Chapter 7: What is science?

[1:] "Is there any way to prove your theory is false?"

[2:] ...(long pause) "No."

[3:] YES! After eight straight hours in a windowless conference room, that "no" made it all worthwhile.

[4:] It was the interregnum [HUH?] in Bill Clinton's governorship of Arkansas, 1981. The Legislature had passed, and the new Governor Frank D. White had signed, Act 590, which required the teaching of Creationism in all Arkansas science classrooms. This was the first major victory for the "creation science" movement led by such figures as Henry Morris and Martin Clark of the Creation Research Society (CRS) whose views are best articulated in the following quote from their book "The Bible Has the Answers:"

[5:] "Evolution is thus not only anti-Biblical and anti-Christian, but it is utterly unscientific and impossible as well. But it has served effectively as the pseudo-scientific basis of atheism, agnosticism, socialism, fascism, and numerous other false and dangerous philosophies over the past century."

[6:] Founded in 1963, CRS proposed "to reach all people with the vital message of the scientific and historical truth about creation." In 1970, a splinter group formed the Creation Science Research Center in San Diego with the aim of reaching "the 63 million children of the United States with the scientific teaching of Biblical creationism." After eleven years, they had won their first major victory and were actively pursuing similar measures in several other state legislatures.

[7:] Fortunately, not all Arkansans were delighted with this turn of events. The leaders of all the state's mainstream churches, teachers, parents, and national organizations (religious and otherwise) joined in a federal lawsuit seeking to block implementation of Act 590. The suit was not an attack on religion, or even on the place of religion in public schools. The issue was what constituted science and thus belonged in science classrooms. The American Civil Liberties Union provided lawyers to argue the case.

[8:] Unfortunately, very few lawyers have taken Frontiers of Science (or anything like it). Many of the expert witnesses called by the State from the CSRC and elsewhere, however, have PhDs in science. So the ACLU brought in reinforcements. I was asked to assist in deposing a witness and arrived as requested at 9AM on a high floor of one of those indistinguishable (and undistinguished) glass and steel towers on the East Side. Following a brief conversation with the ACLU lawyer, I was ushered into the conference room to meet the Arkansas Attorney General, the court stenographer, and the witness, a PhD physicist and member of the CSRC. I was the only person not allowed to speak -- all my questions and rebuttals had to be written on a pad and passed to the ACLU lawyer (even the stenographer had a machine!). It was clearly going to be a long day.

[9:] Long, but fascinating. As noted above, the key issue in the case was the very definition of "science," the subject one should expect to find in a science classroom. The "scientific creationists" had been working for more than a decade to wrap the literal account of creation in the Bible with the trappings of science. They had scientific meetings, refereed journals, theories, data, lots of jargon -- everything that made their "research" sound like science to the uninitiated. The one crucial element they lacked, however, was the essential ingredient of any scientific theory: falsifiability. For a model or a theory to reside within the realm of science, it must, in principle at least, be possible to prove that the model or theory is false -- that is, incompatible with direct observations of nature. Our strategy, then, was to trap the witness into admitting that there was no experiment that could be performed, no observation that could be made, that could change his "model" of creation.

[10:] It took eight hours. The ultimate exchange went as follows:

[11:] Witness: "The short-period comets provide yet another piece of evidence inconsistent with the timescales required by the theory of evolution."

[12:] ACLU lawyer: "How so?"

[13:] Witness: "Each time a comet passes close to the Sun in its elliptical orbit [HUH?], large amounts of material (ice and rocky debris) are blown away by the Sun's heat and light. We can calculate how long these comets can exist by knowing their orbit periods and measuring how much mass is lost with each solar passage. We find they are at most a few thousand years old. Since comets are widely acknowledged to be primordial solar system material -- the detritus left over from the formation of the planets themselves -- it is clear that the solar system cannot be more than 10,000 years old, or there would be no short-period comets left.

[14:] The ACLU lawyer looked at me in panic -- it sounded like an air-tight argument to him.

[15:] I scrawled: Are comets affected by gravity?

[16:] ACLU lawyer: "Are comets affected by gravity?"

[17:] Witness: "Yes. That's what holds them..."

[18:] Interruption by Arkansas AG: "You needn't elaborate, just yes or no will do."

[19:] me: by Jupiter's gravity?

[20:] ACLU lawyer: "Are they affected by Jupiter's gravity?"

[21:] Witness: "Yes."

[22:] me: can Jupiter's gravity change their orbit periods?

[23:] ACLU Lawyer: "Can Jupiter change their orbit periods?"

[24:] Witness: "Yes."

[25:] me: can it change long-period comets into short-period ones?

[26:] ACLU lawyer (finally feeling more confident): "And can Jupiter's gravity then change the orbit of a comet with a long period into one of these short-period comets?"

[27:] Witness (after a pause) "Some people think so."

[28:] ACLU lawyer: "Do you?"

[29:] Witness: "No."

[30:] "Is there any way to disprove your theory that these comets are young?"

