Das Paradox

[artanis_neravar]

Given the vast universe it's virtually impossible that there aren't several species that have figured out how to traverse between galaxies. It is also near impossible that they wouldn't at least want some data on other species. It is also near impossible that at least one of them wouldn't want to either enslave us or befriend us.

So where the fuck are they?

They have a lot of planets to explore, maybe they just haven't made it here. Or they have seen how destructive we are now and are slightly afraid

 

[thethingthatlurks]

"Does a set of all sets contain itself?" Taken from Portal 2

So i ask you this! What is your favourite Paradox, also if you like you can also comment as to why and if you fully understand it.[/b]

There is no set of sets
Although strictly speaking a set does contain itself as a subset, although that is one of the two trivial subsets (the other one is the empty subset).

Sooo...paradoxes, but not really. 1+1=0, 1+3=0, 2+5=0, etc. Yep, those are true statements, and those are indeed integers. If you can, prove why.

I would like to see you proof

Sure, might as well make the most of my math degree
Ok, I'm going to do them case by case, A, B, C.
A) I did say 1 was an integer, and that was indeed correct. However, I did not claim that this operation was taking place in the ring of integers. We are in the group defined by the set of integers modulus 2 (a==b mod 2), with the operation being addition. That means that all elements in the set are the remainder when a number is divided by 2, ie 0 (for even numbers) and 1 (for odd numbers). Since even plus even equals even, the remainder becomes zero. Hence 1+1=0 in this particular construct.
B) Same thing, only this time we're in the group of integers modulus 4, again with addition being the operation.
C) Same thing, but modulus 7.

There you go, math made bizzare. 'course, there are also "proofs" that 1=0 in the reals...

 

[Redingold]

There is no life in the universe (operating under the assumption that there are an infinite number of planets) There are an infinite number of planets in the universe, however we know that no all planet have life, therefore only a finite number of planets in the universe have life. to figure out the percentage of planets with life you need to divide a finite number by infinity. For simplicity sake I'm going to use 1 for the finite number and % to represent infinity. in order to solve 1/% you must take the limit of 1/x as x approaches infinity, as x gets large 1/x gets smaller (1/4 is smaller then 1/2). The limit of 1/x as x approaches infinity is 0 therefore there is no life in the universe and everyone you meet is just a figment of your imagination.
(From the Hitchhikers Guide to Galaxy I just used calculus to prove it)

Fortunately the universe is finite.

Prove it

It started out as a point, and has expanded at a finite rate for 13.7 billion years. It cannot have grown to infinity in this time. Besides, even if it was infinite, you'd still be wrong, because infinity (the number of planets) minus any finite number (the number of known uninhabited planets) is still infinity (the number of potentially inhabited planets left).

Even if there are an infinite number of populated planets, the denominator is still a large (or faster growing) infinity and my math still works out

Ahah. No. All the infinities involved are the same size. Infinity doesn't change size simply by multiplying it by something or adding something to it. You can get different sizes of infinity, but not in this scenario.

 

[orangeban]

My favorite is not really a paradox, but statistics that blows your mind.

Imagine you are in a contest where you can win a car. All you need to do is to chose the right panel - you've got three panels to chose from. Once you point at one panel, someone (who knows behind which panel the car is) reveals one of the other two panels. Now you can either stick to the panel you've selected originaly, or select the remaining one. Which one will you chose?

You choose the other panel, because in your original choice chances are you chose the wrong panel. Very simple logic that becomes tricky because you treat the first choice seperate from the second choice3.

 

[Kingsman]

Paradox of thrift comes to mind- People save money when the economy is bad, but in doing so take more money out of the economy's circulation, thus causing the economy to worsen.

 

[meryatathagres]

Say you open envelope A and find $10 in it. You now know that the other envelope has either $5 or $20. Either option is equally probable, so your expected winnings by switching envelopes is $12.50. This is greater than $10, so your best option is to switch envelopes.

But the same argument would work however much money was in the envelope you opened. So how can it *always* be better to switch?!

That's just simple math. By switching you have chance to gain 10$ or lose 5$. 100% gain is always better than 50% loss.

 

[meryatathagres]

Yes, 33% for you, and 50% for them (assuming they don't know what has happened up to this point and just believe that there are 2 doors with a car behind one of them)

Doesn't require awareness. In any case half of the wrong doors have already been taken out of the equasion. It's easier to get your mind around it if you think of it as not choosing right, but by not choosing wrong.

