Math questions in Facebook

[Upchurch]

One of the interesting side effects of Facebook adding Questions to their user stream is that it is highlighting the the lack of some basic math skills of Facebook users (and, I'm guessing, the population at large). Friends of mine who I consider to be smart people are making stupid mistakes when answering these questions. I find this generally disconcerting.

For kicks and grins, I'll post the latest one I've seen and see if we do any better.

eta: it's a public poll. Your user name will be associated with your response.

[madurobob]

Well, my fifth grader knew the answer. Then again, I have not yet allowed him to set up a FB account.

[Lothian]

Why was I not allowed multiple answers?.

[CriticalThanking]

Decades ago when I did real math, I was taught (and I taught) the following rules in descending priority order, left to right within the same level: parentheses (inner to outer), multiplication and division, addition and subtraction.

When I got into programming, I got tired of debugging people's code with errors around order of operations. When I do code reviews these days, I make a big deal out of adding parenthese for clarity of logic, even if the statement is logically and syntactically correct. My team does a lot of SQL code and I have lost count of how many times the query gave a logically correct but (business) wrong answer because of AND/OR precedence misunderstandings. Use parentheses, darn it!

CT

[paiute]

I will abstain to protest the lack of vinculae.

[Beerina]

Why was I not allowed multiple answers?.

Ya. OP's assuming primacy of multiplication over addition in implied grouping! :mad:

[rwguinn]

took a bit, but I finally make out that's a "Plus" sign, not a "Divide" sign...

[sophia8]

I got caught out by one of those this morning - 5 + 5 x 5. There were only two answers given, 50 and 30. I'd clicked on 50 before I thought "Hang on, where's the brackets - what's being added and multiplied here?"

[Safe-Keeper]

My take: multiplication before addition, so

10 + 10 x 0 =
10 + 0 =
10

amirite?

[Professor Yaffle]

I found this one was more contentious (arguments about whether implicit and explicit multiplication are equivalent wrt to order).

6÷2(1+2)=?

A. 1
B. 9

[Upchurch]

I got caught out by one of those this morning - 5 + 5 x 5. There were only two answers given, 50 and 30. I'd clicked on 50 before I thought "Hang on, where's the brackets - what's being added and multiplied here?"
-5 + 5 x 5 = 20

Whoever wrote the question didn't give you the correct options.

My take: multiplication before addition, so

10 + 10 x 0 =
10 + 0 =
10

amirite?

urrite

[Vortigern99]

I found this one was more contentious (arguments about whether implicit and explicit multiplication are equivalent wrt to order).

6÷2(1+2)=?

A. 1
B. 9

Order of operations states that you do what's in the parentheses first (1+2=3) then do multiplication and division from left to right: 6/2=3. 3x3=9. The answer is 9. :cool:

[madurobob]

My take: multiplication before addition, so

10 + 10 x 0 =
10 + 0 =
10

amirite?

Yes. This is a "Please Excuse My Dear Aunt Sally" problem.

Order of operations is Parentheses, Exponents, Multiplication Division (which ever comes first), then Addition or Subtraction (which ever comes first).

[Professor Yaffle]

Apparently it depends on which casio scientific calculator you use...

http://badscience.net/forum/viewtopic.php?f=6&t=22910&hilit=brackets+maths#p572732

See rest of thread regarding whether implied multiplication trumps division.

[rwguinn]

I found this one was more contentious (arguments about whether implicit and explicit multiplication are equivalent wrt to order).

6÷2(1+2)=?

A. 1
B. 9
What?
Contentious how?

[Dr. Keith]

This is the sort of thing that I found most frustrating about math: abstract calculations.

I liked the word problems, hypothetical problems. Give me a pizza that needs to be split among hungry teens or two trains traveling towards NY, or a man trying to cross a stream. That is far more fun, in my simple little mind.

[Upchurch]

What?
Contentious how?

It is equivalent to

6 ÷ 2 x 3=?

Which do you do first? (division)

[madurobob]

It is equivalent to

6 ÷ 2 x 3=?

Which do you do first? (division)

Sure, in that expression its an easy left-to-right solving. But, with the parentheses:

6 ÷ 2(1+2)=?

People are inclined to solve the 2(1+3) first, assuming the 2 is somehow part of the parenthetical. The discussion Prof Yaffle pointed to on badscience is interesting. Apparently its easier for some people if you add the implied multiplication sign:
6 ÷ 2 x (1+2)=?

[sol invictus]

These are not really math questions - they're questions about the details of a notational convention. As far as I know there is no generally agreed on such convention, so there isn't necessarily a correct answer.

And I don't think I've seen the symbol "÷" since primary school....

[Upchurch]

Sure, in that expression its an easy left-to-right solving. But, with the parentheses:

6 ÷ 2(1+2)=?

People are inclined to solve the 2(1+3) first, assuming the 2 is somehow part of the parenthetical. The discussion Prof Yaffle pointed to on badscience is interesting. Apparently its easier for some people if you add the implied multiplication sign:
6 ÷ 2 x (1+2)=?
Easier, I'm sure, but this just further highlights that people really don't learn (or quickly forgets) how basic mathematical notation works.

[elgarak]

Sure, in that expression its an easy left-to-right solving. But, with the parentheses:

6 ÷ 2(1+2)=?

People are inclined to solve the 2(1+3) first, assuming the 2 is somehow part of the parenthetical. The discussion Prof Yaffle pointed to on badscience is interesting. Apparently its easier for some people if you add the implied multiplication sign:
6 ÷ 2 x (1+2)=?

I believe advanced math practitioners tend to be inclined to do so. People who have reached the level where expressions like 2(n+1) are common and denote just one number.

[madurobob]

Easier, I'm sure, but this just further highlights that people really don't learn (or quickly forgets) how basic mathematical notation works.

:) FWIW, I posted the 10 + 10 x 0 = ?? question as my FB status this morning saying I knew my friends were smarter than the general FB population and would have no trouble with it. The first response was an emphatic "0" from a friend who sat beside me throughout most of my middle and high school math classes.

