Heart

I'm Heart, your friendly neighbourhood admin!

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Ricki
1 hour ago, ChillaKilla said:

New mod? New mod? Election?! :ph34r::D

YOU SHOULD DO THE RUNNING FOR THE IT

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ChillaKilla
7 hours ago, Ricki said:

YOU SHOULD DO THE RUNNING FOR THE IT

IF IT WILL BE THEN I WILL BELIEVE ME

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Jayce
4 hours ago, ChillaKilla said:

IF IT WILL BE THEN I WILL BELIEVE ME

IF YOU DON'T I'LL COME SQUEAL AT YOUR DOORSTEP :P 

 

 

*High five* @Serran good to see you guys taking care of my baby ^_^

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Achromatic Kitty

Hey, I got a question for the admins... Would it break ToS if my bro-pal and my Dad were to use the same IP address to make accounts on here?

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Ricki
15 minutes ago, Kieran The Kitty said:

Hey, I got a question for the admins... Would it break ToS if my bro-pal and my Dad were to use the same IP address to make accounts on here?

Users can't have more than one at once, but if it is different people having their own separate accounts it is acceptable

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Achromatic Kitty

I'm not sure if I should let them on since they MIGHT PO a lot of people with their views...

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daveb

Why do they want accounts?

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Achromatic Kitty

Dad: Because he wants to understand our thoughts and be proven you're not a bunch of Liberals.

 

Bro-Pal: To understand why i quote "Hate women"....

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Serran
2 hours ago, Kieran The Kitty said:

Hey, I got a question for the admins... Would it break ToS if my bro-pal and my Dad were to use the same IP address to make accounts on here?

This one technically should be asked in Site Comments :) But, no, it wouldn't be breaking the rules. Just send a message to an admin so they tag that your IP will be shared with other users, so they don't think you're socking. 

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daveb

Maybe you could just give your dad access to a few members in particular... :P

 

Who hates women, you or your bro-pal? Depending on the answer, my response would also be to give them access to a few members in particular (but different ones depending) :lol:

 

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Achromatic Kitty

Me since I told them i don't do romance at all... But they accept it for now... My bro-pal uses it as a joke but I don't know if that will offend people on here...

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Heart

*shrug* My attitude is to let them on. We'll engage with them in good faith, and if they end up being jerks we'll try to let them know and help them be not-jerks. They, like everyone else, have the fundamental right to burn through the disciplinary system and get themselves banned if they so desire, of course. But there are many good AVENites that will try to talk to them and prove we're not just woman/man haters. And though I'm quite liberal, I'm sure there are those around who aren't ;)

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Kelly

The Cassini–Huygens spacecraft, launched 20 years ago and orbiting Saturn since 2004, is running out of fuel. It is scheduled for a suicide mission to dive into the planet itself on Friday.

 

The dive will be live-streamed.

 

main_900.jpg

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Heart
On 9/13/2017 at 9:29 AM, Kelly said:

The Cassini–Huygens spacecraft, launched 20 years ago and orbiting Saturn since 2004, is running out of fuel. It is scheduled for a suicide mission to dive into the planet itself on Friday.

 

The dive will be live-streamed.

 

main_900.jpg

I WATCHED THAT AND IT WAS SO EPIC!!!

 

I mean. I felt an overwhelming amount of emotions, I can't even begin to imagine how the engineers and scientists who worked on it must have felt. A truly beautiful thing.

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Kelly

This thread had somehow become the Math and Science thread. That seems fitting of the Nobel-worthy @Heart . I shall continue.

 

Bart and Lisa were done discussing work and poured each other shots of Vodka. “An infinite number of mathematicians walk into a bar,” said Bart.

 

“Again?” asked Lisa. “The bartender at the Hilbert Hotel must be overworked by now.”

 

“Yup. But this time, the mathematicians will help. On Saturday night, they will come in, have a shot, and then help serve others. One mathematician will have a shot, then he and the bartender, Gabriel, who is also a mathematician, will serve the next two. Then we have four mathematicians serving the next four, and then eight serving the next eight, and so on. They will be finished in no time.”

 

“Somebody needs to handle all of the shot glasses, Bart.”

 

“They will each bring their own. And they will all be identical. Imagine the curve of y equals one over x, from x equals 1 on, rotated around the x axis, like this.”

 

508938-7.8-50IP1.png

 

“OK, got it, Bart. How much does it hold?”

 

“One pi of ounces of Vodka.”

 

“Go on, what’s the puzzle?”

 

“As it happens, Gabriel had a bad week. He forgot about the mathematicians, and did not stock up on Vodka. He had just enough to fill his own shot glass, which was the same as those of the mathematicians, and sipped his 3.14159 and so on ounces of Vodka. When he was finished, he saw the mathematicians march in one by two by four by eight and on.

 

“He looked down at his shot glass, with wet Vodka residue covering the inside of his basically empty glass, and then to his counter, devoid of any drink of any kind, and panicked. Then he knew just what to do.”

