Posted in zany, offbeat, somewhat silly humor

Craggy Island Calculus Problem

For the sake of argument, say that you happen to be standing on the edge of a beach off the coast of Ireland, directly facing a little island called Craggy Island. Fans of the British television series “Father Ted” will be getting excited at this point, since Father Ted and his fellow renegade priests were exiled to Craggy Island due to some unspecified but nevertheless unsavory behaviour.  But more on that some other time.

Where was I?  Oh yes!  For some inexplicable reason, you have been seized by a powerful urge to kayak to the island, but you don’t know how far away it is.  Assume you’ve never seen “Jaws”.  How could you determine the length of your impending voyage?

Personally speaking, I would just call the Craggy Island Department of Tourism and Limpets (1-877-LIMPETS), and ask them how far it is to their island.  But maybe there’s no answer when you call and maybe you just don’t like taking the easy way out.  So now what?

Well…if you happen to know how fast the lighthouse beacon is rotating, and if you happen to know how fast the beam is sweeping toward you when it hits the (eerily-straight) shore 1/2 kM north of where you’re standing, you could say to yourself: “This sounds like a related-rate problem!  I might be able to use Calculus to solve it!”

220px-triple_integral_example_2-svg

Since you have nothing better to do, you resist the urge to start paddling, so you fly home and spend the next few nights covering page after page with chicken scratch, basically re-deriving Calculus from first principles, since you haven’t taken it for 38 years or so.  (The picture which should pop into your head at this point is that of a large beetle flipped over onto its carapace in front of a blackboard, feebly waving a piece of chalk clutched in its foreclaw.)

beetle-on-backFinally, your son (who oddly enough happens to be taking Calculus at school) takes pity on you after witnessing your struggle and says, “Dad, why don’t you just Google it?”

Since you were born well before Al Gore invented the Internet, you look at him with a dumbfounded expression and reply, “What the heck would I Google?”

He regards you with a sorrowful expression and says,

“I dunno.  Google is pretty clever.  Try typing: ‘Calculus Lighthouse Problem.’ ”

You dutifully follow this directive and to your undying amazement, this search phrase returns a long string of hits, and one of them even refers to Craggy Island!

From there it’s just a short hop to a YouTube video clip (Calculus tutorial) made by an endearing fellow named Bart Snapp who solves your exact problem right before your very eyes!  You really should watch this clip, mostly because I took the trouble to transcribe the intro almost word-for-word, but also because you will find yourself swept away by Bart’s patently obvious love of teaching in general, and Calculus in particular, and also because this guy is great at reading out loud.  I quote:

“Hello there!  Now we’re going to do a problem (waves hands energetically) about a beacon in the ocean, also known as a lighthouse of sorts.  But we’re going to call it a beacon.  All right?

“All right!  Let’s see the problem! (Reads problem enthusiastically and eloquently.)

“All right.  So we have our problem and now we have to… (he pauses for dramatic effect)…Draw a picture! (Bart starts sketching rapidly on a whiteboard)

“All right.  So we have a, we have the shore here, and the shore’s supposed to be straight.  (Draws more-or-less straight line)

“Well.  Well that’s straight enough I guess.  Here’s point A.  (Draws the beacon on a line perpendicular to point A, and presses on)…the beacon has some light that is shining and let’s see…(adds some more notations like dϴ/dt and dx/dt to his diagram).

“What else?…Aha!

“And the water…This is all supposed to be water here.  (Draws blue squiggles.)  That’s great.”

And really, it is great because at that point you see that the beacon, the place where you’re standing directly opposite the lighthouse, and the point where the beam hits the shore 1/2 kM north of you, form a triangle, and you can relate the rotational speed of the beacon (in radians/sec of course) to the sweep rate of the beam along the shore, through trigonometry!

lighthouse

From there it’s only a matter of a couple more days of calculations until you figure out the lighthouse is 1 kM straight out from where you’re standing.  You can easily handle a 1 kM paddle but then you find out that the last person who tried it was eaten by sharks.  What should you do?

