What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...? | Hacker News Reader

2, ...?

thebigquestions.com

106 pointsegorst53 comments

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?

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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?

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Caring about someone often means disregarding their wishes - see the concepts of toughlove or intervention.

I too found them more interesting. Is there a collection of these somewhere?

I think there's some interpersonal utility comparisons in there.

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.

you are part of the equation, no?

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.

the question indicates you do care about them, specifically.

I'd go for B. The experience is bound to be highly memorable for the surviving couple, which should let the dead couple be well remembered.

I'd go for B. Here's my line of thought:

Even though they asked me to be remembered, and I care for them, after they're dead it doesn't matter to them if they are remembered or not. There is no harm in them not being remembered, because they are not there to be harmed.

Keep in mind that there is a non-zero cost to the un-remembered, in that they may be cognizant that they will not be remembered prior to their death.

I would tell the couples that I am going to choose A, but instead choose B.

> I would tell the couples that I am going to choose A, but instead choose B.

Which makes you a bad with respect to most varieties of deontological and virtue ethics.

But deontology and virtue ethics are just shorthand heuristics for consequentialism, to deal with the fact that humans tend to be very bad at doing utilitarianism properly.

When the consequences are clear, and you have no other options, the rational choice is to ignore virtue ethics.

Of course, in real life, there is almost never such a clear-cut problem as this, and pat examples are often used by those who want to throw away virtue ethics out of convenience rather than actual utilitarian benefits.

The most basic requirement for a healthy societies is reproduction, females are the bottleneck in reproduction so killing both males is least bad in the long run.

If a war was expected in the short run, kill one couple as to forego some reproduction in exchange for a soldier motivated to fight.

Killing the two females would result in two depressed soldiers, so I would only pick this option if I was losing the war badly and needed the two males as cannon fodder - essentially killing all four.

argh, option b. because i am part of this equation too.

because its the one I can live with better. the surviving couple may disrespect me, never see me again, hateme, but are likely to be happier in the long run, and the other, dead couple will not me around to care that i ignored their wishes. and I will live knowing i kept one couple i care about together instead of destroying two. in short, i would take the selfish approach, because i have to live with myself.

given more context or a different situation with a similar concept, or more coffee, i may have a different answer.

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?".

The first thing I would have done if I was assigned to this case is to check whether it is really a bug or just a feature.

3 days does sound like a long time if you're an expert in the product.

If they weren't, then those 3 days are very likely well spent.

Are you sure that it wouldn't have taken you 3 days to check that?

It'd take me 3 weeks to check since I'm really poor at this level of math. Probably the reason I'm not going to maintain such software. ;)

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

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).

> rare/unusual

Or "misspelt/misspelled", as we prescriptivists like to call it.

Though when I see hypercorrections like "humourous" on the internet, I begin to suspect that people are using UK/Commonwealth spellings because they think they should, not because they're actually more familiar with those spelling conventions.

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.

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

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.

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.

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.

or any sequence, no? not without context.

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.

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.

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.

"right" needs a definition. true enough for these teasers in many settings, but mathematically, irrelevant, no?

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.

Apparently, "Error establishing database connection.".

This reminds me of another "surprise" series:

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

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.

I have (0!)! = (1!)! = 1 over here.

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

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

Oops, quite right!

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.

His sequence (corrected to 1, 1, 2, 720!, ...) would work for the factorial applied three times. Although the ! pretty much gives it away then.

While the zero is off in the GP's post, he technically could have been talking about the series of n!!!

No, the sequence is correct as originally posted and the rule is:

0, 1!, (2!)!, ((3!)!)!, (((4!)!)!)!, ...

It reminded me of another math 'joke' involving pi:

exp(pi)-pi =~ 20

http://blogs.discovermagazine.com/badastronomy/2007/01/31/ep...

What means the "d" in those formulas?

delta

Actually, it means differential.

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

Delta x is represented as Δx

Here's a good explanation of what it means: http://mathforum.org/library/drmath/view/60949.html

It's a notation for integrals, part of calculus. The "d" doesn't refer to anything http://en.wikipedia.org/wiki/Integral

The differential. It's an operator meaning "infinitely small slice of ..."

Since the Integral symbol represents an infinite sum, Integral( (f(x)*dx) ) is an infinite sum of infinitely small x-wise slices of f(x), thus giving you the area under the curve f(x).

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