If you look at the long march of human understanding, science begins with the idea that we can understand our role in the universe using logic and observation. For example, the stars and planets were mysterious objects for most of human history. Yet ancient Greek philosophers were able to use reasoned arguments and simple geometry to estimate the sizes and distances of our neighbors in space. Similarly, the most important scientific step in understanding Earth's history was not one particular set of measurements, but rather the mental leap of realizing that Earth had a history that could be unraveled by scientific observations and measurements. This happened mostly in the 16th and 17th centuries with the Renaissance and then with a period of time called the Enlightenment. One example of how science works is humanity's long, step-by-step search to find the age of the Earth.
In the Middle Ages, scholars thought they could calculate Earth's age by finding out how long humans had lived on Earth. They assumed that humanity had been around almost since Earth itself formed. Therefore, scholars analyzed ancient records, especially Biblical scriptures that listed the generations since Adam and Eve. They concluded that humanity, Earth, and the whole cosmos were only a few thousand years old. The most famous calculation was made by Irish archbishop James Ussher in 1650. Ussher deduced that the cosmos formed on Sunday, October 23, in 4004 B.C., and that humanity was created on Friday, October 28 the same year. Even today, some people — especially fundamentalist religious groups — still believe that the Earth is only a few thousand years old, based on this method of reasoning.
In the Renaissance, scientists began to question the Bible as a basis for estimating the age of the Earth. They realized that a vast panorama of geological processes must have occurred, for which 6000 years was simply not enough time. In 1519, Leonardo da Vinci noticed fossil seashells embedded high in mountains, indicating that rocks on the peaks had once been under the sea. Such observations led to a new field of study, called natural history. It is certainly possible to imagine that the Earth has always existed and has never changed. It is also possible to imagine that a creator put everything in place just as we see it today. Natural history implied that the world is changing all the time, and physical processes shape and alter our surroundings. The world we see today might not be the way the world was originally created. Scientists worked hard to figure out how long geological processes had been going on.
A breakthrough occurred in the 1670s, at a time when Newton was at the height of his research. Around 1671, the "father of English Natural History," John Ray, observed a bed of sand 100 feet thick deposited on top of cockleshells at Amsterdam. This discovery meant that 100 feet of sediment had been deposited after the cockles had been alive. Ray realized he could calculate how long this deposition process had been active. We can easily follow his logic. He had to make a separate determination of the rate at which sand is deposited. Then he divided the depth of the sediments by their measured rate of accumulation. By making a simple division he was also implicitly assuming that the average rate of deposition did not change much. According to his calculations, it would have taken at least 10,000 years for the sand layers to be deposited. This was "a strange thing," John Ray wrote, "considering [that the age of the Earth] according to the usual account is not yet 5600 years."
The next step toward pinning down the age of our planet was to think about the cooling of Earth. Scientists believed the Earth had once been molten — volcanoes were considered to be evidence of this. This hypothesis suggested a simple question: how long would a molten Earth take to cool to present-day temperatures? Newton approached the problem theoretically. In the 1680s, he calculated that "a globe of red-hot iron equal to our Earth...would scarcely cool...in 50,000 years." Newton's calculation inspired Buffon's odd experiments. Buffon made actual measurements of the cooling times of small solid globes. He then extrapolated to the much larger size of the Earth and concluded that Earth's age must be at least 75,000 years — ten times as long as the Biblical chronology. Buffon even suggested that his result might be too short. He speculated that Earth might be as much as three million years old!
Evidence mounted in the 19th century that the Earth was far older than previously believed. The new field of geology added to this evidence. The method of using layers and deposition rates to date rocks improved in the 1800s. Scottish scientist Charles Lyell, known as the father of modern geology, and others made two important discoveries. First, they studied sedimentary layers exposed in canyons in many parts of the world and realized that the total depth of sediments is immense. One estimate gave 72,000 feet of sediments as a typical figure in some regions. This meant the old estimates of the time needed to deposit the sediment of a single river were much too short for the age of the whole Earth. Second, geologists found evidence that mountains had gone through many cycles of erosion, subsidence, and uplift. Using deposition rates to calculate the age of one area might represent only one cycle, not the age of Earth itself. Lyell, in 1830, like Buffon before him, wrote that "millions of years" would have been required to form all the features seen on Earth. Thus, by the late 1800s, most scholars accepted that Earth must be at least millions of years old. Many suspected that even this was an underestimate since erosion and other forces wear away at the surface of the planet.
You can see why the idea of an old Earth is a conceptual leap. Except for violent events like earthquakes and volcanoes, the geological changes of the Earth are imperceptible. Even over the span of a lifetime, erosion and deposition sculpt our surroundings very subtly. We see a snapshot in a long geological history, and we must use the patterns in the Earth to unravel that history.