Logic’s Conclusion

Non-terminating.

From Algorithms to Live By, by Christian and Griffiths:

The intuitive standard for rational decision-making is carefully considering all available options and taking the best one. At first glance, computers look like the paragons of this approach, grinding their way through complex computations for as long as it takes to get perfect answers. But as we’ve seen, that is an outdated picture of what computers do: it’s a luxury afforded by an easy problem. In the hard cases, the best algorithms are all about doing what makes the most sense in the least amount of time, which by no means involves giving careful consideration to every factor and pursuing every computation to the end. Life is just too complicated for that.

In almost every domain we’ve considered, we have seen how the more real-world factors we include—whether it’s having incomplete information when interviewing job applicants, dealing with a changing world when trying to resolve the explore/exploit dilemma, or having certain tasks depend on others when we’re trying to get things done—the more likely we are to end up in a situation where finding the perfect solution takes unreasonably long. And indeed, people are almost always confronting what computer science regards as the hard cases. Up against such hard cases, effective algorithms make assumptions, show a bias toward simpler solutions, trade off the costs of error against the costs of delay, and take chances.

These aren’t the concessions we make when we can’t be rational. They’re what being rational means.

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