Search found 342 matches

by Gwydion
Fri Jan 08, 2016 3:59 pm UTC
Forum: Logic Puzzles
Topic: Blue Eyes with Superrationality
Replies: 48
Views: 10622

Re: Blue Eyes with Superrationality

I want to expand on SirGabriel's point further. Flewk, what happens in the following scenarios (with superrational islanders etc)? Who leaves, and on what day? 1) There are 5 blue eyed islanders. 2) There are 4 blue eyed islanders and 1 brown eyed islander. 3) You are on an island and see 4 blue eye...
by Gwydion
Wed Jan 06, 2016 2:06 pm UTC
Forum: Logic Puzzles
Topic: Blue Eyes with Superrationality
Replies: 48
Views: 10622

Re: Blue Eyes with Superrationality

They will leave the island after one night instead of waiting two nights like I would. If they waited until the second night, then I know for sure that I am blue because the people who see 3 blues would have left on the first night. Ok, given that statement, what would you need to see to leave on n...
by Gwydion
Tue Jan 05, 2016 11:25 pm UTC
Forum: Logic Puzzles
Topic: Blue Eyes with Superrationality
Replies: 48
Views: 10622

Re: Blue Eyes with Superrationality

They will leave the island after one night instead of waiting two nights like I would. If they waited until the second night, then I know for sure that I am blue because the people who see 3 blues would have left on the first night. Ok, given that statement, what would you need to see to leave on n...
by Gwydion
Fri Dec 11, 2015 5:03 pm UTC
Forum: Mathematics
Topic: Describe an Inconsistent System.
Replies: 44
Views: 8099

Re: Describe an Inconsistent System.

Given a system that contains a contradiction; that system can prove anything (is inconsistent). The system of axiomatic mathematics contains contradictions. Therefore the system of axiomatic mathematics is inconsistent. This is where we have problems, as expertly outlined already. Your use of the w...
by Gwydion
Mon Dec 07, 2015 1:30 am UTC
Forum: Mathematics
Topic: Describe an Inconsistent System.
Replies: 44
Views: 8099

Re: Describe an Inconsistent System.

Part 1. Any proof within an axiomatic system only applies to that axiomatic system. On that we are in agreement. Inconsistent systems tend to be discarded quickly because the ability to prove anything and its inverse isn't very constructive. However, this leaves the nature of inconsistency less exa...
by Gwydion
Fri Dec 04, 2015 4:16 pm UTC
Forum: Mathematics
Topic: Describe an Inconsistent System.
Replies: 44
Views: 8099

Re: Describe an Inconsistent System.

I get the impression that people think the Principle of Explosion is weaker than it actually is... using the Principle of Explosion on an inconsistent system we can prove anything/everything . Given an inconsistent system we can prove that every subset of that system is self inconsistent. Perhaps y...
by Gwydion
Thu Dec 03, 2015 7:26 pm UTC
Forum: Mathematics
Topic: Describe an Inconsistent System.
Replies: 44
Views: 8099

Re: Describe an Inconsistent System.

Given an inconsistent system, we know that we can prove that each statement within that system is both true and false (ref: the Principle of Explosion). As such, every statement within an inconsistent system is, itself, inconsistent. There are no degrees of inconsistency. There is no hierarchy of i...
by Gwydion
Wed Dec 02, 2015 2:07 pm UTC
Forum: Mathematics
Topic: Describe an Inconsistent System.
Replies: 44
Views: 8099

Re: Describe an Inconsistent System.

Let us take Cauchy's argument at face value. Cauchy has proven that a given system is consistent despite a superset being inconsistent. At the same time, it has been asserted by Treatid without proof that every subset of an inconsistent system is inconsistent. Fixed that for you. Please justify you...
by Gwydion
Fri Nov 20, 2015 3:27 pm UTC
Forum: Movies and TV Shows
Topic: Tonight's South Park...(Merged Scott Tenorman)
Replies: 93
Views: 31834

Re: South Park

I'm not aware of South Park ever doing a story arc for more than 3 episodes. So we aren't counting the time Kenny stayed dead for an entire season, and they needed to find a new fourth friend? Admittedly, this season's interconnections have been bigger, but I don't remember an episode that season w...
by Gwydion
Tue Oct 27, 2015 3:02 pm UTC
Forum: Gaming
Topic: Saints Row IV - Greatest Superhero Game Ever
Replies: 18
Views: 6447