She took some convincing, and swears she never heard the "my dear aunt sally" mnemonic.

[rwguinn]

Sure, in that expression its an easy left-to-right solving. But, with the parentheses:

6 ÷ 2(1+2)=?

People are inclined to solve the 2(1+3) first, assuming the 2 is somehow part of the parenthetical. The discussion Prof Yaffle pointed to on badscience is interesting. Apparently its easier for some people if you add the implied multiplication sign:
6 ÷ 2 x (1+2)=?
Actually, I am inclined to use the 2(1+3) convention, because the lack of a * (or "X") implies, to me, that 2(1+2) is a single term.
However, if you enter it into EXCEL as "=6/3*(1+2)", you get 9--which is why I am very careful about parens...(Old FORTRAN Programmer)

[madurobob]

Actually, I am inclined to use the 2(1+3) convention, because the lack of a * (or "X") implies, to me, that 2(1+2) is a single term.
However, if you enter it into EXCEL as "=6/3*(1+2)", you get 9--which is why I am very careful about parens...(Old FORTRAN Programmer)

Yep - I can see the point. If we substituted a variable for the 1+3 like this:
6/2A = X

Then said that A=3, I think even more people would insist X=1.

[rwguinn]

Yep - I can see the point. If we substituted a variable for the 1+3 like this:
6/2A = X

Then said that A=3, I think even more people would insist X=1.
Fat fingers--the 1+3 should be 1+2...
My apologies...

[elgarak]

Actually, I am inclined to use the 2(1+3) convention, because the lack of a * (or "X") implies, to me, that 2(1+2) is a single term.
However, if you enter it into EXCEL as "=6/3*(1+2)", you get 9--which is why I am very careful about parens...(Old FORTRAN Programmer)

Again, I think that's something of a problem of advanced practitioners.

An expression like '2(n+m)' is understood as a single term... if you do handwritten math as a sufficiently advanced practitioner. It's a sloppy rule to save on writing. There are also subtle hints in handwritten formulae that make the meaning clear(er).

However, once you go to typed expressions or computer uses, the ambiguity bites you (there are computer algebra systems than understand the rule. Talk about confusion when you copy'n'paste back and forth between programs that do and ones that don't). More than once have I complained about home work or exams given in a typed/TeX'ed form transferred from an old handwritten form without much thought. In one exam I recall that not even the TA I asked knew which way it was supposed to be. You can bet we students pushed the TA's present to make both interpretations 'official'.

[AvalonXQ]

As others have pointed out, there are definitely rules for order of operations. However, these rules should be an unnecessary back-up; no one should ever have to parse "10 + 10 x 0" because the person should write "(10+10)x0" or "10+(10x0)" depending on what they actually mean. Or at least use spacing and other context to make the intent abundantly clear.

[rwguinn]

As others have pointed out, there are definitely rules for order of operations. However, these rules should be an unnecessary back-up; no one should ever have to parse "10 + 10 x 0" because the person should write "(10+10)x0" or "10+(10x0)" depending on what they actually mean. Or at least use spacing and other context to make the intent abundantly clear.
Absolutely.
Lacking context makes the string unparsable, and there can be several correct answers. If anyone were graded down on a test for answering either 0 or 10 to the above, they should be having a conversation with the teacher...

[IMST]

What?
Contentious how?

I was taught in elementary school that it was multiplication then division, addition then subtraction. I'dve been marked wrong for 9 and right for 1 here.

[rwguinn]

I was taught in elementary school that it was multiplication then division, addition then subtraction. I'dve been marked wrong for 9 and right for 1 here.
Same here--but then I added in the missing *, and put it in excel--got 9
I put it in Mathcad as written, and got 1.
I LIKE Mathcad

[madurobob]

If anyone were graded down on a test for answering either 0 or 10 to the above, they should be having a conversation with the teacher...
Which is why my HS math teachers constantly chanted "show your work". If your answer was marked wrong, but you could show in your work where there was ambiguity in the question, or something else that lead you to get A correct answer but not THE correct answer, then your test would be re-graded. It wasn't uncommon for us to find places where the textbook was wrong, and equally common to find the teacher was wrong.

[Verde]

Same here--but then I added in the missing *, and put it in excel--got 9
I put it in Mathcad as written, and got 1.
I LIKE Mathcad

That is one of the reasons I stopped using Mathcad a long time ago. In actual engineering work it would often give wrong answers unless you were VERY careful about syntax.

Matlab, on the other hand, does not allow implicit terms, so 6/2(1+2) is flagged as an error, so it needs to be explicitly coded as 6/2*(1+2) which gives 9 as the result.

This is admittedly a trivial example, but with very complex calculations it helps to have the rules enforced to have the program barf rather than provide an incorrect answer.

You can of course force the 'implicit' behavior: 6/(2*(1+2)) = 1 if that is what you wanted.

V.

[The Man]

Where’s the “We don’t need no stinking maths on planet X (or in the Electric Universe)” option?

[sophia8]

-5 + 5 x 5 = 20

Whoever wrote the question didn't give you the correct options.



urriteNo - it was correct. That was a hyphen in front - not a minus sign. I'm rather too fond of hyphens - maybe I should stop using them.

[elgarak]

No - it was correct. That was a hyphen in front - not a minus sign. I'm rather too fond of hyphens - maybe I should stop using them.

In that case, you ignore that the standard font here does not distinguish between minus-sign, hyphen, en- and em-dash.

The bigger problem is that you should not use a hyphen at all. The hyphen is used to join words or to separate syllables for clarity, not to separate parts of sentences. The glyph you want is a dash. Either an en-dash with spaces -- with the font used here you can do two "-" with spaces before and after -- or an em-dash with no spaces---three "-".

:D

[rwguinn]

That is one of the reasons I stopped using Mathcad a long time ago. In actual engineering work it would often give wrong answers unless you were VERY careful about syntax.

