In short, the paper argues that we will no longer need theories in science, because we have Google. We can now use computers to look at massive amounts of data, and use them to detect patterns for us. From this, Anderson draws the slightly irrational conclusion that we need no theories.
Petabytes allow us to say: "Correlation is enough." We can stop looking for models. We can analyze the data without hypotheses about what it might show. We can throw the numbers into the biggest computing clusters the world has ever seen and let statistical algorithms find patterns where science cannot …
There’s no reason to cling to our old ways. It’s time to ask: What can science learn from Google?
Anderson’s somewhat fallacious observation is that we don’t need scientific theories or models since Google will give us all our answers anyway. However, what Anderson is talking about is nothing new. He is merely describing a first step in a long-established scientific method called induction, or "data-to-explanation". In its modern form it has been around since at least Francis Bacon (late 16th century), sometimes referred to as the father of scientific induction.
Amputating the inductive method by removing the explanation part (the model, theory) is not the way to go, as then we would effectively be entering a stage of scientific stagnation. It would be a job half-done (to some degree even pointless) for a scientific endeavour to collect data and establish patterns and not try to explain why the patterns are there. The explanation part is essential if we want to understand *why* the patterns exist, and for that we need models. The models need not be established before-hand, of course (even though analysing data without some prior theory is virtually impossible). Finding patterns in data can be, and often is, a perfectly valid impetus for developing (new) explanatory models.
What Google, and the like, does is offer us new methods in handling much larger amounts of data than what has been possible before. With Google, we can find new, previously undetected patterns, some of which our existing theories cannot predict. These, in turn, will create a need for new explanations and new theories. Hence it is more likely that Google will foster even more theories and models, not less.