Re: Saints Row IV - Greatest Superhero Game Ever

I also just started playing through this, after the recommendations from another thread, and it's been a blast so far. I'm concerned the game feels a little short, at least in terms of main story so far, but I'm having a great time running around and shooting things in increasingly ridiculous ways. ...
by Gwydion
Sun Sep 27, 2015 3:14 pm UTC
Forum: Logic Puzzles
Topic: Kings on a Chessboard
Replies: 6
Views: 3411

Re: Kings on a Chessboard

I agree with Jestingrabbit, but only if the kings only care about the spaces they're on. If we add the rules of chess, meaning kings can't move into check, that solution could fail- as soon as white moves into rows 4-5 in columns D-E, black can't legally follow but might have other asymmetric moves....
by Gwydion
Fri Sep 18, 2015 2:38 pm UTC
Forum: Logic Puzzles
Topic: Anti-Gambler's Fallacy
Replies: 162
Views: 26333

Re: Anti-Gambler's Fallacy

No, I accept that there's more likely explanations after witnessing the events, what I'm saying is that it's irrational to think about them on the universe where it happened by chance. That is, either it happened by chance with probability 1, or it didn't. Suppose I have 5 cards of different colors...
by Gwydion
Tue Sep 08, 2015 5:03 am UTC
Forum: Logic Puzzles
Topic: Anti-Gambler's Fallacy
Replies: 162
Views: 26333

Re: Anti-Gambler's Fallacy

Vytron, you said it really well, except in the example given you use incorrect probabilities - using photos of hands including 0-10 fingers would leave us with a probability space of 11 outcomes, not 10. Dropping the option of 0 fingers fixes it... For me, whether I continue has little to do with th...
by Gwydion
Thu Aug 27, 2015 1:21 am UTC
Forum: Logic Puzzles
Topic: Saving the islanders
Replies: 7
Views: 2481

Re: Saving the islanders

Questions 1-2: If the second guru on day k points out at least k blue eyed islanders, that does cut off the chain of logic and keeps anyone else from dying. Cradarc is right that information can't "go away", but one can collapse the possibility spaces in a more desirable fashion. A 4-p...
by Gwydion
Fri Jul 31, 2015 5:25 am UTC
Forum: Mathematics
Topic: Prove that 25+8*(n!)) is not square
Replies: 10
Views: 3394

Re: Prove that 25+8*(n!)) is not square

if n>=25 then 25+8*(n!) is always divisible by 25. So if it is a perfect square it has to be the square of a number divisible by 5. (For n<25 we already know there are no squares by previous poster) That's actually true for n>=10. Since 10! Is divisible by 25. More specifically an odd multiple of 5...
by Gwydion
Tue Jul 21, 2015 8:37 pm UTC
Forum: Logic Puzzles
Topic: Rethinking Blue Eyes - A Logic Puzzle
Replies: 97
Views: 14973

Re: Rethinking Blue Eyes - A Logic Puzzle

And that is giving up, since it has been shown no magic voice can exist that would help the prisoners. Oh well. On the contrary, it only shows that there is a risk that they fail with any magic voice. However, if we take the entire text of the original puzzle as additional givens, we know they do n...
by Gwydion
Thu Jul 02, 2015 2:00 am UTC
Forum: Mathematics
Topic: How many integers between 100 and 999 with repeated digits
Replies: 5
Views: 4359

Re: How many integers between 100 and 999 with repeated digi

many thanks! So, while not really another way, you could also just kind of collapse your cases II-IV into one case... New Case 2: How many integers have two repeated digits? 9 · 9 · 1 · 3 C 2 = 243 Even if it's trivial, can you explain me better this passage? There are 9 ways to choose the first di...
by Gwydion
Tue Jun 16, 2015 8:42 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853

Re: My write-up of the "Blue Eyes" solution (SPOILER A

There are no real people who think there could be someone who didn't already know that the guru can see blue eyes, but there are 24 second-level virtual people who do (A's model of B's model of C, etc) - precisely the virtual people who think someone might leave on the first night. For me, the prob...
by Gwydion
Mon Jun 15, 2015 9:26 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853

Re: My write-up of the "Blue Eyes" solution (SPOILER A

Arklarp, in case you missed the link in the OP, http://forums.xkcd.com/viewtopic.php?f=3&t=80149. Please look carefully at the first couple, and possibly #5 if you still aren't happy. If after reading these you still have concerns, see if you can reframe your objections to explain why they aren'...
by Gwydion
Fri Jun 12, 2015 7:20 pm UTC
Forum: Gaming
Topic: Too Many Games - the backlog thread
Replies: 12
Views: 3175