Matlab, on the other hand, does not allow implicit terms, so 6/2(1+2) is flagged as an error, so it needs to be explicitly coded as 6/2*(1+2) which gives 9 as the result.

This is admittedly a trivial example, but with very complex calculations it helps to have the rules enforced to have the program barf rather than provide an incorrect answer.

You can of course force the 'implicit' behavior: 6/(2*(1+2)) = 1 if that is what you wanted.

V.
As an engineer and having written my own FEA programs, I tend to be very specific about how I write an equation. As someone else pointed out, you can't really use to many parentheses....

[rjh01]

Can anyone give me any good reason for the rule? Otherwise the rule is rather arbitrary. As others said, you need parentheses or the question should be rejected.

[Dr. Trintignant]

Apparently its easier for some people if you add the implied multiplication sign:
6 ÷ 2 x (1+2)=?

Right. On the other hand, 1 / 2x seems to be more obviously interpreted as 1 / (2*x), even if that violates standard basic grade-school OOO.

I'd say that implicit multiplication binds more strongly than explicit multiplication/division. But not before saying that the formula needs more parens.

- Dr. Trintignant

[GreyArea]

I liked the word problems, hypothetical problems.
Why? (http://www.youtube.com/watch?v=BxJF-M9inQM)

[rwguinn]

Can anyone give me any good reason for the rule? Otherwise the rule is rather arbitrary. As others said, you need parentheses or the question should be rejected.
The rule exists to keep it from becoming arbitrary--so everyone is doing the same thing -- in theory. Unfortunately, they apparently don't teach it any more, or you wouldn't be asking...

[rjh01]

The rule exists to keep it from becoming arbitrary--so everyone is doing the same thing -- in theory. Unfortunately, they apparently don't teach it any more, or you wouldn't be asking...

I did learn it, a long time ago. I never did like it as it was an arbitrary rule with no logic behind it.

[bjornart]

I did learn it, a long time ago. I never did like it as it was an arbitrary rule with no logic behind it.

It isn't arbitrary. Having to use parenteses everywhere would be a drag, and giving presedence to multiplication is a choice that makes most algebraic formulae prettier. The relationship between multiplication and division and addition and subtraction, and our normal reading direction of left to right then gives the detailed rule.

with presedence rules:

f(x) = 2x2 + 3x + 2

vs.

f(x) = (2(x2)) + (3x) + 2

without.

Even adding the most basic of rules, evaluate left to right, gives us the unsatisfactory:
f(x) = 2(x2) + (3x) + 2

[drzeus99]

Why? (http://www.youtube.com/watch?v=BxJF-M9inQM)

NICE !!!

The Adventures of Pete and Pete!!

Loved watching that show with my daughter when she was little.

The theme song, "Hey Sandy", by Polaris, is also one of my fav TV theme songs.

Brings back fond memories :D

[rjh01]

It isn't arbitrary. Having to use parenteses everywhere would be a drag, and giving presedence to multiplication is a choice that makes most algebraic formulae prettier. The relationship between multiplication and division and addition and subtraction, and our normal reading direction of left to right then gives the detailed rule.

with presedence rules:

f(x) = 2x2 + 3x + 2

vs.

f(x) = (2(x2)) + (3x) + 2

without.

Even adding the most basic of rules, evaluate left to right, gives us the unsatisfactory:
f(x) = 2(x2) + (3x) + 2

To me there is a difference between 2x +1 and 1+2*x. The former it obvious that x must be multiplied by 2 before adding 1. In the latter there is only the arbitrary rule. We might want the equation to be (1+2)x. This would give a different result. But to get that we need parentheses. Also this is the first post in which x is part of the equation. Previously we have been discussing
10 + 10 x 0 = ?

Your example does not give any reason why we should, in that example, multiple rather than add first, as there is a multiplication sign in the equation, but in your example there is no multiplication sign.

[jiggeryqua]

So 13 of us say 'pot-ah-to' and some of the 97 insist 'pot-ay-to' is the only correct pronounciation? Given the company I'm in, I'm going to say the question is poorly set. That still leaves 3 people with no grasp of maths at all...

[Dave Rogers]

I did learn it, a long time ago. I never did like it as it was an arbitrary rule with no logic behind it.

That's the whole point of it being a rule. If there's a logical reason to perform one operation before the other, then there's no need for a rule; just do what logic dictates. Only when it's a purely arbitrary choice is there a need for a rule to resolve the ambiguity, and as a result the law cannot be anything other than purely arbitrary.

Dave

[Ysidro]

Blah, there's a reason I sucked at math (other than geometry) and this is it.

[sol invictus]

Blah, there's a reason I sucked at math (other than geometry) and this is it.

This discussion has nothing to do with math. Mathematics is about establishing results logically starting from a set of axioms. This discussion is about notation.

It's akin to arguing over whether the correct word for that tasty round red food item over there is "apple" or "pomme".

[jiggeryqua]

It's akin to arguing over whether the correct word for that tasty round red food item over there is "apple" or "pomme".

Three people think it's "lemon"...

[Fnord]

As a programmer, I know that multiplication has precedence over addition. Thus:

10 + 10 x 0 =
10 + (10 x 0) =
10 + 0 =
10

[pgwenthold]

That's the whole point of it being a rule. If there's a logical reason to perform one operation before the other, then there's no need for a rule; just do what logic dictates. Only when it's a purely arbitrary choice is there a need for a rule to resolve the ambiguity, and as a result the law cannot be anything other than purely arbitrary.

Dave

That's not a "rule" it's a convention.

[AvalonXQ]

That's not a "rule" it's a convention.

I don't think there's an objective distinction, is there?

[Dave Rogers]

That's not a "rule" it's a convention.

Can we define "convention" as "arbitrary rule with no logic behind it"?

Dave

[DrDave]

It's akin to arguing over whether the correct word for that tasty round red food item over there is "apple" or "pomme".

And every British schoolboy can tell you, the correct answer is apple

[AvalonXQ]

Actually, the correct answer is "cherry pie".

[pgwenthold]

Can we define "convention" as "arbitrary rule with no logic behind it"?