 

[The Unworthy Gentleman]

Well I like the old going back in time with a purpose thing. If you go back in time to let's say kill Hitler then you go back and shoot him but then in your time he is already dead so there is no reason to come back and kill him so you don't go, but if you don't go then he is still alive so you have a reason to go and kill him and the cycle starts again.

Only if you go back with the intention of killing him. If you were travelling past Hitler in your car and your car spontaneously combusted killing Hitler then you would be caught in an endless loop of going back in time and accidentally killing Hitler, it would become History and nobody would know any different. Unless I've made a mistake in my thought over this.

 

[artanis_neravar]

There is no life in the universe (operating under the assumption that there are an infinite number of planets) There are an infinite number of planets in the universe, however we know that no all planet have life, therefore only a finite number of planets in the universe have life. to figure out the percentage of planets with life you need to divide a finite number by infinity. For simplicity sake I'm going to use 1 for the finite number and % to represent infinity. in order to solve 1/% you must take the limit of 1/x as x approaches infinity, as x gets large 1/x gets smaller (1/4 is smaller then 1/2). The limit of 1/x as x approaches infinity is 0 therefore there is no life in the universe and everyone you meet is just a figment of your imagination.
(From the Hitchhikers Guide to Galaxy I just used calculus to prove it)

Fortunately the universe is finite.

Prove it

It started out as a point, and has expanded at a finite rate for 13.7 billion years. It cannot have grown to infinity in this time. Besides, even if it was infinite, you'd still be wrong, because infinity (the number of planets) minus any finite number (the number of known uninhabited planets) is still infinity (the number of potentially inhabited planets left).

Even if there are an infinite number of populated planets, the denominator is still a large (or faster growing) infinity and my math still works out

Ahah. No. All the infinities involved are the same size. Infinity doesn't change size simply by multiplying it by something or adding something to it. You can get different sizes of infinity, but not in this scenario.

Um...yes they do it's basic calculus

 

[legopelle]

There is no life in the universe (operating under the assumption that there are an infinite number of planets) There are an infinite number of planets in the universe, however we know that no all planet have life, therefore only a finite number of planets in the universe have life. to figure out the percentage of planets with life you need to divide a finite number by infinity. For simplicity sake I'm going to use 1 for the finite number and % to represent infinity. in order to solve 1/% you must take the limit of 1/x as x approaches infinity, as x gets large 1/x gets smaller (1/4 is smaller then 1/2). The limit of 1/x as x approaches infinity is 0 therefore there is no life in the universe and everyone you meet is just a figment of your imagination.
(From the Hitchhikers Guide to Galaxy I just used calculus to prove it)

Fortunately the universe is finite.

Prove it

It started out as a point, and has expanded at a finite rate for 13.7 billion years. It cannot have grown to infinity in this time. Besides, even if it was infinite, you'd still be wrong, because infinity (the number of planets) minus any finite number (the number of known uninhabited planets) is still infinity (the number of potentially inhabited planets left).

Even if there are an infinite number of populated planets, the denominator is still a large (or faster growing) infinity and my math still works out

Ahah. No. All the infinities involved are the same size. Infinity doesn't change size simply by multiplying it by something or adding something to it. You can get different sizes of infinity, but not in this scenario.

Um...yes they do it's basic calculus

You're not going at this right. It's not infinite just as a line on the surface of a sphere. It just appears so. Just because you can travel an infinite distance doesn't make the space infinitive.

 

[SextusMaximus]

I think this is called Curry's paradox:

If this statement is true, then Santa Claus exists.

It can be used to prove anything.

And what if it isn't true? Not much of a proof, is it?

It's irrelevant what the second phrase refers to. Wikipedia can explain it much better than I can: http://en.wikipedia.org/wiki/Curry's_paradox

I just exploded with laughter cause you linked to the Wiki article on curry.

OT: I always lie.

 

[SextusMaximus]

Here's an alternative to the "Which came first, the chicken or the egg?"

It is well known that when you write a program, you must compile it first.A compiler itself, though, is a program, which means that the compiler had to be written and compiled. So the question is, which came first, the Programming Language, or the Compiler?

No, because all a compiler does is convert or "translate" whatever programming language you used to build the program into a language a computer can understand - binary.

Can omni-potent god (an all powerful god) create a stone which he cannot lift.

If he can't create it then he isn't all powerful.

