Treebeard's Stumper Answer

Show Me a Million
Every day we hear about millions and billions and trillions of this or that. But number numbness sets in and imagination falters. It effects our public policy. The stumper is to actually produce a million of something and prove that it really is a million. Sure, a gram is a million micrograms, but I won't accept that. My challenge is to make it vivid! Sometimes even a million is not much. I installed a 120 gigabyte hard drive over vacation, 120 billion bytes of computer storage! What about the extreme metric prefix yotta or 10^{24}. Can you think of a use for it?
One way to visualize a million is to imagine yourself in a huge crowd.
But the stumper is to produce exactly one million, not just lots as in
these historic photos!
Dr. Martin Luther King Jr. delivered his "I have a Dream" speech on August 28, 1963 before a crowd of 250,000+. No one knows how many people were at Woodstock in 1969. The estimates are 500,000+. Don't look for me here. I try to avoid crowds! Estimates are that the Promise Keepers' rally filled the Washington D.C. mall with more than a million people in 1997!
DMS students came to school this week with millions of things! We saw big and small millions. A test tube of salt and a 10 by 10 foot patch of grass contrast nicely with an imagined line of sugar cubes stretching 7.9 miles from Santa Ynez past Los Olivos to the dump. There are abstracts of all our projects below. Big and small also meet in the huge metric prefix yotta or 10^{24}. Many galaxies are more than a yottameter distant. The mass of the earth is about 6,000 yottagrams. And there are about 0.6 yotta carbon atoms in just 12 grams of carbon.
Notes:
Quick ministumper: why are there no billionaires in England? Keep reading for the answer.
A yotta is sure a lotta! Sorry :=) I figured those yottanumbers in my short answer like this:
 Many galaxies are more than a yottameter distant.
A yottameter is about 100 million light years. That's a good distance, but the Hubble Space Telescope is imaging galaxies and quasers that might be more than 10 billion lightyears away! There's lots between us and them.
light speed = 300,000 km/sec = 300,000,000 m/sec m 60 sec 60 min 24 hours 365.2 days 1 lightyear = 300,000,000  x  x  x  x  sec 1 min 1 hour 1 day 1 year = 9.46 x 10^{15} or about 10^{16} meters So 100 million lightyears = 10^{8} x 10^{16} = 10^{24} meters = 1 yottameter
 The mass of the earth is about 6,000 yottagrams.
Mass of the earth = 5.9742 x 10^{24} kilograms 1000 grams = 5.9742 x 10^{24} kilograms x  1 kilogram = 5,974.2 x 10^{24} grams, or about 6,000 yottagrams
 There are about 0.6 yotta carbon atoms in just 12 grams of carbon.
Using the basic chemistry concepts of moles and Avogadro's Number, there are about602,213,670,000,000,000,000,000 atoms, or0.602,213,670 yottaatoms in 12 grams of pure carbon12. That's a small piece of charcoal!There's a quote attributed to Joseph Stalin (who should know):
"A single death is a tragedy; a million is a statistic."That's the problem. We lose touch with these big numbers we hear in astronomy and geology classes as well as daily news reports on national budgets and debts and poverty statistics and death tolls. Our problem with big numbers can cost our humanity. Consider this line between zero and a billion. Where would you place one million?
I made that line exactly 500 pixels long. Since there are a thousand millions in a billion (in the US at least), the million mark is only halfway to the very first pixel! If we put a trillion at the end of the line, then a billion seems just as insignificant. Put a yotta or 10^{24} on the line, and a zetta or 10^{21} seems to disappear. Exponential notation is a remarkable tool that can measure atoms and the universe with equal ease. But it's up to us to learn what those powers of ten mean, or tragedy can slip by unnoticed as mere statistics. It happens all the time.Until World War I, there wasn't much need to think beyond a million with a single word, since the scientists who needed big numbers could always use scientific notation and exponents. As a result, the word "billion" remains ambiguous. Apparently North America, France, and the Netherlands are the only countries that define a billion as a thousand millions (10^{9}). In the rest of the world, a billion is a million millions (10^{12}). That's why there are no billionaires in England! Even Bill Gates doesn't have that much. Surely American TV will change this as soon as people notice. For anyone not using scientific notation, a billion is just lots, kind of like Carl Barks' Uncle Scooge McDuck, with "five multiplujillion, nine impossibidillion, seven fantasticatrillion dollars and sixteen cents." Except Unca Scooge remembers where he got every coin!
