Harvard, Sanders Theatre. About eight hundred students are watching as a professor on stage tears a phone book in half. He’s not doing this just to make a splash. He’s showing them a number that will make almost everything they’ll ever do at work seem slow by comparison.
This figure comes from a phone book with 1,024 pages containing only one name.
Find Smith.
Method one. Open to the first page. turn. turn. turn. In the worst-case scenario - 1,024 flips.
Method two. Open it in the middle. You land on the letter “M.” Smith comes after “M,” so the entire left half is dead weight. He tears it off and throws it on the floor.
512 pages. Open it in the middle again. Tears it off. 256. Tears it off. 128. Tears it off.
Ten tears and one page in left.
1,024 versus 10. This in itself is a good demonstration, and this is where almost everyone stops.
But that’s not the point.
Here’s the point. Double the book’s length. 2,048 pages.
Now the first person needs 2,048 flips. Their work has doubled the very moment the problem doubled.
The second person needs eleven. Just one extra tear.
Double it again - still just one extra tear. This isn't a better result. It's a completely different approach to size.
For all of this to work, two conditions must be met, and he clearly states both. The book must be sorted before you even touch it. And you must be prepared to throw half of it on the floor.
My own note, not his: it’s precisely on the second condition that people actually fail. Throwing away half of what you’re holding seems like a loss of information. So they keep it, go back to the first page, and call it thoroughness.
It’s worth knowing who exactly is tearing it up. Malan was too intimidated to take even a single computer science course during his first year at Harvard. He signed up as a sophomore, pass/fail, so it could not damage his record. He has been running the course since 2007. Two thirds of the people in that room have never written a line of code.
Two-thirds of the people in this audience have never written a single line of code.
The lectures and course materials are posted on cs50. Harvard. edu, accessible to everyone.
Harvard has made them available to millions of people.
The course is free. The willingness to throw half of what you’re holding onto the floor is something no one teaches you.
MIT, Fall 2010. John Tsitsiklis draws a radar on the board that detects a real airplane 99 times out of 100. The alarm goes off. He asks the audience what the odds are that there really is something there.the honest answer is not 99. it is not 90. it is not close to either.
three numbers go on the board.
five percent of the time, a plane is genuinely flying overhead.
when a plane is there, the radar catches it 99 percent of the time.
when the sky is empty, the radar still fires 10 percent of the time.
almost everyone answers 99, because 99 is the number they were handed. but 99 answers a completely different question. it answers: given a plane, will the machine see it. what you actually need is the reverse. given an alarm, is there a plane.
run a thousand sweeps.
fifty of them have a plane. the radar catches about 49.
nine hundred and fifty of them are empty sky. the radar screams anyway on 95 of them.
that is 144 alarms. 49 of them are real.
thirty four percent.
the alarm is wrong twice as often as it is right, and nothing is broken. the equipment is performing exactly to spec.
what destroyed it was not accuracy. it was the base rate. the thing was rare before the alarm, and evidence does not erase rarity, it only moves it.
three questions, and they work on anything:
how often is this true before I look at all.
how often does the signal fire when it is true.
how often does it fire when it is not.
the third one is the one nobody asks. it is also the only one that decides whether the alarm is worth anything.
now go apply it to the indicator with the 90 percent win rate. to the caller who was right about the last three. to the screener that flags forty tokens a day. ask what fraction of the sky was ever going to have a plane in it.
MIT filmed the whole course in 2010 and put it up with slides, problem sets and solutions. no login.
the lecture is free. asking what the base rate was before the alarm went off is the part nobody does.