/sci/ - Science & Math

http://en.wikipedia.org/wiki/List_of_paradoxes
I win
thread over

>>5263811
>http://en.wikipedia.org/wiki/List_of_paradoxes

That's lame man. Pick your favorite one or choose one I have never heard of before that you think is tricky

Schrodinger's cat

> A paradox is a statement or group of statements that leads to a contradiction or a situation which (if true) defies logic or reason, similar to circular reasoning.
It's the opposite of /sci/. Take this infantile crap to somewhere else

>>5263791
doesnt account for acceleration?

Is this really a paradox?

>>5263791

this is fucking dumb. it's not a paradox, simple logic overcomes this.

>>5263840

The cat certainly is both alive and dead until someone observes it, correct?

>>5263854

Its the fact that he has to make up an infinite amount of half-distances. It's the whole .99999 = 1 argument again used to solve it

>>5263791
If "nothing" is a valid answer to "what's in the box" then there is no such thing as "an empty box."

>>5263868

What does empty mean then?

>>5263867
What if the cat observes itself?

>>5263880

>>5263840
No, the cat is either alive or dead. Not both.

>>5263880
Holy shit this

lol@semantics

c'mon. just agree on a language

pascal's wager

>>5263840
>>5263867
>>5263880
>>5263910
>>5263915
Obligatory picture

>>5263791
Solved by the fact that series with strictly positive terms can still converge to a finite number.

>>5263840
Solved by decoherence. Big macro systems can't be in a superpower state.

My turn: Fermi paradox.
Life on Earth basically appeared almost as soon as it wasn't a ball of molten metal.
This tends to show life should have a fairly high chance of developing.
So where da aliens at?

>>5263939
>This tends to show

Oh look, it's non-sequitur time.

>>5263939
>This tends to show life should have a fairly high chance of developing
wrong

>>5263878
Nothing.

heh

>>5263939
>superposed
Fuck autocorrect.

>>5263943
How so?

>>5263947
Not the poster you're replying to, but it's your burden of proof. If you think your conclusion logically follows, then substantiate it. Protip: You can't, because it doesn't.

>>5263944
Considering the short time it took to develop, it's more likely that the odds where high than low.
Do you even chi square?

>>5263880
>What if the cat observes itself?
>>5263880
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>>5263880
dude oh my god

>>5263865
no.

>>5263957
>sample size of one

Cool statistics you got there.

>>5263939
>Big macro systems can't be in a superpower state.
Define "macro"

>>5263939
>>>5263791 (OP)
> Solved by the fact that series with strictly positive terms can still converge to a finite number.

no.

>>5263880
Quantum immortality. Now that's a paradox for you btw.

>>5263947
>How so?
>fuckload of galaxies
>fuckload of stars
>fuckload of planets
>life happens to develop on one of them
therefore life has a "fairly high" chance of developing

>>5263962
Can you even into probability?
It's more fantastic to claim it's just a coincidence than to say the odds were high.
Again, can you even into chi-square?

>>5263968
That's not even a paradox.

>>5263971
I can into probability and you obviously can't.

>>5263970
>durr
Oh look, another high schooler who doesn't understand probability.

>>5263976
It becomes a paradox when the cat observes itself and finds out it is actually dead.

>>5263880
then it must be alive

Is the word "heterological" heterological or autological

>>5263981
it means before the experiment

>>5263976
Of course it's a paradox. It's obviously a false concept, but it kinda follows from some restricted kind of model. Just like Achilles and the tortoise.

>>5263987

>he thinks consciousness is material

>>5264004
>>/x/

>>5264004
He didn't even say anything about invisible non-interacting entities.

I like Hempel's paradox
http://en.wikipedia.org/wiki/Raven_paradox

>>5263999
>Of course it's a paradox.
It really isn't. There's nothing paradoxical about it. It's based on ridiculous premises, but nothing about it is self-contradictory or illogical.

