mathmom's blog

  Why you should study the history of math In the mid 1300s a fad made its way around Italy. Mathematicians would challenge each other to “mathematical duels”. They would post problems for their opponents to solve, sometimes along with their solutions in coded poetry. The winners would get support and funding from rich patrons, the losers would descend into obscurity. One such contest, between Fiore and Tartaglia, involved a new method for solving the cubic. In order to win, Tartaglia worked day and night to find Fiore’s method---unfortunately, Fiore did not do the same and only knew his own method and no others. (*Recall that the formula for solutions to quadratic equations of the form use the quadratic formula, Giorlamo Cardano---physician, philosopher, astrologer and mathematician---convinced Tartaglia to share his method and promised never to reveal it. Then Cardano figured out a more general method, and wanted to share it, but was blocked by his promises. Fortunately (for Ca...

After the last post, we started to be able to see what the fuss was about.  The ones made with twice the butter were the best candy I have ever tasted.  Ever.  So then we started experimenting.  How long do you pull it?  Longer than you think.  And then pull a minute or two after that.  Suddenly every single batch was creaming, pretty much right after we would cut them. I tried adding less than double butter and I think they taste much better (more delicate, according to one taste tester). The latest experiment we did involved using Earth Balance instead of butter.  It cooked pretty much the same as usual, although I was distracted right at the moment I had to pull it off the stove so it cooked maybe a bit longer than usual.  Amanda and I each pulled a quarter, while Luke pulled the bigger half.  Luke's really wasn't turning very fast---perhaps because it was too hot when he took it off the marble.  Mine was turning faster than ...

The last recipe did manage to cream, but after about 2 days.  They were pretty crunchy, and I wonder if I cooked them too long.  But I think we certainly didn't pull them enough. We tried another batch of the same recipe tonight, but this time only made a half recipe.  I took the cool spatula thermometer out of its spatula (leaving just a stick) because it wasn't clear that the temperature measuring bit would be low enough in the liquid to measure.  It turns out that it would have been fine: after adding the butter it bubbles up considerably, but we had forgotten that. I resolved to take the mints off earlier (at 256 or 257) so that it wouldn't get so crunchy, but just at the end the temperature went up and up and up very fast---totally unlike my experience with cooking candy, so I suspect that the thermometer (or the thermometer holder, me) was doing something wrong.  We poured it on the slab and commenced pulling according to directions.  This time we...

Some friends of ours have a granddaughter getting married (and she's a friend of ours as well) and so I agreed to help out with the shower.  Apparently this is to be a "southern" shower, full of tradition and elegance, but not too far over the top. Among things that are needed for a shower are punch with great grandma's punch bowl, sandwiches with cream cheese and green pepper jelly, and southern pulled butter mints.  "Ah, nobody can make those anymore.  We used to know someone, but the tradition needs to be passed down."  Like a fool, I said that I'd be happy to give it a try.  I suffer greatly from "I got a PhD in math, how hard could X be?" where X is something like gardening, or quilting, or cleaning, etc.  It's always harder than I think it will be. "We'll call Mrs. X who makes these, maybe she'll pass down the method.  I hope you don't hate me!"  I was actually planning on doing research online, watching a fe...

I was a part of my first orchestra concert yesterday. I've been in a community orchestra for the past 4 months, made up mostly of people who played in high school or college and who want a reason to practice. There are a few of us who picked up the instrument as an adult. I definitely feel like the weak link, but on the other hand I improve every time I play, and the other members and my teacher assure me that my skills are sufficient. Also, playing next to competent musicians helps me to improve and they seem to be tolerant of my sour notes.  My one strength is that having listened to the music we pay for my whole life, I know how the piece is supposed to go, even if I can't get my body to comply. I learned several things about playing in a concert. First, it was long for me to play. It was about 45 minutes of almost constant playing, and just sitting down for that long is unusual for me, not to mention holding up a viola... I kept expecting our director to stop us and tell u...

