One of the issues I see folks experiencing from time to time is difficulty in grasping large numbers.
I mean, really, do you know the difference between a megabyte, gigabyte, terabyte, and petabyte?
And if you have a grasp of the definitions of each, do you really “get” just how large those numbers are?
We often see visual representations of bigger numbers – representations like the megapenny project, which illustrates several large numbers using one-cent U.S. coins. For example, what would a billion pennies look like? (Spoiler: bricks the size of five full-sized school busses.)
There is one unit of measurement I think might make computer data a little more conceptually tangible.
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The Bible as a unit of measure
I choose the Bible not out of any religious significance, but because it is the world’s best selling and most widely distributed book. Regardless of your faith, regardless of your location, regardless of your take on its contents, chances are you’ve at least seen a Bible at some point in your life.1
Like a penny, it’s something tangible that people can relate to. You probably have a sense of just how big it is. Yes, physical books will vary in size and shape to a certain degree, especially if they include illustrations or ancillary information. The point is that at a visceral level, you likely have a frame of reference for the size of that book.
So, let’s use it as a measure of some of the common rates and capacities we throw around in the tech world.
How big is a Bible?
First we have to understand just how big the Bible actually is.
I downloaded the plain-text version of the complete King James Version of The Bible from Project Gutenberg. It includes old and new Testaments, plus a tiny bit of additional information from the Project Gutenberg, and is formatted very simply.
It comes in at 5,218,805 bytes. That’s approximately five megabytes.23
Since there are eight bits in a byte, that means it also comes in at 41,750,440 bits. That’ll become important in a moment, since some things we care about are measured in bits (a single one or zero), while others are measured in bytes (a collection of eight bits).
How many Bibles fit on your fingertip?
This is a photo of a two-gigabyte microSD flash memory card on my finger.
These memory cards are fairly ubiquitous, particularly in mobile devices, since they’re so tiny. So, let’s do the math: two gigabytes typically refers to 2,147,483,648 bytes, or just over two billion.
It can hold 411 copies of our text-only Bible, all on the tip of my finger.
In fact, that microSD card is rather old. I recently picked one up for my video camera that holds 32 gigabytes. That’s 6,583 Bibles – again, in a device that’s smaller than the tip of your finger.
How many Bibles can you back up?
I often speak about backing up, and recommend that you have an external drive.
Since I started making that recommendation, I’ve purchased several 500-gigabyte external drives.
Over 500 billion bytes is difficult to comprehend – so how about over 100,000 Bibles?
My most recent external drive clocks in at a whopping4 8 terabytes5. That’s 1,685,461 Bibles – or just over 1.6 “megaBibles”, if you will.
Bibles in “the cloud”
It seems somehow fitting to measure some of the cloud storage we have access to in terms of the number of Bibles it could hold.
- Dropbox’s default two gigabytes is the same 411 Bibles we just placed on my fingertip in the photo above.
- OneDrive’s 15 gigabytes could hold 3,086 Bibles.
- OneDrive’s terabyte of storage for Office 365 users equals over 210,000 copies of the book.
You get the idea. You can store a lot of Bibles in the cloud.
How fast can you read The Bible?
Most internet and network connection speeds are measured in bits per second, not bytes. That’s why we need to know that our example Bible is 41,750,440 bits long. How long a download is that?
- At 33kbps (kilobits per second), which is a common dial-up modem speed: 21 minutes per Bible, or about three Bibles in an hour.
- At 768kbps, very basic DSL connectivity: 53 seconds, or just over 60 Bibles in an hour.
- At 10mbps (megabits per second), the speed of basic ethernet, fast DSL, and a common cellular modem speed: just under 4 seconds – around 900 Bibles an hour.
- At 100mbps (fast ethernet, and a common fiberoptic-to-the-home speed), 0.4 second – 9,000 Bibles an hour.
- At 1gbps (gigabit per second), high speed ethernet: 0.04 second – 90,000 Bibles in one hour.
Naturally, all of these are theoretical maximums for each speed, and don’t reflect overhead or other factors.
But that’s not the point.
The point is to get a better sense for what some of these numbers mean.
