Friday, 21 December 2012

A Universe of Data is Not Enough

Colin Picker

Humans have always recorded information (or data). From early cave drawings to Edison’s phonograph cylinders to the photos and music on I-phones, data recordation and storage seems to be a human attribute. But today we live in furious period of data storage. That data today includes pictures, video, music, documents and records of almost every type of human activity and thought (though, a very large percentage is, as has always been the case, pornographic – there are even pornographic cave paintings).

Today that information is increasingly stored at the electronic level. In the future we can expect almost all data to be stored electronically, and even sub-atomically (utilising the smallest constituent parts of the universe). While occasionally we record over past recordings, we more and more produce data that will be archived, eventually producing archives that will be able to last forever—or at least until the end of the universe (assuming there will be such an end, more on that below). As our technological needs increase, more and more data is needed, more and more is therefore going to be stored. But, is there an upper limit to the amount of data that can be stored? I don’t mean the limit on a hard drive, or a very large data storage array. I wonder whether there is a theoretical limit imposed by the very nature of the universe.

I first started to think about such an upper limit when considering the non-existence of infinity (more on that later, though admittedly an unusual thought experiment for a law academic). In any event, my ruminations took me to a place and time where we, humanity, had already moved to store our data at the quantum level, utilising the smallest sub-atomic components to represent the zeros and ones of data (assuming the correctness of quantum limitations). One quark, or whatever will at that time be the smallest unit, would represent one piece of data; another quark, or its specific absence (a non-quark), would represent another piece of data. But, if the universe is finite in size and composition, then there are a finite number of quarks available for use from the existing matter of the universe—including that used in the memory portion of our brains and that which can be converted from the various forms of energy in the universe. There is therefore a finite amount of data that can be stored on that finite number of quarks. True, utilization of that large capacity is a long way off, but it is, critically, a finite long way off. Furthermore, once imagined, it then exists—and that limitation has some very significant metaphysical consequences.

One consequence ties in with my original concern about infinity. One way to consider numbers is that they only exist if they can be represented (in our memory, on paper, as data, as cave drawings, etc). But if there is a data limit on the total representations of numbers, then there is a limit on those numbers. In other words, there is a finite number of numbers that can be expressed, and hence that can exist, a number limited by the data storage capacity of the universe. True, it is a large number, but it is a finitely large number. In other words: not infinite.

But back to the data storage issue. Perhaps the most important consequence is that eventually, when we do hit that data storage capacity, all new knowledge has to displace some of the previously recorded knowledge. Thus, while the composition of that knowledge may change, it can never exceed the total finite storage space. Once replaced, the data will then be lost forever (assuming no duplication, which we should assume, for until we have eliminated all excess duplications there really is no storage problem). While much that will be lost at first will be inane, eventually all the inane and frivolous pieces of data and knowledge will have been deleted to make way for more serious and important information. What happens then? We will need to be careful about the creation of new data (including new memories), for it will then require us to make hard choices about what other data must be erased to make room for the new data.

So, every time you download an “app”, create a new document, take a photo on your camera and then download them to your hard drive or into some data cloud or other, you are hastening the day when we run out of data, and hence limit our collective collection of new knowledge. Maybe, like fossil fuel conservation, we need to start thinking about data conservation – not for us, but for our children. A good start would be to delete this comment from your computer and then to forget all about it.


  1. Your entry is very thoughtful -- I was delighted reading it! A few comments from my side:
    - As far as I know, it is currently not known whether the universe is finite or infinite (in mass and extent)
    - Numbers do not "exist" in an ordinary manner; they are objects of thought; you may see them as Platonic objects, if you want. We might not be able to write down infinitely many numbers, but that does not mean that they are non-existent. For example, pi has an infinite number of decimals, so we can never write it down; but we would have a hard time if, thus, pi does not exist!
    - Finally, you might be right that a finite universe with finite mass can only store a finite amount of data. That's actually what is a consequence of Landauer's principle from the Sixties, which as far as I'm informed has been experimentally verified last year or so. At the same time, the universe can already be seen as a storage device, which is overwritten at each and every time instant. The point in space my grandfather occupied 80 years ago is now occupied by something or someone else. If we want to preserve such information, we need to create a duplicate of the original information, compressed to only its meaningful and important part.

    What is meaningful and important will change over time, as will the accuracy of our sensors increase. We will be ABLE to create more information, but we might DECIDE NOT TO (see the ever-increasing resolution of digital cameras, e.g.: We might come to a point where we stop increasing the resolution, for the sake of storage capacity and since more "hard" information is useless to us). With this in mind, I would even say that for as long as humankind survives on this planet, we will not be able to create more information than our storage devices can handle. But that's just a guess, of course...

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