Earlier today the proverbial Elon Musk replied “Intelligence is as intelligence does” to someone posting a little story about the person with the highest IQ recorded, and exemplified this unparalleled feat saying “she was ridiculed for her answer to what seemed a simple problem. Yet she saw what no one else could.”
My point here is not that I’m smarter than most people, but that this would be the answer most likely BY DEFAULT.
So let’s see this simple logical problem:
There’s a game show and you get to pick between three doors. One of them would reveal the prize of a car, whereas the other two simply hide goats. The clever cultural wink here is that we all need cars rather than goats. So let’s simplify and just say one door is the prize and the other two are empty.
PRIZE / EMPTY / EMPTY
As simple as it is, as long you played D&D and/or have a very basic grasp of probabilities, you pick between three choices, it’s like rolling 1-2 on a d6, or 33.3% chance of being right.
And that’s it.
The added trick is that after the choice is made, one of the other two doors is opened to reveal it is empty. And you make a SECOND choice.
Once again, basic probabilities, you now get to pick between TWO doors, the chance is now 50%.
No matter what happens, this is always the scenario. If you picked the prize correctly the first time, with your 33% chance, the reveal of one of the other two doors will give the opportunity to know you’ve been either right or wrong. The toss of a coin, 50%. But the same happens in every case, because there are always two empty doors, and no matter which you pick, there’s always one left that is empty, to reveal at the second step.
My most stupid default is that it doesn’t really matter what choice you make, it’s always 50%. Either or.
But nope the story here is that people felt outraged by the WRONG answer: “She got over 10,000 letters, with nearly 1,000 from PhDs.”
… Telling her that she was wrong for deciding to switch?
But if the “stupid default” conclusion says that it’s INDIFFERENT, why should you be upset at picking one of two equal options?
Of course the goal here is another, once again political since the target here is the “school system”, part of the current playbook of destroying institutions. But it is quite silly how this was underlined:
“MIT ran computer simulations that confirmed her answer.
MythBusters conducted tests to prove it.
Some academics recognized their mistake and apologized.
But why did so many fail to see it?
I mean, yeah, it’s a tricky problem because of how it is presented. If the default answer is that it’s indifferent, because it’s either/or chance, then you are open to choose to switch as well. The “clever” conclusion is that this is a compounded choice, it builds on the first rather than being in isolation.
What you see as 1 on 2 chance is actually 2 on 3, which is much more convenient, and the reason is obvious. Between the first and second step, no matter what, one of the three options is removed. The fact that it is 33.3% the first, moving onto 50% indicates that something happened and information was added, and while the first choice is set in stone as 1 on 3, the “action” in between produced better chances, up to 50%. If you don’t CHANGE your choice then you are logically stuck with your original 33.3%, rather than the 50% in front of you.
No matter what you think, either you fully grasp the compounded chance OR NOT, the choice to SWITCH in the second stage is ALWAYS the better option.
Once again, you don’t need 228 IQ to figure out, you don’t need computer simulations. There is nothing tricky. There is only one answer, as long you give it enough thought to go one step further than the original 50% chance.
If you still don’t fully grasp the logic, just use a different example: there are 1000 doors, only one has the prize. You choose one, therefore you have 1/1000 chance of being right, which is quite unlikely. At the second step, the other 998 empty ones are removed. You now have only two options, the one you picked, and the one left…
Well, what are you gonna choose?
(there would be more to say, about what is the specific pattern that tricks the mind here, and it is how the heuristic abstraction transforms the reveal of one of the two other choices as equal, which is not, and then the whole theme of superstition matched to randomness, sticking to the choice that FEELS right, which is as old as humanity…)
Does anyone remember Scott Aaronson problem? (I mention Aaronson because the problem was examined in his “Quantum Computing Since Democritus”, but I think it first appeared on his blog?)
It was something like this: there’s a greatly advanced AI that has perfectly mapped human behavior. You know this. It is true. You’re going to face it. This computer AI has prepared two sealed boxes in front of you, one next to the other. The one on the left contains $1.000, you know this. The one on the right EITHER has $1.000.000, OR nothing. Once you arrive in front of those two boxes, the content has already been set and cannot be changed. So you know that the box to the right is either empty or has the bigger prize.
The content of the box on the right has been previously set by the AI following a strict rule: if it predicts you take both boxes, then that box is empty, if you take only the one on the right, then it contains the big prize.
You have one simple choice to make: take with you the box on the right, or BOTH.
Now you need 228 IQ.
—
Late addition:
If you choose red pill, you live in all cases (and everyone lives too, the dilemma is intended as an intuition pump).
If you choose blue pill, you die.
But LOGIC also says that to save lives you need to reach 100% consensus on red pill, but only 51% consensus on the blue.
Given knowledge of the results of the poll, we would need only another +4% on blue side to save everyone’s life, whereas to do the same on the red side you’d need a +46%.
I wonder, would you send your own mom to certain death since you know she isn’t great with logic?
If altruism has sometimes practical limits, individualism always has contextual ones.