Another long, multipart entry
Jul. 16th, 2005 07:31 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
sniffnoyOh, by the way, before the main entry, I'll just say: Steve was right. I passed by the "You're more likely to live here" billboard today, and the intended interpretation is, in fact, the second obvious one. You can tell because right to to the right of it is a billboard about how effective Massachusetts's gun control laws are. Anyway...
So yesterday Matt Szudzik, the guy from Wolfram Research who makes a point of showing off Mathematica before he gives his actual lecture by showing everyone integrals.com, and then having his lecture as a Mathematica presentation rather than just using the board, gave a guest lecture. It was called "Who was Laszlo Kalmar (and what were his functions)?"
It was kind of neat, but pretty pointless. It was about the Kalmar elementary functions, the class of functions from (N∪{0})n→N∪{0} built up from addition, monus (= a-b for a>=b, 0 otherwise), arbitrary sums, and arbitrary products, which, Szudzik told us, had been proved to be precisely the primitive recursive functions which grow no faster than exponentially. He didn't actually prove anything the lecture, which was why I say it was pointless.
But, this being Matt Szudzik, and us having Infinity-boy in the audience, especially, we got some good quotes out of it.
Szudzik says about (I think) how KE functions were used in the proof that there's no algorithm for determining whether a Diophantine equation is solvable. He asks how that might be done.
∞-boy: Take the set of all procedures and show that it's the empty set?
Szudzik [approximately]: Primitive recursive functions were used in the proof of one of the most famous theorems of the 20 century - do you know which one? [He means Gödel's Incompleteness Theorem]
∞-boy: Fermat's Last Theorem?
Also, when Szudzik asked if we knew how to solve any special cases of Diophantine equations, Infinity-boy raised his hand and said "no". Then of course Szudzik wrote "ax+by=c" on the board and ∞-boy realized that he did.
One thing Szudzik kept saying was how all the "traditional" whole number functions of mathematics are Kalmar elementary. His example of a function that was not Kalmar elementary was the tetration function, a^^b=a^(a^(a^(...^a))) (There are b a's in there.) After a bit Josh raised his hand and said, "How are you defining 'traditional'? I believe the tetration function appears in a paper by Euler."
So Szudzik had programmed Mathematica to list all the Kalmar elementary functions of a given length, and he showed us some of the weird-looking functions that came out in some cases when Mathematica evaluated them... but of course this is Mathematica with all its heavy complex analysis machinery and I think really you could just leave it in the sum/product form and it would tell you considerably more about the function... what came out tended to involve zeta functions and weird exponentials. One think that came out included the square of Glaisher's constant, which is, apparently, e^(1/12-ζ'(-1)).
Szudzik: I'm amazed that constant comes out of this.
Me: I'm amazed that constant has a name.
Szudzik says how a good thing on Kalmar elementary functions (or something like that) was written by, he says, "Yuri Matiyesavich... he's Russian." That cracked everyone up.
One thing that made no sense was how Infinity-boy asked if the ζ function was Kalmar elementary, and Szudzik started to say that he'd never seen it proved, but he suspected so, and after a minute or two I finally raised my hand and said, "Um. Wrong codomain?"
So after Szudzik does his demonstration of generating all the KEF expressions of a given length, Infinity-boy asks if you could get a formula for the number of them of a given length. Szudzik replies that since they're built up from binary operations, it's pretty much just counting binary trees. Dustin then asks if you can calculate the number of actual Kalmar elementary *functions*, i.e., not the expressions for them but the actual functions. Szudzik replies that he doesn't know, suspects you can't, as it's shown that it's uncomputable from the expressions for them whether or not two KEFs are equal. A few minutes later Cameron (who's again helping run research labs this year) raises his hand and says he's used this to prove that you can't. (Actually, this proof only seems to show you could use such a function to compute whether two Kalmar functions of the same length are equal, though it would work if the function in question were KEFs of up to a given length instead. The proof is: Assume this function were computable. Then you could compute whether two KEFs were equal as follows: List all KEF expressions of that length. At the start, they're all in the same bin. For each function, compute f(0), f(1), f(2), etc, and each time that not all of the functions in a bin return the same thing, split it into multiple bins based on what they return. When your number of bins equals the total number of KEFs of that length, you stop and just check whether the two functions in question are in the same bin.)
