Math/Philosophy Humor

Another perspective on Zeno's Paradox

Due to unforeseen circumstances I didn't get this posted in a timely manner; better late than never - brought to you by XKCD.

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Wordless Wednesday - Chohua Jasper

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Holier than thou

Illustration from Carolyn Hax's column, 12/7/2011.

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Black Holes on Spinach

From Science Daily 12/5/2011:

"For an astronomer, finding these insatiable black holes is like finally encountering people nine feet tall, whose great height had only been inferred from fossilized bones. How did they grow so large?" [Chung-Pei] Ma said. "This rare find will help us understand whether these black holes had very tall parents or ate a lot of spinach."

LOL! Who said scientists don't have a sense of humor!?!

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Wisdom

*She's Back!* (December 2, 2011)

"On Dec 1, the world's oldest Laysan albatross, a female named
"Wisdom", was sighted by a Fish and Wildlife Service biologist for the
first time this breeding season nesting on Midway Atoll National
Wildlife Refuge. Having survived the tsunami generated by Japan's
earthquakes last March, Wisdom has returned along with her mate. 
She was observed in her normal location behind the Bravo Barracks
and was proudly incubating an egg.  Wisdom is at least 61 years old.
She was banded as a nesting adult in the same location by Chan 
Robbins in December 1956. Robbins estimated that the bird was a 
minimum of 5 years old at the time.

The oldest albatross in the world appears to be a northern royal 
albatross which was located on the South Island of New Zealand
and was named "Grandma."  She reached a banded age of 51.5 
years and probable actual age of 61+ years."

Fish and Wildlife Service: What's New 

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Wordless Wednesday

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Engraver Beetles - art is where you find it

I love the art that results from the beetles feeding beneath the bark. Doesn't do the trees much good though.

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Wordless Wednesday

 

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Just photos

Leucistic Yellow-rumped Warbler

Leucistic Yellow-rumped Warbler

Immature Common Gallinule

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Factorials, revisited from yesterday

I spent yesterday evening playing with factorial values because it was unclear to me why there would be 374 trailing zeros in 1500!. It was evident, even trivial, when I thought about it - I just never had before. All non-trivial factorials end in a string of 0s. I guess in school we never played with such big examples so it wasn't obvious that 0s were piling up at the end. (My school was before calculators or computers - we did all our arithmetic by hand. 1500! would have been extremely onerous and error-prone!)

So then I tried to figure out how to compute the number of trailing zeros - I got close, but missed the leap. Turns out that you just keep dividing the original number by 5 and summing the truncated results. Very cool. So for my 1500 book example:

       1500 / 5 = 300
         300 / 5 =  60
           60 / 5 =  12
           12 / 5 =    2
                     = 374
                        QED!

Numbers are so stinkin' cool to play around with! I should do it more often - one of the few things I left behind of my kidhood. It's nice when something shows up and throws me back into it. Numbers rock!

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Mind Bogglers

So this morning before I got up, I was reading an article in the paper about why No Two Snowflakes Are The Same. The author drifts into a bookshelf analogy that, although I could have intellectually figured it out, triggered laughter of amazement and wonder.

"... Consider the math, which Libbrecht helps explain using a bookshelf analogy. He points out that, if you have only three books on your bookshelf, there are only six orders in which you can arrange them. (That’s 3 times 2 times 1.) If you have 15 books, there are 1.3 trillion possible arrangements. (Fifteen times 14 times 13, etc.) With 100 books, the number of combinations increases to a number that is far, far greater than the estimated number of atoms in the universe."

I went to a factorial calculator on the web and stuck in 1500 (books). Here's what I got: "The resulting factorial of 1,500! is 4,115 digits long.The result also contains 374 trailing zeroes (which constitutes to 9.09% of the whole number)." Holy crap! The answer looks like this.

