We live in the age of algorithms. Only a generation or two ago, mentioning the wordalgorithm would have drawn a blank from most people. Today, algorithms are in every nook and cranny of civilization. They are woven into the fabric of everyday life. TheyвЂ™re not just in your cell phone or your laptop but in your car, your house, your appliances, and your toys. Your bank is a gigantic tangle of algorithms, with humans turning the knobs here and there. Algorithms schedule flights and then fly the airplanes. Algorithms run factories, trade and routegoods, cash the proceeds, and keep records. If every algorithm suddenly stopped working, it would be the end of the world as we know it.. Otherwise, if thereвЂ™s an empty corner, play there.. If programmers are minor gods, the complexity monster is the devil himself. Little by little, itвЂ™s winning the war.. The good news today is that sciences that were once data-poor are now data-rich. Instead of paying fifty bleary-eyed undergraduates to perform some task in the lab, psychologists can get as many subjects as they want by posting the task on AmazonвЂ™s Mechanical Turk. (It makes for a more diverse sample too.) ItвЂ™s getting hard to remember, but little more than a decade ago sociologists studying social networks lamented that they couldnвЂ™t get their hands on a network with more than a few hundred members. Now thereвЂ™s Facebook, with overa billion. A good chunk of those members post almost blow-by-blow accounts of their lives too; itвЂ™s like having a live feed of social life on planet Earth. In neuroscience, connectomics and functional magnetic resonance imaging have opened an extraordinarily detailed window into the brain. In molecular biology, databases of genes and proteins grow exponentially. Even in вЂњolderвЂќ sciences like physics and astronomy, progress continues because of the flood of data pouring forth from particle accelerators and digital sky surveys.. This may sound far-fetched: How could one algorithm possibly learn so many different things and such difficult ones? But in fact many lines of evidence point to the existence of a Master Algorithm. LetвЂ™s see what they are.. If your credit card was used twice after 11:00 p.m. on a weekday, it was stolen.. Another limitation of inverse deduction is that itвЂ™s very computationally intensive, which makes it hard to scale to massive data sets. For these, the symbolist algorithm of choice is decision tree induction. Decision trees can be viewed as an answer to the question of what to do if rules of more than one concept match an instance. How do we then decide which concept the instance belongs to? If we see a partly occluded object with a flat surface and four legs, how do we decide whether it is a table or a chair? One option is to order the rules, for example by decreasing accuracy, and choose the first one that matches. Another is to let the rules vote. Decision trees instead ensure a priori that each instance will be matched by exactly one rule. This will be the case if each pair of rules differs in at least one attribute test, and such a rule set can be organized into a decision tree. For example, consider these rules:. The number of transistors in a computer is catching up with the number of neurons in a human brain, but the brain wins hands down in the number of connections. In a microprocessor, a typical transistor is directly connected to only a few others, and the planar semiconductor technology used severely limits how much better a computer can do. In contrast, a neuron has thousands of synapses. If youвЂ™re walking down the street and come across an acquaintance, it takes you only about a tenth of a second to recognize her. At neuron switching speeds, this is barely enough time for a hundred processing steps, but in those hundred steps your brain manages to scan your entire memory, find the bestmatch, and adapt it to the new context (different clothes, different lighting, and so on). In a brain, each processing step can be very complex and involve a lot of information, consonant with a distributed representation.. But if humans have all these abilities that their brains didnвЂ™t learn by tweaking synapses, where did they come from? Unless you believe in magic, the answer must be evolution. If youвЂ™re a connectionism skeptic and you have the courage of your convictions, it behooves you to figure out how evolution learned everything a baby knows at birth-and the more you think is innate, the taller the order. But if you can figure it out and program a computer to do it, it would be churlish to deny that youвЂ™ve invented at least one version of the Master Algorithm.. Therefore we do what we always have to do in life: compromise. We make simplifying assumptions that whittle the number of probabilities we have to estimate down to something manageable. A very simple and popular assumption is