I solved the last riddle! It was actually last thursday, I went at it for about two hours on the giant whiteboard in my lab's kitchen area. I'm tempted to post the solution . . . but that wouldn't be any good; if it were here, you'd be tempted to just click through and look at it, when what you really want to do is solve it for yourself. :-) Just email me if you really do want to see my solution.
I went out to Walden Pond with Jess, Jim, Patrick & Kirsten last Thursday; Friday night was an end-of-summer Carey Lab party; Saturday night was our last Adams Terrace party. We went with a timecube theme, which I thought was awesome, but appeared to just confuse most people. Ah, well. The reminder email went like this:
4+ ?4 Adams Terrace.
Tonight. Party!
Hey stupid - are you too dumb to know there are 4 different simultaneous 24 hour days within a single rotation of Earth? Greenwich 1 day is a lie. 4 quadrants = 4 corners, and 4 PARTIES, in the same location: ADAMS TERRACE!
Humans are 1-corner beings (1-corner face 4-corner head) who rotate 4-corner lifetimes: baby, child, parent, g-parent. Time Cube debunks god lies.
Evil people deny Time Cube and don't come to party. Educators are flat-out liars. Evil media hides Time Cube and suppresses knowledge of party.
Today is the 4*4 = 16th day of the 4+4=8th month of the f(4)=26th year since Elvis Presley transcended the man-god word world! Party!
I had . . . this is both amusing and distressing . . . been so stressed out about Jess taking the MCATs on Saturday that I'd barely slept the night before . . . I woke up at 4:00 a.m. and couldn't get back to sleep, while she peacefully snoozed all night. This left us both exhausted by the time the party started, but she still made it 'til 1:00, and I made it all the way through to 3:00 am, when the party was finally dispersing. It was a good time.
To come: an essay on the sociological and psychological origins of pride, its applicability at different levels, and a look at the balance between heirarchy, egalitarianism, isolation & internationalism in politics and in religion. Hit me if I don't write it.
Today is math riddle day. Here are three tough ones, maybe in order of increasing difficulty:
(edited to correct two errors in the statement of the problems, 8/13/03 11:00 pm)
(1) Say M is thinking of a number between 0 and 15; what's the smallest number of yes-no questions you'll have to ask M in order to know the number, if M is allowed to lie once?
(2) If you have 5 points on the surface of a sphere, prove that no matter where they are on the sphere, it will be possible to cut the sphere in half and have at least 4 on one half.
(3)
(i) P is told the product of two numbers A and B
(ii) S is told the sum of these two numbers A and B
(iii) A and B are numbers between 2 and 99
P says "I don't know what the two numbers are"
S says "I knew you didn't know them!"
P says "Oh, well, I know them now."
S says "Ah, well in that case, I know them too."
What are the two numbers?
this should be solvable without using a brute force approach
Riddles courtesy of Tania Lombrozo & Nelson Lai. I think I've solved the first one; not so much the last two.
It's really striking, walking by the Stata Center and Tech Square at night, the buildings glowing in the darkness, how different the MIT end of Cambridge is from the Harvard end. So beautifully, optimistically modern. posted by Miles 2:33 PM
Ken Shan, 2003-08-06 13:53:37-0400:
|| There's also Enemyster and Fiendster.
I'm amused. :-)
Of course, I have a dirty mind, too, so it immediately came to mind that there should be a "sexster", which would consist of links between people you've slept with. This way you could figure out how many degrees-of-copulation separate you and . . . some number of other people. Okay, yes, it obviously wouldn't work at all, for privacy reasons. But you can imagine it, because it does actually exist, even if you can't see it. For instance, I've transitively (two steps!) had sex with Alastair, who I played golf with last weekend.
(This has been mocked (up) at std-ster . . . thanks to Kaihsu & (transitively!) Ken for the link)
The (slightly) more innocent original version of this was the hand-made charts of who had kissed/messed-around-with who, that used to get passed around at youth-group conventions I went to when I was a teen. Back then, I didn't make it onto the charts. :-) posted by Miles 3:39 PM
So this weekend, about three different people asked me somewhat out-of-the-blue, "Are you on friendster?" I had no idea what this friendster thing was.
It's strangely compelling. Kind of.
My boy Jordan is the most gregarious, well-connected person I've ever met. We played golf together this weekend, down in CT, and he was raving about how it's the greatest networking tool ever. So, I've got to respect that.
On the other hand, Jess thinks it's totally lame, and only of use to the desperate / in-need-of-affirmation. :-) I can see that perspective, too.
I guess, basically, I just think they've got a trillion-dollar concept on their hands, and they've only built a million-dollar website on that intellectual property. So far; I'm willing to cut them some slack, they've only been at it for a month, or something, and they're still in beta.
My ideas for expansion:
(1) hook up with ebay, or one of the used-car sites, or any p2p web-commerce site that would benefit from increased trust and accountability between parties. wow, this is just begging to be done.
