This is looking a lot like a rule for me; this thing of telling one thing from another.
We must tell the difference between purely human, mathematical, and computer language.
We must also tell what is management from what is Mathematics.
This is all coming from discussing the so famous Monty Hall Problem.
More specifically, it is coming from the post Monty
We must tell the difference between purely human, mathematical, and computer language.
We must also tell what is management from what is Mathematics.
This is all coming from discussing the so famous Monty Hall Problem.
More specifically, it is coming from the post Monty
Imagine a ship that is sinking.
The captain has choices to make, let's say who will get a boat, and therefore who will get saved.
There are 36 seats, and 42 passengers.
The captain may go history and find out that, in an interval of 10 years, whenever they decided to save young people first, a person who mattered the most, let's say, a scientist of many publications, died.
The captain decides to save everyone who is old first.
Because they are slow people, 10 kids have died.
The captain's decision was a managerial one.
The captain has choices to make, let's say who will get a boat, and therefore who will get saved.
There are 36 seats, and 42 passengers.
The captain may go history and find out that, in an interval of 10 years, whenever they decided to save young people first, a person who mattered the most, let's say, a scientist of many publications, died.
The captain decides to save everyone who is old first.
Because they are slow people, 10 kids have died.
The captain's decision was a managerial one.
If people ask mathematicians what they think about it, they will probably answer that there should be enough boats and seats, so that everyone could be saved.
An ex-fellow, from Senai, R., teacher of Physics, told me this joke: The guy was walking and got lost. He found a man in a tree and decided to ask: Where am I? The guy, from the tree answered: You are under a tree, this tree is where I am now, and you are on a road that is inside of a forest. What is the profession of the guy who was in the tree? I starred at R. and had no answer: I don't know, I said. He said: Mathematician (no, don't think like that, that Brazilian men are always hostile to women at work and frequently offend them: It is not true at least sometimes...). I go: Why? R. said: he gave a completely useless and obvious answer (notice that the answer may be useless and obvious, but it is still totally true, restrictions of purely human language considered).
An ex-fellow, from Senai, R., teacher of Physics, told me this joke: The guy was walking and got lost. He found a man in a tree and decided to ask: Where am I? The guy, from the tree answered: You are under a tree, this tree is where I am now, and you are on a road that is inside of a forest. What is the profession of the guy who was in the tree? I starred at R. and had no answer: I don't know, I said. He said: Mathematician (no, don't think like that, that Brazilian men are always hostile to women at work and frequently offend them: It is not true at least sometimes...). I go: Why? R. said: he gave a completely useless and obvious answer (notice that the answer may be useless and obvious, but it is still totally true, restrictions of purely human language considered).
That is indeed the case at least here.
Management has its own ways, so that they may indeed decide to choose Swap all the time because they are lazy, because they have seen the historic results of the game and think they will have more chances of winning.
A mathematician will say: at this stage, on the second question, if you swap, you have 50% of chance of winning. If you stick, you also have 50%. Up to you.
Management has its own ways, so that they may indeed decide to choose Swap all the time because they are lazy, because they have seen the historic results of the game and think they will have more chances of winning.
A mathematician will say: at this stage, on the second question, if you swap, you have 50% of chance of winning. If you stick, you also have 50%. Up to you.
Notice that a larger chance, due to historic results, does not mean you will win if you swap.
You can (obviously) still be the unlucky person who swaps and loses.
In this way, the mathematician would not have any recommendation for you, just like in the case involving the boats and the humans.
If given more time to think, they would probably say that the kids could be a hope of getting a brilliant scientist, the old person could be the person to donate their kidney to somebody important and they would then be saved, their blood type is exotic, etc., like they would probably say that everyone is important in their own way, so that they would not give any decision on what to do in such a situation: each head, a sentence, basically.
The optimiser, however, would say: Swap! They would also say: Old people first. I suppose in this way one can understand better why the confusion appears.
Coming back to R., Mathematics will always tell the truth, that is, what is perhaps obvious, and, for some, interested in real-life situations, perhaps useless.
Mathematics is worried about everything being correct, about all being perfect.
It would be imperfect suggesting that a person always swapped in the game because they may lose.
