Fractal flakes

To decorate for our winter party before the semester-end break, we made paper snowflakes in art class at school.
Being the geek that I am, I made a mobile from the fractal of the Koch snowflake, which starts from a single equilateral triangle, and keeps adding triangles onto the triangles. The mobile is made from the first three iterations, cut out as nested pieces, plus the background to the largest, which is trimmed as a circle.
(The mobile’s crossbar is the metal edge that came loose from a ruler; it’s being employed in this manner to prevent misuse by unruly students.)

mobile made of three successive fractal iterations of the Koch snowflake, and the background piece of the largest
mobile made of three successive fractal iterations of the Koch snowflake, and the background piece of the largest

More on the Koch snowflake:

One Or More

Do you like odd words? If so, today’s post is for YOU!
I enjoy words. I love learning new words, and now and then feel the need to make nifty neologisms. I take pleasure in playing word games and punning around. I use a vigorous vocabulary for producing prose and programming. I revel in vicious verbiage when needing venomous invective.
Weird words are wonderful. Exceptions excite intrigue. Luckily for us, the English language (in its multitudinous international forms) is known for being an absolute mish-mosh of exceptions to dang near every orthographic rule that has been imposed upon it over the centuries. This is not surprising considering how many other languages have been sources for our vocabulary!
Being familiar with many of those weirdnesses is great when one is an editor, writer or proofreader. (Alas, not everyone shares such passions, so we logophiles must sometimes refrain from exercising too much pedantry.*) It also gives me a number of opportunities for musing …
Today I ran some errands on the way home, which caused me to take a different pathway. En route, I espied a cellular antennae tower array (mobile phone mast), one of those tall poles with transceivers and other prickly bits plated upon them. Several of those tower arrays or television UHF/VHF (Yagi-Uda) sets atop houses are called antennas. But — insects sniff their environments with antennae.
Some words are the same whether you have one or more; not just the same spelling in singular and plural, but also the same pronunciation:
Fish (As children, many of us learned this from Dr Seuss, “One Fish, Two Fish, Red Fish, Blue Fish”). Ditto salmon and trout. (I bet readers can inform me of other species of fish.)
Thrips (A small insect that often infests flowers and spreads diseases; especially problematic in greenhouses.)
Sheep, deer, moose.
Bison – pedantic technical note: the North American animal is a bison, not a buffalo, but buffalo is so entrenched in history (i.e. Buffalo Soldiers, buffalo nickel) that the term “bison” seems reserved for ecological/zoological discussions.
The American buffalo has just one species: Bison bison. A single category of interbreeding organism is a species, several are different kinds are also species. “Specie” refers to coins, such as our buffalo nickel. If I recall correctly, one of the new coins the U.S. mint has released in their recent series is a nickel with a bison on one side. Series is another word that is the same in both singular and plural.
Swine (unlike pig -> pigs or hog -> hogs)
Complaint:  people calling plural bovine animals “cows”; the cow is a female that has calved. Call them a herd of cattle. Of course, then one has the problem of knowing if the single animal is a calf, cow, [castrated] steer, or bull. Then again, depending upon where you are, most of the cattle one passes might be breeding or milking cows, or maybe young steers shortly destined to be burgers and roast-beast. But like “buffalo”, “cows” seems to be a common-usage term.
(Except, of course, amongst small children, who invariably call them “moo-cows”, which is odd because I’ve never heard any preschoolers saying “quack-ducks”, “neigh-horses”, “baa-sheep” or “meow-cats”; go figure.)
Interestingly, draft bovine (used for ploughing) are ox -> oxen. There are few words that retain this archaic plural: child -> children, one brother -> several brethren, and hose -> hosen (from when one tied their individual hose onto the hem of a garment). Clothes is one of those words that just comes in single form, except it is by default plural.
When I teach gardening classes, I add a couple seconds pause after explaining, “If you’re making a new garden bed, you can either kill what’s there with glyphosate, or slice off the pieces of turf and re-use them, or compost the turves.” Turves is the correct plural for pieces of turf, but we don’t use the term much, so there’s a bit of a mental speed-bump.
Did you know that J.R.R. Tolkien invented dwarves as the plural for his Middle-Earth race? All other sorts (cutesy fantasy beings, or small-growing forms of plants or animals) are dwarfs.
In Zoology class we learned that the plural of penis is penes. Common usage (when not using one of the many silly slang terms) is penises. But if you are needing to talk discretely over the heads of younger folk, penes will likely be off their radar.
Right now I’m listening to Etta James singing the blues; no one ever sings “a blue” (tho’ you can blow a blue note).
Then there are the pluralisation questions about which only geeks worry: one Mus musculus is a mouse, and several are mice. But what about the computer accessory (um, Mus digitus ?) – computer mouses or computer mice?
One datum, a bunch of data. But when or how the hell does a person have just ONE datum? A single point?  I suppose that’s possible, unlike news. Good or bad, there’s never just one news. A “new”? I tend to get out of the news loop when on holiday; but invariably when I catch up, I find that the news seems more like recycled “olds”!
One spectrum, a wide spectra, as in “spectral analysis” – unless of course, one is doing a bunch of analyses on your spectra data.
How about one index -> two indices. Indexes is a verb: “My program indexes everything for me!” Then of course, it turns around and creates indexes to hold that data. Hmn. Meanwhile, we still have one index -> two indices in science, and on the radio news I hear indices used as indicators of how the world is going.
In geometry, our geometric shapes have sides (planes). Each pair of planes intersect at edge, and several will meet at the corner, called a vertex. A triangular pyramid has four vertices and a cube has eight.