I know I have a good school project when the kids are fighting to present their projects first because they're proud of what they did, and I want to go first for the same reason. This is my webpage, so I get to go first here!
I found the millionth letter in the King James Bible, both with and without spaces and punctuation. I used a simple text version that I found on the Web at http://www.obible.com/ as kjv.txt. Note that I didn't use the more common Project Gutenberg versions kjv10.txt or bible11.txt. These versions contain more formatting and are definately preferable for reading. But I wanted to remove all formatting and chapter headings, leaving just the text. For example, the version I used has each verse on a single long line, while the Project Gutenberg version breaks up long lines with paragraph marks and extra spacing. My version also does not include:
This explains why I got slightly different statistics from those at My Bible Facts. I don't care who's right. This is for fun! I'm not looking for hidden bible codes or studying Kabbalah or Gammantria. I did learn something about manipulating text with this project. Mostly I learned that MS Word 2000 is the wrong tool for stripping huge text files! I'll report at the end.
 The introductory titles in 115 of the 150 Psalms, eg Psalm 3, "A Psalm of David..."
 The 22 letters of the Hebrew Alphabet that divide the sections of Psalm 119
 The closing remarks at the end of 13 of the New Testament books, eg Romans and both Corinthians
After I stripped off the introductory header, I had a text file like this, with hidden paragraph marks at the end of each verse line:
I had to get rid of the paragraph breaks and the chapter:verse title at the start of each line, but the chapter:verse headers were of different lengths. This would be easy with Unix or Perl regular expressions, but I managed to use the MS Word Replace function in two steps. It's complicated because I need to use the MS Word "use wildcards" option, but there's no paragraph marker among the wildcard special choices. So first I replaced (without wildcards) all the paragraph marks with "^" or caret marks, which are not found in the text,Ge1:1 In the beginning God created the heaven and the earth. Ge1:2 And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. Ge1:3 And God said, Let there be light: and there was light. Then I used the wildcard option to find the pattern [caret+anything+colon+anything+space] and replace it with a single space. In Word, this became:
Find ^p ^p = paragraph Replace ^^ ^^ = caret character Now I had a bare text that looked like this, with punctuation and spaces but no line breaks and nothing else:
Find ^^*[:]*[ ] [caret+anything+colon+anything+space] Replace [ ] replace with a single space In the beginning God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. And God said, Let there be light: and there wasFinally I used the MS Word Count feature and trimmed the file back to exactly 1,000,000 characters. The one millionth character, with spaces and punctuation, is the last "R" in Judges 19:18
And he said unto him, We are passing from Bethlehemjudah toward the side of mount Ephraim; from thence am I: and I went to Bethlehemjudah, but I am now going to the house of the LORD; and there is no man that Receiveth me to house. Then I wanted to eliminate spaces and all punctuation to find just the millionth letter. This almost pushed MS Word over the edge, and it took a couple all night runs to finish. It did better when I figured out to turn off the "check spelling as you type" and "background repagination" options! After finally getting rid of all spaces, I worked my way through all the other punctuation marks, and just for the heck of it, I replaced all upper case characters with lower case. I ended up with a file like this:
inthebeginninggodcreatedtheheavenandtheearthandtheearthwaswithoutformandvoidand darknesswasuponthefaceofthedeepandthespiritofgodmoveduponthefaceofthewatersandg odsaidlettherebelightandtherewaslightandgodsawthelightthatitwasgoodandgoddivideThis stripped King James Bible is 3,222,423 characters long, with one word and one paragraph. The one millionth character is the "t" in "king Solomon's table" in 1 Kings 4:27
And those officers provided victual for king Solomon, and for all that came unto king Solomon's Table, every man in his month: they lacked nothing.
