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I recently got a dead battery after a long day at airport logistics. Once again I had spent the day dreaming about how everything could be automated. I thought about the added complexity of having to resort to bins that the plane food goes in. Realistically the whole business is self defeating. It’s kind of funny actually in like a really sad way.
After waiting an hour for my best friend from Roy to come jump my car (none of my compatriots had jumper cables) I drove home unmolested. I took a shower and finished my usual post work, post ISKCON 6 round reality break.
The next morning I work up around 4:45 for Aarti. After Seth getting up I hopped in the car to discover — Battery dead! Damn. After an oil change and getting the tire thing sorted out — This happens. Material reality blows, doesn’t it?
After contemplating the merits of buying a new battery and consulting with the usual authorities I decided to take it to O’Reilly. My roommate suggested them, saying that he had a good track record with them. Sounds good to me.
I pull in. I’m slightly nervous because I don’t want to stop the engine. It was a lot of work coordinating getting the car started. Luckily a perfectly nice salesman was (coincidentally) outside. He greeted me and ensured me that the battery could be tested easily and quickly and if the car died that he could jump it so I could get home. Groovy! What a gent!
He tests the thing — Dead! Oh no! I’m out another 100 dollars I don’t have right now. — Not after the Brian thing. Nope. Alright. Wait. Let’s try to turn her over just to see — She started! Nice! No need for a jump! Seth makes a clever remark, “Wait, if the battery is totally dead why did his car start?” An apt question.
The salesman very confidently replies that the battery may still turn over from the small amount of charge generated from driving from the house to the store. He ensures me that this is common in this situation and suggests buying a new battery. I’d love to — Can’t. Not until I get an ML contract and move out of this rotten city. I decided to drive home telling him I need time to coordinate some things.
Long story short it’s been about — 4 weeks now and my battery has been just fine. I took a 20 minute drive at high revs on the freeway to charge the thing and I haven’t had an issues. Was I scammed? Is the whole thing a scam? Maybe the detector always reads, “dead battery?” I’ve seen Dateline specials about this sort of thing!
Actually though — It’s not that at all! The meter is probably perfectly legitimate. It may even be 99%+ accurate. Here’s the thing though — Baye’s theorem tells us something interesting about accurate tests — In the population pool of instances of positive test results — There are going to be more false positives than real positives! That can’t be right!
In a simple demonstration of this — let’s assume the detector was 99% accurate — If we plug this into Bayes’ Theorem we can actually show that the probability of my battery being dead is actually only around 0.8. That’s for a highly accurate test. Factor in the fact that the test might have some unseen fault and the motivating factor of usual retail scumbaggery as prior values and I reckon the final probability to be closer to 0.3 or in other words — Not.
The question is though — Are auto parts places that do free testing aware of this? I mean — They should be. I can imagine some accountant somewhere having figured this out years ago. That’s the thing though — If you think about it, this is really how the whole of the car-repair industry works. A diagnostic of a part of the car reveals that some critical component is failing — — That’s great and all Mr. Mechanic but my good friend Thomas Bayes tell us that even if your diagnostic test is highly accurate — It’s probably not factoring in Bayes’ Theorem or prior probabilities AND neither is the customer! I wonder how many car repairs are actually necessary? I wonder how much economic inefficiency this creates. Ugh. I can’t wait to own a Tesla. Surely it will never break down. (Elon fingers crossed. Also; Hyperloop)
The moral of the story is — Bayes’ Theorem gives us some insight into probabilities. Things get even funkier when we factor in prior probabilities. If someone says, “Hey mate I tested your so and so and it’s broken — You need a new one” they are either a) Very clever and trying to scam you. b) Omniscient OR c) A well meaning friend/agent who isn’t very well versed in Probability Theory. At any rate — You get a diagnosis of cancer or the like — Get a second opinion! (and a third, and a fourth) Bayes’ Theorem might explain to use why Medical Misdiagnosis is the 3RD leading cause of death in the United States!
— Learn Math. It makes you smart. You can get a good job — Whatever. Forget that. It might just save your life. Stay clever friends. Stay clever!
