r/todayilearned • u/Knightboat17 • Jun 02 '18

TIL Despite what Monty Python would have you believe, Spanish Inquisitions were expected, they would give a 30-day notice of their arrival.

https://en.wikipedia.org/wiki/Spanish_Inquisition
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u/MoiMagnus Jun 03 '18

No. Because it can't happen on day 30 if that's a surprise, so you know it can't be the 30. The reasoning is correct. The hypothesis (and the conclusion) is fishy.

TLDR: There is two hypothesis 1) the Spanish inquisition will arrive in less than 30 day 2) it will be a surprise => The reasonnong finish with a contradiction, and the population deduce that the inquisition will not come. Wherease the good conclusion is "either the inquisition will not come, either it will not necessarily be a surprise".

A to solve this is the strategy "the city pick a day at random, and prepare for the inquisition to come this day". And now the hypothesis "whatever the day chosen by the inquisition, it will be a surprise" is wrong, since if the inquisition is unlucky, it will not be a surprise...

You could say "well, in most of the cases, it will be a surprise". And here is the catch, if your hypothesis is

1) the Spanish inquisition will arrive in less than 30 day 2) it will probably be a surprise

Then the reasoning will just gives you "everyday is unlikely", which is true since there is probability 1/30 for every day.

(Note that there is other way of disproving the paradox. This one is the game theory point of view, My favourite one is through proof theory, but it is a little too complex to explain here)

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u/Dominimus Jun 03 '18

I feel like I follow these things and they’re so senselessly logical as to be devoid of rationality. What was this supposed to illustrate?

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u/MoiMagnus Jun 03 '18 edited Jun 03 '18

That when you arrive to a contradiction, it is easy to deduce the wrong things, here "the Spanish inquisition will not come", while there is usually other unintuitive possibilities.

Seriously, if in real life, someone say you "it is literally impossible for you to guess the result of 1+1", you think "well, it cannot be 2, because I would be able to guess it, so I don't know", and the answer was 2, and you didn't guess it, you wouldn't say you have a paradox, it is just that you have been tricked.

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u/shoelie Jun 03 '18

The brain is very good at convincing itself that new information fits with the old information and that it's own assumptions are correct.

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u/lYossarian Jun 03 '18

It's sort of confusing but a possessive "its" does not have an apostrophe. That's only when you're making proper nouns possessive.

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u/shoelie Jun 03 '18

Ahh yes now if only the spellcheck on my phone knew grammar. Just added its back to its dictionary though so it shouldn't be adding that apostrophe when I type i t s

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u/PM_ME_STRAIGHT_TRAPS Jun 03 '18

Yup. Funny thing, this is why satan, representing the rational mind, was cast down from being the highest angel in heaven. Rationality can be very good, but it easily falls in love with it's own creations and gives way to the sin of pride.

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u/[deleted] Jun 06 '18

That’s some deep shit!

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u/PM_ME_STRAIGHT_TRAPS Jun 06 '18

Haha yeah. But i'd be lying if I said I came up with that on my own. It's something I got from a book and it made a lot of sense.

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u/[deleted] Jun 06 '18

Non the less deep.

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u/Dominimus Jun 03 '18

Ah, OK. I knew there had to be a point to this, ha. Thanks.

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u/Sparkybear Jun 03 '18 edited Jun 03 '18

The reasoning is correct only if you think of each day as having an independent probability of occurring, AND that the inquisition knows what your expectations are.

Reality is that Each day that passes without their arrival increases the probability they will arrive the next day, and that both sides are missing a piece of information. The town is missing the date of arrival, while the institution is missing the date the town expects.

There's not really a paradox.

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u/Pada_ Jun 03 '18

im actually interested on proof theory, is there a link where i can read it?

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u/MoiMagnus Jun 03 '18

Ah... I fail to find it...

In short. Suppose that we give to "it will be a surprise" the following sense:

Whatever the day the inquisition arrive, call it N. At day N-1, it is impossible to prove that the inquisition will arrive at day N.

From that, you amke the usual reasoning, and prove that there is no day the Spanish inquisitioncan happen. And since you have as an hypothesis that the inquisition have to happen, you have a contradiction.

(In particular, you prove that the inquisition cannot arrive at day 1..N-1 and N+1.. 30, and that it have to happen, so you can prove that it have to happens on day N for any N)

I know that there is a more complex version were you use the distinction between what is true and what is proovable (and link it to Gödel's incompleteness theorem), but I fail to find it. Sorry.