Buffalo, WY - Fort Collins, CO Motorcycling

Typical view along 460 km on I-25 Highway between Buffalo, WY and Cheyenne, WY.

15. After our Helena-Buffalo trip yesterday, we rode from Buffalo, WY to Fort Collins, CO on Tuesday, June 21. Total distance is 540 km and the gasoline cost is under $20. It was quite tiring because of the hot weather, but I learned to adjust to the hot weather by having my jacket's ventillation zippers wide open and drinking enough water throughout the ride.

16. The first stage was from Buffalo to Casper, WY. The 180-km stage felt the most lonely stretch so far. There were very few vehicles. There was no service whatsoever along the road until we arrived in Casper, a bustling city that felt like coming out of nowhere after the nothingness I felt to get there. We had juices and salad to fight the hot weather.

17. The 280-km second stage between Casper and Cheyenne, WY turned out to be the same. There was one service stop in Wheatland, about 180 km from Casper. I ended up riding the 280-km stage without stopping. The fuel indicator showed a reserve status for the last 50 km before arriving in Cheyenne. We stopped at the Exxon gas station just off I-25. The restaurant at the gas station has a very good taco salad. We enjoyed our stop after a long ride.

18. I learned to drink water from the Camelbak my wife carried using the Camelbak tube while riding. It requires coordinated steps to have the tube inserted through my helmet safely. The procedure reminds me of the aerial refueling of a fighter plane by a KC-135, except for our riding the KC-135 would be behind the fighter plane. It would've been very tiring, and I would possibly be dehydrated if I didn't drink water at all. The temperature rose to 41 degree C.

19. The third stage between Cheyenne and Fort Collins, CO (Colorado) was a brief 70 km. The wind subsided once we reached Colorado. In retrospect, the I-25 within Wyoming helps train a riding nerve: the 460-km stretch between Buffalo and Cheyenne was the most desolate highway stretch between Calgary and Fort Collins.

20. We were fortunate to meet a fellow traveller in the gas station who has ridden across the US and gave us a tip to ride through Beartooth Pass in Wyoming when we return to Calgary. I'd keep that route in mind since we seemed to have enough of the big prairie landscape in Montana and Wyoming.

Delicious taco salad at the truck stop in Cheyenne.

Helena, MT - Buffalo, WY Motorcycling

On I-90 Highway, between Bozeman, MT and Big Timber, MT.

7. Continuing our Calgary-Helena trip, on Monday June 20 we rode from Helena, MT (Montana) to Buffalo, WY (Wyoming). Total distance this time is 650 km and the gasoline cost is US$20. We left Helena at 10:30 and arrived in Buffalo at 18:30.

8. The relatively low gasoline cost has to do with the F700GS's 800 cc engine and also a cheaper gasoline cost in the US than Canada. It's a fuel-efficient engine although on the road I had wished that the engine were larger for a higher torque at lower rpm. The F700GS has a precise handling on the road to handle twisty sections. Its narrower tires afford a lower steering torque for countersteering.

9. I took Route 287 connecting Helena to the I-90 junction. The 100 km stretch is picturesque along Hauser Lake. Closer to the junction I saw the distant snow-capped mountain range, signaling the Yellowstone National Park area. The route follows Missouri River, which in fact starts at Three Forks, not far from the junction. This is the Missouri River that winds its way through the Midwest to St. Louis, Missouri, where the river merges with Mississippi River.

10. The I-90 highway is pleasant between Three Forks, MT and Bozeman, MT. It has alternating small town and front-range mountain landscapes. It's much less windy as the wind is predominantly eastbound, the same direction as ours. The divided highway gives a welcome change for me.

11. We stopped quickly at a turnout area between Bozeman and Livingston, MT. I had been carrying a Camelbak on my back for 2 days. I asked my wife to carry it since it became a pressure point on my back for our two-up seating and reduced blood flow to my legs. What a big change after I didn't have the Camelbak: I felt much more comfortable and was able to concentrate more on riding.

12. Services between Bozeman and Billings, MT are sparse. A good stop for gasoline and lunch is in Big Timber, about 100 km from Bozeman. I don't remember if there was another stop after Big Timber, until we reached Billings, MT, about 120 km from Big Timber. Billings is an oil city right on the Bakken formation.

13. The landscape changes quickly to a desolate big prairie (steppe) landscape after Billings. The 80-km stretch between Billings and Hardin, MT reminded me of a Nevada landscape, although the latter is mostly desert. The temperature rose to 34 degree C, and we had to soon remove some of our layers to prevent overheating. We stopped for DQ smoothie and ice cream to cool our bodies and remove the layers. My Alberta-riding gloves proved too warm for the 30+ degree C and I had to wear my wife's lighter pair. The glove change improved my riding handling so much.

14. A high plain big prairie landscape between Hardin and Buffalo is magnificent to look at from a motorcycle seat. It is filled with rolling hills that end far away with soaring mountains after a huge flat prairie. I was so relieved to have finally reached Wyoming, after spending 900 km in Montana.

High plain big prairie landscape at the Montana-Wyoming border on the I-90 eastbound.

Calgary - Helena, MT Motorcycling

I-15 Highway, entering Helena, MT, southbound

1. After waiting for the sky to clear, I decided that we go at 10:10 on Sunday, June 19. It was drizzling when we left, and sometimes clouds chased us along Highway 2 southbound. This time we didn't stop in Nanton for refueling. The wind was relatively calm for Highway 2, even after Claresholm toward Fort Macleod.

2. As we rode near Fort Macleod, the crosswind picked up. We refueled there after a 200 km nonstop stretch. Carrying a Camelbak behind my back helps quench my thirst. I didn't have the need to buy a drink at the gas station. The wind gust from the mountain became fierce when we headed southbound along Route 2 from Fort Macleod to Cardston, and then to the Carway US border crossing. My F700GS leaned clockwise about 10 degree to compensate for the crosswind blowing eastbound.

3. The border crossing staff asked where we'd go. I said New Orleans. "Are you going to ride to New Orleans with a motorcycle?" Yes, I reply. He smiled, and pretty soon we passed St. Mary – the gate to the US Glacier National Park – on Route 89. We kept going along twisty mountain curves to reach the fork to Route 287 at Browning. It was chilly along the curves; at times the temperature reached 10 degree C.