that all the effects are independent given the cause. This means that, for example, having a fever doesnвЂ™t change how likely you are to also have a cough, if we already know you have the flu. Mathematically, this is saying thatP(fever, cough | flu) is justP(fever | flu)Г— P(cough | flu). Lo and behold: each of these is easy to estimate from a small number of observations. In fact, we did it for fever in the previous section, and it would be no different for cough or any other symptom. The number of observations we need no longer goes up exponentially with the number of symptoms; in fact, it doesnвЂ™t go up at all.. The second part of the story is how the SVM finds the fattest snake that fits between the positive and negative landmines. At first sight, it might seem like learning a weight for each training example by gradient descent would do the trick. All we have to do is find the weights that maximize the margin, and any examples that end up with zero weight can be discarded. Unfortunately, this would just make the weights grow without limit, because mathematically, the larger the weights, the larger the margin. If youвЂ™re one foot from a landmine and you double the size of everything including yourself, you are now two feet from the landmine, but that doesnвЂ™t make you any less likely to step on it. Instead, we have to maximize the margin under the constraint that the weights can only increase up to some fixed value. Or, equivalently, we can minimize the weights under the constraint that all examples have a given margin, which could be one-the precise value is arbitrary. This is what SVMs usually do.. Clearly, if Robby did know them, it would be smooth sailing: as in NaГЇve Bayes, each cluster would be defined by its probability (17 percent of the objects generated were toys), and by the probability distribution of each attribute among the clusterвЂ™s members (for example, 80 percent of the toys are brown). Robby could estimate these probabilities just by counting the number of toys in the data, the number of brown toys, and so on. But in order to do that, we would need to know which objects are toys. This seems like a tough nut to crack, but it turns out we already know how to do it as well. If Robby has a NaГЇve Bayes classifier and needs to figure out the class of a new object, all he needs to do is apply the classifier and compute the probability of each class given the objectвЂ™s attributes. (Small, fluffy, brown, bear-like, with big eyes, and a bow tie? Probably a toy but possibly an animal.). In the world of the Master Algorithm,вЂњmy people will call your peopleвЂќ becomes вЂњmy program will call your program.вЂќ Everyone has an entourage of bots, smoothing his or her way through the world. Deals get pitched, terms negotiated, arrangements made, all before you lift a finger. Today, drug companies target your doctor, because he decides what drugs to prescribe to you. Tomorrow, the purveyors of every product and service you use, or might use, will target your model, because your model will screen them for you. Their botsвЂ™ job is to get your bot to buy. Your botвЂ™s job is to see through their claims, just as you seethrough TV commercials, but at a much finer level of detail, one that youвЂ™d never have the time or patience for. Before you buy a car, the digital you will go over every one of its specs, discuss them with the manufacturer, and study everything anyone in the world has said about that car and its alternatives. Your digital half will be like power steering for your life: it goes where you want to go but with less effort from you. This does not mean that youвЂ™ll end up in a вЂњfilter bubble,вЂќ seeing only what you reliably like, with no room for the unexpected; the digital you knows better than that. Part of its brief is to leave some things open to chance, to expose you to new experiences, and to look for serendipity.. To sidestep the problem that infinitely dense points donвЂ™t exist, Kurzweil proposes to instead equate the Singularity with a black holeвЂ™s event horizon, the region within which gravity is so strong that not even light can escape. Similarly, he says, the Singularity is the point beyond which technological evolution is so fast that humans cannot predict or understand what will happen. If thatвЂ™s what the Singularity is, then weвЂ™re already inside it. We canвЂ™t predict in advance what a learner will come up with, and often we canвЂ™t even understand it in retrospect. As a matter of fact, weвЂ™ve always lived in a world that we only partly understood. The main difference is that our world is now partly created by us, which is surely an improvement. The world beyond the Turing point will not be incomprehensible to us, any more than the Pleistocene was. WeвЂ™ll focus on what we can understand, as we always have, and call the rest random (ordivine).. Chapter Nine.