 

“Like, what, Bart? Ask the mathematicians to go out and buy more?”

 

“No, Lisa. I gave you all that you need to know. You should be able to solve the case.”

 

What did Gabriel do in order to serve the infinite number of mathematicians?

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michaeld

I'm guessing it must have something to do with the fact that while Gabriel's glass does indeed have finite volume (pi in fact), it has infinite surface area. Kelly mentions the Vodka residue. If the residue film clinging to the glass had a constant width, there would be an infinite amount in volume, but of course it won't have a constant width. The volume left over is obviously finite because the entire glass has finite volume. So unless the mathematicians are content licking a (constant, fixed) area further and further into the glass, I'm not sure...

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Calligraphette_Coe
1 hour ago, Kelly said:
1 hour ago, Kelly said:

k up on Vodka. He had just enough to fill his own shot glass, which was the same as those of the mathematicians, and sipped his 3.14159 and so on ounces of Vodka. When he was finished, he saw the mathematicians march in one by two by four by eight and on.

 

“He looked down at his shot glass, with wet Vodka residue covering the inside of his basically empty glass, and then to his counter, devoid of any drink of any kind, and panicked. Then he knew just what to do.”

 

“Like, what, Bart? Ask the mathematicians to go out and buy more?”

 

“No, Lisa. I gave you all that you need to know. You should be able to solve the case.”

 

What did Gabriel do in order to serve the infinite number of mathematicians

 

What did Gabriel do in order to serve the infinite number of mathematicians

Invoked Hilbert's paradox and hired Georg Cantor to explain, using the concept of transfinite numbers, the _real_ meaning of the advertisement for Mathematician's All You Can Drink Night to them? 

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michaeld

Another idea (though it would make the shape of the glass a red herring). Gabriel the bartender may not have any more vodka, but he does have a collection of Banach-Tarski vodka scoops. So he starts by collecting some of the residue in the Gabriel glass. It's only a tiny bit - a sphere of only a millimetre across. But recall, the Banach-Tarski scoops are special. By taking finitely many scoops of the sphere, you can re-arrange them by rotation and translation to make any number of spheres of the same size. That's enough to give to the first mathematician, leaving some over. Now just repeat this process forever and you're done!

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Kelly

“Gabriel is screwed, isn’t he, Bart?”

 

“Not at all, Lisa. There is an infinite amount of Vodka clinging to the glass.”

 

“Nonsense. The glass holds pi ounces of Vodka and he drank almost all of it, so there is less than that still there.”

 

"The volume of the inside of glass is finite, but its surface area is infinite. You can fill it, say, with paint, but it takes an infinite amount of paint to paint it, that is, to coat the surface. The Vodka residue is infinite.”

 

“What?! No more Vodka for you, bro. I am putting the bottle back in the locker. Go to bed.” She reaches for the freezing bottle of Russian Vodka.

 

“No. Seriously.” Bart takes the bottle and pours both of them another shot. The volume of the glass can be calculated from:”

 

area.png

 

“Where A(x) is the cross-sectional area. Here, it is circles with radius 1/x so A(x) = π/x2. We have:”

 

area2.png 

“The area of a surface of revolution is:” 

area3.png 

“Here, y = 1/x, so we have:

area4.png 

 

The > is because x4 + 1 > x4

area5.png 

“As said, it would take an infinite amount of paint to paint the surface, according to mathematics. So, the residue clinging to the glass is infinite. Gabriel just needs to pour pi ounces of residue from his glass into the first mathematician’s shot glass [it helps that the droplets are mic’s Banach-Tarski scoops :) ]. Then the first mathematician drinks the Vodka until just the infinite residue is left, then she and Gabriel pour residue into the next two glasses. They drink, and then four mathematicians have a glass with an infinite amount of residue in their glasses. They pour into the next four, and so on. Problem solved.”

 

“No, Bart. Just, no. That is a physical impossibility. Eventually, the radius of the glass gets so small that a molecule of Vodka cannot fit. And the glass itself would be too narrow for a molecule of silicon dioxide to exist. The glass is thus not infinitely long in reality. Any physicist can tell you that.”

 

“Ah, dear sis. But these are not physicists; they are mathematicians.”

 

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Calligraphette_Coe

Kelly, 

 

Reading your solution, for some strange reason the idea that this was a  little like the story of Jesus' having fed 5000 with 2 fish and 5 loaves of bread after the Sermon on the Mount. Not to say either way whether the story was spiritual or miraculous, but really.... when you think about it, aren't some of what some of us do with QED in our work a bit spiritual or miraculous? I'm not the least bit religious and I think by and large, religious dogma reveals little about the universe we live in, but sometimes? Llike when you get your first look at Euler's Identity? The hair goes up on the back of one's neck, as if the Universe just winked at you and said, "There. Figure THAT one out!"

