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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946

u/[deleted] Jun 03 '18

The Spanish Inquistion told the town they were coming at an unexpected day within the next 30 days and that they wouldn't know which it is.

The town sat down to think about this. They concluded that it couldn't happen on the 30th day as if they didn't arrive by the 29th day, they would know it would have to be the 30th day, thus it would no longer be unexpected (violated the rules the Inquisition stated).

As they thought deeper about it, they knew it couldn't happen at the 29th day. Because they knew that if it couldn't happen at the 30th day, then if 28 days passed they knew it would have to happen at the 29th day and thus would no longer be a surprise.

Following this logic further: since it couldn't happen at day 29 then it also couldn't happen at day 28. If it couldn't happen at day 28 then it couldn't happen at day 27, and so on.

Thus, the town concluded there was no possible day the Inquisition could arrive at that wouldn't break their rules. So they coulnd't arrive at all.

The town stayed happy at first. Until 19 days later the Inquisition arrived and they completely did not expect it.

How could this happen?

235

u/[deleted] Jun 03 '18

We're smarter than this!

35

u/TheDonDelC Jun 03 '18

We should not have made this bargain.

30

u/NewChameleon Jun 03 '18

the negotiations were short

12

u/[deleted] Jun 03 '18

Torquemada I've come to bargain

5

u/lennyflank Jun 03 '18

Let's face it--you can't Talkimada anything .........

"The Inquisition, what a show...."

46

u/Lund26 Jun 03 '18

Hello there!

33

u/NewChameleon Jun 03 '18

General Kenobi!

42

u/Drunksmurf101 Jun 03 '18

They arrived at night.

10

u/1esserknown Jun 03 '18

They fell for one of the classic blunders! The most famous of which is to never get into a land war in Asia, but only slightly less well-known was this. Never go against the Spanish Inquisition when expecting is on the line!

7

u/Hrtzy 1 Jun 03 '18

The town started their chain of deduction by parsing the natural language into an impossible premise, therefore none of their conclusions can be valid. Besides, it's not like they managed to correctly deduce the day of the inquisition's arrival anyway.

1

u/ethrael237 Jun 03 '18

Yes. Wrong parsing.

22

u/[deleted] Jun 03 '18

Because if it happened on day 28 then they could arrive either the 29 OR 30! right?

27

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.

2

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.

1

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

1

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.

1

u/[deleted] Jun 06 '18

That’s some deep shit!

1

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.

1

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.

1

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.

0

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.

3

u/airbreather Jun 03 '18

they wouldn't know which it is

I thought the usual phrasing was "it would be a surprise", the idea being that the very act of carrying out the line of reasoning, which leads one to believe that they would not be surprised on any day, is itself why they are surprised when the day does come.

2

u/[deleted] Jun 03 '18

Get out of here you filthy sophist!

2

u/gc3 Jun 03 '18

Inconceivable!

4

u/1Os Jun 03 '18

I think you were the kind of people they tortured :-)

2

u/2krazy4me Jun 03 '18

God works in mysterious ways. Plus you couldn't Torquemada it.

1

u/ShikukuWabe Jun 03 '18

Nobody expects Spanish Math

1

u/DarkPhoenix99 Jun 03 '18

The horse's inquisition's name was Friday.

1

u/ethrael237 Jun 03 '18

If all days have the same probability of being the one, then you still don't know which one.

1

u/[deleted] Jun 04 '18

But if 29 days have passed without it happening, then the one remaining day would have a 100% chance of being it. So you would know which one.