We just finished a puzzle!  It is a 1000 piece jigsaw puzzle titled, "Beautiful Santorini." I got the puzzle in the summer when I heard about a tour going to Greece and kept getting beautiful status updates. We started the puzzle way back after the hurricane in September.  The sky was finished almost immediately after we started---the subtle variations in clouds and colors made it surprisingly easy.  Then we started on the city.  It turns out that little bits of windows, doors, televisions, umbrellas, are actually harder to do than swaths of color.  It took about 2 months to make any significant progress on the rocks and grass around the town, and on the buildings of the town.  That's a long time to be without your coffee table... The best part of putting the puzzle together was finding little scenes that are unnoticeable when looking at the entire puzzle from a distance.  For example, there is a piece with a guy climbing over a wall, or pieces of th...

We got some snow. And now Luke is outside shoveling snow. Off the grass. Into a wheelbarrow. To make a fort. He notes that this is not as crazy as the neighbor who was out riding his bike wearing a swim suit. I suppose I agree.

Luke and I have been reading The Black Arrow by Robert Louis Stevenson over the past few weeks.  I remember really enjoying it when I read it as a child, even if I didn't really know who was fighting in the War of the Roses.  And Luke is enjoying it as well, despite the archaic language and difficult to understand motivations. After the third or fourth person was shot in the back and died in front of the main character, he did say, "This is worse than The Hunger Games !"  And I have to say, he's not wrong.  The main character, Dick, kills a spy in cold blood (by surprising him, not really in a fair fight) rather than be discovered, which would mean Dick's certain death.  Then he has to stay all night in disguise in a monk's habit in the abbey praying for the dead spy, after which the monks clean the blood off the floor and prepare for the wedding of Dick's beloved to a greedy, conniving nobleman.  During the wedding, though, the groom is shot through th...

"Do you have to fix something everywhere you go?" Luke, after Michael helped with an LED problem at the house we visited for dinner The answer is yes. Yes he does.

When I was a one and a half years old I was an only child, so I had actual adult supervision. -Eleanor, explaining why she didn't climb up into the cabinets when she was little.

Luke and Amanda are learning a fiddle/violin piece. I love it!

Recently I helped Luke's classmates make geodesic domes out of newspaper, using this website: http://www.pbs.org/wgbh/buildingbig/educator/act_geodesic_ho.html It was very satisfactory: the kids learned about the importance of measuring accurately, keeping track of progress, and how something that looks unimpressive to begin with can be actually amazing at the end.  I was even amazed ("It works!  Math works!" I exclaimed as the kids put the roofs on) and I've done it before. To give the kids something to look at, we made a sturdier but smaller dome out of straws. I used this website, which has a mix of complete, accurate directions and pictures and vague, inaccurate directions, as well as nice pictures of a chicken run geodesic dome: http://sci-toys.com/scitoys/scitoys/mathematics/dome/dome.html One important note: you actually need the following numbers of straws: 90 long (7 3/4") straws, for 6 pointed stars 50 short (6 1/2") straws, for the 5 poi...

At some point in my life, I am going to open a restaurant.  Its name will be, "Caramelized."  All the food will come out 10-20 minutes after you expect it, and will have a blackened crust, or blackened flakes (probably the onions) floating in it.  Every once in a while there will be a fire alarm and everyone will have to leave while someone opens all the doors and lets the smoke out of the kitchen.  The motto will be, "It's not burnt, it's caramelized. " Not that I have any experience with this type of cooking at all.  Sigh.

Most days we go on our merry way without being aware that we are hurtling through space at millions of miles an hour.  The other day I saw something that made me take notice. Eleanor and I were driving to school, and as we drove up the hill out of our neighborhood we saw a beautiful picture of the moon and Venus framed by the trees on either side of the street. It was beautiful, and Eleanor took a picture with her phone. A month later, we were driving at the same time, and saw the same arrangement of the moon and Venus, but it was over to the right, no longer framed perfectly by the trees.  We had moved, the moon, had moved, Venus had moved... It looks like we are on solid ground, but the earth is not actually as static as we assume.  And I'm sad because that picture won't come around again until next year... when my life will have moved to some different place as well.