[31:] ...(long pause) "No."

[32:] Q.E.D.

[33:] The actual trial began in Little Rock on my birthday in 1981. The decision was handed down on 5 January, 1982:

[34:] "Pursuant to the Court's Memorandum Opinion filed this date, the defendants and each of them and all their servants and employees are hereby permanently enjoined from implementing in any manner Act 590 of the Acts of Arkansas of 1981."

[35:] That battle was won, but the war remains far from over. Repackaging "creation science" as "intelligent design theory", the fundamentalists are hard at work in many states, packing school boards, censoring textbooks, and pushing laws that require "equal time" for their "alternative theories" of evolution. While the Bible and many other books -- religious, philosophical, and otherwise -- do offer alternative views of the world and its creation, they do not offer a "theory" in the scientific sense of the word. What is this scientific sense? Indeed, what is science?

[36:] Notwithstanding the sterile, six-step "Scientific Method" you memorized in junior high school, there are many ways to do science (and most are considerably messier that the "Method" lets on). There are many distinct scientific disciplines, each with its own cultural traditions and idiosyncratic conventions. And, of course, there are literally millions of individual scientists who, contrary to popular belief, do not all wear lab coats, thick glasses, and pocket protectors, and who hold rather different views on what science entails. There are some basic notions, however, that permeate the process of doing science, and some simple ideas that find use in a wide variety of disciplines. I have collected my top half dozen here.

[37:] Not all of my colleagues would agree with everything stated below. We came to science via different routes and, once arrived, have pursued divergent paths. Perhaps the one thing we all have in common is curiosity -- we've each retained the insistent how? what? why? of childhood. After all our lectures and seminars this term, I hope it will be clear why we are not asking you to memorize "rules" or "a method" that characterizes science. I also hope it is clear why we scientists are doing what we do. Finally, I hope that this book and this course provide a partial answer to the title of this chapter: What is Science?


[38:] As a scientist, Truth, with a capital T, does not concern me. Nature does, and my finite mind is able to comprehend only a fraction of it. This fraction is vastly larger than that comprehended by Cro Magnon man, by classical Greeks, or by Renaissance polymaths, not because I am smarter (brain size has not changed much in the last 30,000 years), but because of the enterprise we call science. This enterprise has built tools that extend the reach of our senses to realms far too small and far too large to be viscerally experienced. It has collected far more data than one individual could ever amass. It has systematized these data into models and synthesized the models into theories. It has created a body of knowledge (facts, models, and theories) and has refined a methodology for increasing that knowledge. This is science.

[39:] I don't need to wait each evening to see what shape the Moon will be or when it will rise -- I have a mathematical model that predicts this with great accuracy. I don't need to speculate on where the doctor should make an incision to bleed out the foul humours that sicken me -- I have an animal model which can help me find efficacious medicines. I don't need to watch the clouds and wind incessantly to discern whether or not I need to find shelter from a storm -- I have a computer model that predicts the weather several days in advance.

[40:] This does not mean I have found the Truth -- about the weather, about disease, or even about the Moon's orbit. But it sure makes life easier than in caveman times.

[41:] Mathematicians can prove things True. They have constructed axioms that define a system of reasoning within which it is possible to prove rigorously that an assertion (often called a theorem) is the Truth with a capital T. Mathematics is purely the creation of the human mind. We have defined all the terms, specified the rules, and so can, within this closed system which we alone control, define Truth. In this sense, math is more akin to philosophy than to science; indeed, the branch of mathematics called formal logic still resides in the philosophy department at most universities. But mathematics is not a science.

[42:] Scientists cannot prove things True. Indeed, most scientists spend their time proving things -- their models -- to be false. Before you conclude that this is a dreary pursuit, look around you. Heinrich Hertz proved false the notion that light waves were restricted to those we can see -- thus, your cell phone. Louis Pasteur disproved the theory of spontaneous generation -- thus, modern medicine. Lord Rumford disproved the fluid theory of heat -- thus, the SUV.

[43:] Truth is a human construct. The Universe exists independently of us --indeed, it existed about 13.7 billion years before we emerged, and it will be around a whole lot longer than that after we are gone. The mathematicians' Truth will still be true 1,000 years, or 10 billion years, from now; we invented this truth and can define it as eternal. Our scientific understanding of the world, on the contrary, will not be the same next year. We will have shown some of our current ideas to be false, and that will be regarded as progress.

[44:] Rather than a search for truth, then, I would characterize science as a search for falsifiable models. This is the key distinction between the creationist's world view and my own. His model, as a result of his faith in it, cannot conceivably be false; changing his model is fundamentally inconsistent with what he believes to be True. As a scientist, I am required to admit the possibility that his idea may be true -- it may be the case that the Universe, including the solar system and Earth, was formed 6,000 years ago. An omniscient and all-powerful Being could arrange for the light from each of the 1022 stars in the Universe to be on its way to Earth so as to arrive tonight for my amusement. He could certainly have layered the rocks of the Grand Canyon to look very old, and he could have set ticking all the radioactive nuclei on Earth so that their decay rates falsely give an origin four-and-a-half billion years ago. This is a possible model for creation.

