How Big is Big, How Fast is Fast?
28 February 2013

by tmartin on February 28, 2013

EVERY DISCIPLINE HAS ITS OWN vocabulary. Medicine, cooking, automotive repair, computer science … you name it, and it has its own word world.

But there’s one kind of vocabulary that stretches across disciplines, and where its extremes seem to reached in the applications of science and technology: the vocabulary of measurement.

How much? How fast? How incredibly huge? How unimaginably small?

With technology, sometimes I feel like I’m living life in the giga-lane … and I’m not sure I really understand what it all means.

My analog brain has been having a heck of time stretching from yottas to yoctos.  I also started to have a sneaking suspicion that different disciplines use the same terms to mean … well, not exactly the same thing.

With all the noise over Google Fiber (http://fiber.google.com/about/) and its one gigabit home service, the term giga seems to have entered common parlance.

Giga comes from the Greek gigas meaning “giant.” And giga is indeed giant; it means one billion.

Billion with B.

10 to 9th power.

That’s nine zeros: 1,000,000,000.

One thousand million.

But this giant turns out to pretty common and we see it everyday, in things we all do.

Dropbox, the popular shared storage service, said this week its 100 million users now do a cumulative 1 billion file uploads per day.

Also this week, Apple said its iTunesU (http://www.capeeyes.com/2011/09/learning-anything-anywhere-anytime) hit the 1 billion mark of downloaded classes.

Meanwhile, The Wall St Journal pondered Twitter’s $10 Billion valuation (http://online.wsj.com/article/SB10001424127887323384604578328303487784818.html).

In connectivity land, FCC Chair Julius Genachoski issued a “Gigabit City Challenge this past January, at the US Conference of Mayors annual meeting. He called on the group to help create at least one gigabit community in all 50 states by 2015.

Fanned by Google’s giga-promotion engine, cities and states just seem to be scrambling to show that they’ve got the numbers … while Time Warner Cable publicly sniffs that consumers don’t need broadband of the giant type.

With something like connectivity, the measurements get applied in multiple dimensions: volume and time. A gigbit network doesn’t just store a gigbit of data like your hard drive; it moves that data across time. In other words, a one gigabit network moves a gigbyte of data per second.

Brain, process!

My computer has about 150 GB of data stored on it at this moment.  That’s 150 gigbytes. Or 161,061,273,600 bytes. With 8 bits to a byte, that’s 1,288,490,188,800 bits of digital content.  (Purists – yes, yes, see notes below – about base 2!)

So if I wanted to upload my own content somewhere else, I’d need to move around a lot of bits. In those hot-hot-hot google 1 gigbit network,  all my songs and photos and all those toddler year videos would take 1288 seconds to chug on through. That’s just about 21 and a half minutes.

The much ballyhooed 10 Gigabit capacity networks could move my digital life around in 2 minutes. Is this what the future will measure? Years of life flying through the ether in less time than it takes to poach an egg?

At first, that sounds like way more than anyone might need. Until you consider those 1 billion daily uploaded files. And those 1 billion downloaded iTunes U modules. And how those represent just one tiny sliver of all the bits flying around our heads every second of every day. Suddenly, Google’s 1 gigbit starts looking pretty darn attractive.

Russ Rowlett, Director of the Center for Mathematics and Science Education at the University of North Caroline/Chapel Hill put together a handy guide a few years back.

The Dictionary of Units of Measurements (http://www.unc.edu/~rowlett/units/using.html) lays out the list from yottas - that’s 10 to 24th, of 24 zeros. Can you say “septillion”? – to yoctos which are – you guessed it! – 10 to the negative 24th , or one-septillionths.

His alphabetical reference also incorporates both historic and highly vertical terms, like:

methuselah (a large wine bottle holding about 6 liters, 8 times the volume of a regular bottle)

And:

hundredweight (a traditional unit of weight equal to 1/20 ton. The hundredweight is the English version of a commercial unit used throughout Europe and known in other countries as the quintal or the zenter)

How can you not love these words!

The prefixes that show up in everything from telecommunication to my favorite nano-technology advances date back the structuring of the metric system in the 1790s.

