The Language of Math

   You could say that each discipline or area of academic study has its own language and terminology. This is true also for mathematics.  The symbols and numbers enable us to think about our world in terms of size, shape and quantity.  One of the interesting things about math is that, until you get to word problems, foreign students are able to continue to excel in this subject even if their language skills are lacking.
   However, I recently came to realize how one's language of instruction does have an impact upon mathematical knowledge and understanding, thanks to Malcolm Gladwell's book Outliers: The Story of Success.  He points out that the words for numbers in some languages either help or hinder mathematical understanding.  I learned English and Dutch virtually simultaneously before the age of six, so I did not spend much time analyzing the differences between them at that time.  I do remember noticing at one point, no doubt influenced by the fact that I was learning math at school in English, that in Dutch the numbers above 20 seemed backwards to me.  In English, we say "twenty-five", but in Dutch it's literally "five-and-twenty."  (Apparently at some point in history English used that same format of placing the ones before the tens, as preserved in the nursery rhyme "Sing a Song of Sixpence" where "four-and-twenty blackbirds" were baked in a pie.)
   What dawned on me this week is that English has it more backwards than Dutch.  In the numbers between 13 and 19, we place the ones before the ten (or "teen") as we say these numbers.  However, after twenty, English reverses them and places the ones last.

From The Chinese Quest website

   Gladwell did not speak about Dutch in his book; instead he spoke about Chinese.  The words for the numbers 1-9 in Mandarin & Cantonese are much shorter and quicker to say than in English and most other languages.  In addition, after ten they follow a consistent pattern divided into tens and ones.  So, for example, literally 34 is stated as "three-tens-four" and 19 is "one-ten-nine."  These simple differences alone mean that an average Chinese child can count to 40 at the age of 4, while Canadian/American children are expected to reach only 15 by age 4.
   A second mathematical advantage in Chinese has to do with its words for fractions.  We say 3/4 or three-quarters.  For the child learning this, it is not particularly visual.  Yet in Chinese, it is more like "out of four parts, take three" (Gladwell, p. 230).
    Even though math is considered to be a language one can use without words, it would seem from this simple analysis that one's language does influence whether math is seen as a simple, logical discipline or a difficult, frustrating one.

New word and New concept: Coopertition

   We are all familiar with the idea of competition.  Any race, sports match or tournament gains the excitement and intensity from the fact that one player or team is trying to surpass the achievements of others.  Participants and spectators alike enjoy seeing all the hard work of training put to the test in a public forum.

   Cooperation is something entirely different.  Here people are helping one another achieve a greater goal.  Cooperation naturally happens in families, among the members of a sports team, in workplaces where projects require the input and expertise of various employees to be successful.

   How could these two ideas ever fit together?  Although the spelling is different, the idea of "coopetition" has been shared in the last century to apply to the business world.  Two companies might produce some of the same types of products, but they might decide to become partners in certain ways to increase their collective success.  In 2000, the American organization FIRST Robotics built on this concept and made the word into one of its trademarks, literally.  Along with "gracious professionalism", coopertition™ is one of the defining qualities of a world-wide enterprise aimed at recognizing science and technology among youth.  Here is the way FIRST Robotics defines the term:

Coopertition™ produces innovation. At FIRST, Coopertition is displaying unqualified kindness and respect in the face of fierce competition. Coopertition is founded on the concept and a philosophy that teams can and should help and cooperate with each other even as they compete.

Icon from FIRST Robotics

Coopertition involves learning from teammates. It is teaching teammates. It is learning from Mentors. And it is managing and being managed. Coopertition means competing always, but assisting and enabling others when you can.

   At the time I am writing this post, 607 robotics teams from around the world have gathered in St. Louis, Missouri for the world championships of their 2015 robot-game, Recycle Rush.  The teams that built each robot are encouraged to work together as they compete by having three robots on each side of the field to score points (by stacking plastic totes and then placing these stacks on scoring platforms) to build up a score for which they will all receive equal credit.  But coopertition takes on a new level in this game when each side brings one to three special yellow totes to the centre of the field to make a total of four totes.  When this happens, both alliances receive forty bonus points, as the icon above illustrates.