Re: Too Many Games - the backlog thread

A dangerous suggestion. It's difficult to mix in even light games with the monster that is PoE. If you get a little bit distracted because SR4 is so awesome and you don't feel like thinking too hard for a few days, details start to slip. You forget some of the several hundreds of spells and abiliti...
by Gwydion
Wed Jun 10, 2015 3:40 am UTC
Forum: Gaming
Topic: Too Many Games - the backlog thread
Replies: 12
Views: 3175

Re: Too Many Games - the backlog thread

I plan to. Pillars of Eternity still has all of my free time locked down until I finish that.
by Gwydion
Tue Jun 09, 2015 2:11 pm UTC
Forum: Gaming
Topic: Too Many Games - the backlog thread
Replies: 12
Views: 3175

Re: Too Many Games - the backlog thread

Hundreds of games, literally. The most recent additions are Saints Row 4, Sunless Sea, and all of the Total War franchise except for the first Medieval and Shogun games.


And just in case you didn't have this problem yet, the Steam Summer Sale starts in 48 hours or so...
by Gwydion
Fri Jun 05, 2015 2:08 am UTC
Forum: Mathematics
Topic: Stubborn bettor
Replies: 99
Views: 12205

Re: Stubborn bettor

Goahead, it is possible that your theoretical two bettors can both be winners. This can only happen if one of them "wins" and quits, then the other goes on a hot streak afterward. An example of such a sequence would be BBBB (first player quits with 16, second has -4) RRRR (second player ge...
by Gwydion
Thu Jun 04, 2015 8:27 pm UTC
Forum: Mathematics
Topic: Stubborn bettor
Replies: 99
Views: 12205

Re: Stubborn bettor

Using the stubborn method will guaranty you in 98% of the cases to reach 10 dollars with a capital of 490 dollars. You loose only in 2% of the cases. But you lose a lot more when you lose. 98% of the time you win $10, 2% of the time you lose $490. The expected value of this game is 0. Actually the ...
by Gwydion
Mon May 25, 2015 5:25 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1529: "Bracket"
Replies: 191
Views: 50036

Re: 1529: "Bracket"

title="I'm staring at the "doctor" section, and I can't help but feel like I've forgotten someone."

I always feel weird getting Dr Zhivago and Dr Moreau backward...
by Gwydion
Wed May 13, 2015 5:32 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1524: "Dimensions"
Replies: 79
Views: 14570

Re: 1524: "Dimensions"

mattcoz wrote:
Envelope Generator wrote:May I ask you if you've considered all the possibilities that "down" might offer you?

What is "down" in terms of dimensions?

Toward the enemy's gate, of course.
by Gwydion
Tue May 05, 2015 9:33 pm UTC
Forum: Mathematics
Topic: A maths joke I don't get
Replies: 8
Views: 9254

Re: A maths joke I don't get

It's a really lame joke, but I think the answer is probably
Spoiler:
d/dy, as ce^x is not a varying function of y and therefore the partial derivative is 0. The "joke" coming from the fact that d(e^x)/dx is e^x, so e^x is "invincible" to differential operators.
by Gwydion
Sun Apr 19, 2015 6:45 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853

Re: My write-up of the "Blue Eyes" solution (SPOILER A

To prove that it can't be done in less than 100 days, consider it from the other direction. If the blue-eyed people leave on day X, why would they do so? The possibility of 99 blue-eyed people must have been eliminated within the past 24 hours. The guru's statement obviously doesn't do that in that...
by Gwydion
Sun Apr 19, 2015 2:28 am UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853

Re: My write-up of the "Blue Eyes" solution (SPOILER A

Steve - Interesting take, though I think you missed the point when I tried to restate your proposed strategy - if you're allowed to create a strategy that says "go here if A, go there if B", why not take it further? On day one, if you see two islanders with the same eye color, grab their h...
by Gwydion
Sat Apr 18, 2015 7:50 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853

Re: My write-up of the "Blue Eyes" solution (SPOILER A

I would agree with gmal, in that your "go to the dock" is an illegal communication - the islanders don't go to the dock already knowing their eye color, they go because they want to discover it (and depending on the circumstance, they may not). In the case of having a single islander with ...
by Gwydion
Tue Mar 03, 2015 7:46 pm UTC
Forum: Books
Topic: Harry Potter and the Methods of Rationality
Replies: 1036
Views: 404243