4. Route 287 was a good alternative to I-15 Highway between Canada-US border and Great Falls, MT, for motorcycles. It was quiet, not too twisty. We met a couple each riding a Harley from South Carolina when we stopped at Buffalo Joe's in Dupuyer, MT, for lunch. The fried 1/2 chicken at the restaurant was fantastic, highly recommended. We saw the couple dance along the route until Choteau, MT, where we refueled after the 280 km stretch from Fort Macleod.

5. We reached Helena, MT at 18:30 after a 160 km leg from Choteau by continuing on Route 287 and changing to I-15 Highway north of Wolf Creek, MT. 

6. Total gasoline spent for the 640 km trip was US$13 and CD$13. The highlight was the high crosswind section between Fort Macleod and Carway, and also the twisty curves between St. Mary and Browning.

Calgary-Waterton Lake Motorcycling

Waterton Lake beach at the south end of our campground.

A couple of weeks ago during the August long weekend, my friend and I rode to Waterton Lakes National Park from Calgary. It's 270 km one-way via Highway 2 south and then heading west on Highway 3, before finally heading south again to Waterton Lakes NP by passing through Pincher Creek. We brought our families with us so there was a chase car carrying our sons. My wife and I were two-up on my bike, and my friend rode his Harley.

Ours hail from two continents and we get along.

The ride along Highway 2 was going at a 120 km/h speed. Occasionally we had to go at 140 km/h when overtaking some cars and trucks, but the traffic wasn't busy. Several times I saw traffic signs alerting severe crosswinds, and sure enough the wind picked up significantly between Claresholm and Fort MacLeod. In high crosswind area, physics teaches me to increase motorcycle speed to reduce the crosswind's momentum, so I picked up my speed a bit.

The ride on Highway 3 was more exhilarating. It's not a divided highway and the rolling hill landscape helped my eyes relax. There are hundreds of wind turbines around this area, but their blades weren't turning despite the strong wind. We stopped for gas in Pincher Creek and about 50 km along Route 6 later we arrived at Waterton. It took us 2.5 hours to arrive at the Waterton Lakes NP gates. My friend used his Park Pass and I entered the park for free.

There was one campsite left when we got to the townsite campground. We were lucky since I couldn't make online reservation 2 days before. The day was sunny and hot (30 C). The campground was luxurious by my standard: shower, flat ground, cookhouse, and tap water by our site. It is also by the lake and is quite windy. We stayed in the campgrounds for 2 nights, which gave us time to explore Waterton village.

Who's your daddy now?

Waterton village or townsite is situated inside the NP. It has coffeeshops, fancy restaurants, grocery stores, and even laundromat. It's similar to Banff in Banff National Park but smaller. Waterton though has a charming lakeshore to stroll for hours without feeling bored or tired. I even took a nap to soak up the sun. I saw several kayakers and one windsurfer on the lake. Unlike the places in Canadian Rockies I usually go to, Waterton is decidedly more tropical by Canadian standard. We thoroughly enjoyed our time.

Cameron Lake.

We also visited Cameron Lake located 16 km off the main road through a winding road. A highly recommended side trip when you visit Waterton. Cameron Lake is tranquil and great to visit in the morning, especially if you like canoeing or kayaking. We met mountain goats ambling merrily on the road when we rode back to Waterton.

Mountain goats sharing our road. A group of Kansas riders  accompanied us.

We took Highway 22 to return to Calgary. It's the western parallel of Highway 2 and takes us to the foothills of Canadian Rockies. We stopped at Chain Lakes Provincial Park to rest before riding our final stretch to Calgary.

Tips: When riding to Waterton from Calgary, gas stop is recommended in Pincher Creek which is 200 km south of Calgary. It has fast food restaurants: Tim Hortons, A&W, and others for your little passengers to keep them happy. From Waterton, I recommend to refuel in Pincher Creek especially if you take Highway 22 north which has no service until Longview.

15000 Kilometer Perspective

I got my BMW F700GS last year and have accumulated 15,000 km so far. If I still like my bike after these kilometres, I suppose I can say that the motorcycle I got is the one I need. Of course, it goes for any motorcycle owner who still loves his bike after riding such distance.

There are many different motorcycle types: cruiser, bagger, street, naked, touring, adventure touring, dirt, scooter, chopper, and probably more. Unlike cars, motorcycles are very personal since both rider and motorcycle are visible to anyone. A big motorcycle will not suit a short-stature person, and vice versa. A street bike doesn't work for someone who wants to ride mainly on gravel roads, and so on. What I want to do therefore is to outline advantages I feel when owning my motorcycle. It's therefore not a comparison to other motorcycle types and brand names.

1. Versatility. I can ride at 140 km/h two-up on a highway with little difficulty since it has a maximum of 75 hp with a rated top speed of 192 km/h. I haven't come across a situation in which I needed to ride above 150 km/h. I ride everyday to work and it's agile enough in city traffic. I can ride two-up confidently in gravel roads with its not-so-aggresive tire treads and comfortably in highways covering 700+ km per day in rainy or windy days. Suspension travel and ground clearance are at their optimum level between the extremes of dirt bike and bagger.

2. Ride Tech Features. I find three tech features extremely useful: tire pressure monitor, gear indicator, and electronic fuel gauge. I had one flat tire experience on a highway and the tire pressure monitor quickly alerted me that the rear tire was losing pressure. The alert helped me decide a quick u-turn and reach a nearby town before a complete pressure collapse in the middle of nowhere. Gear indicator is absolutely necessary to reduce worry level during riding. Gear indicator is great for city commuting with all those traffic light stops. Electronic fuel gauge helps plan a long touring day and often gives assurance when I have to eat up more kilometres to find a place to sleep.

3. Fuel Economy. I am very happy with its 60 mpg fuel economy. Motorcycling is more risky and less comfortable than driving a car, so it doesn't make sense to me if I pay the same gasoline price for either. Instead of paying $80 to cover 1000 km distance when driving, F700GS allows me to pay $40 even with a passenger.

I used to wanting to get other motorcycles for their looks, sounds, or horsepowers. But I have learned that I am quite happy with what I got. Although I admit the one motorcycle I really want to test ride is Honda Africa Twin.

Calgary-Elko Motorcycling

One great overnight riding trip from Calgary is to ride to any point between Fernie and Cranbrook and to stay overnight there. Fernie, BC is 300 km from Calgary, and Cranbrook is another 100 km to the west.