And lastly, Marshall McLuhan said, “The medium is the message,” meaning that what is used to spread the message is important. Newspapers, YouTube videos, and blogs are all kinds of media. So too are my choice of growing medium for my seedlings.
If some yahoo grabs a can of spray paint as their medium of choice, and scrawls a graffito on the side of a building, you can be sure that someone else will want to join in and next thing you know, there will be graffiti everywhere.
My thanks (always plural) to all my readers!

*Unlike those grammar mavens dedicated to eradicating excessive and misused apostrophes, whom I heartily encourage to be ever-ready with their jumbo-size bottles of correction fluid!
Also, thank you everyone for your tireless efforts trying to rid the world of misspellings; Valentine’s Day is coming up, and I know that I shall be wanting to face-palm with each sale banner for  Valentines Bokay’s.

Set the Wayback Machine

to 1994. Just the ordinary sort of 1994, when my children were two and six years old.
We are watching X-Men during Saturday morning cartoons. My son is really into super-heroes, and in case you don’t know, the X-Men are mutant super-heroes.
My daughter asks me, “What’s a mutant?” I take a deep breath, trying to figure out how to explain genetic mutation to a six-year old. Thankfully, with my children this wasn’t too difficult.
“Remember the other week when I told you what DNA is? The instructions that tell the different parts of your body how to grow?” She remembers. “Sometimes the DNA changes, and that’s called a mutation. A Monoceratops changing into a Triceratops s a mutation.”* We watch some more of the cartoon.
She asks me, “Are all mutants weird like the X-Men, and have super powers?”
“No. That’s just the cartoon part. If you always have yellow flowers and suddenly get a red flower, that’s a mutation. In fact, everything in the world started out as a mutation, or else there would be nothing but itty-bitty plants floating in the ocean.”
She decides that would be boring.
“Why do those people hate the X-Men? The X-Men are good guys.”
“They hate them because they’re bigots. ‘Bigots’ means when people hate other people because of something like what church they go to, or where they’re from, or how they look. The people hate the X-Men because they look different, and can do different things, and they’re scared of them.”
“But that’s not fair,” she complains, “The X-Men are nice.”
“That’s right. Bigotry isn’t fair, and it isn’t nice.”
“I like Storm the best.”
Storm is a black woman with long white hair who can control the weather, and fly. “Me, too.” I answer.
“I want to be Storm for Halloween.”
A few nights later, we are reading The Enormous Egg by Oliver Butterworth. This is one of my favorite stories from when I was growing up, a tall tale about a Triceratops dinosaur that somehow hatches from an egg laid by a chicken, and the consequences for the boy in the story. She has loved dinosaurs since she was a mere tot of two. We read two chapters into the book. She read a few paragraphs, sounding out new words, and then realised, “The chicken laid a mutant egg!”
This is why you should watch television with your children. In one Saturday morning cartoon, we have covered biology and bigotry, and made a tentative Halloween costume decision.
* I know, I know, it’s more complex than that. All you evolutionary biologists out there will have to work with me on that. (-;

