How to Be Uncertain
Building Minds That Know Themselves
The other fountain [of] ideas, is the perception of the operation of our own minds within us.… And though it be not sense, as having nothing to do with external objects, yet it is very like it, and might properly enough be called internal sense.
Essay Concerning Human Understanding, Book II
Is something there, or not? This was the decision facing Stanislav Petrov one early morning in September 1983. Petrov was a lieutenant colonel in the Soviet Air Defense Forces and in charge of monitoring early warning satellites. It was the height of the Cold War between the United States and Russia, and there was a very real threat that long-range nuclear missiles could be launched by either side. That fateful morning, the alarms went off in Petrov’s command center, alerting him that five US missiles were on their way to Russia. Under the doctrine of mutually assured destruction, his job was to immediately report the attack to his superiors so they could launch a counterattack. Time was of the essence—within twenty-five minutes, the missiles would detonate on Soviet soil.1
But Petrov decided that the alert was unlikely to be a real missile. Instead, he called in a system malfunction. To him, it seemed more probable that the satellite was unreliable—that the blip on the radar screen was noise, not signal—than that the United States had sent over missiles in a surprise attack that would surely launch a nuclear war. After a nervous wait of several minutes, he was proved right. The false alarm had been triggered by the satellites mistaking the sun’s reflection off the tops of clouds for missiles scudding through the upper atmosphere.
Petrov saw the world in shades of gray and was willing to entertain uncertainty about what the systems and his senses were telling him. His willingness to embrace ambiguity and question what he was being told arguably saved the world from disaster. In this chapter, we will see that representing uncertainty is a key ingredient in our recipe for creating self-aware systems. The human brain is in fact an exquisite uncertainty-tracking machine, and the role of uncertainty in how brains work goes much deeper than the kind of high-stakes decision facing Petrov. Without an ability to estimate uncertainty, it is unlikely that we would be able to perceive the world at all—and a wonderful side benefit is that we can also harness it to doubt ourselves.
Inverse Problems and How to Solve Them
The reason Petrov’s decision was difficult was that he had to separate out signal from noise. The same blip on the radar screen could be due to an actual missile or noise in the system. It is impossible to work out which from the characteristics of the blip alone. This is known as an inverse problem—so called because solving it requires inverting the causal chain and making a best guess about what is causing the data we are receiving. In the same way, our brains are constantly solving inverse problems, unsure about what is really out there in the world.
The reason for this is that the brain is locked inside a dark skull and has only limited contact with the outside world through the lo-fi information provided by the senses. Take the seemingly simple task of deciding whether a light was just flashed in a darkened room. If the light flash is made dim enough, then sometimes you will say the light is present even when it is absent. Because your eye and brain form a noisy system, the firing of neurons in your visual cortex is not exactly the same for each repetition of the stimulus. Sometimes, even when the light isn’t flashed, random noise in the system will lead to high firing rates, just like the blip on Petrov’s radar screen was caused by atmospheric noise. Because the brain doesn’t know whether these high firing rates are caused by signal or noise, if your visual cortical neurons are firing vigorously it will seem as though a light was flashed even if it wasn’t.2
Because our senses—touch, smell, taste, sight, and hearing—each have access to only a small, noisy slice of reality, they must pool their resources to come up with a best guess about what is really out there. They are rather like the blind men in the ancient Indian parable. The one holding the elephant’s leg says it must be a pillar; the one who feels the tail says it is like a rope; the one who feels the trunk says it is like a tree branch; the one who feels the ear says it is like a hand fan; the one who feels its belly says it is like a wall; and the one who feels the tusk says it is like a solid pipe. Eventually, a stranger wanders past and informs them that they are, in fact, all correct and the elephant has all the features they observed. They would do better to combine their perspectives, he says, rather than argue.
A mathematical framework known as Bayes’s theorem provides a powerful tool for thinking about these kinds of problems. To see how Bayes’s rule helps us solve inverse problems, we can play the following game. I have three dice, two of which are regular dice with the numbers 1 to 6 on their faces, and one of which is a trick die with either a 0 or 3 on every face. From behind a curtain, I’m going to roll all three dice at once and tell you the combined total. On each roll, I might choose to use a trick die that shows all 0s, or a trick die that shows all 3s. For instance, on my first roll I might roll 2, 4, and 0 (on the third, trick die) for a combined total of 6. Your task is to tell me your best guess about the identity of the trick die—either a 3 or a 0—based only on your knowledge of the total.3
In this game, the 0 or the 3 on the trick die stand in for the “hidden” states of the world: whether the missile was present in Petrov’s dilemma, or whether the light was flashed in the case of our visual cortex neuron. Somehow, we need to go back from the noisy evidence we have received—the sum total of the three dice—and use this to work out the hidden state.