An "agreed upon arbitrary rule"

("with no logic behind it" is redundant)

[Dave Rogers]

An "agreed upon arbitrary rule"

So, a rule, then? :p

Dave

[AmandaM]

doh!

I saw the " X 0" and immediately jumped to conclusions. Somehow I saw "implied parentheticals."

[Upchurch]

Can we define "convention" as "arbitrary rule with no logic behind it"?
Well, we could, but it wouldn't be accurate. The logic behind it is that we need be able to convey mathematics to one another in a consistent manner.

How does "syntax" sound?

[Dave Rogers]

Well, we could, but it wouldn't be accurate. The logic behind it is that we need be able to convey mathematics to one another in a consistent manner.

I agree that there's a logical reason for defining the rule, but there needn't be a logical reason for the choice of order the rule mandates. So I suppose that's why the word "arbitrary" is sufficient, without getting into the question of motivation.

Dave

[Ysidro]

This discussion has nothing to do with math. Mathematics is about establishing results logically starting from a set of axioms. This discussion is about notation.

It's akin to arguing over whether the correct word for that tasty round red food item over there is "apple" or "pomme".

See, this is what I mean! They taught me this stuff in Math class! How's a brother supposed to cope?

[3point14]

I agree that there's a logical reason for defining the rule, but there needn't be a logical reason for the choice of order the rule mandates. So I suppose that's why the word "arbitrary" is sufficient, without getting into the question of motivation.

Dave

There's no logical reason why 'TWO' = '2', but it does. The only reason it does is because we all agree.

Same for the 'My Aunt Sally stuff'. Without arbitrary conventions we simply couldn't do maths.

[DallasDad]

Well, I suppose one could make the argument that rules of precedence for operators are required to preserve symmetry. If we only used left-to-right ordering, then 10 + 10 x 0 would not equal 10 x 0 + 10. The algorithm that specifies doing multiplication before addition preserves the equality when the expression changes.

Anecdotally, left-to-right ordering seems very well known, either because it's intuitive or because it's the only thing remembered from 7th grade. When I've shown 10 x 0 + 10 to people who got the original wrong, they used exactly the same algorithm (left-to-right, without regard to precedence), and didn't seem discombobulated at coming up with a different answer.

I suspected at first that people who got 10 + 10 x 0 wrong were confused because they saw that both addition and multiplication were commutative, and erroneously assumed that an expression using mixed operators would therefore also be commutative. From what I could gather, however, this interpretion is too generous: They simply did left-to-right, building an intermediate result with each pair of operands, using the intermediate as the first operand of the next pair, until reaching the equals sign.

[Psi Baba]

The problem with expecting the reader to parse that expression as written is akin to using poor grammar or ambiguous means of expression and when someone complains about the lack of clarity in the statement, responding with, "Well, you know what I meant!" Furthermore, the problem with the 10 + 10 x 0 example is that the "X zero" part of the equation gives the false impression that everything in the expression is being multiplied by zero and that the answer is therefore zero. You can argue that the reader made an false assumption or jumped to conclusions, but that could have been prevented with better communication. It's like bomb diffusing instructions that read: Step 1: Cut the blue wire. Step 2: Before cutting the blue wire, remove the black screw!
Oops. :covereyes

[epix]

Friends of mine who I consider to be smart people are making stupid mistakes when answering these questions. I find this generally disconcerting.


That reminds me of a seemingly nonsensical puzzle which asks to fill the spaces between numbers

a) 1 2 3 4 5 6 7 8

b) 1 2 3 4 5 6 7 8

with symbols for addition and multiplication in non-random way. The puzzle was formulated this April in Wales.
http://www.cropcircleconnector.com/2011/innage/innage2011a.html

Look at all those pictures for a clue. The pics don't show a nuclear reactor in the vicinity of the puzzle in the field, but that nuclear reactor is an important part of the clue.

The puzzle looks very difficult to crack, but remember that it doesn't ask for a unique solution, just for a non-random choice based on association.

[bjornart]

f(x) = 2x2 + 3x + 2

To me there is a difference between 2x +1 and 1+2*x. The former it obvious that x must be multiplied by 2 before adding 1. In the latter there is only the arbitrary rule. We might want the equation to be (1+2)x. This would give a different result. But to get that we need parentheses. Also this is the first post in which x is part of the equation. Previously we have been discussing
10 + 10 x 0 = ?

Your example does not give any reason why we should, in that example, multiple rather than add first, as there is a multiplication sign in the equation, but in your example there is no multiplication sign.

There's an implied multiplication sign, but more importantly the variables are place holders for numbers, and as soon as I replace them I need actually multiplication signs. So the next thing I want to do is calculate a specific value of f. Lets say f(2).

I can either have:

f(2) = 2*22 + 3*2 + 2 with rules of precedence

or

f(x) = 2*(22) + (3*2) + 2 without.

I'd, like history has, pick the first one, and once I've done so it's convenient to apply those precedence rules universally.

[roger]

The problem with expecting the reader to parse that expression as written is akin to using poor grammar or ambiguous means of expression and when someone complains about the lack of clarity in the statement, responding with, "Well, you know what I meant!" Furthermore, the problem with the 10 + 10 x 0 example is that the "X zero" part of the equation gives the false impression that everything in the expression is being multiplied by zero and that the answer is therefore zero.It comes down to how you 'read' math, I guess. The problem as written was trivial and basically impossible for me to get wrong. Endless nested parenthesis that just enforce the already well defined rules tend to be hard for me to read.

2n2 + 3x + 2 is far easier for me to read than ((2*(n*n)) + (3 * x)) + 2, and that is a very simple equation. The working assumption is that the parenthesis are needed because the ordinary ordering rules cannot be followed, so you end up parsing very carefully, and for what? I usually find myself going back and double checking to make sure I didn't misread something.

I cannot recall a math textbook or a published paper with mathematics that did not utilize the rules in favor of extraneous parenthesis. No one does math that way. I'm not trying to be rude, but pretty much only the math illiterate have any problems with operator precedence. If they are your audience perhaps a few extra parenthesis are called for.

