216
A fake Facebook event disguised as a math problem has been one of its top posts for 6 months (www.engadget.com)
submitted 1 year ago by to c/technology@lemmy.world
177 comments fedilink hide all child comments
you are viewing a single comment's thread
view the rest of the comments
[–] 3 points 1 year ago* (17 children)

Maybe I'm wrong but the way I explain it is until the ambiguity is removed by adding in extra information to make it more specific then all those answers are correct.

"I saw her duck"

Until the author gives me clarity then that sentence has multiple meanings. With math, it doesn't click for people that the equation is incomplete. In an English sentence, ambiguity makes more sense and the common sense approach would be to clarify what the meaning is

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 17 child comments
    •
  • [–] 1 point 1 year ago (7 children)

    100% with you. "Left to right" as far as I can tell only exists to make otherwise "unsolvable" problems a kind of official solution. I personally feel like it is a bodge, and I would rather the correct solution for such a problem to be undefined.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 7 child comments
    •
  • [–] 3 points 1 year ago (5 children)

    It's so we don't have to spam brackets everywhere

    9+2-1+6-4+7-3+5=

    Becomes

    ((((((9+2)-1)+6)-4)+7)-3)+5=

    That's just clutter for no good reason when we can just say if it doesn't have parentheses it's left to right. Having a default evaluation order makes sense and means we only need parentheses when we want to deviate from the norm.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 5 child comments
    •
  • [–] 0 points 1 year ago (4 children)

    It’s so we don’t have to spam brackets everywhere

    No it isn't. The order of operations rules were around for several centuries before we even started using Brackets in Maths.

    ((((((9+2)-1)+6)-4)+7)-3)+5

    It was literally never written like that

    we only need parentheses when we want to deviate from the norm

    That has always been the case

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 4 child comments
    •
  • [–] 0 points 1 year ago (3 children)

    You're literally arguing nothing right now. THEY took the position we should have brackets defining the order in every single equation or otherwise have them as undefined TODAY. It doesn't matter when they were invented. Obviously it's never been written like that. They are the one arguing it SHOULD BE. I said that would be stupid vs following the left to right convention already established. You're getting caught up in the semantics of the wording.

    What you inferred: they're saying brackets were always around and we chose left to right to avoid bracket mess.

    What I was actually saying: we chose and continue to choose to keep using the left to right convention over brackets everywhere because it would be unnecessary and make things more cluttered.

    And yes, that IS a position mathematicians COULD have chosen once brackets WERE invented. They could have decided we should use them in every equation for absolute clarity of order. Saying we should not do that based on tradition alone is a bad reason.

    The "always been the case" argument could justify any legacy system. We don't still use Roman numerals for arithmetic just because they were traditional. Things DO change.

    Ancient Greeks and Romans strongly resisted zero as a concept, viewing it as philosophically problematic. Negative numbers were even more controversial with many mathematicians into the Renaissance calling them "fictitious" or "absurd numbers." It took centuries for these to become accepted as legitimate mathematical objects.

    Before Robert Recorde introduced "=" in 1557, mathematicians wrote out "is equal to" in words. Even after its introduction, many resisted it for decades, preferring verbal descriptions or other symbols.

    I could go on but if you're going to argue why something shouldn't be the case, you should argue more than "it's tradition" or "we've done fine without it so far". Because they did fine with many things in mathematics until they decided they needed to change or expand it.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 3 child comments
    •
  • [–] 1 point 1 year ago (2 children)

    THEY took the position we should have brackets defining the order in every single equation or otherwise have them as undefined TODAY

    Who's this mysterious "THEY" you are referring to, because I can assure you that the history of Maths tells you that is wrong. e.g. look in Cajori and you'll find the order of operations rules are at least 2 centuries older than the use of Brackets in Maths.,

    It doesn’t matter when they were invented

    The rules haven't changed since then.

    They are the one arguing it SHOULD BE

    ...and watch Physicists and Mathematicians promptly run out of room on blackboards if they did.

