I love numbers. I have a decent grasp of them, including orders-of-magnitude: the idea that 1000 is ten times 100, and so on. This comes from long, long experience, especially in astronomy. Also, writing a book where the last chapter deals in practical terms with numbers like 1092 years kinda gives you a serious feel for big numbers.
Still, not everyone gets that kind of experience. In everyday life we deal with the number a billion, especially with computers, but honestly, do you have a real grasp of how much bigger a gigabyte is than a megabyte? Sure, it’s 1000x bigger, but that doesn’t really give you the visceral feeling of what kind of number a billion really is.
Enter Jay Epperhart. He decided to figure out just what a billion means, and put up a pretty cool page describing it.
My favorite is the graphic depicting a million dots. They’re too small to see in the inline image, and even when I clicked it my browser didn’t display it at full resolution. When I finally displayed it in full res, the idea of just how big a million really is reached through my monitor and flicked my ear.
That was pretty nifty.
He goes on to talk about the number of stars in the galaxy and galaxies in the Universe… but I won’t spoil it. Head over there and give it a read. It’s megagigacool.
March 4th, 2010 at 11:43 am
My favorite “big numbers” demo is to show folks a sheet of paper with 1000 dots on it, then point out that the paper needed to display 1 billion dots would roughly fill our planetarium to the roof (15.2 m dome).
March 4th, 2010 at 11:50 am
But how big is “billions and billions”?
March 4th, 2010 at 11:51 am
Hmm… 300 DPI printer. Print every other dot across and down, perhaps with a gap every 10 dots, and a larger one every 10 groups of 10 (sort of like the “milliondot.gif” file above), and print 1000 across and 1000 down. That will fit nicely on an 8-1/2 x 11 sheet of paper.
That’s one million (very small) dots, assuming your printer doesn’t run the dots together.
You’ll probably need a magnifying glass to see anything more than shades of gray, of course.
March 4th, 2010 at 12:03 pm
Just to nitpick: a gigabyte is 1,024 megabytes, not 1,000:
Similarly a MB is 1024 kilobytes, and a terabyte is 1024 gigabytes.
March 4th, 2010 at 12:04 pm
one of my middle school science teachers printed out 1000 stars on 1000 sheets of paper and put them up on the classroom walls.
he explained what it was to the students. there are 1 million stars here on these sheets of paper.
one of my friends raised his hand and said “no. there aren’t 1 million stars.”
the teacher said “sure there are. 1000 times 1000 is 1 million.”
my friend showed the teacher one star he had torn off the corner of one of the sheets.
March 4th, 2010 at 12:07 pm
My good friend Walt made up a CAD drawing depicting a human approximately 5’10″. When he zoomed out one could see that he had drawn, next to this human, a line one mile long. Zooming out again would show the relative size of the state of Delaware to the line a mile long. The human was now a dot. Zooming out again would show a rough outline of the US. Now the mile was a dot and the human was gone. Zooming out again would show the planet Earth and Delaware was a dot.
Subsequent zooms would show the orbit of the Moon around the Earth. The Earth’s orbit around the Sun, etc.
Another interesting and cool illustration of scale.
March 4th, 2010 at 12:09 pm
Here’s another good example:
http://www.kokogiak.com/megapenny/1.asp
March 4th, 2010 at 12:13 pm
How big is a BILLION?
Originally in Britain, a billion used to mean 1,000,000,000,000 or 1012, but some time ago, in the mid-1970s, we adopted the American definition of 1,000,000,000 or 109 — it’s the ‘Hollywood’ influence!
P.S. Oh, er… you wrote a book?
March 4th, 2010 at 12:14 pm
Phil – I think you mean (soon to be) hellacool.
As a physicist I’ve worked to develop my sense of large numbers — as someone that follows the food industry (sorry to shift subjects) it still blows me away that the number of chickens slaughtered each year for meat typically exceeds 9 billion in the US and 50 billion worldwide. I don’t recall the most recent estimates of number stars in our galaxy (~100 billion?), but if chickens were stars, the US would consume the galaxy in ~10 yrs.
