the art and science of dunking

One of the main problems that scientists have in sharing their picture of the world with a wider audience is the knowledge gap. One doesn't need to be a writer to read and understand a novel, or to know how to paint before being able to appreciate a picture, because both the painting and the novel reflect our common experience. Some knowledge of what science is about, though, is a prerequisite for both understanding and appreciation, because science is largely based on concepts whose detail is unfamiliar to most people.

That detail starts with the behavior of atoms and molecules. The notion that such things exist is pretty familiar these days, although that did not stop one of my companions at a dinner party from gushing, "Oh, you're a scientist! I don't know much about science, but I do know that atoms are made out of molecules!" That remark made me realize just how difficult it can be for people who do not spend their professional lives dealing with matter at the atomic or molecular level to visualize how individual atoms and molecules appear and behave in their miniaturized world.

Some of the first evidence about that behavior came from scientists who were trying to understand the forces that suck liquids into porous materials. One of the most common manifestations of this effect is when coffee is drawn into a dunked doughnut or tea or milk into a dunked cookie, so I was delighted when an English advertising firm asked me to help publicize the science of cookie dunking because it gave me an opportunity to explain some of the behavior of atoms and molecules in the context of a familiar environment, as well as an opportunity to show how scientists operate when they are confronted with a new problem.

I was less delighted when I was awarded the spoof IgNobel Prize for my efforts. Half of these are awarded each year for "science that cannot, or should not, be reproduced." The other half are awarded for projects that "spark public interest in science." The organizers have now changed these confusing descriptions for the simple "First they make you laugh; then they make you think."

It was a pleasure, though, to receive letters from schoolchildren who had been enthused by the publicity surrounding both the prize and the project. One American student sought my help to take the work further in his school science project, in which he studied how doughnuts differ from cookies. He subsequently reported with pride that he had received an "A" for his efforts.

This chapter tells the story of the dunking project and of the underlying science, which is used to tackle problems ranging from the extraction of oil from underground reservoirs to the way that water reaches the leaves in trees.

Doughnuts might have been designed for dunking. A doughnut, like bread, is held together by an elastic net of the protein gluten. The gluten might stretch, and eventually even break, when the doughnut is dunked in hot coffee, but it doesn't swell or dissolve as the liquid is drawn into the network of holes and channels that the gluten supports. This means that the doughnut dunker can take his or her time, pausing only to let the excess liquid drain back into the cup before raising the doughnut to the waiting mouth. The only problem that a doughnut dunker faces is the selection of the doughnut, a matter on which science has some surprising advice to offer, as I will show later in the chapter.

Cookie dunkers face much more of a challenge. If recent market research is to be believed, one cookie dunk in every five ends in disaster, with the dunker fishing around in the bottom of the cup for the soggy remains. The problem for serious cookie dunkers is that hot tea or coffee dissolves the sugar, melts the fat, and swells and softens the starch grains in the cookie. The wetted cookie eventually collapses under its own weight.

Can science do anything to bring the dedicated cookie dunker into parity with the dunker of doughnuts? Could science, which has added that extra edge to the achievements of athlete and astronaut alike, be used to enhance ultimate cookie dunking performance and save that fifth, vital dunk?

These questions were put to me by an advertising company wanting to promote "National Cookie-Dunking Week." As someone who uses the science underlying commonplace objects and activities to make science more publicly accessible, I was happy to give "The Physics of Cookie Dunking" a try. There was, it seemed, a fair chance of producing a light-hearted piece of research that would show how science actually works, as well as producing some media publicity on behalf of both science and the advertisers.

The advertisers clearly thought that there would be keen public interest. They little realized just how keen. The "cookie dunking" story that eventually broke in the British media rapidly spread worldwide, even reaching American breakfast television, where I participated in a learned discussion of the relative problems of doughnut and cookie dunkers. The extent of public interest in understandable science was strikingly revealed when I talked about the physics of cookie dunking on a call-in science show in Sydney, Australia. The switchboard of Triple-J, the rock radio station, received seven thousand calls in a quarter of an hour.

The advertisers had their own preconceptions about how science works. They wanted nothing less than a "discovery" that would attract newspaper headlines. Advertisers and journalists aren't the only people who see science in terms of "discoveries." Even some scientists do. Shortly after the Royal Society was founded in 1660, Robert Hooke was appointed as "curator of experiments" and charged with the job of making "three or four considerable experiments" (i.e., discoveries) each week and demonstrating them to the Fellows of the Society. Given this pressure, it is no wonder that Hooke is reported to have been of irritable disposition, with hair hanging in disheveled locks over his haggard countenance. He did in fact make many discoveries, originating much but perfecting little. I had to tell the advertisers in question that Hooke may have been able to do it, but I couldn't. Science doesn't usually work that way.