[45:] Indeed, in the course of the creationist's deposition, we reached a point where this idea of prearrangement arose and he invoked the "five-second-agoers" in its defense. The ACLU lawyer looked blankly at me, and I looked equally blankly back. It turns out, "five-second-agoers" believe that everything could have been arranged just five seconds ago: all your memories, your plans, your bruises -- and those memories others have of you, shared precisely as they are, for all time -- could be a setup, constructed about the time you began reading this sentence.

[46:] They may call it a model, perhaps a theory even. And I cannot prove it is false. In fact, nobody can prove it false, because, by definition, it is not a falsifiable model. Hence, it is not science.

[47:] If, while relaxing at the beach, I asked you to show me a particle, you would most likely pick up a grain of sand -- a small solid entity with a mass, a shape, and a color, sitting motionless on your fingertip. If I then asked you to show me a wave, you would point to the undulating motion of the ocean, the water moving rhythmically up and down until it breaks and the wave's energy is dissipated as the water is thrust up the beach. There is a clear and obvious distinction between the particle and the wave -- a solid, stationary object versus a periodic motion carrying energy.

[48:] The world inside an atom, however, is very different from the one you routinely experience. Its constituent components do not recognize the clean distinction you make between "particles" and "waves". In exploring the subatomic world, we can perform experiments on these components and measure how they behave. In some circumstances, their behavior is best described as that of a particle, while in different circumstances, they look for all the world like a wave.

[49:] In describing this to students, I am often asked "But what is the electron really like? What is its true nature? Is it a particle or is it a wave?" My answer is rarely viewed as satisfactory: "I don't know, and I don't care."

[50:] I really don't. I cannot, ever, in principle, experience life as an electron, so it is a waste of time worrying about what this would "truly" be like. I am comfortable with the notion that I will never be like an electron. But I am fascinated by how electrons behave in atoms -- how their internal dance produces the light coming out of the fluorescent tube over my head, how their patterns determine the links they can form with neighbors, and how those links make a lemon sour and an orange sweet. So I use the tools of science to poke around inside atoms, gather data on their behavior, and build models of their reality. It is just fine if their reality is not like mine. But if my models work -- and until I falsify them, they do -- I can predict the sweetness of oranges and the sourness of lemons, and I can control the color balance of my fluorescent lights. I have gained a partial understanding of some natural phenomena, and can use it for my pleasure and entertainment. Who needs Truth?

[51:] I have used the simple English words "data," "model" and "theory" several times in the foregoing. These words are used in many contexts by people of many backgrounds and predilections. When applied by non-scientists in a scientific context, they are, in fact, often misused. For example, students struggling in my introductory astronomy course often say: "I really like the theoretical aspects, but I can't get the math." To physical scientists, this is an oxymoronic statement: theory is a mathematical formulation of an idea (although this is not always the case in other branches of science). In order to facilitate communication, definitions are useful. I provide below one scientist's view as to the meaning of these terms.


[52:] Contrary to the views of some postmodern literary critics, scientists generally accept the notion that an objective reality exists and that one can sample that reality with measurements and observations that produce "data." In most branches of science, data are quantified, i.e., they are represented by numbers. These numbers can arise by simply counting -- the number of tree species in Central Park or the number of stars belonging to the Pleiades star cluster -- or from some other process that yields a numerical value: the speed of nerve signal transmission or the depth of a glacial ice core. In the latter two cases, the numbers will have associated units that describe the quantities measured and tie them to a standardized system of measurement. Nerve speed will most likely be in meters/second and glacial depth in kilometers). Furthermore, all good measurements include an uncertainty or "error" (see Chapter 5).

[53:] Data are the raw material of science. They provide the basis for constructing models and the means by which such models are tested. They are gathered with great care. Every effort is made to minimize effects that might conflate the measurement of one quantity with another. Systematic errors are ruthlessly sought out and suppressed. Random errors are diminished through repeated measurements (see Chapter 5). The great machines of science -- telescopes, fMRI machines, particle colliders, oceanographic ships -- are all designed to collect data with the minimum of interference from effects extraneous to the question at hand: what fact can I uncover about the universe today? Science without data is not science.


[54:] While quantitative data lie at the heart of our exploration, we are not always able to measure the thing we really want to know. Sometimes this results from the nature of the phenomenon under study and/or the limitations of our measuring instruments: it is, for example, difficult to imagine how we will ever directly observe elementary particles that pop in and out of existence in 10-23 seconds. In other circumstances, the numbers we really need simply do not exist; e.g., in charting the long-term history of Earth's climate, it is important to know the temperature of the planet over very long periods stretching back to before humans, let alone thermometers, were around to record the numbers. In these and many other cases we resort to using "proxies," stand-ins for the true quantities of interest.

