Measurement, Memory, and Mathematics

“Five hundred twenty five thousand six hundred minutes/Five hundred twenty five thousand moments so dear/Five hundred twenty thousand six hundred minutes/How do you measure, measure a year?” –“Seasons of Love”

Yesterday, we took Alex to a family restaurant for dinner, and as soon as we sat in our booth, he realized that he had forgotten to wear his watch. In the past, he might have panicked that he didn’t have his watch to keep track of the time, and we would have had to leave immediately. However, he has learned to roll with things much better lately, staying calm and solving problems. First, he looked around the restaurant for a wall clock, but there was none to be found. Then, he decided he would just borrow one from us. In a scene reminiscent of “Goldilocks and the Three Bears,” he tried and rejected our watches. Ed’s watch had the wrong date, which was unacceptable, and my watch was too snug on his wrist. Finally, I handed him my cell phone with the digital clock showing on the screen, and this item, like Baby Bear’s porridge, chair, and bed, satisfied Alex, who found this substitute for his watch to be “just right.” Crisis averted.

As I have mentioned in previous blog entries, Alex makes sense of the world by measuring it and keeping records of statistics that matter to him. His favorite subject has always been math, and he possesses almost savant skills in working with numbers, enhanced by his amazing visual memory. From memorizing nearly 1500 digits of the irrational number pi to remembering people’s birthdates to calculating math problems mentally, he has a gift for remembering and understanding numbers. To assist him with measuring the important aspects of his world, Alex always keeps his measuring tools close at hand, which are among his prized possessions. Calendars, clocks, tape measures, calculators, and thermometers line his bedroom desk and chest of drawers, ready when he needs them. Because he relies upon them greatly, he has more than one of each type of measuring tool in case he mislays one of them and can’t find it. In addition, he keeps notepads and pens handy to record his measuring data.

When dealing with measurements, Alex values precision. If I tell him something costs six dollars, he will correct me and say, “Or $5.99.” If I tell him something will last about a week, he will ask, “Approximately a week or exactly six days?” When his behavioral therapist or music therapist arrives for his sessions, he immediately records their precise arrival time on a notepad as he consults his watch. Even though I have told him that they will be here around 1:00, he wants to keep track of the minute that they actually ring the doorbell. We have also learned not to dispute him when he proclaims certain information about when past events have occurred. For example, he likes to keep track of gasoline prices and will tell us how much gas cost in a particular year. Even when the figures seem a bit off, I never question them. Whenever I go online to check his accuracy, I discover that he is always right, and I find his keen knowledge of the history of gas prices a little eerie.

While some people with autism have amazing abilities to calculate days and dates, I don’t really think Alex possesses that skill. So-called calendar savants can be given a particular date and immediately figure out what day of the week that date was. Recently, my aunt and uncle came to visit from out of town, and Alex commented that my uncle had been born on a Sunday. My uncle didn’t seem to know what day of the week he was born, but trusting Alex’s confidence, he thought that fact was likely. After looking up my uncle’s birth date on a perpetual calendar in the almanac, I confirmed that Alex was right about what day of the week my uncle had been born. However, I suspect that Alex probably had also used the almanac as his source of data instead of calculating the day in his mind.

Nonetheless, Alex does possess outstanding mental calculation skills. A couple of weeks ago, I asked him how he had liked the dinner I had made. After quickly assessing his plate, he told me he liked it “91.6 percent.” Although we’ve grown accustomed to Alex’s percentage rating scale for meals, we were surprised by this odd figure since he usually rates foods in less specific figures, such as 90 percent or 85 percent. When we asked him how he had arrived at that number, he said, “Pasta 90 percent, sauce 90 percent, Italian sausage 95 percent.” As I was trying to add up and divide those figures, Ed, who is much better in math than I am (and from whom Alex has probably inherited his math skills), quickly confirmed the accuracy of Alex’s calculations.

Similarly, yesterday Alex was telling me that he had a “little voice” in June of 2004. Alex has a great fascination with people’s voices, especially those of children, whom he says have “little voices.” I suppose he was reflecting upon when his own voice changed. After I figured out how old he would have been in June of 2004, I commented that he would have been twelve and a half years old in June 2004. However, he corrected me by noting that he was thinking of when he was “12.482 years old.” Fortunately, he shows patience with my lack of mathematical precision, seeming almost bemused by my approximation.

At the restaurant yesterday when he was using my cell phone clock as a substitute for his forgotten watch, Alex noticed the message on the bottom of the screen and asked me what “232 service days left” meant. I explained that my phone service is “pay as you go,” and that I had paid for a year in advance and had that many days left before I need to renew my phone. He didn’t respond, but then he quickly said, “November 24^th.” Ed and I exchanged a look and then realized that Alex had rapidly calculated back to the date I had renewed my phone contract. When he said that, I remembered that I had signed up for a year of phone service around Thanksgiving, so his comment seemed likely. A couple of minutes later, Ed, who had been contemplative, commented that Alex was right because he had mentally calculated to see if Alex’s date was correct. The two of them astonish me with how quickly they can figure out in their minds the problems I need some time and a calculator to solve. However, I am grateful that not only has Alex inherited Ed’s math skills but that he also finds using numbers entertaining and satisfying, a way to make sense of the world that sometimes overwhelms him.

