Quote Originally Posted by Xei View Post
He means they can't take a group of statements that they agree on,

0 + 1 = 1
0 + 2 = 2
0 + 3 = 3
0 + 4 = 4

and create a generalised statement,

0 + x = x.

I think this is more interesting than it seems on the surface, because in my opinion such a generalisation is fundamentally what 'intelligence' is; seeing a pattern and forming a symbol for a generalised circumstance. The really interesting thing is that generally (lol) such generalisations are 'unprovable' in a formal sense, if they are not tautological. Take the above, where we are conceiving the numbers in the traditional way (where 5 is a generalisation of 5 trees, 5 socks, etc.), and 0 to be a generalisation of 'no trees', 'no socks', etcetera (and + meaning 'the generalisation of what you get when you put the two together'). The other path we could have taken is defining 0 as the additive identity, i.e. defining 0 to be a symbol so that 0 + x = x for all x, but then of course any attempt to prove 0 + x = x would be a complete tautology, and would not actually refer to anything. Anyway, can you prove that 0 + x = x, given the former context? I predict that you can't. The question is what this then makes of intelligence, if the knowledge it gives us is not seemingly provable. There are many answers to this 'problem of induction'; a reassuring way to think about it is to just look around you and consider how ridiculously successful intelligence has been; there must be something to it. Indeed, from a biological perspective, its successfulness is precisely WHY we have such a thing in the first place.
Ok, so I guess I understand what he means now.

Quote Originally Posted by PhilosopherStoned View Post
I generally feel like a complete and total moron. I guess it's because of my interests and hobbies. They're not easy. Then I run into somebody of seemingly normal intelligence that can't grasp the meaning of the statement "for all x, x + 0 = x". 5 + 0 = 0? Fine. 8/3 + 0 = 8/3? no problem. Generalizing it? No can.
Maybe I was thrown off by this bit - . 5 + 0 = 0
It equals .5, not 0.

But I don't understand why you can't prove it.

Just take, as you say. 0 socks, and then put 5 socks down. You have 5 socks. Done.

Quote Originally Posted by Savy View Post
I don't necessarily think this makes you intelligent if you can solve these under 30 minutes, but it's a fun puzzle. I like stuff like this. It reminds me of that other puzzle which says things like "8 t of the o" and you have to complete the unfinished words. I assume there is a set of correct answers, but it looks everyone else is taking it as a test of creativity. I'm not sure which it actually is anymore, but I'll give it a try anyways.

a) H+K=B; Humans + Killing = Blood
b) O+H=W; Oxygen + Hydrogen = Water
c) A+W=T; Americans + War = Trouble
d) A+W=O; Apple + Woman = Original Sin
e) S+S=S; Selling + Sex = Strippers
f) B+Y=G; Blue + Yellow = Green
g) Y+Y=B; Youth + Yale = Brains

Haha yea, so I fail. I couldn't think of what they actually meant and I was running out of time, so I just went ahead and picked the most plausible thing I could think of instead. If my first instinct was right, and they do have actual answers, then I know that all of these (maybe excepting f and b) are wrong. The other type I mentioned before are much easier as word puzzles.
The test was stupid. I'll give you a hint and the ridiculous reasoning why my answers were wrong. Which is the same reason yours are wrong.

Spoiler for HINT:


Spoiler for RIDICULOUS REASON: