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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