[55:] Take the example of global climate history. Paleoclimatologists have developed highly reliable proxies for temperature in ancient times. One such indicator is the ratio of heavy-type to normal-type Oxygen atoms, 18O/16O, where warmer temperatures correspond to higher values of this ratio [WHY?]. We can, for example, extract oxygen-containing glacial ice and measure this ratio quite precisely; we then assign a time to each measurement by simply counting the number of annual ice layers below the current year's accumulation of snow.

[56:] The result can be represented by a standard time series plot of 18O/16O ratio vs. time . This is a literal representation of the measurements. But the thing of interest is temperature vs. time. By carefully comparing the results from the last 125 years during which simultaneous, direct thermometer measurements of temperature are available, we can "calibrate" our proxy; i.e., we equate various oxygen ratios to their respective temperatures. We can then plot the real data (oxygen ratio vs. time) and the quantity of interest (temperature vs. time) on the same graph, labeling the left vertical axis with 18O/16O and the right axis of the plot with a temperature scale.

[57:] Proxies are invaluable in our quest for a quantitative understanding of nature. It is important, however, that we chose proxies carefully, and that we never confuse the proxy with the real quantity of interest. A good proxy has a direct connection to the datum we want to know and is not heavily influenced by other, extraneous factors. The latter criterion may be difficult to satisfy, and the confounding influences may remain hidden from view for a long time. For example, for more than a quarter of a century, astronomers used the relationship between the pulsational period of a certain class of variable stars and the stars' energy output to infer their distances. Since these stars are very luminous and can be seen across great distances, they provided the basic meter stick we used to measure the size of the Universe. But the proxy of pulsation period for actual luminosity (and thus distance) was corrupted by the fact that observers failed to recognize that stars with different chemical compositions behave differently -- chemically distinct stars can exhibit the same period of pulsation despite having very different luminosities. When the error was finally realized, our estimate of the size of the Universe doubled!

[58:] All proxies involve assumptions (see below), and the best way to avoid some of the pitfalls that proxies introduce is to be as explicit as possible about what assumptions underlie the substitution of the proxy for the real quantity of interest. Used appropriately, proxies extend the reach of science far beyond the bounds of space and time that we can directly observe in the laboratory.

selection effects

[59:] Assuring the integrity of one's data is one of a scientist's foremost responsibilities. Not only must the systematic errors and statistical uncertainties of each measurement be reduced as much as possible, but care must be taken that the data obtained represent a fair sampling of the phenomenon under study. This latter requirement does not come naturally to humans. As noted in Chapters 3 and 4, our brains have evolved to be very good at finding patterns, but not at gathering comprehensive and scrupulously unbiased data. We are always ready to find the remarkable coincidence in the fortune cookie's prediction and the events of our day, ignoring all the events to which it had no connection; we note the eerie repetitions of history (Lincoln's secretary was named Kennedy and Kennedy's secretary was named Lincoln; both had a VP named Johnson) and ignore the thousands of incongruencies (what about Lincoln's wife and kids and butler and Secretary of the Treasury?). In science, such blinkered observations lead to what we call "selection effects," or "selection bias."

[60:] Selection effects can come in many guises. The most obvious, and most egregious, is the selective reporting of the results of one's experiment or observation, displaying only those data that support one's hypothesis and discarding the rest. If done deliberately, this is considered scientific misconduct; if inadvertently, incompetence. A more common bias arises in situations where it is only possible to measure part of the whole range of conceivable properties. This type can result from the limitations of one's instrumentation. For example, the physical nature of light is such that the ability of a telescope to distinguish two nearby objects depends only on the wavelength of light being observed and the diameter of the telescope mirror; no cleverly designed camera or meticulous observing technique can overcome this physical limitation. Thus, in a survey to see how many nearby stars have companions, the size of the telescope being used limits our ability to see stellar pairs separated by less than our telescope's particular limiting angle.

[61:] The most subtle types of selection bias arise when some variable beyond our knowledge or control is hiding a subset of measurements from view. In conducting a telephone survey for a polling organization on yacht ownership in Manhattan, two classes of people will be missed completely: those without phones and those with unlisted numbers. While the former group might not be expected to represent a large yacht-owning class, the latter may well represent the majority of such people, and the survey's value would be seriously compromised. When counting lemur species in Madagascar by day, one will inevitably miss the strictly nocturnal animals. If one can recognize the possibility of such hidden data, a new experimental approach might eliminate the selection effect; e.g., obtaining the state registry of yachts and culling all those with Manhattan addresses could solve the unlisted phone number problem. But if nature evinces a phenomenon whose existence we have not yet recognized (such as the extremely dust-ridden quasars -- see Chapter 3), the selection bias may persist unrecognized for decades.