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michaeld

Kelly that solution was what occurred to me at first - in the first post. But the problem with it isn't physical - it's mathematical. The residue film clinging to the glass cannot have constant height (even if you forget about molecules) because the diameter of the glass tends to 0 the further along you go. Hence infinite surface area doesn't imply the residue is infinite. Or alternatively: it can't be infinite as the total is pi.

 

I wish there was some way of getting infinite residue from infinite surface area, but I don't see it. :(

 

The feeding of the 5000 also occurred to me though when thinking about Banach-Tarski just now, which interestingly it hadn't before...

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Kelly

Indeed. Lisa is correct in that the glass has less than pi ounces after Gabriel drinks his shot. It isn't infinite. Bart was playing on the absurdity of the Gabriel's horn paradox. His math is correct, though, the horn does have a finite volume but infinite surface area. It would take an infinite amount of paint to paint the outside of the horn.

 

More on infinity paradoxes:

 

 

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michaeld
1 minute ago, Kelly said:

Indeed. Lisa is correct in that the glass has less than pi ounces after Gabriel drinks his shot. It isn't infinite. Bart was playing on the absurdity of the Gabriel's horn paradox. His math is correct, though, the horn does have a finite volume but infinite surface area. It would take an infinite amount of paint to paint the outside of the horn.

Yes unless the paint is allowed to get thinner and thinner the further you go, in which case you can do it with a finite amount of paint again.

 

How about supertasks? Got any of those to share? 😛

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michaeld

Here's a nice little probability puzzle I heard recently.

 

There are 3 people. Someone randomly puts either a white or black hat on each of their heads. The probability of getting a white hat and a black hat are 50% for each person, and all 3 are independent. Each person can see the other two hats but not their own.

Here is the game. They have to guess the colour of their own hat - or abstain. They must make these guesses or abstentions simultaneously - they can't wait to see what any of their colleagues did or didn't guess. (Or if you like, they place their guesses or abstentions in a sealed envelope.)

 

In order for them to win as a group, (a) everyone who guesses - i.e. doesn't abstain - must be correct about the colour of their own hat, (b) at least one person must actually guess correctly: they can't all abstain.

 

They can't communicate in any way once they've seen their colleagues' hat colours. However they can confer before they've seen the other hat colours to devise a strategy.

Here is one possible strategy. The first person makes a random guess - say "white". The other two abstain. The chance they win as a group is 50% - because they will win if and only if the first person - the only guesser - gets it right, which for a blind guess is 50%.

Question: can they devise a strategy with a better success rate than 50%? Why or why not?

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TheAP
Spoiler

They should use this strategy: If you see two hats with the same colour, guess the opposite colour; otherwise, abstain. If all three hats are the same colour, they'll all guess and get it wrong, and will lose. But if there's one hat with a different colour, that person will be the only one to guess, and will win. But since there's a higher chance that one hat is of a different colour than that all three hats are the same colour, their chance of winning will be higher than 50%, I think.

 

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michaeld
On 6/3/2018 at 10:02 AM, TheAP said:
  Hide contents

They should use this strategy: If you see two hats with the same colour, guess the opposite colour; otherwise, abstain. If all three hats are the same colour, they'll all guess and get it wrong, and will lose. But if there's one hat with a different colour, that person will be the only one to guess, and will win. But since there's a higher chance that one hat is of a different colour than that all three hats are the same colour, their chance of winning will be higher than 50%, I think.

 

Spoiler

 

Great work, TheAP!

 

Yes, you got it. Your strategy wins 3/4 of the time in fact. Out of the 8 possibilities for the hats - WWW, WWB, WBW, WBB, BWW, BWB, BBW, BBB - only WWW and BBB will lose if they follow this strategy. The other 6 out of 8 possibilities will lead to a win.

 

What's hugely counterintuitive about it is this reasoning, which appears to show you can't do better than 50%. In order for them to win, at least one needs to guess. This person is going to be guessing blind as they have absolutely no info about the colour of their own hat - from their point of view, they can do no better than 50%. And if they guess wrong the whole team is sunk. So it seems impossible to do better than 50%. But not so, as TheAP has shown...

 

Another way of looking at it: if they follow TheAP's strategy, then from the point of view of the guesser(s) - i.e. those who see same coloured hat for their colleagues, of which there will be at least one - it really is 50%. They have no more than 50% confidence that their team will win. But that's because of their own perspective, which is biased by the fact they are seeing two hats of the same colour. That they personally experience this biases the odds (from their point of view) towards the case where all hats are equal (i.e. the conditional probability of that goes up, conditioning on seeing two hats the same), which is the case the team loses. So in the end, the guesser really is only 50% sure, but the team overall still wins 75% of the time.

 

 

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michaeld

As this is originally Heart's thread, and she'll no doubt recognise this, AND it's on-topic, I have got to post this pic I took yesterday. 😛

 

3PvOZGT_LmaCdkyb_L25bHIQM46vQ9NGYNQyr8an

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