The first thing you should do is ask yourself whether this whole eaten-by-ravenous-sharks while-attempting-to-paddle-to-Craggy Island thing is true or is it an urban legend?  And does Craggy Island even exist, or is it the product of the imagination of a couple of half-baked Irish writers named Arthur Matthews and Graham Linehan?

This is important because urban legends are everywhere these days, thanks to Al Gore, and you just can’t be too careful.  Consider the story I read recently about an intoxicated Marine in the state of Kansas who was arrested after a failed attempt to foil his car ignition interlock by having a raccoon breathe into it.

Right away you have to be suspicious that this is an urban legend because there are no raccoons (or Marines for that matter) in the state of Kansas.  Actually, I’m lying.  I made up the Kansas part, and if you consult Google, you will discover that Kansas is literally teeming with raccoons.  I quote from the Kansas Department of Wildlife, Parks and Tourism website: “Highly intelligent and adaptable, the raccoon (Procyon lotor) is one of our most abundant furbearers. “ But all that aside, your first clue that the story is b.s. is that everyone knows Marines don’t drink.

Anyway, the point is that you have to be careful not to waste your time on drivel like the story of The Raccoon and The Breathalyzer. Instead I want you to recall The Owl and The Pussycat, a poem by British artist, illustrator, musician, cookbook author and all-around oddball Edward Lear (1812-1888) and then check out the poem I just wrote.

owl-and-pussycat

With apologies to all the people of Britain, except Prince Charles:

The Owl and the Pussycat did some maths, with the aid of Barton Snapp
They related dtheta to dx (by dt) but they found themselves in a trap
They set forth for the Isle but in a short while, the water began to boil
Attacked by a shark, in the cold and the dark, off shuffled their mortal coil(s).

 

 

Well, it’s time to shut this thing down.  I’m going to heat up a plate of leftover limpets and then get ready for my paddle to Craggy Island first thing in the morning.  But just one nagging thought remains:

I think I’m going to need a bigger boat.

bigger-boat

Posted in zany, offbeat, somewhat silly humor

Toilet Seat Lore

Well, it looks like I’m cranking these things out somewhat less often than I’d like to, but echoing the immortal words of John Cusack explaining to his prof why he was late to class in The Sure Thing (1985): “Well you see there was this problem and I’m late because of it.”

The problem is that a few weeks ago we woke up one morning and decided to adopt a seven year old border collie named Mickey. Everything you read about border collies says they need to have a job, so Mickey’s job is to play fetch 23 hours a day and look at me reproachfully the rest of the time.

So between Mickey and the treadmill, there’s not a lot of spare time these days. Plus, I didn’t have anything worth writing about until last week when we had visitors from head office, aka The Mothership. For the sake of argument, I’ll call one of the visitors Lisa Kearns (not her real name). “Lisa” was relaying to one of the people I share an office with what a great stay she had had in the Hotel Elan (otherwise known as the Hotel Elan), “a unique, business-friendly boutique hotel in Calgary, located uptown just off vibrant 17th Avenue SW.”

hotel-elanI wasn’t sure what a boutique hotel is so I Googled it.

A boutique hotel is “a small stylish hotel, typically situated in a fashionable urban location.” I read a few more entries and found a pearl of wisdom from Kobrun Vidisdottir, of Reykjavík, Iceland.

According to her, a boutique hotel is “an accommodation that makes their guests feel happy and contented while staying there, makes them feel extraordinary, makes them to realize that they should revert soon and makes them to recognize that this hotel is worth discussing with others.”

I followed most of what Kobrun was trying to say, but I got stuck at the part where she started talking about reverting. Reverting to what? Her maiden name? Windows 7? Human form? Then I figured out she meant return soon. Which reminds me, I should return to the theme of this column, which is supposed to be about toilets. But remind me to tell you a little bit more about Reykjavík in a minute.

Anyway, “Lisa” was going on about the heated and lighted toilet seat in her hotel room, which in her words “changed my life.” I asked her if her life routinely involved sitting on ice-cold toilet seats and she said no, the heated seat was just a particularly pleasant experience. Plus the underside of the seat was ringed with LEDs, which emitted a pleasing blue light.

