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It'll give too much away, but let me know if you want to know and I'll PM you..Quote:
Originally Posted by Xei
..but..
Deducing what you already can from what's been posted, why don't you have a go? BTW The original test conditions are already compromised. No-one interviewed had any access to others and their thoughts and answers, so you're at an advantage.
I didn't assume that at all. I assumed that was the answer for the last one. Which is a reasonable assumption since you quoted my answer, chuckled, and wrote that.Quote:
Originally Posted by Oneiro
I assume you're trying to say that I made the mistake that the answers were unrelated, or related. But you're trying to sound smart by being cryptic. Clever....
Where did you work?
Ok so it's obvious there's no correct answer, so you just chose the people who had answers which fit your work place the most or something like that.
Unless there's one answer which fits more.
a) H+K=B; Height + Kangaroo = Bounce
b) O+H=W; Oxygen + Hydrogen = Water
c) A+W=T; Aeons + Waiting = Time
d) A+W=O; Air and Water = Organic
e) S+S=S; SS = Ship
f) B+Y=G; Blue + Yellow = Green
g) Y+Y=B; Yin + Yang = Bi-polar
FAIL.Quote:
Originally Posted by tommo
FAIL.Quote:
Originally Posted by tommo
Wrong.Quote:
Originally Posted by tommo
Go for it tommo..Quote:
Originally Posted by tommo
Oooooh. FAIL.:(Quote:
Originally Posted by tommo
Same schoolboy error again.
PM me if you want to know what you've done wrong.
There obviously is no correct answer. I've just shown that with two different answers.
And some differ in the way I interpreted it. i.e SS instead of two words etc.
Go ahead, PM me what I "did wrong". I'll prove you wrong.
Wrong.Quote:
Originally Posted by tommo
Ha! No you won't. You're gonna kick yourself. PM on its way.Quote:
Originally Posted by tommo
a) H+K=B;
b) O+H=W; Oxygen + Hydrogen = Water
c) A+W=T; Apple + Water = Tree
d) A+W=O;
e) S+S=S;
f) B+Y=G; Blue + Yellow = Green
g) Y+Y=B; = Blue
Found another pattern. Just gonna edit this before I check the pm
Meh, fuck it.
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.
Then I feel like I have above average intelligence. In fact, I'm smarter than pretty much everybody that I meet. :(
Smarter than a chimpanzee, at least. So it seems.Quote:
Originally Posted by PhilosopherStoned
I don't understand "Generalizing it? No can."Quote:
Originally Posted by PhilosopherStoned
Of course you don't understand. It's genius talk.Quote:
Originally Posted by tommo
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. :P 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. :P
He means they can't take a group of statements that they agree on,Quote:
Originally Posted by tommo
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 Xei
Maybe I was thrown off by this bit - . 5 + 0 = 0Quote:
Originally Posted by PhilosopherStoned
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.
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.Quote:
Originally Posted by Savy
Spoiler for HINT:
Spoiler for RIDICULOUS REASON:
Read my post closer, I went to a lot of length explaining this... I was not asking for proof of '0 + 5 = 5', I was asking for proof of '0 + x = x'. If you thought I would ever ask for proof of the former then the message of my post totally went over your head; please try to read it with more concentration.Quote:
Originally Posted by tommo
This has nothing to do with Philosopher's post by the way; he was just making the point that many people can't cope with simple abstraction. I was elaborating way beyond that, Phil probably doesn't even agree with me.
I read it a few times to make sure I was getting it right.Quote:
Originally Posted by Xei
But 0 + x = x is just an abstraction. It doesn't mean anything by itself.
So all you have to do is substitute the x for a number of something.
And see if it is correct. Then you have proven it.
If you mean you can't prove it without doing that - being tautological - well that doesn't mean anything either :lol:
I don't understand you. 0 + x = x does mean something: it means,Quote:
Originally Posted by tommo
0 + 1 = 1
0 + 2 = 2
etcetera
where the symbols have the definitions I ascribed to them. The statement represents every single substitution for x, not just one. How can you possibly prove 0 + x = x by taking a single value of x and showing that it is correct? I really don't understand your meaning. Take another statement, for example, 'if x is odd then it cannot be divided [by a smaller whole number than 1] without remainder'. Well, let's sub in 1. 1 is odd and it can't be divided without a remainder. So that proves the statement..? Check it some more. 3 can't be, 5 can't be, 7 can't be. Man, there's no way this statement isn't right!
