
What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...? - egorst
http://www.thebigquestions.com/2012/03/26/loose-ends/
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ralfd
I actually did find the "nightmare dilemmas" on the site more interesting.

<http://www.thebigquestions.com/2012/03/22/another-nightmare/>

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Today’s Dilemma In front of you are two childless married couples. For some
reason, it’s imperative that you kill two of the four people. Your choices
are:

A. Kill one randomly chosen member from each couple. B. Kill both members of a
randomly chosen couple.

All four people agree that if they die, they want to be well remembered.
Therefore all four ask you, please, to choose A so that anyone who dies will
be remembered by a loving spouse.

If you care about the four people in front of you, what should you do?

\--------------------------------

Argument 1. For goodness’s sake, they’ve told you what to do. If you care
about them, of course you should respect their wishes. Choose A.

Argument 2.Once the killings are over, Option A leaves two grieving spouses,
whereas Option B leaves one relieved couple. Surely two dead plus two happy is
better than two dead plus two sad. Choose B.

Which argument do you buy? And what’s wrong with the other one?

\--------------------------------

~~~
Symmetry
That's actually a fairly neat question for sifting different types of
Utilitarians. Do you care about other people's happiness, or about their
utility as they define it? In B you're really screwing over one of the
couples, but they won't be around to be unhappy about it.

~~~
dedward
you are part of the equation, no?

~~~
Symmetry
Yes, but unless they have a very strong attachment to one or both of the
couples our hypothetical utilitarian judge is going to be a very small part of
the equation. For the record, I'm not a pure utilitarian myself.

~~~
dedward
the question indicates you do care about them, specifically.

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benjoffe
While the story at the end about the bug report is humourous, it's a pretty
mean thing to do. Perhaps 3 days lost work was longer than the expected
damage, but one would imagine it would waste at least a few hours of someone's
time, which is not something I'd feel good about.

On an unrelated note, sometimes using a computer not configured to British
English I get spelling corrections for words like "humourous" above, as a
sanity check I usually Google the word, it would be really helpful if Google
displayed a message that it was the British version of the word, instead of
displaying: "Did you mean _humorous_?".

~~~
m_for_monkey
Interestingly, while humor/humour is a US/British difference,
humorous/humourous is not, the latter is just rare/unusual.

<https://en.wiktionary.org/wiki/humour>

<https://en.wiktionary.org/wiki/humourous>

~~~
benjoffe
Ah I see, thanks, there are certainly better examples though, after a few
minutes I found 'unshakeable'* which google tries to correct to the American
version, yet is standard British English.

* <https://www.google.co.uk/search?q=unshakeable> (even makes the mistake on the UK Google site).

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davidjohnstone
This is why I don't like "what comes next in this sequence" questions. Most of
the time I can come up with a reason for choosing the answer I do, but that's
not necessarily the same reason as the question asker has for their "correct"
answer.

~~~
CodeMage
Precisely. The correct answer to such questions, whenever they don't include
additional context/restrictions, is "Anything at all."

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jl6
Given an arbitrarily long or short sequence of numbers, random or otherwise,
it is possible to find a polynomial which interpolates them, hence gives a
reasonable rule for finding the next number in the sequence.

~~~
Symmetry
Usually the right next number in a sequence is the one with the lowest
entropy, but of course the answer that the post's author says is the "correct"
one is far from the simplest way to generate the same sequence of 7 numbers.

~~~
jerf
Entropy is relative to your encoding scheme plus or minus a constant. Usually
you can ignore this fact when dealing with large amounts of information,
because almost all human-interesting encoding schemes are related by
relatively small constants, but when handed a small set of numbers it suddenly
dominates as the constant for very reasonable schemes relative to other very
reasonable schemes can exceed the size of the bits given to you in the form of
the original numbers.

This argument basically collapses back down to, no, there still isn't enough
information in a short sequence to identify the next number truly uniquely.

~~~
Symmetry
Yes, a function's Kolmogorov Complexity[1] does indeed depend on the encoding,
but you would certainly have to go out of your way to find an encoding where
the official answer can be expressed more easily than "f(n) = pi/2".

[1]<http://en.wikipedia.org/wiki/Kolmogorov_complexity> I didn't use the term
because I didn't think most people would recognize it, but we're getting
technical now.

~~~
jerf
First, I was speaking to the general case.

Second, for any given function there exists an encoding for which it is simply
the shortest possible string, so no, you don't really have to go "out of your
way" to find such an encoding. Trying to create criteria whereby that is
somehow "illegal" or "cheating" hits some rocky shores very quickly.

~~~
Symmetry
By having to go out of your way, I meant that every encoding I could think of,
whether English or Python or turing machine would rank these two solutions in
the same order. In fact, I would be somewhat surprised if there were any
encoding that had been used by more than one person in all of human history
that would rank the algorithm offered by The Big Questions as simpler than
pi/2.

Using unusual encodings like that isn't cheating in general, but when you play
a guessing game with other people like the blog author did then social norms
start to enter into the picture, and in this case I think it would be
reasonable to say that the author did cheat. Either that or, for the reasons
jl6 outlined, it was entirely meaningless.

But this isn't entirely confined to games people play. The only difference
between the hypothesis that General Relativity is correct and that General
Relativity has always been correct but in 5 seconds the rules of the universe
will change" is the complexity of the two statements, and I don't think that
the fact that you can specify an encoding where the second is simpler is going
to convince them that its a equally valid scientific hypothesis.

------
Jabbles
I'm not sure I like the idea that there's anything special about this. Making
an arbitrary sequence that suddenly diverges isn't hard: f(k) =
k^(max(0,k-5)). Involving real numbers just adds to the repertoire of hiding
techniques.

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brentashley
Apparently, "Error establishing database connection.".

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conanite
This reminds me of another "surprise" series:

    
    
      0, 1, 2, 720!, ...

~~~
civild
You gave it away with a slight error - the sequence is 0, 1, 2, 720...

For the curious, the sequence follows factorial (!) applied twice, i.e. (0!)!,
(1!)! etc. (3!)! is 720, and (4!)! is 6.20448402 × 10^23.

~~~
benjoffe
In that case the sequence should be 1, 1, 2, 720... as zero factorial equals
one _.

_ <https://www.google.com/search?q=0>!

~~~
civild
Oops, quite right!

~~~
dedward
0 is correct pragmatacally, and makes the puzzle harder for those not wise
that 0!=1 by the definition of factorial. (as opposed to proof.... factorial
being a shorthand for math and ths being convenient. if there were a proof it
would be a theorem, which its not.)

i knew factorial but i had to read up on 0!, news to me too.

on another note, without context, we could say there is an infinite set of
functions that satisfy any such question.

"what could come next and why" or something.

edit: 1 is indeed correct for the sequence, ignore that part... my bad.

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icode
What means the "d" in those formulas?

~~~
est
delta

~~~
alex1
Actually, it means differential.

~~~
lclarkmichalek
While delta is technically wrong, it is correct in that dx represents delta x,
where delta x tends to 0.

~~~
manojlds
Delta x is represented as Δx

