If you want the best odds of getting the best apartment, spend 37% of your apartment hunt (eleven days, if you've given yourself a month for the search) non-committally exploring optinos. Leave the checkbook at home; you're just calibrating. But after that point, be prepared to immediately commit – deposit and all – to the very first place you see that beats whatever you've already seen. This is not merely an intuitive satisfying compromise between looking and leaping. It is the provably optimal solution.
Persian mathematician al-Khwārizmī, author of ninth-century book of techniques for doing mathematics by hand. (His book was called al-Jabr wa'l-Muqābala – and the "al-jabr" of the title in turn provides the source of our word "algebra.") The earliest known mathematical algorithms, however, predate even al-Khwārizmī's work: a four-thousand-year old Sumerian clay tablet found near Baghdad describes a scheme for long division.
"Someone at Michigan" was almost certainly someone named Merrill Flood. Though he is largely unheard of outside mathematics, Flood's influence on computer science is almost impossible to avoid. He's credited with popularizing the traveling salesman problem, devising the prisoner's dilemma, and even with possibly coining the term "software".
We think of chess, for instance, as medieval European in its imagery, but in fact its origins are in eight-century India; it was heavy-handedly "Europeanized" in the fifteenth century, as its shahs became kings, its viziers turned to queens, and its elephants became bishops.
A record of 0-0, an arm that's a complete unknown - has an expected value of 0.5000 but a Gittins index of 0.7029. In other words, something you have no experience with whatsoever is more attractive than a machine that you know pays out 70% of the time! As you go down the diagonal, notice that a record of 1-1 yields an index of 0.6346, a record of 2-2 yields 0.6010 and so on. If such 50%-successful performance persists, the index does ultimately converge on 0.5000, as experience confirms that the machine is indeed nothing special and takes away the "bonus" that spurs further exploration.
Chester Barnard, "To try and fail is at least to learn; to fail to try is to suffer the inestimable loss of what might have been."
First, assuming you're not omniscient, your total amount of regret will probably never stop increasing, even if you pick the best possible strategy - because even the best strategy isn't perfect every time. Second, regret will increase at a slower rate if you pick the best strategy than if you pick others; what's more, with a good strategy regret's rate of growth will go down over time, as you learn more about the problem and are able to make better choices. Third, and most specifically, the minimum possible regret - again assuming non-omniscience - is regret that increases at a logarithmic rate with every pull of the handle.
... where people were given a choice between two options, one with a known payoff chance and one unknown - specifically two airlines, an established carrier with a known on-time rate and a new company without a track record yet. Given the goal of maximizing the number of on-time arrivals over some period of time, the mathematically optimal strategy is to initially only fly the new airline, as long as the established one isn't clearly better. If at any point it's apparent that the well-known carrier is better - that is, if the Gittins index of the new option falls below the on-time rate of the familiar carrier - then you should switch hard to the familiar one and never look back.
More generally, our intuitions about rationality are too often informed by exploitation rather than exploration. When we talk about decision-making, we usually focus just on the immediate payoff of a single decision - and if you treat every decision as if it were your last, then indeed only exploitation makes sense. But over a lifetime, you're going to make a lot of decisions. And it's actually rational to emphasize exploration - the new rather than the best, the exciting rather than the safe, the random rather than the considered - for many of those choices, particularly earlier in life.
debeaking chickens on farms may be a well-intentioned but counterproductive approach: it removes the authority of individual fights to resolve the order, and therefore makes it much harder for the flock to run any sorting procedure at all. So the amount of antagonism within the flock in many cases actually increases.
"ordinal numbers" (which only express rank) to "cardinal" ones (which directly assign a measure to something's caliber)
The researchers showed that simply knowing more makes things harder when it comes to recognizing words, names, and even letters. No matter how good your organization scheme is, having to search through more things will inevitably take longer. It's not that we're forgetting, it's that we're remembering. We're becoming archives.
The best time to plant a tree is twenty years ago. The second best time is now.
In the face of uncertainty [...] for time management: each time a new piece of work comes in, divide its importance by the amount of time it will take to complete. If that figure is higher than for the task you're currently doing, switch to the new one, otherwise stick with the current task.
[heterogeneous collection of short tasks] "interrupt coalescing"; if you have five credit card bills, for instance, don't pay them as they arrive; take care of them all in one go when the fifth bill comes.
power-law distributions / scale-free distributions, characterize quantities that can plausibly range over many scales.
Examining the Copernican Principle, we saw that when Bayes's Rule is given an uninformative prior, it always predicts that the total life span of an object will be exactly double its current age.
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Bayes's Rule indicates that the appropriate prediction strategy is a multiplicative rule; multiply the quantity observed so far by some constant factor. For an uninformative prior, that constant factor happens to be 2, hence the Copernican prediction; in other power-law cases, the multiplier will depend on the exact distribution you're working with.
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In a power-law distribution, the longer something has gone on, the longer we expect it to continue going on. So a power-loaw event is more surprising the longer we've been waiting for it - and maximally surprising right before it happens. A nation, corporation, or institution only grows more venerable with each passing year, so it's always stunning when it collapses.
In a normal distribution, events are surprising when they're early - since we expected them to reach the average - but not when they're late. Indeed, by that point they seem overdue to happen, so the longer we wait, the more we expect them.
And in an Erlang distribution, events by definition are never any more or less surprising no matter when they occur. Any state of affairs is always equally likely to end reguardless of how long it's lasted.
It is indeed true that including more factors in a model will always, by definition, make it a better fit for the data we have already. But a better fit for the available data does not necessarily mean a better prediction.
If the study were repeated with different people, producing slight variations on the same essential pattern, the one- and two-factor models would remain more or less steady - but the nine-factor model would gyrate wildly from one instance of teh study to the next. This is what statisticians call overfitting.
So one of the deepest truths of machine learning is that, in fact, it's not always better to use a more complex model.
Taste is our body's proxy metric for health. Fat, sugar and salt are important nutrients, and for a couple hundred thousand years, being drawn to foods containing them was a reasonable measure for a sustaining diet.
But being able to modify the foods available to us broke that relationship. We can now add fat and sugar to foods beyond amounts that are good for us, and then eat those foods exclusively rather than the mix of plants, grains, and meats that historically made up the human diet. In other words, we can overfit taste.
