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.