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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