Dear Long Live Yorke

[keith crime 8]

ignore

[Shimmering Wang 1]

Okay, my turn.Let's say a friend comes up to me and gives me the following offer:He's going to put a certain amount of money in one envelope and twice that amount of money in another envelope. He then hands me one of the envelopes and lets me open it and see the amount of money inside. I do so. He then gives me the chance to switch envelopes. Should I switch or should I stay?Here's my solution:Well, there's clearly a 50/50 chance that I pick either the smaller one or the bigger one. So, if I switch, I could either double or half the money I have with a 50/50 probability. So, .5 * 2x + .5 * (1/2)x = 1.25xSince 1.25x > x, the amount of money I have, I should switch.But of course this solution makes no sense. Had I picked the other one, I would have come to the same conclusion and switched. What's the resolution?

Let x = the amount of money in the SMALLER of two envelopesOur expected equity, then, is (x + 2x)/2, or 1.5xIf we choose an envelope, it will either contain x dollars or 2x dollars. If we switch, we will either gain 1x (when we pick the envelope with less money, and switch to more) or lose 1x (when we pick the envelope with more money, and switch to less)Case 1: Pick BIG, stay: Money received, 2x Case 2: Pick BIG, switch: Money received, 1xCase 3: Pick SMALL, stay: Money received, 1xCase 4: Pick SMALL, switch: Money received, 2xIn all cases, there is a 50% chance we'll gain a unit, and a 50% chance we'll lose a unit by switching. .5(1) + .5(-1) = .5 -.5 = 0Our switching equity is always neutral.The mistake you made, yorke, is in your definition of x. If x is "the amount of money in the envelope," it is oscillating, and is therefore THE AVERAGE of the two possible amounts. There aren't x$'s in the envelope. There are 1.5x$'s. Because half the time there's 2 bucks, and the other half there's one. I think.

[brvheart 1,752]

LOL at everything about this. I had the old avatar since day 1. I'm digging the new one.

The new one sucks. The straight-on head shot made him look less gay and more real. It's science.

[Shimmering Wang 1]

It can be theoretical money, but what determines how much money is put in the envelope? How can you come up with a system that determines what goes into the envelopes? At some point, a person or a machine or something must actually put the money in the envelope, or decide the value, or whatever. If you make a machine that does this, it at some point must have been given some sort of probability distribution that controls what money it puts in the envelope. If it's a human, then we internally have some sort of distribution. Either way, there's no way we can have a flat probability over the entire number line, since it would integrate to infinity.

Smaller amount is 1x, bigger amount is 2x. Total money, on average, is 1.5x. Your math is wrong. Losing half a unit is not the same as gaining a whole unit. Going from 1 unit to .5 units is NOT THE SAME as going from 1 unit to 2 units. We're actually going from 1.5 units to either 1 unit or 2 units. That's where you're messing up.

[LongLiveYorke 38]

Let x = the amount of money in the SMALLER of two envelopesOur expected equity, then, is (x + 2x)/2, or 1.5xIf we choose an envelope, it will either contain x dollars or 2x dollars. If we switch, we will either gain 1x (when we pick the envelope with less money, and switch to more) or lose 1x (when we pick the envelope with more money, and switch to less)Case 1: Pick BIG, stay: Money received, 2x Case 2: Pick BIG, switch: Money received, 1xCase 3: Pick SMALL, stay: Money received, 1xCase 4: Pick SMALL, switch: Money received, 2xIn all cases, there is a 50% chance we'll gain a unit, and a 50% chance we'll lose a unit by switching. .5(1) + .5(-1) = .5 -.5 = 0Our switching equity is always neutral.The mistake you made, yorke, is in your definition of x. If x is "the amount of money in the envelope," it is oscillating, and is therefore THE AVERAGE of the two possible amounts. There aren't x$'s in the envelope. There are 1.5x$'s. Because half the time there's 2 bucks, and the other half there's one. I think.