   I do not consider myself a very technologically skilled person, but through the participation of my husband and son in a FIRST robotics team over the past three years, I have appreciated that it is not just about being able to program a computer or about getting wealthy corporate sponsors to help pay for the materials involved in the build-process.  The merging of competition and cooperation will have the most lasting benefit for any student or adult mentor that becomes involved.  It can even inspire the spectators, like me.

Leave a comment if you've observed coopertition at work anywhere else.

Vitamin Presentation (B-12)

In my Grade 5/6 science class, students are preparing to give presentations about a different vitamin or mineral to the rest of the class.  One of my staff colleagues gives a sample presentation whenever he assigns something new and less familiar to the student.  I decided to do the same.  The students are free to use a variety of formats to present their information, but I chose to do a short story with a dialogue to teach about Vitamin B-12

Let me tell you a story about Vitamin B-12 and a school girl named Laura Carrot.  Laura has been a vegetarian for two years.  She does not eat any kind of meat—no pork, no beef, no chicken, no duck, no lamb, no venison, no sausage, no bacon, no fish, no salmon, no shrimp—nothing that was once part of an animal.  But Laura Carrot has recently decided to go one step further.  She is going to become a vegan.  A vegan also does not eat any product that came from an animal.  No eggs, no milk and no dairy products whatsoever, including cheese, yogurt or pudding.

                Laura Carrot is missing two important food groups in her diet-meat and dairy-and that will have an impact on her health.  She will miss out on protein, which helps your cells be built up and repaired.  But, if Laura is careful, she can get pretty much all the protein she needs from beans, like kidney beans and chick peas as well as tofu, a soybean product.

                Here comes the bigger problem.  Vitamin B-12 is found ONLY in animal products.  Laura Carrot will be missing out on this product.  She’ll be OK for about one year because a person’s liver stores up about 12-month supply of Vitamin B-12, but eventually she will have what’s called a “deficiency”—her body will not have enough.  What does Vitamin B-12 do?  It works with the mineral Iron to help produce healthy blood cells.  It is also important for the nervous system, so some people who do not have enough of this vitamin report unexpected tingling in their arms and legs because the nerves are not working properly.  When your body does not have enough Vitamin B-12, you can get anemia, which makes you feel weak, lethargic and lacking in energy.  Your body has to take in Vitamin B-12 regularly to keep in good health.  Since your nerves and blood go everywhere in your body, everything is affected.

                Laura Carrot has gone to see her doctor to find out how she can stay healthy as a vegan.  Here is their conversation:

• Doctor:  Hi Laura, I understand you’re planning to change your diet from vegetarian to vegan, and you’ve come for some advice.
• Laura: That’s right, doctor.
• Doctor: Laura, I have to say I’m quite concerned about your decision.  What is the reason you want to cut eggs and dairy products from your diet?
• Laura: It just seems really mean how we take eggs and milk from animals.  The chickens should be allowed to hatch their own eggs, and the cows should give the milk to their own babies. It’s like stealing!
• Doctor: Do you like the taste of eggs and milk products?  Do you have any reactions to them?
• Laura: No, I like the taste and I don’t have any reactions or allergies to them.
• Doctor:  As a Christian, I know that God gave us the animals for food.  If it bothers you to eat meat, that is one thing.  But eggs and milk have been eaten for good health since we’ve had records of human civilization.  It is not the same as stealing.  If all the eggs that chickens laid were allowed to hatch, we’d be overrun with chickens.  Even if the cow’s milk was given to the calves, there would always be some left over.  God designed things so that if we use them properly we will not run short.
• Laura:  Is there something else you’re not telling me?
• Doctor:  Laura, since you are just 12 years old, your body is still growing.  The vitamins found in meat, eggs and dairy are hard to get anywhere else, especially Vitamin B-12.  Since it is so important for the production of blood cells and a healthy brain and nerves, it is not optional.  You would have to take a daily Vitamin supplement if you decided firmly to become a Vegan.  These pills are not for swallowing, but you dissolve them on or under your tongue, just one per day.
• Laura: Thank you for explaining this to me.  I never really understood the importance of animal products in our diet.  Now that you gave a Christian point of view about using animal products, I see that my idea about stealing from animals was kind of silly.  Being a vegan is a trendy thing on my soccer team, but I need to tell the girls on my team that it can really affect their bodies.  I will talk it over with my parents too.  You know, I think I might even try eating meat once in a while, but never shrimp!