Infinity-boy then asks if you can, given the *function*, get the KEF expression. Szudzik actually gave a great reply to this: "Ah! This is what we call 'the art of computer programming'."
So some people went to Harvard Square the other day and ran into a group of LaRoucheians there, standing there with a whiteboard, drawing weird graphs and spouting LaRoucheian nonsense about the economy. And somehow they got into a discussion with Lucas about geometry; apparently they were saying something about how we ought to base our economic policy on Euclidean geometry - or perhaps it was some sort of weird analogy about taking things back to fundamentals; I'm not really sure. Anyway, somehow, the LaRoucheians for some reason started talking about how you could construct square roots of numbers with straightedge and compass. So Lucas thought to ask them if you could construct 21/3, and, amazingly, they said yes. Lucas offered to prove that this was impossible, but the person just, ah, coincidentally, was unable to find a marker for him to write with.
They also picked up a bunch of LaRouche's pamphlets, which should make for some interesting reading later...
So yesterday the JC's did the skit, and they got it right, although they decided to do it a bit differently, by including a third character. Lucas was Cameron, Tom was Arthur, but when Tom said "NOT MATH?!", instead of Lucas continuing as normal, Fergie burst out of the closet and continued his part with "That's right!" Then they did it again (complete with Fergie jumping out, completely expectedly this time) to announce the talent show next week. And we don't know what the Default Act will be, but this year, it's supposed to be pretty bad...
Yesterday's actual Mandatory Fun was Casino Night, where we get fake money, play games which much of the time are not gambling at all, possibly actually bet fake money on them and possibly ignore it and give it away, and, at the end, after many of the people have escaped, use it to bid on prizes, and, of course, pool it so we can actually win the big ones. Yeah, really not much to say about that. Except the bidding on the prizes - it was all candy, except for the 4 big prizes. Issao was the auctioneer. So for the 4 big prizes, he decided that what the prize actually was would not be revealed until all 4 had been sold. The fourth turned out to be some small math book. The third, a better version thereof. The second, a big stack of paper which was some paper about Galois theory. And first prize... "It's party... it's party... it's party peanuts!"
So a whole bunch of people left Mandatory Fun early to go to a Harry Potter party at Barnes & Noble. ...yeah, I don't really have much to say about that, but it will be important later. I think.
So early on during Mandatory Fun, Eli was playing the poking game, or, as Josh calls it, "finger fencing", against Victoria. The game is simple: you clasp one hand with the other person, index finger stuck out. You have to poke the person. No using your other hand. Well, Eli's style of play tends to involve a lot of jumping around, going down on the floor, just whatever he can think of, and so, once, when he was lying on the floor exhausted as a result of all this, I went and took his shoes.
And I ran around the room with them on my hands for a bit, and announced "I have Eli's shoes!", but eventually I realized I didn't particularly want his shoes. But I can't give them back so quickly afer stealing them, so I decided to turn them over to someone. I happened to spot Alex right then, and so I turned them over to her.
At this point in the story when I was recounting this to Josh, he replied, "Oh, well Alex wouldn't do anything wrong with them..." Well, in fact, she went and hid them. One behind the couch in the C Tower lounge (not the TV room), and the other in a plant (not really very well hidden, actually) in the "Study Space". Quite a while later, as the people were going to leave for the Harry Potter party, Eli comes up to me and asks me where his shoes are. I don't know, I said, I gave them to Alex. She's not here, he says. Oh, I say, she went to the Harry Potter party?, not aware it hadn't started yet. No, he said, she went to MIT! (What for, I have no idea.) So he ended up borrowing someone's sandals for the Harry Potter party. Alex arrived back before they did, and I told her about how Eli had been looking for his shoes, and she tells me that she hid them, and shows me the one behind the couch, and tells me about the one in the plant. Then the Harry Potter people get back and she shows Eli the one behind the couch, and I think she also tells him about the one in the plant...
Except, much later, after the Illuminati game, I pass by the Study Space and I see Eli's shoe in the plant. So he only got one shoe, I thought. Then I came back to the lounge and I see that Eli's other shoe is actually still there! He didn't take either shoe! But I'm quite certain Alex at least showed him that one... so I took Eli's shoes up to my room for the night, and I just realized now that I didn't give them back to him yet. I'll go do that after I finish this entry.