Scientists don't set out to make discoveries; they set out to uncover stories. The stories are about how things work. Sometimes the story might result in a totally new piece of knowledge, or a new way of viewing the nature of things. But not often.

I thought that, with the help of my friends and colleagues in physics and food science, there would be a good chance of uncovering a story about cookie dunking, but that it was hardly likely to result in a "discovery." To their credit, the advertisers accepted my reasoning, and we set to work.

The first question that we asked was "What does a cookie look like from a physicist's point of view?" It's a typical scientist's question, to be read as "How can we simplify this problem so that we can answer it?" The approach can sometimes be taken to extremes, as with the famous physicist who was asked to calculate the maximum possible speed of a racehorse. His response, according to legend, was that he could do so, but only if he was permitted to assume that the horse was spherical. Most scientists don't go to quite such lengths to reduce complicated problems to solvable form, but we all do it in some way — the world is just too complicated to understand all at once. Critics call us reductionists, but, no matter what they call us, the method works. Francis Crick and James Watson, discoverers of the structure of DNA, didn't find the structure by looking at the complicated living cells whose destiny DNA drives. Instead, they took away all of the proteins and other molecules that make up life and looked at the DNA alone. Biologists in the fifty years following their discovery have gradually put the proteins back to find out how real cells use the DNA structure, but they wouldn't have known what that structure was had it not been for the original reductionist approach.

We decided to be reductionist about cookies, attempting to understand their response to dunking in simple physical terms and leaving the complications until later. When we examined a cookie under a microscope, it appeared to consist of a tortuous set of interconnected holes, cavities, and channels (so does a doughnut). In the case of a cookie, the channels are there because it consists of dried-up starch granules imperfectly glued together with sugar and fat. To a scientist, the cookie dunking problem is to work out how hot tea or coffee gets into these channels and what happens when it does.

With this picture of dunking in mind, I sat down with some of my colleagues in the Bristol University Physics Department and proceeded to examine the question experimentally. Solemnly, we dipped our cookies into our drinks, timing how long they took to collapse. This was Baconian science, named after Sir Francis Bacon, the Elizabethan courtier who declared that science was simply a matter of collecting a sufficient number of facts to make a pattern.

Baconian science lost us a lot of cookies but did not provide a scientific approach to cookie dunking. Serendipity, the art of making fortunate discoveries, came to the rescue when I decided to try holding a cookie horizontally, with just one side in contact with the surface of the tea. I was amazed to find that this cookie beat the previous record for longevity by almost a factor of four.

Scientists, like sports fans, are much more interested in the exceptional than they are in the average. The times of greatest excitement in science are when someone produces an observation that cannot be explained by the established rules. This is when "normal science" undergoes what Thomas Kuhn called a paradigm shift, and all previous ideas must be recast in the light of the new knowledge. Einstein's demonstration that mass m is actually a form of energy E, the two being linked by the speed of light c in the formula E = m[c.sup.2], is a classic example of a paradigm shift.

Paradigm shifts often arise from unexpected observations, but these observations need to be verified. The more unexpected the observation, the harsher the testing. In the words of Carl Sagan: "Extraordinary claims require extraordinary proof." No one is going to discard the whole of modern physics just because someone has claimed that Yogic flying is possible, or because a magician has bent spoons on television. If levitation did prove to be a fact, though, or spoons could really be bent without a force being applied, then physics would have to take it on the chin and reconsider.

One long-lived horizontal cookie dunk was hardly likely to require a paradigm shift for its explanation. For that rare event to happen, the new observation must be inexplicable by currently known rules. Even more importantly, the effect observed has to be a real one, and not the result of some unique circumstance.

One thing that convinces scientists that an effect is real is reproducibility — finding the same result when a test is repeated. The long-lived cookie could have been exceptional because it had been harder baked than others we had tried, or for any number of reasons other than the method of dunking. We repeated the experiments with other cookies and other cookie types. The result was always the same — cookies that were dunked by the "horizontal" technique lasted much longer than those that were dunked conventionally. It seemed that the method really was the key.