[62:] In the last few years, a lot of effort has been expended in astronomy studying the relationship between the masses of the black holes that reside at the centers of most galaxies and the number of stars that swarm around them. This began with a claim, illustrated in this graph, that these two numbers are highly correlated and that this correlation must be telling us about an intimate link between the black hole's creation and the formation of its host galaxy. Maybe. But I am troubled by this graph for the following reason. Big black holes are easier to measure than small ones, and all black holes are easier to spot in low-mass galaxies than in high-mass ones. Thus, if small black holes existed in very massive galaxies, they would be impossible to see. The fact that the lower right-hand part of the diagram is empty may be because big holes and big galaxies always go together, but it could also be because it is impossible to see a small black hole in a big galaxy -- we can't measure such situations even if they exist. In my view, this graph suffers from a severe selection effect: our inability to measure any points in the diagram's lower right quadrant. This makes the putative correlation suspect.

[63:] Another kind of selection effect arises from the sociology of scientific publishing. Scientists are people, and people like to report positive results. Likewise, journals like to publish positive results. Suppose you decide to perform an experiment using your classmates to test the popular (although largely exaggerated) left brain-right brain dichotomy. Each day, for three weeks, you buy a different friend an ice cream cone and then surreptiously watch how they eat it. Do they sculpt it into elaborate shapes with their tongues, producing veritable ice cream art, or do they just systematically munch through it? You find both behaviors and score each person on a scale of 1 to 10 where 1 is a straightforward muncher and 10 has the tongue technique of Rodin's fingers. You also note if each friend is right- or left-handed, and ask them their major (science and math types are supposedly "left-brained," and artistic types are "right-brained"). When you compile all your data, it looks as though you've wasted $60 on ice cream. There is no apparent connection between ice cream consumption styles and the putative dominant brain types. To avoid wasting more time on this, you do not bother to write up the results for publication.

[64:] But you did do an experiment: you collected data and you got a result. Now imagine that thousands of other curious undergraduates and thousands more serious scientists have done similar experiments on left-brain/right-brain phenomena. And suppose that 99% of them got null results just like you and didn't bother to publish. That would still leave several dozen studies that yielded positive correlations -- all of which do get published. The consensus in the scientific literature would be clear: human behavior is governed by which side of your brain is dominant. But is it?

[65:] While the situation I have described is extreme (and unrealistic,) there is little doubt that publication bias exists and is a significant problem in some fields. Studies that examine many papers about a phenomenon in an attempt to discover small trends that might not be apparent in any single experiment (so-called "meta-analysis") actually take publication bias into account explicitly so as not to reach erroneous conclusions. Fortunately, in most scientific fields generalized skepticism is sufficiently strong (see below) that surprising results are tested many times, and negative conclusions do get published -- theories get falsified.


[66:] The range of scientific inquiry is vast -- from the quarks inside a proton to the edge of the visible Universe, from the behavior of a single nerve cell to the evolution of an ecosystem. Unsurprisingly, the kinds of scientific tools employed and the modes of data collection vary widely from discipline to discipline. There is one broad dichotomy, however, that is worth a brief comment: experiments versus observations. In many areas of physics, chemistry, molecular and organismal biology, psychology, neuroscience, etc., the scientist has her hands (or tools which are the extension thereof) on her subject matter. In such circumstances it is possible to do "experiments:" human-created situations in which the environment is controlled, the start and stop time are carefully scheduled, the manipulations are of the experimenter's design, and the results spew forth in a pre-determined format. In astronomy, oceanography, climate studies, ecology, and some other scientific endeavors, the systems under study are so remote in space and/or time, or are so vast and complex and uncontrollable, the scientist is often reduced to making "observations."

[67:] Both experiments and observations, if well-designed, can yield quantitative and unbiased data concerning the behavior of the universe. But the observer has less control over the environment in which his subject is operating, and must take extra care to minimize (or measure) the effects that the variables beyond his control may have on the data of interest. Nineteenth-century naturalists in Britain collected volumes of data on local bird species and meticulously measured their physical attributes, breeding and feeding habits, migratory timings, etc. But with a large heterogeneous population of birds, a strong seasonal variation in climate, multiple food sources, and a broad distribution of natural topography and human land use, the factors determining things like beak size were far from apparent. In the Galopagos, Darwin found a very limited population of finches, isolated from their parent population for a long time, living on a few small islands with different microclimates and vegetation. The striking differences in finch species found in different locations formed a cornerstone of his subsequent theory of evolution. For the observer, it is a constant battle not only to identify all the influences affecting the object of study but also to discern which are relevant for the question under consideration and which can be safely ignored.


[68:] Models provide the conceptual framework for interpreting the data we collect. They come in many forms:

[69:] physical -- a rotating tank with two fluids of different densities can be used to study the onset of turbulence which leads to magnetic storms on the sun;

[70:] biological -- a mouse engineered to be missing the huntingtin gene cannot produce the protein that the gene codes for, and thus can be used as a model for humans with Huntington's disease;

[71:] numerical -- the millions of lines of computer code that comprise a General Circulation Model capture the complex interaction of oceans, ice sheets, atmosphere and plants to predict the future course of Earth's climate;

[72:] analytical -- Newton's simple equation describes the flight of a ball after it leaves a bat and allows us to calculate where it will land.