Synergy: Thoughts on Romans 8:28

My apologies to my regular readers that it has been so long (11 days) since my last post.  The reality of my new roles at school meant working almost full time for the past two weeks, even though I'm actually a part-time employee. 

   A comforting verse in the Bible is Romans 8:28, which states "All things work together for good for those who love God."  The Greek for "work together" is the root word of our English word "synergy."
   An online dictionary [dictionary.reference.com] gives this definition for synergy:

 the interaction of elements that when combined produce a total effect                                          that is greater than the sum of the individual elements, contributions, etc.

Synergy takes place in the body when multiple muscles and nerves work together to achieve health and wellness; likewise, particular medications can work together to promote healing.  

   The first time I remember encountering the English term "synergy" was about twenty years ago when I studied the book Seven Habits of Highly Effective People by Steven Covey as part of a course.  The sixth habit that he laid out is entitled "Synergize."  He explained that working with others and accepting their different viewpoints and backgrounds enables people to solve problems and address issues in a way that could never occur if each person worked at them separately.
   During the past week I have observed synergy at work.  My school colleagues and I were led in a two-day workshop on Restorative Practices.  At the heart of this philosophy of relating to people is to give opportunity for people to speak face to face with a clear structure so that everyone is respected and listened to.  When a conflict has occurred and harm has been done, all the parties can be brought together to share how they have been affected.  Each individual also contributes to the way things can be resolved or made better.  When you participate in a restorative circle/conference like this, you cannot predict in advance how the disclosures of the people around the circle will affect the others, or how synergy will occur to bring about a measure of healing.  We were taught as facilitators-in-training to trust the process and to trust the stakeholders involved to arrive at an agreeable solution.
   During our lunch break on the second day a film of a restorative conference was shown.  In 2004 six young men had burned down Mood's Bridge, a historic covered bridge in Pennsylvania.  These young men wanted to meet with members of the community to express their remorse for what they had done. Both the offenders and the community members could have their say without interruption.  It was very moving as the community members who had initially been very angry accepted the regrets and sorrow of the young men and encouraged them to become builders in the remainder of their lives, not destroyers.  The agreement that the conference came to included each offender paying for a sixth share of the cost of rebuilding the bridge.  They would also put in hundreds of hours of volunteer labour in its reconstruction.  While the young men did serve a short sentence in jail, the synergy of the restorative conference led to a more satisfying resolution of their crime than punitive measures alone.  [The bridge has now been rebuilt in the style of the original.]

Image from wildblueberries.com 

   Getting back to Romans 8:28, the synergy that the Apostle Paul is talking about is slightly different.  Here he is pointing to the experiences in a believer's life, the ups and downs, the conflicts and the triumphs, the false accusations and the blessings.  All of these work together or synergize for the ultimate GOOD of those who love the Lord. God is able to take all the pieces that do not seem to fit together and by his Holy Spirit works them together for a purpose.  That purpose involves developing character, which is more valuable than material gain.

Lessons in Character from the Snowy Owl

   On a bit of a whim, I picked up a PBS documentary from my local library last weekend entitled Magic of the Snowy Owl (2012).  The film crew captured footage of one pair of snowy owls during the 82 day period from nesting/hatching to the time the owlets could take flight.  These impressive birds demonstrated a few striking qualities that we humans could learn from.  To avoid being preachy, I'll let my readers make the personal connections for themselves.

Loyalty & Teamwork

   Amid a hostile environment, the snowy owls recognize that they need each other to survive.  The mother and father are equally involved in the nurture of their young.  A total of five owlets hatched from eggs, about one every couple of days.  However, the youngest owlet, being weakest, did not get its fair share of the food in those early days when lemmings and small songbirds were not plentiful.  Eventually this owlet grew weaker and weaker, but its mother seemed to recognize its struggle and tenderly placed it under her wing. Abandoning the weak may fit Darwin's "survival of the fittest" model, but the film crew observed something quite different.  

   

Perseverance

   Two significant examples of persistence among the snowy owl clan stood out to me.  One was the father, whose instinctive task is to provide food for his mate and the owlets.  At first, he had difficulty finding enough prey to feed the brood.  However, the film crew observed that he continued his search, even though it took him an extra mile away from the nest.  His perseverance ended up paying off with many lemmings occupying the new hunting ground; later on the male is pictured holding a dead lemming in its beak with no takers.