[epix]

2n2 + 3x + 2 is far easier for me to read than ((2*(n*n)) + (3 * x)) + 2, and that is a very simple equation.
What would be the purpose of those two outermost parentheses? (a + b) + c doesn't set any order of operations due to the associative property of addition.

[Ladewig]

I am too stupid to continue posting at JREF - I may have to commit suicide by mod.

I understood the rule.
In fact I explained the rule to some people at work not 8 days ago.
When I opened the thread, I said, "Aha, multiplication first; therefore final result result is zero." D'oh!

[Evilgiraffe]

I am too stupid to continue posting at JREF - I may have to commit suicide by mod.

I understood the rule.
In fact I explained the rule to some people at work not 8 days ago.
When I opened the thread, I said, "Aha, multiplication first; therefore final result result is zero." D'oh!

I went through exactly the same thought processes and also ended up with the wrong answer. It has confirmed, which I have long suspected, that I am a complete drooling idiot.

[jasonpatterson]

I will abstain to protest the lack of vinculae.

For what reason would a vinculum (horizontal bar used in mathematical notation, like the middle bar in a fraction or the bar placed over a repeating decimal) be included or helpful in this expression?

[George152]

10 x 0 = 0
10 x 1 = 10

[69dodge]

For what reason would a vinculum (horizontal bar used in mathematical notation, like the middle bar in a fraction or the bar placed over a repeating decimal) be included or helpful in this expression?

It's sometimes used for grouping, as parentheses are. For example, it groups together everything that we're taking the square root of, in an expression like:$\sqrt{x^2+y^2+z^2}$

[Alan]

I was taught BODMAS, so I answered 10.

[The Whether Man]

Out of curiosity, I posted the same poll on my Facebook page as well. It's not looking good for the correct answer, popularity has zero as the favourite, with 20 a close second.

[CaveDave]

It comes down to how you 'read' math, I guess. The problem as written was trivial and basically impossible for me to get wrong. Endless nested parenthesis that just enforce the already well defined rules tend to be hard for me to read.

2n2 + 3x + 2 is far easier for me to read than ((2*(n*n)) + (3 * x)) + 2, and that is a very simple equation. The working assumption is that the parenthesis are needed because the ordinary ordering rules cannot be followed, so you end up parsing very carefully, and for what? I usually find myself going back and double checking to make sure I didn't misread something.

I cannot recall a math textbook or a published paper with mathematics that did not utilize the rules in favor of extraneous parenthesis. No one does math that way. I'm not trying to be rude, but pretty much only the math illiterate have any problems with operator precedence. If they are your audience perhaps a few extra parenthesis are called for.

I agree completely.

Actually, I am inclined to use the 2(1+3) convention, because the lack of a * (or "X") implies, to me, that 2(1+2) is a single term.
However, if you enter it into EXCEL as "=6/3*(1+2)", you get 9--which is why I am very careful about parens...(Old FORTRAN Programmer)

After learning FORTRAN and PL1 in 1970 or so I have ever since automatically reverted to those precedence rules when there was any doubt. IIRC it goes:
Parenthesis nesting (inner to outer) -> built-in functions -> powers/roots -> multiply/divide -> add/subtract -> left to right.

ETA: Forgot "Negation" (-x), which goes with "powers/roots" and the book I just looked at The ESSENTIALS of PL-1 programming language (http://books.google.com/books?id=6g60Y-Lq8soC&pg=PA17&lpg=PA17&dq=pl1+precedence+rule&source=bl&ots=TVH02RVk0u&sig=Jezo4hd1SZ2nZNN8d39FrBRza9E&hl=en&ei=01_hTZf4IMjn0QHCncmGBw&sa=X&oi=book_result&ct=result&resnum=3&sqi=2&ved=0CCUQ6AEwAg#v=onepage&q&f=false) pp 17-18, order is right-to-left! WEIRD!!??!!

I had a personal preference of avoiding parentheses entirely by using RPN (http://en.wikipedia.org/wiki/Reverse_Polish_notation) (Reverse Polish Notation) AKA Postfix similar to FORTH (http://en.wikipedia.org/wiki/Forth_%28programming_language%29).

Practical implications

* Calculations occur as soon as an operator is specified. Thus, expressions are not entered wholesale from right to left but calculated one piece at a time, most efficiently from the center outwards.
* The automatic stack permits the automatic storage of intermediate results for use later: this key feature is what permits RPN calculators to easily evaluate expressions of arbitrary complexity: they do not have limits on the complexity of expression they can evaluate.
* Brackets and parentheses are unnecessary: the user simply performs calculations in the order that is required, letting the automatic stack store intermediate results on the fly for later use. Likewise, there is no requirement for the precedence rules required in infix notation.
* In RPN calculators, no equals key is required to force computation to occur.
* RPN calculators do, however, require an enter key to separate two adjacent numeric operands.
* The machine state is always a stack of values awaiting operation; it is impossible to enter an operator onto the stack. This makes use conceptually easy compared to more complex entry methods.
* Educationally, RPN calculators have the advantage that the user must understand the expression being calculated: it is not possible to simply copy the expression from paper into the machine and read off the answer without understanding. One must calculate from the middle of the expression, which is only meaningful if the user understands what he or she is doing.
* Reverse Polish notation also reflects the way calculations are done on pen and paper. One first writes the numbers down and then performs the calculation. Thus the concept is easy to teach.
* The widespread use of electronic calculators using infix in educational systems can make RPN impractical at times, not conforming to standard teaching methods. The fact that RPN has no use for parentheses means it is faster and easier to calculate expressions, particularly the more complex ones, than with an infix calculator, owing to fewer keystrokes and greater visibility of intermediate results. It is also easy for a computer to convert infix notation to postfix, most notably via Dijkstra's shunting-yard algorithm—see converting from infix notation below.
* Users must know the size of the stack, because practical implementations of RPN use different sizes for the stack. For example, the algebraic expression 1-1.001^{(-6.2 - 2^{3 \pi})}, if performed with a stack size of 4 and executed from left to right, would exhaust the stack. The answer might be given as an erroneous imaginary number instead of approximately 0.5 as a real number.
* When writing RPN on paper (something that some users of RPN may not do) adjacent numbers need a separator between them. Using a space requires clear handwriting to prevent confusion. For example, 12 34 + could look like 123 4 +, while something like 12, 34 + is straightforward.
* RPN is very easy to write and makes practical sense when it is adopted. The "learning" process to adopt RPN in writing usually comes later than adopting RPN on a calculator so that one may communicate more easily with non-RPN users.

