That is the point of my comparison to the Reals. No accountant or mechanical engineer or architect need ever read, let alone understand, any proofs that the Reals exist or the fundamental construction of arithmetic. I know several highly successful economists who don't know the construction of statistics, anymore than knowing that the proofs exist and could be found somewhere, if it ever really mattered (it doesn't). As a developer, you are not a theoretical mathematician. You use math.
Game development is not fundamentally more hard than any other field of applied engineering or mathematics. It isn't theoretical mathematics. You just use the math.
Needing to "understand" root construction before "being able to use" is just procrastination.
> Needing to "understand" root construction before "being able to use" is just procrastination.
since I feel personally attacked by that statement (I say in jest), it's more charitably viewed as a risky investment. Understanding now might help you use it more efficiently later.
3D Rotations are traditionally very tricky to represent in a computer! It's only in "modern" times that basically everyone has settled down on quaternions as the best parameterization. I think the comparison to anything about real numbers misses the point. It's not about rotors themselves, or real numbers themselves, it's about how they model something we care about. Money isn't a real number, but we model a balance in an account using one. And an accountant definitely needs to understand operations such as "debiting", "crediting", "accruing interest". So they need to understand addition, negative numbers, and multiplication. But that's just because of the choice of the model.
funny enough, it seems like lots of accounting existed a while before negative numbers were obvious, so there are all sorts of to-me funny ways of representing negative numbers, or subtraction (I don't have any clear evidence to back this up). Everyone was doing accounting just fine before, but really it just feels more obviously elegant to use a negative number to represent a deficit.
You "can" be a "good" engineer while thinking the Earth is flat. (Unless you're working on space-related projects of course.)
You "can" be a "good" scientist without knowing anything about epistemology, Popper, Kuhn...
(But can you, really, be a good one ?)
(Also IMHO most of today's economists are just charlatans akin to the astrologers of old, misusing math because math gets your more respect, and it's probably related...)
That's fine if you're building something that's already been made. Games don't do that, when you push the boundaries you need to know how your math works. You won't get more performance than the competition without understanding the tools you are using.
It didn't need it. That was just the solution the devs created. They could have done it with 32-bit floats, or hell, 32-bit integers, if they wanted, given the right representation. But they chose 64-bit floats to solve the problem, the problem did not choose 64-bit floats.
It really does need it. 32 bit positioning breaks down fairly quickly on planet scale. Shifting the world origin is not a streamlined process and doing it frequently for each client in a large multiplayer game is nearly prohibitive. You could invest the effort into making world shifting and planet scale work in 32 bit, and the lesser of the two evils would still be implementing 64bit positioning. You gain so much and lose so little for having done it.
Game development is not fundamentally more hard than any other field of applied engineering or mathematics. It isn't theoretical mathematics. You just use the math.
Needing to "understand" root construction before "being able to use" is just procrastination.