Math videos and other click bait (e.g., 6÷2(1+2) )

[Tinker Grey]

So I ran across a video (didn't watch) asserting that calculator's lie (literally, the videographer's words).

What you find out there in the wild is those that assert PEMDAS before everything else; AND others why PEMDAS is wrong. (Parens, Exponents, Mulitplication, Division, Addition, Subtraction).

Aside: The guy (according to title alone) is asserting that all the engineers and scientists and technologists who had a say in how calculators work, were wrong. Yeah.

Anyway, here's my point: All the click bait arguers out there are missing the point. And it's this, all math exists to represent some reality (or adjacent reality -- not trying to shut down pure math). That is, math is for communication. If your audience can misinterpret what you wrote, you wrote it wrong!! IF someone wrote the above equation to represent something in reality, they either wrote it for the calculator (simplest[?] representation), or they failed to communicate what it was they were trying to calculate.

Thoughts?

 

[keith99]

Notation is just that, notation. A fool not understanding that because he failed to read the manual merely shows he is a fool.

Reverse Polish notation is just as valid as any other notation, and honestly works better for calculators.

My bet is 99% of the trolls mentioned above have no idea what Reverse Polish Notation is.

There are other notations where the formal definitions differ from what often gets said, like APL. The formal definition says functions have long right scope and short left scope. In practice that usually is the same as performing operations right to left, which is the definition many use. But not if there is an embedded assignment. Which normally is the sort of you wrote it wrong that Tinker Grey referred to. There are a few other more subtle cases, but since I have not used APL for over3 decades I do not recall them.

 

[Tinker Grey]

Notation is just that, notation. A fool not understanding that because he failed to read the manual merely shows he is a fool.

Reverse Polish notation is just as valid as any other notation, and honestly works better for calculators.

My bet is 99% of the trolls mentioned above have no idea what Reverse Polish Notation is.

There are other notations where the formal definitions differ from what often gets said, like APL. The formal definition says functions have long right scope and short left scope. In practice that usually is the same as performing operations right to left, which is the definition many use. But not if there is an embedded assignment. Which normally is the sort of you wrote it wrong that Tinker Grey referred to. There are a few other more subtle cases, but since I have not used APL for over3 decades I do not recall them.

I did some APL some 40 years ago. I had an HP calculator with RPN.

 

[PsaltiChrysostom]

I remember the HP-10s when I was in 8th grade. We never really got instruction on using them compared to the TI calculators. So those were just the "weird ones that did math wrong"

 

[keith99]

I did some APL some 40 years ago. I had an HP calculator with RPN.

I worked for STSC. I was in a marketing office as a programmer, but we shared space with a development office. I often played charades with them. Know anywhere else where 'Ontogeny recapitulates phylogeny' gets solved in under a minute?

 

[Bradskii]

If you write it 6/2(1+2) so you have a numerator and a denominator (I haven't written those words for over 50 years) then the answer seems obviously to be 1. We used BODMAS when I did maths (Brackets of Division, Multiplication, Addition and Subtraction). But using that in this format...

6÷2(1+2)​

...it seems to be 9.

 

[Tinker Grey]

If you write it 6/2(1+2) so you have a numerator and a denominator (I haven't written those words for over 50 years) then the answer seems obviously to be 1. We used BODMAS when I did maths (Brackets of Division, Multiplication, Addition and Subtraction). But using that in this format...

6÷2(1+2)​

...it seems to be 9.

My calculator gives 9. Originally, I was taught that MD are of equal weight as AS are of equal weight. If they are of equal weight, then, here in the west, the answer should be 9. But, if you do PEMDAS where M always has higher precedence than D, then you get 1.

My point is that if you are trying to communicate what you are doing, then the formula in the title fails -- you haven't communicated what you are doing.

 

[Bradskii]

My calculator gives 9. Originally, I was taught that MD are of equal weight as AS are of equal weight. If they are of equal weight, then, here in the west, the answer should be 9. But, if you do PEMDAS where M always has higher precedence than D, then you get 1.

My point is that if you are trying to communicate what you are doing, then the formula in the title fails -- you haven't communicated what you are doing.

I used to programme CAD software and if I had to write that in (pseudo) code then:

(6/(2(2+1))) = 1
((6/2)(2+1)) = 9

You really had to know where your brackets needed to go.

 

[Chesterton]

That is, math is for communication. If your audience can misinterpret what you wrote, you wrote it wrong!!

Agreed. Math is a language for communication, and it's up to the writer to avoid ambiguity. Equations can be written which are analogous to this sentence: "I saw a man with binoculars", which allows for two interpretations. (Actually three interpretations, since I could have used binoculars to see a man in possession of binoculars, lol.) This should be avoided both in language and in math.

 

[durangodawood]

Agreed. Math is a language for communication, and it's up to the writer to avoid ambiguity. Equations can be written which are analogous to this sentence: "I saw a man with binoculars", which allows for two interpretations. (Actually three interpretations, since I could have used binoculars to see a man in possession of binoculars, lol.) This should be avoided both in language and in math.

I hope you are using a power saw so its over quickly.

 

[essentialsaltes]

Yes, it's obnoxious clickbait. They set up an ambiguous situation and then, given the general innumeracy of the populace, (at least) two opposing Dunning-Kruger armies join the fray to show why their answer is the unambiguous one (when there's no such thing).

 

[essentialsaltes]

I have two physics degrees, it's clickbait.

 

[durangodawood]

Maybe it is actually computationally indeterminate, which is why they say it equals "?"