A /sci/ related paradox : http://en.wikipedia.org/wiki/St._Petersburg_paradox

The Monty Hall Problem

The probability has to be 50%.

>>5264019
>The probability has to be 50%.
but it's not. it's not a paradox, you're just stupid

>>5263939

Possible reasons
1. We're the most advanced here so far
2. Distances are too long for any advanced civilization to contact us
3. We are just one civilizations out of many, therefore advanced civilizations see no reason to observe or cooperate with our mundane attempts at contact
4. All advanced civilizations follow an advance code of observation so as to not disturb us with too high techology that may possibly destabilize our progress
5. We have not learned any "advanced" modes of communication yet to contact advanced civilizations; a certain criterion must be reached before we can join the "club"

-Quoted from "The Limits of Science and the Science of Limits"

>>5263971
no evidence we are the only existence of life

>>5263939
no evidence we are not the only existence of life

>>5263977
I'm sorry to say you don't.
Consider probability of life appearing per year.
Consider resulting probability of life having appeared as soon as it did or sooner.
Apply chi-square.
Surprise, it's fairly high.

And before you go "hurf surf one data point", it's taken into account into the chi.

>tfw Internet badasses think knowing probability means repeating "hurr sample too small" every time they are confronted with a probability problem

>>5264016
Again, same for most famous "paradoxes", see Achilles and the tortoise...

>>5264025
>no evidence we are the only existence of life
I never made that claim. I'm merely reminding you of the fact that there's no evidence for aliens either. By now you have not only shown your lack of reading comprehension and your ignorance of probability theory but you also committed the "absence of evidence is evidence of absence" fallacy. You are the second dumbest person I met today.

>>5264031
Would you please formalize that in mathematical language? What's your probability space and your probability measure? You do know basics of measure theory, don't you? I mean if you didn't, you wouldn't talk shit about probability, would you?

>>5264032
Again, it's not a paradox and your comparison to Zeno's paradoxes is simply wrong, because those actually do create illogical, paradoxical situations.

>>5264031
>Consider probability of life appearing per year.
Zero, because there are finitely many organisms that have ever lived on earth and time is infinite
>Consider resulting probability of life having appeared as soon as it did or sooner.
That doesn't even make sense.
>Apply chi-square.
Pointless with an expected frequency of zero.

>>5264019

Not a paradox, assume the most likely event (2/3's of the time) which is you choose a door that has a goat behind it, the host reveals the door that has the other goat behind it, then the unopened door MUST have the car.

tl;dr : You pick a goat 2/3 's of the time ∴ if you switch you will win 2/3 's of the time.

Even Erdos refused to believe you were better off switching...

>>5263841
that IS /sci/

>>5264070
>two choices
>one is goat, the other isn't
>implying probability not 50%

its a fucking paradox

Then the cat would be alive

>>5263933
This.

6 = A(x+1) + B(x-1)

Fine.

But then they solve and get A = 3 when x = 1 and say that no matter WHAT x value we put in there A will equal 3.

But if I put in x = -3 then 6 = -A - 3B. So let A = 0 and B = -2. This ALSO solves the equation. Why?

>>5264082

Every time you pick a goat on your first door you win (because you switch).

The probability of picking a goat on your first door is <div class="math">\frac{2}{3} \therefore</div> you will win <div class="math">\frac{2}{3}</div> 's of the time.

>>5264115
Then I will lose when I switch, because 1/2 is less than 2/3.

>>5264082

Every time you pick a goat on your first door you win (because you switch to the car).

The probability of picking a goat is <span class="math">\frac{2}{3}[/spoiler] ∴ the probability of winning is <span class="math">\frac{2}{3}[/spoiler].

>>5264120
See >>5264118

>>5264118
>I will lose when I switch even though I'm more likely to win when I switch.

You will lose <span class="math">\frac{1}{3}[/spoiler]'s of the time. <span class="math">\frac{1}{3} < \frac{2}{3}[/spoiler]


It is better to switch.