481199779677977486016699009358137978183480804067261380813085594116305751890010955912922305852067338518684640096193435851940520911246181662702714818813
933314316279628102998441493337890446893955104871678797693253036994704678292343992633265456528607486050757463669283236066454922775411200834380867273693
778876760002114053184802443542074196048641769699505814352221988511945689840957059455495890545683217923389191494429859199577347929594024990968456430204
018693811756039644243332221141259743748178042426333097698042939528700346193541250142100456476640632401620075601086652905686461283425571473509853587241
546232533718674707651204220738679639357752586921097530417620943435690504974703535317644815031747509118582309069983610660847877583161105857360133653774
318607385722613257382336568352719473526951808655730438340279555390127654893726450425044065977523574819315328723566354112245783340405222947464028295854
584787087783463794318623688248190091770914440348859413943193439102231686558697617996690750595276085024655931813985662147868012116516572220041234564982
585131203591260228430385350837097961015659348594832039334433086014758131083630741185624044124201919471275854829191721730459611221227014342978706919321
540829869459547482511057821815863972758203421014704573006335901395129195494741137217116169125197141917606999355098102548499670876359361811763639542241
860313466829288784928722494854566901388316101353779163279405037014002901255091321407826146404957335180486709833601340978603647626386588948731744998701
335593648054434308314595059878092153933533872320781775629750214605954223585731280854171623360302351386527354380530345319626208115660198968792752571639
883520908749303461155183312029272637084467293943818798888395497318769786822493206285996316286623755088262098547546319842763926709192169230027700777347
560775490359429762091594162115814394614845095493703574867702768076875445801643146475950313689484902828971733280135184357587000564259226384118894965279
758460527179580448137370868066001719937035794858640293832087145289503032538813608126311621347501003077726343374670128204707156508107146899051214322595
285054830539304022174006860616124716596301924348640945398280856774653830261283537710711523041975497988707061398936091400456597562854357877716362582536
665921021512361421327244258509912057200204936605808966008918885946596129277243578662659345176158412987891544622491696888600926402847563824317461203577
679331195892804686873480617880729863627885822270194652634748285906460484510707029234344227143495958576548436995423218493636527677719783146810135894429
552198797020080689340966246506257697052333334628260138600986981551803311453656524534829554979799155864384746873456778744511177022504417115048446384144
852100922613972719705710290385818730699511613304957723105087605282497065142383842698086395070804182983183113613736285120417164151968683342541191371395
891495972100321535459411146665304989065292407981648040073947759278360456685739933164289725399327457571719474024542571426337008159224072784036405953551
420755994460563379867172123162232577634121641808995327220393832444625114103466461488633972370962768226561575611946655457570174298424048403097589256186
505079210430072416378779398258110593391389255261245144676271265481267950787840226728608862519745813621417827864074028963096780089096632639870185381070
508861934890124974050058207272712327337281417751327220138605911696206927892904567946984098085574477567013118832660108590160275922523977545082516288082
935377765365696081113305847971606948478989231967439702444518427022664033263173190921171511439716795000425902692550931302159844180974184354743004672819
497982271025298737327490279920797002872759008562411729028809095465517032632028535844980853589553076737171779619020810986187290463488490602496000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000

It's so big it clobbers the blog formatter. But this, too, shall pass.  :)
   

Note to self: never, ever rearrange your books if you want to find anything!

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The world needs a time-out

It seems to me that everyone is angry about everything these days. There are a gazillion USs (as in us, not U.S.) and a gazillion THEMs. We all hate each other - we're all angry with everyone. Nothing is working and nothing will until everybody chills and tries to regain their common sense.

I hold out no hope.

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Hoarfrost

Sunday at the farm - priceless - hoarfrost on the grasses, clear, crisp fall day. We need more of these.

 

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Incredible x 2

On October, 12, 2011, I was amazingly lucky to see a Green Violetear in Cecil County. It was a damp, dreary, drizzly day - when the hummer showed up at the feeder - I can't describe it - stunning deep green and blue, the colors deepened by the dark day. I'd come straight from work via an appointment in Baltimore so no camera. I could just watch and enjoy. And I did for its three visits to the feeder - the last visit I watched before I left turned out to be its last visit. I felt amazingly blessed and somewhat teary - he was that beautiful.

And then lightning struck twice. On October 24, I got word that, incredibly, a violetear was coming to a feeder in my home county, a couple miles away. Midmorning the next day I bailed out of work with my camera. This time it was a bright, sunny day. The bird showed and I got some unexciting photos. The colors were deeper and more intense in the drizzle, but there was iridescence in the sun! Here's one photo of mine and a link to a video (not mine) that shows off the colors.

