Dear Voters of California

Today is Write to Marry Day, in which bloggers write about their opposition to Proposition 8, the proposed amendment to the California constitution that would take away the rights of same-sex couples to marry.  This is a post I've been working on for a long time in my head, and thanks to the impetus of the day, is finally coming out on the page!

Dear Voters of California,

This coming Tuesday, you will be voting on an issue that is near and dear to my heart.  I really wish that I could be one of you so that I could vote against Proposition 8.

Why?  Because if there's one thing in this world that's important to me, it's my family.  I love my husband, I love my son, and my sisters and my parents too.  I love my in-laws, my bonus family members, and my outlaws too.

Outlaws?  Yes, I have outlaws.  They're people who, in my mind, are in-laws, except for the whole lack of legality business.  You see, half my first family is gay.  This means that the loving, loyal, supportive lifetime partners of my family members are considered complete strangers to my family members under the law, because between the two partners there is not exactly one Y chromosome.

But in California, my same-sex-coupled family member/outlaw pair could be considered as legitimate as my husband and I, and share the same sorts of rights and responsibilities that he and I do.  They could be considered first-class citizens with the same rights toward each other that any single-Y-chromosome pair of adults who love each other can have by paying a modest fee to the County Clerk's office.

That is, provided that you vote down Proposition 8.

Proposition 8 is designed to take away rights -- rights that anyone should have -- to marry, regardless of the content of their chromosomes.  And that, Californians, is just plain wrong.

The opponents of marriage equality, knowing that there is no legitimate legal argument for their opposition, have resorted to lying -- saying that legalizing same-sex marriage would force churches to marry same-sex couples or lose their tax exempt status.  That is untrue.  Churches could choose to not marry same-sex couples, just like they can choose not to marry couples who don't follow any of their other religious tenets.  If a church doesn't have to sanctify the marriage of an atheist, they won't have to sanctify the marriage of a same-sex couple, either.

No, this is not about upending other people's religions.  This is about respecting the civil rights of people who are different from you.  This is about leading the way in tolerance, love, and justice.

I hope that you in California vote down Proposition 8, and that it energizes the country so that sometime soon, I will be able to weep with joy as I watch my family members and their same-sex partners united in matrimony, not only spiritually but legally.

Sincerely,

Rebecca, loyal sister, daughter, and friend to LGBT people

Sleep Slippage

Dearest Internets, I am at my wits' end! I appeal to your wisdom. Seriously, any advice is welcome.

We are having trouble with getting Vinny to go to bed. Here's the situation:

He sleeps (or, I should say, ideally he would sleep) in a toddler bed that is simply his crib with one side off. We removed the side about six months ago, because we thought it would help in the mornings when he woke up and was bored. That way he could just slip out of bed and play.

Well, he figured out a couple of months ago that if he wasn't really tired, he could just open the door of his room and leave. So we installed a child-proof doorknob cover on the inside of his door. But this just made him angry, and if we put him to bed, he would run over to the door and kick it and hit it, while screaming and crying. Eventually he would get tired and fall asleep right in front of the door. If you opened the door a few hours later, you would hit him with the door. I did manage to squeeze through and put him in his bed but it was hard to do so without waking him up.

Then we decided to install a gate in his doorway, because we thought he might be afraid of the dark and need some light from the hallway. But that actually made things worse, because he can hear what's going on around the house a lot better, plus he can see you leave.

Here's what I've tried.

• I can go through the nighttime ritual and then put him to bed awake, which results in him screaming and crying and doing what I have described above.
  
• After the nighttime ritual, I can continue to hold him and rock him to sleep in his rocking chair, and then set him down in his bed. He will sleep for a few hours until he wakes up in the night and realizes that I'm not there, and then begin screaming and crying and rush over to the door. The crying is genuine, or at least, he does produce tears.
• I got him a nightlight, thinking that it could be fear of the dark that's bothering him. But unfortunately, he tends to pull the night light out of the outlet, which scares me that sometime he'll end up shocking himself.
  
• I can take him to bed with me, and (usually) he falls asleep and sleeps through the night. Sometimes, such as this past Friday night, he does not want to fall asleep and then we don't get to bed until obscenely late (2 am, in this case).
  
