Favorite science and math paradoxes thread? I'll start.

>>7692153
Fuck off

>>7692153
none of the things you named are paradoxes

Don't you have college applications to fill out OP

>>7692153
Lightyear long pole communicates information faster than light

My favorite math paradox is how if you get 367 people in a room, two of them will have the same birthday.

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>>7692153
>thinks Schrodinger's cat is a paradox

Ladies and gentlemen, i give you the average /sci/ browser.

>>7692153
Aside from the stupidity of OP I think one interesting exception to the 2nd law of thermodynamics is evolution of life itself. It's the one process I know of that tends to move towards order.

Physicists be mad.

>>7692212
>calls OP stupid
>posts stupid bait shit
Kill thineself

>>7692153
>banach tarski

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From /lit/, my new favorite lolcow board.

>>7692197
>Monty hall
that's not a paradox either

OP thinks he's smart because he understands 2 taught experiments

>>7692153
OK, what about the two envelopes problem?
I've got two envelopes, each with a check in it.
One check is twice as much as the other.
Could be $1 and $2, could be $1,000,000 and $2,000,000.
You know all this.
You can pick either envelope, no telling which is which.
After you pick, but before you open, you have the option to switch.
Should you switch?
(cont)...

>>7692240
...(cont)
It seems like it couldn't possibly matter whether you switch, but wait!
Let's call the amount in the envelope you picked "x".
You don't know how much it is, but let's try comparing it to the other envelope.
If switching gets you more money (50% chance), the other envelope has 2x dollars.
if switching gets you less money (50% chance), the other envelope has 0.5x dollars.
The two equally likely outcomes average to 1.25x.
Why/how am I wrong?

So far this is the standard "two envelopes problem", and it's pretty easy to solve.
But check back later, because I've got a variation that I can't figure out.

>>7692240
Any interpretation of this for which the answer is "it doesn't matter" does not understand the principals of probability. The Monty Hall thing only works because he's guaranteed not to show you what's behind the door you chose so you've lost independence and gained information.

>>7692245
>Any interpretation of this for which the answer is "it doesn't matter" does not understand the principals of probability.
Hmmm...
Any logic I give (including>>7692244) could just as easily be applied to the envelope you didn't pick.
They can't both be the better choice.
The symmetry should make it obvious that switch vs stick doesn't matter.
The real puzzle is: "what's wrong with this idea: >>7692244"

>0.999=1
nice bait

i love legit paradoxes

>>7692262
>i love legit paradoxes
By definition, no paradox is "legit".

>>7692244
You've pretty much breached the realm of probability and are no longer modelling what is actually going on. Probability only works if the two rolls are independent of each other, but your expectation of the switched envelope is dependent on your expectation of the unswitched envelope. Put simply, you cannot create new information out of no where and the value "x" is new information.

One envelope has y in it and the other has 2y. If you pick one you have 50% chance of it being y or 50% chance of it being 2y.

On the condition that it's y then switching will get you 2y.
On the condition that it's 2y then switching will get you y.

Without further knowledge the expected value of not switching is 1.5y and the expected value of switching is 1.5y.

>>7692212
2nd law of thermodynamics is irrelevant you piece of shit, it only works in a closed system, we have a sun which gives us a high amount of energy.

>>7692266
thanks fag i wasn't sure

>>7692268
the value you get when choosing any of the envelope is 1.5y

when you switch the envelopes is like choosing again so the value is still 1.5y

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>>7692268
tldr: "x" isn't the same in both the cases I present.
Very good.

Now what happens if you open the envelope *before* you decide switch vs stick?
Lets say you discover the envelope you picked has a check for $10.
Now let's give you the choice of switch vs stick.
No more "x".
Switching will get you $5 or $20, both equally likely.
Seems like you should pick "switch".
But wait, couldn't you have just pretended to open the envelope in the first scenario?
The same logic in this version would apply regardless of the dollar amount you discover by opening the envelope.
I'm genuinely lost, help me out here.

>>7692287
If it is known before you open the envelope that one of them had double the other then we're back in the same position. The actual value of one envelope does not give you new information because it could be either y or 2y.

A scenario where it would be different is if were given an envelope and it had a set sum in it, say $10. And then a new envelope were created at random to be either $5 or $20. Do you see how NOW the information is dependent on the value you opened whereas before it's independent? NOW switching would be better, but if both envelopes were created at the same time then switching is irrelevant (at least from a probabilistic view).

>>7692287
>tfw a shitthread turns interesting

>>7692238
> taught experiments
> taught
Must be a togh life with Down- syndrome

>>7692287
Even though the statistics are easy to explain it's hard to explain why this is so counter-intuitive. I guess it's simply that people value information that they HAVE more than abstract information they you're told.

You want to believe that holding $10 gives you new information about the initial conditions of the trial: now that I have $10, there's a 50% chance that one was $20 and the other was $10 or there was a 50% chance that one was $10 and the other $5. But that's not true. Just because you don't know which one it is does not mean they are both equally likely. In fact you have no means of measuring the probability of the initial conditions.