This is a completely insignificant result! But I'd like to ask a rabbi what those verses signify. The first text seems to be horrible story of personal abuse and violence that triggered a war, and the second is a celebration of the glory of King Solomon's reign. I don't think the ancient Bible authors of Judges and Kings had the notion of a million, though Archimedes went way beyond a mere million in The Sand Reckoner. Meanings aside, I think it's pretty cool to see the Bible without spaces or punctuation. I believe that's the way Hebrew, Greek, and Latin were all originally written. I'm interested in those "inbetween" words that appear without spaces, but I'll save that for a future stumper.
I learned a few lessons by doing this:
I also learned some obscure Bible trivia! By my reckoning, the King James Bible contains:
 MS Word does NOT like a document with 3+ million characters in one word! It took forever to do anything, but I have to admit it never crashed.
 Check the MS Word Option menu when you're doing something unusual. Turning off "check spelling" and "background repagination" made a big difference.
 There are better tools. A Hex Editor like the freeware XVI32 can do in seconds what took hours in Word!
66 books 1,189 chapters 31,103 verses 789,635 words 4,137,819 characters with punctuation and spaces 3,348,183 characters with punctuation but no spaces 3,222,423 characters with no punctuation or spaces 789,636 spaces 125,760 punctuation marks 26,145 . periods 70,683 , commas 12,721 : colons 10,139 ; semicolons 3,297 ? question marks 1,997 ' apostrophes 313 ! exclamation marks 221 ( ) left and right parentheses 23  dashes 0 @ # $ % ^ & * + = \ / < > [ ] { }  ~ ' 115,919 capital letters, like this:
A 17,834 J 6,348 S 4,829 B 4,642 K 530 T 7,609 C 1,646 L 9,169 U 292 D 8,747 M 3,027 V 100 E 2,569 N 1,838 W 2,395 F 2,313 O 8,852 X 0 G 6,086 P 1,749 Y 542 H 3,184 Q 5 Z 902 I 13,208 R 7,503 You can tell I had fun with my million project! The Dunn Middle School kids did too, but I limited them to short abstracts which I cut and pasted from their email. Here they are with no editing. Remember these are kids in grades 68. I expect some revisions.
DMS Kids Show Me A Million! I calculated how many thirtysix pound bags it would take to make 1,000,000 pieces of dog food. I found that I needed 2083.3 pounds, which was 8333.3 cups, to make roughly 1,000,000 pieces. This would take 58 thirtysix pound bags of adult dog food. (Lenora) I typed one million letters on the computer. I typed one million letters, then I copied and pasted the letters until I got one million. I didn't want to waste all of that ink and time, so I printed two pages of letters and put fiftyseven empty pages in the middle. (Emily) I have 1,000,000 threads, 250 threads in every square inch of a Supima cotton bed sheet. I divided 250 into 1,000,000 which equated 4,000 which was how many square inches I needed. I cut a 40" X 100" piece from the sheet to get 1,000,000 threads. (Nikki) I tried to find 1 million beats of techno music and put it onto a CD. First I counted how many beats there were in 10 seconds of a techno song. Then I cut the song down to the 10 seconds, and pasted it 185 times, then burned it on a CD. I made 5 copies of the CD and figured that would be 1 million beats. (Thomas K.) For my project I found out how long a line of 1 million ants would be head to end. I figured that each ant was a 3 mm long. Then I multiplied 1 million by 3 mm and then reduced it to 3 km then multiplied it by. 621 to convert it to miles and came up with 1.863 miles. (Mary) I found how many lab book squares are in a million. I got the number of squares on a page. Then I multiplied the number by the number of pages. Then I divided that into a million. I got that it took about 2.8 books to make a million squares. (Robert) For my project I counted 1 million words in books. what I did was got the average of the number of words one page and multiplied the average by the number of pages. After 6 books the millionth word is on the last page of The Fellowship of the Rings. (Brett) How many sprinkles do you need for a million? To start get 1/2 tsp. and count, I got a 1,000 rounded, go from there and you can end up with 10.4. (Lorena) I