|Since Helen of Troy was fabled to have the beauty that
launched 1000 ships, beauty can be rated in milli-Helens, which is the
beauty to launch one ship.
"Once you learn how to read food recipes, you can
|What happens in science and social science is that people examine phenomena
that they find interesting or curious in some way or that they want to
know more about for whatever reason, and in examining it they notice, or
think they notice something that might be a useful way to look at it, perhaps
some relationship or a pattern or perhaps a concept or theoretical entity
they invent -- a construct, such as an imagined object or agent or perhaps
just a mathematical function, such as a ratio, that is given a name. It
might be something useful to pursue or it might lead to a dead end in terms
of usefulness; it might not even hold to be true. Unfortunately,
once something is found that is true or useful, it tends to be presented
in books as though it were obvious or very straightforward, when in fact
it may be neither, and may have taken years, and chance, to discover.
I want to go through the process with a fictitious illustration -- finding
a "mating factor" and a "divorce factor".
But first, I want to illustrate the difference between an explanation and pseudo-explanations of certain sorts, because many times science texts, and even scientists, give pseudo-explanations for phenomena when they think they are explaining the phenomena. The most common, I think, form of pseudo-explanation is to give a name to a phenomena, consider that name to name some sort of trait, and then explain the occurrence of the phenomena in terms of the "existence" of the trait.
For example, imagine that a student gets mostly B's in school. Parents and teachers, and even the student himself, may come to think of him as a "B student". Notice that at this point, that just means that the student gets B's generally. It is synonymous with saying that he gets mostly B's. If someone asks you how you kid does in school, you can answer either "He gets mostly B's" or you can answer "He's pretty much a B student." Both of these statements in this context mean the same exact thing. Now there is no problem with this terminology unless people, including the student, begin to think that he gets B's because he is a B student. "Why didn't you get an A on this exam, son?" "Dad, I couldn't; I am just a B student." The reason this is not an explanation is because it just says essentially that the student gets B's because he gets B's. For "being a B student just meant that one received B's for the most part." It is not that getting B's necessarily means a child has some sort of trait that causes him to get B's.
If this sort of explanation were a real explanation, then we could explain everything using it. The ozone layer is getting a hole in it because of ozone depletion. Jones is a geat bowler because he bowls mostly strikes. Jones gets mostly strikes when he bowls because he is a great bowler. Smith is a great high jumper because he can really jump.
It does not take too much thought to see, if you are looking for it, that these are not really causal explanations. Unfortunately science takes this sort of thing a step further quite often by disguising the terminology or by having intervening terms. For example, one might asks why certain objects fall, and be told they fall because they are heavier than their surroundings (say, air, in this case) and because they are acted upon by the force of gravity, which causes heavy things to fall to the ground.
There are at least two reasons this is not a good explanation. The first is that objects are found to be heavier than air because they cause a balance to fall when placed opposite a container of air of the same volume. So "falling" is built into what it is to be "heavier" than the surrounding fluid medium.
But also gravity is in part, a pseudo-explanation for the falling of bodies because "force" -- in this case gravitational force -- is just a word that is used in Newton's law to, in a sense, merely describe any change in motion, whether a change in velocity or direction. Newton's first law is that "a body at rest tends to remain at rest, and a body in motion tends to remain in motion in a straight line at the same velocity, unless acted upon by a force." The notion of force is intuitive where we see or feel forces acting upon an object, as when you pick up a bowling ball and have to exert force, or where you have to exert a lot of force to open a jar.
But it is not at all intuitive where forces cannot be felt; and those are perhaps the majority of cases. Even in the bowling ball case, one feels one has to keep applying force to the bowling ball to keep it from falling onto one's foot. Just starting it in upward motion does not keep it moving upward at a constant velocity, as the first law would seem to imply should happen -- if forces were the kinds of things we "feel" or directly perceive. Before Newton suggested looking at motion via the above law, people thought there were no forces operating at times we now say there are. They understood why a spear would move while it was in your hand and you were drawing it back and then moving your arm forward with great force; what they did not understand was why it kept moving after you let go, because they saw no force continuing to push it. Your arm was no longer pushing it, so why did it keep going? Newton suggested, not an answer, but a different question: he said let's not ask why it keeps going after you release it; let's ask why it stops. And he said it keeps going because that is what things do -- they keep going in a straight line unless acted upon by a force. That means there must be some force that stops it and brings it down to the ground. We will call that force gravity. If he had named the force "the falling force" it would have been obvious that saying things fall because a falling force acts on them is just to say that they fall because they fall. And we would have seen that is a pseudo explanation. But there is more going on, something that is useful, but just not in the way it appears to be.