“A terabyte of storage” or “a gigabyte per second speed” are both just phrases until you have some kind of frame of reference. Since you have some sense of how big the Bible is, storing 210,000 copies, or transferring 90,000 Bibles in an hour, might give you a better feel for just how much data we’re talking about.
At least it’s been an entertaining thought exercise.
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Holy
sh…Bible.This is really a fascinating corollary that puts the emerging storage capacities in perspective. I remember being stunned when I was able to load my first book on a floppy… An amazing time to be alive.
Thanks Leo!
Chris
An amazing corollary that really puts into perspective the vast storage capacities that are emerging. Back in the age of dinosaurs, remember being stunned when I realized I could load my first book onto a floppy disk.
Thanks Leo!
Chris
Fascinating. An excellent thought exercise.
Good job explaining using familiar objects. Very similar to Grace Hopper’s nanosecond presentation.
https://www.youtube.com/watch?v=OQ4Iwoo0Kdo
Great site Leo! Thanks
Using the Bible as a base is probably more familiar than using some other very large literary work (such as a complete Encyclopedia Britannica or an Oxford Unabridged Dictionary). However, the Bible is a poor technical choice, as there are multiple recognized Bibles (each obviously of differing content size). Following the System International is the only rational way to talk about very large and very small numbers, and we should move toward harmony with that system rather than inventing new base systems.
That’s why Leo was so careful to specify the plain-text version of the King James Bible from Project Gutenberg.
Hi Leo
A small change is required…whooping is a crane, whopping is huge.
Rick
Thanks, fixed.
This reminds me of a guy I worked with years ago. Ask him directions to somewhere, he’d give a precise answer using liquor stores & bars as points of reference.
You can also go the other way in numbers:
Pico-seconds
Nano seconds
Computers have now given us the “ono-second”!
That is the time it takes to realize that you hit the wrong button! “OH NO”!!!
Here’s an oldie from the past … What is a nanosecond? A really fast billy goat. :-)
i do not understand-gigs,megs,teras,all this sort of computer lingo,leo has given me some good tips,but my main problem is,checking my security i,e,malware,trojans ,unwanted mail/spam,now i dont know if i have put this right,i have KASPERSKY,security,now they tell me i am coverd,but why do i still get things pop up on my screen saying i have loads of infections/malware,and i need to call some one to get rid of it.but when i try to do anything my screen freezes,and i have to turn it off,then back on,but it comes back again a bit later!!!!.
if i have a security system on my computer,how can people tell me i,e,phone calls,my system is infected.
If you get a phone call telling you you’re infected: THEY CAN’T. It’s a scam, nothing more. Hang up.
I too have often been astounded by the revolutions in storage technology. More than 25 years ago I worked with DEC VAX mini-computers. Our whopping VAX-11/785 had two dish-washer sized CDC 9766 disk drives. Each disk “pack” had a dozen 14″ aluminum platters giving 19 recording surfaces (+4 guards — top/bottom platters unused for data, 1 servo surface) in a package the size of a large wedding cake. Storage capacity? 256 MB formatted or 101 Bibles (give or take). Or 4 minutes of MPEG-4 video. The magnetic heads “crashing” into one or more surfaces was a sight and sound to behold. Backup? Nine-track magnetic tape reels! You can find these drives, etc on Google, eBay, etc for $100 or so. Did I mention the 220v outlets? And the air conditioning needed?
Nice article putting space and time in greater perspective. In the 5th bullet under “How fast can you read The Bible?” it seems (gigabyte per second) should be (gigabits per second).
You’re mostly right. It should be gigabit (singular as it’s only one) per second. I fixed it.