 

Green Violetear, Howard County

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More virtual cats

Simon's cat is my other virtual cat. This video totally cracked me up.

 

Double Trouble

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Crawling around with Rainer Maria Rilke this weekend - he fits my mood of late... Everything below is his from various writings. Indentation and text color brought to you by the vagaries of cut-and-paste.

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The only question is whether I will manage to keep out all intrusions and stay as quiet and undiscovered as I have been accustomed to being elsewhere.

Your solitude will expand and become a place where you can live in the twilight, where the noise of other people passes, far in the distance.

Therefore, love your solitude and try to sing out with the pain it causes you.

What is necessary, after all, is only this: solitude, vast inner solitude. To walk inside of yourself and meet no one for hours -- that is what you must be able to attain.

If there is nothing you can share with other people, try to be close to Things. Things will not abandon you. The nights are still there, and the winds that move through the trees and across many lands. Everything in the world of Things and animals is filled with being, of which you are part.

I beg all those who love me to love my solitude too, for otherwise I would have to conceal myself even from their eyes and hands, like a wild animal hiding from enemies bent on its capture.

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Rock Show

Yesterday the birding was bad, and I found myself at the Rock and Mineral Show at the fairgrounds. I was in trouble by the time I left the first booth - they had jasper and agate slabs. But my best find was about midway down the aisle - Polish flint. I'd never heard of it, never seen it, fell in love with it. It reminds me of tulip poplar wood with more action.

Here are pictures of the slab I bought (about 9x5 inches) - these are dry shots, it doesn't need to be wet to be beautiful. And it's even better in person. Wow!

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Polish Flint Slab

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These I believe...

1. Businesses and insurance companies sending Christmas cards doesn't induce anyone with a brain to buy their products. (Let me know if I'm wrong about this.) Yet another waste of resources.
2. Leaf-blowers and hoses weren't created to deal with leaves (well, maybe they were, but they shouldn't have been); rakes and brooms were.
3. Challenge is highly over-rated.
4. I propose the following for the 2012 election: Republicans support the position that the world is flat; Democrats support the position that the world is a pyramid; independents - you have the cylinder. Whoever wins the election is right, and all textbooks will be rewritten to support the new order.
5. The losses of true darkness and true silence have had a major detrimental impact on our individual and collective psyches.
6. Turning on your turn signal after you've slowed down or changed lanes is too late!
7. We should not be wiping our butts with virgin forest.
8. We should not be flushing our toilets with some of the cleanest drinking water in the world.
9. A politician's job is to govern even if it means he/she won't be re-elected.
10. Hawaii 5-0 is not Hawaii 5-0 without Jack Lord. Period. End of discussion.

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International Day of Peace - September 21, 2011

Frazz, as usual, has the words...

 

 

Frazz 2011-09-21

  

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Peace on earth, goodwill toward its inhabitants - all of them.

  

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Growth

"We do not grow absolutely, chronologically. We grow sometimes in one dimension, and not in another; unevenly. We grow partially. We are relative. We are mature in one realm, childish in another. The past, present, and future mingle and pull us backward, forward, or fix us in the present. We are made up of layers, cells, constellations."  ~ Anaïs Nin

In my opinion, a very Feldenkraisian way of looking at growth.  :)

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Virtual cats

My virtual cat, whom I'm borrowing while catless, is either driving a Winnebago or morphing into a turtle in his most recent video. His name is Maru, and he lives in Japan.

 

Maru's channel

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Noodle

It's been exactly two years tonight, sweetie. Can I let you go yet?

3/31/96

My kitten turns somersaults with reckless abandon off chairs and beds while chasing calico tails and little gray rats and q-tips and shoestrings and tissue paper and other less visible threats.

My kitten pushes her water bowl with her paw, creating tsunamis she watches with wonder, and then drinks from the puddles on the floor, puzzled when her paws get wet because she has yet to put two and two together.

My kitten kicks herself in the face while trying to include her hind paws in the fun her fronts are enjoying and opens doors ala Chuck Norris or Bruce Lee, jumping at them feet first, then entering smugly.

My kitten is spoiled by my friends, although not, of course, by me, and the floor looks as though a dozen kitten pinatas exploded, releasing untold numbers of baubles and trinkets.