Now this is important because everyone knows that if you wake up in the middle of the night and turn on a yellow or orange light, it will immediately shut down your melatonin. Everyone  also knows that the last thing you want to do is sit on an ice-cold toilet seat and shut down your melatonin when all you really want to do is take a pee and go back to sleep. But I guess it’s this kind of thing that separates a normal hotel from a boutique hotel. It’s still sort of surreal though, like going to the bathroom in 2176 AD.

Speaking of going to the bathroom in 2176 AD, Calgary happens to have a few choice, futuristic, public washrooms strategically located about the city. I had the chance to use one a few years ago, but to refresh my memory about the entire experience, I paid a visit to one near my house, at the Tuscany LRT station. (My house is not at the Tuscany LRT station; the futuristic public washroom is at the Tuscany LRT station.)

toilets-1

For starters, it’s pretty futuristic-looking. You approach the door, push a button, the door slides open and you find yourself in a little room with a lot of stainless steel including a stainless-steel toilet, with no toilet seat.

first-button

You push another button (“Toilet Seat”) which triggers a bunch of disturbing mechanical noises. A panel in the wall slides open and a toilet seat deploys from behind the panel, spraying liquid in the process. (I am not making any of this up.) You half-expect that some robot arms with metallic claws will appear, seize your eyelids and pry them open, like in “A Clockwork Orange.” A mellifluous robotic voice guides you through the whole process, accompanied by a stirring rendition of “The Ride of the Valkryies.” (kidding)

second-buttonYou go to the bathroom, and if you can’t figure out how to flush, there are instructions to help. Once you wash your hands, the toilet seat folds back into its nook, the panel slides back down and you’re good to go. (I thought you went.)

third-button

But say you’re still sitting down or just remaining immobile for some reason (shock probably). The mellifluous robotic voice comes back on and tells you that you have about 20 seconds until the cubicle door opens, unless you start moving around soon. If you don’t move around, the voice starts counting down. Seriously.

I actually filmed this whole thing and you can check it out here:

(Futuristic Public Washroom video clip)

My son Ty got quite panicky once, when the mellifluous robotic voice announced the countdown while he was still working on Step 2 or whatever. He leaped up from his perch and began waving his arms madly, until he gained the precious seconds he needed to finish his business.

The whole setup is just so weird that I fully expected to emerge from that washroom to find myself catapulted two or three centuries past 2176 AD and face to face with a Dalek or else “Robot” from Lost in Space. “Danger, Will Robinson! Danger!”

verdarobbyThere is another high-end toilet (intended for household use although I’m sure a boutique hotel somewhere has one), which automatically deploys a menacing-looking probe from somewhere in the bowels (pun intended) of the toilet bowl. The probe emits a gentle spray of water which you direct with a complicated remote control. But since I can barely use my TV remote, I probably won’t buy one of those washing probe-equipped commodes, even if I could afford one. I’m saving up for a time machine.

Last but not least, if you happen to have to go potty in O’Hare Airport in Chicago, brace yourself. When you’re in the cubicle, you press a button on an apparatus situated on the back of the toilet. You hear mechanical noises and then a protective plastic sleeve shoots out and envelopes the toilet seat. You do what you went in for, then get up and after more mechanical whirring noises, the sleeve disappears into the apparatus behind the toilet seat.

My only question is: what happens to the sleeve you sat on? Do they just toss it, or is it sent back around for the next unsuspecting victim? I know, I probably shouldn’t worry about these things, but I just can’t help it. Call me a Luddite, but I just think things are getting way too complicated here in 2015.

I think I’ll move to Reykjavík. Quoting here from Randburg.com (whatever that is) about the downtown area: “The old city center is atmospheric and relaxed. Many excellent cafes, bars and restaurants are located there and there are also many shops, including stores specializing in traditional souvenirs and stocking a good selection of merchandise, including crafts, replicas of Viking artifacts, ceramics, jewelry, playing cards, books, calendars, sheepskin products – and Iceland’s famous wool products. “

Sounds great. I’m fresh out of Viking artifacts, so I’ll definitely check it out.  But I bet the toilet seats are freezing.