So the others got me to play a game of Illuminati tonight. Josh and Rebecca, they pointed out, won't be there (they were at the Harry Potter party). We only got 4 players - me, Chris, Tom, Erick - so we played with that many. As we play no joint victories with 4 players, we decided to also include the Gnomes of Zurich, which normally we leave out because it's so powerful (although we did have its goal be 200 MB rather than just 150). Chris was Zurich, I was Bavaria, Erick was Cthulhu, and Tom was Network. (I should note here that, because Servants of Cthulhu is the one group where progress towards their special goal does not generally help them with their generic goal, we also play with the modification that every time they destroy a group, their income increases by one.)
Early on, Erick decided he wanted Special Persecutor when the rest of us didn't want him to have it, and so, he went and actually made a privileged attack on it. Um... OK... we didn't do anything about it immediately, but a bit later when we wanted to make Chris spend money, we had him attack to neutralize some of Erick's stuff.
Eventually Josh and Rebecca returned. Rebecca just sat there reading Half-Blood Prince, while Josh watched the game and kibitzed despite all our attempts to tell him not to. At one point, Josh tells Tom he can win this turn. Tom, not knowing all the rules, hadn't realized that taking another player's group means you get all its puppets along with it; he asked if that was the case, and we told him yes, and we realized he could make a privileged attack and win. Now, at this point, I had no specials, Chris and Erick each had one, and Tom had I think 4, though we knew what most of them were. Chris and Erick, realizing what Tom was going to do, hastily arranged (right before the attack was declared!) for one of them to give his special to the other so they could abolish privilege. Erick saw Chris's special, Chris saw Erick's special, and it was seen that Erick's special was Interference so, instead of either giving away their special, Erick would just use intereference. (I was the one being attacked.)
Chris's special, though, Erick saw, was Swiss Bank Account, i.e., get 25 MB. He realized that, in fact, *Chris* (who goes right after Tom) would probably win on his turn if we didn't do anything... so after Tom's attack failed, he made a second attack, this time to neutralize Chris's South American Nazis (who, by the way, controlled the Video Stores), and thus Chris was prevented from winning. Chris blamed the whole thing on Josh, saying he would have won if Josh hadn't pointed out to Tom that he could win this turn. Later it was decided that it wasn't really Josh's fault as Tom didn't know the relevant rules, or something like that.
Soon after, Erick did it again, making a pointless privileged attack to take a group we didn't want him to have; right afterward, he left, and Josh took his place. This was OK, as there weren't any more specials at this point. Josh said he had no idea what Erick had thought he was doing, and dropped the group Erick had just taken to avoid our wrath.
So the game went on for quite a while, with me finally realizing, hey, I'm Bavaria, I can make privileged attacks for just 5 MB, and hey, there's probably some branches with 3 groups I can steal... when the others saw what I was going to do, they rearranged their power structures, although now that I think of it, that was on my turn, so how in space was that legal? It's too late to fix that now, obviously, but I didn't make the attack, and the game continued.
Finally, we started running out of money. When I told Eli about this, he said, "You were running out of money and the Gnomes hadn't won yet?" Well, that's the truth. Finally, there wasn't enough money left for Josh to take his income. Might we take money from Rebecca's set? No, there would be no way to separate it back out afterward. I would have gotten my Crimelords set, only sometime during Mandatory Fun, it had gone missing. I suspected Brian Lee and them had taken it, and now I suspect it considerably more, but I couldn't get it back from them now, so, after a lot of searching, I suggested we just call the game a draw. No, Josh said; that other game had been called a draw because it had stabilized, whereas there was still a lot of room for instability in this game - and so we went and actually wrote down the gamestate. And so presumably we'll continue it later tonight. If we can find Crimelords.
...wow, did I just spend 90 minutes writing an LJ entry? Well, I suppose I don't have *that* much work left...
-Sniffnoy
So yesterday Matt Szudzik, the guy from Wolfram Research who makes a point of showing off Mathematica before he gives his actual lecture by showing everyone integrals.com, and then having his lecture as a Mathematica presentation rather than just using the board, gave a guest lecture. It was called "Who was Laszlo Kalmar (and what were his functions)?"