    You’re getting caught up in the semantics of the wording

    No, you're making up things that never happened.

    they’re saying brackets were always around and we chose left to right to avoid bracket mess

    and that's wrong. Left to right was around before Brackets were.

    we chose and continue to choose to keep using the left to right convention over brackets everywhere

    and you're wrong, because that choice was made before we'd even started using Brackets in Maths, by at least a couple of centuries.

    it would be unnecessary and make things more cluttered

    They've always been un-necessary, unless you want to deviate from the normal order of operations.

    They could have decided we should use them in every equation for absolute clarity of order

    But they didn't, because we already had clarity over order, and had done for several centuries.

    Saying we should not do that based on tradition alone is a bad reason.

    Got nothing to do with tradition. Got no idea where you got that idea from.

    Things DO change.

    The order of operations rules don't, and the last change to the notation was in the 19th Century.

    I could go on

    and you'd still be wrong. You're heading off into completely unrelated topics now.

    you should argue more than “it’s tradition” or “we’ve done fine without it so far”

    I never said either of those things.

    Because they did fine with many things in mathematics until they decided they needed to change or expand it

    And they changed the meaning of the Division symbol sometime in the 19th Century or earlier, and everything has been settled for centuries now.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 2 child comments
    •
  • [–] 0 points 1 year ago

    100% with you. “Left to right” as far as I can tell only exists to make otherwise “unsolvable” problems a kind of official solution

    It's not a rule, it's a convention, and it exists so as to avoid making mistakes with signs, mistakes you made in almost every example you gave where you disobeyed left to right.

  • permalink
  • fedilink
  • source
  • parent
  • [–] 0 points 1 year ago (8 children)

    until the ambiguity is removed

    There isn't any ambiguity.

    all those answers are correct

    No, only 1 answer is correct, and all the others are wrong.

    Until the author gives me clarity then that sentence has multiple meanings. With math

    Maths isn't English and doesn't have multiple meanings. It has rules. Obey the rules and you always get the right answer.

    it doesn’t click for people that the equation is incomplete.

    It isn't incomplete.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 8 child comments
    •
  • [–] 0 points 1 year ago* (7 children)

    Can you explain how that is? Like with an example?

    Math is exactly like English. It's a language. It's an abstraction to describe something. Ambiguity exists in math and in English. It impacts the validity of a statement. Hell the word statement is used in math and English for a reason.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 7 child comments
    •
  • [–] 0 points 1 year ago (6 children)

    Can you explain how that is? Like with an example?

    I'm not sure what you're asking about. Explain what with an example?

    Math is exactly like English. It’s a language

    No it isn't. It's a tool for calculating things, with syntax rules. We even have rules around how to say it when speaking.

    It’s an abstraction to describe something

    And that something is the Laws of the Universe. 1+1=2, F=ma, etc.

    Hell the word statement is used in math and English for a reason

    You won't find the word "statement" used in Maths textbooks. I'm guessing you're referring to Expressions.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 6 child comments
    •
  • [–] 0 points 1 year ago (5 children)

    Those rules are based on axioms which are used to create statements which are used within proofs. As far as I know statements are pretty common and are a foundational part of all math.

    Defining math as a language though is also going to be pointless here. It's not really a yes or no thing. I'll say it is a language but sure it's arguable.

    And again laws are created using statements. I have plenty of textbooks that contain "statements"

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 5 child comments
    •
  • [–] -1 points 1 year ago (4 children)

    Those rules are based on axioms

    Nope! The order of operations rules come from the proof of the definitions in the first place. 3x4=3+3+3+3 by definition, therefore if you don't do the multiplication first in 2+3x4 you get a wrong answer (having changed the multiplicand).

    As far as I know statements are pretty common

    And yet you've not been able to quote a Maths textbook using that word.

    are a foundational part of all math

    Expressions are.

    It’s not really a yes or no thing

    It's really a no thing.

    And again laws are created using statements

    Not the Laws of Maths. e.g. The Distributive Law is expressed with the identity a(b+c)=(ab+ac). An identity is a special type of equation. We have...