[73:] Models explain data in the very limited sense that they provide a way (note that I say "a way," not "the way") of systematizing and describing what can be a very large number of measurements in a relatively compact form. In addition, if they are good models, they also produce predictions of how a natural system will respond if looked at, or tweaked, or probed in a different way. Suppose we look at the fly ball from the stands instead of from behind home plate, or smear the ball with a little grease before throwing it, or play the game on the Moon instead of in the Bronx. A good model will still get the outcome right -- it is a home run or it is not. The datum shows that the ball either lands in the stands or on the field. The model is good if it can predict the outcome in advance.

[74:] It is always important to keep in mind that a model is not the real thing -- a model airplane is not an airplane (it can't get you from New York City to San Francisco in five hours), and the model of a physical situation or event is not the same thing as that situation or event itself. The model is an abstract human construction that attempts to incorporate the essential ingredients of a natural process or system and to make predictions about future behavior. We strive to include all the important parameters and relationships among them but, inevitably, we use approximations to do so and incorporate assumptions along the way. As a result, the model predictions have an associated uncertainty. Just as it is critical to assign realistic uncertainties to our measurements, it is essential to recognize and to quantify the uncertainties in our model predictions. Only then can a statistically meaningful comparison of the real world to our model world be made.

feedback effects

[75:] It is a standard feature of school assemblies: the principal steps to the microphone, begins to speak, and an ear-piercing shriek emerges from the sound system. Feedback. What's actually going on?

[76:] The sound system includes three principal components: a microphone, an amplifier, and a speaker. The microphone picks up the tiny vibrations of air molecules that constitute the sound of a voice and transforms (transduces is the technical word) them into an electrical current. The amplifier magnifies the size of this variable current and passes it along to the speakers, where the electricity is transduced back to sound by driving membranes to vibrate back and forth, jiggling the air molecules in synchrony with the sounds being picked up by the microphone. If the microphone receives some of these increased vibrations from the speakers, it obviously records them as well and passes them on through the amplifier to be boosted again, raising the sound volume coming out of the speaker, leading to greater microphone input. This "feedback loop" of ever increasing sound soon saturates the amplifier leading to the predictable shriek.

[77:] Many natural (and social) phenomena exhibit feedback, which can be described succinctly as a process wherein "the effect affects the cause"; that is, the outcome of some physical process, some biological activity, or some social interaction either enhances or suppresses that process, activity, or interaction. In the case of the microphone, the amplification and reproduction of the sound originating from the input to the microphone results in a greater amplitude of sound at that input. This is called "positive feedback": the effect amplifies the cause. Despite its name, positive feedback often leads to negative consequences. Consider the following feedback loops:

[78:] Unemployment rises --> income tax revenues fall --> government expenditures for construction projects fall --> unemployment rises further

[79:] The Earth's temperature rises -->more water evaporates into the atmosphere --> more solar radiation is trapped near Earth's surface --> the temperature rises further

[80:] Your little brother hits you --> you are irritated --> you hit him back --> he gets mad -- and hits you harder

[81:] Alternatively, the effect can suppress the cause; this we call negative feedback. Note that this is not the same as the colloquial sense of this term: "My teacher gave me negative feedback on my paper; it was covered with red ink." Rather, negative feedback is a technical description of a process in which the result damps down whatever triggered the process in the first place. For example:

[82:] Unemployment rises --> disposable incomes fall --> lower demand depresses prices and lowers wages --> exports are cheaper --> demand for exported products rise --> people are hired to make the exported goods --> unemployment falls

[83:] The Earth's temperature rises -->more water evaporates into the atmosphere --> more clouds form --> more sunlight is reflected back to space --> less solar energy penetrates the atmosphere --> Earth's temperature falls

[84:] Your little brother hits you --> you feel a pang of guilt for all the frustration your success has bred in him --> you hug him and slip him a $20 --> he smiles and doesn't hit you again all day

[85:] Negative feedback often has positive consequences. Whatever the value judgement associated with the outcome, however, negative feedback is a stabilizing influence, while positive feedback tends to lead to runaway situations.

[86:] The natural world, as well as geopolitical, economic, and social intercourse, are rife with positive and negative feedback loops, often running simultaneously. In building models of these phenomena, we must be cognizant of feedback and take care to incorporate it appropriately. One of the more extreme examples of a system dominated by complex, interacting feedback loops is the global climate system. The accuracy of current global climate models is limited not so much by the accuracy of the equations employed or the abundance of data to constrain them, as by the many subtle feedback effects that must be considered in how the Earth's ice, oceans, land, air, and biology interact in the presence of a steady flow of energy input from the Sun. Understanding feedback is essential for progress in modeling almost all complex natural (and social) systems.