It was kind of neat, but pretty pointless. It was about the Kalmar elementary functions, the class of functions from (N∪{0})n→N∪{0} built up from addition, monus (= a-b for a>=b, 0 otherwise), arbitrary sums, and arbitrary products, which, Szudzik told us, had been proved to be precisely the primitive recursive functions which grow no faster than exponentially. He didn't actually prove anything the lecture, which was why I say it was pointless.
But, this being Matt Szudzik, and us having Infinity-boy in the audience, especially, we got some good quotes out of it.
Szudzik says about (I think) how KE functions were used in the proof that there's no algorithm for determining whether a Diophantine equation is solvable. He asks how that might be done.
∞-boy: Take the set of all procedures and show that it's the empty set?
Szudzik [approximately]: Primitive recursive functions were used in the proof of one of the most famous theorems of the 20 century - do you know which one? [He means Gödel's Incompleteness Theorem]
∞-boy: Fermat's Last Theorem?
Also, when Szudzik asked if we knew how to solve any special cases of Diophantine equations, Infinity-boy raised his hand and said "no". Then of course Szudzik wrote "ax+by=c" on the board and ∞-boy realized that he did.
One thing Szudzik kept saying was how all the "traditional" whole number functions of mathematics are Kalmar elementary. His example of a function that was not Kalmar elementary was the tetration function, a^^b=a^(a^(a^(...^a))) (There are b a's in there.) After a bit Josh raised his hand and said, "How are you defining 'traditional'? I believe the tetration function appears in a paper by Euler."
So Szudzik had programmed Mathematica to list all the Kalmar elementary functions of a given length, and he showed us some of the weird-looking functions that came out in some cases when Mathematica evaluated them... but of course this is Mathematica with all its heavy complex analysis machinery and I think really you could just leave it in the sum/product form and it would tell you considerably more about the function... what came out tended to involve zeta functions and weird exponentials. One think that came out included the square of Glaisher's constant, which is, apparently, e^(1/12-ζ'(-1)).
Szudzik: I'm amazed that constant comes out of this.
Me: I'm amazed that constant has a name.
Szudzik says how a good thing on Kalmar elementary functions (or something like that) was written by, he says, "Yuri Matiyesavich... he's Russian." That cracked everyone up.
One thing that made no sense was how Infinity-boy asked if the ζ function was Kalmar elementary, and Szudzik started to say that he'd never seen it proved, but he suspected so, and after a minute or two I finally raised my hand and said, "Um. Wrong codomain?"
So after Szudzik does his demonstration of generating all the KEF expressions of a given length, Infinity-boy asks if you could get a formula for the number of them of a given length. Szudzik replies that since they're built up from binary operations, it's pretty much just counting binary trees. Dustin then asks if you can calculate the number of actual Kalmar elementary *functions*, i.e., not the expressions for them but the actual functions. Szudzik replies that he doesn't know, suspects you can't, as it's shown that it's uncomputable from the expressions for them whether or not two KEFs are equal. A few minutes later Cameron (who's again helping run research labs this year) raises his hand and says he's used this to prove that you can't. (Actually, this proof only seems to show you could use such a function to compute whether two Kalmar functions of the same length are equal, though it would work if the function in question were KEFs of up to a given length instead. The proof is: Assume this function were computable. Then you could compute whether two KEFs were equal as follows: List all KEF expressions of that length. At the start, they're all in the same bin. For each function, compute f(0), f(1), f(2), etc, and each time that not all of the functions in a bin return the same thing, split it into multiple bins based on what they return. When your number of bins equals the total number of KEFs of that length, you stop and just check whether the two functions in question are in the same bin.)
Infinity-boy then asks if you can, given the *function*, get the KEF expression. Szudzik actually gave a great reply to this: "Ah! This is what we call 'the art of computer programming'."
So some people went to Harvard Square the other day and ran into a group of LaRoucheians there, standing there with a whiteboard, drawing weird graphs and spouting LaRoucheian nonsense about the economy. And somehow they got into a discussion with Lucas about geometry; apparently they were saying something about how we ought to base our economic policy on Euclidean geometry - or perhaps it was some sort of weird analogy about taking things back to fundamentals; I'm not really sure. Anyway, somehow, the LaRoucheians for some reason started talking about how you could construct square roots of numbers with straightedge and compass. So Lucas thought to ask them if you could construct 21/3, and, amazingly, they said yes. Lucas offered to prove that this was impossible, but the person just, ah, coincidentally, was unable to find a marker for him to write with.
