The limitations of technology

In this age of technology, this era of digital revolutions, the question becomes more and more relevant how far technology can get us and what its limitations are. Surprisingly enough, already one century ago, even before the first computers existed, these limits have been settled. These had been found by Kurt Gödel and Alan Turing. They proved that so-called “self-reference” was always inevitably leading to logical paradoxes destroying the rigorous foundations of both mathematics and computer science. Self-reference is the ability to completely describe yourself - stepping back and reflect on yourself.

Their proofs are ingenious, both simple on the high level as complicated on the detailed level. But let’s take some time to step back and reflect ourselves; bear with me and try the following thought-experiment to better understand what Gödel and Turing were saying.

Suppose I would offer you the perfect VR device, that is one where you cannot not tell the difference between the "real" reality and the virtual reality. Would you dare to wear it? The reason for asking, is how to be sure you can put the device off again? Because the device could create the perfect illusion suggesting that you are actually taking it off, while in fact you are tricked by it in only thinking that you are taking it off, but you are not. So would you dare to put it on?

As a matter of fact, how can you even be sure that you are not wearing it right now, and are already trapped inside a Matrix without knowing it? Or will there always be, as in the Matrix-movie, these glitches in the system; these déjà vu's that you've been in the same situation before as you are now? Notice, by the way, that a déjà vu is yet another example of self-referencing.

Did you already decide (not) to wear it? In the end it all boils down in being able to distinguish a virtual reality from the “real” reality; whether our reality can be computed by technological means such as VR and AI, or not. In the one case, our reality is computable - the perfect VR exists - and we will never be able to decide in which reality we are living. In the other case, our reality is beyond computability - the perfect VR does not exist - and we can always decide which reality is which. So computer technology is limited: it either leads to undecidability or accepting that not everything is computable. This is what Turing has proven.

There is a beautiful mathematical equivalent of this, which has been proven by Gödel (before Turing). The concept of self-reference inspired him to proof that there are mathematical truths beyond provability, that there are intuitions and understanding beyond mere reasoning. When you strip down reasoning from all its softer arguments and intuitions, he proved that mathematics will be either inconsistent or incomplete.

Turing was the first to describe the workings of what a computer should be and what its limitations are - that there are always undecidable problems for such computers. It inspired Roger Penrose to rephrase Gödel’s so-called Incompleteness theorems, saying that Artificial Intelligence, that is machines, will never be able to think as humans do. To which Gödel added the more precise statement that either we humans are no machines or that we are deluded machines thinking we are not.

It is the Christmas time of the year. Traditionally the time of the year for reflection; to be with our loved ones and commemorate the ones we lost - family, friends, colleagues. Perhaps being able to reflect, makes the difference between humans and machines: to have intuitions and inspiration, going beyond technology. So I'm not offering you the perfect VR device this Christmas, but only my best wishes: a Merry Christmas and a Happy New Year. And lots of inspiration!