Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

thebigquestions.com

Post reply on HN
Print view View original

41–50 of 58 posts

Re: What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

#41

Post by dedward »

civild wrote: post #18
benjoffe wrote: post #17

Earlier quoted context omitted.

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.

Re: What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

#42

Post by reitzensteinm »

civild wrote: post #13
conanite wrote: post #5

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.

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

Re: What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

#43

Post by dedward »

ralfd wrote: post #20

I actually did find the "nightmare dilemmas" on the site more interesting. http://www.thebigquestions.com/2012/03/22/another-nightmare/ -------------------------------- -------------------------------- 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 b…

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.

Re: What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

#44

Post by dedward »

Symmetry wrote: post #32
jl6 wrote: post #22

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.

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

Re: What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

#45

Post by dedward »

jerf wrote: post #36
Symmetry wrote: post #32

Earlier quoted context omitted.

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 th…

or any sequence, no? not without context.

Re: What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

#46

Post by dedward »

Symmetry wrote: post #31
ralfd wrote: post #20

I actually did find the "nightmare dilemmas" on the site more interesting. http://www.thebigquestions.com/2012/03/22/another-nightmare/ -------------------------------- -------------------------------- 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 b…

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?

Re: What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

#47

Post by Symmetry »

jerf wrote: post #36
Symmetry wrote: post #32

Earlier quoted context omitted.

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 th…

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.

Re: What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

#48

Post by jerf »

Symmetry wrote: post #47
jerf wrote: post #36

Earlier quoted context omitted.

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 th…

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.

Re: What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

#49

Post by Symmetry »

jerf wrote: post #48
Symmetry wrote: post #47

Earlier quoted context omitted.

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.

Re: What comes next: π/2, π/2, π/2, π/2, π/2, π/2, π/2, ...?

#50

Post by noblethrasher »

Splines wrote: post #39
roberto wrote: post #35

Earlier quoted context omitted.

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.

Post reply on HN