When I was eight, my dad came home from work one day and handed me a sheet of paper. It said, “The statement on the other side of this paper is false.”  I turned it over, and on the back it said, “The statement on the other side of this paper is true.”

       I flipped the paper back and forth a couple of times, and then I got it. If the front is true, the back is false, and if the back is true, the front is false. “It’s called a paradox,” my dad said.  

       I thought it was totally cool, and just confirmed what I already suspected:  my dad was a demi-god. In addition to being brilliant and funny, he took me seriously, which I’ve noticed isn’t something you can necessarily count on if you’re a girl.

       That started me collecting paradoxes. Once you start looking for them, you find them everywhere. Turns out there are like a gazillion different types. My dad’s is an example of what’s called a self-negating paradox. Just last month, my math teacher told me that a famous mathematician named Bertrand Russell discovered self-negating paradoxes over a hundred years ago. Well, not exactly discovered, but kind of made everyone sit up and take notice. I went to the library to find books on Russell, but the only thing they had was his Autobiography. So I checked it out. Most of it is just about his life and stuff, but there’s a paragraph in it where he explains his paradox. It took me a really long time to figure out what he was saying, and even longer to figure out why it was basically the same as my dad’s paradox. I’d explain it to you, but believe me, you’d have to really be into paradoxes to want to hear it. 

       After a while, I got interested in other kinds of logic puzzles. Here’s a simple one I like, which is kind of the reverse of self-negating paradoxes:  Statements that are logically implied by other things you’ve said or by circumstances, and hence go without saying, but you say them anyway. I don’t know if mathematicians have a name for these, but I call them “NIMPS,” short for “necessarily implied.” Here’s a simple one: “I am able to speak.”  The fact that you are speaking at all necessarily implies you are able to speak. So you could have gotten the same information across if you’d said, “Please pass the mashed potatoes”--and gotten yourself some mashed potatoes to boot.

       By the way, there’s a great NIMP in Russell’s Autobiography: “There was a footpath leading across New Southgate, and I used to go there alone to watch the sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more of mathematics.”

       The thing that probably jumped out at you when you read that was, what on earth is mathematics doing in the last sentence?  I mean, is it really possible that someone could be about to kill himself, but then think, nah, I’ll just turn down the gas and nail the Pythagorean theorem first?  I like math as much as the next kid—more-- but I don’t think math has much to say to suicide. They just aren’t talking the same language. 

        Turns out that old Bertrand was forever contemplating suicide, and then thinking, nah, I won’t do it because I promised my wife I’d be home for lunch.     He was one weird dude. And not exactly your dream husband. Exhibit #1, seven years into his marriage to his wife Alys: “I went out bicycling, one afternoon, and suddenly, as I was riding along a county road, I realized that I no longer loved Alys.”  Of course Bertrand decided he just had to share that epiphany with Alys right away, like she’d be just as excited to learn about it as he was. After he told her, they lived in the same house for ten more years, with Alys pining after him, and him not giving a damn about her, until they had an awful fight about his screwing someone else. Which brings us to Exhibit #2:  “After she [Alys, that is] had stormed for some hours, I gave a lesson in Locke’s philosophy to her niece.... I then rode away on my bicycle, and with that my first marriage came to an end.” Makes you wonder how life would have turned out for him without that trusty bicycle.  

       After that, he didn’t see Alys again for forty years. I’m not kidding. I know, what a jerk. But there were some really great things about him too—I mean as a person, not just a mathematician. I guess people are complicated.              

       Anyway, I loved that suicide and math thing, but what jumped out at me was the NIMP:  “I did not, however, commit suicide.” I mean, if that doesn’t go without saying, what does?

       Speaking of “it goes without saying,” that’s kind of an interesting case itself. If you think about it, whenever someone tells you something “goes without saying,” they go on to say exactly the thing they just told you goes without saying. That makes it look sort of like a self-negating paradox. But of course, it isn’t really, because when people say “X goes without saying,” they don’t really mean ‘we needn’t say X’ or even ‘we shouldn’t say X.’  What they mean is, you can bet the farm on X’s being true. As in, say, “It goes without saying that he would never sleep with his wife’s best friend,” or, say, “It goes without saying that he slept with his wife’s best friend.” 

