The Problem with Infinity

March 03 2013

Historically speaking, making something meant it was tangible, and having more resources, such as time, money, and natural resources, meant more physical objects could be created. With physical items, there’s always a one-to-one trade: creating things demands resources, and creating lots of things demands lots of resources.

After physical objects are made, the one-to-one trade-off carries over into the business world when some form of currency is accepted for the object. You give me this, and I give you that. Simple.

The written word, whether by printing press or by human hand, has been around for millennia. When Gutenberg invented the printing press in 1450s, he didn’t change the fundamental limitations of physics, however, he did increase the efficiency of making a large number of physical items. More books in less time. After selling the first batch of books, more books need to be made if I want to sell more.

These days, enormous libraries contain an unfathomable number of pages, covers, and letters holding vast amounts of information and stories. And yet, there is a limit to how many physical books can exist. Between the resources it takes to create books and the physical space it takes to store books, we are still faced with limits.

Infinity (Close Enough)

In the digital world, space is cheap and abundant. While the available physical space on Earth is decreasing, the space in the digital world seems to be expanding at break-neck speeds. Whether we’re talking about the Cloud, or just personal computers and mobile devices, these all have a vast space incomparable to physical space in their dimensions. The digital world may as well be infinite.

Our brains find the concept of infinity difficult to understand, and yet we’re creating products which live solely in that world. We’re trying to use the same one-to-one model we use with physical items to solve the problems we’re encountering. A you give me this, I give you that” thought-process doesn’t quite work when our products aren’t limited by resources in the same way as physical items. We should approach the problem with a different model altogether with entirely different variables.

One Copy to Rule Them All

Back to books for a moment. If our magnificent libraries decided to completely replace their entire collection with digital items, they could dramatically reduce the physical space they’re currently occupying. If they convert all their paper materials into .ePub, .mobi, and PDF files and place them onto servers, you no longer need many amenities physical libraries need. 

In fact, digital libraries already exist. You don’t need to drive there, you don’t need to open a door to walk in, and most importantly, there is no longer the physical limitation of one copy in existence.

When you go to a physical library and check out a book, you now have that book. Although the content may be the same, the book which you’re holding is unique; to break it down to an unnecessary level, each copy of a book has its own set of molecules unique to it. 

Before the librarian will allow you take the book home, you must give a promise to return the book. There’s our one-to-one model at work. I give you this; you give me that.

However when we introduce infinity into the mix, we can check out the book, leave, and the next person in line right behind us can check out the same book. And the next person. And the next person. All the way into infinity, and you’ll never run out of any of that book. In fact, there are no molecules” at all with digital items, which means they are the exact same item. Clones, if you will. And each time another clone is created and sold, the benefit to the merchant increases exponentially. Our work involved to create the item stays the same, while we continue to generate income. It’s as close to money growing on trees as we can get.

There is a Trade, Not One-to-One Though

There is a caveat. Since the electronic universe exists inside this physical universe, we still have to deal with physics. When a book is checked out of a physical library, remember there is more happening than simply a book getting checked out. The door opens when patrons walk in and out causing the heating and cooling system to work a little bit harder; the librarian may have to stop doing one important task in order to check out your book; after you return the book, the shelver has to spend time to put the book back on the shelf in the right location.

These little happenings in a physical library are far less in a digital one, but they still exist. Servers have to be cooled, and when 10,000 people download a book in a short amount of time, the servers will work harder and heat up a little more, causing the cooling system to work harder.

They can’t lend any more books than they have, but in our digital world, we’re not limited by the number of books. So, what is the magic number of books available to check out?

I don’t think there is a single magic number. The one-to-one trade we’re using for physical items requires a magic number of one. You give me this, and I give you that. However, our digital universe requires a more complicated thought process; it’s no longer a one-to-one trade.


For example, Pinboard, a paid bookmarking service, uses a formula to inform the cost to join: the number of users multiplied by $0.001. So the earlier you join, the cheaper it is. Although the cost to run Pinboard will increase with the number of users, Maciej has implemented a system to handle the scaling.

If a million people download an ebook in an hour, the server’s cost goes up. Maybe the price during high traffic times should go up as well. Maybe if you’re a patient and frugal shopper, you’re willing to wait until another time to make the purchase to get a better deal and more value. In the case of the library (where you don’t have to purchase anything), maybe there are a limited number of ebooks available for download at high peak times, rather than the infinite number of ebooks ready for download at low traffic times.

Whatever formula or algorithm we use, we should not use the same simple pricing models for digital items as we’ve been using with physical items since the invention of trade. Our technologies to create things have changed dramatically, and our economics for digital storefronts should try to keep up.