If he creates it but then is unable to lift it he still isn't all powerful.

Not a paradox, you just prooved the lack of existence of an Omni-potent God.

 

[Blindswordmaster]

By your argument, if I shot in the shoulder with an arrow, said arrow must have always been in your shoulder. But you know this isn't the case. On an object at rest tends to stay at rest and an object in motion tends to stay in motion, unless acted upon by another force. Physics *****!

 

[Celtic_Kerr]

Actually it's just bad math. The guests paid $27, it's true. The manager kept $2, so $27-$2=$25, the cost of the room. The $2 tip is included in the $27 paid by the guests, so there is no need to add it in.

The real question isn't "where did the dollar go?", but "where did the extra $2 come from?". $27(paid) + $2("kept") + $3(returned) = $32.

Yay math!

Wouldn't that be $25(Paid)+3(returned)+2(kept). There is no extra 2.

Yes. That's what it should be. But that's not what is being presented in the problem. The problem pulls $2 out of thin air.

It's like asking two tens for five.

You're thinking of the $27 and the $2 tip as two numgber, when they are included.

Remember, the room is only $25, not $27. So with the the %$9 they each pay for the room, $0.66666666666 of the $9 went to the door man.

What you are imagining with the extra two dollars would be if they first paid $27 (by paying $9 each) at the front lobby in the first place, but ocne they got to the door, the door man would still realize the room was overpaid $2 and pocket it as a tip. Therefore:

Paying $30 first:
They pay $30 ($10 each)
find out room is only $25
got $3 ($1 each) back
remaining $2 is pocketed as tip

$25+$3+$2 = $30

Paying $27 first:
They pay $27 ($9 each)
They each have an extra $1 in their pocket (total $3)
find out room is only $25
extra $2 is pocketed as tip

Room ($25) + Money they didn't spend ($3) + Tip ($2) = $30

The problem is designed to make you think of the money in a different way and perceive that the amounts have changed

 

[Steve Butts]

Paradox. par·a·dox/ˈparəˌdäks/: "A statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory."

There's a lot of talk about Zeno's Paradoxes but many people miss the point of them.

They're meant to be taken as a group and show the errors of two competing views of reality. The point in question was whether or not magnitudes of space or time were infinitely divisible or not. In other words, could you get down to a distance or moment so small that there is no room to divide it further? It was, apparently, a hot topic in Ancient Greece. The Paradox is not any one of Zeno's individual arguments, but rather the collection of seemingly contradictory mathematical propositions.

Those who said magnitudes are infinitely divisible had to contend with Zeno's argument about Achilles and the Tortoise. If you keep dividing time and distance, Zeno claims, Achilles never catches up. Therefore, magnitudes can't be infinitely divisible. But if magnitudes are not infinitely divisible, how does the arrow move? If the arrow can't be between the two smallest increments of time or space, then it must be warping between them. But if it's not warping from A to B, then time and space must be infinitely divisible. Which brings you back to Achilles. Zeno's Paradoxes were an attempt to refute this either/or definition of reality.

The problem was that the ancients had no mathematical value for infinity, which is the key to reconciling the contradictions. Aristotle came close to figuring it all out, but we ultimately had to wait until the fairly recent discovery of calculus and the repeating decimal before we were able to crack this problem.

 

[Ranorak]

I'm not sure if this counts as a paradox or not, but it's an interesting thought

Lets say you have a boat. As parts of the boat wear out, you replace them with new parts. Eventually, you have replaced every part of the boat. Is it still the same boat?

Better yet.
your body now doesn't have any of the molecules left from when you were born.
Are you still you?

 

[redisforever]

As for a paradox, you are standing ten feet away from your goal, with every step you take you cover half the remaining distance.

Yeah, you'll never get there, because the distance would never be 0.

 

[universaltraveller]

I'm so GLaD i joined this site today, I didn't think there would be a paradox discussion here, and thanks to Portal 2 for starting all this.

As for my favorite paradox, it's Olbers Paradox, 'Why is the night sky dark, if the universe is infinite?' Even though this does have an answer, I love all the physics it took too get there.

Also has anyone read about how quantum computers work, and how, if you try to measure the workings of the computer it simply crashes?

*edit*

Oh and I forgot, I also love the Gandfather paradox, and all the time related ones. Has anyone ever seen the film Timecrimes? Also I'm gussing people have seen Twelve Monkeys.