The International Bureau of Weights and Measures (http://www.bipm.org) maintains the International System of Units, aka SI, to which giga and nanos belong. These prefixes define values based on10’s – this is the metric system after all.

For fun reference and handy cocktail party conversation, here’s the list for your reading pleasure:

Wicked big:

Yotta (Y) – 10 to the 24th, 1 spetillion

Zetta (Z) – 10 to the 21th, 1 sextillion

Exa (E) – 10 to the 18th, 1 quintillion

Peta (P) – 10 to the 15th, 1 quadrillion

Tera (T) – 10 to the 15th, 1 trillion

Giga (G) – 10 to the 9th, 1 billion

Mega (M) – 10 to the 6th, 1 million

Kilo (k) – 10 to the 3rd, 1 thousand

Hecto (h) – 10 to the 2nd, 1 hundred

Deka (da) – 10. Just 10.

Incredibly small:

Deci (d) – one-tenth

Centi (c) – 10 to the negative 2nd, one-hundredth

Milli (m) – 10 to the negative 3rd, one-thousandth

Micro (a greek symbol normal people don’t type, that looks like a lower case u with a trunk and a tail: µ) – 10 to the negative 6th, one-millionth

Nano (n) – 10 to the negative 9th, one billionth

Pico (p) – 10 to the negative 12th, one trillionth

Femto (f) – 10 to the negative 15th, one quadrillionth

Atto (a) – 10 to the negative 18th, one-quintillionth

Zepto (z)- 1- the negative 21st, one-sextillionth

Yocto (y) – 1 to the negative 24th, one-septillionth

Think you’re getting it? Hmm, I did too. Not to mention I’d added some good Scrabble words. But then, I dug in further and confirmed my suspicion that the same words weren’t meaning exactly the same number.

Communications, electronics, and physics measurements like frequency, physical mass, power, energy, electrical voltage, and electrical current all use that nice power of 10s standards.

But – and here’s where it really makes your head spin – when it comes to data storage, like on your hard drive, everything is based on a binary system: on/off. And so measurement is based not on that power of 10, but on the power of 2. Using the same prefixes, of course.

The tiniest element is the bit. Every bit is either on or off, yes or no. Bits get represented by a lowercase b.

Bits are grouped into bytes, containing 8 bits. Bytes get represented by an uppercase B.

Now let’s do the math(!)  One kilobyte, 1KB, means 2 to the 10th, or 1,024 bytes. Which is kinda’ close to 1000.

One megabyte, 1MB, represents 2 to the 20th or 1,048,576 bytes, which is kinda’ close to 1 million.

One gigabyte, or two to the 30th, equals 1,073,741,824 bytes. Which is about one billion.

(Yes, yes, to answer those purists, this does mean that my 150 GB of data really means 1,061,061,273,600 bits of data. Which moves through a 1 gig connection in 1061.-612736 seconds … or 17.68 minutes.  However, when the necessary transmission overhead gets factored back in, that original 20 minutes still remains a pretty good rule of thumb!)

However, for me the overarching mind-bender isn’t the notation, but the sheer scale that we work with in our digital world. For storage and speed, we reach more zeros than we can comprehend. For drilling down to cell and atomic particles we remove more zeros than we knew existed.

I sometimes feel like I’m gazing into two infinity mirrors, whose reflections grow endlessly larger one way and endlessly smaller the other. Maybe we are all Alice in Wonderland.

Yet as the prefixes appear day after day, they become normalized. We stop seeing the zeros and we substitute our own mental images.

The literal one-billionth of nano may be incomprehensible … but we get the idea of smaller than small. Gigs are bigs, but teras and petas loom even larger. We drop the zeros and just place them on a sliding scale.

In the end, we do need words to count and measure … but to use the things that get counted and measured, we just need a sense of the relative relationships.

So don’t make yourself crazy with base 10 and base 2, unless you happen to be a mathematician, scientist, or just a stickler for accuracy.

For most of us mere mortals, it’s enough take a look at what we use from time to time, to see its size, and check that we’ve enough space and speed to manage it … and to know without fear that we can handle both the petas and the femtos of the future.

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