My kitten is a slightly diluted calico, with black and orange splotches on white, with one amber eye and one green, a pink nose with a black blot in the middle and one on each side, and pink and black toe pads, indications of a cheery artist.

My kitten is armed on all fours with sharp little kitten claws which got clipped just two weeks ago for the first time to the relief of my hands and feet, and her belly is pink and downy soft, clear-cut like the hills above Seattle, bearing witness to her recent surgery.

My kitten has street smarts for she was feral and spent the winter of 96 -- the blizzard and subsequent floods -- living in a storm drain with her mother and two brothers or sisters, helped out by the kindness of strangers who dug out the drain and left food and water.

My kitten was trapped when she was four months old by well-meaning folks and released into a woman's apartment, but because my kitten was wild and terrified, not cute and cuddly, she was not wanted so I got a call one Sunday night in January.

My kitten was cowering under closet debris when I arrived and perforated a fingernail with her first bite and a finger on my other hand with her second, but that time I held on, and we got her into the cage, and I had bonded.

My kitten lived in the bathroom and yowled through the nights so I bought earplugs for the neighbors and got no sleep trying to comfort a frightened hostage torn away from her world, and I cried for her pain and mine and for my last cat, dead not quite a year, who left long before I was ready to say goodbye.

My kitten was lonely, said a friend, so I gave her a teddy bear and a clock and put an old sweatshirt in with her to get her used to my smell, but my kitten peed all over the shirt and I laughed because my kitten was nobody's fool... and still she yowled.

My kitten peered out at me with big dark eyes through the slits of her (open) cage while I, during a week's maternity leave, sat on the bathroom floor and read A Child's Garden of Verses and Winnie the Pooh and sang numerous camp songs to her, but I could tell she was not impressed.

My kitten's head was examined and her hind leg inoculated during her first trip to the vet, but the rest of her was tightly encased in the towel we used to pluck her from the Venetian blinds after her vain attempt to escape, and the vet said it might take 4 weeks before I could move her out of the bathroom, and my heart sank.

The fourth morning my kitten sat on the rim of the bathtub, looked me in the eye and meowed, then walked across my lap to her water, and when I turned out the light, she let me pick her up, and she purred while I cried because maybe it would all work out and partly because I hadn't slept the last four days (and was as yet unaware of the three days to come).

My kitten was relocated to the small bedroom that day but freaked when she jumped to the window sill, and I thought, "Oh, swell, now there are two of us trapped indoors where we don't belong", but only one of us was vocal; the other was older, resigned and silent, while the younger yowled at the window for three long nights.

My kitten pigged the entire pillow the next night and purred in my ear, and I was sleepless once again, but I was so proud of her and she was so proud of her that neither of us minded, thus the yowling ceased and we let the games begin.

My kitten had the run of the place within two weeks of her arrival, well ahead of schedule, and I cried when she started walking around with her tail straight up instead of between her legs because she had come so far and maybe so had I.

My kitten cries urgently these days when I walk in the door to remind me of our combination kitten field trials and dressage competition in which my job is to throw a little gray rat which she then retrieves, returning with a proud high-stepping trot, head and tail erect, a vision of feline self-esteem.

My kitten jumps onto the table when I am computing, walks onto my chest and curls up under my chin, leaving me with but one hand for typing, and that one ends up stroking instead because my kitten purrs... then turns, stretches and, heaving a huge kitten sigh, falls asleep with soft kitten snores, her belly up to the gods, leaving me with no hands and the thought that she seems to feel secure.

The Noodle, by proclamation 6 months old today, has trained me well the last 2 months and 10 days, and, I think, will let me stick around which is good, because I have cried enough for one year, and though the telltale marks on my fingernail will soon be gone, I will remember them, for they were the start of the journey.

-- The Noodlemom

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Noodle, 1996

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Structured learning

Frazz 8/31/2011

8.7 million species exist on Earth...

... according to an article in the Washington Post. I love what Jesse Ausubel (quoted in the article) said:

"There are 2.2 million ways of making a living in the ocean. There are half a million ways to be a mushroom. That’s amazing to me."

Half a million ways to be a mushroom! Sometimes it doesn't take much to make me smile...