I usually ride to the Rockies via Banff and Lake Louise, but after I rode on Highway 3 in June I felt I haven't spent enough time exploring Alberta and BC along the Crowsnest Pass and Highway. One advantage of camping along the Highway 3 corridor is the warmer weather compared to Banff and surrounding areas. There is about 10 C difference, so the evening becomes perfect and warm to gaze at sunset in a lake.

My wife and I left Calgary at 4:30 pm right after work two weeks ago and we arrived in Fernie at 8:30 PM after stopping for break in Chain Lakes Provincial Park. I stopped at Mount Fernie Provincial Park to find a campsite with no luck. We then continued west until Elko, where Highway 93 South junction is located, to check Kikomun Creek Provincial Park which has 110+ campsites. To our disappointment all were occupied.

I glanced quickly at my watch. It's 9 PM, and we had nowhere to camp. The Kikomun Creek PP staff suggested me to check private campgrounds along Jaffray Baynes Lake Road that runs along the northern shore of Koocanusa Lake. She also suggested Norbury Lake Provincial Park – some 40 km toward Cranbrook – but I wasn't keen on reaching another Provincial Park at sunset time without camp site guarantee.

So, I decided to try the private campgrounds option. It's always safer to book campsite in advance, but I often feel it is more adventurous to eat and sleep wherever the motorcycle takes me. Part of continuous adventure riding training is train my brain to dealing with uncertainties. We always bring two sleeping bags and a two-person tent in our side bags whenever we ride for this situation. We bring food and stove as well so we can purchase food at local grocery stores. We ask people we meet in towns we stop. I review campgrounds and motels around estimated stop locations using Google Maps before we go since I don't have a GPS unit in my motorcycle.

The adventure option gave us a new experience. And that's what we got in a good way. I saw a campground sign when we rode along the Jaffray Baynes Lake Road. There is about 1 km of gravel road to ride before we arrived at Ayes Ranch Campground. Its staff were generous to us –free pops for us when they saw how little we carried – and we were happy to stay there, as it faces Koocanusa Lake so we enjoyed fantastic sunset views. There is no running water near our campsite nor lake water is recommended for drinking, so I got ample chances to ride my motorcycle on bumpy gravel road to fill up my water bottles.

We stayed overnight and the next morning we headed back to Calgary on Saturday July 11. We were greeted by a severe thunderstorm that blew my motorcycle sideways and drenched our jackets. We had to wait at Braeside Tim Hortons for an hour until the rainstorm disappeared.

Homogeneous & Particular Solutions of Second Order Equation

The easiest way to remember that homogeneous equation is one of two solutions to a second order ordinary differential equation is that even if the right hand side is zero:

y'' + b(x) y' + c(x) = 0,

this equation will still yield a solution y(x). The second solution appears, in addition to the homogeneous, if the right hand side is not zero:

y'' + b(x) y' + c(x) = r(x).

Physically, the homogeneous solution represents the internal response of a mechanical system, while r(x) represents an external force that drives the system. The driving force r(x) will produce a particular solution of the system in response to the external driving force. This is - in my opinion - a more practical way to think about homogeneous and particular solutions.

It is also important to point out that the initial conditions only influence the homogeneous solution. This feature helps to tell apart the homogeneous and the particular in a first order equation when we use an integration factor to solve it. The homogeneous solution is simply one that has the integration constant. This aspect is important to remember since we often think that homogeneous and particular solutions appear only in second and higher order equations.

There is a theorem in differential equation that describes the above more succinctly. I could not recall it today in lectures, and it motivated me to find an alternative way to describe homogeneous and particular solutions of second order equation.

Why Motorcycling

This blog is a reflection of evolution of outdoor activities I have done over the past 15 years. I started it all with motorcycling when I was in grade 5. I grew up in Indonesia, where almost everyone learned to ride motorcycle at around that age. One group in Indonesia, who does not have this early learning privilege, is girls since their parents often forbid them out of fear of accidents. Some parents, however, allow their daughters to learn riding.  I did running and swimming also when I was in high school but I was never an athletic type, so they were not competitive.

I had several motorcycle accidents when I was in high school. Two accidents in particular I remember. One involved a family of four who all rode one motorcycle – this is still a common sight in Indonesia – that I hit at an intersection. Another involved my brand-new Honda motorcycle on the way to check my high school entrance result. Both were at about 40 km/h speed so they were not serious. These didn't dampen my motorcycling enthusiasm mainly due to a combination of high speed thrill and free-wheeling motorcycling nature.

When I went to university in Canada, I stopped riding because I couldn't afford buying a motorcycle. I then forgot about it and literally buried my riding passion for 25 years. That's what family responsibility and work-study life gave me. 

But I continued running and I got better at it. I always dream of going long and far. And I did run half-marathon length many times even in winter although I never participated in a running competition (it's too expensive for me to pay for running.) I carried a Camelbak and had granola bars in my pocket, and off I went. I have developed a layered clothing system to handle temperature change from 10 C to -40 C. I admire long-distance runners who can run hundreds of kilometers and always wish to have time to train for that ability. But I never did.

Although running is a great activity and meditative as well, I picked up cycling after running seriously for about 5 years. The main reason is that running limits me to about 40 km a day distance. I wanted to extend the distance per day target. Cycling is great and is as effective as running in keeping me fit. I often cycled to Bragg Creek from Calgary and back, which is about 100 km total distance, in the weekend. I cycled to Highwood Pass from Calgary and back, which is about 350 km in 3 days. And I have done Bandung-Jakarta cycling trip (200 km) in 2 days. The point I'm trying to make here is that cycling allows me to reach about 120 km a day distance. One student told me he did Calgary-Lake Louise (175 km one-way) in a day, so with consistent training I might hope to cover 150 km distance a day by cycling.

I outfitted my touring bike with panniers, pocket-size sleeping bag, small stove, bivy sack to go the distance. And a good distance challenge for someone living in Calgary is to cycle all the way to Vancouver. That's 1000 km distance, and I reckon I could do it in 9-10 days one way. That was precisely what I planned to do last year. It would take me 2 weeks to do a Calgary-Vancouver loop by not cycling back to Calgary. My wife would pick me up in Vancouver and we would drive back to Calgary. Or I would take a bus back to Calgary. The 2-week window to cover 1000 km distance in the end proved too long for me. There was really no other way to shorten the time while maintaining the adventure nature of a trip. This was when I decided to pick up motorcycling again.

So after 25-year hiatus I picked up motorcycling last year. It allows me to cover 800 km a day distance, a 6-fold increase over cycling, and effectively infinity-fold over running when the target is distance per day. Instead of 2 weeks or more to get to Vancouver and back, I only need 4 days.