We can at most say what is said: historically, people who swapped won more times.
Even so, it is possible that that is not a reality in the history of the game: we could easily have the least likely option always happening, all the way through, and that is actually what a mathematician would be obliged to tell you.
It is quite possible that, in another show, that be not Monty Hall's, everyone who stuck to their first choice, absolutely everyone, won, and most of the people who swapped lost.
If probability meant something, everyone who chooses it would win the Lotto.
Yet, if the games were for that purpose, the organisers would break quite frequently, is it not?
Games are always chancy things.
All we can say, as mathematicians, is what we say: At that stage, you have 50-50.
As another point, stick and swap is not what you are actually doing in the problem at that height: you are actually choosing one in two doors instead.
Of course, this is when we are talking about Mathematics, and, as R. said, mathematicians are useless and all they say is obvious, so that everything is the most objective thing as possible.
Sticking and swapping are not as objective as choosing, which is definitely what repeats.
Combinatorics is about repetition, and sticking and swapping are novelties introduced there to confuse us.
We are repeating action, not doing something new: what we are doing is choosing again, this time between two instead of three.
Mathematics needs the right words to be used, and that is why we created Classical Logic.
It does not work in any other universe.
Please read Words for Science.
In R.'s terms, useful would be someone who can tell others what to do: Swap or stick.
In the Mathematicians' World, we give people choices: We only talk about things that are one hundred percent true.
If we advised people, and then told them to always swap when they went to the Monty Hall Show, we would be taking away their freedom: We must make sure they choose and take responsibility for their choices.
If they lose, they will blame the optimiser and R., not us.
We are useless in the sense that we don't tell you what to do.
We are useful in the sense that we truly empower you.
You can (obviously) still be the unlucky person who swaps and loses.
In this way, the mathematician would not have any recommendation for you, just like in the case involving the boats and the humans.
If given more time to think, they would probably say that the kids could be a hope of getting a brilliant scientist, the old person could be the person to donate their kidney to somebody important and they would then be saved, their blood type is exotic, etc., like they would probably say that everyone is important in their own way, so that they would not give any decision on what to do in such a situation: each head, a sentence, basically.
The optimiser, however, would say: Swap! They would also say: Old people first. I suppose in this way one can understand better why the confusion appears.
Coming back to R., Mathematics will always tell the truth, that is, what is perhaps obvious, and, for some, interested in real-life situations, perhaps useless.
Mathematics is worried about everything being correct, about all being perfect.
It would be imperfect suggesting that a person always swapped in the game because they may lose.
We can at most say what is said: historically, people who swapped won more times.
Even so, it is possible that that is not a reality in the history of the game: we could easily have the least likely option always happening, all the way through, and that is actually what a mathematician would be obliged to tell you.
It is quite possible that, in another show, that be not Monty Hall's, everyone who stuck to their first choice, absolutely everyone, won, and most of the people who swapped lost.
If probability meant something, everyone who chooses it would win the Lotto.
Yet, if the games were for that purpose, the organisers would break quite frequently, is it not?
Games are always chancy things.
All we can say, as mathematicians, is what we say: At that stage, you have 50-50.
As another point, stick and swap is not what you are actually doing in the problem at that height: you are actually choosing one in two doors instead.
Of course, this is when we are talking about Mathematics, and, as R. said, mathematicians are useless and all they say is obvious, so that everything is the most objective thing as possible.
Sticking and swapping are not as objective as choosing, which is definitely what repeats.
Combinatorics is about repetition, and sticking and swapping are novelties introduced there to confuse us.
We are repeating action, not doing something new: what we are doing is choosing again, this time between two instead of three.
Mathematics needs the right words to be used, and that is why we created Classical Logic.
It does not work in any other universe.
Please read Words for Science.
In R.'s terms, useful would be someone who can tell others what to do: Swap or stick.
In the Mathematicians' World, we give people choices: We only talk about things that are one hundred percent true.
If we advised people, and then told them to always swap when they went to the Monty Hall Show, we would be taking away their freedom: We must make sure they choose and take responsibility for their choices.
If they lose, they will blame the optimiser and R., not us.
We are useless in the sense that we don't tell you what to do.
We are useful in the sense that we truly empower you.
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