Nice way to make fairly large numbers ‘tangible’. Most people have a faint idea what “90 000 bibles” (or a trillion pennies, if you wish) really look like. Even when you translate it to a number of trucks or the fraction of the height of the highest building on the planet, It remains a very small number. Psychologically comprehensible, one would think. Now remember great events, like mega sports encounters or huge rock concerts. There are some 20 sports stadiums worldwide with a capacity between 90.000 and 110.000 supporters. The 15 largest concerts/festivals ever each attracted between 1.000.000 and 3.500.000 people. Are those numbers comprehensible for someone who visited a 60.000 attendants event? Some would say “easy, no problem”, others “maybe, but I prefer something smaller” and others still may say “no way, 60.000 is too big a lot of people”. Now imagine yourself on the way to such an event, travelling e.g. by small ferry with a capacity of 2.000 over a distance of 250 kilometres. No big deal. Only, the ferry goes down taking 300 lives. Or the event runs out of hand and 350 dead is the final casualitycount. What does that say about the meaning of “big numbers”? Of course mathematicians, scientists and ICT-specialists (to name just a few) take a different view on big numbers and large quantities. The current world population is some 7,3 billion (http://www.worldometers.info/world-population/) or, “7.3 times 10 to the power 12”. The number of neurons and non-neuronal cells in the human brain is some 160 billion per individual. Calculate the number of human braincells for all of humanity and you get (7,3 x 160 billion billion). Rephrase that to bits and bytes to establish a unit that befits us. No need for Bibles, Korans/Qurans or Shakespeare’s collected works or what have you. Finally, what to make of a “googol” (10 to the power 100, or a 1 followed by 100 zero’s), or a “googolplex” (10 to the power ‘googol’)? Are those really big numbers? And what would you consider to be the biggest possible number that could be ‘written’ without totally exhausting our known universe’s resources? We have many bits and bytes to go…
Good presentation and quite practical. I remember an article going from an average book to the library of congress relative to bytes. So is the 200,000 Bibles = 1 terabyte in the same power of 10 with the L of C.
A fine example of taking something almost abstract and making it concrete. During my career in IT (called other things over the years, e.g. DP, MIS) I used this technique a lot. Whether I used analogies to a car or a house or the technique you just used I usually found that people (including some less technical IT persons) could grasp what I was trying to explain. A good medical doctor does this for his patients. I often wonder why good technicians in IT can’t or won’t. I recall an instructor of mine from many, many years ago stating that if you cannot explain something so that others can understand it then you don’t really understand it either.
Here’s another way to look at it: “How much *information* is there in one Bible?” That could also be measured in bits, so let’s compare it to a picture. As above, 1 Bible = 41,750,440 bits.
The sensor on my camera is 2816×2112 pixels (“6mp”) by 24 bits/pixel; that’s 142,737,408 bits/picture. Each picture has 3.4 ‘Bibles’ worth of information in it. However, I think that’s unfair to the Bible, as the picture is compressed when stored; the typical .jpg image is around 3.5 megabytes, or ~28 megabits. Comparing that with one Bible’s information implies that one picture has about 1.46 “Bibles” in it.
What’s that old saw, “A picture is worth 1,000 words?” Since the Bible contains about 800,000 words, a picture is really worth about 600,000 words!
Hey, I still use my old Commodore-128 on occasion; its 1541 disk drive writes to 5.25″ floppies (!) with a storage capacity of 168,656 bytes (!!). That’s 3.23169767792e-2 Bibles (and no, I have no idea how much that is, only that it’s much less than one complete Bible!)! :)
Ooooh! I stand corrected! My Commodore-128 uses a 1571 disk drive rather than the 1541; the 1571 has exactly twice the storage capacity of the 1541, so that’s 337,312 bytes… and even more Bibles. :o
Ouch. I just checked those numbers over again. I never was any good at math, or even basic arithmetic. Those figures are all inverses! Ugh. I stand humiliated. :(
But at least I do admit when I’m wrong — not everyone does. (No, that’s not a slur on you!)
Hmmm… Your examples of “big books,” include the King James Bible, the Qur’an (which BTW is the correct spelling, since it isn’t our language, but theirs) and even War And Peace… but you don’t include Harry Potter And The Sorcerer’s Stone… interesting. :)
I just purchased a 2 TB thumb drive for less than $20.
The storage on an IBM 360 I programmed FORTRAN IV on 1968 Was much less than what Jeffrey C. Naismith’s description of similar disk drives for RAM. We also had many magnetic tape machines refrigerator size for permanent storage.
Now nanotube architecture is coming. DNA replication.
Wat a long strange trip its been. Mahalos to Gordon Moore and those who Do the work
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Running Windows 7 with Kaspersky. Purchased the software,but it’s so much grief, I just quit using it. Their tech support wasn’t any help and I think that’s the last time I’ll buy expensive software, preferring to use free versions instead. Then at least,if I can’t get it to work properly, I won’t be out $50.00′