Getting Mathematical on Weeds.

Dandelions amaze me.

We tend to take them for granted.

“Huh.  They’re just stupid weeds. ” , many of us might say.

But if you look closer, they’re actually quite beautiful.

And if you zoom in REALLY close, you’ll find something even more amazing.

Notice, there’s definitely a spiral pattern there.

If you connect the dots, you can definitely count 13 curves in the clockwise direction.

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But if you connect the dots in a counter-clockwise direction, you get 21 curves.

Now, remember those numbers, (13 and 21), while I digress for a bit.

Consider this mathematical sequence of numbers.

0,  1,  1,  2,  3,  5,  8,  13,  21,  34,  55,  89….

For those of you who don’t recognize this,   these are Fibonacci numbers, where any given number is the sum of the previous two.

It’s quite simple:

0 + 1 = 1

1 + 1 = 2

1 + 2 = 3

2+ 3 = 5…and so on.

Now, if you draw a series of squares,  based on the Fibonacci sequence, and you get something like this:

And if you draw a continuous arc though each square,  it forms a spiral seashell pattern, like this:

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This is called the Fibonacci Spiral

Now, let’s take my 13 clockwise red-curves:

And if I take them, one by one, and superimpose them on the Fibonacci Spiral, I get this:

Kinda fits, doesn’t it?

Same thing if I take the 21 counterclockwise curves…

Again, each curve also seems to fit, when superimposed  on the counter-clockwise Fibonacci spiral:

Now, let’s just recap:

I zoomed in on a photo or a dandelion, connected dots and generated some rough curves.

And the shape of these curves fit a spiral based on the Fibonacci sequence.

Not to mention, the number of clockwise and counter-clockwise spirals are 13 and 21.
Which are Fibonacci numbers themselves.

What’s going on here?   Is this magic?   Or  a fluke?

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Actually, this is no accident.

You see, Nature tends to like Fibonacci numbers.   For example, you rarely see flowers with 4 or 6 petals.  But you see many with 3, 5 or 8.

Flowers seed pods are also arranged this way.  The number of spirals are always Fibonacci numbers…one clockwise, one counter-clockwise.

In this case, with my dandelion,  it was 13 and 21.  With larger flowers (like Sunflowers), you’ll find numbers 34 and 55.

But why Fibonacci numbers?

Basically, it has to do with Nature trying to optimize itself.  With flowers, if seeds are arranged in Fibonacci spirals, you can fit more of them onto the plant,  and you get more bang for your buck.    There’s a good interactive exercise that demonstrates this.

I won’t get into the whole mathematical explanation.   But you can find some good discussions here and here.

It’s not just dandelions.  You’ll also find Fibonacci sequences with pine cones, pineapples and asparagus and seashells.       Plant leaves are arranged in Fibonnacci spirals, to optimize the sunlight they recieve.

Fibonacci numbers are everywher in Nature   More examples are shown here.

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It’s pretty amazing, when you think about it.

Take an abstract concept.   A sequence of pure, unadulterated numbers:

0, 1,  1,  2,   3,  5,  8,  13,  21,  34….

And it’s architecture upon which much of Creation is built.

It’s staring at us, in our face.

The miracle of Pure Math, combined with Mother Nature.

Even with a lowly dandelion.

..and THAT’s why they amaze me.

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Friar’s List of Favorites, Crappy and Otherwise.

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CRAPPY THINGS

My favorite body of water
Lake Titicaca

My favorite character from a children’s book
Winnie the Pooh

My  favorite dog breed
The shihtzu

My favorite game of chance
Craps

My favorite type of mushroom
The shiitake

My favorite fowl dish
Turducken

My favorite polynesian dish
The Pu pu platter

My favorite Swiss Alp
Crap Sogn Gion

My favorite sportfish to catch
The crappie

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OTHER THINGS

My favorite card, in French
As de Pique

My favorite gelatin dish
Aspic

My favorite French animal
Phoque

My favorite ski wax
Fart

My favorite flower, in French
Pissenlit

My favorite part of plant anatomy
The pistil

My favorite rodent
The titmouse

My favorite bird
The tit

My favorite primate
The titi 

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Nothing Smells Fishy To Me

Ah.  The lilacs are in bloom.