Postfix algorithm

The algorithm for evaluating any postfix expression is fairly straightforward:

While there are input tokens left
Read the next token from input.
If the token is a value
Push it onto the stack.
Otherwise, the token is an operator (operator here includes both operators, and functions).
It is known a priori that the operator takes n arguments.
If there are fewer than n values on the stack
(Error) The user has not input sufficient values in the expression.
Else, Pop the top n values from the stack.
Evaluate the operator, with the values as arguments.
Push the returned results, if any, back onto the stack.
If there is only one value in the stack
That value is the result of the calculation.
If there are more values in the stack
(Error) The user input has too many values.


A fun variant on precedence rules happens in INTERCAL (http://en.wikipedia.org/wiki/INTERCAL) where "Sparks" ['] and "Rabbit Ears" ["] are used for grouping instead of "Wax" [(] & "Wane" [)].

From "C-INTERCAL 0.29 Revamped Instruction Manual (http://www.catb.org/~esr/intercal/ick.htm)"

Grouping Rules

Because there are no operator precedences in INTERCAL, there are various solutions to specifying what precedences actually are.

The portable solution
All known versions of INTERCAL accept the INTERCAL-72 grouping rules. These state that it's possible to specify that an operator takes precedence by grouping it inside sparks (') or rabbit-ears ("), the same way as wax/wane pairs (parentheses) are used in other programming languages. INTERCAL-72 and earlier C-INTERCAL versions demanded that expressions were grouped fully like this, and this practice is still recommended because it leads to portable programs and is easier to understand. Whether sparks or rabbit-ears (often called just `ears' for short) are used normally doesn't matter, and programmers can use one or the other for clarity or for aesthetic appeal. (One common technique is to use just sparks at the outermost level of grouping, just ears at the next level, just sparks at the next level, and so on; but expressions like ''#1~#2'~"#3~#4"'~#5 are completely unambiguous, at least to the compiler.)

There are, however, some complicated situations involving array subscripting where it is necessary to use sparks and ears at alternate levels, if you want to write a portable program. This limitation is in C-INTERCAL to simplify the parsing process; INTERCAL-72 has the same limitation, probably for the same reason. Compare these two statements:

DO .1 <- ,3SUB",2SUB.1".2
DO .1 <- ,3SUB",2SUB.1".2~.3"".4

The problem is that in the first statement, the ears close a group, and in the second statement, the ears open a group, and it's impossible to tell the difference without unlimited lookahead in the expression. Therefore, in similar situations (to be precise, in situations where a group is opened inside an array subscript), it's necessary to use the other grouping character to the one that opened the current group if you want a portable program.

One final comment about sparks and rabbit-ears; if the next character in the program is a spot, as often happens because onespot variables are common choices for operands, a spark and the following spot can be combined into a wow (!). Unfortunately, none of the character sets that C-INTERCAL accepts as input (UTF-8, Latin-1, and ASCII-7) contain the rabbit character, although the Hollerith input format that CLC-INTERCAL can use does.
Positional precedences: CLC-INTERCAL rules
The precedence rules used by CLC-INTERCAL for grouping when full grouping isn't used are simple to explain: the largest part of the input that looks like an expression is taken to be that expression. The main practical upshot of this is that binary operators right-associate; that is, .1~.2~.3 is equivalent to .1~'.2~.3'. C-INTERCAL versions 0.26 and later also right-associate binary operators so as to produce the same results as CLC-INTERCAL rules in this situation, but as nobody has yet tried to work out what the other implications of CLC-INTERCAL rules are they are not emulated in C-INTERCAL, except possibly by chance.
Prefix and infix unary operators
In INTERCAL-72 and versions of C-INTERCAL before 0.26, unary operators were always in the `infix' position. (If you're confused about how you can have an infix unary operator: they go one character inside a group that they apply to, or one character after the start of a constant or variable representation; so for instance, to portably apply the unary operator & to the variable :1, write :&1, and to portably apply it to the expression '.1~.2', write '&.1~.2'.) CLC-INTERCAL, and versions of C-INTERCAL from 0.26 onwards, allow the `prefix' position of a unary operator, which is just before whatever it applies to (as in &:1). This leads to ambiguities as to whether an operator is prefix or infix. The portable solution is, of course, to use only infix operators and fully group everything, but when writing for recent versions of C-INTERCAL, it's possible to rely on its grouping rule, which is: unary operators are interpreted as infix where possible, but at most one infix operator is allowed to apply to each variable, constant, or group, and infix operators can't apply to anything else. So for instance, the C-INTERCAL '&&&.1~.2' is equivalent to the portable '&"&.&1"~.2' (or the more readable version of this, "&'"&.&1"~.2'", which is also portable). If these rules are counter-intuitive to you, remember that this is INTERCAL we're talking about; note also that this rule is unique to C-INTERCAL, at least at the time of writing, and in particular CLC-INTERCAL is likely to interpret this expression differently.

Enjoy the Head-Trip!:D

Cheers,

Dave

[jiggeryqua]

I'm not trying to be rude, but pretty much only the math illiterate have any problems with operator precedence.

You're not trying not to be rude either, given that you've acknowledged that it is rude and said it anyway.

