A cool mathematician gives a little talk here about his position that data can never truly represent reality.
I'm not really sold on this. Two objections come to mind:
1) First, the "can all this really be represented by numbers?" argument is basically the "argument from incredulity", and has an in-built emotional appeal. It's also nearly identical to a classic argument about why "souls" exists: "are
you really just physical matter or is there something more that mere matter?" is basically the same as saying "numbers cannot represent the ineffable nature of consciousness". "Mere matter" in one case, "mere numbers" in the other case. In both cases there's an emotional value judgement about what "mere" physical matter or "mere" numbers can do.
2) Second, his argument is that two numbers cannot truly represent a vector, since it would be ambiguous. However, if you specify
six numbers instead of two, then you can fully represent a 2D vector along with the coordinate system that it's embedded in. So, that example is misleading about "what numbers can't do" because he specified a situation where merely
omitting some of the salient numbers caused an ambiguity. So that example fails to be convincing. He then says "numbers cannot represent this, so how can they represent a human being" which is back to the "argument from incredulity" and appeal to emotion, along with being a flawed scenario in itself. In fact, 6 numbers can represent
any 2D vector in a coordinate-agnostic format, but there are in fact an infinite number of possible representations of the same vector. That makes numbers more expressive, not less expressive: in other words, the same set of numbers can carry multiple levels of context along with them, which means you have explicit meaning and implicit meaning, an infinite variety of ways to convey the
same information with numbers, but each way of saying it carries different meta-knowledge about contextualization, that you can choose to decode or ignore.