![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
sniffnoySo some days ago ago Eric Frackleton was walking past Fenway Park and saw a giant billboard that read: "Massachusetts: You're more likely to live here."
So far we've come up with several interpretations of this, I don't think any of which are what the makers intended.
There's the first obvious interpretation, which is that the population of Massachusetts exceeds that of the rest of the world, so any random person is more likely to live in Massachusetts. This is clearly false, however, so there's the second interpretation, which is that if you're in Massachusetts, you're more likely to live than to die. Then there's Stansifer's interpretation, a more restricted version of the second interpretation, which is that if you commit a crime in Massachusetts, you're less likely to get the death penalty. That is almost certainly not what they meant, so finally we have... well, I forget who came up with it, but it was that, given that you are standing here at Fenway Park reading this billboard, you most likely live in Massachusetts.
Ack, correction: I just signed on to AIM for a moment, and his away message read "Welcome to Massachusetts. You're more likely to live here." So that was probably the sign. So while the last interpretation was probably the most sensible, it doesn't really make much sense if the sign is *welcoming* you to Massachusetts, does it?
Tomorrow is the first guest lecture - it's going to be Matt Szudzik, that Mathematica guy - "This was version... uh... it's not letting me scroll down" - again. And it's again going to have to do with Mathematica, and it looks like he's again going to try to advertise it. Blech.
So today in zeta function Rohrlich did the extension of ζ to C\{1}, and how to get ζ of negative integers! Yay! Pointing out that these are also based on the Bernoulli numbers, but without any powers of pi in them, he said, "Who ate the pi?"
So problem 9 on this week's ζ pset - it has nothing to do with the zeta function or with the Bernoulli numbers/polynomials/functions (which is really what the rest of the problem set is about); "The purpose of this problem is to give another example of an exponential generating function and also to point out that Bk has more than one meaning in the mathematical literature." Anyway, what it is is Bell numbers - the number of partitions of a set of k elements. However, he introduces them from their exponential generating function, e^(e^x-1). 9a is to show that Bk can be expressed as this sum of all these multinomial coefficients divided by factorials, and then 9b is to show that Bk is, in fact, the number of partitions of a k-set, which is obvious from 9a. Now, 9a is supposed to fall right out of the generating function; however, the first thing I thought to do upon seeing the generating function was to differentiate, which immediately got me a recursion for Bk. I decided to go and do 9b by showing that the number of partitions of a k-set satisfied this same recursion. :D Now the question is, do I use 9b to show 9a, or do I go and do 9a the way it was supposed to be done? Perhaps both?
So yesterday someone left this topology book lying around, I forget who it was by, it was just called Topology. Anyway, I started looking through it a bit, not really reading it, but I found two very amusing things in it: firstly, at one point (right after it said what a closed set was) it said something similar to, "Thus, the answer to the old mathematical riddle 'How is a set unlike a door?' is 'A door must be open or closed, and cannot be both, while a set can be open, or closed, or both, or neither!'". Awful. But really great was how, at the end of the "Note to the Reader", he said how, in topology, it's easy to get caught up finding "weird counterexamples"; however, this is not really the point of topology, and is very hard to do, and so, he listed right there all the topologies that he would use for weird counterexamples throughout the book.
Oh, a weird spam I got: It was from "Stewart D. Milton, Jr", the subject was "yups", and the text was "Luke is missing jumping today."
Yeah, that's really it.
-Sniffnoy
So far we've come up with several interpretations of this, I don't think any of which are what the makers intended.
There's the first obvious interpretation, which is that the population of Massachusetts exceeds that of the rest of the world, so any random person is more likely to live in Massachusetts. This is clearly false, however, so there's the second interpretation, which is that if you're in Massachusetts, you're more likely to live than to die. Then there's Stansifer's interpretation, a more restricted version of the second interpretation, which is that if you commit a crime in Massachusetts, you're less likely to get the death penalty. That is almost certainly not what they meant, so finally we have... well, I forget who came up with it, but it was that, given that you are standing here at Fenway Park reading this billboard, you most likely live in Massachusetts.
Ack, correction: I just signed on to AIM for a moment, and his away message read "Welcome to Massachusetts. You're more likely to live here." So that was probably the sign. So while the last interpretation was probably the most sensible, it doesn't really make much sense if the sign is *welcoming* you to Massachusetts, does it?
Tomorrow is the first guest lecture - it's going to be Matt Szudzik, that Mathematica guy - "This was version... uh... it's not letting me scroll down" - again. And it's again going to have to do with Mathematica, and it looks like he's again going to try to advertise it. Blech.
So today in zeta function Rohrlich did the extension of ζ to C\{1}, and how to get ζ of negative integers! Yay! Pointing out that these are also based on the Bernoulli numbers, but without any powers of pi in them, he said, "Who ate the pi?"
So problem 9 on this week's ζ pset - it has nothing to do with the zeta function or with the Bernoulli numbers/polynomials/functions (which is really what the rest of the problem set is about); "The purpose of this problem is to give another example of an exponential generating function and also to point out that Bk has more than one meaning in the mathematical literature." Anyway, what it is is Bell numbers - the number of partitions of a set of k elements. However, he introduces them from their exponential generating function, e^(e^x-1). 9a is to show that Bk can be expressed as this sum of all these multinomial coefficients divided by factorials, and then 9b is to show that Bk is, in fact, the number of partitions of a k-set, which is obvious from 9a. Now, 9a is supposed to fall right out of the generating function; however, the first thing I thought to do upon seeing the generating function was to differentiate, which immediately got me a recursion for Bk. I decided to go and do 9b by showing that the number of partitions of a k-set satisfied this same recursion. :D Now the question is, do I use 9b to show 9a, or do I go and do 9a the way it was supposed to be done? Perhaps both?
So yesterday someone left this topology book lying around, I forget who it was by, it was just called Topology. Anyway, I started looking through it a bit, not really reading it, but I found two very amusing things in it: firstly, at one point (right after it said what a closed set was) it said something similar to, "Thus, the answer to the old mathematical riddle 'How is a set unlike a door?' is 'A door must be open or closed, and cannot be both, while a set can be open, or closed, or both, or neither!'". Awful. But really great was how, at the end of the "Note to the Reader", he said how, in topology, it's easy to get caught up finding "weird counterexamples"; however, this is not really the point of topology, and is very hard to do, and so, he listed right there all the topologies that he would use for weird counterexamples throughout the book.
Oh, a weird spam I got: It was from "Stewart D. Milton, Jr", the subject was "yups", and the text was "Luke is missing jumping today."
Yeah, that's really it.
-Sniffnoy
no subject
Date: 2005-07-14 11:38 pm (UTC)no subject
Date: 2005-07-15 12:28 am (UTC)Steven Ehrlich
I'll probably be stopping by next week. I'll let you know here when I know.
no subject
Date: 2005-07-15 02:45 am (UTC)I just thought of another one: Now that you've read this sign, you're more likely to come live in Massachusetts.