Re: Harry Potter and the Methods of Rationality

post 114/115 speculation: Does Harry have enough time turner mojo left to make the bad things that happened on the way to the graveyard only seemingly bad? The obvious technique would be to relay a message back to Dumbledore, making the mirror "trap" a fake somehow. Another thing that cou...
by Gwydion
Tue Feb 10, 2015 7:30 am UTC
Forum: Mathematics
Topic: How do axioms specify a new system vs continuing an old one?
Replies: 81
Views: 10706

Re: How do axioms specify a new system vs continuing an old

Neither A nor B assert that x and !x are true simultaneously (for any statement x). This is where I disagree. I don't think A and B are distinct. Your argument is that A and B are distinct systems. As such, a statement in B has no impact on A. However, we are using A to specify how the axioms of B ...
by Gwydion
Tue Feb 10, 2015 2:10 am UTC
Forum: Mathematics
Topic: How do axioms specify a new system vs continuing an old one?
Replies: 81
Views: 10706

Re: How do axioms specify a new system vs continuing an old

We have a number of true and false statements with respect to system 'A'. If we assert that a false statement is true (or vice versa), then that newly true statement is a contradiction of what we have already established. We have created an inconsistency with respect to system 'A'. Now, we take tha...
by Gwydion
Sun Feb 08, 2015 3:42 pm UTC
Forum: Mathematics
Topic: How do axioms specify a new system vs continuing an old one?
Replies: 81
Views: 10706

Re: How do axioms specify a new system vs continuing an old

You suggested we could mix true and false statements from A to form a set of axioms. Given that A is the context for interpreting those axioms - mixing true and false statements will lead to a contradiction. This isn't a question of whether the individual statements are true or false. In the contex...
by Gwydion
Sat Jan 31, 2015 8:30 pm UTC
Forum: Mathematics
Topic: Circularity in Formal Languages?
Replies: 51
Views: 13903

Re: Circularity in Formal Languages?

1. Any contradiction in an axiomatic system means that every statement of that system can be contradicted. Such a system is null. 2. A statement only has meaning with respect to a (defined) set of axioms. 3. Axioms are, themselves, statements. 4. Informal languages (and the elements thereof) are no...
by Gwydion
Tue Jan 27, 2015 4:41 pm UTC
Forum: Mathematics
Topic: Circularity in Formal Languages?
Replies: 51
Views: 13903

Re: Circularity in Formal Languages?

Treatid, I'm not sure I understand your entire response there, but I'll take one part that stands out, namely your response to FG saying that ZFC is inconsistent. If you choose to define the empty set in the way that you did, namely as being a set that contains itself, then that axiomatic system whi...
by Gwydion
Fri Dec 19, 2014 12:18 am UTC
Forum: Movies and TV Shows
Topic: Primquel Sub Titles
Replies: 10
Views: 3563

Re: Primquel Sub Titles

The Matrix Rewatchable?

This really is harder than it sounds
by Gwydion
Fri Nov 28, 2014 8:43 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853

Re: My write-up of the "Blue Eyes" solution (SPOILER A

Let's consider the two-person case further, as you state that two people with blue eyes can not deduce their own eye color. Given that this is true, imagine you (a brown-eyed person) standing with those two people. Can they deduce their eye color now? Since you don't know your own eye color, you kno...
by Gwydion
Sat Nov 22, 2014 2:18 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853

Re: My write-up of the "Blue Eyes" solution (SPOILER A

Potatoberg - You keep asserting that the desired solution requires unjustifiable, unreasonable, or otherwise "wrong" assumptions. You've previously stated that a perfect logician should not make any assumptions at all, a statement that invalidates many of the popular puzzles on this forum....
by Gwydion
Thu Nov 13, 2014 2:13 am UTC
Forum: Movies and TV Shows
Topic: Star Wars: Episode 7: Electric Boogaleven
Replies: 479
Views: 115012

Re: Star Wars: Episode 7: Electric Boogaleven

It's the only title so far that doesn't refer to a character or a group of them (presumably). A New Hope? Luke is the new hope, surely. Anakin was their only hope, but he turned evil and now they've got a new one. Fixed for you. And I don't have a problem with the new title, mostly because I still ...

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