Sometimes this is easy. If I tell you the combined total is 4 or less, then you know that the third die must have been showing 0 to produce such a low sum. If the combined total is greater than 12 (two 6s plus a quantity more than 0), then you know for sure that the third die must have been showing 3. But what about quantities between these extremes? What about a total of 6 or 8? This is trickier.
One way we might go about solving this game is by trial and error. We could roll the three dice ourselves many times, record the total, and observe the true state of the world: what was actually showing on the face of the third die on each roll.
The first few rolls of the game might look like this:
And so on, for many tens of rolls. An easier way to present this data is in a chart of the number of times we observe a particular total—say, 6—and the identity of the trick die at the time (0 or 3). We can select particular colors for the trick die number; here I’ve chosen gray for 0 and white for 3.
After ten rolls the graph might look like this:
This isn’t very informative, and shows only a scatter of different totals, just like in our table. But after fifty rolls a pattern starts to emerge:
And after one thousand rolls, the pattern is very clear:
The counts from our experiment form two clear hills, with the majority falling in a middle range and peaks around 7 and 10. This makes sense. On average, the two real dice will give a total of around 7, and therefore adding either 0 or 3 from the trick die to this total will tend to give 7 or 10. And we see clear evidence for our intuition at the start: you only observe counts of 4 or less when the trick die equals 0, and you only observe counts of 13 or more when the trick die equals 3.
Now, armed with this data, let’s return to our game. If I were to give you a particular total, such as 10, and ask you to guess what the trick die is showing, what should you answer? The graph above tells us that it is more likely that the total 10 is associated with the trick die having 3 on its face. From Bayes’s rule, we know that the relative height of the white and gray bars (assuming we’ve performed our experiment a sufficient number of times) tells us precisely how much more likely the 3 is compared to the 0—in this case, around twice as likely. The Bayes-optimal solution to this game is to always report the more likely value of the trick die, which amounts to saying 3 when the total is 9 or above and 0 when the total is 8 or lower.
What we’ve just sketched is an algorithm for making a decision from noisy information. The trick die is always lurking in the background because it is contributing to the total each time. But its true status is obscured by the noise added by the two normal dice, just as the presence of a missile could not be estimated by Petrov from the noisy radar signal alone. Our game is an example of a general class of problems involving decisions under uncertainty that can be solved by applying Bayes’s rule.
In the case of Petrov’s fateful decision, the set of potential explanations is limited: either there is a missile or it’s a false alarm. Similarly, in our dice game, there are only two explanations to choose between: either the trick die is a 0 or it’s a 3. But in most situations, not only is the sensory input noisy, but there is a range of potential explanations for the data streaming in through our senses. Imagine a drawing of a circle around twenty centimeters across and held at a distance of one meter from the eye. Light reflected from the circle travels in straight lines, passing through the lens of the eye and creating a small image (of a circle) on the retina. Because the image on the retina is two-dimensional, the brain could interpret it as being caused by any infinite number of circles of different sizes arranged at appropriate distances. Roughly the same retinal image would be caused by a forty-centimeter circle held at two meters, or an eight-meter circle at forty meters. In many cases, there is simply not enough information in the input to constrain what we see.
These more complex inverse problems can be solved by making guesses as to the best explanation based on additional information drawn from other sources. To estimate the actual diameter of the circle, for instance, we can use other cues such as differences in the images received by the two eyes, changes in the texture, position, and shading of nearby objects, and so on.
To experience this process in real time, take a look at these two pictures:
Most people see the image on the left-hand side as a series of bumps, raised above the surface. The image on the right, in contrast, looks like a series of little pits or depressions in the page. Why the difference?