printed out one quarter of a million people. I figured it by getting a picture of two hundred people and making 1280 copies of it. I pasted them on two poster boards. Because I wanted to have more so I came up with an estimate that one million people could fit on 18.5 football fields. I realized that one million people, is a whole lot of people. (Drew) I counted 1 million rice grains. I counted the grains in 1/8 cup, and then added, finding grains per cup. The bag said how many ¼ cups inside, which I made cups. I was 200,000 grains over, so making that cups, I removed 21 cups. Having 1,000,000 rice grains. (Becca) I found a million pieces of Dentyne Ice Gum. Since there are 12 pieces in each pack and 12 packs in each box I figured it would take about 7000 boxes to hold a million pieces. This amount of boxes could fit in two 5x4x4 foot pallets. Imagine how many million pieces of gum each Costco sells a year. (Ryan S.) I typed 1,000,000 I's on the computer. Then I used Word Count to make sure there were exactly a million I's. There were 999,999 I's, so I typed one more I to reach 1,000,000. My results were that it took 20 pages of the letter I in size 2 font to record one million I's. (Clay) For my one million I took an ordinary liter bottle of soda and thought how could I get one million out of it. I found out on the internet that there is one million microliters in one liter (micro meaning one millionth). (Jordan) What we were trying to accomplish was to see hoiw big a box would be in order to fit 1,000,000 magic cards would be if they were stacked face to face, and then we multiplied 10,000 by 1.25 (because 100 cards equaled 1.25 inch.) and multiplied that anwser by 18 ( the height of the box), and then we converted that anwser into feet. We divided that anwser (158,400) into 1,000,000 and figured out that the box would be 26.57 by 26.57 by 26.57 ft. big. (Austin and Nick F.) My prolect was get a million of something and show it. I chose bird seed. After i found how many seeds were in one bag i divided that number into a million and with the numbers left over i figured how many bags it would take to get a million seeds. It took 3 1/2 bags. (Kelsey) For my one million I chose to find out how long one million sugar cubes would be if you stacked them on top of each other in a line. First I found how many inches long it would be, and then converted it to miles. One million sugar cubes stacked on top of eachother would be 7.9 miles long, or from Dunn School to Beulton. (Billy) My lab book's pages have tiny squares on them, 1776 whole squares. To have 1 million tiny squares I must have 612 pages and 825 extra squares. (Jp) I figured out how long it would take a single person to chew a million sticks of gum, given they spend 30 minutes on each. By multiplying 30,000,000 minutes down to years and found out that it would take 62 years. (Lauren) I researched how many pads of graph paper it would take to cover one million squares. First I got how many squares were in a pad and divided that by one million. Which told me that 13 pads and 18 pieces of paper added up to one million squares. (Amanda P.) For my million project I wanted to see how many feet in my backyard I would need to 1,000,000 blades of grass. The first thing I did was, I counted how many blades of grass there are in a square inch, I counted 32 blades of grass per square inch. After a little math I came out with, for 1,000,000 blades of grass I would need a square that is 14,7 feet by 14.7 feet. And that was my million project. (Louis) For my 1,000,000 project I figured out how many square feet of carpet you need to have one million rug fabrics. First, I counted how many rug hairs where in a square inch, then I divided that into 1,000,000, and I got 2,500 square inches. Then I converted that to feet and got 17 feet has 1,000,000 rug hairs in it. (Thomas H.) I found a million words in books. I counted the average of words on a page, then I multiplied that by the number of pages. I did that until I had a million words. I ended up with thirteen and a half books with different print sizes. (Thalia) I found out how many pages in a King James Bible contains a million words. I got an average number of words on a page and how many times