## Search found 198 matches

Thu May 03, 2007 8:01 am UTC
Forum: Logic Puzzles
Topic: A subset of the unit square
Replies: 15
Views: 4100
Oh right. (Duh.)
Thu May 03, 2007 6:27 am UTC
Forum: Logic Puzzles
Topic: A subset of the unit square
Replies: 15
Views: 4100
Ah thanks, ptveite, that was actually the version of the puzzle that I was misremembering. If we require that the columns are not only uncountable, but in fact contain all of [0,1] but a countable subset (i.e. are co-countable), then skeptical's method doesn't work (though it does for the puzzle as ...
Wed May 02, 2007 10:25 pm UTC
Forum: Logic Puzzles
Topic: A subset of the unit square
Replies: 15
Views: 4100
Nope, not every column is uncountable in that set, only one is.
Wed May 02, 2007 10:02 pm UTC
Forum: Logic Puzzles
Topic: A subset of the unit square
Replies: 15
Views: 4100

### A subset of the unit square

Does there exist a subset S of the unit square with the following properties?:

(a) Every row is countable. I.e. for every y in [0,1], the set of x such that (x,y) is in S is countable.
(b) Every column is uncountable. I.e. for every x in [0,1], the set of y such that (x,y) is in S is uncountable.
Wed May 02, 2007 7:26 pm UTC
Topic: The ethics of teleportation
Replies: 116
Views: 43466
If so, then which is your consciousness? Both. Neither. The question assumes a uniqueness and continuity of consciousness that isn't really there. I wouldn't use it. I don't want to die. "You" die every second of every day. The consciousness thinking about reading this now is not the same...
Wed May 02, 2007 7:02 pm UTC
Topic: The ethics of teleportation
Replies: 116
Views: 43466
HenryS: I don't mean that there is no value in people. I mean that if everything we are is within our bodies [imprecise, but you know what I mean], then in a fundamental sense we are no different from animals or inanimate objects - hell, the root word for inanimate is anima, isn't it? Well yes... I...
Wed May 02, 2007 5:36 pm UTC
Topic: The ethics of teleportation
Replies: 116
Views: 43466
While you'd technically be something new, there would be no other you that would now be dead, because in fact death and life are the same if there is no soul, since whether a person is alive or not is just a consequence of the order of atoms in the universe and can easily be changed using the prope...
Fri Apr 27, 2007 2:20 am UTC
Forum: Logic Puzzles
Topic: A field of theorems
Replies: 12
Views: 3144
I read it as: T is the set of all theorems that can be derived from the set of axioms that define a field (so, presumably, ZF + field axioms or something?). Find a field structure on T. That is, some theorem should correspond to 0 in the field, some theorem to 1. There should be two binary operation...
Tue Apr 24, 2007 12:07 am UTC
Topic: On The Validity of Paradox and Irrationality
Replies: 30
Views: 5255

### Re: On The Validity of Paradox and Irrationality

to get a little godel escher bach on y'all paradox must exist in any complete system and for me ethics meta physics and morality must be complete to be of any value so the aforementioned must have some paradoxes. this being said does godels theorem make other paradoxes valid? do paradoxes have esse...
Mon Apr 16, 2007 1:39 am UTC
Forum: Logic Puzzles
Topic: Building houses
Replies: 108
Views: 26824
Castaway wrote:HenryS, your 4x4 was cute, and the one that required 25 was fun.
Is 25 the maximum or are there examples that need more?
Sun Apr 15, 2007 8:55 pm UTC
Forum: Logic Puzzles
Topic: Building houses
Replies: 108
Views: 26824
And here's a 4x4x4 that requires 25:

Code: Select all

`Top:XXXXXXXXXXXXXXXXFront:X    X    X    XXXXRight:XXXXXXXXXXXXXXXX`
Sun Apr 15, 2007 8:51 pm UTC
Forum: Logic Puzzles
Topic: Building houses
Replies: 108
Views: 26824
I hypothesize that any puzzle configuration can be solved with 16 blocks or less. But, I'm not sure about the 16th block. Can anyone come up with an example that necessitates 16 blocks? I think there must be problems that need at least 17 blocks. Here's a 2x2x2 problem that requires 5: Top: XX XX F...
Sun Apr 15, 2007 2:46 am UTC
Forum: Logic Puzzles
Topic: Building houses
Replies: 108
Views: 26824
So... how many solutions are there to 10?
Fri Apr 13, 2007 2:54 am UTC
Forum: Logic Puzzles
Topic: 100 prisoners and a lightbulb
Replies: 45
Views: 23682
Man, I always feel bad for the poor schlubs in this puzzle. Why don't you make it 20 prisoners instead of 100, and at least give them a chance of getting out before Andy Dufresne? As we noted in http://www.segerman.org/prisoners.pdf (lots of spoilers), there are strategies for 100 prisoners with ex...
Wed Apr 04, 2007 1:15 am UTC
Topic: Organ donation and cannibalism
Replies: 33
Views: 7857
If we look for evolutionary reasons for the morals we have now, one good reason that cannibalism would be shunned (or at least have a big yuck factor) is that you need to have a human dead for it to happen, and so ties in with the yuck of murder. There's another yuck with dead things, which makes se...
Mon Mar 19, 2007 7:32 pm UTC
Replies: 79
Views: 19604