The illusion is generated by your brain’s solution to the inverse problem. The left and right sets of dots are actually the same image rotated 180 degrees (you can rotate the book to check!). The reason they appear different is that our visual system expects light to fall from above, because scenes are typically lit from sunlight falling from above our heads. In contrast, uplighting—such as when light from a fire illuminates the side of a cliff, or spotlights are projected upward onto a cathedral—is statistically less common. When viewing the two sets of dots, our brain interprets the lighter parts of the image on the left as being consistent with light striking a series of bumps and the darker parts of the image on the right as consistent with a series of shadows cast by holes, despite both being created from the same raw materials.
Another striking illusion is this image created by the vision scientist Edward Adelson:
Adelson’s checkerboard (Edward H. Adelson)
In the left-hand image, the squares labeled A and B are in fact identical shades of gray; they have the same luminance. Square B appears lighter because your brain “knows” that it is in shadow: in order to reflect the same level of light to the eye as A, which is fully illuminated, it must have started out lighter. The equivalence of A and B can be easily appreciated by connecting them up, as in the right-hand image. Now the cue provided by this artificial bridge overrides the influence of the shadow in the brain’s interpretation of the squares (to convince yourself that the left- and right-hand images are the same, try using a sheet of paper to cover up the bottom half of the two images).
The upshot is that these surprising illusions are not really illusions at all. One interpretation of the image is given by our scientific instruments—the numbers produced by light meters and computer monitors. The other is provided by our visual systems that have been tuned to discover regularities such as shadows or light falling from above—regularities that help them build useful models of the world. In the real world, with light and shade and shadows, these models would usually be right. Many visual illusions are clever ways of exposing the workings of a system finely tuned for perceptual inference. And, as we will see in the next section, several principles of brain organization are consistent with this system solving inverse problems on a massive scale.
Building Models of the World
One of the best-understood parts of the human and monkey brain is the visual system. Distinct regions toward the back of the brain process different aspects of visual input, and each is labeled with increasing numbers for more advanced stages of image processing. V1 and V2 extract information about the orientation of lines and shapes, V4 about color, and V5 about whether objects are moving. Downstream of these V regions we hit regions of the ventral visual stream that are tasked with putting all these pieces together to identify whole objects, such as faces and bodies and tables and chairs. In parallel, the dorsal visual stream contains regions that specialize in keeping track of where things are and whether they are moving from place to place.4
The right hemisphere of the human brain. The locations of the four cortical lobes, the cerebellum, and key visual pathways are indicated.
At the start of the ventral visual stream, individual brain cells encode only a small amount of the external world, such as a patch in the lower left of our field of view. But as we move up the hierarchy, the cells begin to widen their focus, similar to a camera zooming out. By the time we reach the top of the hierarchy, where a stimulus is displayed matters much less than what it depicts—a face, house, cat, dog, etc. The lens is completely zoomed out, and information about the object’s identity is represented independently of spatial location.
Crucially, however, information in the visual system does not just flow in one direction. For a long time, the dominant view of information processing in the brain was that it was a feed-forward system—taking in information from the outside world, processing it in hidden, complex ways, and then spitting out commands to make us walk and talk. This model has now been superseded by a raft of evidence that is difficult to square with the input-output view. In the visual system, for instance, there are just as many, if not more, connections in the reverse direction, known as feedback or top-down connections. Information travels both forward and backward; upper levels of the hierarchy both receive inputs from lower levels and send information back down in constant loops of neural activity. This way of thinking about the mind is known as predictive processing, and it represents a radically different understanding of what the brain does—although one with a long intellectual history, as the range of references in the endnote makes clear.5
Predictive processing architectures are particularly well suited to solving inverse problems. Instead of just passively taking in information, the brain can harness these top-down connections to actively construct our perception of the external world and shape what we see, hear, think, and feel. Higher levels furnish information about the type of things we might encounter in any given situation and the range of hypotheses we might entertain. For instance, you might know that your friend owns a Labrador, and so you expect to see a dog when you walk into the house but don’t know exactly where in your visual field the dog will appear. This higher-level prior—the spatially invariant concept of “dog”—provides the relevant context for lower levels of the visual system to easily interpret dog-shaped blurs that rush toward you as you open the door.
The extent to which our perceptual systems should rely on these regularities—known as priors—is in turn dependent on how uncertain we are about the information being provided by our senses. Think back to Petrov’s dilemma. If he was sure that his missile-detection technology was flawless and never subject to error, he would have been less willing to question what the system was telling him. Whether we should adjust our beliefs upon receiving new data depends on how reliable we think that information is.
