In his very detailed and neater than a pin garage workshop Doug Sanders stands next to his 3D printer holding two of the Mobius strap designs he has created for school kids. Doug uses Mobius zippers and Mobius straps, which are one-sided and pose an interesting math concept as one way to get kids interested in the field of mathematics. In his working life Doug was an actuary and worked with difficult mathematic concepts. Staff photo/Brian Larsen
He didn’t know it as a child, but the work of two German mathematicians in 1858, Johann Benedict Listing and August Ferdinand Mobius, who would co-discover a ruled surface with only one side and one boundary component that would be named a Mobius strip, would one day prompt Doug Sanders to create a Mobius Zipper.
“Many years ago I made a crude Mobius Zipper attached to the round, hollowed top of an orange powdered drink container,” said the inquisitive Sanders. “This device was used with other matters toward enhancing presentations to students about careers in mathematics.
“At times a piano would be rolled into the classroom. I would ask students if they knew what the square root of two sounded like. I then produced the sound and described a bit of music mathematics.”
Before we get into what the heck the square root of two sounds like on the piano, let’s first meet Doug Sanders.
Today Doug and his wife Mary are retired and living in Grand Marais where they are both active in community events. Doug is a volunteer who serves on the board of the Cook County School District 166 Education Foundation, and he is also active in the Lions Club. He is a strong supporter of the school’s robotics team and helped to pair them up with Duluth East this year.
Doug was born and raised in Duluth, Minnesota. He graduated from Duluth East High School and then went to the University of Minnesota Duluth (UMD) and graduated with a bachelor’s of science and mathematics degree.
After UMD he was off to the University of Iowa where he earned a Master of Science, Actuarial Science, and Mathematical Sciences diploma.
What followed was a long, interesting career as an actuary.
Typically, he said, an actuarial career usually begins as an apprenticeship and requires passing 10 professional exams. Doug was employed at four insurance companies before creating his own company, Sanders & Associates, Inc. And yes, Doug did pass all 10 tests.
While he was at UMD, he met Mary. Today they have two adult children and five grandchildren.
“We honeymooned in Grand Marais,” said Doug. And then, much later, decided to retire here.
When asked what motivated him to pursue a career based in mathematics, Doug said, “There were several experiences in my youth and in my adult life that led to my engagements in three different mathematical areas.”
Climate Change
What could climate change and mathematics have in common? Plenty, it turns out.
Doug recounted several incidents in his youth that would shape his future life. As a preschooler in the early 1940s, at his paternal grandmother’s house in Lester Park, he would watch for wolves crossing over to Wisconsin on frozen Lake Superior.
Also, he said, “As a preteen in winter visiting my grandma’s house, I would observe how water and waves became a snow and ice bed.
“In my preteen and teen years, my dad and I trout fished in virtually all the streams and rivers of Cook County. I became aware of how the weather would affect fishing results. Trout were easily spooked on bright sunny days.
“On our road trips to and from Cook County, my dad and I observed effects of cold and warm air layers over Lake Superior. We witnessed ship and land illusions. Once we sighted a large upside down ore boat in the sky.
“As a teen newspaper boy during the 1950s, there were some winter days colder than 30 below zero. Today the winters are milder.
“My interest in weather was enhanced by my actuarial career. Actuaries in Canada and USA developed a Climate Change Index (CCI) used to help price the climate component of property insurance – residential, public, business, etc.
“Persons doubting climate change are nevertheless paying for it in their own property insurance. CCI is based on data collected by Canada and U.S. throughout North America.”
Sanders pointed to the changing weather in Cook County as an example.
“Cook County, today, is currently scored with a nil CCI. Expect more hardwood forests to grow and more rain to fall. Expect a low CCI for some time. In contrast, the Climate Change Index is increasing exponentially in many areas along the Atlantic and Pacific coasts.
“For high school students of mathematics, actuaries developed standard deviations for geographic specific, climatic events during 1961-1990. CCI is computed as multiples of standard deviations during that period.” To view the CCI and maps, Google “Society of Actuaries” and “Climate Index,” said Sanders.
“During my actuarial career, I developed an insurer’s computerized hurricane model permitting input of the Weather Bureau’s estimated hurricane strength and target. My insurance company then responded to the model’s estimate of damages by creating radio and TV ads announcing the arrival of claim adjusters in the target area. They were on the scene as fast as the Red Cross and Salvation Army.”
Actuarial Mathematics
As a teen cutting grass in a Duluth cemetery, Sanders noted tombstones engraved with birth and death dates.
“I also observed a predominance of widows vs. widowers caring for burial lots,” he added.
Later, he confirmed the fact that women live longer than men, just as he noticed as a teen mowing the cemetery lawn.
“Actuaries have established mortality rate tables derived from U.S. census data. Such data confirms women outlive men.
“Mortality for older Americans has been improving 2 percent per year. Many elderly in the United States will age to triple digits. Actuarial mathematics includes methods to combine mortality projections with investment considerations.
“Working with other actuaries, I developed computer models using mortality tables applied against insured populations. Such models assisted insurers budgeting for future claims.”
Hurricanes
“I developed an insurer’s computerized hurricane model using Weather Bureau’s estimated hurricane strength and targeted location. Such models would estimate upcoming damages due to the insurer. The insurer would then initiate media advertisements about an appropriate size team of claim adjusters being sent to the hurricane’s target location.
“Also, I proved mathematically that tornadoes do ‘see’ mobile home parks and go after them.”
Mathematics applied to music
“When Mary and I moved to Grand Marais in 1999, no resident piano tuner existed. I obtained computer software, lessons, and tools toward tuning our own piano. Math discoveries ensued.
“Now, when presenting mathematical careers to high school students, I would request a piano be rolled into the classroom. Upon asking the students ‘Do you know what the square root of 2 sounds like?’ No takers. I would then perform playing a note simultaneously in the middle of any octave and the note at the beginning of the octave.
“From the tuning equipment, I learned that the audible frequency for each musical note on the piano increases by the 12th root of 2. Being that our Western music octave includes 12 notes.
“If one plays a note simultaneously in the middle of the octave – say F# and the note at the beginning of the octave, the ratio of those two frequencies is precisely the square root of two. The sound made here is discordant. The ratio of F# to C frequencies is 1.414…. and sounds discordant. Math shows us this ratio is an ‘irrational number’ where series of digits do not repeat.
“Contrarily, a ratio of frequencies in a C chord (C E & G) is pleasant sounding and proves to be a rational number wherein series of digits are repetitive.
“The brain does instant math when listening to music chords. Ancient Greeks had an eight-note octave and could not play a C chord.” Mobius Zipper
Along the way, Doug has enjoyed sharing his knowledge and love of math with kids. That’s one of the main reasons he developed a patent-pending Mobius Zipper. It has the mathematics aspects of paper folding origami. An example he cited was a dual-decahedron (20-sided polyhedron), which can collapse to a bird with wings that flap.
At any rate, said Doug, “I did not know how to multi produce the Mobius Zipper until 3D printers were introduced at District 166. For a while, I informed Mary ‘I’m getting a 3D printer.’ For a while, Mary informed me ’Oh no you’re not.’
“Then, Carolyn Dry moved next door with three 3D printers. The Mobius Zipper you and your son have was generated off my own 3D printer. I already gave one to each of the four math instructors at District 166. Other such folks including Carolyn Dry also now have a Mobius Zipper,” said Sanders.
And pretty soon, if Doug has his way, Mobius Zippers will be in a lot more classrooms, and kids’ curiosity about the field of mathematics will be piqued.
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