       But here’s the interesting thing I’ve realized over the past year. “It goes without saying” can be self-negating in a different sort of way. Some things not only go without saying; they go only without saying. If you say them, you destroy them-- or maybe you just prove they never existed to begin with.   Take, for example, the guy who says to his wife, “It goes without saying that I’d never sleep with your best friend.” If he hadn’t said anything, in a million years it probably wouldn’t have crossed his wife’s mind to worry about it. I mean, how many jerks are there in the world who actually sleep with their wife’s best friend, and if she loved him enough to marry him, why would she suspect he’d turn out to be one of them?  But just by saying it, he’s proved he’s exactly the sort you should worry about. If you really love someone enough not to betray them, no matter what, wouldn’t it go without saying— wouldn’t it have to go without saying? Who says these things if they really mean them? 

       Sorry, I’ve just been jabbering away and haven’t told you anything about myself. My name is Louise. I’m thirteen, and I live with my mom in a small town outside of Boston. It’s only thirty minutes by car, but like most people who move out to the suburbs and tell themselves they’ll go into the city all the time, we almost never do. Last time we went was Christmas, when my mom took me to the Nutcracker. She’s usually three years behind the curve with me. But we had a nice time anyway.

       My mom’s kind of quiet. I used to get incredibly nervous when my dad had to work late and it was just my mom and me at dinner, like maybe the world would come to an end if we just sat there without anyone saying anything. So I’d rummage around for things to tell her about my completely boring day, and then babble on about them like I was the official town crier or something. One day I decided to shut up for a change and see what happened.   What happened was that after five minutes, my mom started talking. It’s a good thing I figured that out, because, since my dad left, it’s just the two of us most nights, and I’d be pretty worn out by now, trying to ward off the apocalypse singlehandedly and all. 

       In the first couple of months after my dad moved out, what my mom mostly wanted to talk about was how I was “doing.” I’d tell her I was “doing” fine—which I was. I guess she finally believed me, because she stopped asking.

        Lately, at dinner, we mostly talk about her work. At first, I asked just to be polite, because she and my dad used to talk about work every night at dinner and I thought maybe she missed that. But after a while, I started to get really interested. My mom’s a research doctor. She works on cancer. She and her colleagues are trying to figure out what turns on the process of cell division in cancer cells, so they can figure out how to turn it off. A couple of years ago, she won some kind of award for her research, and my dad and I went to the dinner in her honor. There were a lot of speeches about the great things she’d done, and I guess that’s the first time I realized she’s kind of a big deal. As they say, you can’t always judge a book by its cover, even when you’ve been living with that cover your whole life.    

        You’re probably wondering what happened to my dad. Well, it turned out he wasn’t a demi-god at all. Uber-jerk is more like it. Six months ago, my mom went to a conference in Europe and stayed on for a couple of weeks to travel with a friend. My dad had a ton of work to do, so we agreed we’d have an early dinner together and then do our own things. Turned out his thing was screwing a colleague. The first week, he stayed at work until 9 or 10. The second week, he didn’t come home until after midnight. When my mom got back, he told her he’d have to work late for the next couple of weeks to finish off a grant application. After about three weeks of his being gone most of the time and not exactly there even when he was there, I guess my mom figured out he had more on his mind than just a grant application.

       Anyway, late one night I heard my parents talking in the living room.  They must have thought I was asleep, but I wasn’t. When I heard my mom say, “Tom, please have enough respect for me to tell me the truth,” I got out of bed and stood by the door.

       He told her. A colleague was also working late at the office trying to meet a deadline, one thing led to another, he was in love and couldn’t think about anything else, he was really sorry to hurt her this way, she deserved better, she wouldn’t want him to go on pretending any longer, blah, blah, blah.

       I went back to bed and curled up around my pillow. After a while, I heard my mom’s footsteps outside my door. She must have heard something, because she stopped and opened the door.

       “Are you up, Louise?”

       I didn’t say anything. 

       She came in and sat down on the edge of my bed.   I didn’t make a sound for a long time, and just lay there like a roly poly in its shell, hoping she’d think I had drifted off to sleep, and sort of hoping she wouldn’t.

       Finally she said, “Did you hear dad and me?”

       I said yes, my face buried in the pillow.

       She put her arm around me, and said,  “I’m so sorry, sweetie.”

       That did me in. That’s what I hate about bodies. You’re doing a pretty good job sorting things out in your mind and keeping yourself together, and then all of a sudden your body has ideas of its own, and it’s all over. My mom just sat there and held me, while I sobbed my guts out. I don’t know how long I cried, but when I finally stopped, I had a splitting headache and felt like I hadn’t slept in a month.

       My mom got me some aspirin, and then asked if I thought I could sleep now. I said yes, I thought so. “Dad’s going to stay with a friend for a while,” she said. “But he’ll come by tomorrow night so he can talk to you himself.”