    Numerals

    Pronumerals

    Expressions

    Equations (or Formula)

    Identities

    No statements. Everything is precisely defined in Maths, everything has one meaning only.

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 4 child comments
    •
  • [–] 1 point 1 year ago* (3 children)

    Order of operations is not a hard rule. It is a convention. It's something agreed upon but is it not something that is universally true.

    Solve for X

    X^2=4

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 3 child comments
    •
  • [–] 0 points 1 year ago* (2 children)

    Order of operations is not a hard rule

    Yes it is.

    It is a convention.

    Left to right is a convention. Left Associativity is a hard rule. Left to right is a convention which obeys the rule of Left Associativity.

    It’s something agreed upon

    It's something that is a natural consequence of the definitions of the operators in the first place. As soon as Multiplication was defined in terms of Addition, that guaranteed we would always have to do Multiplication before Addition to get right answers.

    is it not something that is universally true

    Yes it is! All of Maths is universally true! 😂

    Solve for X X^2=4

    You know that's no longer an order of operations problem, right?

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 2 child comments
    •
  • [–] 1 point 1 year ago* (last edited 1 year ago) (1 child)

    What proof do you have that using a left to right rule is universally true?

    From my understanding It's an agreed convention that is followed which doesn't make it a universal truth. If we're all doing it just to make things easier to understand, that implies we could have a right to left rule. It's also true that not all cultures right in the same way.

    But here is an interesting quote from Florian Cajori in his book a history of mathematical notations.

    Lastly here is an article that also highlights the issue.

    https://scienceblogs.com/evolutionblog/2013/03/15/the-horror-of-pemdas

    Some of you are already insisting in your head that 6 ÷ 2(1+2) has only one right answer, but hear me out. The problem isn’t the mathematical operations. It’s knowing what operations the author of the problem wants you to do, and in what order. Simple, right? We use an “order of operations” rule we memorized in childhood: “Please excuse my dear Aunt Sally,” or PEMDAS, which stands for Parentheses Exponents Multiplication Division Addition Subtraction.* This handy acronym should settle any debate—except it doesn’t, because it’s not a rule at all. It’s a convention, a customary way of doing things we’ve developed only recently, and like other customs, it has evolved over time. (And even math teachers argue over order of operations.)

  • permalink
  • fedilink
  • source
  • parent
  • hideshow 1 child comment
    •
  • [–] 1 point 1 year ago

    What proof do you have that using a left to right rule is universally true?

    From my understanding It’s an agreed convention that is followed

    Read what I wrote again. I already said that left to right is a convention, and that Left Associativity is a rule. As long as you obey the rule - Left Associativity - you can follow whatever convention you want (but we teach students to do left to right, because they often make mistakes with signs when they try doing it in a different order, as have several people in this thread).

    that implies we could have a right to left rule

    You can have a right to left convention if the rule is Right Associativity.

    It’s also true that not all cultures right in the same way

    Yeah, I don't know how they do Maths - if they do it the same as us or if they just flip everything back-to-front (or top to bottom - I guess they would). In either case all the rules on top stay the same once the direction is established (like I guess exponents would now be to the top left not the top right? but in any case the evaluation of an exponent would stay the same).

    But here is an interesting quote from Florian Cajori in his book a history of mathematical notations

    Yeah, he's referring to the conventions - such as left to right - not the rule of Left Associativity, which all the conventions must obey. For a while Lennes was doing something different - because he didn't understand Terms - and was disobeying Left Associativity, (which meant his rules were at odds with everyone else), but his rule died out within a generation of his death,. Absolutely all textbooks now obey Left Associativity, same as before Lennes came along.

    Lastly here is an article that also highlights the issue

    Not really. Just another person who has forgotten the rules.

    "as it happens, the accepted convention says the second one is correct"

    No it isn't. The Distributive Law says the first is correct (amongst 4 other rules of Maths which also say the answer is only 1). The second way they did it disobeys The Distributive Law (and 4 other rules) and is absolutely wrong.

  • permalink
  • fedilink
  • source
  • parent