The setup cost for motorcycling is about four-times higher than cycling, as a good touring bicycle now costs about $3000 when you outfit it with panniers etc. This cost difference, however, is paid back by the cheaper operating cost of motorcycling when you want to cover 1000 km. Motorcycling costs about five times cheaper due to the shorter time to cover that distance. The setup cost difference is recovered when I make about 15 trips of 1000 km distance.

In my estimation, the accident risk of motorcycling is higher than touring cycling, but not ten times higher. So roughly their risks are similar. I have done both, so let me explain my basic reasoning. Most motorcycling risk comes from its speed and fragility when colliding with cars and trucks, but these two factors can be mostly controlled by a motorcyclist when he exercises a defensive riding strategy. Bicycling accident risk, however, is often beyond the control of its rider. A bicycle occupies a narrow shoulder of a highway and is completely at the mercy of passing trucks and cars. What these facts imply is that I can reduce my motorcycling accident risk but I cannot reduce my bicycling accident risk.

I still cycle to work and run during weekend to keep me fit, but I now ride when I want to cover a big distance. One more benefit of motorcycling is that now I can go with my wife. To keep cost down, I chose a motorcycle with a good fuel economy.

Calgary-Vancouver Riding with My 12-Year Old Son

My son in action in Kitsilano Beach, Vancouver.

I rode my BMW F700GS with my 12-year old son from Calgary to Vancouver on June 24. I took a two-days off from campus to clear my head. (It happens quite often when I miss my riding days.) I had promised my son that we would ride together to Vancouver about a month before. So we did.

Our first day ended in Kamloops RV Park in Kamloops, BC. It was a 600-km ride from Calgary. Other than rain between Roger's Pass and Revelstoke, the ride was great. The RV Park has about 10 tent sites and the camping rate is $26 per night including tax. The shower room and washroom are clean. There is no time-limit for shower, and it doesn't cost coins. My son and I enjoyed our stay, with the exception of loud traffic and train noises from Highway 1 and nearby rail tracks. We would recommend Kamloops RV Park despite the noise since Kamloops doesn't have many nearby campgrounds. Kamloops RV Park's location is extremely convenient. You simply take the Lafarge Road off-ramp when heading west on Highway 1, before you arrive in Kamloops.

On the next day we hit Highway 5 (Coquihalla Highway) to reach Vancouver from Kamloops. This highway is fast as most cars go at least 120 km/hour. I maintained my speed at 120 km/h and sometime had to increase it to 140 km/h when overtaking trailer trucks and cars. 

To stay affordably in Vancouver, we rested in Surrey, which is about 15 km east of Vancouver. It's only 30-minute ride from Surrey to get to Vancouver downtown. We stayed in Canadian Inn, Surrey. I highly recommend this hotel. It charges a motel rate for a single queen bed ($80 before tax) but our room feels like a hotel. Our room was clean and very comfortable. We stayed in this hotel for 2 nights.

Ramen! Banzai!

We rode around Vancouver beaches and visited Marutama Ramen for its exquisite chicken broth. It is just off Robson St. and is about 1km from Stanley Park, where my son took a morning nap before having lunch at Marutama Ramen. You can say we rode 1000 km from Calgary just to have a great ramen!

Before entering Creston.

Our ride back to Calgary from Surrey was scorching hot due to heat wave from Pacific Ocean. This time we took Highway 3. It's longer (1300 km compared to 1000 km on Highway 1) to reach Calgary, but it was a lot of fun. There are twisty sections - and switchbacks too - between EC Manning Provincial Park and Princeton, and also around Osoyoos. It was 35 C when we arrived in Hope, but the temperature went up to 41 C around Osoyoos and Christina Lake. We covered 740 km in 12 hours – including many drink breaks every hour to avoid dehydration – from Surrey to Creston. We stayed in City Centre Motel in Creston. I highly recommend this motel when you are staying in Creston: simple, clean, and quiet for $77 a night including tax.

We reached Calgary at 4:30 pm on Sunday after about 500 km ride from Creston. As usual, Highway 22 (Cowboy Trail) was windy and to compensate for the crosswind I had to go at around 120-130 km/h along the highway. It was one helluva trip that involved one flat tire near Christina Lake; one scorching heat riding day; an RCMP car with a blaring siren wanting to catch me crossing solid yellow lines before I even crossed them yet in Princeton; a near-miss of hitting a deer crossing Highway 3 before Cranbrook; and a fast riding day on Coquihalla Highway.

Port Mann Bridge, Surrey-Burnaby border.

ROI of University Education is at least 100%

I read a CBC (Canadian Broadcasting Corporation) article today on student cheaters who use the services of custom essay writers for submitting course papers. Such writer charges $150 to $500 per paper, and one writer reported that there are 20 papers in one course. The $150 charge is for an easy paper, and it can go up to $500 per paper if it is difficult.

This piece of information is useful for estimating the value of university education because it is a real business transaction that happens between a university student and a custom essay writer. $150 to $500 is the cost a student is willing to pay to have his paper authored by someone else in order to get a good grade. Although it does not directly reflect the income the student will make after he graduates, the $150 to $500 cost reflects directly how much the student values his good grade.

The value of his university education can thus be evaluated in real dollar amount by the cost per paper as this cost reflects his salary expectation of a job he will have after graduation. After all, he won't be willing to part with his money if he believes he won't be able to graduate and makes enough money to pay back the cost.

The 20 papers per course is an extreme number for a course, I admit, but on average for an arts degree I estimate there may be 8 papers per course, while for engineering, in contrast, the number of papers goes down to 1-2. The difficulty level of paper submitted for an engineering course will be higher since it is more technical and there are not many custom essay writers who can plagiarize engineering papers easily. Thus, on average the price of a university course is

($150 × 8 + $500 × 2)/2 = $1100.

There are usually 10 courses per academic year, so the total cost is $11,000. $11,000 is the expected value of higher education yield in one year.

A Canadian student pays about $5,500 tuition fee (per year): this is the cost of university. Hence, the expected return of investment (ROI) of university education is at least 100%.

The ROI of university education is at least 100% since we do not put values into the network a student develops while studying at a university. Having a university degree is one of the best financial decisions one can make as it is quite rare to have a business with at least 100% ROI annually over four years.

Fisika 10 Menit di Youtube. Berbahasa Indonesia. Yeah!