• If we move him to his room when he's fast asleep, he will wake up in a few hours and cry and rush to the door. If he does fall asleep with us, sometimes he lies completely still and sleeps peacefully; other times he kicks us in the head all night. Usually he is very mobile when he is close to waking up.

So we do have a solution that usually works: letting him sleep with us. But it is not the most convenient for us, and I would like for him to sleep in his own bed. Any suggestions?

Weekend Adventures with Grandparents

In honor of our beloved son's second birthday, Jeff and I decided to rent a cabin at Big Ridge State Park and invite his four grandparents to join us. Jeff's parents and my dad and bonus mom came down on Friday.

On Friday afternoon, they went on a tour of my lab, including a tour of the area I work in. Then we headed for the cabin. We got there after closing time, and didn't know how to get the key to our cabin. Luckily, there was a ranger from a different park coming out of the restroom at the time, and she was able to find out with a phone call that our key could be found in the mailbox.

After unpacking our bags and putting our food in the fridge in the cabin, we headed out to a nearby town for pizza (Vinny's favorite food). We found a local pizza place and shared two pizzas before returning to the cabin for the night.

In the morning, I had planned to make some pancakes for us all to enjoy. I'd mixed all the dry ingredients at home, and would mix in the wet ingredients at the cabin. But I realized that I had forgotten my two-burner griddle, and sent Jeff back to our house for it and a few other things (such as allergy medication). Then, after he got back, I realized we had forgotten the eggs, so Dad and Marvis went out to get some eggs. Finally, we had all the ingredients for our breakfast, which we enjoyed at about noon.

In the afternoon, we took Vinny down to the playground at the park. He really enjoyed slides for the first time. He figured out how to slide down a slide by himself, which is a pretty big development. In fact, there was a corkscrew slide that he was somewhat intimidated by, so I offered to help him go down it, but before I could get seated, he'd accidentally fallen down it. I was worried that it would freak him out but it seemed to have the opposite effect. He couldn't get enough of that slide, and he must have gone down it a dozen times or more.

That evening, we cooked hamburgers and brats on the charcoal grill for Vinny's birthday dinner. We enjoyed the hamburgers and brats along with some red potatoes with rosemary, potato chips, and fruit salad. After dinner, we opened Vinny's presents to give us some time to make room for cake and ice cream.

I had made Vinny a cocoa devil's food cake (my standard chocolate cake) with raspberry filling between the layers and white frosting on the outside. As it turns out, my son is more of an ice cream eater than a cake eater. He ate all his ice cream and some of mine, but ate only a few bites of the cake.

Having so much sugar so late made it a little difficult to put Vinny to bed, but eventually he did fall asleep. In the morning, Jeff and his parents went to Quaker Meeting, while the rest of us cleaned up the cabin before taking Vinny back to the playground one more time. Then, we drove back home, where Dad and Marvis assembled Vinny's new Vinny-sized table for him.

Eventually Jeff and his parents arrived home again, but we discovered that Jeff's dad had left his camera at the cabin, so Jeff and his dad drove back there to retrieve it.

Over all, it was a really fun weekend together. We all had so much fun getting together and appreciating Vinny. We may all differ when it comes to politics, religion, or other matters of opinion, but one thing we all agree upon is that Vinny is a fantastic little boy.

Richer Than God!

Confused about the credit crisis? Need an explanation that even Barbie and Ken can understand? You are in luck, my friend!

My sister Rachel and her friends teamed up to provide a video explanation of what happened and why we're now in this financial pickle. It will help you to understand what we're all being asked to pay twelve figure bailout payments for. Click and learn!

Adventures in Interval Arithmetic

I realize that some people read this blog just for the math. Those people have been mighty bored for the past several months as I've prattled on about Vinny, the fact that I am really busy, my vacation, etc. I need to remedy this problem and get talking more about math, as this blog's title implies it is about. So, math fans, this post is for you!

