But for all that we have of Bede’s work, even more of it no longer exists. Bede wrote a great deal of English poetry, nearly all of which has been lost. However, we have most of the Venerable Bede’s important scholarly works. In order for knowledge to be discovered, and to be recombined in novel ways for new facts to be unearthed, it first needs to be preserved. For every one of Bede’s books, how many books of others do we not even have a memory? How much knowledge is fated to remain forever hidden?
A Cornell professor of earth and atmospheric sciences20 named John Cisne decided to tackle this question. Using the works of the Venerable Bede as a guide, he employed the same technique I did in chapter 5: He brought biology to the world of handwritten manuscripts. While I examined mutations and evolution, Cisne wanted to see how often medieval manuscripts go extinct while being copied. So he used population and demographic models to understand how Bede’s works spread.
Just as organisms reproduce and die out, so do manuscripts, in a fashion: They “reproduce” by being copied and can die by being lost or destroyed. Reproduction in this case follows a logistic curve, just like bacteria in a petri dish. Since books cannot grow without bound, a logistic curve is a more realistic function to use than a simple exponential. The logistic allows for growth in which there is a certain carrying capacity—the maximum number of copies of a book that can be made.
Cisne used mathematics from the world of population biology to describe this simple state of affairs, and he was able to create a model that fit the number of the Venerable Bede’s technical books that have survived from each century. From this Cisne arrived at the likelihood that a document would be copied. Specifically, he found that documents from the Middle Ages were fifteen to thirty times more likely to be copied than destroyed.
In addition, he calculated the half-lives of these books: how long they would last before the destruction of half of the copies. He found that the half-lives were between four and nine centuries, a surprisingly long time. Cisne was able to conclude that most documents from the early Middle Ages, and perhaps even antiquity, have, in fact, survived.
We have certainly lost a great deal; time ravages much knowledge. But when it comes to hidden knowledge, it’s heartening to know that many facts aren’t lost to history; they can indeed be discovered.
• • •
SO we now know that facts are seldom lost. And as long as knowledge is preserved, we have the raw materials for unearthing hidden knowledge. As we’ve seen earlier in the chapter, that still doesn’t prevent much of knowledge from remaining hidden—witness everything from Mendelian genetics to the true import of clinical trials—but through modern technology, we now have computational ways of connecting and recombining disparate bits of knowledge to create new facts.
In fact, hidden knowledge and its discovery is no longer the domain of the medieval scholar or information scientist, or even of the robotic mathematician. Tools related to hidden knowledge are being created for everyone, enabling a certain renaissance in the discovery of knowledge; facts can be spread and mixed in novel ways, unburied and shown the sunlight. One of these tools is Mendeley, which is designed for the average scientist.
One of the most annoying and tedious parts of publishing scientific work is in the details—specifically, the details of formatting. Each journal has its own specific rules for fonts, the organization of the paper’s content, and, most maddening, how to format the citations. When you write a paper, you carefully format each reference specifically for the journal to which you are submitting. But woe betide the scientist whose paper is rejected, forcing her to reformat for another journal and a resubmission. And lest you be surprised by this tedium, multiple submissions are more often the rule than the exception.
Into this detail-oriented morass have stepped a number of computational tools to help deal with these issues. The most popular of these is EndNote. This is a computer program that allows references to be imported easily from scientific databases, or to be entered manually. Creating a bibliography for a specific journal becomes as simple as selecting it from a drop-down menu. Want to submit to Nature? Easy. Rejected from Nature and now aiming a paper at Proceedings of the National Academy of Sciences? This too is a simple matter, requiring little more than a single click.
But a new online tool has arrived recently, called Mendeley. In addition to simplifying reference importation, synchronizing one’s bibliography online, and many other wonderful features, it has another: social networking. Instead of the scientist simply working with the set of references they use to write their papers in isolation, it allows them to see their friends’ references; it acts as a sort of social network for scientists.
As Mendeley grows in popularity—and it seems that it’s hitting the critical mass that’s necessary for any social Web site to thrive—it allows for the collaborative exposure of knowledge that each of us individually hasn’t been aware of.
But it provides another important feature: It allows scientists to see articles that are related to ones that they’re already looking at. By automatically finding topic relationships between papers, Mendeley brings undiscovered public knowledge to the scientific masses. Scientists can now find a paper on psychology that can shed light onto network science or a math paper that can help with X-ray crystallography. In doing so it can help create new facts.
These capabilities are even being brought to the everyday user. There are a wide variety of computer tools that allow someone to collect snippets of information—quotations, references, pictures, articles, Web pages, and more—in a simple and searchable place. Some store these notes in the cloud, some on a desktop, and some even allow these notes to be shared with others.