[87:] When a model has developed to the point where it has successfully predicted the outcome of many different kinds of experiments, has made lots of testable predictions, and has been around for some time, it can gradually morph into a "theory" (although, since there are no clear boundaries dividing models from theories, whether or not something is called a theory is sometimes related to the size of its proponents' egos). The theory of evolution allows us to understand the transformation of slime molds into Columbia undergraduates: start with DNA, add energy, allow mutation, follow natural selection, and voilà - your roommate. There are lots of details, of course, which the theory does not specify. But it makes lots of predictions that tens of thousands of evolutionary biologists are testing every day and, remarkably, it seems to work.

[88:] When a theory is around for a long time and continues to explain successfully a large body of data, it is sometimes promoted to the status of a "Law of Nature." I have never much liked this formulation myself. Humans invented the notion of "laws" to regulate social behavior, and the "rule of law" is often cited as an important element in the advance of human civilization. However, nature, the physical universe in which we live, has not presented us with an inventory of its laws, nor is it bound to follow the ones scientists invent. Newton's "Universal Law of Gravitation" was spectacularly successful for nearly three centuries at explaining ever more refined measurements of the motions of the moons and planets, as well as describing motion on the Earth's surface; indeed, the epithet "Universal" was meant to tie together earthly and celestial phenomena with a single theory, a radical break with Aristotelian philosophy which regarded the two as fundamentally different. But this "Law," it turns out, is neither "universal" nor even "right." Careful measurements of the orbit of Mercury show that this planet does not follow the Law's dictates. Einstein's General Theory of Relativity, completely different both in its conceptualization of gravity and the mathematics that describes it, has now displaced Newton's Law as our "theory of gravity." Perhaps out of appropriate humility, the General Theory remains just that -- a theory, not a Law.

[89:] This is not to imply that Newton's Law is useless. Indeed, when we need to send a space probe a billion miles to explore Saturn, we calculate the trajectory using Newton's gravity. Newton's law is a very good approximation to the way nature works -- meaning it is a good theory. General Relativity is a better approximation, because it subsumes all that Newton's theory predicts and does a better job describing nature where gravity is strong (such as near the Sun in the case of Mercury's orbit and under the more extreme conditions near such bizarre celestial objects as neutron stars and black holes). But we still regard it as an approximation -- it does not, for example, allow us to say what must have happened in the first 10-35 seconds after the Big Bang, implying that it, too, is an incomplete description of nature. Nonetheless, it is still a very good Theory.

[90:] It is important to note that for a scientist the word "theory" has a precise meaning: a usually mathematical formulation describing testable and predictive models of the world. It is not a synonym for speculation, as in "I have a theory about why the Red Sox always end up losing to the Yankees;" nor is it a nebulous concept, as in "I heard this theory that rocket launches affect the weather"; nor is it a cover for reluctance, as in "Well, in theory I would like to go with you to the all-day Gregorian chant festival, but I have to count the number of sheets of toilet paper we have left to see if I need to buy some." The epithet frequently hurled by creationists, that "Evolution is just a theory", completely misses the point. Evolution is indeed a theory -- and, as such, lies at the heart of a scientific approach to the world.


[91:] It is difficult to get up in the morning if you do not make assumptions. You assume the floor will be there when you roll out of bed and that the air you are comfortably breathing while supine exists several feet higher in the room as well. You assume that the bathroom will be where it was last night and that when you mix hot water with dark brown grains you'll experience the familiar sensation of a cup of coffee. When you get in the elevator, you assume it will descend in a controlled way and deposit you gently in the lobby. And you assume that the professor in your first class will deliver a scintillating lecture of great clarity, wit, and intellectual profundity. These assumptions are all based on experience; most of them (perhaps with the exception of the last one) will be borne out by your experience and will thus reinforce your faith in those assumptions tomorrow. Indeed, they have by now receded into your unconscious, and you don't recognize them as assumptions at all.

[92:] In science, a vigilant awareness of one's assumptions is essential. This is not to say that scientists do not carry around the same unconscious assumptions about elevators and bathrooms as you do, but in gathering data, constructing a model, or attempting to falsify a theory, rigorous attention to all relevant assumptions is required. Phrenology -- the inference of personality traits from the study of bumps on the skull -- started from the assumption that particular parts of the brain controlled particular behaviors. This assumption has been borne out by a century of work in neuroscience. However, phrenology also assumed that the size of each brain region determined how much of a particular behavior a person would express and, furthermore, that the size of different regions were reflected by protrusions on the skull. Both of these assumptions are wrong, explaining the demise of phrenology as a key to human behavior.

[93:] Most assumptions are testable, and many are quantifiable. Early global climate models assumed the Sun's energy output was constant. This assumption was consistent with the available measurements taken from the Earth's surface, but such measurements are only accurate to a few percent. Now that we have accumulated thirty years of satellite data on the Sun, we can see fluctuations in its output at the level of two-tenths of one percent over its eleven-year sunspot cycle -- and we can relax our assumption of constancy and incorporate the changes in the model. However, if our goal is to reconstruct the dramatic changes in Earth's climate over the past million years, we must revert to our assumption of long-term constancy and recognize the limitations this assumption imposes on our results.