Sejak Januari 2014 saya membuat seri video Fisika 10 Menit di Youtube. Selama ini sudah 7 video yg sudah saya upload:

1. Posisi, Kecepatan & Akselerasi: Video #1 memperkenalkan konsep posisi, kecepatan, dan akselerasi. Bagaimana arah dan besar kecepatan dan akselerasi berhubungan satu sama lain. Kecepatan adalah derivatif posisi, sementara akselerasi adalah derivatif kecepatan.

2. Gerak Percepatan Sama/Konstan: Video #2 membahas solusi posisi dan kecepatan untuk gerak yang dipengaruhi oleh akselerasi konstan. Kasus percepatan konstan ini kasus dasar yang melandasi hampir semua soal-soal ujian fisika SMA yang berhubungan dengan mekanika/dinamik. Aplikasi konsep posisi, kecepatan, dan akselerasi di Video #1 diterapkan untuk menurunkan rumus-rumus dasar di video #2.

3. Tiga Contoh Gerak Percepatan Sama: Video #3 membahas tiga contoh gerak yang berlandaskan rumus-rumus dasar untuk gerak percepatan konstan yang diperoleh di video #2. Contoh-contoh ini dipilih khusus untuk memperjelas aplikasi rumus-rumus dari video #2.

4. Hukum Gerak Newton: Video #4 membahas tiga hukum gerak Newton: inersia, F = ma, dan aksi-reaksi. Hukum gerak Newton ini melandasi hubungan antara posisi, kecepatan, dan akselerasi yang diterangkan di video #1 sampai #3. Hukum gerak Newton baru dikenalkan di video #4 agar subscriber seri Fisika 10 Menit bisa terbiasa dulu dengan rumusan gerak berdasarkan posisi, kecepatan, dan akselerasi tanpa harus berpikir mengapa mereka terhubungkan seperti itu.

5. Gerak Dua Dimensi: Video #5 membahas gerak dua dimensi karena gaya tarik gravitasi bumi. Saya bahas konsep horizon dan asumsi bumi datar dengan memandang bumi sebagai bola. Saya juga bahas darimana gaya tarik gravitasi bumi berasal. 

6. Gaya Hambat: Video #6 menggabungkan gaya tarik gravitasi bumi dan gaya hambat udara (drag force). Solusi persamaan dari hukum gerak Newton menjadi lebih rumit, tapi saya paparkan darimana solusi ini berasal. Contoh terjun payung menggambarkan bagaimana rumus fisika yang didapat bisa diterapkan di kasus nyata.

7. Gerak Koordinat Polar Silinder: Video #7 membahas gerak partikel memakai sistem koordinat polar/silinder. Sistem koordinat polar/silinder ini dibutuhkan untuk gerak berputar yang banyak kita temui di aplikasi mesin. Kinematik (hubungan posisi, kecepatan, akselerasi) memakai sistem koordinat polar/silinder diterangkan dengan jelas. Hukum gerak Newton kemudian dijabarkan memakai sistem koordinat ini.

Harga Gas Elpiji Indonesia $0.017 per kubik kaki dan lebih mahal 2.4 kali lipat harga di Calgary

1. Saya baca di tribunnews.com bahwa harga elpiji nonsubsidi kemasan 12 kg naik sebesar Rp 3.959 per kilogram. Total kenaikan harga untuk kemasan 12 kg ini berarti sama dengan 12 × Rp 3.959 = Rp 47.508. Jika harga awal elpiji 12 kg ini Rp 80.000, maka harga baru menjadi Rp 127.508. Konsumen yang membeli eceran akan membayar sekitar Rp 150.000.

2. Berat tabung elpiji 12 kg ini hampir semua dari berat tabung baja karena kepadatan gas 0.7 kg/m³ sementara kepadatan baja 7900 kg/m³. Singkatnya, untuk volume yg sama, baja lebih berat 11.286 kali lipat. Ini bisa dikonfirmasikan oleh dimensi tabung elpiji 12 kg yang saya taksir sekitar 60 cm tinggi dan 30 cm diameter. Volume tabung ini berarti 0.0424 meter kubik = 1.497 kubik kaki.

3. Berat tangki elpiji 12 kg saya taksir sekitar 16.7 kg dengan mengasumsikan ketebalan tabung 3 mm. Harga material plat baja dengan berat 16.7 kg sangat murah dan sekitar Rp. 150 saja. Ini bisa dihitung dari harga plat baja sekitar $750/ton. Proses pengelasan, pengecatan, dan penambahan komponen lain untuk membuat tabung elpiji 12 kg tentunya menambah biaya, tapi saya tidak bisa melihat harga tabung baja seberat 16.7 kg ini lebih mahal dari Rp 15.000 per tabung termasuk transportasi.

4. Penjelasan diatas berkesimpulan bahwa harga tabung elpiji 12 kg ini 88% datang dari harga elpiji itu sendiri yg sebesar Rp 127.508 – Rp 15.000 = Rp 112.508. Harga Rp 112.508 ini sama dengan dollar Canada CD$10.23 dengan memakai kurs Rp 11.000 = CD$1. Volume tabung elpiji 12 kg sebesar 1.497 kubik kaki. Untuk tekanan 1 bar, berat gas elpiji untuk volume ini sebesar 30 gram.

5. Pada saat elpiji diisikan ke tabung elpiji 12 kg, berat gas elpiji adalah 12 kg. Dengan mengasumsikan ideal gas law, ini berarti jumlah molekul gas yang diisikan adalah 400 kali lipat. Ini berarti tekanan gas elpiji adalah 400 bar = 40 MPa. Kekuatan tarik baja sekitar 500 MPa, jadi tekanan ini masih aman. Volume total gas elpiji (ekuivalen di tekanan 1 bar) dengan tekanan 400 bar di tabung 12 kg sebesar 1.497 ft ³ × 400 = 600 ft ³.

6. Harga CD$10.23 ini untuk membeli volume gas elpiji sebesar 600 ft ³. Ini berarti harga jual gas elpiji di Indonesia sebesar CD$0.017/ft ³.   

7. Harga CD$0.017 per ft ³ ini amat sangat mahal karena di bulan Desember 2013 saya membayar total CD$145.23 di Calgary untuk total energi sebesar 20.1 gigajoules (GJ) dari gas elpiji untuk memanaskan rumah dan air. Gross heating value untuk elpiji sekitar 1000 BTU/ft ³ atau 1 mega joules (MJ) per ft³. Berarti konsumsi per bulan rumah tangga saya 20.100 ft ³ (dua puluh ribu seratus kubik kaki volume). Jadi saya cuma membayar kurang dari 1 sen per ft ³. Harga gas elpiji di Indonesia per ft ³ jadinya 2.4 kali lipat lebih mahal dari di Canada.

