Travelling to Northern BC

Every year. Every year since I've met my wife*, I have made the trek north to Smithers, Hazelton, Kispiox, etc., BC to visit her mom, aunts, uncles, cousins, grandparents, friends.

It's a very long drive. Interestingly, it's essentially the same distance from Edmonton as it currently is from Calgary: 1,150 kms. While it would only take light under 0.004 seconds to travel that distance, it takes us 12 hours.



12 hours in our little Toyota Matrix. The kids sleep, eat, read, eat, play on the iPad, ask for snacks, tell me to turn down the music, and eat.



The first 4 hours take us through world class national parks Banff and Jasper. I never tire of driving Highway 93 through the Columbia Ice Fields.



Everytime I've driven Highway 93 at this time of year it has been covered in a thick pack of snow. This year it was bone dry allowing us to make good time. And it didn't muck up our undercarriage.



Amber reserved us rooms at the Hostels International in Jasper, which is just outside of Jasper. The common area is beautiful and peaceful. I played card games with three guys I met after Amber and the kids went to bed. During that time however, there was a group of 8 guys who were very loud and very rude.

We had a private room. My kids were tickled to sleep in a bunk bed. I had a hard time getting to sleep with all the comings and goings and loud conversations and dance music (?!).



The next morning, I drove to McBride, BC where we stop to pee. We pass Mount Robson, the highest mountain in British Columbia, on this leg. Amber drove the next 2 hours to Prince George. She got to drive through the blizzard. The weather can be different every 2 hours as you cross through different mountain ranges.



We stopped to stretch our legs less than an hour from Smithers at the little highwayside park in Houston. They boast the largest fly fishing pole.





Then we enjoy the warm hospitality of our hosts and the cool mountain air and bits and pieces of northern life.



















*Almost every year. Every year minus 3, so just 15 times.

K-12 Integer Sequences

The K-12 Integer Sequences Conference was organized by my good friend Dr. Gordon Hamilton (Dr. Pickle) of MathPickle.com and Dr. Neil J. A. Sloane, the founder of the On-line Encyclopedia of Integer Sequences (OEIS). I was fortunate enough to attend as a math educator among other educators, math professors, and curriculum developers.



The goal of the conference was to identify 13 integer sequences that could be promoted for use in classrooms from K-12. The sequences would help students practice or learn level appropriate curricular goals, but they would also introduce the students to the wonderful world of mystery found in integer sequences. You can watch our large group sessions in these videos. Three sessions were spent in smaller groups - mine sought to identify sequences for grades 10-12.



The event was hosted by the Banff International Research Station (BIRS) at the Banff Centre which means they provided the hi-tech and comfortable conference facility (pictured behind me) and the lodging for the attendees. BIRS is dedicated to math research and collaboration.



Naturally, if you are still reading this, you are keen to learn which sequences will be promoted as a result. As with many collaborative conferences, there are still some **loose ends to tie up. I will feature a few here though.



Kindergarten: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, ...

A034326 This is the clock sequence. I think it's brilliant. You can have kids do some skip counting on it where they will be exposed to factors of 12 (when you skip by 4s, you will always land on the same 4 numbers, when you skip by 5s, you don't!). There is of course the excellent recursive nature of this sequence which mimics time.

Grade 3: 14, 7, 5, 3, 1, 2, 4, 6, 8, 10, 12, 24, 22, 11, 9, 18, 16, 32, 30, 15, ...

A254873 This sequence is a modified Recamán sequence developed by a 15-year old student. Starting at the seed number (14) the sequence continues by dividing, subtracting, adding or multiplying by the step number (2). Division gets precedence over subtraction which gets precedence over addition which gets precedence over multiplication. The new number must be a positive integer and not previously listed. The sequence terminates if this is impossible.



Grade 5: 4, 9, 7, 20, 6, 33, 13, 23, 16, ...

