a Harvard professor opened a phone book and explained why some algorithms survive a billion entries while others collapse.
he didn’t begin with code. he simply asked the class to find one name.
the obvious method starts on page one and checks every name until it finds the right one. with 1,000 pages, that could require 1,000 steps.
then he showed them a different method.
open the book in the middle. if the name comes later alphabetically, discard the first half. if it comes earlier, discard the second. then repeat.
1,000 pages become roughly 10 checks. 1 million entries become roughly 20. 1 billion become roughly 30.
the amount of data can double, but the work increases by only one step.
computer scientists call it binary search.
same computer. same information. completely different result.
@vladuah the best math explanations give you one picture you can keep returning to. a secant line slowly becoming a tangent makes the derivative feel obvious in a way the formula alone never could
@0xNoryxx this is such a clean explanation of what approximation really means in physics: you don’t remove the impossible part, you keep pushing it one order deeper until what remains is small enough to ignore.
an MIT professor put his students into two auctions.
in the first, everyone tried to outsmart the room. in the second, the smartest strategy was simply telling the truth.
the difference was one rule.
in a first-price auction, the highest bidder wins and pays their own bid, so everyone has an incentive to bid below what the item is actually worth to them.
but in a second-price auction, the highest bidder still wins and pays only the second-highest bid. your bid decides whether you win—it doesn’t decide what you pay.
value the item at $100 and bid $70, and you might lose it for a price you would have accepted. bid $130, and you might win when the price is higher than your actual value.
bid exactly $100, and both mistakes disappear.
the students didn’t suddenly become more honest. the system made honesty rational.
that might be the most important lesson in game theory:
if you want better behavior, don’t just ask people to behave better.
change the incentives.
@0xMoysei the uncomfortable part is that expected value is a great decision tool, but a terrible moral framework, especially when the people placing the bets aren't the ones absorbing the downside
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