>>7692306
they are usually taught in high school, he said nothing wrong

>>7692287

You have 10 dollars if you switch you either get 20 or 5 so expected utility is 12.5.

Someone make this go away im retarded. Should be exact same way as other situation?

>>7692153
Sleeping beauty problem
From wiki:

Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: On Sunday she will be put to sleep. Once or twice, during the experiment, Beauty will be awakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes her forget that awakening. A fair coin will be tossed to determine which experimental procedure to undertake: if the coin comes up heads, Beauty will be awakened and interviewed on Monday only. If the coin comes up tails, she will be awakened and interviewed on Monday and Tuesday. In either case, she will be awakened on Wednesday without interview and the experiment ends.

Any time Sleeping Beauty is awakened and interviewed, she is asked, "What is your belief now for the proposition that the coin landed heads?"

Somebody please nuke this fucking board.

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>>7693228
>Someone make this go away im retarded. Should be exact same way as other situation?
I know, right?

>>7693231
I don't get it.
50% of the time, she's interviewed only on Monday,
50% of the time she's interviewed twice.
Either way, there's a 50% chance the coin landed heads.
She'll be asked twice if it's tails, sure, but even then, each time, the answer is 50-50.

>>7692266
Wait, I thought that was the point. It is a paradox in itself. Or am I being dim here.

>>7693277
No, he's just being pedantic and unimaginative. Probably a CS student.

>>7693284
Figures

"This logical sentence is false"

>>7693277
i was posting grade A shit all morning and i raked that sucker in

>>7693263

If the experiment happens 1500 times. She will be expected to be awoken .5*1500+.5*1500*2. or 750 interviews where heads was flipped and 1500 interviews where tales was flipped. Thus each time she is awoken the chance is 1/3 of heads. This seems like a frequentist interpretation? I was initially convinced of 1/3 but now I think its 50/50 even though heads is wrong more then 50% of the time she is interviewed its not just intuition but I can't seem to put my logic into words. Pretty good problem imo. I'll think about it more latter.

>>7693316
Look at it this way: What if she were not awakened at all if the coin were heads. Then 100% of the time she was woken up she should know that the coin was tails.

Or if that's too trivial, instead say that if it landed heads there was a 50% chance they would wake her up whereas if it landed tails then there was a 100% chance they would wake her up. The conditional probability of it having been tails had she been woken up is 66.6..%.

It's the same concept. It really depends on your interpretation of "should" in the question "what should she say?" (or rather "belief" in the question as you phrased it) Is it better be wrong once 50% of the time or wrong twice 50% of the time? If you lost $1 every time you were wrong or something then obviously the expected value would be better if she said she thinks it landed tails.

>>7693349

Not originally my question and I believe it is just a copy from wikipedia. Sure if every time you wake up you say it was tails you will be right more 2/3 vs 1/3. But does that mean every time you wake up you should believe there is a 2/3 chance the coin was tails? I believe The question wants what degree of probability you assign the coin flip having been heads.

>>7693295
ur shitty sentence can be both illogical and true at the same time

>>7692190
the pole would compress/bend in parts -- the speed that the energy would travel through the pole would be FAR slower than light

>>7693367
"Belief" is not a mathematical definition. You could "believe" that it's heads 50% of the time because you think that it doesn't matter how many times you're revealed to be wrong, it only matters what you determine. Someone else might "believe" that it's heads 33.33...% of the time because he finds that the way the survey is set up offers no continuity of self between the two instances of the tails set up and thus there are 3 separate theoretical answering people and that he has an equal chance of being any one of those people, most of which woke up in a world where tails was flipped.

What do YOU believe?

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>>7692194

>>7693395

Im not really interested in semantics. If the sleeping beauty is perfectly rational what probability will she assign the coin having been heads considering the information that is given. Though tails will be sampled more the experiment is still equally likely to occur in both variations. Saying tails every time you wake makes you right 2/3 times it doesn't mean the coin you flip at the start will be tails 2/3 times you flip it. Would the information that you have woken up in the experiment really make it more likely you are in the tails experiment given you will always wake up least once.

>>7692183
>>7692183
>>7692183

>>7692272
Indeed. See: complexity theory; spontaneous order

>>7692235
Holy shit, they don't understand incompleteness at all

>>7692235
>>7692235
Jesus fuck. Philosophy people tend to be retarded too.

>>7693374
no it wouldn't get schoold boi

>>7693439
First I'm not answering the question that was asked and now the new question that is asked is the one I was answering before.

She ascribes that there was a 50% chance that the coin WOULD HAVE been heads or tails. She ascribes that there is a 33.33...% chance that the coin HAS BEEN heads given the new information that she is awake. Information which is DEPENDENT on the flip of the coin. The information that you have woken up gives you information about the roll because the PROBABILITY that you will have waken up to a tails roll is greater because it happens twice as often.