Starting with 1, on the first step add 1/n, and on subsequent steps either add 1/n or take the reciprocal. What is the smallest number of steps needed to return to 1? This number of steps is the nth term of the sequence. (Note: the n=0 and n=1 terms are not defined, so the sequence actually starts with the 2nd term.)

eg. let n=2: 1, 3/2, 2, 1/2, 1 therefore the number generated is 4 because it took 4 steps
eg. let n=3: 1, 4/3, 5/3, 2, 7/3, 8/3, 3, 1/3, 2/3, 1 took 9 steps
eg. let n=4: 1, 5/4, 3/2, 7/4, 2, 1/2, 3/4, 1 took 7 steps

This one is a lot of work, but I think it works to help students see that just because you work with increasing fractions, it doesn't necessarily mean it will require more steps. It really depends on the factors of n.



This time, I brought Amber along since I knew she would enjoy the tranquility, beauty and opportunity to relax in such surroundings.

My mom took the kids for most of the weekend, then Jasen for the last bit - we are very grateful.



Getting away to Banff now means being able to chow down and drink at the Banff Ave Brewing Company. Their beers are notable - especially their recent addition of an imperial IPA. Their food portions are ridiculously huge. I ate one burger for two meals.



The sequences have been determined in full! Here they are at the OEIS.org.

Whitemud Park

Went for a walk in Edmonton's Whitemud Park in mid-December with some good old friends. Lots of up and down on some rather slick hills, but the views were sights were stellar. The low winter sun and low lying fog on Whitemud Creek provided some wonderful visuals.

Touring Victoria, BC

Flew into Victoria Int'l on Friday night after a delayed connection in Vancouver due to fog. The flight from Van was only 13 minutes. The delay was over an hour. I walked off the plane into a light mist and then to the bus stop where the bus rolls by once per hour. I had called transit and learned the bus would depart 20 minutes after arrival. While the shuttles were filling up, I sat alone on little bus. It was a 6 minute ride to the exchange just off the highway where I waited for the 70X which goes between the ferry docks of Schwartz Bay and downtown Victoria (a 30 minute drive (or 60 minute bus ride). 70X was a little late, but I didn't care! It was a double-decker bus and there was a free seat on the upper deck. Too Cool. I got off 2 blocks from my hostel, Ocean Island Backpackers Hostel.

I arrived too late to eat at a restaurant, so I enjoyed a delicious curry bowl at the Ocean Island Cafe. I slept on a bunkbed in a dormitory and only met a couple German girls who are travelling the west coast. The other guests came in after I was sleeping and were still sleeping when I left in the morning.



As I was there for the marathon, I went for a quick 3 km run through downtown and along the shore. I watched harbour light up and absorbed the cool air. It took me right back to living in the Marshall Islands.

A quick shower and check-out/check-in to the room Marc and I shared and I was off in a light drizzle to Discovery Coffee, six blocks away. I ordered a couple baked goods and a light roast espresso which was stellar! So stellar that I ordered another.



I read by book, Culture, Commonweal and Personhood by Lazar Puhalo (just across the water), whilst taking in the coffee, cafe aromas, groovy tunes, and the torrents of rain outside. I ordered a third coffee - a pour over light roast. So yummy.



I met up with Marc at Ocean Island and we picked up our marathon package at the fitness fair. Then we were ready to carb up. I picked Swan's Brewpub and had a flight with Riley's Scotch Ale, SOS Oatmeal Stout, IPA, and Coconut Porter. Oh and a big plate of eggs, sausages, bacon and pancakes. Marc and I chatted about religion.





Marc went to visit an aunt and uncle, so I went for a walkabout in the north-central part of downtown initially hoping to sample some Phillips beer at their brewery, but it was pretty crowded with folks filling growlers and I had already tried the ones they had on tap, so I just had a look around. Most impressive was Phillips yard of fermenters and kegs ready to ship.

There was a nice furniture store and a Value Village that drew me in for a while. I browsed VV's book section and formed a nice collection of books that I had no choice but to re-shelve and leave behind. I enjoyed some edamame (so many I couldn't finish) and a giant veggie burrito at Ocean Island along with a pint of Blue Buck before heading to the theatre to see Gone Girl - which was spectacular.