I don't believe myself to be 'math illiterate' any more than I consider math graduates to be drooling gibbons because they don't write poetry, even if they can spell and form sentences. At no point in my life has anything but the ego of some mathemiticians and one particular poor question setter hung on whether I knew some arbitrary rule from the math club. My mathematical literacy suffices for real life. 'You're not a mathematician!' isn't rude, but I'd be surprised if you bothered saying it (and a tad concerned for you too). "You don't know something you don't know!" isn't rude either, but again, would you say it? Only "you're illiterate" is rude, as you acknowledge, and its rudeness seems to be the only reason to choose to say it.

[Lukraak_Sisser]

Can anyone give me any good reason for the rule? Otherwise the rule is rather arbitrary. As others said, you need parentheses or the question should be rejected.

It's part of the 'grammar' of mathemathics, which in theory is standardized, in the same way that most scientific expressions are standardized to prevent problems when different people from different countries work together

MgCl2 not Cl2Mg is a chemistry equivalent.

This has been standardized by mathematicians probably centuries ago. Parentheses solve the problem, but you try writing complex equations by hand and not forgetting one. Its easier to write them down when you can limit the amount of parentheses, and the rules were invented long before computers would alert you to a mistake.

It's quite possible that this will change as we become more used to computers. But at the moment the convention is 10 + 10 x 0 gives 10, unless you write (10 + 10) x 0. The parentheses then denote that you want the calculation done in a different order than the rules would suggest.

[Evilgiraffe]

MgCl2 not Cl2Mg is a chemistry equivalent.

I think this would be closer to a chemistry dialect rather than grammatically wrong. It looks and sounds funny but it isn't ambiguous and still represents the same compound, magnesium chloride.

ETA. for chemical notation where order matter, that unambiguously assigns arbitrarily complex molecules, see InChI (http://en.wikipedia.org/wiki/International_Chemical_Identifier).

[jiggeryqua]

But at the moment the convention is 10 + 10 x 0 gives 10, unless you write (10 + 10) x 0. The parentheses then denote that you want the calculation done in a different order than the rules would suggest.

This may already have been stated, but for the math illiterate, is there an overriding reason why the convention isn't to use parentheses to denote you want the calculation done other than in the order you wrote it? 10 x 0 + 10, for example, would get the result you want, by writing the question in the right order. Unless the result you want is to 'catch out' the mathematically illiterate.

[Lukraak_Sisser]

This may already have been stated, but for the math illiterate, is there an overriding reason why the convention isn't to use parentheses to denote you want the calculation done other than in the order you wrote it? 10 x 0 + 10, for example, would get the result you want, by writing the question in the right order. Unless the result you want is to 'catch out' the mathematically illiterate.

Why we can't sentence write a this way?
It's not to 'catch out' a math illiterate. It's a set of rules designed to ensure that people all over the world get the same answers when they check each others calculations.

Anyone not knowing these rules is unlikely to use maths to a degree where it matters, as they are among the first things taught in any semi-advanced (mid highschool at latest) maths class.

It's about the same as someone who never plays chess complaining that the rules for pawns are not straighforward. If it's not relevant to you, why worry about it? And if it is, you either have to play by the rules or seek to change them (which, while hard, is by no means impossible).

[CaveDave]

This may already have been stated, but for the math illiterate, is there an overriding reason why the convention isn't to use parentheses to denote you want the calculation done other than in the order you wrote it? 10 x 0 + 10, for example, would get the result you want, by writing the question in the right order. Unless the result you want is to 'catch out' the mathematically illiterate.

SHHHH! [Looks 360 deg and covers mouth]

Yes, you have discovered the reason "Illuminati of mathematics" have willfully obfuscated arithmetic for so many centuries! How else could they ensure the supremacy of their "Priesthood" than by keeping the huddled masses ignorant of the arcane nature of their practices?

Just as in Guild Socialism (Unions and "Government Licensing"), they must strictly limit the number of ways the "pie" must be cut; to keep their monopoly on employment, lest the rabble be allowed to force down their prices! Careful now; if it is discovered you know the secret, your life will be made miserable (imagine what can be done to your bank accounts, wages, and credit rating by merely "misplacing" a decimal)!1!!11!
[/mozinarant]


:rolleyes:;):p

Why we can't sentence write a this way?
It's not to 'catch out' a math illiterate. It's a set of rules designed to ensure that people all over the world get the same answers when they check each others calculations.

Anyone not knowing these rules is unlikely to use maths to a degree where it matters, as they are among the first things taught in any semi-advanced (mid highschool at latest) maths class.

It's about the same as someone who never plays chess complaining that the rules for pawns are not straighforward. If it's not relevant to you, why worry about it? And if it is, you either have to play by the rules or seek to change them (which, while hard, is by no means impossible).

Precisely.

Cheers,

Dave

[hodgy]

Why we can't sentence write a this way?

Everyone (who speaks English) uses plain English every day and is therefore well practised in its grammar. Most people have no need to know or practice the rules of mathematical operators precedence on a regular basis.

The precedence rules are completely arbitrary - I do not see why I should have to Google them every time the odd occasion arises that some smart-arse wants to remind us that he or she knows operator precedence.

Use parenthesis.

[666]

I was taught BODMAS...
Likewise in Scotland. Must be a Commonwealth thing.

[Lukraak_Sisser]

Everyone (who speaks English) uses plain English every day and is therefore well practised in its grammar. Most people have no need to know or practice the rules of mathematical operators precedence on a regular basis.

The precedence rules are completely arbitrary - I do not see why I should have to Google them every time the odd occasion arises that some smart-arse wants to remind us that he or she knows operator precedence.

Use parenthesis.

Clearly you've never been anywhere where a regional dialect is spoken.
And you've never spoken to or read anything by either an american or british person (depending on where you're from)

But of course you're entitled to your opinion. If you want parenteses to be used as a matter of course, I'd suggest you write a convincing paper to either Nature or Science and get the movement started from there.
Once you've got the mathematicians on board you only need to wait until all governments around the world order the school books re-written and the new rules to be adapted. It should be done in, oh, 20 years or so?

But if it works at least you won't need to spend 1 minute googling something trivial anymore.