       When he came over the next night, my mom disappeared, leaving me alone with him in the living room. If he was waiting for me to say something, he was going to have to wait until hell froze over. Finally he said, “Louise, your mom and I have been having some difficulties, and we both decided it would be best for us to live apart for a while and then see where we are.”  

       “Don’t bother, dad,” I said. “I know what happened.”

        His eyes got really wide.

        “Don’t blame mom,” I said. “She didn’t tell me. I heard you talking last night. Besides, you’d have to be a complete idiot not to figure it out. And, whatever you may think, I’m not a complete idiot.”

       He looked pretty miserable, which was fine by me. He deserved it.

       He sighed, and then said, “Louise, I know this must be really hard for you. But honey, you have to know that whatever happens with mom and me, I’ll always be there for you.”

       “Like you were there for mom?” I said.

       He didn’t answer for a while. Then he said, “Louise, I really wish for your sake that this had never happened. But it did happen, and I can’t just pretend it didn’t.”

       I didn’t say anything. What I thought was, I didn’t expect you to pretend it never happened. I expected you not to have done it in the first place, in which case there’d be nothing to pretend about.

       We sat there for a minute or two, not saying anything. Finally, he said, “Maybe you’d like some time alone to digest this. How about we have dinner together on Friday?’

       To tell you the truth, I wasn’t all that interested in continuing the conversation, Friday or any other day. But I just shrugged and said “Whatever,” like one of my moronic classmates.     

       My mom dropped me off at the restaurant on Friday. I made up my mind ahead of time that he was going to get through dinner without any help from me. But he caught me off guard. First thing he said was, “Hey, I discovered this mathematician named Raymond Smullyan, who’s into logic puzzles big time. I’ve been working on a Smullyan problem all week. I keep thinking I’ve got it and then I realize I don’t. Would you look at it and see if you can get anywhere?”

       OK, I admit it. I just folded. I’m pathetic. We worked on the problem for the rest of dinner, but didn’t get very far. After dad dropped me at home, I had a mini-breakthrough, and e-mailed it to him. The next night, he e-mailed me back, and so on. By Monday we had figured it out.

       We fell into a regular routine of having dinner together once a week. My dad would bring along a Smullyan puzzle for us to work on. If we couldn’t solve it by the end of dinner, we’d finish it off by e-mail during the week. A couple of times, he asked me if I wanted to meet what’s-her-name. I said no thank you, I thought I’d forgo that pleasure, and he dropped the subject.

       At first, things were kind of tense between my mom and dad. But after a couple of months they seemed pretty friendly when dad picked me up. One night after he left, I asked my mom if she and dad were going to get back together. She said, “I don’t think so, sweetie. Sometimes you just can’t put the genie back in the bottle.” OK, I thought. I can live with that.    

       About two months ago, my dad picked me up for our usual Friday gig.   He was pretty quiet in the car. When we got to the restaurant, I noticed that he didn’t have Smullyan with him. He didn’t look too happy.

       “Why so glum, sugarplum?” I said. 

        He said, “Louise, there’s something I want to tell you.”

        I’ve noticed that whenever someone says that to you, it’s a sure bet you don’t want to hear whatever it is they are so hot to tell you. So I didn’t say anything—no point in encouraging him. He’d ruin my evening soon enough.

       “Mindy got offered a really great job in California.” (Mindy is what’s-her-name’s name.) “I can do what I do pretty much anywhere, but for Mindy, this is a once in a lifetime opportunity.”

        I just stared at him.  

        “Sweetie, I’m really, really sorry. This is the last thing in the world I wanted to happen. I wouldn’t even consider moving if I didn’t think you and I could make this work. But I figure if you spend school breaks and summer with us, we’ll actually spend more time together than we do now. I’ll take the summer off from work, we can just hang out and do whatever you want.”  

       “No thanks,” I said. “I’d just as soon stay here.”

       “Well,” he said, “if you’d rather, Mindy and I could come east for the summer, maybe the three of us could rent a place in Vermont.”

       “I think I’ll pass.”

       “You sound really upset,” he said. 

       “Not me,” I said. “I’m fine. You’re the one who’s made a complete mess of his life.”

        As soon as I said it, I knew it was a mistake. 

        “Louise, you are entitled to feel any way you want about your life, and to think anything you want about mine. But you’re still my kid, and there are things you are not entitled to say.”

       “Well, you’re still mom’s husband, and there are certain things you’re not entitled to do.”