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Thought for today: Epicurus

Epicurus once said, ‘If a little is not enough for you, nothing is.’ 

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Beefsnake Charlie

(c) ncm sundogger

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I saw my belt hanging on the door and thought "that's what a cow would look like if it morphed into a snake". Then things deteriorated.

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Canoes

Last week a friend sent me a link to an article in The Atlantic called "Caring for your Introvert". That reminded me of a list I came up with way back in 1995. Here it is: 

Why Canoes are Better than People

Canoes don't think it's weird when you need to be alone.

Canoes don't care if you don't want to spend every minute of every day with them.

Canoes let you be in whatever mood you want to be in, for as long as you need to be in it.

You can be alone with a canoe.

Canoes don't up and leave you. 

You don't have to pretend with a canoe. Anything you are is good enough.

You can't hurt a canoe's feelings.

You can't screw up a canoe's life.

Canoes don't screw up your life.

Canoes don't expect you to do stuff you're not smart enough to do.

Canoes don't ask more of you than you can give.

Canoes know how to be quiet.

Canoes don't rock the boat.

Canoes are an aid to thinking - people aren't.

Canoes don't force you to make decisions you don't want to or can't make.

Canoes go with the flow.

Canoes leave you alone when you need to be left alone and don't always ask how you are in a concerned tone of voice.

Canoes don't make me feel inferior - they let me feel real.

Canoes don't blow up buildings or throw trash into lakes.

Canoes are as shy as I am.

Canoes never fall off their pedestals.

Canoes don't tell you how to run your life or how you should feel or how you should do anything.

I fit in with canoes.

Canoes are forgiving and tolerant.

Canoes are one with the world and let you come along for the ride.

Canoes are slow and steady.

Canoes are asocial, too.

Canoes let you be whatever mental ages you are, all at the same time - you can be 5 and 125 simultaneously in a canoe.

Canoes don't give a rip whether or not you conform.

Canoes think cut-offs, T-shirts, and bare feet are ALWAYS the most appropriate attire.

Canoes think it makes sense to talk to species other than your own or even to non-species.

Canoes understand God.

Canoes know how to listen to the silence of the world.

Canoes know how to listen to my silence.

Canoes are comforting and comfortable.

Canoes don't try to categorize you.

Canoes act as a resonating chamber for your dreams - people stifle them with pragmatism.

Canoes don't know how to use telephones.

Canoes can get you away - unfortunately they always bring you back. So far anyway. Someday maybe it won't make me come back.

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Tyler II

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August weekend on MD's Eastern Shore

This weekend there was a boat trip out of Lewes, DE, for pelagic (ocean) birds. On the way there, this dorky Tri-colored Heron amused me in Worcester County, MD.

 

A bunch of us on the upper deck of the Thelma Dale V out at the continental shelf - about 65 miles east of Ocean City. Bright sunshine out here while the rain was pouring down on the mainland. The pelagic species we ran across were Audubon's, Great, and Cory's Shearwaters, Pomarine Jaeger, and Wilson's and Leach's Storm-Petrels (I missed the Leach's). My big camera didn't get to go out on the boat - I have a hard enough time picking out the birds in binocs. Maybe next time.

On the way home, this Little Blue Heron posed nicely for pictures on Assateague. I picked the goofiest one.

I obviously have to work on my sizing pictures for the blog so subjects aren't too small. Hopefully I'll get better.

What sort of sundogs am I dogging?

I thought I should start by explaining the name. The sundogs I'm interested in are not solar hot dogs nor are they a musical group. They are the atmospheric phenomena known as parhelia, aka sundogs. If you take the sun, throw in some hexagonal ice crystals of a certain shape (high, thin clouds are best), add your eyes, and mix in the magic of physics ... you might get a pair of sundogs - one on each side of the sun.

One of my favorite pictures of a sundog was taken by Ian Parker. He has a web site called Evanescent Light, which has incredible photographs. Here is a tiny version of his sundog, but you should go to his site and see the full-sized version.

Sundog by Ian Parker

So, those are my sundogs - look up once in a while, and you're bound to see one sooner or later. 

Anyway, that's the derivation of the name. And this may or may not be the only post about sundogs I'll ever do.

-- a Sundogger