Before heading to bed I laid out my marathon gear and packed up everything else. The hostel was pretty loud through the night, but I had earplugs.

BC/Alberta Circuit - Summer 2014

Day 1

• Claresholm, AB: Visitors Centre and Museum
• Head-Smashed-In Buffalo Jump World Heritage Site
• Frank, AB: Frank Slide Interpretive Centre
• Fernie, BC: Thrift Store
• Cranbrook, BC: Frank's Steak and Schnitzel Haus
• Moyie Lake Provincial Park

Day 2

• Creston, BC: Black Bear Books Cafe & Kingfisher Used Book Store
• Nelson, BC: Hume Hotel Restaurant, downtown shopping, market festival
• Kokanee Creek Provincial Park

Day 3

• Nelson, BC: Oso Negro Cafe
• Osoyoos, BC: Tamri Campground, the beach, and fruit stands

Day 4

• Highway 3: driving through E C Manning Provincial Park
• Hope, BC: lunch at info centre
• Dewdney, BC: Monastery of All Saints and visit with Lazar Puhalo
• Abbotsford, BC: Supper & evening with 2 of Amber's aunts

Day 5

• North Vancouver, BC: Lions Gate Hospital to visit 2 day old nephew twins
• Horseshoe Bay, BC: Ferry to Nanaimo
• Nanaimo, BC: Longwood Brew Pub
• Honeymoon Bay: Stay with friends on Lake Cowichan

Day 6/7

• Honeymoon Bay: hike Mesachie Lookout, relax and swim in Lake Cowichan
• Duncan, BC: Just Jakes with Craig St. brews

Day 8

• Victoria, BC: visit with friends, walk around harbour
• Schwartz Bay, BC: Ferry to Tsawwassen
• North Vancouver: supper and evening with Amber's aunt, uncle, and sister

Day 9

• Vancouver, BC: St. Augustine's Pub
• Langley, BC: supper & evening with 3 of Amber's aunts, her mom, sister and cousin

Day 10

• Langley, BC: badminton with Scott
• Hope, BC: lunch with college friends
• Coquihalla Canyon Provincial Park: swim in the Coquihalla River

Day 11

• Dewdney, BC: Orthodox Liturgical Service at All Saints Monastery
• Langley, BC: Mark and Sarah's wedding

Day 12

• Chilliwack, BC: visit and play at river with Grammy and another aunt and uncle
• Squamish, BC: settle into our rented house, Howe Sound Brew Pub

Day 13-17

• Squamish, BC: 10 cousins/3 siblings together, mini-golf, wedding anniversary dinner, Porteau Cove, Murrin Lake, Alice Lake, Howe Sound Brew Pub
• Squamish Valley Music Festival: Strumbellas, The Matinée, A Tribe Called Red, Bruno Mars, Foster the People, Lykke Lik, Serena Ryder, The Head and the Heart, Mayer Hawthorne, The Zolas, Sam Roberts Band, Tokyo Police Club, Black Joe Louis, Broken Bells, Arcade Fire

Day 18

• Langley, BC: Allison and Paul's wedding celebration

Day 19

• Kamloops, BC: Noble Pig brew pub
• Revelstoke, BC: Williamson Lake, spend evening with cousin

Day 20

• Calgary, BC: Watch the odometer turn to 3,748 km, see Arcade Fire

Monastery of All Saints

During our travels through southern BC, I was able to drop in to the Monastery of All Saints in Dewdney. The monastery has three residents and is presided over by Most Reverend Lazar Puhalo (Vladika), a retired archbishop (his biography is quite fascinating). I have been watching his YouTube videos for 3 or 4 years now, off and on. He is a polarizing figure in the Orthodox community, but I find the depth and breadth of his knowledge to be a great source of wisdom.

We stopped in one Sunday afternoon just as people were clearing out after a potluck. Since we were driving through the area, I thought I would pop in and shake his hand, thank him for his ministry and leave. I ended up having an almost 2 hour visit with Vladika over coffee and cakes. My wife and kids were welcomed graciously and they visited with Bishop Varlaam, a very kind and attentive man. My family also strolled the gardens and watched ducks on the pond.