When you take a measurement of something (such as the temperature of your sick child, the height of your house's ceiling, or the RPM level of your car's engine), this measurement is not exact. For example, the thermometer we use to measure Vinny's temperature is digital, and displays the following: xyz.t (where x, y, z, and t represent any of the digits 0-9). Assuming that its method of measuring temperature is completely accurate, there is still error inherent in reading this measurement, because the precision of the readout is limited to increments of one-tenth of a degree Fahrenheit.

For example, if Vinny's actual temperature were 101.138˚F, we would see only 101.1 on the readout, because the temperature would be rounded to the nearest tenth of a degree. Therefore we would be unable to distinguish the temperatures from 101.05 to 101.149999.... They would all show up as 101.1. If we say that a is the actual temperature and â is the measured temperature, then for a in the interval [101.05, 101.15), â = 101.1.

Rebecca, you might say. Your parentheses don't match. You are correct! I did that on purpose. In mathematics we use [ or ] to mean "closed interval" and ( or ) to mean "open interval." Any number between 101.05 and 101.15 is within the interval. The only questions are about the numbers at the end of the interval. If a = 101.05 exactly, then it falls within the interval. But if a = 101.15, then it does not fall within the interval. A number infinitesimally smaller than 101.15 falls within the interval, but 101.15 itself does not. This is because a temperature of 101.15 would be rounded up to 101.2.

This is what we have to work with in interval arithmetic: these ranges. So, for example, if we want to figure out what Vinny's temperature range is in Celsius when the thermometer reads 101.1˚F, then we can convert the interval to Celsius.

Recall that C = 5/9 (F-32), where C = the temperature in Celsius, and F = the temperature in Fahrenheit.

So, we could take the minimum part of the interval and convert it, and then convert the maximum too, to create the Celsius interval. This works because [a, b] + x = [a+x, b+x], and µ [a, b] = [µa, µb] for non-negative µ. Thinking about it in geometric terms, picture the number line, and place a and b arbitrarily along the line such that b is greater than a. If you add the same number to both a and b, all you're doing is translating the interval to a different place along the line, but not changing the ordering of a and b. If you multiply by a non-negative number, you're just stretching the interval to be µ times its original width (or shrinking it, in the case of a µ less than one). Multiplying by a negative factor simply reverses the ordering of the interval, i.e., -µ [a, b] = [-µb, -µa].

So, if we do the interval conversion we obtain [101.05, 101.15)˚F = 5/9 {[101.05, 101.15) -32}˚C = 5/9 [69.05, 69.15)˚C = [38.36111…, 38.41666…)˚C.

Multiplication of intervals creates an interesting situation. Suppose you've measured the height of your ceiling and the length of a wall and you want to calculate the area of the wall. If the wall is 2.50 meters tall and 4.63 meters wide, and your measurements are accurate to the nearest centimeter, then the intervals are [2.495, 2.505) and [4.625, 4.635), respectively.

So how would you figure out the range of the area of the wall? When multiplying two intervals [a, b] and [x, y], there are four possible numbers to consider as the maximum or minimum of the interval: ax, bx, ay, and by. In general, we can't just take [ax, by] as the interval; for example the range for [-3, 1] [-1, 2] is [-6, 3], not [3, 2] -- which doesn't even make sense as an interval. In the case of the wall, though, there are no negative numbers to worry about, so the wall area is anywhere from [11.539375, 11.610375) m².

The examples I have given here may seem silly or unimportant, but there are actually some very important applications of interval arithmetic. A big one is computer arithmetic.

Computers have a limited capacity to express numbers. A number such as 1/3 cannot be expressed as a fraction on a computer; instead it is expressed in a form similar to a truncated decimal representation (i.e., like 0.3333). It's not actually a decimal representation because computers represent numbers in base two, but the concept is the same.

As a result of this, if you subtract two numbers that are pretty close to one another, you may end up with a grossly inaccurate result. This phenomenon is known as catastrophic cancellation. For example, if we had a computer that had four digits of accuracy, and we used it to take the difference of 13/12 and 14/13, we would get 1.083 - 1.077 = 0.006. The real answer, 1/156, is approximately 0.006410, so we are not far off. But if our computer had only three digits, we would have 1.08 - 1.08 = 0.00 as the answer!