[94:] Some assumptions in science last a very long time. From Aristotle to the physicists at the turn of the twentieth century, it was assumed that space was filled with aether. To the Aristotelians, this was a philosophical preference, since they assumed "nature abhors a vacuum". To James Clerk Maxwell, who unified electricity and magnetism in our modern theory of light, the aether was a necessary assumption -- the light waves needed a medium to travel through. But when Albert Michelson set out to measure the properties of the aether, he discovered it was not there -- a two-thousand-year-old assumption swept away, laying the path for the relativity revolution.


[95:] Science is neither a collection of unquestioned facts nor a simple recipe for generating more facts. Rather, it is a process of inquiring about nature and, given that nature is not only much bigger than humans, but has been around a lot longer, it should come as no surprise that we haven't finished the job: there is no complete scientific description of the universe. That's what makes science fun.

[96:] Science is an intensely creative activity, but it differs in several important ways from other creative human activities such as art, music, or writing. Science is teleological. It has a goal toward which it strives -- an ever more accurate and all-encompassing understanding of the universe. Artistic endeavors do not share such a goal. Sculptors since the time of Michelangelo have not been striving to improve on the accuracy of his sculpture of David. Writers have not been searching for four hundred years to find arrangements of words more universal than "A rose by any other name would smell as sweet." Scientists have, however, been working steadily on Galileo's ideas of motion, expanding their scope and improving their accuracy to build a more comprehensive theory of motion through space and time.

[97:] Science and art also differ regarding the role of the individual. Artistic creativity largely expresses one individual's vision. Contrary to some caricatures, science is a highly social activity. Scientists have lots of conferences, journals, websites, and coffee hours -- they are constantly talking and writing, exchanging ideas, collaborating, and competing to add another small tile to the mosaic of scientific understanding. It is from the conventions of this social web that the self-correcting nature of science emerges.

[98:] At any given moment, many "scientific" ideas are wrong. But, as the last 400 years have shown, science as a whole has made enormous progress. The reason for this progress is that wrong ideas in science never triumph in the end. Nature is always standing by as the arbiter and, while the aether may have survived for two millenia, as soon as the physical and mathematical tools were in place to measure its properties, its absence was readily discovered.

[99:] The enterprise of science has developed several habits and techniques for enhancing the pace of correcting false ideas. Perhaps the foremost of these is skepticism. While many people regard skepticism rather negativly, it is a scientist's best quality. Indeed, it is essential to be skeptical of one's data, always to look for ways in which a measurement might be biased or confounded by some external effect. It is even more essential to be skeptical of one's own models and to recognize them as temporary approximations which are likely to be superceded by better descriptions of nature. When one's data agrees with one's model, euphoria must be tempered by a thorough and skeptical critique of both.

[100:] When the results of one's experiment or observation are ready for public display, community skepticism springs into action. The description of one's work must provide enough detail to allow other scientists to reproduce one's results -- they're skeptical and want to make sure you did it right. The article itself is subject to a formal skeptical review by one or more referees chosen by the journal editor for their expertise in your field and their skeptical quality of mind. These days, instant publication of results via the Internet often precedes formal publication in a journal, exposing the author to dozens or hundreds of unsolicited, skeptical reviews from those who scan new postings each morning.

[101:] All this skepticism screens out a lot of nonsense right at the start. Furthermore, it optimizes the ability of both the original author and other scientists to root out errors and advance understanding. The constant communication through both formal and informal means rapidly disseminates new ideas so they can be woven quickly into the fabric of our current models, offering further opportunities to find inconsistencies and eliminate them. This highly social enterprise with this highly skeptical ethic is central to the rapid growth of scientific understanding in the modern era.

[102:] My celebration of skepticism and emphasis on falsifiability and the temporary nature of models should not be misconstrued as supporting the popular notion that science consists of an endless series of "Eureka moments." The news media are committed devotees of this false view. Each week, the Science Times needs half a dozen "news" stories, and if they can use words like "stunning," "revolutionary," and "theory overturned" in the headlines, so much the better. Scientists are complicit in this misrepresentation, all too easily using phrases such as "breakthrough", "astonishing", and the like, not only when talking to reporters, but even when writing grant proposals and journal articles. Some philosophers of science share the blame by concentrating their studies on "paradigm shifts" and "scientific revolutions". Science isn't really like that.

[103:] Science is much more like building a cathedral than blowing one up. Thousands of hands place the stones, weave the tapestries, tile the frescos, and assemble the stained-glass windows. Occasionally, a new idea might require the disassembly of some work already completed -- invention of the flying buttress allowed the walls to go higher. Very infrequently, on timescales typically measured in centuries, a genuinely new conception of the cathedral's architecture emerges. While a major supporting wall or facade may need to be removed, we use many of the stones again, rehang some of the old tapestries, and always enclose most of the old building within the new. Our cathedral gets larger and ever more ecumenical, drawing a greater swath of the universe within its doors as the weaving, the leading, the ceramics, and the stonemasonary goes on. It is extraordinarily gratifying work.