You could reduce the programming aspect to a single register and a table based lookup, as follows: HumongousIntRegister state; const HumongousInt BehaviorTable[MAX_HUMONGOUS_INT]={...}; for(;;) state = BehaviorTable[state|getinputs()]; The lower n bits of the state registe...
Sat Mar 17, 2007 6:39 pm UTC
Replies: 79
Views: 19604
The primary confusion--dare I even say, the error being made--is the one between what is "actually there"--the ontology, the "physical" if you want to call it that, and what can be addressed with physics--the objectively modelable. In essence, the error is that the objective can...
Sat Mar 17, 2007 8:50 am UTC
Replies: 79
Views: 19604
Might I ask--is there a physical difference between 2+2 and 5? Both of these are non-physical entities. If they are non-physical entities, why are you asking if there is a physical difference between them? This seems to me to be obfuscating the point. The existential status of mathematical objects ...
Sat Mar 17, 2007 5:35 am UTC
Replies: 79
Views: 19604
Presumably, you are objecting to my statement that "If it's just electrical impulses in the brain, that should mean that other electrical devices are conscious too." So what's so special about the human brain that makes it conscious when other things (presumably) aren't? If it's just made...
Sat Mar 17, 2007 4:41 am UTC
Replies: 79
Views: 19604
So, what's the deal with televisions then? If it's just electrical impulses hitting the screen, that should mean that other electrical devices are audio visual entertainment products too. Are you watching Buffy when you turn on your electric can opener? I don't think so. (In less snarky language: yo...
Thu Mar 15, 2007 11:35 pm UTC
Topic: Math
Replies: 55
Views: 16449
That's not an important case, though. For any meaningful statement, truth and untruth are the only possible states. Mathematical reality exists independently of our ability to prove things--just because A isn't provable doesn't mean it isn't true. What about something like the Continuum Hypothesis,...
Tue Mar 13, 2007 6:56 pm UTC
Topic: Holes in the theory of Evolution?
Replies: 132
Views: 37293
It has a blind spot where the optic nerve is attached. Why didn't evolution fix these problems? This one is really good evidence for evolution. (IANAB, but I read this explanation somewhere:) In the human eyes, the nerves coming out of the retina cells come out forward, into the interior of the eye...
Sun Mar 11, 2007 10:41 pm UTC
Topic: Atheism
Replies: 781
Views: 105999
Atheism = Faith/belief in a lack of 'something' I don't really like the word "belief", I'm never entirely sure what it means. Let me paraphrase you, in the hopes that it hasn't changed the meaning for you? Atheism = Being absolutely sure that there is a lack of existence of 'something' Th...
Sun Mar 11, 2007 9:18 pm UTC
Topic: Atheism
Replies: 781
Views: 105999
I struggle to understand why people have struggles in accepting that athieism *is* a faith. Not necessarily a relgion, as IMO, a religion implies serious dogma.. but the scientific method *is* serious dogma, in a fashion. The scientific method is something everyone uses in some way, every day. When...
Sat Feb 24, 2007 7:31 pm UTC
Forum: Logic Puzzles
Replies: 23
Views: 5646
This problem happens to be of the nature that if any of them cheat just a little , the problem will be solved. So this is kindof a deep question actually. Cheating just a little would have to mean unlinking hands briefly to relink around the other side of some arm (thus requiring the minimal amount...
Tue Feb 20, 2007 10:44 am UTC
Forum: Logic Puzzles
Replies: 23
Views: 5646
I've seen this game played, and also heard the claim that it is always possible to disentangle. In the game the arm links are randomly chosen, and so it is possible to make a trefoil. Perhaps this should really be a question of why it is that trefoils (or other knots) apparently never come up in &qu...
Wed Feb 07, 2007 10:46 pm UTC
Forum: Logic Puzzles
Topic: Fornicating Chesspeople
Replies: 20
Views: 6281
What if they really are chessmen and chesswomen, and two pieces of opposite genders are required to be next to a square to reproduce into it?

