The Half-Life of Facts (18 page)

At that point in history this notion was nothing more than a hope. 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, like 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.

Here’s what Ising recognized: There is a temperature value that can be solved for mathematically and that precisely represents the transition between the two phases: between when everything is the same color and when it’s all random.

The Ising model—which is referenced by thousands of articles in fields that range from biology to the social sciences—is a mathematical abstraction that has been used to explain all sorts of phase transitions, many outside the realm of physics. Phase transitions have been used to understand all types of rapid change, from ecological models that explore ecosystem collapse and abrupt climate change to tipping points for how fads and fashions spread.

But what about facts? Can these sorts of models provide insight into how changes in knowledge operate?

It turns out that knowledge is not that different from abstract magnetic models. While the underlying changes in our knowledge develop over time, we can have big sudden jumps in something else we might be examining. In the Ising model, we change something slowly and continuously—temperature—and this change yields a sudden jump in something else: the state of the system, from gas to solid, for example. In the world of facts, this sort of thing can also happen: A sudden jump in our knowledge might be due to some other facts changing and being slowly accumulated. But this still sounds very abstract; how might this work in practice?

.   .   .

ONE
of the biggest facts in human history was overturned abruptly, and it was done in a single footprint: Since the dawn of history, no human had walked on the moon. That was a fact whose status hadn’t
budged at all for thousands of years. At no point did someone walk on the moon even a little bit. At 10:56
P.M
.
EDT on July 20, 1969, this all changed with a single step.

But could this phase transition have been predicted as growing out of some underlying regular change? Yes. There were underlying quantifiable patterns occurring over the previous decade that would have allowed the prediction of this phase transition in humanity’s place in the solar system.

Prior to Apollo 11, multiple unmanned and manned Apollo missions had been launched. Apollo 10 actually did everything but land on the Moon—it left the earth’s orbit, circled the moon, and returned home. It even came within fifteen kilometers of the moon’s surface. Despite what appears to be an abrupt transition in what we know, there was a steady progression of underlying changes that can explain the jump.

In fact, it’s not even the few missions just prior to the moon landing that could help explain the transition; hundreds of years of smooth data can actually be used to explain this steady march. In 1953, Air Force scientists in the Office of Scientific Research and Development created a simple chart of the fastest man-made vehicles at each moment in history for the previous couple of centuries. They found something incredible: If they extrapolated the exponential curve outward, the data showed that speeds necessary to leave the Earth’s surface could be reached within four years! A curve had implied the existence of the first artificial satellite well before Sputnik’s launch, and exactly as predicted (Sputnik went into orbit on October 4, 1957).

Furthermore, the Air Force scientists realized that the chart predicted that the speeds required to land on the moon were reachable a few years after that. And the moon landing came to pass, just as expected. Interstellar spacecraft are also included in the plot, and while we haven’t succeeded in that domain yet, NASA recently announced an initiative to begin thinking about ships with the capability of reaching the stars.

What this means is that the factual phase transition of the
moon landing was long in the cards—it was simply due to a steady change in the underlying speeds we could achieve.

These sorts of phase transitions occur in many places in the world of facts. As mentioned before, Pluto was a planet for nearly a hundred years, and then, suddenly, it wasn’t. Everyone knew that smoking was fine for you. Doctors even endorsed certain brands. Then, in the 1950s, it became abundantly clear that smoking kills.

But these can likely be explained by underlying steadier changes. The detection of larger and larger objects at the fringe of the solar system meant that Pluto’s status was due for reconsideration. And the proliferation of medical studies meant that it was only a matter of time before we would learn of the dangers of smoking.

In contrast, the number of mammals that we know of is a slower, steadier progression of knowledge. No single discovery greatly changes our awareness of the number of species. If we know of thousands of mammals, no single additional discovery is going to overturn that fact.

Sometimes, though, the line between these two types of knowledge change is a bit less clear. For example, while finding the first extrasolar planet is a phase transition, going from 400 to 401 known extrasolar planets is a more subtle and steady progression. In these cases, and many others like them, knowledge accretes slowly, and often according to the regular patterns discussed in
chapter 2
.