In fact, Bayesian versions of predictive processing tell us that we should combine different sources of information—our prior beliefs and the data coming in through our senses—in inverse proportion to how uncertain we are about them. We can think of this process as being similar to pouring cake batter into a flexible mold. The shape of the mold represents our prior assumptions about the world. The batter represents the sensory data—the light and sound waves hitting the eyes and ears. If the incoming data is very precise or informative, then the batter is very thick, or almost solid, and will be hardly affected by the shape of the mold (the priors). If, in contrast, the data is less precise, then the batter will be runnier, and the shape of the mold will dominate the shape of the final product.
For instance, our eyes provide more precise information about the location of objects than our hearing. This means that vision can act as a useful constraint on the location of a sound source, biasing our perception of where the sound is coming from. This is used to great effect by ventriloquists, who are seemingly able to throw their voices to a puppet held at arm’s length. The real skill of ventriloquism is the ability to speak without moving the mouth. Once this is achieved, the brains of the audience do the rest, pulling the sound to its next most likely source, the talking puppet.6
It makes sense, then, that keeping track of uncertainty is an inherent part of how the brain processes sensory information. Recordings of cells from the visual cortex show us how this might be done. It’s well known that moving objects such as a waving hand or a bouncing ball will activate neurons in an area of the monkey brain known as MT (the human equivalent is V5). But cells in MT do not just activate for any direction of movement. Some cells fire most strongly for objects moving to the left, others for up, down, and all other points of the compass. When firing rates of MT cells are recorded over multiple presentations of different motion directions, they begin to form a distribution like the ones we saw in our dice game. At any moment in time, these populations of MT cells can be thought of as signaling the uncertainty about a particular direction of motion, just as our noisy dice total signaled the probability of the trick die being a 0 or a 3.7
Uncertainty is also critical for estimating the states of our own bodies. Information about where our limbs are in space, how fast our heart is beating, or the intensity of a painful stimulus is conveyed to the skull by sensory neurons. From the brain’s perspective, there is little difference between the electrical impulses traveling down the optic nerve and the neural signals ascending from our gut, heart, muscles, or joints. They are all signals of what might be happening outside of the skull, and these signals are subject to illusions of the kind that we encountered for vision. In one famous experiment, stroking a rubber hand in time with the participant’s own (hidden) hand is sufficient to convince the participant that the rubber hand is now their own. In turn, the illusion of ownership of the new rubber hand leads the brain to wind down the neural signals being sent to the actual hand. Just as the voice is captured by the ventriloquist’s dummy, the synchrony with which the rubber hand is seen and felt to be stroked pulls the sense of ownership away from the real hand.8
Harnessing Uncertainty to Doubt Ourselves
Of course, no one is suggesting that we consciously churn through Bayesian equations every time we perceive the world. Instead, the machinery our brains use to solve inverse problems is applied without conscious thought, in what the German physicist Hermann von Helmholtz called a process of “unconscious inference.” Our brains rapidly estimate the effects of light and shade on the dips, bumps, and checkerboards we encountered in the images on previous pages, literally in the blink of an eye. In a similar fashion, we reconstruct the face of a close friend, the taste of a fine wine, and the smell of freshly baked bread by combining priors and data, carefully weighting them by their respective uncertainties. Our perception of the world is what the neuroscientist Anil Seth refers to as a “controlled hallucination”—a best guess of what is really out there.
It is clear that estimating uncertainty about various sources of information is fundamental to how we perceive the world. But there is a remarkable side benefit of these ingenious solutions to the inverse problem. In estimating uncertainty in order to perceive the world, we also gain the ability to doubt what we perceive. To see how easy it is to turn uncertainty into self-doubt, let’s consider the dice game again. As the numbers in the game tend toward either 15 or 0, we become surer about the trick die showing a 3 or 0, respectively. But in the middle part of the graph, where the gray and white bars are of similar height—totals of 7 or 8—there is limited support for either option. If I ask you how confident you are about your response, it would be sensible to doubt decisions about the numbers 7 and 8 and to be more confident about smaller and larger quantities. In other words, we know that we are likely to know the answer when uncertainty is low, and we know that we are likely to not know the answer when uncertainty is high.