This is so clearly wrong I doubt it's what you meant, though, so could you please explain further.
ARGHHHH I should be going to bed lol
The point is, if you use something enough times and it works, it is most likely the correct way to do it.
Plus 0 + x = x can just be shortened to x = x. And anyone with half a brain knows that if you have some thing, it is some thing and not some other thing.
You prove it by changing it around (forgot what that's called now) and seeing if it works out the same way.
Your statement 'if x is odd then it cannot be divided without remainder' should be 'if ALL x...."
Otherwise you are only saying that one given odd x cannot be divided without remainder.
I'll post more tomorrow.
If all x is... odd? The correct statement is 'for all x, if x is odd, etc.', but of course that is implicit in the 'if x is odd', and the 'for all x' is often omitted. To be really strict we should be saying 'for all positive integers x, etc.', but from the context of the discussion we already knew what we're talking about. But sure.
With respect to 'if it works enough then that is likely correct': well, that is the whole point of my post; that is, the problem of induction. The point is that 'yeah that's probably right' is not in any sense a proof. What is the basis for even thinking that, because the statement checks out for a few numbers, it'll check out for all of them? Take the (for these purposes very simplified) statement, 'x is less than 1,000,000,000,000,000'. You could work at that via your method of proof for a lifetime and be convinced that it is universally correct.
Now, the most interesting part of what you said. Bearing in mind that what we're trying to achieve is a proof of 'for all positive whole x, 0 + x = x': can you delineate exactly how your proof works? As it stands, it's running roughly as
x = x
hence
0 + x = x
(because the former is just 'the latter shortened')
but what is your basis of this being a valid inference? It seems to me that what you have done is added 0 to the left of both sides, and then, on the right, used the fact that 0 + x = x. But... that's what we are trying to prove in the first place, you can't use it as part of your proof.
No no no, you guys. To understand solving for x, you must first think like x. You have stated that 'x is less than 1,000,000,000,000,000' but this is absurd, because x is a number; not a letter. Then you have the word "hence" right in the middle of your math equasion!
Furthermore, tommo stated that anyone with half a brain knows that if you have some thing, it is some thing and not some other thing, but sometimes something is the same thing as nothing and some other thing can be full of things or something.
Dummies.
Speaking of generalization, Phil, you're signature is hilarious. :)
Phil is gone, DuB.
...unless there is something I don't know.
I'll quote cloud who quoted someone else at one point
intelligent enough to know that I know very little
or "more intelligent" than 50% of the gen. pop, depending on my self-esteem.
can't measure that shit etc
Phil Stoned, or AaronQuote:
Originally Posted by sloth
tommo's objective view on subjective riddles is very silly, by the way
::facepalm::
I generally agree. I don't see why you think that I wouldn't. I thought it was fairly common knowledge that your knowledge has to start somewhere. I don't however think the situation is quite as hopeless as you're making out. The vast majority of mathematics can be proven. It ultimately comes down to things that we can't prove and I think that this will always be the case. Those things are exceedingly obvious. But dig this.Quote:
Originally Posted by Xei
for all x, x - x = 0 right? Now add x to both sides to get x = 0 + x. QED. :lol:
Or how about this one.
1 + 0 = 1. Now suppose, for induction, that n - 1 + 0 = n - 1. Then add one to both sides to get (n - 1) + 0 + 1 = (n - 1) + 1 and so n + 0 = n. :fame:
Finally, suppose (for a contradiction), that for some n, n + 0 =/= n. Then (n - n) + 0 =/= n - n => 0 + 0 =/= 0. But we know that 0 + 0 = 0: contradiction. :laugh:
Of couse In the first and last "proofs" I assumed that x - x = 0 which is equivelant (so circular) but perhaps more obvious, and in the middle one, I used induction. We need to have already developed the integers to do that and presumabley, we need what we're trying to prove to have done that.
Hum. We make mathematical models to simulate real life systems. Can we do the reverse, and create a real life model of the mathematics in question such that it can prove the math, or not?
And by "real life model" I mean the use of physical objects that we can apply definitions to such that they and their actions can perform as mathematical symbols in various operations.
Ex:
I have rocks. A rock, as made distinct from other rocks by its solid surface that makes it whole and separable from the other rocks, can represent the number one. Joining this rock with another rock will be defined as addition, and the resulting formation of rocks (when only a rock and a rock is used and not more than those) we will call the number two. Did I prove that 1+1=2, or is that inherent in the definitions I used? Also, is that any different than using the symbols on paper? :|