8. Jika saya tinggal di Indonesia dan mengkomsumsi gas elpiji sebesar 20.100 ft ³, saya akan butuh 34 tabung elpiji 12 kg. Keluarga saya akan bangkrut tidak sampai sebulan karena biaya 34 tabung elpiji 12 kg ini Rp 5 juta per bulan.

9. Komponen biaya gas elpiji yang saya bayar tiap bulan di Calgary termasuk biaya administrasi, infrastruktur pipa, dan pengiriman gas yang dilakukan memakai pompa karena langsung memakai pipa bawah tanah ke tiap rumah. Perbandingan harga Indonesia dan Canada ini jadinya proportional, alias "apple-to-apple price comparison". Biaya $145.23 yang saya bayar adalah harga pasar yang saya bayar langsung ke perusahaan gas di Calgary. Ini tidak berbeda dengan membeli gas elpiji di toko eceran di Jakarta.

10. Pertanyaan saya: (i) Siapa yang paling diuntungkan dengan harga gas selangit di Indonesia? (ii) Berapa banyak kerugian rakyat karena ketidakmampuan pemerintah mengontrol harga demi kesejahteraan rakyat?

Keadaan Darurat

Keadaan di Indonesia sekarang sudah bisa dikategorikan keadaan darurat. Ada beberapa alasan mengapa saya bilang keadaan darurat. Pertama, kerusakan alam Indonesia. REDD (Reducing Emissions from Deforestation and Forest Degradation), yang merupakan kerangka acuan agar negara berkembang bisa mendapatkan ganti rugi jika bisa mengurangi emisi karbon, bilang bahwa area hutan Indonesia berkurang sebanyak 1.17 juta hektar setiap tahun sementara total area hutan sebesar 131.3 juta hektar. Pengurangan sebesar 0.87% per tahun ini akan membawa bencana banjir dan kekurangan air minum tanpa harus menunggu semua hutan lenyap. Tidak ada perhatian serius untuk mengurangi kerusakan alam yang pada akhirnya mempengaruhi kehidupan sehari-hari, mulai dari asap knalpot berkadar elemen kimia timbal (Pb) yang beracun dan sungai-sungai hitam penuh kotoran dan plastik.

Kedua, pemerintah dan pemimpin Indonesia tidak efektif dalam memperjuangkan hak hidup layak rakyat. Korupsi merajalela: saya baca di koran 70% pemimpin daerah - termasuk gubernur dan walikota - korup. Karena mereka yang membelanjakan uang negara dan jika bisa diasumsi level korupsi mereka sekitar 10% dari total belanja negara sebesar Rp 1683 trilyun tahun 2013, maka uang negara yang hilang sebesar Rp 118 trilyun = 70% × 10% × Rp 1683 trilyun. Ini perkiraan minimum tapi jelas menggambarkan rusaknya sistem ekonomi nasional. Korupsi menjadi industri di Indonesia dan mendistorsi harga tanah, bangunan, dan perilaku pasar secara umum. Pelaku usaha industri korupsi adalah politikus, aparat pemerintah dan hukum yang kemudian berkolusi merusak semakin parah tatanan sosial, ekonomi, dan alam.

Uang Rp 118 trilyun ini menjadi sekitar Rp 1 juta per tahun jika dibagikan rata ke jumlah penduduk miskin yang berkisar 40% dari total 250 juta rakyat. Uang yang dikorupsi pasti akan cukup untuk membiayai sekolah anak miskin dari SD sampai SMA dan menjamin kesehatan mereka. Kenapa ini tidak bisa dilakukan? Karena uangnya dicuri koruptor-koruptor yang merajalela di tanah air.

Ketiga, pemerintah telah membodohkan rakyat dengan tidak memberikan sistem pendidikan yang memadai dan mampu mencetak lulusan yang mandiri dan berpikiran merdeka. Dari pengalaman saya mewawancarai pelamar kerja saat bekerja di Indonesia 2011-2012, saya terkejut dengan rendahnya kemampuan berpikir logis dan analitis insinyur lulusan beberapa perguruan tinggi yang terbilang punya nama. Lulusan insinyur mesin tidak bisa menjelaskan efisiensi mesin bakar. Lulusan2 insinyur tidak mampu menjelaskan hubungan persamaan matematika dengan fisika. Lulusan2 ini lah yang nantinya menggantikan senior mereka dan menjadi pemimpin di lingkungan mereka. Tidak berlebihan jika saya pesimis akan kemampuan Indonesia untuk mewujudkan visi memakmurkan rakyat.

Rasa pesimis ini karena juga melihat sistem pendidikan dasar dari SD sampai SMA yang dijejali hafalan informasi tanpa ada pelatihan berpikir kritis. Sistem pendidikan buruk ini dilanjutkan ke perguruan tinggi. Penjejalan rumus dan hafalan selama kuliah akan memperparah keadaan. Para lulusan insinyur dan sarjana ini tidak akan mampu berpikir mandiri.

Tidak mungkin Indonesia bisa sejajar dengan Cina, Korea Selatan, apalagi Canada dan Amerika Serikat sampai kapan pun jika sistem pendidikan Indonesia tidak dirombak total.

Motion and Energy

(The image above is not a link to the pdf. The link is provided below.)

I wrote a short chapter over the weekend on Lagrangian mechanics and how the concept of energy is defined from the so-called Lagrangian which is the difference between kinetic and potential energy. You can read it by clicking here. I think this chapter can be useful if you want to learn about Lagrangian mechanics which generalizes the Newton's laws of motion.

I am planning to add discussions on conservation of momentum and angular momentum, and thus give 1-2 more examples.

If you are already familiar with the Lagrangian mechanics concept, you can drop me a line. I'd like to hear what you think about this short chapter. Thanks.

Discrete Probability Distributions: Sampler of Our Textbook

My ex graduate student, Deborah Gaffney, and I finally completed an undergraduate-level probability and statistics book titled Elementary Concepts of Probability & Statistics. I started writing in November 2012 and finished writing it in June 2013. You can download a chapter on discrete probability distribution functions by clicking here. Enjoy reading! Send me a feedback to tell me what you think.