Bayes’s rule provides us with a mathematical framework for thinking about these estimates of uncertainty, sometimes known as type 2 decisions—so called because they are decisions about the accuracy of other decisions, rather than type 1 decisions, which are about things in the world. Bayes’s theorem tells us that it is appropriate to be more uncertain about responses toward the middle of the graph, because they are the ones most likely to result in errors and are associated with the smallest probability of being correct. Conversely, as we go out toward the tails of each distribution, the probability of being correct goes up. By harnessing the uncertainty that is inherent to solving inverse problems, we gain a rudimentary form of metacognition for free—no additional machinery is needed.9
And, because tracking uncertainty is foundational to how brains perceive the world, it is not surprising that this form of metacognition is widespread among a range of animal species. One of the first—and most ingenious—experiments on animal metacognition was developed by the psychologist J. David Smith in his study of a bottlenose dolphin named Natua. Smith trained Natua to press two different levers in his tank to indicate whether a sound was high-pitched or low-pitched. The low-pitched sound varied in frequency from very low to relatively high, almost as high as the high-pitched sound. There was thus a zone of uncertainty in which it wasn’t always clear whether low or high was the right answer, just like in our dice game.10
Once Natua had got the hang of this task, a third lever was introduced into the tank that could be pressed to skip the current trial and move on to the next one—the dolphin equivalent of skipping a question on a multiple-choice quiz. Smith reasoned that if Natua declined to take on decisions when his uncertainty about the answer was high, he would be able to achieve a higher accuracy overall than if he was forced to guess. And this is exactly what Smith found. The data showed that Natua pressed the third lever mostly when the sound was ambiguous. As Smith recounts, “When uncertain, the dolphin clearly hesitated and wavered between his two possible responses, but when certain, he swam towards his chosen response so fast that his bow wave would soak the researchers’ electronic switches.”11
Macaque monkeys—which are found across Asia (and are fond of stealing tourists’ food at temples and shrines)—also easily learn to track their uncertainty in a similar setup. In one experiment, macaques were trained to judge which was the biggest shape on a computer screen, followed by another choice between two icons. One icon led to a risky bet (three food pellets if right, or the removal of food if wrong), while the other, safe option always provided one food pellet—the monkey version of Who Wants to Be a Millionaire? The monkeys selected the risky option more often when they were correct, a telltale sign of metacognition. Even more impressively, they were able to immediately transfer these confidence responses to a new memory test without further training, ruling out the idea that they had just learned to associate particular stimuli with different confidence responses. Adam Kepecs’s lab, based at Cold Spring Harbor in New York, has used a version of this task to show that rats also have a sense of whether they are likely to be right or wrong about which of two perfumes is most prominent in a mixture of odors. There is even some evidence to suggest that birds can transfer their metacognitive competence between different tests, just like monkeys.12
If a sensitivity to uncertainty is a fundamental property of how brains work, it makes sense that this first building block of metacognition might also be found early in the lives of human babies. Taking inspiration from Smith’s tests, Louise Goupil and Sid Kouider at the École Normale Supérieure in Paris set out to measure how eighteen-month-old infants track uncertainty about their decisions. While sitting on their mothers’ laps, the babies were shown an attractive toy and allowed to play with it to whet their appetite for more playtime in the future. They then saw the toy being hidden in one of two boxes. Finally, after a brief delay, they were allowed to reach inside either of the boxes to retrieve the toy.