I mean, I agree with all of this, this is all very true and it should be since the problem is symmetric. I guess the real question should have been, "What is wrong with the following line of reasoning?" in relation to my original "solution."

[runthemover 39]

I don't finish reading a thread before posting

I'm a bit sad that Keith Crime got there first too.

[LongLiveYorke 38]

Okay, we've beaten this one to death. I'll try to find a new one. I like that one, but it's more of a puzzle in reasoning rather than a real puzzle that could have a real solution instead of just showing where someone is wrong.

[JoeyJoJo 18]

Okay, we've beaten this one to death. I'll try to find a new one.

I'm not sure you understand the concept of a Dear LLY thread.Don't stop, I like what you're doing.That's what she said.You wish.

[LongLiveYorke 38]

I'm not sure you understand the concept of a Dear LLY thread.Don't stop, I like what you're doing.That's what she said.You wish.

Fine then, I'll open myself up and do whatever anyone wants me to do....that's what she said.

[Shimmering Wang 1]

I mean, I agree with all of this, this is all very true and it should be since the problem is symmetric. I guess the real question should have been, "What is wrong with the following line of reasoning?" in relation to my original "solution."

Oh.

I'm a bit sad that Keith Crime got there first too.

Haha! Joke's on you! I don't read the thread PERIOD!

[keith crime 8]

Fine then, I'll open myself up and do whatever anyone wants me to do....that's what she said.

can you explain vectors and differential equations and why i wasted 1/36 of my college career studying them

[runthemover 39]

Haha! Joke's on you! I don't read the thread PERIOD!

WWWWAAAAAAAAAAAAAANNNNNNGGGGGGGGGGwait. how do you manage to get posts that are on topic? me thinks you're reading first posts, or possibly you have a boy who gives you thread summaries in return for bread and sometimes soup.

[keith crime 8]

WWWWAAAAAAAAAAAAAANNNNNNGGGGGGGGGGwait. how do you manage to get posts that are on topic? me thinks you're reading first posts, or possibly you have a boy who gives you thread summaries in return for bread and sometimes soup.

the question wasn't until like the tenth posthe reads every thread and every post including all the I don't think Daniel is concentrating enough on his game threads

[navybuttons 15]

soup.

[Ouch-8s 4]

WWWWAAAAAAAAAAAAAANNNNNNGGGGGGGGGGwait. how do you manage to get posts that are on topic? me thinks you're reading first posts, or possibly you have a boy who gives you thread summaries in return for bread and sometimes soup.

i categorically deny this.

[Swift_Psycho 1]

Fine then, I'll open myself up and do whatever anyone wants me to do....that's what she said.

Couldn't have let someone else have the punchline, could you?

[LongLiveYorke 38]

can you explain vectors and differential equations and why i wasted 1/36 of my college career studying them

Sure. Vectors have many definitions. A vector space is a set of things that can be added together and scaled in a linear way and form a group. A vector in the physical sense is any object that rotates like spacial coordinates.Differential equations are implicit equations for a function that obeys certain properties that involve derivatives of this function. Often, a differential equation has many solutions, so really it implies a family of functions and not just one particular function unless proper boundary or initial conditions are included.

[coesillian 0]

If i put a boat in a closed body of water, how much water is displaced. I think it displaced its equivalent weight in volume of water. So if theres an ice cube floating in a glass of water and it melts, does the water level change at all?

[timwakefield 68]

including all the I don't think Daniel is concentrating enough on his game threads

Hey man, when Daniel gets off his game and starts playing badly he'd be sunk if he couldn't turn to random internet donks to tell him to play better and that he is washed up. Come on, who here doesn't follow Daniel's ups and downs on an hourly basis????? Nobody.

[LongLiveYorke 38]

If i put a boat in a closed body of water, how much water is displaced. I think it displaced its equivalent weight in volume of water. So if theres an ice cube floating in a glass of water and it melts, does the water level change at all?

