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<3 (media.piefed.social)
submitted 1 year ago by to c/mathmemes@lemmy.blahaj.zone
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[+] -18 points 1 year ago (12 children)

Imma be weird and argue that the answer actually should be 4.

Dear Aunt Sally is great or whatever, but syntax also fuckin matters. We can all probably agree that the faster, more intuitive answer is obviously 4. Most of those in the western world (meme's largest audience) read left-to-right and there is nothing the delineate that division must actually come before inverse addition until one has carefully examined the entire the problem (which you should definitely be doing, dumb-dumb) and slapped on another layer of thinking (inefficient waste of time when doing quick mafs). Use the damn parenthesis, ffs!

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  • [–] 8 points 1 year ago (4 children)

    Using parentheses where a few simple rules will do seems awfully inefficient. Both to write and to read.

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  • [–] 2 points 1 year ago

    I find it far more efficient to parse. I also put superfluous parenthesis in my code where I feel it helps readability.

    It's something to judge on a per-case basis, it'd also work very well to use whitespace (i.e. 25 - 5/5 instead of 25 - 5 / 5). Of course you don't want to parenthesis everything but it can help a lot.

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  • [–] -3 points 1 year ago (1 child)

    Simple rules are only simple if they are intuitive and consistently applicable. Otherwise, they are nothing more than yet another thing to remember and think about, yet another source of error, and yet another possible point of confusion. With enough time/ effort, one can brute force the intuitiveness, but that doesn't automatically make the rule good or universally useful.

    As a math teacher, I can assure you that not everyone has the same level of understanding or knowledge when it comes to order of operations. Some people struggle to remember the specific order, and mnemonics are worthless. Others struggle to read or visually process problems written with unclear or inconsistent symbology. Hell, most people don't even learn exactly the same fucking rules. Tell me, where is the simplicity in all of that?

    When I teach order of operations, the glass eyes and exasperated sighs of frustration come out. But when I teach just the parenthesis and exponent stuff, lightbulbs and understanding. Suddenly, people "too dumb" to do 2+2 are doing algebra and getting excited about math for the first time ever. Some of this is certainly a failing of our collective education system, but we can't just forget that everyone has their own flavor of learning disability, neuro-diversity, and life experience. Simple rules quickly fail to be simple in the face of complex people.

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  • [–] 4 points 1 year ago (6 children)

    Following your logic,

    2*7²+5*3³ becomes (2(7²))+(5(3³))

    Talk about inefficient waste of time.

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  • [–] 3 points 1 year ago (5 children)

    I find this to be unironically both easier to read (by an incredibly wide, dyslexic margin) and faster to write and type.

    Parenthesis consists of only two symbols that only require two keyboard keys and a single stroke of a pen to write compared to the four keys and varying strokes of the standard operators (aka. more efficient). But, far more importantly for me anyway, "+", "×", "*", "÷", all look nearly identical unless I stare the keyboard or problem for an agonizing century (waste of time, perhaps?) and even then it's a mystery whether my brain processed the symbology correctly or put the numbers in the right spot to do math (yep, waste of time). The humble ( ), however, is very easy to see, and it creates neat little windows that don't leave much room for misinterpretation.

    2*7²+5*3³ = accessibility nightmare

    (2(7²))+(5(3³)) = readable with clearly defined order of operations

    I did preface this by pointing out I'm weird.

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  • [–] 2 points 1 year ago (4 children)

    Oh, you're trolling. Carry on, then.

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  • [–] 0 points 1 year ago (3 children)

    Oh, you don't know how to read, carry on then.

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  • [–] 1 point 1 year ago (2 children)

    lol are legitimately saying this was not a joke?

    Parenthesis consists of only two symbols that only require two keyboard keys and a single stroke of a pen to write compared to the four keys and varying strokes of the standard operators

    The humble ( ), however, is very easy to see, and it creates neat little windows that don't leave much room for misinterpretation.

    2*7²+5*3³ = accessibility nightmare

    (2(7²))+(5(3³)) = readable with clearly defined order of operations

    I mean, I guess I have no reason to doubt your word so I'll just believe you were being serious and respond in kind.

    Time savings you might gain from parentheses being easier to write and requiring less keystrokes is lost on you needing to use twice as many since they come in pairs.

    Furthermore, with the exception of *, which we don't even write most of the time, you still need to use all of the other operators even with parentheses, so using them everywhere isn't even a trade off, it's a net loss. This also means that parentheses will not help you differentiate between the operators because you'll still be using them.

    Finally, the only reason you find the example I gave easier to read with parentheses is because I used a lot of multiplication, but you have multiplication to thank for that, not parentheses. In most cases, it would have fairly simple expressions like this:

    1+2+3+4+5+6+7+8

    turned into this:

    1+(2+(3+(4+(5+(6+(7+(8))))))

    If you truly want to eliminate ambiguity, have a look at reverse polish notation. I find it confusing as hell but some people like it.

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  • [–] 0 points 1 year ago (1 child)

    Ok, now I'm curious, why is it only after I call you out that you decide to read what I wrote with any criticality? What about my argument (which I happily acknowledged was based purly on personal experience, and therefore not all parts are universally applicable to everyone) makes you think I'm nothing more than a dumb internet troll with no meaningful opinions or thoughts worth sharing or discussing like adults?

    Sure, parenthesis need a buddy, but I still find them a lot faster to type simply because it is always the exact same two keys. No stopping to hunt for operators and symbols that seem to move or disappear every, single, fucking, time. When handwriting, parenthesis only takes one single, quick stroke that stays in line with what you are writing (maybe a small thing, but I find it important if my hands hurt, aka. always).

    At no point have I argued the elimination of the operators, only that using them exclusively determine order of operations presents an accessibility issue and is largely unintuitive for many individuals.

    The actual reason I find the parenthesis easier to read is because it isolates the problem into distinct, physically easier to read sections that eliminates a hard to distinguish operator and creates a clear step-by-step process to solving the problem that doesn't really on any rule beyond working from the inside out.

    Single operator problems can be solved in any sequence, no parenthesis or order of operations needed. In your example, it's literally no different than combining like terms. But beyond basic cases like that, parenthesis always create a more comprehensible problem. Tell me, which is more clear and has less room for error:

    1+2+3×4+5+6

    1+2+3÷4+5+6

    1+2×3÷4*5-6

    OR

    (1+2+3)(4+5+6)

    (1+2+3)/(4+5+6)

    1+((2×3)/(4×5))-6

    Literally, all I'm arguing is that parenthesis make math easier to read and less prone to error or unintentional misinterpretation and should therefore replace the potential amigousness of order of operations. On top of that, I find them to be dramatically more efficient. Not everyone feels the same, fair enough, not really trying to paint with broad strokes on that front.

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  • [–] -1 points 1 year ago*

    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.

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