Well, Yes, that's what the debate is about. Just to make this clear (in case someone else reads this thread), this is an ongoing debate in the philosophy of mathematics and not just something people muse about on Quora and Stackexchange. What's important for me is that the notion of physical realizability is understood correctly. It does not pertain to philosophical arguments or common sense, it really means that something can be present as a quantity in nature (actuality) without violating existing physical laws. When someone argues that a mathematical structure or entity cannot be physically realized, the argument must concretely show that the realization would violate some currently well-confirmed laws of nature or fundamental physical principles.
There is no disagreement with you. I just wanted to clarify that (hope you don't mind). I didn't have just any arguments against irrational numbers in mind but a specific type of arguments.
Your idea of physical realizability seems to me to be questionable. Because there are many abstractions in a chain starting from mental concept to a final physical object where each link is necessary to get to the final result (eg. a modern computer). Do not get caught up in metaphysical arguments of philosophers on mathematics which are often just playing with words rather than substance (eg. my link above to God created the irrational numbers by a PhD in Philosophy).
Finally to conclude this thread; i highly recommend reading The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner if you haven't already done so.
> your idea of physical realizability seems to me to be questionable.
I made it abundantly clear that is not my idea but an ongoing discussion in the philosophy of mathematics. You're telling me to not get caught in philosophical arguments and in the very sentence before that presuppose the idea that mathematics is a mental construction, which is just one out of many philosophical views in that area. By the way, I'm interested in philosophical issues because I am a philosopher. Just because you don't like these issues or find them "questionable" doesn't mean anything. Some of my colleagues defend an Anti-Fregean formal foundation of mathematics to which physical realizability seems to pose a huge problem. If they want to get their papers published, they'll have to address the issue.
I'm aware of Wigner's paper, it's a well-known classic. Finally, to conclude this thread from my perspective, while I'm personally not interested in the (broadly conceived) metaphysics of mathematics and am happy to leave these issues to mathematicians interested in them, the way you're just presupposing that mathematical objects are mere mental constructions cannot really count as engaging with the problems yet. If you read what I wrote above again, you'll realize that I presented an argument why irrational numbers cannot be abstractions, yet you keep talking about abstractions. In a nutshell, it's not that simple.
There is no disagreement with you. I just wanted to clarify that (hope you don't mind). I didn't have just any arguments against irrational numbers in mind but a specific type of arguments.