We will revisit the clustering of random data. This is an interesting effect in which humans see apparent patterns, or clusters, in purely random data. Try this clustering demo to see for yourself. Run it with different numbers of dots and see the clusters appear!. Remember - the points are random. Keep this in mind when you hear about such things as "cancer clusters."
Here's another thinking fallacy - extrapolation. Thisis the practice of extending a function beyond the range of data it is known to cover. We used two examples. First - Prof. Scalise had found a listing of world record times for the men's outdoor mile run. The 4-minute barrier was finally broken in 1929 when Roger Bannister did it in 3:59.4. Times have been steadily coming down. The data indicate, from 1929 to 1974, an approximate function of 4 -.000622(y-1929) minutes, where "y" is the year. Solve this for 1974. (y-1929) is 45 years. Then 45 * .006222 gives about 0.28 minutes, which you subtract from 4 to get 3.72 minutes, or 3:43. That's correct according to the table of data. So this function gives a close (not exact) result between 1929 and 1974. Let's extrapolate. How fast will someone run the mile in 2100? Work it out. The function predicts about 3 minutes flat! How about in 2200? This we gotta see! Someone should run the mile in 1:40! Oh really? How fast do you have to run to do this? About 35 miles per hour! Not likely. The extrapolation is not valid.
We used another example, this one deadly serious. We all remember the loss of the shuttle Columbia. Prof. Cotton had read a portion of the Columbia Accident Accident Investigation Board report. You may recall that the piece of foam that struck Columbia's wing and damaged it was seen on liftoff films from long-range cameras. NASA had a program for evaluating foam strikes for the simple reason that they happened frequently. The program, called Crater, accepted a number of parameters of the foam and the shuttle tiles and made a prediction of how much damage might be expected. Crater was a conservative algorithm, which means thats its predictions was worse than reality; this is a safe way to do it. They used Crater to attempt to estimate the effect of the foam block that struck Columbia, but that foam block was about 400 times larger than the largest foam piece for which Carter was validated. As a result, the estimate indicated that, though there would be some damage, it would not be severe. We all know that the damage was a hole in the leading edge of the left wing, which, being unsurvivable, certainly qualifies as severe. In this case, Crater was being used far beyond its validated range in an unjustified extrapolation.
Science involves finding explanations for phenomena and then testing those proposed explanations. A really good explanation is useful beyond the original phenomenon; it can be used to predict and explain other things as well.
We have gone over experiments for finding a causal link, such as A causes B in population C. The next step is to understand the mechanism: Why does A cause B in C? Is there some physical law of the universe that describes whatever is going on? Is there an understandable process that explains it?
Suppose you hear that a thunderstorm last night produced a large power outage. How does a storm do that? By producing high winds that break off tree limbs and cause them to fall into power lines, taking the lines down.
In science, the answer to one question often begets another. Why does someting fall to the ground when you let go? Because of gravity. How does gravity behave? Newton's Law of Gravity describes it mathematically. Why does gravity act this way? Einstein figured out that is a result of space curved by the presence of mass. Why does mass curve space? Stay tuned.
It is possible to know that A causes B without knowing why. Science will look for a mechanism by which A causes B. Such a mechanism mat not be easy to find. Carey cites the now well-known result that cigarette smoking is a major cause of lung cancer. The actual mechanism involved, however, is not well understood. Astronomers have known for some time that high-mass stars end their existence by exploding. These explosions are frequently seen in the universe. Theory indicates that the massive core collapses and a supernova explosion results. Understanding of the precise mechanism through which the collapsing core (falling inward) produces the biggest blast in the universe (going outward) has been difficult.
Universal physical laws describe how things behave in the universe. Drop something and it will fall (gravity). Double your distance from a light and the light intensity where you are will be 1/4 of what it was (inverse square law). Force equals mass times acceleration (Newton's First Law). Such a law can explain why A causes B.
In many cases there is some physical process going on that explains why A causes B. For example, high motor vehicle weight causes poor fuel mileage. Big SUVs burn a lot of fuel. A (great weight) causes B (lousy fuel mileage). There is a reason. Every time you start moving, you have to add energy (kinetic energy) to the vehicle. Kinetic energy is energy of motion. This energy has to come from somewhere else, and in this case comes from the fuel. It takes a lot more energy to get a 7,000 pound vehicle moving than is required for a 2,500 pound one.
You have seen something like this already. What you have to do (not always easy) is to design a test which satisfies two conditions. The "something" is the prediction made under your explanation.
This should sound familiar. Recall the tests of psychics. For that you need an experiment such that
Here are basic principles for good experiments.
Let's put these to use in evaluating an example given by Carey. It involves a dog and comes from the book "Test Your ESP."