(2) allow searches by N-degrees. this is SO important. right now you can see your friends, and you can search within a four-degrees-of-separation (4-DOS) set; it's GOT to be easy to make this flexible, so that you can search only within 2 or 3 degrees.
(3) have an "abilities", "talents", or "business" field, rather than just "interests" . . . so that, for instance, if I want to friendster a D.J. for my upcoming party I can search for someone capable; testimonials could be domain-specific.
(4) hook up with blogspot &/or geocities, to create instant access to more detailed info; this should be made visible in a DOS dependent way.
(5) write a mapping function, so you can see the geographic distribution of your connections, with different colored "pins" for each degree of separation.
(5a) create a parallel "travel" service, allowing people to designate themselves as "hosts" for folks in need of a place to stay (potentially with a small attached fee) . . . or just in search of someone to go out for drinks with, in a new town.
Anyway, check it out, if only just to get the idea. And just look me up by name & add me as a friend, if you dig it. posted by Miles 11:06 AM
Jess and I were talking about the development of moral and social reasoning this morning, over coffee & pastries at Carberry's. She asked when kids learn to cooperate to succeed at a task; I didn't know, but I thought it was a great, very relevant question.
So, this is from an email I just sent my advisor: (read the first link - none of what I say may make any sense, without it, and it's interesting stuff)
We seem to focus on Theory of Mind as the root of social cognitive development; this makes lots of sense, to me, as you're pretty limited in your ability to reason about social situations if you lack understanding of the internal beliefs, desires, etc of agents around you.
We had a conference on Moral Development, and this made a little less sense to me; there was discussion of the development of empathy, and some Theory of Mind, and some nativist proposals concerning innate moral rules. This was all interesting, but I've always had trouble looking at the world through a moral lens; morals aren't very real, to me: they don't map onto the physical world, and they don't seem to offer very deep explanations of human action.*
Basically, I see the world this way: moral rules are a shortcut to socially functional behavior. The "Golden Rule", or the "ethic of reciprocity", for instance, is simply stated, simply understood, and pretty effective (if followed) for a culture; however, from a social psychology (or game theoretical) perspective I think you would say there's a _reason_ this is a "good" ethic: if you consistently follow this rule, you will generally not piss people off, and if others notice this, your reputation (honor) will improve and other individuals will trust you. All of this will result in: (A) a maximization of cooperative opportunities with greater rewards than are obtainable alone, and (B) a minimization of retributive actions against you. There are always other good (but high risk) strategies like "leverage your power and exploit everybody else because they can't do anything about it", but this only really works for a few individuals; most would get hurt by retribution.
In any case, if you want to follow this effective "ethic of reciprocity" you can either (1) learn the rule, or (2) understand all the social psychology.
It seems marginally obvious that (1) is easier.
But. It doesn't generalize that well; while the ethic of reciprocity is a really good one, there are lots of other moral/ethical rules to learn, and they pretty much all conflict, from time to time, with immediate interests or desires that you have. When faced with such a conflict, you have a decision to make: you have to consider your desire D, your moral code M, and (if you want to think a little harder) the social consequences \ of your possible actions \.
Adults consider social consequences all the time, regardless of whether ethics are involved. My position (not supported by any data, that I know of) is that 95% of the time when there is a conflict between D & M (such that ethics might be involved) the choice of action based on consideration of social consequences will match the choice of action based on your moral code, as, at least in the long term, violations of cultural-norm morals lead to deep, negative social consequences.
This means that if you're willing to invest in a careful consideration of social consequences, you don't need moral or ethical codes.
The point of all of this is really simple:
I suspect kids are limited in their understanding of social dynamics, as compared to adults. (duh)
I suspect there's a gradual transition from rule-based strategies to consideration of social consequences . . . late in development (adulthood?) for most people; possibly never, for some.
And finally . . .
I think there's an important difference between a basic-level belief/desire theory of mind (what I've seen in the literature), and a "dynamic" theory of mind that integrates the affects of our actions on the internal states of others. This latter dynamic ToM seems like the real core system of adult social cognition. I suspect this system begins to develop fairly early on; once you have a full "static" ToM and any kind of general learning mechanism, you've got all the tools you need to build it.
I'm trying to think of an empirical way to get at this; it seems like there should be something simple from game theory - some variation on the prisoner's dilemma adaptable to a toddler game/task - that would let me test whether kids understand the affect of their actions towards a co-participant, in an initial stage, on their success / reward in a second stage that has a large "cooperative" payout. However, I realize that attempting to simulate real, rich social interactions and social learning in a brief "game" or "task" might be a poor approach. Might there be a way to do this with "verbal reasoning" style questions concerning fictional social interactions detailed in (very) short stories?
Arrest This Man, He Talks In Maths 
Tuesday, August 19, 2003