The other night I was exhausted and feeling ill, so after getting Luke to bed (early, because he was sick as well) I told Amanda, "You need to put yourself to bed.  Get to bed at a reasonable hour." Eleanor piped up, "Oh, you get 'reasonable hour' privileges!"  It struck me that the choice of when to go to bed one of the stepping stones on the road to adulthood.  Giving someone that privilege is not an assumption that they will always make the right choice (ask me whether, as a supposedly responsible adult, I always go to bed at a reasonable hour!). On the other hand, it does assume that the person can judge what the reasonable hour is, take steps to get to bed at that time, and take responsibility for their mood when they make a mistake.  The final step in responsible adulting involves evaluating whether what you did worked well, and adjusting your actions so that they are more constructive in the future. Unfortunately for Amanda, I then looked at the c...

Luke helped decorate the Christmas tree today---he's home sick, but you don't always feel like lying on the couch if you are sick.  He decided that the glass ornaments should be put on the lower branches, because, "If the tree falls, they are less likely to break."  It wasn't too long ago that putting the glass ornaments on the lower branches made it more likely that they would break. He also helped check every light on a string to find the ones that were burnt out so that the string would light again.  In the course of going through the lights we found some that made the string blink.  He wondered how it worked---after all, the bitty bulb wasn't big enough to have a computer controller in it.  When he looked inside at the bulb he saw a thick strip near the filament.  "A bi-metalic strip! That's brilliant!"  He was impressed by the genius of a bi-metalic strip for the next few hours.  I wonder if that's how they really work...

I asked Amanda if she wanted to bring her violin on this year's vacation to see grandparents.  It can be fun to make music with cousins and it is good to keep up on practicing while traveling so you don't lose your progress. It also gives structure to the days which can sometimes be long and boring. However, Amanda said that she had written a note to herself telling her not to bring her violin along.  I understand that, I make imaginary notes to myself all the time.  But then she got out her notebook and showed me a page on which she had written, "Note to future Amanda: Do not bring your violin on a vacation."  Not an imaginary note---there it was, in black and white.  So we didn't bring the violin this time.  I think future Amanda appreciated the foresight. Poor Luke plays piano.  On the one hand, he absolutely cannot bring his instrument along with.  On the other hand, many places have pianos and then he can practice.  We are still work...

One of the great things about this age is that I can show all the movies and TV shows I loved as a child to my kids.  The peril is that sometimes they really do not hold up. I watched MacGyver with the kids.  They really enjoy his can-do attitude he has and the way he turns chewing gum wrappers into explosives (whether or not the things he builds would be possible in real life).  They see why Dad has MacGyver as his nickname.  On the other hand, women really have one purpose in this series: to be rescued by McGyver.  Even the extremely smart scientists are there to be rescued.  I had found myself skeptical about whether women really had bad parts in TV shows from my past: I was wrong.  It is that bad.  Maybe in the later episodes their roles improve, but I doubt it.  It really makes me appreciate modern writing: it's so much more exciting when everyone gets to help. We watched The Goonies .  I remembered it as being a fun adventure ...

The other day we were looking at the school dress code.  After noticing how silly it was, she noted, "Well, it doesn't seem to forbid Starfleet uniforms." Indeed.  (Well, it might forbid some of the ones from The Original Series...)

Today Amanda was reading at the restaurant where we ate lunch.  I told her it was time to go and she looked around for a bookmark.  She picked up the ketchup packet and placed it delicately between the pages of her book... Immediately I was besieged by visions of books with ketchup stains all over the pages, goopy ketchup all over Amanda's face and hands, napkins failing to contain all the mess... "No no no no no!" I said, and then (and only then) Amanda saw what the problem was.  I always feel like Cassandra standing at the gates of Troy before the Trojan War, foretelling doom and gloom.  I am constantly warning children that if they don't eat they will be hungry during errands, if they don't drink they will get migraines, if they don't put away their shoes they will not be able to find them later, if they carry that down the stairs that way they will fall, and so on.   It is interesting, because biologically speaking their fore brains are not as well d...