They also picked up a bunch of LaRouche's pamphlets, which should make for some interesting reading later...
So yesterday the JC's did the skit, and they got it right, although they decided to do it a bit differently, by including a third character. Lucas was Cameron, Tom was Arthur, but when Tom said "NOT MATH?!", instead of Lucas continuing as normal, Fergie burst out of the closet and continued his part with "That's right!" Then they did it again (complete with Fergie jumping out, completely expectedly this time) to announce the talent show next week. And we don't know what the Default Act will be, but this year, it's supposed to be pretty bad...
Yesterday's actual Mandatory Fun was Casino Night, where we get fake money, play games which much of the time are not gambling at all, possibly actually bet fake money on them and possibly ignore it and give it away, and, at the end, after many of the people have escaped, use it to bid on prizes, and, of course, pool it so we can actually win the big ones. Yeah, really not much to say about that. Except the bidding on the prizes - it was all candy, except for the 4 big prizes. Issao was the auctioneer. So for the 4 big prizes, he decided that what the prize actually was would not be revealed until all 4 had been sold. The fourth turned out to be some small math book. The third, a better version thereof. The second, a big stack of paper which was some paper about Galois theory. And first prize... "It's party... it's party... it's party peanuts!"
So a whole bunch of people left Mandatory Fun early to go to a Harry Potter party at Barnes & Noble. ...yeah, I don't really have much to say about that, but it will be important later. I think.
So early on during Mandatory Fun, Eli was playing the poking game, or, as Josh calls it, "finger fencing", against Victoria. The game is simple: you clasp one hand with the other person, index finger stuck out. You have to poke the person. No using your other hand. Well, Eli's style of play tends to involve a lot of jumping around, going down on the floor, just whatever he can think of, and so, once, when he was lying on the floor exhausted as a result of all this, I went and took his shoes.
And I ran around the room with them on my hands for a bit, and announced "I have Eli's shoes!", but eventually I realized I didn't particularly want his shoes. But I can't give them back so quickly afer stealing them, so I decided to turn them over to someone. I happened to spot Alex right then, and so I turned them over to her.
At this point in the story when I was recounting this to Josh, he replied, "Oh, well Alex wouldn't do anything wrong with them..." Well, in fact, she went and hid them. One behind the couch in the C Tower lounge (not the TV room), and the other in a plant (not really very well hidden, actually) in the "Study Space". Quite a while later, as the people were going to leave for the Harry Potter party, Eli comes up to me and asks me where his shoes are. I don't know, I said, I gave them to Alex. She's not here, he says. Oh, I say, she went to the Harry Potter party?, not aware it hadn't started yet. No, he said, she went to MIT! (What for, I have no idea.) So he ended up borrowing someone's sandals for the Harry Potter party. Alex arrived back before they did, and I told her about how Eli had been looking for his shoes, and she tells me that she hid them, and shows me the one behind the couch, and tells me about the one in the plant. Then the Harry Potter people get back and she shows Eli the one behind the couch, and I think she also tells him about the one in the plant...
Except, much later, after the Illuminati game, I pass by the Study Space and I see Eli's shoe in the plant. So he only got one shoe, I thought. Then I came back to the lounge and I see that Eli's other shoe is actually still there! He didn't take either shoe! But I'm quite certain Alex at least showed him that one... so I took Eli's shoes up to my room for the night, and I just realized now that I didn't give them back to him yet. I'll go do that after I finish this entry.
So the others got me to play a game of Illuminati tonight. Josh and Rebecca, they pointed out, won't be there (they were at the Harry Potter party). We only got 4 players - me, Chris, Tom, Erick - so we played with that many. As we play no joint victories with 4 players, we decided to also include the Gnomes of Zurich, which normally we leave out because it's so powerful (although we did have its goal be 200 MB rather than just 150). Chris was Zurich, I was Bavaria, Erick was Cthulhu, and Tom was Network. (I should note here that, because Servants of Cthulhu is the one group where progress towards their special goal does not generally help them with their generic goal, we also play with the modification that every time they destroy a group, their income increases by one.)
