life and if you smoke you have an increased chance of losing your life. First of all, to examine these statements closely, there is no way of eliminating the likelihood of death; we will all die sometimes. All that the studies show, is that if you smoke, the chance you will die sooner is higher.

In the case of smoking, the study is very broad based since there is very little error in death. Either you are alive or you are dead. The way to do a broad based study is to pick a standard age’ let us say seventy. A survey can be taken on all people who passed away at age seventy. All they have to do is inquire as to whether the person smoked or not. They would find that there are more people dying at age seventy that smoke than do not. Does this show that smoking causes an early death? NO! It shows that there are more people who die at age seventy who smoke than people who die at that age and do not smoke. Once again the mathematical meaning of these statements have to be examined.(There is at least one cow in this country that is black) Let us pick the age of ninety. What you will find in raw numbers, is that there are no more people dying at age ninety who do not smoke than people dying at that age that do. Does this mean that smoking is bad for you at age seventy but good for you at age ninety?

That is one possible interpretation but a more likely interpretation is that the number of nonsmokers at age ninety vastly out number the number of smokers. How many possible deaths can occur in a group of one(the smokers group)? ONE. How many possible deaths in a group of ten(the nonsmokers group)? Ten. If there were even one death in the nonsmokers group, the survey would show that the risk of dying is equal amongst nonsmokers and smokers.

This is why it is important to analyze how information is gathered. The results and conclusions that we get from the analysis of the information that statistics presents, is what we call knowledge. The trick is applying that knowledge; one could consider this the very definition of intelligence.

Obviously, the only person left to discuss is the logician. Now so far, I have drawn the ire of all of those in mathematical disciplines in daring to draw a distinction between mathematics and statistics (statistics being after all, a branch of mathematics).

I am know going to create an uproar by trying to distinguish between logic and mathematics. After all, mathematics MUST be logical. Well, just to give our math buffs a paradox, all mathematics is logical BUT is all logic mathematical?

The answer (the epistemologists in the audience know this very) is NO. Not all logic is mathematical nor is all logic logical. Head beginning to hurt? Once again we must explore one of my favourite terms, the definition.

Too often people begin the analysis of a problem without settling on definitions. So what is a definition? Here is the first stab at it. A definition is the collection of ideas that define the entity that is being defined.

Annoying isn ‘t it? and I ‘ve broken the cardinal rule of definitions which is not using the word to define itself. Let ‘s try again. A definition is the ideological representation of the entity that is being defined.

I think we have got it this time. So let ‘s run through a few definitions.

Statistics – the branch of mathematics that seeks to define the quality of the knowledge that information gives us.

Mathematics – the study of the manipulation of ideas. (We ‘ll get back to this)

Statement – a sentence that is True or False (Trust me, we ‘ll need this one)

Logic – the ideological connection between statements.

Ah Ha!

There in lies the crux of the matter. What if we believe that two statements are connected. That connection is called our logic. What if we are wrong in our belief? Then that situation is described as having flawed logic. Our logic at that point is illogical. The connection does NOT exist. Mathematics demands a connection (logic), a TRUE connection between its statements.

This also explains why most people who usually speak of logic in common situations are also idiots. We all know the type we mean. The ones that use the fact that we do not have complete knowledge to support one position to defend the opposite which goes against common sense. They use what is known as convoluted logic.

Please do not confuse my meaning to say that all people who speak against the common sense are idiots. There are many such great thinkers who have advanced humankind by opposing and overcoming the common knowledge.

Let us examine the common applications and misapplications of logic. First, let ‘s examine our joke. Both the mathematician and the logician in this case, are correct in their analysis of the statisticians test. The mathematician ‘s criticism of the test is that the statistician has only looked at one cow. Using common sense (or common knowledge) it is known that cows in any country have many colours. No information has been presented to suggest that the cows of this country should be just one colour and that colour should be black. The logician on the other hand criticizes the test, in that the statistician has only looked at the half of the cow that was facing him. The logician did not draw upon his common sense that would have told him that usually cows like most other animals are symmetrical. Although there are many animals that are not uniform, it is very rare to see on half of animal being uniform, and the other half not conforming to that uniformity. While the mathematician logic suggests that not all cows in the country are black which is both a reasonable and logical statement; the logician suggests that the other half of the cow does not resemble the visible half which is not so reasonable. In short the mathematicians logic is sound or logical; the logician ‘s logic is flawed or illogical.

Finally, let use an example that will challenge our common sense, our knowledge and our intelligence. We all know that the world is round. We could say, that we have knowledge of the world being round. Throughout history, many people have proven it through very many ways. Either they have measured the circumference of the earth, or traveled around it, or finally even left the planet and looked at from outer space. The world is round. Ok, then step outside and look at the world. Does it look round? Where I grew up, on the Canadian prairies, in Winnipeg, where you can see your dog running away for three days, the world looks flat. For lack of better words, our common sense, the information we most easily gather, tells us the world is flat. The information that has been gathered through effort and analysis tell us the world is round. The question I give you is, can YOU show that the world is round?

Now you say, how will I do that without a deep knowledge of mathematics, a ship, a plane or a rocket?

Easy, all you need is a car or a good pair of legs. Walk (or drive) along a long flat road. Yes, this much easier to do on the Prairies. What you will see is that if there is a tree or a telephone pole along the side of the road, you will see the top first and the body and finally the bottom of the erection (yes I chose those words). Why does this happen? Because objects that are below the horizon are beyond the visible curve of the earth. Yes, of course air pollution and buildings have limited our horizons but even without those things, our horizons are limited by our height. The horizon is always where the line that goes through our eyes and just meets the earth is. Objects that are past that point can not be seen. As you approach them, there tops go above that line first, and therefore we see the top first.

You will observe these phenomena in every direction everywhere in the world. The shapes that could allow this is all over the world are round shapes. If the earth were flat, there would be huge discrepancies in the distance of the horizon.

So there you have an example of common sense, in conflict with our knowledge, and the use our intelligence to resolve that conflict.

If only the rest of life were that easy.

Because I ‘m a horrible person…………………………………………And so are you
Humans as a whole are a pathetic lot. The vast majority have been given capacity that far out strips their intelligence or awareness. The common sentiment is that we continue to stumble.

This is another example of one of those linear assumptions. We assume that we will continue to progress as we always have, that there is no asymptote. This case is highly unlikely. We have the underprivileged who consume very little but through sheer quantity are a drain upon the environment and on the other hand we have the vastly over privileged who consume at such a rate to strip it bare.

We know we should do many things. Eat right, exercise, conserve energy, pollute less, give to charity etc.
Why do we not do these things?

Tea Time

In our rush to fight obesity and find healthy cheap alternatives, one very powerful solution has been overlooked; tea.

This simple, low (or no) calorie beverage is an incredibly cheap simple alternative to soft drinks, expensive coffees, and alcoholic beverages. If you take a can of pop (180 calories or 2 miles walked) and compare that to the zero calories in a cup of tea, you are almost prepared to accept the calories from a few dollops of cream.

I was surprised to learn that so many places carry tea. In fact the staff at the theatre where I saw my last movie, was also surprised to learn they serve tea. The beauty of tea is that it stays fresh (when dry) for much longer than coffee. Where as the chic of coffee is now in the fresh grind, the humble tea bag can sit on the shelf for months before being called upon. At $1.50 for a cup, it is an incredible bargain. Even the high end coffee places will sell you exotic (caffeine free) herb teas for the same price.