The amount of water displaced is the amount of water whose mass is equal to the mass of the boat. This is Archimedes' principle. If I have an ice cube in water, it will displace an amount of water equal to the mass of the ice cube. So, the volume of water displaced is equal to the mass of the ice cube divided by the density of water:V = m/R, where R is the density of water and m is the mass OF THE ICE CUBE. When the ice cube melts, it will have the density of water and therefore have the same volume V as the displaced water.So, if we imagine that we can freeze time and remove the ice cube from the water, there will be a rectangular void in the top of the water where the ice cube was. The volume of shape is equal to the volume of the water displaced, which is V. When the ice cube melts, it will as water have volume V, and so we can imagine that it forms just enough water to perfectly fill this void, and therefore the overall height of the water doesn't change.

[BigLebowski 0]

Let's say we start with the numbers 1-5. One has the density of gold = 19.3g/ml and five has the density of water = 1g/ml. How would you rank Radiohead's albums?

[AmScray 355]

What programs would you suggest for an adult learner to better their math skills?I've been able to get my foot in the door of a damn good school (later in life, though lies and sympathy) and I'm already "OK" at math, but it's definitely my Achilles heel, particularly at the higher levels.I'm pretty sure it isn't because I'm incapable of doing it, but rather that I've never learned how to do so properly.

[LongLiveYorke 38]

What programs would you suggest for an adult learner to better their math skills?I've been able to get my foot in the door of a damn good school (later in life, though lies and sympathy) and I'm already "OK" at math, but it's definitely my Achilles heel, particularly at the higher levels.I'm pretty sure it isn't because I'm incapable of doing it, but rather that I've never learned how to do so properly.

Hmm, that's a very good question, and one that I'm not sure I have a great answer to.Math, like anything else, is something that you get good at my doing it a lot. But math, unlike other things, also requires that you actively think about it. In order to be good at computations, you need to try them several times, but in order to understand concepts, if requires that you read about them, go away and think about them, read about them again, and think about them some more until you can in your own head convince yourself of their truth. In general, I think taking any type of class would be extremely helpful. A community college isn't going to be as good as Harvard, but it's really not going to be all that much worse since the majority of learning that you'll do will be by yourself. The class should be there to guide your studies, to serve as motivation, and hopefully to provide a person that you can discuss troubles and issues with on a one-on-one basis. It's hard to tell you exactly what to do since I'm not sure exactly what your level is. I'm guessing that you want to be better at math that could potentially come up in life. If this is the case, I would recommend focusing on calculus, probability, and statistics. These are the types of classes that are offered everywhere and are more or less uniformly taught at every institution across the country. Also, there are probably really good textbooks that, if your comfortable, you could attempt to read on your own. If you want to go it alone, I can't stress enough the importance of actually doing exercises. You'll never really learning anything if you don't. Also, I would recommend to go slow and to be sure that you more or less fully understand a chapter before moving on.I'm not sure that I have any specific recommendations for good intro books. I think amazon or google would be more helpful in guiding you to a decent textbook than I would be.

[AmScray 355]

It's hard to tell you exactly what to do since I'm not sure exactly what your level is.

I take classes that give me papers that have symbols on them that I don't even know what they are. I then have to go to google to figure out what they are, what they're telling me to do and from that point, I have to decipher the problem- painfully.

[LongLiveYorke 38]

I take classes that give me papers that have symbols on them that I don't even know what they are. I then have to go to google to figure out what they are, what they're telling me to do and from that point, I have to decipher the problem- painfully.

Lol at who you are.It sounds like I was right. If you need math for another subject, it most likely means you need Statistics, Calculus, and some Probability. For your purposes, I think you could get away with reading books so you can at least interpret what you're looking at. Try to find a book that is geared toward your particular subject of interest, if this is possible. If you're into psychology, for example, you could look for "Statistics for Psychology" or something as obvious as that. Most calculus textbooks will cover a lot of symbols that you're bound to encounter, including sums, factorials, exponentials, logarithms, integrals, derivatives, products, and all that fun stuff.Honestly, Wikipedia is a pretty darn good source for math. If you're reading something and want to know exactly what it is, Wiki will serve you well.