>>5264082
It's not a contradiction. You are looking at probability the wrong way. What you are saying is that the 2 outcomes have equal chances of occurring when they actually don't. Just because there are 2 choices or outcomes doesn't make it a 50/50 shot.

>>5264145
I had a chance of 2/3 to win after the goat was released. If I switch I have a chance of 1/2. I dont' want to reduce my chance.

>>5264149

Why are you talking about goats being released?

>>5264149

That switching has a probability of 2/3 of winning the car runs counter to many people's intuition. If there are two doors left, then why isn't each door 1/2? It may be easier to appreciate the solution by considering the same problem with 1,000,000 doors instead of just three (vos Savant 1990). In this case there are 999,999 doors with goats behind them and one door with a prize. The player picks a door. His initial probability of winning is 1 out of 1,000,000. The game host goes down the line of doors, opening each one to show 999,998 goats in total, skipping over only the player's door and one other door. The host then offers the player the chance to switch to the only other unopened door. On average, in 999,999 out of 1,000,000 times the other door will contain the prize, as 999,999 out of 1,000,000 times the player first picked a door with a goat—the chance that the player's door is correct hasn't changed. A rational player should switch.

>>5264155
The guy opens a door and releases a goat. Then there's only two doors, probability becomes 1/2.

>>5264171
Don't post copypasta.

>>5264175

You don't have to try and read this time, you just have to look. This is hopefully easy enough for you to follow.

The barber is a man in town who shaves those, all those and only those men in town who do not shave themselves.
Who shaves the barber?

>>5264188
Can't be right. The probabilities in the branches don't add up to 1.

>>5263811
most of those suck

>>5264194
This isn't middle school.

>>5264237

>says the person who can't into middle school probability

>>5264229
Then why are you here?

>>5264239
>projecting

You are the one who doesn't even understand that probabilities have to add up to 1.

>>5264194
If you switch every time you will win <span class="math">\frac{2}{3}[/spoiler]'s of the time because you pick a goat <span class="math">\frac{2}{3}[/spoiler]'s of the time.

Is this really that hard to understand?

>>5264249

http://en.wikipedia.org/wiki/Game_tree

>>5264253
I don't want to pick a goat, I want to pick the car.

>>5264194
(1 + 2) / 3 != 1

Thanks sci! you teach me new things every day.

>>5264257
What he posted wasn't a game tree.

>>5264261
1/3 + 0 =/= 1
2/3 + 0 =/= 1

>>5264258

You pick a goat <span class="math">\frac{2}{3}[/spoiler]'s of the time because there are 3 doors and 2 of them are goats.

Imagine you pick a door that has a goat then the host reveals the other door that has the goat, the unopened door MUST CONTAIN THE CAR so you MUST switch if you want the car.

This happens <span class="math">\frac{2}{3}[/spoiler]'s of the time therefore you will get the car <span class="math">\frac{2}{3}[/spoiler]'s of the time.

>>5264268
jebus you are stupid.
The only random part about the monty hall problem is the door you choose at the start, 2/3 odds of goat, 1/3 of the prize.

Swapping gives you the prize if you picked a goat, and gives you a goat if you picked the prize. Probability of all outcomes adds up to 1, swapping is the superior strategy.

This statement is false.

<span class="math">10 + t * v_t = t * v_a[\math]

What is it with ancient philosophers being retards about moving objects?[/spoiler]

>>5264277
There are two doors. I could swap a hundred times, it wouldn't change anything.

>>5264285
either you're trolling, or you're stupid beyond help.
Monty hall has been explained enough in this thread, no point in going on with it.

>>5264268

Retard version :
- You are more likely to pick a goat so pretend you always pick a goat.
-Host man shows other door which has goat.
-Unopened door must have car.

>>5264281
It all changes when one goat is released. Then there's only two doors left.

>>5264284

Oh shit. Wrong slash.