March 4th, 2010 at 12:15 pm
A meter stick had always helped me visualize a billion. I’d just imagine a billion contiguous cubes one millimeter on a side.
March 4th, 2010 at 12:27 pm
You wrote a book?
edit: dangit IVAN! I thought I had that one. Phil’s getting trixy!
March 4th, 2010 at 12:30 pm
Twin Cities Public Television has an interesting series geared toward kids called “Dragonfly TV”, with an episode devoted toward Nanotechnology. (http://pbskids.org/dragonflytv/show/whatsnano.html) In it, two kids go around trying to find a “1 in a billion” comparison. (If I remember correctly, it ended up that a blade of grass in a football field was pretty close). If you’re looking for ways to convey large number concepts to kids, it might be worth checking out…
March 4th, 2010 at 12:42 pm
I’m going to start using “gigacool” in casual conversation. And, then in fourteen months or so I’m going to start using “teracool” and perhaps after that, “petacool.”
March 4th, 2010 at 12:47 pm
Now that you have the idea of 1 billion in your head, think about this: The annual budget of the United States federal government is roughly $3500 billion. Yes, that 3500 times 1 billion.
March 4th, 2010 at 12:53 pm
Further to my comment above, Wikipedia has more on the history and definition of the term billion: Long and short scales.
@ Greg in Austin (#11),
Here in London, UK, I’ve got 6 hours’ advantage over you!
March 4th, 2010 at 12:57 pm
Don’t you hate it when other blogs beat you to it?
http://failblog.org/page/45/
March 4th, 2010 at 1:21 pm
I kinda like this big number:
http://cbs13.com/local/hella.big.uc.2.1529825.html
March 4th, 2010 at 1:26 pm
When a “believer” objects to the idea of a single-cell organism evolving into, say, Albert Einstein, I like to point-out that a comparison like that can give one an idea about just how long 3.5 Billion years is.
March 4th, 2010 at 1:34 pm
My favourite comparison involves time. A second is a short time, right? Ask people to guess how long a million seconds is. (It’s about eleven days). Then ask about a billion seconds. While they’re trying to multiply in their heads, tell them it’s about thirty-two years…
And a trillion seconds is longer than human civilization has exsisted. Sorta puts the U.S. National Debt into perspective…
March 4th, 2010 at 2:08 pm
This is my favorite for getting a feel for large numbers. It’s specifically about your chances of winning something like the Mega Millions jackpot which are something like 1 in 176 million. All you have to do is mouse over the “jackpot” pixel. It keeps track of how much you “spend” before you actually find it… assuming you ever do.
http://tinyurl.com/3x2r9w
March 4th, 2010 at 2:09 pm
@Wintermute (#4) … that depends. Although I grew up with 1 KB = 1 kB = 1 kilobyte = 1024 bytes, I can’t help think now that this is non-standard usage, especially as disk size usage tend to be 1000 based, where as memory 1024 based usage. Phil’s comments could be either system.
Since the SI defined these, we should probably use their terminology consistently with computers. Hence to be accurate and precise then I think one should take use binary prefixes for memory. (I’m not holding out much hope though
)
http://en.wikipedia.org/wiki/SI_prefix
March 4th, 2010 at 2:10 pm
Speaking of megabytes (MB) and gigabytes (GB) my computer has a 300-GB hard drive (a litte over a quarter of a terabyte, TB)
March 4th, 2010 at 2:32 pm
I’m sorry, but I refuse to take it on faith that there are really 1M dots there, so I’m going to verify by counting them and get back to you.
BRB.
March 4th, 2010 at 2:33 pm
A billion is 10^18 times smaller than a hella.
March 4th, 2010 at 2:59 pm
I was going to write a comment about the issue of whether “a billion” of something is a linear something, an area of something, or a volume of something. I decided it was blog-post-worthy…
Check it out: How big is a billion? Well… it depends.
March 4th, 2010 at 3:30 pm
The first thing I thought about, was a quote I’d read in a book once about ‘saving a billion dollars here and a billion dollars there, and it soon mounts up to REAL money’, but I can’t find the reference; “A billion here, a billion there, and pretty soon you’re talking real money” has been ascribed to Senator Everett Dirksen, but he has denied it, but probably wished he had said it.
