[paganel]

Not the OP, and he/she mentioned "physical observations" so maybe he/she was only referencing hard sciences like Chemistry or, indeed, Physics, but I am of the same opinion to him/her when it comes to the gap between mathematics and social (for a lack of better word) sciences, which social sciences (and the underlying social component behind them, i.e., us, humans) play a very important role in, well, how the Universe runs, or is seen as running.

In other words, mathematics is very bad at modeling and explaining human behavior, be it in economics, history or even political science (even though one of the best political scientists that ever was, Hobbes, wrote his most famous book by trying to imitate Euclid's "Elements"). This is starting to become particularly important now because we try to build some "AI" functionalities that should imitate humans (and even surpass them) based mostly on mathematics (and some underlying data), but it is my opinion that because of this "gap" between how humans are and what mathematics can tell us about how humans are and behave, it is my opinion I say that those "AI" functionalities will never "become" human enough. Stanislaw Lem's "The Cyberiad" does a much better job compared to me at showing this gap between humans and "machines built on mathematics".

[taoistextremist]

In my opinion this is less of a gap and more of a misapplication of what mathematics is. Mathematics isn't a tool for describing human behavior, though social sciences may use results of mathematics (and I would argue to much greater accuracy than they'd otherwise have) and the fact that mathematics can't describe human behavior is not due to gaps (results of mathematics are consistent with reality, as far as I'm concerned) but because we aren't answering questions in the domain of mathematics.

The physical observations, though, I'm still waiting on an answer from OP about that. It's fairly weasely to say something like that with no example.

[paganel]

> but because we aren't answering questions in the domain of mathematics.

And then one can ask “what is the domain of mathematics?” or even “does mathematics have a domain?”, questions which lead us into a “philosophy of science” discussion with no end in sight.

I’ve felt for quite some time that the fact that mathematics can model/answer some aspects related to physical reality is just a happy coincidence at best, which we shouldn’t insist too much upon, for fear of then risking to miss the forest because of some trees that absorb our view, like “isn’t this mathematical equation perfectly describing how galaxies interact billions of light-years away?” might obstruct from us the very dire truth that there is no math to describe what will be my cat’s movings around the room in the next 5 minutes (and it’s not for lack of trying, just look at the billions of dollars invested by hedge-funds into mathematics so that they could “model”/predict the future; I don’t think they’re scientifically anywhere close to that).

[taoistextremist]

> And then one can ask “what is the domain of mathematics?” or even “does mathematics have a domain?”, questions which lead us into a “philosophy of science” discussion with no end in sight.

I think these are useful conversations even if we can't foresee them ending. It's what's helped us move physics beyond stuff like Newtonian mechanics where we expect things to line up with these nice equations, and apply math in a more appropriate fashion to our observations. i.e. We treat math as something we apply to our observations, and reconsider models as we run into problems, as opposed to demanding our observations line up with our initial model.

[Torwald]

> Can you elaborate on how Hobbes tried to imitate Euclid's "Elements?"

Please!

[Torwald]

Can you elaborate on how Hobbes tried to imitate Euclid's "Elements?"