<span class="math">10 + t * v_t = t * v_a[/spoiler]

Why was movement so hard for ancient philosophers to understand?

>>5264290
>pretend you always pick a goat

I don't. I can pick the car. If there were three goats the game wouldn't make sense.

>>5264294
>doesn't understand probability
>yells "troll"

Go away, underagedb&.

>>5263987
The cat keeps itself alive using the quantum Zeno effect. That's why cats are immortal.

>>5264298

You CAN pick the car WELL DONE!!!!!!!

But you can also pick a GOAT!!!! In fact there are 2 of them !!!!!!

It is more likely you pick a goat every time!

We use this thing called probability to help us with questions like these!

If you are more likely to pick a goat every time then it is better to play as if you HAVE picked a goat everytime!!! This is called IMAGINATION!!!

>>5264310
Math works with numbers and equations, not with imagination.

>>5264311

You know about numbers!!

And that big word equation as well!!

I am very impressed with you!!

I'm ignoring the "famous" part.

Consider a mass m subject to a constant force F, starting from rest at time t = 0. If K(t) is its kinetic energy and v(t) its velocity, then
<div class="math">\frac{dK(t)}{dt} = Fv(t) = F \sqrt{\frac{2 K(t)}{m}}.</div>Since K(t) = 0 implies dK/dt = 0, the mass should never start moving.

>>5264311
http://www.youtube.com/watch?v=0NkdEfvmr5g

Everyone calm the fuck down. The Monty Hall problem and related experiments like the boy/girl problem are inherently subtle. In the case of Monty Hall the situation depends heavily on how the host comes to open the door with a goat behind. You see, if the host will always open a door with a goat behind by looking at what's behind the door, then a probability theoretic analysis gives you that the best way to proceed is to always switch. HOWEVER, if the host randomly opens any one of the two remaining doors and it happens to be a goat, then it really doesn't matter what you do. The paradoxical part here is that if you haven't seen the game being played before or haven't participated in it yourself, at that instance when you're in the show you really can't know whether switching or not doing anything in particular is preferred. If you however are the director of the show and know that the host will always consciously pick the door with a goat behind it then it makes perfect sense to switch if one day you're part of the game. To rephrase, the paradoxical thing here is that depending on your prior knowledge of the process with which the hose opens a door, there are different preferred strategies, even if the practical outcomes are both the same (i.e. the host opening a door with a goat behind it). THIS is what trips most people up, and hence one has to be very careful with the wording to include the rule that the host will ALWAYS open the door with a goat behind it. If you formulate the whole thing in way which only talks about one instance where "oh you pick a door, the host opens another one showing a goat, what do you do?", then it really isn't clear at all what should happen.

>>5264339
dK(t)/dt = 0 does not imply a(t) = 0

>>5264383
>then it really isn't clear at all what should happen.

Yes it is, you switch = 2/3 chance of winning, you don't 1/3 chance of winning, whether the host knows what's behind the doors or not provided he opens a door showing a goat. When the host shows a goat, whether it was planned or not, you should always switch because then your probabily of success goes from 33% to 66%.

>>5264339
What you have there is an ODE for K(t) which has other solutions than K(t)=0. There is no paradox there, and if you try the solution K(t)=a t² you see that this is a solution for some value of a. So the mass should indeed start moving.

>>5263791
The problem with your shitty paradox is you're applying mathematics to a physical problem

>>5264383
if the host randomly opens a door revealing a goat, switching is still superior, if he opens the prize then you loose no matter what since there are only goats in your remaining options.

Doesn't matter how the host picks his door, just that you now know that there's a goat behind it.

Why can't /sci/ into conditional probability?

>>5263865
No, it's basic calculus.

>>5264483

It's not Calculus. It's Analysis you dumb, retarded mongoloid pleb.

>>5264500
You can use integration to solve it.

Sir! The gates to the truth is guarded by confusion, and paradox:

Thus: How can you have Tea and no Tea at the same time?