In reality, the toy was sneakily removed from the box by the experimenter. This allowed the researchers to measure the infants’ confidence about their choice of box. They reasoned that, if the babies knew whether they were making a good or bad choice, they would be more willing to search for the (actually nonexistent) toy when the correct box was chosen compared to when they chose incorrectly. This was indeed the case: when babies made wrong moves, they were less persistent in searching for the toy. They were also more likely to ask their mother for help in retrieving the toy when they were most prone to making an error. This data tells us that even at a young age, infants can estimate how uncertain they are about simple choices, asking for help only when they most need it.13
We cannot know for sure how animals and babies are solving these problems, because—unlike human adults—they cannot tell us about what they are thinking and feeling. A critic could argue that they are following a lower-level rule that is shared across all the tasks in the experiment—something like, If I take a long time to decide, then I should press the “uncertain” key—without forming any feeling of uncertainty about the decisions they are making. In response to this critique, ever more ingenious experiments have been designed to rule out a variety of non-metacognitive explanations. For instance, to rule out tracking response time, other studies have given the animals the chance to bet on their choices before they have started the test and before response-time cues are available. In this setup, macaque monkeys are more likely to be correct when they choose to take the test than when they decline, suggesting that they know when they know the answer—a hallmark of metacognition.14
There is also evidence that otherwise intelligent species fail to track uncertainty in these situations, suggesting that feelings of uncertainty might really be picking up on the first glimmers of self-awareness, rather than a more generic cognitive ability. Capuchin monkeys, a New World species found in South America, share many characteristics with macaques, using tools such as stones to crack open palm nuts, and living in large social groups. But capuchins appear unable to signal that they are uncertain in Smith’s task. In a clever twist, it is possible to show that capuchins have no difficulty using a third response key to classify a new stimulus, but they are unable to use the same response to indicate when they are uncertain. This data suggests that when comparing two similar species of monkey, one may show signs of metacognition while another may not.15
Once uncertainty tracking is in place, it opens the door to a range of useful behaviors. For starters, being able to estimate uncertainty means we can use it to decide whether or not we need more information. Let’s go back to our dice game. If I were to give you a total near the middle of the graph—a 7 or an 8—then you might reasonably be uncertain about whether to answer 0 or 3. Instead, you might ask me to roll the dice again. If I were to then roll a 5, a 4, and a 7, all with the same three dice, then you would be much more confident that the trick die was a 0. As long as each roll is independent of the previous one, Bayes’s theorem tells us we can compute the probability that the answer is a 3 or a 0 by summing up the logarithm of the ratio of our confidence in each hypothesis after each individual roll.16
The brilliant British mathematician Alan Turing used this trick to figure out whether or not to change tack while trying to crack the German Enigma code in the Second World War. Each morning, his team would try new settings of their Enigma machine in an attempt to decode intercepted messages. The problem was how long to keep trying a particular pair of ciphers before discarding it and trying another. Turing showed that by accumulating multiple samples of information over time, the code breakers could increase their confidence in a particular setting being correct—and, critically, minimize the amount of time wasted testing the wrong ciphers.17
In the same way, we can use our current estimate of confidence to figure out whether a new piece of information will be helpful. If I get a 12 on my first roll, then I can be reasonably confident that the trick die is showing a 3 and don’t need to ask for the dice to be rolled again. But if I get a 7 or 8, then it would be prudent to roll again and resolve my current uncertainty about the right answer. The role of confidence in guiding people’s decisions to seek new information has been elegantly demonstrated in the lab. Volunteers were given a series of difficult decisions to make about the color of shapes on a computer screen. By arranging these shapes in a particular way, the researchers could create conditions in which people felt more uncertain about the task but performed no worse. This design nicely isolates the effect a feeling of uncertainty has on our decisions. When asked whether they wanted to see the information again, participants did so only when they felt more uncertain. Just as in the experiments on babies, the participants were relying on internal feelings of uncertainty or confidence to decide whether to ask for help.18
Shades of Gray
Being able to track uncertainty is fundamental to how our brains perceive the world. Due to the complexity of our environment and the fact that our senses provide only low-resolution snapshots of our surroundings, we are forced to make assumptions about what is really out there. A powerful approach to solving these inverse problems combines different sources of data according to their reliability or uncertainty. Many aspects of this solution are in keeping with the mathematics of Bayesian inference, although there is a vigorous debate among neuroscientists as to how and whether the brain implements (approximations to) Bayes’s rule.19
Regardless of how it is done, we can be reasonably sure that computing uncertainty is a fundamental principle of how brains work. If we were unable to represent uncertainty, we would only ever be able to see the world in one particular way (if at all). By representing uncertainty we also acquire our first building block of metacognition—the ability to doubt what our senses are telling us. By itself, the ability to compute uncertainty is not sufficient for full-blown self-awareness. But it is likely sufficient for the rudimentary forms of metacognition that have been discovered in animals and babies. Nabokov’s bright line between humans and other species is becoming blurred, with other animals also demonstrating the first signs of metacognitive competence.
But tracking uncertainty is only the beginning of our story. Up until now we have treated the brain as a static perceiver of the world, fixed in place and unable to move around. As soon as we add in the ability to act, we open up entirely new challenges for metacognitive algorithms. Meeting these challenges will require incorporating our next building block: the ability to monitor our actions.