However, one program has an ability that others lack: DEVONthink uses something called semantic and associative data processing. The other programs require searching for certain words or combinations of words. If a note has these words, it shows up; otherwise the program can’t find it. DEVONthink, however, is a bit more clever. It uses a special computational technique to analyze the entire text and find relationships between words. So if the search is for the word house and there is a note that is a quotation about the wonderful nature of the home, DEVONthink is likely to find such a relationship. It can also tell which notes are similar to one another, providing cognitive connections that are not always available to us, since we can’t hold thousands, or even hundreds, of notes in our minds at once. But computers can, and they can draw the connections for us, providing the substrate for new facts and bits of knowledge.
Steven Johnson, a writer whose books rely on the connectedness of disparate ideas, uses DEVONthink a great deal, and he reports that it has benefited him greatly. From an essay in which he praises this tool’s powers, he gives an example:
This can create almost lyrical connections21 between ideas. I’m now working on a project that involves the history of the London sewers. The other day I ran a search that included the word “sewage” several times. Because the software knows the word “waste” is often used alongside “sewage” it directed me to a quote that explained the way bones evolved in vertebrate bodies: by repurposing the calcium waste products created by the metabolism of cells.
That might seem like an errant result, but it sent me off on a long and fruitful tangent into the way complex systems—whether cities or bodies—find productive uses for the waste they create.
New facts are all around us. And due to the algorithmic properties of modern technology, we now have the possibility of discovering them.
• • •
DIGGING up hidden knowledge is now far from an impossibility, or even from being solely the domain of the specialist; it has become eminently possible and easy. Knowledge doesn’t get lost or destroyed any longer, and that seems to have happened even less often than we used to believe. Facts are now commonly digitized, and are ripe for being combined and turned into new fact
s. We are in a golden age of revealing hidden knowledge.
When this happens it can sometimes lead to drastic, sudden changes in what we know. These changes—when what we know is fundamentally overhauled in an abrupt and dramatic way—are also subject to quantitative regularity, and are the subject of the next chapter.
CHAPTER 7
Fact Phase Transitions
IN 1750, Thomas Wright, a British astronomer,1 published a diagram in his book An Original Theory or New Hypothesis of the Universe. This diagram showed a whole host of stars. But there was more in the diagram than just stars; the stars weren’t alone. Each star was surrounded by a small cloud of orbits, an entire planetary system. What Wright was clearly implying was that our sun was not particularly special: Other planets orbited around every star, much like the ones in our solar system.
At that point in history this notion was nothing more than a hope, and a somewhat sacrilegious one at that. It was no more than a logical deduction derived from the Copernican notion that our place in the universe need not be a particularly privileged one.
More recently, in Carl Sagan’s 1980 documentary Cosmos, Sagan is shown speaking to a classroom of schoolchildren. In his characteristically excited and inspirational manner, he speaks of our solar system and hands out pictures of the different planets and moons to each of the students. Then he begins to muse about ideas that are a bit more speculative but which are just as exciting. Explaining the fundamentals of detecting extrasolar planets—planets outside the solar system—he tells them that humanity will discover such planets in their lifetimes. He predicts that we would one day find other planets like our own Earth, as well as ones similar to all the other planets throughout our solar system.
We have had this yearning for centuries, to know of the existence of worlds orbiting other stars like ours. It would give us a sense of our place in the universe and flesh out the true details of our stellar neighborhood. While to some these discoveries would make our stellar home a bit more ordinary (and a few find it a very worrisome idea), others have been sure that this feeling of drabness would certainly be offset by how these planets outside our solar system can provide us a way of viewing ourselves.
When Sagan spoke to those schoolchildren, he was right. In 1995, the hypothetical became the factual when the team of Michel Mayor and Didier Queloz announced the discovery of a planet orbiting 51 Pegasi, a star much like our own sun.
Since 1995, thousands of such exoplanet candidates have been detected by various methods. These planets vary widely in their characteristics, with many far larger than Jupiter and orbiting closer than Mercury. But the first discovery was something special. In addition to a higher likelihood of having its place in the history books, 51 Pegasi produced a rapid shift in our knowledge. Humanity, in the course of a single issue of Nature, overhauled its view of the universe. We went from knowing of no planets orbiting sunlike stars like our own to knowing that they exist. To oversimplify, everything before that discovery was speculation, and everything else after that was simply collecting more examples of the same: more extrasolar planets.
• • •
WHEN facts change we can often anticipate the speed at which the change occurs. Populations grow according to certain rules, medical knowledge accumulates in a regular fashion, and new technologies allow us to do things at faster and faster rates—but all in a way that is well understood and regular.
