• You know that “something” exists.
• If you have mental experiences, then you know that “you” exist (though coming up with a reasonable definition for what “you” means can be remarkably tricky).
• If your mental experiences are varied, then you know that whatever exists creates varied mental experiences.

With some cleverness, you may be able to add to this list a few more things that you know with total certainty, but not many. In fact, almost everything that we think we know we cannot be completely sure about. For instance:

• You take it for granted that five minutes from now you will still be alive, but there is a non-zero probability that your heart will give out before then.
• You feel as though the world you see around you is reality, and yet, that is also what it would feel like if you were in fact in an extremely detailed simulation of reality (for instance, your brain could be hooked up to some sort of computer). So you cannot know for certain that you are not now living in a simulation rather than having experiences based on physical reality itself.
• You cannot know, with total certainty, that you are not dreaming right now.
• You cannot know, absolutely, that you have not gone mad. Many things that you think are real could be delusions. Of course, you’d expect your delusions to feel totally correct to you, and not seem delusional at all.

Virtually everything involves some amount of uncertainty (even the best predictions will contain some error), and many things are highly uncertain (in the sense that our attempts to model them lead to uncertain predictions). Consider our uncertainty about processes on different physical scales.

On a large scale there are weather systems and economies, which depend on very large numbers of variables that are difficult to measure accurately. Weather depends on temperatures, pressures, geography, sun output, cloud cover, pollution, bodies of water, etc. Economies are impacted by spending behavior, regulation, war, technology, disease, culture, and so forth. What makes large systems especially hard to predict is that many of them are chaotic in nature, so small changes in the values of the variables by which they are influenced can lead to large changes down the line. For instance, a relatively small shift in the pressure and temperature in one area of the world may eventually lead to a hurricane hitting a far away area. Or, in an economy, a piece of legislation passed today that deregulates certain company behaviors could lead to increased use of leverage, which could result in a market collapse a decade later. Political events are another good example of large-scale uncertainty, because they tend to be highly complex and chaotic. That means they should be hard to predict. In fact, the empirical data says that most political forecasting “experts” are not significantly more accurate than random guessing or a non-expert predictor, though some fairly small fraction of such experts do seem to have meaningful predictive power.

On a medium scale, there are humans and roughly human-sized objects. Objects on a human scale, like balls and bookcases, tend to be quite each to predict, in part because they are accurately modeled by the relatively straightforward laws of Newtonian Mechanics. If you throw a ball you have a decent idea of where it is going to go, though the details of its trajectory will still be uncertain. If you drop a bookcase off of the Empire State Building, you know it will fall downward, and can roughly estimate when it will hit the ground, though exactly where it will land will depend on unpredictable factors involving air flow across its surface. However, predicting the location of the cracks along which it will shatter when it finally hits the ground is far beyond our ability to forecast.

Unlike balls, which are fairly straightforward, human minds are very unpredictable. The problem is three-fold: the complexity of the brain, our lack of knowledge about brains in general, and the inaccessibility of the present state of any particular brain. It can be hard enough to tell if someone you’re talking to is annoyed, engaged in a pleasant day-dream, or feeling awkward. But predicting what they will say next will be even more difficult. Brains can even act as uncertainty generators. You can give a man a physical object, like a book, which can lead him to believe some idea that he then feels compelled to spread. If he is successful enough in his proselytizing, he may spread this idea to hundreds of others, who themselves spread the idea to tens of thousands more. The large-scale fate of the world may be altered due to one particular person having seen one particular book, a result that was dependent on the great complexity of the human brain.

Knowledge of psychological studies does, of course, allow us to predict some things about human behavior. For instance, in Milgram’s famous experiment, it was found that if a person who seems sufficiently authoritative insists that a test subject administer high voltage shocks to another person, even though it seems obviously dangerous to do so, about two-thirds of the test subjects will comply. The trouble is that even robust psychological findings like this one involve much uncertainty. For one thing, it is difficult to predict in advance who the one-third of non-compliers are going to be. Furthermore, the fraction of participants that comply is influenced by a variety of factors, so one cannot assume that this two-thirds number will hold in similar situations. For instance, when the authority was not in the room with the test subject, communicating only by telephone, compliance fell from two-thirds to only about twenty percent. When other test subjects (actually actors who are confederates of the experimenter) refused to comply with the authority, only ten percent were willing to continue with the experiment.

While there are some human behaviors that can be predicted very accurately (if you touch a hot pan, I predict you will pull your hand away, if you are handed a deep-fried oreo, I predict you will eat it, if you attempt a certain extremely difficult logic puzzle, I predict you will not be able to solve it in 5 minutes). But, at this stage of our understanding, much of the human behavior that we care about predicting can only be modeled in a probabilistic fashion, with a lot of uncertainty in our estimates. We are forced to use statements like “most of the time when you put a person in situation X, they will have behavior Y.”

While one might hope that at the small-scale things become certain, this is unfortunately not the case. It is now known that atoms are governed by the laws of quantum mechanics, which involve inherent, fundamental unpredictability. In fact, in quantum mechanics it doesn’t make sense to even talk about the exact position and velocity of a particle. We can only know the probability of a particle being measured to be within a certain distance of a particular location, and having a velocity within a certain range of values. The Heisenberg Uncertainty Principle makes this idea more precise, encapsulating the idea that the more certain we are of the position of a particle, the less certain we must be of its velocity, and vice versa. As systems of particles become larger and larger (forming objects such as carrots and boulders) the uncertainty principle can be essentially ignored, because the size of the quantum uncertainty is very small compared to the size of the object itself.

Uncertainty is inescapable. It manifests in large-scale chaotic systems, like economies and weather systems, in the details of the trajectories of medium-scale objects, in human behavior, and in small-scale systems . For many of the most interesting predictions we would care to make, we cannot avoid making them in terms of probability. Rather than being able to say, “X will happen,” we end up only being able to speak in terms of “the probability that X will happen.”