So today, I thought I’d try again.

I grabbed a bunch, brought them to my nose, inhaled deeply, and smelled…

…nothing!

Well, what did I expect?   It’s not as if anything has changed.

I should have known:  the odor of lilacs means nothing to me.   As do all flowers.

You see, I don’t’ have a sense of smell.

I never did. I was born this way.

It was checked out by the doctors.  There’s a mild glitch in my brain.  It has something to do with the olfactory center, near the pituitary gland.   Things are a bit out of whack.

Not that there are any major health problems or anything.   I just can’t smell.

So all the odors people talk about, mean nothing to me.

Flowers.  Freshly-cut hay.  Wood smoke.   Freshly-baked bread.  Bacon frying.   BBQ.   Perfume.    Anything to do with food…

I get NOTHING.

They say taste is related to smell.    So yes…I do taste food.  But my sense of taste is probably a lot weaker than everyone else’s.    I enjoy mainly strong flavors.  Especially fatty, salty tastes (hence my love of bacon).  Or strong tomato-ey tastes (pizza, lasagna, etc).

But subtle flavors…forget it.   Herbs and spices like oregano or basil?    Don’t ask me.    Garlic?  Yes…I can taste garlic,  if the food is almost drowning in it.   I find it’s kind of salty with a bit of a tang.

People say spices enhance the taste of food.  It’s the opposite for me.  Spices just kill the taste of food.  I might as well be eating cardboard.

Not having a sense of smell makes for interesting stories, though.

Like the time a girlfriend was offended because I never complimented her on the perfume she wore (How the hell was I supposed to know?)

Or siting at my desk in grad school, and continuing to work while there was a hydrogen sulfide leak in the lab next door. (Someone had to come in and tell me to get the hell out).

Constantly showering and changing clothes, because I never know if I have body odor unless someone tells me.   (But if my armpits ever sting…if it gets to that point, I know it must be pretty bad).

Throwing out food that’s probably still good, because I cant’ trust if it’s gone bad or not.

Once, I forgot my soaking- wet sweaty hockey clothes in a duffle bag for a week.   When I found them,  I figured “This has gotta reek!   Let’s see what happens.”   So I put my nose to the bag…inhaled deeply, and I got…

…NOTHING !!!

(For crying out loud).

Though, to be fair, there are a few things I can smell.

Like really strong peppermint…when it’s so concentrated, you can almost taste it on your tongue.   I can smell that.   And also Vicks Vapor Rub.

Oh yeah.   And the time I went into a sweltering Porta-Potty during the summer, I smelled ammonia.   It wasn’t unpleasant…in fact, I was actually delighted… because it was such a novelty to be able to smell anything, even if it was the chemical breakdown of urine.

But there are advantages of not being able to smell.   Because I don’t have to worry about the BAD odors people complain about.

Like body odor.   Farts.   Vomit.    Shit.  Raw sewage.   Pulp mills.   Pollution.   Road kill.   Dead things.   Rotten food. Skunks.  Bad cologne or bad perfume.  Tobacco.

Huh.  Doesn’t bother me in the least.

So am I missing out by not being able to smell?

Oh, probably.  I suspect the good smells more than make up for the bad.

But does it bother me, having four senses instead of five?

I dunno…not really.

I can’t miss what I never had.

Stupid Sentimental Things I’ll Never Throw Out (*)

(*) Disclaimer:   No, I am not a hoarder.

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Dog Carving

I bought this in 1976, during a week-long Grade 6 field trip along the Gaspé Coast.  We stopped at the town in St. Jean Port-Joli, which is renowned for its wood carvings.

I blew a big chunk of my budget on this dog (I love dogs).   I remember is cost $4.00 at the time.

Not bad, actually, (even in 1976 dollars), when you consider this was hand-carved.

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1960’s Therm-O-Ware Glasses

These were originally used in our house when I grew up.  Then they fell out of style, and got relegated to the back of the cupboard.

