Nothing weighs nothing, even data. We don’t think about this, but — in addition to our phones and computers — we carry information around every day. The reason we don’t think of our iPhone photo library as weighing us down isn’t that it’s weightless, just that it’s light. So what would it take for us to notice the information we keep in our front pocket? How much data would a device need to store for us, as humans, to be able to feel the difference?

The first thing we need to consider is the nature of data’s mass. All data is binary, composed of 1s and 0s. When you store data in flash memory, you’re changing 1s to 0s and 0s to 1s. As John Kubiatowicz, professor of computer science at the University of California, Berkeley, explains, flash memory functions by either holding electrons in place or not. When electrons are held in place, they become more energetic. And that’s where Einstein comes in: As energy increases, so too does mass.

Now, the data in a single, simple email — if said email is only about 50 kb, and so 8 billion electrons — is said to weigh two ten thousandths of a quadrillionth of an ounce. Old, hopelessly outdated estimates of how much data is on the internet place the figure around 5 million terabytes, and the resultant weight of the internet at 0.2 millionths of an ounce. (For our purposes, we don’t need the actual size of the internet; if we may assume that 5 million TB is indeed equal to .0000002 ounces, then we can go from there.)

But understanding the weight of data is only half the battle here. We also need to figure out what weight discrepancies humans can discern. If I’m holding an eight ball and a cue ball and I’m particularly in tune with my senses, I might be able to tell that the cue weighs half an ounce more than the eight ball. Or so thought Ernst Heinrich Weber, who’s responsible for Weber’s law, which states that humans should be able to detect a difference in weight between two objects down to 5 percent of one object’s weight. In other words, if you’re holding an iPhone 6 in your left hand and an iPhone 6 along with a few small coins in your right hand, you should be able to detect a difference. (An iPhone 6 weighs in at 4.55 ounces, which is equivalent to 129 grams. Five percent of 129 grams is 6.45 grams, or about the weight of a few small coins.)

Now, using our data-to-weight equivalencies, we need to figure out how much data weighs 6.45 grams. Luckily, iPhones use flash memory, so the energized electrons in data storage ought to equate to more mass. (Unlike more traditional, magnetic hard drives.)

Let’s begin. The presumed weight of the internet, 0.2 millionths of an ounce, is equal to .0000056699046 grams. If we divide 6.45 grams by that miniscule amount, we get 1,137,585.3. That’s how many times the presumed weight of the internet goes into the desired 6.45 grams. Switching back over to the data side of the equation, we can multiply the presumed size of the internet — 5 trillion terabytes — by the same magnitude: 1,137,585.3.

Which gives us — drumroll, please — 5,687,926,000,000,000,000 terabytes. Or, in a more comprehensible form: 5.7 quintillion terabytes. That number is itself the same as 5.7 quadrillion petabytes, which is the same as 5.7 trillion exabytes, which is the same as 5.7 billion zettabytes, which is the same as 5.7 million yottabytes. (This isn’t me channeling Vonnegut — these are real terms.)

Here’s some reference for you. In The Singularity Is Near, Ray Kurzweil estimated that a human’s functional memory was 1.25 terabytes. Online Computer Library Center Chief Scientist Thom Hickey estimated in 2005 that the Library of Congress’s entire collection was 10 terabytes. In 2014, Facebook’s data warehouse could hold 300 petabytes of information.

So, then. What’ve we learned? To change the weight of an iPhone, we’d need more than twice as much data as is stored in every hard drive on Earth. When people wonder why every process needs to go digital, tell them that. We don’t have to carry the weight of information any longer. Well, we don’t need to feel it anyway.

Photos via Rethought/Flickr