Absent For A Bit ....

I am away for a little while working on a few or more episodes for The Adventures of My Space Alien Alter Ego story ... will return (to Earth) soon!

Notice: Blogger has screwed up and lost a bunch of photos out of my blog! They are replaced with a gray silhouette of a human head. I will eventually get them replaced with the correct photo, it may take a while to find and fix everything. So some of my stories don't make much sense without their photos, sorry for the inconvenience.



In Seconds Place

The online cartoon xkcd is one of my favorite things. It is published three times per week on M-W-F. One episode, number 1047, gave approximations for physical events. One of the items mentioned was the number of seconds in a year. It has a fairly exact value of

60 seconds x 60 minutes x 24 hours x 365.25 days per year = 31557600 seconds per year

The approximate value given on http://m.xkcd.com/1047/ for the number of seconds in a year was 75^4 = 31640625

31640625 is 0.263% higher than 31557600

Today I was playing with differences of factorials on my TI-89 and found a closer approximation.

317! ÷ 314! = 31554200 which is 0.0108% lower than 31557600

Update: After reading Rob's comments I decided to see how long the 0.0108% of a year was in hours, and eXpress that value as a factorial division.

31557600 - 31554200 = 3400 seconds

One hour equals 60 x 60 = 3600 seconds per hour

So 16! ÷ 13! = 3360 which leaves 40 seconds

40! ÷ 39! = 40

But that last step is just cheating to get to an eXact number, because

X! ÷ (X-1)! = X

So one year equals (317! ÷ 314!) + (16! ÷ 13!) + (40! ÷ 39!) seconds

But then I noticed that 17! ÷ 14! = 4080 which is fairly close to 3400, and keeps the equation pretty with translational symmetry, the repeating of the 17 and 14's.

So calculating an approximate pretty value 317! ÷ 314! + 17! ÷ 14! = 31558280 which is 0.0022% larger than a real year

Pretty is important!!!


Mia said...

I would love to know how the spam bots read a post like this.

esbboston said...

Mia: Spam bots stop maps.

Rob Z Tobor said...

I prefer the lower approximation as I think that gives me some seconds to spare where I can sit back and chill. I'm just glad you did an average leap year although in all the confusion I don't now know if I only have some spare seconds on leap years. I have my own solution to Spam Bots


esbboston said...

I made an update to the blog post to get a prettier equation. My original gap was about an hour.

New Blog for My Abstract Art ... Come Visit

Click HERE for the Art of Ernest S B Boston

These are pieces that I have generated mainly using computer art tools. Enjoy !

Something New:

I am also in the process of linking my poetry blog entries together. This project is only partially finished. A "Poetry LINK" at the bottom of the blog entry points to the next older piece of poetry.

First poem in the series of linked poems ....

Turn Gold Out of the Darkness

Turn Gold Out of the Darkness

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These are some of my abstract art pieces. They are available as prints, send me a note if you are interested.

Couch Glow

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