that went into a million. I found that that certain Bible needed 185 more pages to contain one million words. (Tracy) By using the dots on a basketball I am trying to determine how many basketballs required to make a 1,000,000 dots. I found there was 14,400 dots per basketball. I divided 1,000,000 by 14,400 to conclude it required 69.4 basketballs to equal 1,000,000 dots. (Justin) I typed my name a million times. Ityped my name on a page and it came out to be 3,150 maxs on a page. Then Idivided that by one million. I ended up with 158 pages double sided with my name 1,000,000 on all together. (Max) For my one million project I decided to find out how many square yards it would take to fit one million blades of grass. I measured a square inch of grass and got about 60 blades then I divided that into one million and got 16666.6 then I divided that by 144 to get square feet and then 9 to get square yards. I got 13 square yards would contain one million blades of grass. (Kevin) To Show 1 Million I drew 2819 tiny cubes on one 81/2 by 11 inch paper. I then divided 1,000,000 by 2819 and Came out with 355.113 which would be the number of sheets of paper. Then i multiplied that by 11 (inches)and divided that by 12 (1 foot) and got 325.52, which is how many feet long the sheets would be when laid one next to the next. That seems like a lot of paper but if you stack it one ontop of another it would only be about an inch tall. (Brian) For my 1,000,000 of something I got a crate that would hold 1,000,000 lima beans. I counted 400 beans per lb. I devided 1,000,000 by 400 and I got 2,500 the amount of lbs for 1,000,000 beans. The crate held 2,500 lbs and was 4 feet by 5 feet by 4 feet. (Andrew) For my million I decided to get print out a million periods. To do this I got the smallest type size possible, decreased the margins to the smallest, typed period, space, period, space, etc., and ran a word count. It came out to 12,280 periods on a page so I figured that I would need about 81.5 pages so I went and copied 40 double sided papers and 1 one sided paper. (Will) I used pennies for my one million project. First I counted 100 pennies and weighed them. I then multiplied the weight by 10,000. Then I got the answer on how many 1,000,000 pennies weigh. 276.2g x 10,000 = 2,672,00 g. The answer I came up with was 2,672,000 g = 1,000,000 pennies. (Bri) For my million project, I chose the relatively simple 1,000,000 mm^3. I cut 6 10cm^2 (100mm^2) squares and put them together to form a cube. From this I recalculated the volume of the cube and came up with 1,000,000 mm^3. (Morgan) I set out to calculate how big of an area a million blades of grass would take up. First I counted the amount of grass blades in a single square inch, which was 76 blades, and divided that into a million to see how many square inches it would take. I used feet instead and the number was 91. (Caiti) I made 1,00,315 bytes of disc space. What I did was, I added a bunch of files from My Documents and got as close as I could to 1,000,000. The amount of bytes I got is about 977kb. (Brandon P.) For my millions project I counted the holes in a screen. I first had to measure a square with a hundred holes in it, which was 1.5 centimeters, then after this I had to measure the width and the length of the screen, it was 115 cm by 85 cm, from this I figured that i would need a screen about 150 cm by 150 cm to have one million holes. So it would take my screen and a screen fit for a door to have one million holes. (Molly) I measured 1,000,000 grains of rice by counting 300 grains which filled 1 tsp. Then I multiplied and figured out that 900 grains equals 1 Tbsp, 1 cup equals 14,400 grains, and 69 1/2 makes 1,000,000 grains of rice. It almost filled an 18.5 liter water jug. (Whitney) I figured out how much 1,000,000 Hershey’s Kisses would weigh. My first thing was to find the weight of one kiss which was .25 ounces, then multiply .25 by 1,000,000 and got 250,000 oz. Then I reduced it to tons. The weight of 1,000,000 Hershey’s Kisses is 7.8 tons. (Nick M.) To show 1,000,000 water drops, I filled a beaker with 1,000 eye dropper drops of water. Since 1,000 is 1,000th of 1,000,000,I multiplied the 59 ml measurement of water by 1,000,equaling 59,000 ml. With 3,785 ml in one gallon, I calculated 15.58 gallons of water in 1,000,000 drops. (Chase) I have 1 million grains of rice, and I wanted to see how much that would weigh. I counted 100 grains of rice and weighed it, and it was 1.70 grams. I then figured that 17,000 grams would be the weight of 1 million grains. I figured it out in pounds and it was about 40 pounds. (Hayley) For my project I calculated how many bathtubs 1,000,000 half teaspoons would fill. There are 78 tsp in one cup. I filled a bathtub full of tsp. There were 77064 half tsp of water on a bathtub. 