V1brat0rs for Ensuring All Your Cucumber Needs

Bug G. Membracid recently had a radio show appearance!  (Is it called an “appearance” when you’re on a wireless programme and no one can see you?  Nevermind.)
But it featured her line about honeybees being ‎”little flying phalluses” – which is really funny when you remember that worker honeybees are girls!
That in turn reminded me of a story during a horticultural study tour to a Dutch production greenhouse …
Tomatoes and peppers do not need insects to transfer pollen between flowers, as the flowers are “perfect” (have both male & female parts). But for the pollen to get moved/bumped from the pistils to the stigma there still needs to be some kind of wind or other vibration.
There’s not enough wind for this to naturally happen (or rather, efficiently happen) in a greenhouse, especially when the panes are shut to the weather. So it used to be that the operators would equip their greenhouse workers with *little vibrating wands* (oh yes), which they used to buzz-pollinate Every. Single. Fresh. Flower. (Insert inevitable sniggers from the undergrads.) Of course, that’s a lot of paid worker hours.
Nowadays the thrifty Dutch use bumblebees, who work for much cheaper wages of cardboard nesting boxes and some supplemental nectar. The big, gentle bees still visit all the flowers for the pollen, and resultant heavy buzzing results in flower fertilization for good crops.
[N.B.  Derf; “cucumbers in the title is incorrect – they DO need to be insect pollinated! Except of course for the parthenogenetic cukes, which basically set fruit by a sort of “virgin birth” process…]

Kitchen HazMat: Allyl propyl disulphide

My daughter stopped and looked at me, puzzled.
Safety goggles,” I explained.  The elastic strap was losing its spring, so the limp tail ends hung down past my ears as I worked.  “Because I couldn’t find my chem-lab goggles.”
I continued to trim the tops and tails off the onions and slice them up with the mandoline.  “These are really loud onions,” I added.
She walked past me to the refrigerator and suddenly exclaimed, “Omigod, they just attacked my eyeballs!”
A few minutes later my son-in-law walked by the sofa, making a small snork noise at my incredibly nerdy appearance.
“I heard that!”
“I  didn’t ‘say’ anything!”
“Hey, four pounds of onions is a lot of onions!”  Apparently the pungent Allyl propyl disulphides had not yet diffused as far as the living room.
Later he came by to ladle up his French onion soup from the big stock pot, and found the pong to still be strong.  I opened the kitchen window a crack, mumbling, “Just imagine what it was like when I was slicing them up fresh!”
I don’t care how the goggles look – they are excellent for making onion-slicing painless.  (Well, at least for the cook.)  They’re now sitting on a kitchen cabinet shelf, since I cut more onions than I do lumber.


My hungry 9-month old grandson is being a wiggle-worm.  He wants his banana now, and like Prot, is trying to eat it whole, peel and all.
“Come on lad, let Grandma mash this up for you – no, we don’t eat the peel – here’s your high chair -”
Much squirming and complaining, “NANA NANA!”  (I’m not sure if by “nana” he means banana or some pet name for grandma; I’m usually the one who brings home the bananas from the market, and the one who feeds him an evening snack of “happy smile fruits” — our code name for the nosh of choice, especially if we’ve run out.)
“Ow no let go of my glasses, Grandma can’t feed you until you’re in your chair-”  This operation of Insert Boy B Into Chair C almost takes two women.
I revert back to child-training using simple commands. Given enough repetitions, it will sink in, just like “OPEN” [mouth], “NO BITING”, “TOUCH GENTLY” [flowers, cats], “STILL” [stay in place for diapering], “REACH UP” [un/dressing], and all those other thrilling conversations.
“IF eat, THEN sit!”
The lad was sufficiently startled by this novel command to pause a split-second, thus allowing us to plop his tuchis on the chair and snap on the tray.  We’ll be using the IF-THEN logic construct for the next few years, along with FIRST-THEN.  (There’s nothing like reinforcing order of operations, whether mathematical or procedural.)
Now I can finally start spooning mashed banana into the lad’s mouth, and he’s thumping his feet and smacking his hands on the tray with delight, exclaiming a pleased, “Nom-nom nom!”  (Seriously.)
“That’s a good boy,” cooed his mum, “Listen to Grandma’s Boolean logic!”
Ah, the great moments of geeky family life – gotta love ’em!

P.S.  4011 refers to an imaginary line of programming code, and also to the grocer’s PLU number for bananas.