I decided to write this textbook because I feel many textbooks are too thick (600+ pages) and too expensive ($150 or more). Students have to invest a lot of time to read such textbook. Why not explaining the concepts more clearly and concisely? We sell this textbook for a lot less and it has only 124 pages. 

Our textbook is not typical since it does not have many example and exercise problems as it focuses more on explaining concepts as good stories. Lecture notes that accompany our textbook bridge this gap as they provide many example and exercise problems.

I am testing our textbook now in a summer probability and statistics for engineers course. I will update you on how it goes.

Konsep Tuhan

23. Di 6 blog sebelumnya: Ongkos Beragama, Paradoks Beragama, Kebebasan Beragama, Makna Beragama, Etika Humanis, dan Karya Hidup, saya tulis bahwa karena surga neraka tidak bisa dibuktikan keberadaannya, maka sebaiknya kita tidak berharap kehidupan baru setelah mati. Hidup sekarang bukan untuk hidup setelah mati. Hidup sekarang untuk berkarya tanpa mengharapkan pahala dan takut dosa.

Dengan berkarya, kita akan sadar tidak ada gunanya takut mati. Selain itu, ketakutan akan kematian ongkosnya mahal, baik uang maupun waktu. Jika kita takut mati, kita akhirnya membuang hidup yang sekarang untuk yang belum tentu ada.

24. Lantas dikemanakan Tuhan? Bukan berarti Tuhan tidak ada jika surga neraka tidak bisa dibuktikan keberadaannya. Tuhan bisa ada, tapi dia bisa tidak membuatkan surga neraka buat kita. Alam semesta ini amat sangat luas dan kita menempati satu titik kecil. Tuhan bisa jadi tertawa geli melihat kita merasa yakin kita makhluk hidup yang terpenting sealam semesta.

Namun Tuhan pun tidak bisa dibuktikan keberadaannya. Ribuan tahun terlewati dan ribuan buku ditulis untuk mengupas tentang Tuhan, tapi tetap tidak ada bukti konklusif adanya Tuhan. Yang sudah terjadi selama ribuan tahun ini adalah sains secara pasti menggantikan fungsi Tuhan sebagai pengatur alam semesta.

25. Sains bisa melihat janin berumur beberapa bulan dan memastikan jenis kelaminnya sebelum lahir. Sains bisa memprediksi dengan persis kapan gerhana bulan dan matahari terjadi. Sains membuat orang di belahan bumi lain membaca blog ini beberapa detik setelah saya publish. Sains bisa mengantar saya terbang ke mana saja dengan kecepatan 800 km/jam. Sains memperpanjang umur kita dengan berbagai obat dan terapi medis.

Kesemua hasil sains ini sangat nyata buat yang berpikir. Kebanyakan kita memilih untuk tidak peduli dengan tidak sengaja karena kita dibutakan oleh pendidikan yang kita terima dari kecil. Pendidikan yang berlandaskan agama kerap bertentangan dengan prinsip sains karena sains mengajarkan kita untuk tidak percaya dan selalu bertanya jika tidak ada bukti kongkrit dan konsisten.

Banyak dari kita yang beranggapan sains sangat sombong karena tidak mau mengakui adanya Tuhan. Sesungguhnya keteguhan sains ini bukti kerendahan hati sains karena sains tidak bisa memastikan sesuatu jika memang belum ada bukti nyata. Bukankah justru kita sombong jika kita mengabarkan keyakinan kita ke orang lain dan berusaha mempengaruhi orang lain padahal kita tidak punya bukti konklusif akan keyakinan kita?

26. Konsep Tuhan tapi tidak akan hilang selama pendidikan berbasis sains belum mencapai semua orang. Karena konsep Tuhan dibutuhkan untuk memberikan tujuan hidup jika kita tidak mempunyai pegangan hidup berdasarkan sains atau yang lain. Selain itu akan ada sebagian kita yang berusaha keras mendamaikan sains dan Tuhan.

Sebagian kita butuh Tuhan ada – walau tanpa ada bukti Tuhan itu ada – karena Tuhan ini yang memberi tujuan hidup. Selama ajaran agama yang berlandaskan ketuhanan kita pakai sebagai landasan etika, maka tujuan hidup berketuhanan adalah hak setiap orang.

Yang sering jadi masalah adalah jika keyakinan adanya Tuhan masuk ke ranah publik dan Tuhan dipakai untuk menakuti orang lain. Kesombongan agama seperti ini yang perlu kita jauhi. Biarlah kepercayaan kita menjadi urusan pribadi antara tiap kita dan Tuhan kita masing-masing.

London's Cheap Eats

There are many great places to eat in London – for sure – but I am cheap so I never have fancy expensive meals unless someone else pays them. I stick my nose close to the ground and experiment with cheap places to eat. Having said that, I never plan my trip to any city with restaurants as trip anchors either.

London has many Lebanese-style kebab eateries. They are not fancy: wall ledges to place plates and eat while standing and 3-4 chairs and a table if lucky. But no matter; a great and cheap food tastes good regardless. When I feel hungry, I am bound to find a kebab eatery nearby. 

And did I find a great one! It is located on 1A Great Eastern Street, at the southwest corner of Shoreditch High Street and Great Eastern St., about 5 minute walk northbound from the Liverpool St. Tube station. I was in this East London neighborhood to check out the Brick Lane and Curtain Rd. where some vintage clothing stores and artisan coffee shops are located.

The Lebanese eatery is called Corner Savoy and I went there twice in a week. The first time they charged me £7 for rice, chicken shawarma, salad, hummus, and garlic dressing. They were surprised at my request and came up with the price since it is not on the menu. But it was not disappointing at all. The chicken shawarma is juicy, and the hummus, the dressing, and especially the salad are wonderfully fresh.

The second lunch time I was there I didn't have breakfast. Mido, the Egyptian staff who served and was busy preparing a chicken shawarma, charged me £6 for the meal I had the first time. Maybe partly because I told him I took subway all they way from South London for a repeat. He and his friend laughed, and his friend told me Mido (photo below) and the eatery are famous for their shawarma in the neighborhood. I told him I was from Canada and he said he would set up a business in Canada someday. Without breakfast, I ordered another shawarma, this time smaller, lamb no less, with falafels. An excellent meal for £3; the total damage was £10 with a bottled water.

The second place I went to has even lower meal prices. Maybe for that reason, it is called Happy Family :), a Chinese and Oriental eatery on 311 Kennington Road, about 10 minutes north of the Oval tube station on Clapham Rd. and Camberwell New Rd. in South London. It has 4 school benches to sit and the place is simple but quiet. I like that.