       He looked at me like you might look at someone you were about to hit, if you were the hitting sort, which he isn’t. Then he just sighed, and said “Sweetie, your mom’s a great person. But the fact is, we haven’t been happy together for a long time. I think she would tell you the same thing if you asked her. If Mindy hadn’t come along, we probably would have stayed together because of you. But she did. I’ll do whatever I can to make this OK for you, but you have to meet me partway.” 

       I could feel my eyes pooling up. Not this time. “I want to go home,” I said. I left the table and waited outside while my dad paid the check. Neither of us said a word all the way back to my house. As I got out of the car, my dad said, “Are we on for next Friday?”

       “I’m busy.”  

       "How about Saturday then?” he said.

       "Busy then too,” I said.

       “Well, how about if I e-mail you to set something up for the following week?”

       “Suit yourself,” I said. As if he needed any encouragement from me.

       When I opened the front door, my mother was standing in the hallway.   “You’re home early,” she said. “Everything OK?”

       “Swell,” I said. “By the way, dad and what’s-her-name are moving to California.”

       “I know,” my mom said.

       “He’s a complete douchebag.   I can’t believe he’d leave you for her.”

       “That’s very sweet of you,” she said. “I appreciate the vote of confidence.”  

       “Aren’t you mad?” I asked.

       She looked really tired, and maybe like she had been crying. “Sure,” she said. “And sad, and a whole bunch of other things too. But I guess I don’t think of your father as a douchebag, as you so delicately put it. We all do some great things in life, and some not so great things. It’s not so easy to say what it all adds up to.”

       Personally, I hate that ‘we’re all sinners in the eyes of god’ stuff. If I were god, I’m pretty sure I’d notice that some people were douchebags and some weren’t, and I’d want to save the smiting and the boils and all the rest of that jazz for the ones who were. 

       “I think I’ve had enough of this day,” I said. “I’m going to bed.”

       When I got to my room, I logged on to my computer. There was an e-mail from my dad. I sent it to trash without reading it and emptied the trash. The next day, there was another one, which I also trashed. After a few days, the e-mails stopped coming. Then I came home to find a box from Amazon on my desk. Without thinking, I opened it. It was from my dad. Smullyan of course. I should have guessed. I threw the book in the wastepaper basket. Over the next few weeks, two more packages arrived, and three letters. I threw all of them in the trash, unopened.

       Last week, I went into my mom’s bedroom, looking for a pair of scissors. There, stacked on the bottom shelf of her bedside table, were all the packages and letters from my dad, still unopened. My mom came in just then, and saw me staring at them.  

        "You know, Louise, sometimes it’s harder than you think to stop loving someone.”

        “Yeah, and sometimes it isn’t.”

       To tell you the truth, I’m getting a little sick of paradoxes. Last week I decided I’m going to teach myself geometry instead. My math teacher says that if I can get through the whole course by May, he’ll let me skip 9th grade math next year. I’ve also gotten hooked on internet scrabble. You can log on any hour of the day or night, and somewhere in the world someone is just sitting there waiting for you to show up. Pretty cool, huh?

       The other day, my mom had the radio on in the car, and some science dude was talking about Darwin. The interviewer asked him, “Did Darwin think it was possible to believe in evolution and also believe in god?”  The science dude said, “Yes, I think he did. And of course we know he was right. After all, millions of people do it every day.”

       I don’t think the two of them meant the same thing by “possible.” Me, I’m with the interviewer. Of course it is possible to believe anything, no matter how obviously untrue it is. After all, millions of people do it every day.  The question is, is it reasonable? 

       Take me. I used to believe that my dad loved me more than anyone else in the world. I kept believing it even after he moved out, falling for those stupid Smullyan puzzles and emails and Friday night dinners. But at a certain point, the evidence on the other side becomes overwhelming. If you still can’t let it go, then it pretty much goes without saying that you have no one to blame but yourself. 

       There’s a great passage near the end of Russell’s autobiography, where he’s describing a time in his life when he was really unhappy. He says:  “Pain made me sentimental, and I used to construct phrases such as ‘Our hearts build precious shrines for the ashes of dead hopes.’” I love that sentence, because it really nails how ridiculous people are. They talk about love as if it were a living thing, like a virus, that gets inside you and digs in for the long haul.

       But it isn’t. It’s just an idea about someone, about what they are to you.   It exists only because you are willing to think it, and when you stop thinking it, it’s gone. Of course, you can’t always stop thinking something, just like that. Sometimes you really have to work at it.