“Great is the Lord! He is most worthy of praise! No one can measure his greatness.” Psalm 145:3

Daylight Savings Time

“Time, time, time, see what’s become of me while I looked around for my possibilities…Hang onto your hopes, my friend. That’s an easy thing to say, but if your hopes should pass away, simply pretend that you can build them again.”
--“Hazy Shade of Winter” by Paul Simon

On this first day of daylight savings time, I admit that I dread this annual “springing forward” where the clocks are turned ahead one hour. Since I have to get up by six o’clock every morning to get ready for my job as a teacher, I know that for the next few weeks, I’ll be waking up in the dark again after the past few welcome weeks of awakening to early sunlight. I also know that my body will need a few weeks to adjust to going to bed earlier and getting up earlier as my system tries to reset its circadian rhythms.

I’m certain that those who decided daylight savings time is a good idea probably don’t have to get up as early as my colleagues and I do. In doing some background reading about the origins of this concept of shifting time, I ran across an online article [To read this article, click here.] from National Geographic that indicates Ben Franklin first came up with this idea of making better use of daylight. During World War II, the United States mandated daylight savings time as a way to save resources. In my home state of Indiana, until 2006, most of the state opted not to go on daylight savings time, so in the spring, summer, and early fall, all counties were on the same time, but in the late fall and winter, a handful of counties were an hour behind the rest of the state. Interestingly, a study in Indiana showed that daylight savings time really did not save energy, one of the primary reasons given for moving the clocks ahead one hour.

Besides my resistance to get up earlier in the dark, I always fret about how the time change will affect Alex, who is sensitive to changes. Although he has understood the concept of daylight savings time and has been very aware of telling time, even when he was little because he loved clocks, Alex doesn’t always readily adapt to the time changes in the spring and fall. Over the years, we have tried adjusting his bedtime by a few minutes each night in the days prior to the time changes, and that never really seemed to make a difference. Like his mother, within a few weeks, he simply adapted to the changes and was able to adjust his sleeping habits.

This year, we’re hoping that daylight savings time is the change Alex needs to reset his internal clock that has been off for several weeks. Like a preschooler, he has been getting sleepy shortly after supper and going to bed in the early evening, which means he also awakens between 5:30 and 6:00 A.M. Also, he has been insisting that he wants to eat dinner about an hour earlier than we normally eat, telling us he’s hungry around 4:00 or 4:30 when we usually eat dinner between 5:00 and 5:30. I guess because he starts the day about an hour earlier than he used to has completely thrown off his internal clock and shifted his basic routines of sleeping and eating forward an hour. With fingers crossed and prayers said, Ed and I are hoping that shifting the clocks forward an hour will remedy this situation so that he’ll get up around 7:00, go to bed after 9:00, and be ready to eat dinner at 5:00 or 5:30. In fact, we were tempted to not change the clocks so that Alex would rely on his biorhythms instead of the actual time. So, we shall see how he adapts and hope for the best. Maybe this daylight savings time will be one to celebrate instead of to endure. If Alex adapts nicely, it will be worth getting up in the dark—at least that’s what I’ll tell myself tomorrow morning as I stumble out of bed an hour earlier than my body is used to doing.

“For everything there is a season, a time for every activity under heaven.” Ecclesiastes 3:1

Acccessories

One of the most interesting aspects of my job as a part-time middle school teacher is that I can observe [mostly] “normal” teenage behaviors. Often I compare and contrast how my students act with how Alex does to note how autism has impacted his behavior. The apparent need for teenagers to travel with accessories is something I have noticed in my seventh grade students as well as in Alex, so this must be a characteristic of teenagers in general. While my students frequently carry electronic devices, such as cell phones and iPods (although they may not display them openly during class since school rules prohibit their use during class time), Alex carries around different accessories that reveal his interests and needs.


Before and after school, students often use their cell phones to text, e-mail, and call their friends and parents. Because we cannot trust Alex to use a cell phone wisely, he—unlike most teenagers—doesn’t have one. I’m not sure who he’d call or text anyway, other than maybe 911, and we don’t need the police showing up on our doorstep to answer Alex’s false alarms. Besides, communicating verbally with others doesn’t rank highly on Alex’s list of priorities, anyway. Instead of a cell phone, Alex prefers to carry an electronic dictionary, perhaps so that he can look up the meanings of words he wants to know. In addition, he often carries around the more traditional dictionaries, in the form of books, but he likes the convenience of the compact electronic version.