I think if you get to choose the gender of each new piece then it doesn't really change much, but maybe there's some interesting variant along these lines?
Sun Dec 10, 2006 1:29 am UTC
Forum: Logic Puzzles
Topic: Envelopes puzzle
Replies: 10
Views: 6027
The two envelopes contain \$x and \$2x. You have either x or 2x with probability 1/2 of each. Your expected gain on switching is therefore x * 1/2 + (-x) * 1/2 = 0.
Sat Dec 09, 2006 7:50 pm UTC
Forum: Logic Puzzles
Topic: Not a puzzle, just a quick question
Replies: 5
Views: 3547
I think maybe "hyper volume", but more usually just "volume", and we know what dimension we are talking about from context.
Mon Dec 04, 2006 3:33 am UTC
Forum: Logic Puzzles
Topic: 3 Spiders and a Fly [solution thread]
Replies: 15
Views: 6425
I think I see a way for 3 more-than-double-speed spiders to catch a fly on an octahedron.

The general problem seems kindof hard, too much dependence on specific lengths and speeds to be able to make many general statements.
Sun Dec 03, 2006 9:57 pm UTC
Forum: Logic Puzzles
Topic: 3 Spiders and a Fly [solution thread]
Replies: 15
Views: 6425
Indeed, what are the restrictions on the spiders' and fly's motion? Do they move at exactly a particular speed at all times, or do they merely have maximum speeds? Assuming we allow them to reverse direction, any speed less than their maximum may be approximated arbitrarily well by an appropriate p...
Sun Dec 03, 2006 9:34 pm UTC
Forum: Logic Puzzles
Topic: 3 Spiders and a Fly [solution thread]
Replies: 15
Views: 6425
The_Spectre and skeptical scientist both got the solution I did. There are other solutions, involving knowing what epsilon is, doing one thing until we know the fly has to be in a certain place, then switching to doing another. The problem naturally extends to other graphs, so one could define the &...
Sun Dec 03, 2006 8:39 pm UTC
Forum: Logic Puzzles
Topic: 3 Spiders and a Fly
Replies: 11
Views: 5535
Torn Apart By Dingos wrote:Edit: They can't be points, or the spiders would have to make space-filling curves, which I hope isn't the solution.
They are on the edges and corners of the tetrahedron, not the faces, so no space filling stuff is necessary.
Sun Dec 03, 2006 7:42 am UTC
Forum: Logic Puzzles
Topic: 3 Spiders and a Fly
Replies: 11
Views: 5535

### 3 Spiders and a Fly

Three spiders and a fly are moving along the edges of a regular tetrahedron. The spiders are trying to catch the fly. Unfortunately the fly is invisible, hyperintelligent and psychic. Fortunately, the fly is also very slightly slower than the spiders (say epsilon slower). The spiders know they have ...
Sat Dec 02, 2006 9:15 am UTC
Forum: Logic Puzzles
Topic: Temperatures
Replies: 60
Views: 13356
One can multiply in any group (or even in a monoid), which certainly doesn't need a -inf, or anything like it. For that matter, the strictly positive real numbers under multiplication are another group.
Fri Dec 01, 2006 11:13 pm UTC
Forum: Logic Puzzles
Topic: Snakes on a Plane solution thread (spoilers)
Replies: 29
Views: 9006
From this we can see that (A,E,F) touch (B,C,D). This is the "three utilities to three houses" problem, which is a known impossibility on the euclidean plane. So we should also be looking at "Snakes on a torus", "Snakes on a projective plane" etc etc. Edit: Dashiva's 6...
Mon Nov 27, 2006 8:05 pm UTC
Forum: Logic Puzzles
Topic: Robots on a Plane(t) [SOLUTIONS + SPOILERS THREAD]
Replies: 96
Views: 27802
Hix wrote:That would be the function "f"...
Oh right, that's a neat solution :)
Mon Nov 27, 2006 10:06 am UTC
Forum: Logic Puzzles
Topic: Robots on a Plane(t) [SOLUTIONS + SPOILERS THREAD]
Replies: 96
Views: 27802
I don't quite see which continuous transformation of the sphere planck is talking about, could you elaborate? In any case, I haven't checked all the details, but I think they can be fleshed out, and the following algorithm, running on both robots of course, will work: Name the start position of a ro...