Friar’s Mom resurrected them when she  donated them to me when I left home for university.

I know these are at least 43 years old, because they’re in a photo with me blowing out the candles on my cake on my fourth birthday.

I like these…they remind me of my earliest childhood.

And I still use them.

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Dog Puppet

This was a gift from my Mom when I was 8, back in 1973.     I was at the Montreal Children’s General Hospital, going through some allergy tests.

This involved getting something like 20-30 needles in each arm.   It wasn’t a fun time.

Friar’s Mom felt so sorry for me, we went to the hospital gift shop, and she bought me this dog puppet.

You have to realize that we didn’t have that much money back then, so a gift like this was a big deal for me.  I named him “Napoleon”.

A few years ago, Napoleon was sitting around Friar’s Mom’s house, and she was considering passing him on to my free-range screaming nephews.

“No way!” I said, “They’ll destroy him!”

This was my special gift.  Not theirs.   And it reminds me of my Mom.

So Napoleon now stays with ME.

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Ratty old moose T-shirt

There are many reasons I like this 20-year old T-shirt.

First, it’s green, one of my favorite colors.

Second, it has a moose, which is one of the few herbivores I respect.

Third, it was purchased in Algonquin Park, one of the coolest places on the planet.

But mostly, because of when I got this.    It was during a camping trip with some fellow grad students.

I was in my mid-20’s, which I remember as a happy, wonderful time of my life, before I got burdened down with adulthood and responsibility.

Anyway, the T-shirt’s worn down now and full of holes.   I can’t wear it in public anymore.

But it brings back good memories, so I still use it.

Even if it’s only to sleep in or hang around the house in.

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Adjustable Screw Driver

This was back in ~ 1984.   I was getting ready to leave for 2nd year University and Dad was helping me pick up some things at Canadian Tire.

He bought me this screw driver with the different attachments.  He said it was a good practical tool for me to have for school.

It was my first “real” tool.   And I’ve held on to it ever since.

Dad’s gone now.  But I still have his screwdriver.

And it’s still the first one I use, above all the others.

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Cheesy Globe Piggy Bank and Purple Tonka Volkswagen

The cheesy globe was a Christmas gift when I was in Grade 1.

It survived my childhood.

I brought it with me all through my university years.   And it’s followed me during all my multiple moves after I graduated.

It’s forty years old.   It’s tacky.  It’s dented.

It’s stupid.

And I  don’t know why I like it.

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As for the Volkswagen, that’s another matter.

I love VW bugs ever since I could remember.

I’d draw them, I’d count them on the highway, I was nuts about them.

So imagine how thrilled I was, when my Grampa took me and my cousin to a toy store, and bought us each a Tonka Volkswagen.

Just like that, out of the blue.  And a month before Christmas.  I was five.

Like I said earlier, my family didn’t have too much money at the time. So this was HUGE !!!

Of course, Grampa’s long since gone.  He passed away in 1973.

But I still have the VW bug he bought me.  It’s one of the few reminders I have left of him.

And (as you can see), I’ve started collecting other bugs as well.

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Last but not Least

Those of you who follow my blog will recognize Junior Bear.

He was a gift from a girl friend around 1991 (or 92?)

The girlfriend has long since gone, but The Bear Remains.   And he’s taken on a life of his own.

I take him with me on all my travels and road-trips, and photograph him in various locations.

The Bear has been to the Empire State Building,  the Arctic Circle,  the Grand Canyon, and the Great Barrier Reef.

The top of Mt Washington,  NH.  Cow Head, Newfoundland.   And Smashed-in-Head Buffalo Jump National Park, Alberta.

Not to mention Wawa Ontario, Dawson City (Yukon) and Tuktoyaktuk (NWT)

And I have the pictures to prove it.

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Useful (?) Squirrels

Tulips growing right out of my lawn.

Nice.

Gee, I wonder who did that…huh?

You SQUIRRELS wouldn’t have had anything to do with this, now, would you?

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You varmints probably stole the bulbs from my own garden.