>>5264311
Awww where'd the Monty Hall Troll go.
I was laughing my ass off!
Come back for more shenanigans

>>5263915
>doesn't understand Schrodinger's cat

I'm a senior at a vocational school and I'm 'majoring' in Architectural Drafting. I'm sort of having an existential crisis.
Is anyone here knowledgeable in this field? Is this a good thing to do for a living?

>>5263880
>>5263910
>>5263922
>>5263961
just...wow. what a bunch of retards. If the cat observes itself then obviously it is fucking alive, doesnt it?

>>5265019
*isnt it?
before someone starts bitching

>>5264048
No, they don't. They come to a conclusion that diverges with our observation of reality and leave it at that. Quantum immortality does the same.

>>5263791
Most paradoxes result from interpretation. For example, most would consider Cohen's proof of the independence of the CH from the axioms of set theory to be paradoxical, but given the structure and interpretation that mathematics is now accustom too, this technique of proof is no longer thought of as paradoxical. Instead, it is called forcing. Same could be said for Russell's paradox. It is only paradoxical if you ignore the restraints of the VCP.

>If we are all so smart, why tfwnogf?

"A gender dysmorphic male becomes a lesbian."

It's an interesting concept but not necessarily a paradox. We were discussing this kind of gender binary philosophy the other day and this quote popped up.

>>5265019
Jesus are you guys kidding me? Do you not understand what a thought experiment is? The Schrodinger's cat business was to help explain how two wave functions can exist until an observer causes them to collapse. Particles aren't cats.

>>5263880

this statement already presupposes that the cat is alive;it would have to be alive to observe itself

>>5265225
Keep in mind it is a quantum cat and can be dead and alive at the same time.

>>5265153
>Particles aren't cats.

but cats are particles

>>5264283
Statement "truthness" can not be an element of itself. This is a axiom of logic we agreed upon i do believe.

If you think otherwise solve this problem; There is only one barber in a village who cuts everybody's hair who doesn't cut it themselves. Who cuts the barber's hair?

>>5263880

Regardless, Schrodinger's cat was used to poke fun at the idea of quantum randomness, not be sued as an analogy towards it.

The idea behind this being that, of course, a cat being simultaneously alive and dead is absolutely absurd.

>>5265292
since he only cuts the hair of those who don't cut their own hair it's obvious that he simply cuts his own hair.

>>5265240

That's a nice fallacy there;
"Oh, <span class="math">A \Rightarrow B[/spoiler], so with my tiny smidgen of logic I'll assume that <span class="math">B \Rightarrow A[/spoiler]!"

>>5263878

people dont usually account for air when they open a box and dont find what they expected.

>>5263791

>Paradox

The apparent paradox is a result of the flawed assumption that time progresses in discrete and decreasing intervals.

What happens when Pinocchio says his nose will grow?

>>5265615
Well if he's telling the truth his nose won't grow, therefore making it a false statement and causing his nose to grow, thus making his initial statement true so

fuuuuuck

Envelope Paradox

I have 2 envelopes. Both of them have money, but one is double the other.

I open up envelope A and receive $A. I can keep it, or I can switch and take whatever's in envelope B. Envelope B has the property that it is equally likely to have double as it is to have half. Therefore the expected value of switching is 1/2*2A+1/2*1/2A = 5/4*A.

This is true if we do not open the envelope. Both envelopes have the property "the other envelope is equally likely to be worth twice as much as it is half as a much" so if we open neither envelope and are given the chance to take the other envelope as much as we want, we can switch envelopes n times and receive an expected value of A*(5/4)^n which increases without bound. Therefore a method exists in which we can create infinite money from 2 finite sources as long as we know neither of them.

>>5263791
Infinite geometric series has a limit.

Clearly can see that 2/3 times you win the car if you switch.

>>5265630
you redefine A from being the smaller amount to the larger amount which invalidates the equations.

No math student would make that mistake, are you in high school?

>>5265661
No I'm trying to trick you.