"At mealtime you might put out two feedpans instead of one for your dog or cat. The feedpans should be located so that they are equally convenient to the animal. They should be placed six to eight inches apart. Both should contain the same amount of food and avoid using a feedpan the animal is familiar with. Pick the dish you want the animal to eat from and concentrate on it. In this test the animal has a 50% chance of choosing correctly half the time. You may want to keep a record of his responses over several weeks to determine how well your pet has done." (50% chance half the time???)
The author has worded it badly. The hypothesis here is that animals can be sensitive to human thoughts using ESP. Therefore your thoughts can direct the pet to the desired dish significantly more often than the 50% you would expect by chance alone. Would this satisfy condition 1 above? It would - provided you accept a fishy assumption. Look at it this way. You are going to attempt to communicate your dish preference to your pet. Let's forget ESP for a moment and image that say in a monotone "the red dish, the red dish, the red dish." What's the probability that a dog or cat will understand that? How do teach a cat what "red" means (or anything else for that matter)? If your pet can't understand spoken words, it isn't likely that your thoughts will do any better. Would a cat respond to an actual photograph of the red dish? A photograph of anything? (maybe a dog...)
The proposed "something" (pet choosing desired dish) will occur if you think hard about the dish ONLY if you grant the assumption that the animal can understand human language. Also - now consider condition 2 above. Has it been satisfied? Would the pet choose the "right" dish for another reason? Sure could. Animals can be very observant of their humans. If the human happens to subconsciously react when the animal chooses the "right" dish, the animal may pick that up. The human could move a bit, look at the "right" dish, or otherwise pass physical cluse. Remember Clever Hans, the calculating horse! The human might inadvertently bias the result by thinking about the dish the pet has chosen. Thus, condition 2 is NOT satisfied.
Now we get into somewhat familiar territory. We've been here before. Alien encounters, UFO crashes, psychic readings, communicating with the dead, dowsing for water (or brains!), ghosts, all constitute some really extraordinary claims for events or powers. These claims share a few properties. First, although there may be some "evidence" supporting the claim, it is sketchy at best and largely anecdotal. Secondly, if the claim were to turn out to be really true, it would force reevaluation of a lot of current science. Scientists would consider such a discovery as VERY significant. Scientists are not old fossils who reject every new idea; they just want solid evidence. Anecdotes and claims won't do it. The late Carl Sagan said that he would love to meet an alien. It would be great if they would land their flying saucer, get out and introduce themselves. As he said, this would save us a LOT of work. It would be evidence satisfactory to the grossest skeptic.
Copernicus' heliocentric system was not accepted until Kepler and others began producing evidence that the old geocentric idea of the planets was wrong. The Copernican idea was finally accepted, but not in its original form. Copernicus had postulated circluar planet orbits, but Kepler had shown that orbits were elliptical. Wegener's continental movement idea was slow being accepted, as feasible alternate explanations existed. Finally, as more data piled up, the idea became accepted. Now we have means of actually measuring the drift. But - the current model contains a description of a process that causes the movement, something Wegener's original idea lacked.
Anecdotal evidence exists for just about every kind of strange happening you could imagine. The problem is evaluating it. What can you make of it? Remember the phrase "extraordinary claims require extraordinary evidence." Claims about alien encounters, psychic key-bending, making things move by thinking at them, reading minds, communicating with the dead, and many other "supernatural" things will not be accepted unless the claimants produce some really good evidence.
The best way to deal with such anecdotal evidence is skeptical disbelief. Remain skeptical until properly controlled tests begin to produce evidence that the claim is valid.
There's another basic problem with anecdotal evidence. Many times the people relating the story are not giving a factual account of what they saw. A breathless description of a very bright UFO hovering in the west turns out to be a report of seeing the planet Venus. It seems that making accurate factual descriptions of events is a skill not possessed by everyone. In far too many cases the report or anecdote contains poor descriptions of facts mixed up with far-out explanations. The report, far from being a careful account of observations, turns out to be loaded with interpretation and explanation. The problems becomes one of trying to pick out the factual kernels from amidst the interpretive chaff.
Be sure to use the Baloney Detection Collection and Fuzzy Thinking pages of the course website. They address this very subject.
Carey points out the difference between a mistaken belief and bad reasoning. The geocentric model of the Solar System stood for 1500 years, even though it was wrong. The measurements and observations necessary to falsify it were not available until the end of the 16th century and the beginning of the 17th. It had been useful for predicting planetary movements and it fitted the then current church dogma. The mistaken idea was finally overturned by better data and a better (and simpler) explanation. A fallacy, on the other hand, is flawed thinking that does not yield useful results.
Carey details three important questions to ask about any investigation, scientific or otherwise.
Stephen Carey's book will give you some real background for interpreting some of the stuff you will encounter in life. We heartily recommend it for your libray. It is not difficult to read and is full of good insights.