Or maybe the neighbor’s.

But I have to admit, it’s kind of neat, having tulips come out of my lawn.

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It seems you’ve actually done something constructive for a change.

Instead of chewing up electrical wiring, or trying to nest in my roof,  or scolding me from your tree-throne,  you’ve created beauty.

So I’ll let this one go…THIS time.

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But don’t let it go to your head.

You rodents are still a-holes, in my book.

Yeah, but I caught a trout.

There’s something special about catching a trout, especially a wild one on a lake that hasnt’ been stocked.

Because, as I’ve written about before, these are magical fish.

When you catch one,  you’re not just happy at the moment it happens.

There’s a lingering euphoria, a deep sense of satisfaction, that lasts for days afterward.

Bass, pike, walleye…they’re all fun to catch too.

But there’s nothing quite like catching a fresh trout on a pristine lake, just after ice-out.

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It’s hard to describe.  You feel like you’re a successful hunter-gatherer.   You feel like the cat that’s caught the canary.  You feel that you’ve accomplished something.

And you keep chucking to yourself:  “I caught a trout! “,  over and over.

And it makes you happy.

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It doesn’t matter what happens for days (or even weeks)  afterward.

The fact that you’ve caught a trout makes things a little bit easier to take.

Case in point:

My car’s rusting out and it will cost a lot of money to fix.
Yeah, but I caught a trout.

I’ll probably get yelled at for not getting that report done on time.
Yeah, but I caught a trout.

I have to deal with so-and-so today, and they’re really annoying.
Yeah, but I caught a trout.

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Try it yourself, and see.

It works.

And it’s cheaper than a $100/hour therapist.

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A Tribute to Mother’s Day

This is Friar’s Mom, skiing down a double-black diamond run last winter.

Friar’s Mom is 70.

Friar’s Mom was in a wheelchair with a broken pelvis 18  months earlier.

Friar’s Mom is insane…but in a good kind of way.

And I want to be just like her when I grow up.

Useful Statistical Trends Everyone Should Know

Data Compiled by F-Stats (*) Canada.

(*) Friar Stats   aa

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Bittersweet Crocuses

I always liked crocuses.     They’re kind of special to me. .

They’re delicate, they don’t last long.   They’re the  “real”  flower of spring.

I remember as a kid, having fond memories of seeing the first ones come up.

It meant that Easter (and Easter chocolate) was right around the corner.

And it meant that there were only a few  months of school left, until summer vacation.

But that’s changed.

Now, when I look at crocuses,  it’s a bittersweet moment.

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You see, it was five years ago, about this time of year, when the crocuses were out, that I visited my parents.

One of the neighbors down the road had a yard full of them, and I went crazy taking all kinds of photos, not unlike the ones here.

The visit was nothing out of the ordinary, but I remember it as one of my better visits in recent memory.

It was just me and my folks.   No other siblings were  around, I was like the “only child” again.

Everyone was relaxed.   My Dad was especially in a good mood.   I returned home on Monday with a camera full of crocus images to paint.

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Little did I know that was the last time we’d all be together.

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A couple of weeks later,  back in my own home, I was chatting with Mom and Dad long-distance, and then I stayed up late to finish a painting of one of my latest crocus photos.

This painting.

Sometimes during that night, Dad passed away.

Just like that.   No warning.    He died in his sleep.

It’s funny…how this painting spans his life.

When I started it, he was probably still alive, asleep in bed.

And the next morning, he was gone.

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I won’t go into the details of the months that followed, the grief, the pain.

That was five years ago, and I’ve mostly gotten over it.

But I’m still at a loss as what to do with this painting.

I can’t bear to frame it and hang it in my house…it’s too painful.

But I can’t bear to part with it either.   Not ever.

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So now, every spring, when I see those damned crocuses pop up, it brings me back to that special weekend five years ago, and how quickly things changed after that.

 Like I said…crocuses are kind of special to me.

They’re delicate, they don’t last long.   They’re the  “real”  flower of spring.

But they also make me hurt inside,  just a little.

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That’s why they’re bittersweet.

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