Science is very good at understanding the largest and smallest things in our universe. We understand to amazing precision how planets move around stars, to the point where we can shoot space probes and satellites millions of miles through space. We understand how electrons and other fundamental particles behave so well that we have confirmed quantum electrodynamics, our modern theory of how electrons and photons behave, to almost 9 decimal places. That’s like keeping track of exactly how many people there are on this planet!
Everything else that’s smaller than a planet or larger than an electron – so pretty much everything we care about – is only understood to a much smaller level of accuracy. The reason for this uncertainty has to do with emergent behavior, the idea that systems with interacting parts tend to behave in unanticipated and complex ways.
Perhaps the most famous example of emergent behavior is the question of how many water molecules you need to get the quality of “wetness”. Surely a single molecule of water wouldn’t be wet, right? After all, the reason water is a liquid normally is because water molecules attract each other slightly, preventing each other from floating off. But if you have enough water molecules, it would be wet, so how many do you need?
It’s not clear at all that this question has a satisfactory answer. You could experiment to see how much water you need for a human to feel “wetness”, but this would probably depend on conditions like the temperature, where you placed the water, and how the person was trying to test its wetness.
It also seems questionable that “wetness” should rely on a human to interpret it – wouldn’t it be better and less biased for an electronic sensor to detect wetness? The problem is that while a machine can easily detect the presence of liquid water (we used them to search for water on Mars), the quality of wetness is much harder to describe technically to a machine.
Regardless, we can still take “wetness” as a good example of an emergent behavior. We cannot predict or study wetness using only a single molecule of water, and only with a large number of interacting water molecules can we arrive at something that is “wet”.
There are a lot of other common concepts that are similarly emergent: for example, pressure emerges from large numbers of small gas molecules bouncing off solid objects. Stickiness comes from large numbers of molecules attracting each other and creating a macroscopic force (i.e. strong enough that humans can feel it). Your thinking is an emergent process, created from large numbers of cells (neurons) interacting via chemical and electrical signals. Even the working of a computer is emergent, based on electrons moving through carefully arranged transistors and interacting with each other.
Thinking about things this way, it seems that pretty much any composite object performs emergent behavior. Why then can we still understand planet orbits really well? After all, planets are made up of enormous numbers of atoms and molecules. If it’s hard to predict how a human thinks or a computer works, how much harder would it be to understand a planet that includes billions of times as many atoms?
As it turns out, we do have techniques to deal with emergent behavior, especially for emergent behavior that comes out of very homogenous material (like a glass of distilled water). The field of statistics (or its parallel in physics, statistical mechanics) comes to the rescue. Statistics makes a bargain: trade away detail to gain perspective. Rather than focus on everything, we look only at the averages.
With a planet’s orbit, for example, we assume the rest of space is empty except for the Sun or other planets. This approximation turns a very complicated problem – describe how all atoms in the universe change over time – to a much simpler one – describe how the eight planets (sorry Pluto!) and the Sun orbit each other. In the case of orbits, this approximation is very reasonable (the rest of space truly is about empty), giving us very high accuracy in predictions.
For a computer, we can approximate the transistors and the rest of the circuitry as simple logic gates, and again because this is mostly true (due to clever engineering to make it as true as possible), we can understand how a computer works at the abstract level of following instructions and executing code. Thus, we see that the more homogenous a system, the easier it is to understand its emergent behavior and make predictions.
As a final thought, consider how diverse and non-homogenous humans are, whether physically (your complicated internal organs) or non-physically (our diverse thoughts and beliefs). This diversity makes most approximations very inaccurate. That’s why biology, psychology, and economics are such inexact fields: while statistics can help with system that have a lot of parts, it fails with systems that have a lot of different parts.