I read once again the claim to a radical difference between computers and empirical reality, because the former is discrete (discontinuous) and the latter is not. This claim states that computations are digital, reality analogous, and concludes that big data will never fully account for social life. This argument is bullshit.
First of all, let me acknowledge that there might be radical differences between computers and the empirical world, and the computations might never be able to grasp certains things. But I call bullshit on the argument that concludes it only from the discreteness of the digital.
To make it easier to understand, here is an example of the argument.
When one phenomenon either appears in the form of numbers or is converted in quantitative indicators, the continuity disappears since calculation requires discretisation, even though it looks blurred in fuzzy logic algorithms, for instance, or highly granular in Leibniz’s infinitesimal calculus. For that reason, classification is as critical in computer science as categorisation is in social science. It introduces discretisation into a living experience, that is, of course, continuous and analogous.D. Boullier, in Médialab stories: How to align actor network theory and digital methods
I have two points against the argument. The first is quite short, the second even shorter.
Firstly, arguments stating that something is impossible are suspiciously imprudent. What can or cannot non-human beings do? Since centuries, our science (and societies) have proven chronically overconfident on that matter. We believed that animals could not think, or at least not like us, that we had a radical difference like a soul or something. Until we found out that cats can dream, that crows can solve puzzles as well as five-year-olds, and that dolphins call themselves by unique names. Now it is the computer’s turn. Didn’t we just realize that computers can hallucinate? But surely, there must be other things they cannot do.
The argument is weak because it is generic. Maybe certain computers cannot do certain things for some reasons. This could constitute a good point, if we know which computers cannot do which things and why. If the argument is specific. But in the classic “computers are discrete” argument, we do not know what exactly they cannot do. Because of course, as soon as you state something specific, a computer scientist pops up with a counterexample.
The argument is also weak because it relies on a belief. The existence of the human soul is a belief, and a reckless ground for the inexistence of animal intelligence. The radical difference between the continuous and the discontinuous is a belief. It is a belief until you can properly unpack it, which is harder than it sounds (spoiler: Leibniz and Turing are clichés of no help). Calling unspecifically to the powers of mathematics is not different from calling to gods, an argument of authority. Continuity is far from a triviality. It is a highly abstract concept, that we cannot distinguish from discontinuity in our everyday life, with a complicated history and multiple, problematic mathematical definitions.
Our empirical reality is not continuous. Or at least, we don’t know for sure. You might think that the laws of physics have to be continuous, that the physical equations could not work on the basis of a discrete space-time. You would be wrong. We already know it’s a valid possibility. Knowing if space-time is discrete or continuous is an empirical question, and it is yet unsettled.
It is usually assumed that space-time is a continuum. This assumption is not required by Lorentz invariance.H. Snyder in Quantized Space-Time, 1946
The point of this presentation is not to convince readers that space-time really is discrete but rather to convince them that we do not yet know whether or not it is.P. Forrest in Is Space-Time Discrete or Continuous? — An Empirical Question, 1995
Maybe empirical reality is continuous after all. But so far, this world’s best physicists cannot tell. At least we can know one thing from sure: we are profoundly inapt at telling the difference. We cannot tell the difference between what discrete systems and continuous systems can do. So if there is a radical difference between computers and living experience, it is not that one.