Steve Novella has a nice comparison; the human brain has a 100 million neurones, which is the same number of stars in the Milky Way and the same number of galaxies in the visible Universe, giving a total of 10 to the 22nd power stars (about 10 sextillion; sextillion, now that’s a word I’d like to drop in general conversation).
Makes the Bible prediction of God multiplying humans like the stars in the heavens sound rather ambitious “I will multiply your descendants as the stars of heaven, and will give your descendants all these lands; and by your descendants all the nations of the earth shall be blessed”(Genesis 26:4. Have I set a record and been the first to quote scripture on Bad Astronomy?).
The wikipedia has a nice article which drops a lot of biggish numbers http://en.wikipedia.org/wiki/Observable_universe
March 4th, 2010 at 3:42 pm
come on, pablo (#9), don’t you know we eat our chicken *with* our stars? (Though, to be fair, sometimes we forego the stars for regular-sized, just as taste-less noodles.) They’re pre-mixed in a red and white can, last I checked…
March 4th, 2010 at 3:58 pm
Wintermute:
If you’re talking to a programmer, or a RAM manufacturer, yes. If you’re talking to a hard drive manufacturer, then no — they deal with “mega” as 10^6, and “giga” as 10^9.
A gigabyte of RAM is 1,073,741,824 (2^30) bytes, but a gigabyte HD is 1,000,000,000 bytes.
March 4th, 2010 at 4:17 pm
Also, Apple hath decreed that hard drive marketers had it right all along and changed the definition of MB, GB, etc. with snow leopard. In 10.5 and prior, 1 MB was 1,048,576 (2^20) bytes (and still is in windows, and every other OS). In 10.6, it’s a cool 1,000,000.
Thus spake Jobs.
March 4th, 2010 at 4:29 pm
Damn, I said 100 MILLION not BILLION in my comment. They shouldn’t put the B and M so close together on the QWERTY keyboard.
March 4th, 2010 at 8:11 pm
They have that gif in book form. It’s called A Million Dots by Andrew Clements. It’s a book with nothing but a million dots and a bit of trivial here and that at certain points (like thing X is Y miles big at dot Y).
March 5th, 2010 at 1:46 am
There are a million millimetres in a kilometer.
You can see both, simultaneously, if you are at an open location.
Just tell people that that ratio, that measurement-difference, which they can see, right in front of them, is a million.
A US billion, is of course, 1000 times larger than that – the prefix “G” for Giga is used…
And 10^12, is “T” of course.
March 5th, 2010 at 4:23 am
Pffft – that’s nothing. Check out ‘Graham’s Number’. THAT is a big number. For those that haven’t heard of it, Graham’s number, if each numeral was written in a cube with sides equal to the Plank scale, still would not fit in the observable universe. It was up until recent the largest exact number ever used in a mathematical proof.
Now, if you follow the web comic xkcd, then you may have seen this post: http://www.xkcd.com/207/
Calling the Ackermann function with Graham’s number as the arguments – THAT IS A FRIGGIN BIG NUMBER. You can have your mere million
March 5th, 2010 at 8:53 am
A dutch billion is 1000 times bigger/more than a us billion.
The dutch have a “miljard” between a million and a billion (“biljoen”)
Which always give translation errors in the numbers.
March 5th, 2010 at 9:01 am
Wow. I’d never really been able to wrap my brain around the size and immensity until the article showed the picture of the lots’o'galaxies and then said that there need to be 31 *MILLION* more of these pictures, to cover every direction in space.
Heh.. I feel so.. insignificant!
March 5th, 2010 at 9:50 am
This is why we have words like “mebibyte” and “gibibyte” now.
March 5th, 2010 at 9:51 am
@35
sounds like Monty Python with a twist.
“You are all insignificant!”
“WE ARE ALL INSIGNIFICANT!!”
“no, i´m not”
March 5th, 2010 at 11:32 am
Graham’s number is so big that you can’t even write the second step of computing it in the observable universe.
March 10th, 2010 at 11:26 pm
[...] Hat tip Jay Epperhart via Bad Astronomy [...]