However, there are other facts that don’t seem to adhere to this sort of logic. Knowing DNA’s structure, or whether Pluto was a planet, or that airplanes were possible—all of these happened in extremely rapid shifts. The iPhone appeared so rapidly in the world of technology that executives from a rival company thought many of its claimed specifications were lies, and Marc Andreessen has argued that it’s as if it appeared from the future, incredibly ahead of its time. One day there was a certain understanding of how we thought the world works, and the next day humanity’s factual environment had undergone a fundamental change.
But can these actually be explained? Astonishingly enough, there is in fact an order to these rapid shifts in our knowledge. We can find regularities in them, and sometimes even predict them before they happen.
This type of rapid change in knowledge—when we go from one state of awareness to another—is one example of a larger class of phenomena in science that are termed phase transitions. This term is well-known in physics, and most of us are no doubt familiar with them on a daily basis. When water freezes, when dry ice becomes carbon dioxide (by a process known as sublimation), even when gold is melted—all of these are examples of matter changing its phase. These are so much a part of our lives that we do not marvel when they happen. But while everyday occurrences, phase transitions are intriguing to physicists for a simple and powerful reason: They are clear cases when small changes make a big difference.
In general, through a small change of an underlying parameter, such as temperature, we get a small change in the overall properties of what we’re looking at. Warm a cup of water by a small amount and it becomes a bit hotter. Or put metal in a furnace and it becomes warm to the touch.
But at some magical point a tiny shift in the underlying parameter induces a rapid and pervasive change in the system. Warm that water just a little bit more, and suddenly it’s not just a warmer liquid—it’s a gas: steam.
While entirely unextraordinary, something complicated is happening at the microscopic level that leads to these changes.
What is it about the boiling point of water that allows a small change in temperature to produce a massive change in the overall structure of all of its molecules? Or, in a slightly less familiar area, why does heating a magnet cause it to lose its magnetization (and even weirder, when it’s cooled, to stay demagnetized)? In the parlance of condensed matter physics, the branch of physics that examines these phenomena: What causes this cascading behavior and resulting phase transition?
And what about facts? Can the same sort of rapid cascade occur in the world of facts, when a large-scale shift in what we know about the world is due to some smaller underlying change?
The answers to these questions can be found in a simple mathematical model of how magnets work, developed by a physicist named Ernst Ising.
• • •
THERE are all sorts of mathematical models for physical systems. Some try to actually mimic the complex mess we see around us, the most well-known of these being weather models. We don’t just want to understand how weather changes; we want to know how likely it is that it will rain tomorrow. So we input temperature details from throughout the country; wind speeds; barometric pressure values measured over time; and much more. These values are then put into complex equations and simulated in a powerful computer, allowing us to see what they all will be in the future, inside the computational world that has been created.
But these kinds of models, while very powerful, don’t allow us to say anything general about them. We can’t write down a simple equation for how the average air temperature of the entire country will affect rain, because the model is far too complex for that. To understand that sort of thing, or any other system for which we want to explain a certain phenomenon, we need to create much simpler models. These don’t make any claims for verisimilitude. Instead, they go to the other extreme and claim the following: We can make an extremely basic model that even with all the complexity of real life stripped away still has certain features of our complicated world. And if we can capture these features of our world, maybe we can understand why they occur. In our case, the question is whether a simple model can be made that exhibits phase transitions. This is exactly what Ising set out to do.
How does the Ising model work? Imagine we lay out a large deck of cards, in which each card is black on one side and white on the other, into a grid. When the cards are all on the same side—either black or white—the system is considered to be in one state, li
ke a solid. Entirely uniform and understandable. However, if the cards are flipped randomly, and there are no regions of a single color, we have something much more irregular. We know such a system as a gas.
How does this system change? We choose a card and flip it. If we start with all the cards on their black sides, pretty soon we’ll start getting cards showing white, and soon enough we will have something that looks random and fits what I described as a gas.
As I’ve explained the system thus far, it seems like we’re just flipping cards at random. And a moment’s thought shows that flipping the cards at random will result in no overall change. If any part of a random grid of black and white cards is changed at random, the details of the picture will change: which specific cards are black and which are white. But if you zoom out, we still get the same overall picture: static.
But here’s where the model gets interesting. If, whenever we flip a card, we have the possibility of also flipping its neighboring cards to the same color, this little twist is enough to yield strikingly different behavior. In the Ising model, whether an individual card is black or white depends on two things: the “temperature” of the system and the neighbors.
The parameter that we call temperature is related to how likely it is that a card gets flipped when its neighbor is flipped. At high temperatures lots of cards flip, but simply because it’s hot and the temperature is making everything jumpy. But as the system cools down, things start becoming more clumpy, because now neighboring cards are affected when a card is flipped. So whole patches of cards can change color quite rapidly.
When the temperature drops low enough, the grid of cards will snap into a single color, either white or black. Now we’re in an entirely different state, which we can call a solid, since it’s a solid block of color.
The Half-Life of Facts Page 13