What was the explanation? One possibility was diffusion, a process whereby each individual molecule in the penetrating liquid meanders from place to place in a random fashion, exploring the channels and cavities in the cookie with no apparent method or pattern to its wanderings. The movement is similar to that of a drunken man walking home from the pub, not knowing in which direction home lies. Each step is a haphazard lurch, which could be forwards, backwards or sideways. The complicated statistics of such movement (called a stochastic process) has been worked out by mathematicians. It shows that his probable distance from the pub depends on the square root of the time. Put simply, if he takes an hour to get a mile away from the pub, it is likely to take him four hours to get two miles away.

If the same mathematics applied to the flow of liquid in the random channels of porous materials such as cookies, then it would take four times as long for a cookie dunked by our fortuitous method to get fully wet as it would for a cookie dunked "normally." The reason for this is that in a normal dunk the liquid only has to get as far as the mid-plane of the cookie for the cookie to be fully wetted, since the liquid is coming from both sides. If the cookie is laid flat at the top of the cup, the liquid has to travel twice as far (i.e., from one side of the cookie to the other) before the cookie is fully wetted, which would take four times as long according to the mathematics of diffusion (Figure 1.1).

The American scientist E. W. Washburn found a similar factor of four when he studied the dunking of blotting paper — a mat of cellulose fibers that is also full of random channels. Washburn's experiments, performed some eighty years ago, were simplicity itself. He marked off a piece of blotting paper with lines at equal intervals, then dipped it vertically into ink (easier to see than water) with the lines above and parallel to the liquid surface, and with one line exactly at the surface. He then timed how long it took the ink to reach successive lines. He found that it took four times as long to reach the second line as it did to reach the first, and nine times as long to reach the third line.

I attempted to repeat Washburn's experiments with a range of different cookies provided by my commercial sponsor. I dunked the cookies, each marked with a pencil in fivemillimeter steps, vertically into hot tea, and timed the rise of the liquid with a stopwatch. The cookies turned out to be very similar to blotting paper when it came to taking up liquid. Just how similar became obvious when I drew out the results in a graph. If the distance penetrated follows the law of diffusion, then a graph of the square of the distance traveled versus time should be a straight line. If it took five seconds for the liquid to rise four millimeters, it should take twenty seconds for the liquid to rise eight millimeters. And so it proved, for up to thirty seconds, after which the sodden part of the cookie dropped off into the tea (Figure 1.2).

These results look very convincing. Numerical agreement with prediction is one of the things that impresses scientists most. Einstein's General Theory of Relativity, for example, predicted that the sun's gravitation would bend light rays from a distant star by 1.75 seconds of arc (about five tenthousandths of a degree) as they passed close by. Astronomers have now found that Einstein's prediction was correct to within one percent. If astrology could provide such accurate forecasts, even physicists might believe it.

That's not the end of the story. In fact, it is hardly the beginning. Even though the experimental results followed the pattern of behavior predicted by a diffusion model, closer reasoning suggested that diffusion was an unlikely explanation. Diffusion applies to situations where an object (whether it is a drunken man or a molecule in a liquid) has an equal chance of moving in any direction, which seems unlikely for liquid penetrating a cookie, since the retreat is blocked by the oncoming liquid. Diffusion models, though, are not the only ones to predict experimentally observed patterns of behavior. Washburn provided a different explanation, based on the forces that porous materials exert on liquids to draw them in.

The imbibition process is called capillary rise, and was known to the ancient Egyptians, who used the phenomenon to fill their reed pens with ink made from charcoal, water, and gum arabic. The question of how capillary rise is driven, though, was first considered only two hundred years ago when two scientists, an Englishman and a Frenchman, independently asked the question: "What is doing the pulling?" The Englishman, Thomas Young, was the youngest of ten children in a Quaker family. By the age of fourteen, he had taught himself seven languages, including Hebrew, Persian, and Arabic. He became a practicing physician and made important contributions to our understanding of how the heart and the eyes work, showing that there must be three kinds of receptor at the back of the eye (we now call them cones) to permit color vision. Going one better, he produced the theory that light itself is wave-like in character. In his spare time he laid the groundwork for modern life insurance and came close to interpreting the hieroglyphs on the Rosetta stone. The Frenchman, the Marquis de Laplace, also came from rural origins (his father was a farmer in Normandy) and his talents, too, showed themselves early on. He eventually became known as "The Newton of France" on account of his incredible ten-volume work called Mécanique céleste. In this work he showed that the movements of the planets were stable against perturbation. In other words, a change in the orbit of one planet, such as might be caused by a meteor collision, would only cause minor adjustments to the orbits of the others, rather than throw them catastrophically out of synchrony.