Newton's second law further defines what a force is: it is the "thing" which accelerates a mass. Now mass itself is something of a complex or vague concept, but I wish to skip over that here and focus on "acceleration". Acceleration is a more precise concept; it involves a particular kind of change in velocity -- in this particular case, talking about change in speed and not just change in direction. I am going to ignore accelerations that involve directional changes rather than speed changes. Acceleration, as it pertains to speed changes, means that there is a constant rate change in speed, not an intermittent or impulse-like change in speed. It means that every second an object is going the same amount faster than it was the second before. I.e., if something is accelerating by 10 feet per second, it is going to be going 10 feet per second faster after 45 seconds than it was going after 44 seconds, and it was going 10 feet per second faster after 44 seconds than it was going after 43 seconds. Its speed will be increasing at a constant rate of increase. Things which accelerate are not just going faster than they were, but they are going faster and faster and faster yet every moment. They keep on increasing in speed. To say then that gravity is a force is to say more than just that things fall; it is to say or to imply that things fall with a constant acceleration (at least under ideal or vacuum conditions). I believe it was Gallileo that discovered that things fall with a constant acceleration (presuming there are no other forces acting upon them to slow them down) and that this constant acceleration was the same for objects of any mass -- whether a cannon ball or a penny or a feather (where air is not a factor, as in a vacuum).
But notice, while we are giving more information by saying that "things fall because of gravity" (meaning that they not only fall, but they fall at a constantly increasing rate), we are not giving more information if we say "things accelerate toward the ground because of gravity". For that is just to say that things accelerate toward the ground because things accelerate toward the ground. Gravity is just the name of the force we have fabricated to fill in the "F" in the equation "F=ma". Gravity is not the "cause" of the acceleration; it is just another name for the appearance of acceleration of a mass. At best, it is a theoretical construct, not something that necessarily actually exists. Now, it may turn out that there is something that we can someday find that does what gravity does -- causes masses to accelerate; and we might say then that we have discovered what gravity is. That sort of thing is what happened when it was determined that DNA was the actual substance that behaved in the way "genes" behaved, but genes were just a term for genetic factors that were posited to exist after Mendel showed certain kinds of regularities and patterns with regard to traits in descendence lines of plants -- traits that were then said to be inherited. Einstein, I believe, thought that gravity might be explained by a constant rate of expansion of mass, but I don't know that the details of that worked out. At any rate, to say gravity exists is not to say that there is some particular "thing" that is what gravity is. It is just the name for the phenomena that any two masses accelerate toward each other.
The notion or concept of gravity and other important forces in nature and in physics is important because, and only because:
Mathematics is a way of expressing patterns. Newton saw that there were some basic patterns to the behaviors of physical objects that could be expressed mathematically in certain ways. Einstein and others later saw that there was a more general way to view those patterns and still to express them mathematically -- a way that accounted for some of the phenomena that did not fit Newton's model. Many of these phenomena involved either extremely high velocities (near the speed of light) or extremely small entities (at the quantum level). My latest information is that there are occurrences at the quantum level that physicists cannot yet see patterns that they can quantify other than statistically. In that sense, physics is in the same boat as predicting things like the overall quantity of traffic fatalities on a holiday weekend. Statistically one can know there will be 324 traffic fatalities without being able to say precisely where they will be or when they will happen.
There are cases where we can know and predict behaviors without knowing the causes and without being able to generalize or mathematically describe the behavior. If one knows one's spouse or parents or children, one can predict how they will respond to certain situations with a fair degree of accuracy even though one is not using a mathematical model and does not understand any underlying causes. Similarly physical phenomena could be understood in the same sorts of trial-and-error ways without doing things mathematically. A baseball pitcher, for example, determines the trajectory of a pitch, the force he needs to deliver it, the angle of release, etc. without doing any mathematical calculations, and the batter swings to hit the ball in the same way. Basketball players and automobile drivers and toddlers learning to walk, learn what they need to know without studying underlying causes or doing mathematics. Math is only a way to describe more general patterns that can be noticed. First, however, one has to find the patterns. Unfortunately, too often in science the patterns, or the math behind the patterns, are taken to be an explanation of a phenomena rather than as a characterization or description of it, or of correlations involving it.