Another accessory middle school girls carry is lip gloss, which they sometime surreptitiously apply during class. A few months ago, Alex went through a phase where he carried around lip balm. He only applied the lip balm before he went to sleep, but he liked to carry not one but two tubes of Blistik with him—one regular type and one mint flavored. If he couldn’t find his, he’d take mine. Before he went to bed, he had to make sure that he put the lip balm on his dresser. At some point, his fascination with lip balm ceased, and now I occasionally find tubes that he’s left behind in various places.


Of Alex’s accessories, his favorites are his clocks. Because of his fascination with time, he rarely goes anywhere that he doesn’t carry a clock with him. Although he has several battery-operated clocks that he can move from room to room, he seems to have three that are particular favorites. One is a talking clock that announces the time, often startling me when he’s left it behind in a room where I’m sitting. Alex especially likes clocks that also have thermometers built in so that he can keep track of the temperature along with the time. The other day, taking advantage of a temperate November afternoon, Alex went outside and sat on our backyard deck, carrying, of course, his clock with a thermometer. As he happily watched the time pass before his eyes on the clock, he noted the temperature changes as the sensor sat in the sunshine. While most teenagers would prefer listening to music on their iPods, Alex enjoys watching the numbers change on his digital clock/thermometer as the temperature varies and the seconds and minutes go by. Even though Alex carries different accessories than his peers do, he seems to enjoy the same sense of security, comfort, and entertainment they provide for him that similar items do for other teenagers. Hopefully, soon he’ll prove trustworthy enough to earn the accessory most of his peers possess—the ever-present cell phone. Of course, knowing Alex, he’ll just be thrilled that he can use it to find the time and temperature; he doesn’t need much to make him happy.

"Those who use the things of the world should not become attached to them. For this world as we know it will soon pass away." I Corinthians 7:31

Snapshot

As I walked into our kitchen the other afternoon, I discovered Alex had left an interesting arrangement of his belongings on the kitchen table. Realizing how much that array of items revealed about him, I immediately grabbed the digital camera to record what he had left behind, the way an archeologist records ancient artifacts to demonstrate how people in other civilizations lived. For those who have not lived with a child who has autism, I offer this visual evidence along with explanations of the significance of each essential item.

In the top left of the picture, a size 9 Nike athletic shoe can be observed. This shoe, a right one, happens to belong to Alex, who apparently placed it on the kitchen table himself since Ed and I don’t put shoes on the table. While some may be surprised to find a shoe on the kitchen table, around here we find Alex’s shoes in all sorts of unusual places. Whenever he gets tired of wearing his shoes, he takes them off and leaves them right where he is. Often, we find them on the couch where he’s been reading, in the middle of the bathroom floor after he’s been using the toilet, or anywhere in the house where he’s been walking and decided he’d prefer to be shoeless. As the spirit moves him, Alex takes off his shoes and dumps them where he’s standing. That answers the question of why his shoe is on the table, but the next logical question might be, “Where is the left shoe?” or “Why is there only one shoe on the table?” Sometimes Alex decides to only remove one shoe, which has led us to nickname him over the years as “Johnny One Shoe.” He often does the same thing with his socks, wearing a sock on one foot and going barefoot with the other, which has led us also to dub him as “Johnny One Sock.” Fortunately, he finds both nicknames amusing. As for that left shoe, it was under the kitchen table; maybe he didn’t find it worthy of being on the table with the right one. That’s a question I can’t answer, and Alex certainly won’t reveal his reasoning.

In the center of the table are the remains of his afternoon snack, gluten-free and casein-free cake. Alex frequently leaves one or two bites of food on his plate, as illustrated in this photograph. Also, like a typical kid, he eats all the frosting but leaves a little cake in his dish. After discovering that Alex had food sensitivities to glutens (the proteins in most grains, including wheat) and caseins (the proteins in milk and milk products, such as cheese), for several years we have kept him on a strict diet that avoids these proteins. He never complains about his restricted diet, and we are fortunate that he eats a variety of foods well. With more people on gluten-free diets, the availability of gluten-free products on the market has increased significantly since he started on the diet, which makes life so much easier for us. I used to make all of his treats from scratch, carefully measuring three different gluten-free flours (rice, tapioca, and potato starch) to make the perfect baking blend along with xanthum gum powder, which helps hold the ingredients together, the way glutens do in most flours. Last year, Betty Crocker came out with gluten-free baking mixes that are readily available at grocery stores, and this has made baking cakes for him much easier. The cake in the bowl was from a Betty Crocker gluten-free (and casein-free, made with Fleischmann’s unsalted corn oil margerine) yellow cake with Duncan Hines classic vanilla frosting (also gluten-free and casein-free). This particular cake was baked for Ed’s birthday although I also made a chocolate chip cheesecake for Ed. Whenever we have birthdays, I typically make two cakes, one Alex can eat on his restricted diet and another one with typical ingredients for everyone else to eat. I never want him to feel as though he’s missing out on the celebration because of his special dietary needs. I’m just thankful that he enjoys eating the cakes I bake for him.