We can use interval arithmetic to see that while our answer is far from accurate, the interval of uncertainty contains the correct answer. So, in the case of the three-digit accurate computer, we would have [1.075, 1.085) - [1.075, 1.085) = [1.075, 1.085) + (-1.085, -1.075] = (-0.01, 0.01). (Subtracting is like adding the negative of the interval. And when we have the sum of an open and closed bound, the result is open, because (a + almost b) = almost (a+b).) As you can see, the interval of uncertainty contains the true answer, so using interval analysis we can find an upper bound on the margin of error for our calculation.

There are other cases in which an analysis using interval arithmetic is also useful, and I hope to write another application up soon. In the meantime, I hope you have enjoyed learning about interval arithmetic and if you have any questions feel free to ask!

Two Years of Vinny

At this moment two years ago today, I was in all kinds of pain because I hadn't yet given in to common sense and requested an epidural.

Today, as I scrubbed the kitchen floor, I thought about how different from that day two years ago is today. I'd much rather scrub the kitchen floor than give birth, I mused.

Yet, that labor was very much worth all the pain. From it came someone who has changed my life for the better: a little person from whom I have learned so much.

I had forgotten that everything is wondrous. I did not remember how satisfying a drink of milk could be, or how fascinating a button is, or how beautiful music sounds. I never knew it was possible to be so happy upon seeing someone you love after a day of separation. I didn't realize that I was worth loving so much, so purely, and so unconditionally.

I am truly fortunate to have this little boy in my life. All the pain and sleep deprivation -- it was worth it. Happy Birthday, sweet boy.

Mariachi Night

Today was a big day: it was performance night for our Mariachi band. It went really well!

We had a rehearsal in the afternoon in the auditorium. It is in the local high school, but it is no ordinary high school auditorium. The auditorium, along with the rest of the high school, has been recently renovated -- the ribbon cutting ceremony was just last month. The auditorium is bigger than some University venues I have played in, and the acoustics are wonderful.

Then we attended a pre-performance reception sponsored by my employer's international friendship club. I had to leave early because I was asked to speak at the pre-concert discussion of the music. I explained how our group was formed and a little bit about the music to an audience of interested music lovers.

Then, it was time for the orchestra concert. We Scientificos Locos (mad scientists) sat in the audience during the first part of the concert. During intermission we got our instruments and waited back stage while the orchestra played a short piece. Then, we were on stage.

I suffered no stage fright (after all the recitals I've done, this performance was nothing). My fellow Scientificos Locos did not freak out either. We went out there and just had a lot of fun, and thanks to that, we did great. Oh sure, there were a few mistakes, but nothing major. Our enthusiasm more than made up for it. We got a lot of applause when our three pieces were over.

After another piece by the orchestra, the concert was over. As the audience enjoyed some Mexican desserts at the after-concert reception, we got lots of compliments and gratitude for performing.

I had a really good time performing. The only thing I wished was that Jeff and Vinny could have been there. I had some complementary tickets reserved for them, but unfortunately Vinny was too tired and cranky to make it through the concert. Jeff wisely took him home after the pre-concert reception.

Checking In

I really am still alive, just very busy with crazy things like WORK!  I have an interesting post planned on a movie that Jeff and I recently saw, but it takes time to work these things into final blogging form.

So instead, I'll leave you with an anecdote.  The other day, I was talking to a man who made an inappropriate joke (i.e., racist, sexist -- it doesn't matter what exactly).  I had once read, maybe at Thus Spake Zuska or somewhere else, that when you encounter an inappropriate joke, a good tactic is to feign ignorance and ask the person to explain the joke.  I thought this was a perfect opportunity to try out this tactic.

So I put a puzzled expression upon my face, and said, "Was that a joke?  I see you're laughing, but I don't get it."  

"You've got to be kidding me," he said.

"Oh no, I really don't understand what's funny.  Perhaps you could explain it to me."

He grew uncomfortable and embarrassed.  "It was an inappropriate joke that I shouldn't have made.  Never mind."

In this way, I was able to make him realize that what he said was inappropriate, without lecturing him (which would probably make him unreceptive to the message) or coming off as self-righteous.  So thank you, whoever had this idea!  It worked well in this case.