Early on, Erick decided he wanted Special Persecutor when the rest of us didn't want him to have it, and so, he went and actually made a privileged attack on it. Um... OK... we didn't do anything about it immediately, but a bit later when we wanted to make Chris spend money, we had him attack to neutralize some of Erick's stuff.
Eventually Josh and Rebecca returned. Rebecca just sat there reading Half-Blood Prince, while Josh watched the game and kibitzed despite all our attempts to tell him not to. At one point, Josh tells Tom he can win this turn. Tom, not knowing all the rules, hadn't realized that taking another player's group means you get all its puppets along with it; he asked if that was the case, and we told him yes, and we realized he could make a privileged attack and win. Now, at this point, I had no specials, Chris and Erick each had one, and Tom had I think 4, though we knew what most of them were. Chris and Erick, realizing what Tom was going to do, hastily arranged (right before the attack was declared!) for one of them to give his special to the other so they could abolish privilege. Erick saw Chris's special, Chris saw Erick's special, and it was seen that Erick's special was Interference so, instead of either giving away their special, Erick would just use intereference. (I was the one being attacked.)
Chris's special, though, Erick saw, was Swiss Bank Account, i.e., get 25 MB. He realized that, in fact, *Chris* (who goes right after Tom) would probably win on his turn if we didn't do anything... so after Tom's attack failed, he made a second attack, this time to neutralize Chris's South American Nazis (who, by the way, controlled the Video Stores), and thus Chris was prevented from winning. Chris blamed the whole thing on Josh, saying he would have won if Josh hadn't pointed out to Tom that he could win this turn. Later it was decided that it wasn't really Josh's fault as Tom didn't know the relevant rules, or something like that.
Soon after, Erick did it again, making a pointless privileged attack to take a group we didn't want him to have; right afterward, he left, and Josh took his place. This was OK, as there weren't any more specials at this point. Josh said he had no idea what Erick had thought he was doing, and dropped the group Erick had just taken to avoid our wrath.
So the game went on for quite a while, with me finally realizing, hey, I'm Bavaria, I can make privileged attacks for just 5 MB, and hey, there's probably some branches with 3 groups I can steal... when the others saw what I was going to do, they rearranged their power structures, although now that I think of it, that was on my turn, so how in space was that legal? It's too late to fix that now, obviously, but I didn't make the attack, and the game continued.
Finally, we started running out of money. When I told Eli about this, he said, "You were running out of money and the Gnomes hadn't won yet?" Well, that's the truth. Finally, there wasn't enough money left for Josh to take his income. Might we take money from Rebecca's set? No, there would be no way to separate it back out afterward. I would have gotten my Crimelords set, only sometime during Mandatory Fun, it had gone missing. I suspected Brian Lee and them had taken it, and now I suspect it considerably more, but I couldn't get it back from them now, so, after a lot of searching, I suggested we just call the game a draw. No, Josh said; that other game had been called a draw because it had stabilized, whereas there was still a lot of room for instability in this game - and so we went and actually wrote down the gamestate. And so presumably we'll continue it later tonight. If we can find Crimelords.
...wow, did I just spend 90 minutes writing an LJ entry? Well, I suppose I don't have *that* much work left...
-Sniffnoy
no subject
Date: 2005-07-17 04:47 am (UTC)also some girls *pretends it wasn't her* spent quite some time discussing the possibility of stealing his other shoes and making an exhibition (aka "Eli's life from the standpoint of his shoes"). thanks for the updates
-Dina
no subject
Date: 2005-07-17 08:01 pm (UTC)no subject
Date: 2005-07-17 09:17 pm (UTC)Steven Ehrlich
no subject
Date: 2005-07-17 10:33 pm (UTC)no subject
Date: 2005-07-18 03:37 am (UTC)I might be up sometime either (a) next weekend or (b) early August, when my parents are taking a week off for a vacation. What is the potential situation for me staying in a sane person's room? [And by that I mean not Fergie, and not a few other people.]
no subject
Date: 2005-07-18 11:47 pm (UTC)no subject
Date: 2005-07-18 06:27 pm (UTC)