And even worse, sometimes patterns are described that are not helpful patterns at all, or not even real patterns. For example, physics books tend to describe entropy as a measure of disorder, pointing out that entropy (and therefore disorder) increase in the universe. As examples of entropy they show things that are very different from each other -- heat going from a warmer source to a colder one, gases or liquids dispersing, certain spontaneous chemical reactions, changes of state from a solid to a liquid or a liquid to a gas, etc. One particular gas dispersion example is particularly interesting to me -- gas flowing from a full flask into an empty one where the claim is that this represents an increase in entropy. It is not that I am saying this is not true; what I am saying is that I don't know what this means, for the following reason: suppose we move all the furniture in your house into one or two rooms. In what sense does that cause there to be an increase in the order of your house or of your furniture? No normal sense; and, in fact, most people answer it would be just the opposite. We talking of unpacking boxes after moving, for example, as getting the new house in order, not as getting it in greater disorder.
Furthermore, the book has an illustration of "processes [which] have positive values of [entropy change] and tend to occur spontaneously." The first two diagrams show a solid changing to a liquid and a liquid changing to a vapor. But bricks and cars and furniture don't seem to melt and then evaporate. Ice cream and ice, of course change states in those directions at room temperature or temperatures above their freezing points, and metals will melt if you get the temperature high enough, but they also go in the other direction at lower temperatures. So it is not clear what they mean, or why they say, these processes "tend to occur spontaneously". They do not occur spontaneously in the normal sense of the term.
So although there may be some precise definition or notion of "entropy" that is useful, it cannot be just "measure of disorder" with the claim that disorder is always increasing only because you already know which "direction" phenomena occur and then call that direction the direction of increased entropy. That is like saying objects fall because they are heavier than air, and rise because they are lighter, where what tells you which objects are which is that you know they rise or fall when released under normal conditions. Yet, that is what some physics texts seem to do. (And not only textbooks. At http://www.garlikov.com/science/thermody.htm I have also put up the Funk & Wagnall's "Knowledge Center" Web Page explanation of entropy, with response comments and questions of mine in appropriate places.)
Furthermore, the physics text my daughter is currently using in high school seems to talk about the relationship among Gibbs free energy, enthalpy, and entropy as though there is some way to calculate all three quantities independently to show that the relationship always holds, whereas it might end up being that the relationship always holds only because one of the variables is derived from the other two and, of course, then always plugs back into the equation to make it come out correctly. It is impossible to tell from the explanation in the text what is actually meant or being described here, or what the evidence is exactly for the claim about the relationship among the three concepts. Students are left to memorize the equation and to apply it by plugging in numbers, but not to understand what is really being claimed about the universe. The analogy seems to be that students are being given recipes about this and told to be doing chemistry, when all they are doing is reconstructing information someone else has collected and somehow translated into the recipe. This is not learning chemistry any more than learning a food recipe, with ingredients already set up for you, is learning how to cook.
I think that the body of existing scientific knowledge would better be taught by explaining to students what the observations to be accounted for are or were, what the ideas about those observations are or were, describing how concepts are arrived at and why they seem useful, and then explaining what correlations can be found among phenomena by the use of those concepts in various applications.
Suppose one is interested in discovering the factors that cause people to fall in love and/or choose a mate, and suppose they are interested in discovering whether certain factors, available to be known before marriage, correlate with divorce.
Typically one begins to look at what seem to be obvious or intuitive factors -- in this case, for choosing a mate for oneself. One might assume that people choose attractive people for mates.
But then one looks at couples in a church directory or in the engagement announcements of the newspaper and sees a great many unattractive people who have got married.
So then, perhaps one notices in checking out those pictures that people seem to choose people who look like them in some way. Well, there may be some ways to study that; you might collect wedding pictures and look at couples to see whether they look alike or not. But that could be time-consuming and it also begins to be very subjective because you might think two people look alike, but somebody else thinks they don't. So you decide that you need to measure "looking alike" in some way, and you come up with something like comparing hair color, eye color, skin color, weight, height, facial shapes (where you have six or eight or ten facial shapes, or however many different shapes you can find to choose from: oval, pear shaped, round, square-jaw, pointy chin, etc.), nose width, nose length, eye-shapes, eye-depth, etc., etc. You devise a scale, and how couples score on that scale is there LA factor, their "look-alike factor". So you get a bunch of wedding photos and compute couples' LA factors and look for correlations and you come up with nothing.