My conversation with Bishop Puhalo wound through many topics. I explained where I was in my journey and how I am fascinated with the Orthodox Church and its theology and practice and that I am deeply connected to my protestant church and protestant church school. My greatest regret is that I didn't anticipate having his ear and therefore I did not have any really good questions to ask of him. If I did have the time and forethought, this is what I would have brought to the conversation:

Why is there not a more formal pronouncement from the Eastern Orthodox Church acknowledging the validity of the Protestant concerns regarding things like decentralized power among the clergy, separation of church and state, and church abuses of power?

Notwithstanding the offences in western countries despite western church presence there, why have we seen such devastation in traditionally Eastern Orthodox countries - Serbia, Russia, Ukraine, Greece, Romania, etc.? In other words, has the church not had the influence in its population that it ought to as far as transforming hearts and culture? Why has the church lost its influence/relevance?

How does a protestant (like me) incorporate orthodox practices into his life without become an orthodox christian? Everything is so foreign (sometimes literally in foreign languages) and inaccessible.

The following week, I was back in the area and I attended a Sunday morning service. I was one of 4 attendees of matins (or "the hours"), the preliminary 1 hour service. Everyone except for the elderly or young mothers stands for the whole service (which, including matins, lasted nearly 3 hours). Bishop Varlaam welcomed me and got me situated with a copy of the liturgy. A married couple sang back and forth through the liturgy which consisted of many Psalms which are organized to retell the whole story of redemption from Creation to Fall to Resurrection to Glory.

The main service continued the liturgy of St. John Chrysostom and includes many rites and congregational responses that I mostly did not understand. Archbishop Puhalo spoke for about 15 minutes for the homily. I didn't partake in the eucharist as I am neither a member nor did I fast ahead of time.

What was of incredible impact to me was that the whole liturgy is sung - this is a visceral experience where your entire body begins to resonate with the truths you sing and intone. Not only is the music of salvation ringing throughout the room, but your sight is stimulated by the dozens of ikons on the walls, your nose is filled with incense, your mouth takes in salvation if you are partaking in the eucharist and wine, and your flesh contacts holy objects as you enter the room and kiss ikons and crosses and the Holy Bible. It is a time that affirms the importance of the physical realm while infusing it with spiritual truth. This sensory worship is in stark contrast to the strictly intellectual and emotional services in the protestant world.



Upon my first visit at the monastery, Archbishop Lazar blessed me with several books from the monastery's printing press, Synaxis. The books are very scholarly and grounded in quotes from early church fathers. I am excited to read through these as I have read a few of Lazar's books in the past and they have been very helpful.

Goat Lake, Waterton Lakes National Park

Heading northwest from the Red Rocks in Waterton Lakes National Park is one of my friend's favourite hikes. Chris has done this hike six times and will likely do it several more times.  Our family sets out late morning on July 7 with Chris and Christie for a 7 km hike (with an elevation gain of 500 m).



The first 4.5 km follow a very well maintained path (an old fire road) along a creek between Anderson Peak and Mount Glendowan. We cross a part of that creek at one point by stepping on rocks.







For the last 2.5 km to the lake are a series of switchbacks on Mount Glendowan with stunning views of the valley. Wildflowers dot the steep edges and there is occasional shade from the spruce trees.









The final kilometre is mostly scree and I hold Acadia's hand to ensure she doesn't slip down the mountainside. The kids are enamoured with Chris's walking sticks and he is kind enough to stop, readjust, lend them and then repeat several times as they return and borrow them again and again.





The lake refreshes mightily. I am the only one to jump in and everyone on the mountain hears me exhale girlish screeches. Chris had packed up his dingy and we take turns paddling the kids around Goat Lake. Chris fails to catch a single trout after having talked up the feast of fresh fish we would be having. It turns out they are spawning and therefore not interested at all in his lures.



I have to say that the children impressed me greatly! They managed a 14 km hike with a 530 m elevation gain!! It took us all day, but they were in a good mood at the end and we all devoured our gourmet hot dogs in downtown Waterton.