makes you think I’m nothing more than a dumb internet troll with no meaningful opinions or thoughts worth sharing or discussing like adults
Holy fuck. I called you one out of all of those and it was the one who isn’t even a pejorative. I thought you were joking, because your comment sounded like you were joking. There’s really no deeper meaning to that.
No stopping to hunt for operators and symbols
That’s what I’m saying, using parentheses won’t make the operators and symbols go away. You’ll still have to stop and hunt for them, you’re just adding parentheses in addition to that.
because it isolates the problem into distinct, physically easier to read sections
That’s only true for simple expressions, though. Once you try to type something more complicated, parentheses get very confusing very fast. Anyone who’s ever had WolframAlpha refuse to evaluate an expression because of a missing parentheses knows what I mean.
As for your examples,
1+2+3×4+5+6
1+2+3÷4+5+6
In these, the version with parentheses is different from the one without because you want the operations to be done in a certain order that isn’t indicated anywhere.
1+2×3÷4*5-6
And in this one, you’re mixing several operators with equal priority on the same line while not indicating which one you want to be done first.
What I’m getting at is that you’ve provided the exact examples where you have to use parentheses so it makes no sense to ask which one is clearer because only one version is correctly written. It would be like me asking you if (24)+1 is clearer than 2*4+1 and concluding parentheses are confusing because you didn’t divine I wasn’t typing twenty four but instead wanted you to multiply the 2 and 4.
Finally, the order of operations isn’t just some arbitrary convention, it might seem that way when we limit ourselves to only numbers but its intuitiveness really shows in algebra. Take the polynomial:
2x²+1
Even if you’ve never heard of the order of operations, there’s absolutely zero confusion about which order you’re meant to do the operations. It would take a madman to decide that “+1” is part of the exponent or that you’re supposed to add the 1 to the x² and then multiply it by 2.
In this case, adding parentheses here would turn it into
2(x(²))+1
which is unnecessary and it gets annoying very fast. For example:
(2(x))+(3(x(²)))+(5(x(³)))+(8(x(⁴)))
vs
2x+3x²+5x³+8x⁴
You might say that’s not fair because this expression clearly needs no parentheses so I just added them to make it seem more confusing and you’d be right but that’s the point: there has to be an arbitrary line where we decide parentheses are no longer necessary and that’s the order of operations. We settled on that because that’s what works in algebra. When it comes to what’s intuitive in arithmetic, left to right is obviously the best (for westerners). Unfortunately for arithmetic, we’ve decided that intuitiveness in algebra is more important than intuitiveness in arithmetic.
Holy fuck. I called you one out of all of those and it was the one who isn’t even a pejorative. I thought you were joking, because your comment sounded like you were joking. There’s really no deeper meaning to that.
That’s what I’m saying, using parentheses won’t make the operators and symbols go away. You’ll still have to stop and hunt for them, you’re just adding parentheses in addition to that.
That’s only true for simple expressions, though. Once you try to type something more complicated, parentheses get very confusing very fast. Anyone who’s ever had WolframAlpha refuse to evaluate an expression because of a missing parentheses knows what I mean.
As for your examples,
In these, the version with parentheses is different from the one without because you want the operations to be done in a certain order that isn’t indicated anywhere.
And in this one, you’re mixing several operators with equal priority on the same line while not indicating which one you want to be done first.
What I’m getting at is that you’ve provided the exact examples where you have to use parentheses so it makes no sense to ask which one is clearer because only one version is correctly written. It would be like me asking you if (24)+1 is clearer than 2*4+1 and concluding parentheses are confusing because you didn’t divine I wasn’t typing twenty four but instead wanted you to multiply the 2 and 4.
Finally, the order of operations isn’t just some arbitrary convention, it might seem that way when we limit ourselves to only numbers but its intuitiveness really shows in algebra. Take the polynomial:
2x²+1
Even if you’ve never heard of the order of operations, there’s absolutely zero confusion about which order you’re meant to do the operations. It would take a madman to decide that “+1” is part of the exponent or that you’re supposed to add the 1 to the x² and then multiply it by 2.
In this case, adding parentheses here would turn it into
2(x(²))+1
which is unnecessary and it gets annoying very fast. For example:
(2(x))+(3(x(²)))+(5(x(³)))+(8(x(⁴)))
vs
2x+3x²+5x³+8x⁴
You might say that’s not fair because this expression clearly needs no parentheses so I just added them to make it seem more confusing and you’d be right but that’s the point: there has to be an arbitrary line where we decide parentheses are no longer necessary and that’s the order of operations. We settled on that because that’s what works in algebra. When it comes to what’s intuitive in arithmetic, left to right is obviously the best (for westerners). Unfortunately for arithmetic, we’ve decided that intuitiveness in algebra is more important than intuitiveness in arithmetic.