1,000,000/ 77064 =12.976. It would take about 13 bathtubs to hold 1,000,000 tsp of water. (Arielle) For my million project I typed one million 'i's. I copied and pasted the i's until the word count said that I had exactly one million characters. Or, divide a million by 10,664, the number of i's in a page. I found out it takes about 94 pages to fit one million i's. (Annie) For my million project I found out how many hairs are on my dog. I figured out his surface area with an 11 x 14 inch paper towel and here are some of the numbers. 14 x 11 = 154 square inches per sheet of towel. Boomer’s body is covered by 12 sheets of towel. Therefore Boomer has a surface area of 12 x 154 = 1,848 square inches. That's 700 x 16 = 11,200 hairs per square inch and 11,200 x 1,848 = 20,697,600 hairs. I found that there are 20,697,600 hairs are on my dog, so 1/20th of his body would equal 1,000,000 hairs. (Georgie) I have 1,000,000 salt crystals which equals 60 grams.I first counted 50 salt crystals which was 0.003 grams. Then I divided 1,000,000 by 50 and that was 20,000. Then I multiplied 20,000 by 0.003, that equals 60. I needed 60 grams of salt to equal 1,000,000 salt crystals. (Jillian) I have a quarter of a million XOs. I know this because after I typed it I did word count. I had exactly a quarter of a million. I ended up with sheets of paper that had very small Xs and Os. (Alicia) For my finding a million project, I determined how long a million, 11 inch papers would be. I multiplied 11 by one million and got 11 million; then I divided it by 12, then by 5280 to find how many miles it was. It turned out to be 173 miles! (Tommy R.) I was seeing what one million sugar cubes looked like. I figuered it out by, measuring one cube=1/2 inch cubed, then I took the one million and divided it by 2=500,000 inches, I then converted it to miles=7.9 miles. That is the distance from the Los Olivos Dump to Santa Ynez plus 1/2 mile which is shown with a scale map. (Liz) Measuring gravel showed that an average piece equals .1 cm3. 1002 105mm x 95 mm boxes would hold one million pieces of gravel. This equals 24 across and six up. (Seandon) I had 1 million dot candies. I figured out how many dots were in a square foot there were 360. I divided 360 into 1,000,000 there were to get how many layers are in 1 million there were 27.I ended up finding that a 12x12 stack of dots would be about as high as an 8 story building. (Anne) Our school project was to find one million items of something. My choice was to measure the height of one million sheets of paper. I took stacks of paper 2.25 inches high, containing 500 sheets. I calculated that one million sheets stacked would be 375 ft. tall. (Sophia) My science project was to bring a million of something. I chose roses because they're easy to count. I figured that ten roses equal one square foot and that divided by one million is one hundred thousand square feet. I ended up with a field of roses is 316.3 feet by 316.3 feet. (Lydian) The million that I thought of was one million codes for entertainment systems. I have a magazine that has 10,000 different cheat codes. The dimensions of this magazine are 10.5 inches long by 8 inches wide by .25 inches deep, or 21 cubic inches. To get one million codes, I would need 100 magazines which would fill a box 10.5 inches long by 8 inches wide by 25 inches deep or 2100 cubic inches. I decided it was easier to make a square box 12.8 inches by 12.8 inches by 12.8 inches (also 2100 cubic inches). (Ryan H.) Here are some links for further research on millions of things:
(I'm out of time tonight, but I have lots of interesting links to add!
Back to Stumper
Last modified .