So you think it may have something to do with personalities, or with mutual interests, or with a combination of the two. So you devise some sort of way of determining personality traits and/or interest traits, and you then compare married couples on them. Again, maybe you get nowhere.
But you mention your research to students and they get curious about trying to find a "marriage factor", so they start looking for things to check.
Perhaps one of them thinks your original idea of people seeking out those who are attractive to them is a good idea but that you didn't conceive it correctly, because you did not take into account that beauty is in the eye of the beholder. So s/he does a study that asks 10,000 non-involved high school students which sorts of features they consider attractive and which sorts they consider repugnant, and then goes back 10 years later to see whether the respondents married people with what they had previously considered to be attractive features. Suppose that comes up empty also.
Suppose then that someone in the group is a biochemist and has read studies about endorphin levels in the brain and knows that being in love has the same effect on the brain as does chocolate in that it releases endorphins that cause a natural "high". But this biochemist also knows that people have said there is a diference between being high on chocolate and being in love -- that eating chocolate is like being in love, but without the aggravation. So s/he starts to wonder about the relationship between endorphin levels, physical and/or personality characteristics, and aggravation levels. Perhaps a study has been done somewhere that shows that aggravation can be related to blood pressure, and that a measure of "aggravation" has been constructed, called the SSOJ unit or "specific shrew or jerk" unit which is the amount of aggravation that will elevate blood pressure one point above normal. But since blood pressure can fluctuate slightly on its own, the TFSJ is the more important measure -- the ten-fold shrew/jerk unit -- which is equivalent to 10 SSOJ units, or the amount of aggravation that will elevate blood pressure by 10 points above normal. Moreover, it is not the amount of aggravation you have above normal that matters, but that part of the above normal blood pressure that can be attributed to your spouse. In other words, suppose you have some sort of stress because you are worried about something and elevates your blood pressure. If you have the kind of spouse who is not only not sympathetic, but who says things to make the situation even worse for you, then it is the amount worse that matters, so what we need is something like an RSOJ -- a "relative" shrew or jerk unit. And suppose there are also LC units which are the amount of love required to raise the endoprhin levels the same amount that one gram of chocolate does. Eventually all kinds of studies get under way that correlate marriage choices with LC units, and divorce with a rise in the ratio of TFSJ units to LC units or a diminution in the reciprocal, named the SA (Stability/Acrimony) unit, which is essentially considered to be the amount of love divided by the amount of aggravation.
Suppose it then turns out that one of the studies shows that teenagers get higher endorphin levels when they are around people who have personality traits opposite to parents'. But that as people age, marry, and have children, they often tend to take on traits similar to parents and thus lower their partner's SA measurements. Furthermore, as familiarity itself breeds contempt and boredom, TFSJ measurements tend to increase, further reducing SA.
At any rate, when all is said and done it might be that scientists will have all kinds of units and measurements that describe the state of a relationship in terms of nothing that is intuitively obvious. And you will be in your science chapter on marriage and divorce and they will start out by defining LA factors, SSOJ, RSOJ, TFSJ units, LC units and say that successful marriages are caused by a high SA measurement. Only a few students may be interested enough to work through all the jargon, and they may or may not come to an understanding of what is really understood about marriage, or how little is understood by just knowing all these things. And students will consider the subject extremely difficult, not because it really is difficult, but because it has been made more difficult to understand than it has to be.
So, to repeat, I think that the body of existing scientific knowledge would better be taught by explaining to students what the observations to be accounted for are or were, what the ideas about those observations are or were, describing how concepts are arrived at and why they seem useful, and then explaining what correlations can be found among phenomena by the use of those concepts in various applications. First, make the problem come to life for the students and then examine various ways to try to solve it, comparing ideas they might have themselves with results that were obtained historically. If they suggest a path that has been tried, point out the problems (found) with that path. Let them adjust their proposals to account for that evidence. If they get stuck, then explain that is how others got stuck and what the proposal was that finally seemed to get somewhere, and how it worked.
Reset June 21, 2000