I admittedly did not finish reading the paper, but I find the idea not persuasive at all. Maybe the paper addresses my objections past the point where I starte

I admittedly did not finish reading the paper, but I find the idea not persuasive at all. Maybe the paper addresses my objections past the point where I started just skimming it, but I did not notice anything like that. There seems to be a huge asymmetry between our universe or reality or whatever you want to call it on the one hand and mathematics on the other hand; the set - or is it a class? - of all mathematical structures seems to be enormously richer than reality. On the one hand it seems quite unproblematic to think that there is a set of mathematical structures that are useful to describe reality, on the other hand it seems quite problematic that all mathematical structures are embodied in reality. In what sense does a 79 dimensional vector space over GF(43) exist? Sure, you can take a huge pile of stones, arrange them in groups forming sets of stones, combine those sets to build natural numbers, and work your way through layers upon layers of abstraction to end up with an arrangement of stones that, under the right interpretation, represents whatever mathematical structure you had in mind. But that seems a pretty wired way to justify that a 79 dimensional vector space over GF(43) really exists, I would be much more inclined to say that you managed to emulate it with what reality offers you. I also would bet that there are mathematical structures that are impossible to emulate in this sense in our universe. And if the position is that there is another universe separate from our universe which is a 79 dimensional vector space over GF(43) or which allows emulating it in a more meaningful way than can be done in our universe, that seems not very appealing either. You are postulating a rather strange collection of universes without any obvious benefit. And it seems like you also get all the problems of Platonism - how do we know about and work with this vector space if it is in a separate universe. As a lesser point I find the idea repelling because it seems incredibly convoluted, at least in the way presented here. For a - at least at first glimpse - simple idea like all mathematical objects exist, there are a lot of technicalities and complications just to state what you really mean without becoming inconsistent and failing right from the start. So yes, I am really unable to see any merits here. I probably also did not do a good job explaining my position, I don't like this comment at all. But I hope anyone reading this will at least be able to get an idea of what I mean and want to say even if the comment is rather rough and not without flaws.