I ordered beef chow mein in my first visit for £3.60. I stayed at a bed & breakfast through www.airbnb.com on Southey Road off Brixton Rd. I walk for about 20 minutes along Brixton Rd and then Kennington Rd. to get to meet my Happy Family. A good walk and I am usually hungry when I get there, lol!

The food is very good – not great – but I like also the old chap who waits on the counter. He is British, so I wasn't sure if he would be willing to be photographed, so I didn't ask (regret, ugh!). He was watching a science program on teve about space travel when I went there for the second time. Very proper and I enjoyed his company. We talked about teleportation and black hole while I enjoyed my food. This time it was beef in black bean sauce for £4.20 and wan ton soup for £2.40. I know: I splurged a bit, lol!

I always hold dear eateries like them. Mom-and-Pop operations with gracious open services. They color my days. I always remember them. They represent the city they live in, and I have to say I really like London!

Londoner

I could be a Londoner, walking everywhere 

Along its treed sidewalks and vast parks.

Tube stations at important corners not far from

Simple red brown row houses with clean interiors.

This city is a proof that people can be enriched

Immensely by shared properties – parks, transport,

Museums, markets, coffee shops with yummy

Mustard salt beef sandwich and thick sticky

Blueberry muffin.

I could marry a Londoner, the pretty girl standing

Across from me in a subway car. Her British

Demeanor and wits, and warm hugs that will fill 

My days with joys and wonders.

I always search for a soul home, and I might just

Find one in this isle at the edge of Europe. Its quiet

Diligent people with ferocious independence.

This city is lovely and intelligent as its people are.

Peran Individu

Beberapa hari saya berada di London dan Birmingham. Baru pertama kali ini saya berkesempatan menengok negara yang mempunyai pengaruh besar dalam menentukan arah gerak peradaban dunia. Amerika Serikat dan Canada - tempat saya tinggal - awalnya koloni Inggris. Indonesia pun sempat jadi koloni Inggris. Sukar untuk tidak berpikir sejenak tentang bagaimana rakyat Inggris bisa melakukan semua ini.

Sekilas tidak ada yang berbeda dengan kota-kota di Amerika Utara yang pernah saya tinggali atau kunjungi. Orang Inggris pendiam, tidak banyak omong di depan umum. Saya menginap di bed & breakfast lewat www.airbnb.com karena dana kampus yang saya terima tidak cukup untuk tinggal di hotel berbintang. Ini menguntungkan karena justru saya berkenalan dengan banyak orang. 

Pemilik flat di London – tempat saya menginap – cerita sekarang banyak warga Eropa tinggal di London untuk mencari kerja. Teman baru Spanyol saya cerita angka pengangguran di Spanyol sekarang 26%. Pemerintah Spanyol suka membuat proyek-proyek megah tanpa guna jelas. 

Pemilik flat yang pernah beberapa tahun tinggal di Spanyol cerita orang Spanyol suka pamer. Dia pernah berkunjung ke rumah teman dan temannya ini bertanya apa dia suka dengan sofa yang baru dibeli, apa dia suka dengan gaya rumahnya. Orang Inggris tidak akan pernah bertindak seperti itu, cetusnya. Sekilas saya berpikir: orang Inggris rupanya tidak beda jauh dengan orang Jawa.

Kota London dipenuhi taman-taman besar nan rindang. Regents Park, Clapham Common, Hyde Park, dan yang lain. Taman-taman ini rupanya dulu tanah swasta yang kemudian di era ratu Victoria dijadikan taman umum agar semua orang bisa menikmati. Visi ini terbukti benar. Enak sekali jalan menyusuri London. Rumah-rumah tertata rapi diselingi hijau pohon-pohon rindang. 

Peran individu di sejarah Inggris sangat besar. Saat raja Inggris tidak cocok dengan kebijakan Vatican, tidak ada keraguan untuk mendirikan sekte kristen baru, yang kita kenal sebagai gereja Anglican.  Sejarah sains dipenuhi orang-orang Inggris. Michael Faraday, William Rowan Hamilton, Paul Dirac, James Clerk Maxwell, Lord Rayleigh, Stephen Hawking. Belum lagi orang-orang Inggris yang berperan besar di politik, ekonomi, dan lainnya. Mereka bergerak sebagai individu-individu yang membawa perubahan sendiri-sendiri.

Saat di Birmingham saya menyusuri Jewellery Quarter, pusat pabrikan dan perdagangan emas Inggris. Area dekat pusat kota Birmingham ini adalah bukti Birmingham pusat kreativitas manufaktur Inggris. Birmingham mempunyai peran sentral di Revolusi Industri. Pabrik mobil Morgan, Land Rover, Jaguar ada di kota ini. 

Jelas terlihat di arsitektur gedung-gedung tua yang masih tegak berdiri baik di London maupun Birmingham peran individu dalam menentukan roda ekonomi. Inovator dan industrialis bergerak bersama menghasilkan produk-produk baru, yang kemudian mempekerjakan ribuan orang. Pemerintah mempermudah dan memastikan kegiatan ekonomi inovatif ini tidak merugikan banyak orang. Simbiosis mutualisme ini berjalan baik, terbuktikan oleh bagusnya infrastruktur kereta api dan bawah tanah, jalan, air dan sungai. Lahan pertanian yang membentang dari London sampai Birmingham tertata rapi. Keteraturan ini berjalan tanpa mengekang kreativitas individu dan menjadi teladan buat masyarakat Amerika Utara yang juga ikut merasakan hasil positif jerih payah peran individu.

Hukum Kekekalan Momentum

Gerak tidak pernah hilang di alam semesta

Derap kaki kecil dibalas sama oleh bumi

Gelombang suara memancar segala arah

Pantulan bergaung, tatapan pejalan kaki 

Riak kecil itu tetap getar tak punah lelah

Semakin lebar semakin kecil tanpa lenyap

Gerak kecil kita membahana kemana mana

Menjadi kumpulan berarah tumbuh besar

Tanpa hilang tajam jika arah kita sejajar 

Arah jadi sangat penting penentu jumlah

Jika gerak kecil kita tertuju satu titik

Lenyap semua saling menarik mendorong

Energi semua seakan terbuang percuma 

Menjadi panas menguap suara tak terarah

Tak pernah hilang tak pernah ada pula