   For some reason the mother owl begins leading the owls on a trek towards to the coast.  This is the direction where the male has found good hunting.  The naturalists also speculate that the coastal breezes are also favoured because they ward off the plague of mosquitoes.  As the awkward and flightless owlets trudge through the flat and grassy landscape, they come upon a river that blocks their path.  They cannot fly over it or wade through it.  But they do not give up.  These young owls flap their wings in the water and maneuver themselves to the other side.  This had never been documented or filmed before!

Acceptance of Life Stage

   The young owls learn to fly at the end of the Arctic summer.  They will not winter in the Arctic even though their parents will.  There is no shame for these novices to fly further south, where conditions are more favourable to their survival.  Whenever a snowy owl is spotted during a Southern Canada or the Northern U.S. winter, in all likelihood it is a juvenile owl beginning to master hunting and other skills that will enable it to eventually winter in the tundra.

   

Bumblebees

This summer my husband and I have been learning more about bumblebees.  A nest underneath our front step means that when we sit there, we can observe their noiseless take offs.  We can also watch their deft landings, which are accompanied by a glimpse of the load of yellow pollen on hind legs.

   We cannot actually see the nest, but judging by the amount of activity during the day time, it is a full-size colony of at least 50 bees.[1]  Our front garden, adjacent to our front step, contains a few vegetable plants, but the plant nearest the step is producing the most beans.  We wonder if we should thank our fuzzy boarders for that.  Although bumblebees collect nectar and pollen and thus contribute to pollination of crops, they make only enough honey to feed their young.  Unlike honeybees, bumblebee hives do not survive the winter but start over again each spring with a queen that has hibernated on her own.

   Taking the time to closely observe the little creatures of our world can help us grow in appreciation for their Designer.  Basil the Great (330-379), who was a church bishop in Caesarea is quoted as having said, "If you speak of a fly, a gnat, or a bee, your conversation will be a sort of demonstration of His power whose hand formed them; for the wisdom of the workman is commonly perceived in that which is of little size." 

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[1] According to www.kentbee.com, it is rare for a colony to grow beyond 70 individuals

Little Known Regrets II

   This second story about regret is not an isolated one.  Scientific advances that one researcher intends for good can be taken by someone else and used for evil.  I am reminded also of Albert Einstein's dismay that his breakthroughs in the area of physics led to the devastation of atomic bombs.

   I recently learned about the French geneticist named Jerome Lejeune, who discovered in 1959 that an extra 21^st chromosome is what causes the condition of Down’s Syndrome.  He received awards and much fame after his finding. 

   However, he quickly discovered that his research was being used to do genetic testing on pregnant women.  As a result, those showing the trisomy-21 condition were being recommended for abortion.  A 10 year-old boy with Down’s Syndrome he knew from his practice was also aware of this trend and felt a strong solidarity with the plight of these pre-born babies.  He pleaded with Lejeune to “save us because we are too weak.”

   Even though it cost him all the prestige and credibility among his professional peers, this kind-hearted and devoutly Catholic man began to speak up for these children, pointing not only that abortion was problematic but also to the potential that these children have despite their disability.  Lejeune campaigned internationally for the sanctity of life during the remaining 35 years of his life.  

  “They brandish chromosomal racism like the flag of freedom,” he once wrote. “That this rejection of medicine—of the whole biological brotherhood that binds the human family—should be the only practical application of our knowledge is beyond heartbreaking.”[1] 

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[1] http://www.lifesitenews.com/news/if-i-dont-protect-them-i-am-nothing-the-man-who-discovered-down-syndrome

Little Known Regrets I

Most of us have experienced regrets about something we have said or done that led to negative events.  While misgivings are inevitable in our lives, they usually remain private and unknown to others.  When certain regrets belong to a more public figure, however, they may reveal something remarkable.  In the course of the past month I came across two such stories, and I will share the first one here.