At the top is yet another typical reminder of Alex, a kitchen timer. As I’ve mentioned in previous blog entries, Alex is obsessed with time, so he often consults calendars, clocks, stopwatches, and timers. I’m certain that his love of math and numerical values is related to this extreme interest in measuring time. He can usually be seen carrying around at least one timer or small battery-operated clock as he moves from room to room, and for some reason he must have something that measures time when he eats. The timer pictured is a particular favorite of his; my parents bought it on sale and thought he’d like to have it. Often we’ll hear random beeping coming from another room and realize that either Alex is setting the timer or has set the timer previously to make it beep. He’ll even carry around timers and clocks that need new batteries just because they seem to make him feel secure, whether or not they are working. One of the good things about Alex’s love of clocks is that he has learned how to set the time for every clock—and we have many—in our house, which comes in especially handy on days like today, where the time change necessitates adjusting all the clocks. Now if we could just get him to put his shoes where they belong, that would be helpful, too.

“Don’t worry about your personal belongings, for the best of all the land of Egypt is yours.” Genesis 45:20

Marking Time

Since Alex loves numbers, he finds the concept of time interesting, and he values the tools used to measure seconds, minutes, hours, days, months, and years. He has collected a variety of stopwatches, clocks, and calendars so that he can keep track of the passing of time himself. Alex especially likes precision when discussing time. For example, if we tell him that we’re leaving in five minutes, he might ask, “Five minutes approximately or seven minutes exactly?” Or if we tell him something will happen in a couple of months, he’ll correct us by saying something like, “About two months or exactly two months and four days?” Apparently he subscribes to the idea expressed in American Idol Kris Allen’s song “Live Like We’re Dying”: “We’ve only got 86,400 seconds in a day to turn it all around or to throw it all away.” Alex sees each second as precious—even fractions of seconds matter because he bought a stopwatch that measures thousandths of a second so that he could time the exact length of television segments and commercials.

When Alex was younger, he was obsessed with time and would repeatedly ask us what time it was, even though he knew how to tell time. Unlike many children of his generation who can only read digital clocks, Alex has been able to interpret analog clocks since he was little. Despite his interest in time, he refuses to wear a watch because he doesn’t like the feel of it on his wrist. Therefore, he relies on the numerous clocks we have in nearly every room of our house. Fortunately, he has mastered how to change all the various timepieces we own. This skill is especially handy if the power goes out or when Daylight Savings Time begins or ends, requiring the clocks to be turned back or ahead one hour. For the rooms that don’t have clocks, Alex carries a battery-operated alarm clock with him. He takes a black clock into the bathroom with him, and he brings a silver clock and puts it on the table to watch as he’s eating. How he determined which one was for which purpose remains a mystery, but he never uses the eating clock in the bathroom or the bathroom clock in the kitchen. For a while, he would also set the kitchen timer because he only wanted to eat for ten minutes. Once the buzzer went off, he was through with the meal unless we granted him bonus time to finish. Probably his favorite clock, though, is the atomic clock in his bedroom, which measures the time precisely using radio waves. He takes comfort in knowing that the atomic clock provides exactly the correct time.

In addition to his clocks, Alex also has several calendars that he keeps in his bedroom. While most people use calendars to know what the date is and to plan events, Alex likes to study calendars and the patterns that they follow. He finds perpetual calendars especially fascinating, seeing how one year leads into another and how Leap Year impacts the way the days fall in the months. Last year, when we asked him what presents he would like for Christmas, he told us he wanted “old calendars.” After giving his request some thought, I decided to look online at the website eBay to see if I could find him vintage linen towel calendars and was amazed to find several available. After surveying the selection, I bid on some of these linen towels and was able to get him relatively inexpensive calendars from various decades: 1957, 1963, 1974, and 1989. He was thrilled with these old calendars and would lay them out to study them. This summer, he specifically requested calendars for 1996, which is the first year he can remember, and 2004, which was the year Ken Jennings set the record for most consecutive wins on the game show Jeopardy. Fortunately, I was able to obtain calendar towels for those years, as well. In addition, his aunt in New York sent him a calendar towel for the current year, 2010, to add to his collection. Despite Alex’s insistence upon accuracy of time measurement, he has always done things on his own timetable because of his developmental delays. Perhaps this is why he needs tools to measure time himself and make sure that nothing passes him by as he waits to master skills in his own good time.

“At the time I have decided, my words will come true. You can trust what I say about the future. It may take a long time, but keep on waiting—it will happen!” Habakkuk 2:3