I'll be brief (therefore intriguing, right?)
The link below is not usually language-related, but today it was:
Reactions? (I hope I posted in somewhere approaching the right area)
Dave the Phrog
Fro: Thank you for this. Clearly Aproposism is a neologism and a portmanteau or blend as well, like "babelicious" and "dreadline"
Since there are about 50,000 common words, prefixes, and suffixes in the Mother Tongue, one cannot help wondering how many such combinations are possible. Barring triads and larger as well as multi-word expressions, it must approximate 50,000-factorial, a very big number
When I began collecting neologisms and the like, I was often hard pressed to decide whether a particular expression was worthwhile and upon what criteria do a modern dictionary compiler rely
Using the no. of hits as a guide, I employ several online sources, including Google and OneLook, but I'm open to suggestions
A very big number indeed -- in fact unimaginably big, far far greater than the humber of protons in the entire universe. It gives me a headache just trying to get a handle on a number of that magnitude. It's even bigger than the US national deficit under Dubya.
For the math-challenged (probably a fairly low percentage in this crowd ), the factorial of an integer is that number multiplied by ALL the integers less than itself, i.e. 9! = 9*8*7*6*5*4*3*2 = 362,880. Factorials get real big real fast; 13! = 6,227,020,800 is the number at which my H-P 11C runs out of digits and switches over to exponential notation. 50,000! is so huge that your exponent would have to have an exponent.
This reminds me of the Indian fable in which a commoner did a Rajah a favor such that the grateful potentate offered the man basically anything he wanted: jewels, gold, virgins, whatever. The man said that all he wanted was some grains of corn, specifying the amount thus: on a chessboard (8*8 = 64) one grain on the first square, then doubling the amount for each successive square, on up to 64.
You can see the punchline coming, right? the Rajah says "Is that all?" and orders a sack of grain to be brought in. Well, the sack is empty before the end of the first row, and there is not enough corn on the planet to get to the third row.
And factorials increase in magnitude muuuuch faster than THAT!
The version of the tale I heard had the commoner being put to death by the rajah for being such a clever clogs. The (a)moral of the story being along the lines of "if you're smart, and you know you're smart, and you know you're smarter than your boss, it never pays to publicise the fact, unless you like being pulled apart by elephants". Or something.
Fro: Thank you for that. If you are interested in how the thread arose:
You can't fill the board, of course, but by my math you can cover a good deal more than that.
Assuming a grain to be ¼ cubic inch (which seems generous even for maize, let alone wheat), I compute that the first two rows of the chessboard (16 squares) will require less than a cubic foot of grain. It's only later that you get to the really big numbers.
Starting at the first square having 1=2^0 grains, the 17th square would have 2^20=1,048,576 grains. Assuming 1/4 cubic inch(a number which our calculations very easy), it would thus take 4^3 = 2^12 = 4096 grains to fill a cubic inch. 2^20/2^12 = 2^8 = 256, giving us 256 cubic inches of grain. A cubic foot is 12^3, which is considerably greater than 2^8. So yes, you could easily get to the third row. This is as far as I care to go without using a calculator, paper, or brain power.
Using a calculator, the first square in the first row would have 0.148 cubic feet. The first row in the fourth row would have ~38 square feet. First in the firth, 9709 cubic feet, which is large, and first in the sixth row, 2.48 million cubic feet.
I think you typoed. Wouldn't the 17th square have 2^16 grains, or roughly 65,000? (And the sum of the preceding 16 squares would be one less than that.)
At the other part of the calculation, isn't "4^3 = 2^12" inaccurate? 4^3 = 64 = 2^6.
Re: Grains of corn on chessboard
Well that'll learn me. Can't slip anything sloppy past this bunch.
My statements regarding the first & third rows were, it must be admitted, casual estimates -- and in particular, I think I had 2^16 (65,536) in mind when I said the sack would run out in the first row (2^8 = 256). Shows how long it's been since my active bit/byte-twiddling days.
I used to be pretty good at ballpark estimates. Sigh.
Reminds me of something I read in an article (it may have been Martin Gardner's column -- dating myself -- in Scientific American) many years back. In a math class at NYU (some (or all?) of which is in a mannhattan skyscraper), the prof pointed out the window at the Empire State Building and asked them to estimate it height in feet. The answers -- these are college students -- ranged from 100 feet to several miles! The saddest part of this story is that, when he asked the students how they had arrived at their guesses, almost none of them had had a plan (like estimating # of stories and story height, then multiplying); mostly, they just made a wild guess.
Now I don't feel quite so bad ...
If you take a sheet of paper and fold it in 2, it becomes half as wide and twice as thick.
If you repeated this process 50 times, assuming the paper was 100th of an inch thick, how thick would the folded piece of paper end up?
I'm too thick to work it out; the very thought maketh me thick.
It wouldn't. It's physically impossible to fold any piece of paper of ane size or thickness more than about seven or eight times.
"No man but a blockhead ever wrote except for money." Samuel Johnson.
My current blog.
Photographs to accompany Anyone Can DO It available from www.lulu.com
My photoblog The World Through A lens
Not anymore. American high school student Britney Gallivan derived the loss function for folding paper in half in 2001, then set a new world record by folding paper in half 12 times in January 2002.
So, I'll let you cut it and then put the pieces on top of each other. No restrictions on cutting or time.
How thick? Actually, I should say, how high?
Well, rather than hunt down my rusty micrometer (Now where could it be? Why, I remember seeing it just last millennium ...), I cheated and measured the height of a ream of printer paper (7 cm) and divided by 500. Multiplying that by 2^50 gave me 157,625,987 kilometers (give or take) -- which is very roughly the distance from the earth to the sun.
David the ex-math major -- VERY ex
Actuall, in my problem I gave you the thickness of the paper - 100th of an inch - so you didn't need your mic. But your answer is not far out anyway.
Yes but Richard, I dunno how to convert from mediaeval measures (still used only in third-world countries like GB & UK) such as inches into modern metric mensuration.
Oh hell, I meant "US" not "UK". Sorry, didn't mean to insult you twice (i.e. be redundunant) and I of course intended to include my native land in order to (partially) defang the affront.
<tongue firmly in cheek> David
& that's "redundunDant" -- if there's such a thing as misspelling a neologism.
I better quit while I'm behind ...
One hundredth on an inch is 2.117 micrometres.
Alternatively it is 0.00008819 of a Japanese mon, 6.35 Chimese Imperial hu; 2.237e-22of a light year, 0.000106 of an Ancient Roman digit, 0.00000463 of a cubit or 0.0000119 of an Old Russian pyad.