   Admiral FitzRoy was the captain of several navy ships, including the HMS Beagle famous for its five-year journey that included the young Charles Darwin.  Admiral FitzRoy was a dependable sea captain, who never lost any of his crew.  He was also interested in science, including taking precise weather measurements and observing plants and wild creatures.  He invited Charles Darwin to join the expedition that went to the Galapagos Islands among other tropical places.

   Although Darwin’s previous education had been in theology, he was a keen naturalist as well.  However, as both FitzRoy and Darwin observed the natural world they came to “vastly different conclusions”[1].  Where FitzRoy marveled at God’s design for each creature that enabled it to thrive in a particular environment, Darwin reasoned that small changes within a species could be extrapolated to explain the origin of life through purely natural processes.

   After Darwin published his famous book On the Origin of Species, Admiral FitzRoy was distressed and took various opportunities to write and speak out against it.  On one auspicious occasion at Oxford (UK), a debate was taking place between Darwin’s disciple Thomas Huxley and Reverend Samuel Wilberforce (son of the William Wilberforce who spearheaded the campaign to end the slave trade).  From the back of the room Admiral FitzRoy walked up to the front holding a large Bible.  He explained how he had known Charles Darwin and proclaimed, “Believe God rather than man.”

   In a letter to a friend, Fitzroy expressed regret at having invited Darwin to join him on their shared expedition.  I found this worthy of pondering.

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[1] As quoted from the documentary film entitled The Mysterious Islands: A Surprising Journey to Darwin’s Eden.

Mathematical Providences

   My title may be surprising because the “p-r-o” word most people would expect to follow “mathematical” is “probability”.  This branch of mathematics deals with chance and possibilities that can be predicted with some level of certainty, from the flip of a coin to the probability of winning a lottery.

   However, some lectures by Professor Edward B. Burger in a DVD Course entitled Zero to Infinity: A History of Numbers, inadvertently (from his point of view) brought a new awareness of providence to my thinking about math. He explained the phenomena in nature of certain numbers and proportions being consistent.  It is called the Fibonacci sequence because it was first pointed out by a man of this name who lived in 12^th century Italy.  The numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.  Spirals found in creatures as diverse as snails and uncurling ferns follow a pattern.  They are also found in non-living things like hurricanes and spiral galaxies viewed through a telescope.  This images may help to picture it.  The Fibonacci numbers are part of the blueprint for our universe, and they tell me something about the intelligence of its maker.

   During another lecture Professor Burger explained that if a number is chosen at random, it will NEVER be a whole number.  If a number were to be chosen randomly (using the digits 0-9), you would never get an infinite number of zeroes after the decimal place.  OK, you say, so what?  Well, our world consists of whole numbers.  We have two eyes, ten fingers, 46 chromosomes, and the list goes on.  The fact that our lives (except dollars and cents) consist of whole numbers speaks to me of the design of God.  We are not here by random accident.  

The Beginning of Science

   Last summer I was reading through the book of Proverbs intensively by reading each chapter multiple times and in different versions and languages.  As I read Proverbs 1:7 in French, I was struck while reading “The fear of the Lord is the beginning of la science.”  Furthermore, each time when the word knowledge is used in English, the French uses science. 

   As I thought it over, I wondered why it should surprise me that science is in the Bible.  It must be that I am conditioned by my culture to see science and religion as two separate categories that do not belong together.  By pondering this a little more, I recognized that the writer of many of the biblical proverbs was indeed a scientist himself.  King Solomon was a keen observer of the created world and a recognized authority:

He described plant life, from the cedar of Lebanon to the hyssop plant that

grows out of walls.  He also taught about animals and birds, reptiles and fish.  

Men of all nations came to listen to Solomon’s wisdom.  (1 Kings 4:33-34)

   Returning to the connection between science and faith, medieval church father Saint Thomas Aquinas (1225-1274) saw no contradiction when he called theology “The Queen of the Sciences.”  Two other well-known scientists of the past who demonstrated that the Greeks had faulty notions of planetary motion (Johannes Kepler) and the properties of light (Sir Isaac Newton), respectively were believers in God’s grandeur and gave him glory as they made their discoveries.  Kepler is quoted as saying, “We see how God, like a human architect, approached the founding of the world according to order and rule and measured everything in such a manner.”[1]

   There is still a place for people of faith in science today.  True science begins with the fear of the Lord.  Hymn writer William Cowper said it well:

Blind unbelief is sure to err

And scan his works in vain

God is his own interpreter

And he will make it plain.[2]

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[1] Quoted in J.H. Tiner’s book Johannes Kepler—Giant of Faith and Science. 1977 (inside front cover)

[2] From his hymn “God moves in a mysterious way”, 1774

Sparrows are not Celebrities

“God sees the little sparrow fall

It meets his tender view

If God so loves the little birds

I know he loves me too”

            -Maria Straub  (1874)

“Are not five sparrows sold for two pennies?  Yet not one of them is forgotten by God.  Indeed the very hairs of your head are all numbered.  Don’t be afraid; you are worth more than many sparrows.”         
 -words of Jesus Christ recorded in Luke 12:6-7

   A short time ago my family went to a bird banding station.  Migrating birds fly into humane nets, which are checked periodically.  Each bird is carefully extracted, placed into a cloth bag and brought into the station.  Here volunteers reach in to see what has been caught.  A band is placed around one of the bird's legs,  measurements taken and then the bird is released. 

   The public is allowed to watch this process at set times, and it is just as exciting for them to see what comes out of the bag.  We saw a golden crowned kinglet, a Magnolia warbler, a purple finch and a gray catbird among others.  Only one was a sparrow--a white throated sparrow.  We were excited for a close-up view of the less common birds, but if all of the bags had contained sparrows we would have quickly lost interest.

   Therefore, it’s so interesting that Jesus chose the common sparrow as the creature to highlight as the one God cares for.  If he cares for the ordinary and plain birds, we humans don’t need to become celebrities to catch his attention!

Seven Days = A Week

   Every fall when I teach my Kindergarten class about the days of creation I am reminded about the anomaly of a seven day “week”  All our other classifications of time are related to something definite in our solar system:

• A day = 24 hours, the time it takes the earth to rotate once on its axis
• A month = 28-30 days, roughly the time it takes for the moon to go through all of its phases
• A quarter/ a season = the times between equinox and solstice, when the earth’s tilt gives us different weather patterns as it circles the sun
• A year =365 days, the time it takes for a full revolution of the earth around the sun.

   But a week is not like that!  It seems completely arbitrary.  Why not have a ten-day week to match the metric system?  In fact, the architects of the French Revolution tried to do just this because they recognized a seven-day week as an acknowledgement of God and his work in creation.

   The pattern of six days of work plus one day of rest was established by God Himself in the beginning.  Every calendar gives testimony of God’s creation for those with eyes to see it.

The Year of the Dragon

We are currently in “the Year of the Dragon,” according to the Chinese calendar.   Have you ever noticed that all of the other creatures in this twelve-year cycle (the rat, ox, tiger, rabbit, snake, horse, goat, monkey, chicken, dog and pig) are animals we are all familiar with by direct experience?  Isn’t it curious that in the midst of these ordinary animals there is one mythological creature?  Does it at least suggest that what we consider mythical today may at one time in human history have been very real?

   In addition to the Chinese calendar, there are accounts of Australian Aboriginees never taught about dinosaurs in an academic setting recognizing them as entities that their ancestors feared and faced.[1]  An ancient carving from the ruins of the temple at Angkor Wat resembles a stegosaur[2].  Why do cave paintings of woolly mammoths have credibility and not those of dinosaurs except that they fit in with what science has declared to be true?[3]

   Both dragons and dinosaurs have a modern fascination appearing in films like Jurassic Park and more recent young adult fiction series such as “The Last Dragon Chronicles” by Chris D’Lacey and the Inheritance Cycle by Christopher Paolini.  These fantasies place humans and dragon/dinosaurs together despite the timelines taught to children from Kindergarten that dinosaurs died out long before humans appeared on planet earth.

   It is striking that the theme park “Canada’s Wonderland” chose to name its newest ride after a mysterious creature named in the Bible, namely Leviathan.  It joins the already popular ride Behemoth.  Their descriptions in the oldest book of the Bible, Job 41 and Job 40: 15 ff respectively are intriguing to the open-minded.

  

  

  

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[1] Geelong Advertiser, July 1845, reprinted in the same newspaper in 1991. 

[2] www.atlasobscura.com/place/dinosaur-angkor-wat

[3] http://creation.com/messages-on-stone