How 'The Smartest Person In The World' Was Wrong When She Was Right, or How i Learned To Stop Worrying And Blew Up Statistics

src

i am obsessed with the relationship between meaning and context. Rabbit. Several years ago, at the time when i was first being born into the loveliness of clear observation and thinking, i decided to deeply consider "meaning" as a phenomenon. i broke it down like this: the meaning of words, the meaning of a bird chirping in a forest, the meaning of a fish swimming away from a shark. Did all of those scenarios have "meaning"? What did it mean for something to have a "meaning"? Was there something in common about the different meanings those scenarios had if indeed they had them? Just what was the meaning of meaning? One of the things i discovered within that inquiry is that meaning and context arise together. There is no meaning apart from context; and that fact fascinates me.

You, dear reader, are also obsessed with the relationship between meaning and context. Any of your countless searches for meaning, whether large, or lowercase like the looking up of a word in the dictionary, are at one-and-the-same-time searches for context. Those of you who have forgotten the word "rabbit" after the opening sentence of this article have done so because of a lack of meaning due to an absence of relevant context. Those of you who remembered the word did so because of the seeming irrelevancy between the word "rabbit" and the context of meanings that constitute this article thus far. Those of you who laughed did so because "context rabbit." is fucking hilarious in the context of a heady, boring, or dry opening sentence, or funny in the context of too much information and a reluctance to read another blog post. In that case, i suggest running through the forest as soon as possible... Not like a jogger thinking, "I'm running because it's good for me... By golly, that air sure does smell fresh... Is that cedar.... or pine...." , but like a kid pretending to be a mad warrior-hunter leaping over logs at topspeed barefoot. If you felt anger on the heels of context rabbit you did so in the context of being somewhat of a dick (and should see suggestion above). "Is 'context. Rabbit.' a typo? Is this bastard just trying to be clever? What does it mean?"

Context and meaning are simultaneous orgasms, they come together. That is one of my most fundamental intellectual tools, so when my esteemed steemian friend @youdontsay introduced me to something called "The Monty Hall Problem" in a recent article, i began to look at the problem with that in mind.

The basic set up of the problem/solution is this: You have three doors, behind two of which are goats, behind one of which is a car. Your initial choice has a 33.333% probability of being correct. When the host reveals a goat behind one of the doors you did not pick, he then asks you if you want to change your choice to the other remaining door you did not pick. Counter intuitively, so the solution says, the remaining two doors do not have an equal probability of being the correct door because the door you picked still has a 33.333% probability of being correct. That leaves the second door with a 66.666% probability of being correct since probability can't exceed 100%, and thus you are more likely to get a car if you switch doors. One of the authors of the answer, a woman named Marilyn Mach vos Savant (very cool! @youdontsay. Also, i wish i'd been born 37 years earlier! Seems quite a lovely person.), encouraged teachers to mobilize their students in testing out the solution after receiving a great number of letters telling her she was wrong (what a cool thing to do!). Well, the data from the students proved that her solution was correct... But i still think that second door is the devil, condemning you to anguish eternally in a lake of fire (with the somewhat ameliorating benefit of roasted goat meat). "Why?", i hear you breathlessly ask. Well alright, i'll tell you.

I don't know. Just kidding... I might. First, the context has changed, therefore the meaning has changed. A solitary outcome, whether goat or car, of a choice to change doors through a single round of choosing tells you nothing about statistics since it is not a statistically significant "population" of outcomes. Correct? It is a context different from the context of "statistical significance". Conversely, averaged probabilities of two different door choices arising from a statistically significant population of outcomes through a thousand rounds of choosing tells you nothing about your three→two-door-one-choice-one-round system. It's a different context. You standing in front of two doors having to make a single choice is not in the universe of the three→two-door-one-choice-THOUSAND-ROUND system, it is in the universe of the three→two-door-one-choice-ONE-ROUND system, therefore the meaning of the thousand-round system, i.e. its statistical probabilities, give you no advice about the choice you should make within your system, because ITS probabilities are not YOUR probabilities.

Intuition, unschooled by statistics, tells you that the two remaining doors have an equal chance of being correct; that they are each in the state of a 50% probability. That is TRUE, because your context of the three→two-door-one-choice-one-round system has changed its state. It has evolved into a two-door-one-choice-one-round system, and such a system has 50% probability of any choice being correct. The context of you standing in front of two doors with one choice did not, will not, and CANNOT EVER change its state in such a way that it evolves into a thousand-round system. And since a 50% probability is equivalent to "random chance" even the correct probability tells you nothing of what you should do. Furthermore, the 50% probability of you getting a car, given any door choice, is also FALSE, because you may have a greater or lesser probability of being correct than another individual given unknown criteria specific to you.

Now, please listen carefully, I'm not saying that what was "proven" by thousands of school kids testing probabilities was wrong, i'm saying it was different than what is commonly believed to have been proven. Those kids proved that a group of people through several rounds of choices had a collective average probability of 66.666% of picking the right door if they switched doors in a thousand-round system. They did not prove that the INDIVIDUAL increased their chances of winning to 66.666% by switching doors in a two-door-one-choice-ONE-ROUND system. Therefore Ms. vos Savant was wrong in her advice to an individual, while she was right in her calculation of probabilities for groups, as well as probabilities for individuals through several rounds of choice, but only right in the context of an absence of other criteria.

What i have tried to prove is that it is a logical fallacy to apply statistical probabilities derived from certain parameters to an individual case with different parameters. That it is a conflation of contexts to do so. I'm not sure if i have proven it, but if i did, and if no one has beaten me to it, i'd like to dub it "The Single-Context Fallacy" for posterity, or possibly "The Roasted-Goat Fallacy". What do you think? (12-29-2018 Addendum: It turns out that i may have discovered a case of what is already called "The Ecological Fallacy". Defined as: Incorrectly assuming that an association on the population level reflects an association on an individual level. But my reason is strained to the max here. So anybody out there who might have a leg up, i sure could use a boost...)

Go with your gut. Statistics do not apply to decisions in an individual case because the outcome of a single decision is not probabilistic, it is actual. They are therefore not valid criteria for making a decision. That doesn't mean you should stick to your guns. Change doors if you want to, but guided by a gut uninfluenced by the tantalizing smell of roasted-goatmeat-statistics. Look to your own wits. For, "It is Our WITS that make us men!" And women, obviously. Otherwise we remain -or become in some particular moment- mental 10 year olds. Do we not? Freeeeedoooooooom!

Post Script: There is another mystery here. What mechanism causes cars to be placed behind unpicked doors more frequently than picked ones?

Post Post Script: i may have made some mistakes in some of my formulations. If you can show me where and how, i'd be much obliged...

UPDATE (the nutshell argument as of April 15th, 2020): Probabilities are not objective properties of a single case, they are mathematical descriptions of expected regularities of outcomes in multiple cases. Therefore, we are led somewhere into the neighborhood of the following definition of The Roasted Goat Fallacy: Mistaking the expected rates of the occurrence of an event for an inherent property of a single event. (Boy, it sure is difficult to reason above my pay grade, but a correct answer is only less than half of what i'm after. The other part is in the reasoning itself, often with too few data and always with no formal training, but in the attempt to bootstrap myself up another cognitive stage in thinking. Why? Because it's fun, and some things can be know that way, and every once in a while something true can be thought that not many people have thought before.)

This has been a public service announcement. Paid for by taxation of the very cutting edge of The Million Things' current ability to reason out correctly. Thanks for listening.