When I was a LabKitten, I took karate lessons at a local strip mall. This in an attempt to ward off the Nelson Muntzes and Scut Farcuses of the world. All for naught it turned out, and a CCP makes the whole enterprise rather moot. Still, the instructors were quite good, especially for a strip mall dojo. They took their job seriously. It certainly wasn't Cobra Kai, but scrapes and bruises and bloody noses weren't uncommon.
I had a favorite instructor, who for the sake of discussion I shall call Doug because that was his name. Doug was the nicest guy you'd ever want to meet. He was also a genuine badass. I forget what degree black belt he was, but I remember watching the black belt tests. At that level, the school would bring in the head honcho from overseas and he would decide what the test would be. It seemed to me the test was always something like "the last person not unconscious, passes."
Doug was a fantastic teacher -- patient, attentive, skilled in getting a point across. He genuinely wanted his students to progress. But he was terrifying to spar against. He would line up in front of you and the friendly instructor you thought you knew would vanish. Instead, some impostor with dead eyes would take you out for a ride. I felt like Paul Atredes sparring with Gurney Halleck, thinking his beloved mentor had sold out to the Harkonnens and was trying to kill him. Looking back, I understand now Doug was teaching us about facing a situation where you are unquestionably going to lose. What are you going to do about it?
You're probably wondering why I told you this (cool story, bro!). I've owned a copy of Sheldon Ross'Introduction to Probability Models for over 15 years (sixth edition -- old school). The entire time has been one giant love/hate relationship. I could never put my finger on why. And then it finally dawned on me: Ross is Doug in textbook form.
Probability starts off simple enough. If we don't know what value a variable will be, but we do know what values it can be, that is a random variable. If we know both it's just a normal variable. If we don't know either, I don't know what that is. Philosophy, I guess.
However, going from there to all the useful and interesting places probability models take us requires work. The trip is critically assisted by a competent guide. In no other field is the variance (zing!) of textbooks so stark. Good probability books are great; bad probability books are not only useless, they undo what you already know.
I2PM is a great probability textbook. Ross begins at the very beginning, and by the end he is presenting some of the most sophisticated probability models ever developed. And the writing is superb. Ross is a fantastic teacher -- patient, attentive, skilled in getting a point across and genuinely wanting the reader to progress. But he is terrifying to spar against. At any moment, in any given example or exercise, the friendly author you thought you knew from the last page or the last 100 suddenly vanishes. Ross is going to take you out for a ride.
Looking back, I understand now this is necessary. Working with probability models is -- I'm struggling for the right word here. Slippery? It's really no more difficult than any other math topic. But it has it's own mindset, its own brand of intuition. If you simply work the same comfortable problems over and over, you're never going to develop that intuition. You must get bloodied from time to time or you will never get stronger. Ross, like Doug, is there to push your envelope. Doug, like Ross, did it for the right reasons. They both have a good heart. Neither is ever a show-off or bully.
I suppose such is true in all fields. But probability in general, and Ross in particular, is maddeningly bipolar. His explanations are lucid and unassuming. Open to any page and you think Holy cow -- anyone could understand this! And probability can be big fun. The Monty Hall Problem. The Best Present Problem. The Buffon Needle. The Drunkard's Walk. Ross turns up the heat in later chapters but the topics become more fascinating. Markov Processes. Queueing theory. Reliability theory. Brownian motion. The epically-tragic Black-Scholes financial model...
And then you bump into a one-sentence exercise that leaves you staring at the page for a month.
F Footnote: If your idea of probability is measure theory and Lebesgue integration, you can probably eat Ross for breakfast. When I write anyone could understand this, I mean normal people. You know, people who have an SO and drink beer, not mathozoids who sit at home on Saturday night with a Rubik's cube and goat's blood.
Morituri te salutamus, the gladiators would call when they entered the arena. We who are about to die salute you. I was told -- although I have never been able to verify it -- Caesar would reply: We who love you most, punish you best. An exchange to keep in mind, whether you're opening Ross' Introduction to Probability Models or stepping onto the tatami.
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