If you want to get overly into semantics (which you appear to want to do despite statements to the contrary) there IS some ambiguity of selection with regard to the instances of persons being not randomly chosen but a continuity of a predetermined person, but this can only possibly cause different answers than the statistical explanation on a philosophical level, not a mathematical one.

>>7692235
that's fucking hilarious

>>7692287
Why not just switch? If I get it wrong I get half of the cake. If I'm right I get twice the cake. Either way I get cake. The odds of me getting more cake is in my favor regardless.

Well.. Unless the cake is a lie.

>>7693462

I can see why you think it is obvious. But i still have reservations. I just don't see how being woken up really introduced new information to the problem, you say the information is dependent on the flip but how is it dependent if that exact information is introduced regardless of the outcome of the flip? I have tried thinking of the problems in extremes like if it is tales the person is put to sleep and woken up again and again for the rest of their life but it is no help. Both answers still seem like they could be correct. I guess it might just be a problem of semantics/definitions as you kind of said, but i don't think the ambiguity is where you seem to say it is.

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>>7692235

>>7692234
So much this

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>>7693462
Another anon trying to chime in here

Something you seem to take for granted is that the probability of having woken up to a tails roll happens twice as often because it has twice the amount of awakenings a heads roll would have. However, could it not be viewed so that the awakenings for tails happen with a lower probability?

Suppose that the coin falls a tail and she is informed on being awoken that the coin is a tail. She still does not know whether she is in the first (B) or second (C) awakening. In fact, the probability that she could guess her correct awakening of these two given this supposition is 1/2 (this probability being based on the equal division of a two-day time interval). If the coin fell as a head and she were told of this fact there is only one awakening which occurs with probability 1 (outcome A).
It is easy to compute the composite probabilities available to SB. The probability that the coin falls a head and she knows which awakening she is at is P(H)P(A)=1/2x1=1/2. The probability the coin falls a tail and she is at the first awakening is P(T)P(B)=1/2x1/2=1/4. The probability the coin falls a tail and she is at the second awakening is P(T)P(C)=1/2x1/2=1/4. So the probability of a head is the first alternative 1/2 and the probability of a tail is the sum of the second and third ones 1/2.

>>7692197
A cat being dead and alive at the same time certainly contradicts the laws of logic. Hence a paradox.

>>7692153
Hello newfriend

>>7692153
The grandfather of all paradoxes

>>7694136
I think the paradox is the box. You don't know if the cat is alive or not

>>7695637

The point is the cats state as described by a particular interpretation of quantum mechanics is both alive and dead which is paradoxical.

>>7695657
Yeh. I Agree. The point is the state of the particle. Layman here. Should've thought more about that before posting

If a dog and a dolphin can get along, why can't our mom and his dad?

>>7695657
On third thought I think I was right with my thought process. We were arguing whether it was a paradox or not. I agree with anon that it's not. It's more of an analogy for a scientific principle. What I was saying was the paradox would be the box because you can't open it to confirm the state of the cat. Again layman but I'm familiar with the analogy. Or paradox. Whichever it is

>>7695657
The point of the analogy/principle is the state of the cat though

>>7695657
Although as a natural law it does defy logic. I'm not sure though if a natural law can defy logic. It is, what it is. I'm stumped

>>7695869

That was my first message on the subject. The point of the scenario is to demonstrate the seeming failure of an interpretation of quantum mechanics to model it. If someone subscribes to the idea of wave function collapse upon observation then what does this mean for the cat before it is observed? The box can be opened to check the state whenever you want but if you believe the wave function collapses upon observation then where does that leave the cat if you have not checked on it?

If someone believes in wave function collapse upon observation then they must reconcile the fact that this model predicts prior to opening the box the cat is neither alive nor dead, with the fact that it seems obvious the cat must already be either alive or dead prior to observation.

You can think about it any way you want but someone describing it as a paradox really isn't wrong.

>>7692197

>thinks he is smart for telling of an obvious bait
>is still wrong

>>7695869

I will add if you are familiar with zenos paradoxes. schrodingers cat is similar.

>>7692194
kek

>>7694136
No. It's not a paradox. The point of it is to demonstrate that quantum mechanics is absurd on the macroscopic scale and goes against your intuition.

>>7695637
a box or a pussy,
'tis the question

>>7695988

Ok i guess nothing is a paradox. No that is not the point see >>7695961


>>7695961

>complete and total bait OP
>75 replies
^^^when you know this board shit affff

>>7692153
The paradox of why you made this thread when none of those are paradoxes.

>>7694136
>>7694136
>A cat being dead and alive at the same time certainly contradicts the laws of logic. Hence a paradox.
It doesn't defy the "laws of logic," the normal interpretation of QM just doesn't cleanly fit in with *classical* logic.

There has been a lot of work done to show how it's perfectly compatible with logics that don't take LEM to be axiomatic, such as some intuitionistic and many-valued logics

>>7692153
the only paradox I see here that your post was so stupid that you should not be able to breathe.

>>7696017
you dont get the point
you cant apply quantum physics on a bigger scale. thats the point