[akama1]

Hate to say it, I have a minor in maths, (And majored in Comp Sci-programing ) and still answered 0,

why?

Having spent so long programming and dealing with compact dealings, my brain overlooked something from high school. 10 + 10x where x=0 or 10 + (10 * 0)i would of answered correctly. But 10 + 10 * 0, I overlooked the fact when given advanced notation i automatically action */ first +- second (ie 2a +3/b +3), but when looking at it as a simple expression without structure, I fail to use the same rules as I do in day to day life. Having spent so much time using parenthesis to make sure there is no ambiguity in any calculations, I get caught by the same ambiguity myself.

Also I've never trusted and program to handle calculations correct and always add full parenthesis :/

So it's not just Maths Illiterate that can get it wrong :)

[CaveDave]

Clearly you've never been anywhere where a regional dialect is spoken.
And you've never spoken to or read anything by either an american or british person (depending on where you're from)

But of course you're entitled to your opinion. If you want parenteses to be used as a matter of course, I'd suggest you write a convincing paper to either Nature or Science and get the movement started from there.
Once you've got the mathematicians on board you only need to wait until all governments around the world order the school books re-written and the new rules to be adapted. It should be done in, oh, 20 years or so?

But if it works at least you won't need to spend 1 minute googling something trivial anymore.

Nominated.:)

Cheers,

Dave

[Gandalfs Beard]

I'm just lucky that I remember relatively simple "rules" or "conventions" such as Precedence Order. It's how I used to skate through algebra courses without doing the homework. I just remembered the basic rules and applied them to the equations given me. I didn't run into the brick wall until I hit Trigonometry, which requires more than memorization skills. At that point my Easy A's turned into Hard D's.

Of course that was decades ago, and I don't really have to bother with anything but the simplest algebra now (so don't bother testing me). Although I still have a math Crush on Quadratic equations because I like the fact that they have more than one correct answer. I also get a kick out of Imaginary Numbers because I thought I had discovered them. My algebra teacher sort of smirked at me, and said we'd be getting to that in advanced algebra.

But honestly, in regards to the OP poll, it's fairer to put parentheses so people don't get caught in what appears to them to be a trick question. Most people don't have to use more than basic math in their work and daily lives; and when they do, they usually have calculators and computers to get them by.

[jiggeryqua]

Why we can't sentence write a this way?
It's not to 'catch out' a math illiterate. It's a set of rules designed to ensure that people all over the world get the same answers when they check each others calculations.

Anyone not knowing these rules is unlikely to use maths to a degree where it matters, as they are among the first things taught in any semi-advanced (mid highschool at latest) maths class.

It's about the same as someone who never plays chess complaining that the rules for pawns are not straighforward. If it's not relevant to you, why worry about it? And if it is, you either have to play by the rules or seek to change them (which, while hard, is by no means impossible).

Well I understood your sentence, so it perhaps wasn't the best example to make your point, but more to the point, you missed my point...which was your point: that labelling those of us who got the 'wrong' answer to a poorly-presented question as 'math illiterate' is a little harsh, when it doesn't matter except to mathematicians.

You seem to have missed the post I was responding to - I'm not complaining about pawns or the arcane practises of mathematicians. I was responding to someone who called me (and LibraryLady among others) 'math illiterate' for not having specialist knowledge.

[jiggeryqua]

SHHHH! [Looks 360 deg and covers mouth]

Yes, you have discovered the reason "Illuminati of mathematics" have willfully obfuscated arithmetic for so many centuries! How else could they ensure the supremacy of their "Priesthood" than by keeping the huddled masses ignorant of the arcane nature of their practices?

Just as in Guild Socialism (Unions and "Government Licensing"), they must strictly limit the number of ways the "pie" must be cut; to keep their monopoly on employment, lest the rabble be allowed to force down their prices! Careful now; if it is discovered you know the secret, your life will be made miserable (imagine what can be done to your bank accounts, wages, and credit rating by merely "misplacing" a decimal)!1!!11!
[/mozinarant]


:rolleyes:;):p


Precisely.

Cheers,

Dave

See above, since you've also leapt into the middle of something and taken it out of context. :rolleyes: You've compounded your error, of course, by tossing out (it seems the most appropriate verb) some banal conspiracy strawman slurs masquerading as comedy. There are rules of writing too, for the specialist, but since you can at least spell and construct a sentence I'll refrain from you calling you illiterate.

[jiggeryqua]

But of course you're entitled to your opinion. If you want parenteses to be used as a matter of course, I'd suggest you write a convincing paper to either Nature or Science and get the movement started from there.
Once you've got the mathematicians on board you only need to wait until all governments around the world order the school books re-written and the new rules to be adapted. It should be done in, oh, 20 years or so?

But if it works at least you won't need to spend 1 minute googling something trivial anymore.

It was a trivial question on Facebook, which is itself trivial. As you said earlier, people don't actually need to know this stuff unless they're in a position where it matters, in which case they will. Can you explain why the question wasn't written 10 x 0 + 10, which would have enabled the 'math illiterate' to get the right answer too? That doesn't even need parentheses. The sole purpose of the question is to identify non-math-specialists - and then, apparantly, to insult them. :rolleyes:

[jiggeryqua]

Nominated.:)

Cheers,

Dave

For the Language Award?? :rolleyes: We can tell you're a mathematician...

[Gandalfs Beard]

Well I understood your sentence, so it perhaps wasn't the best example to make your point, but more to the point, you missed my point...which was your point: that labelling those of us who got the 'wrong' answer to a poorly-presented question as 'math illiterate' is a little harsh, when it doesn't matter except to mathematicians.

You seem to have missed the post I was responding to - I'm not complaining about pawns or the arcane practises of mathematicians. I was responding to someone who called me (and LibraryLady among others) 'math illiterate' for not having specialist knowledge.

Some people just like to feel superior to their peers (it's a rather common failing here on the JREF forums, ;) and I plead guilty to that as well). I felt that way for a whole semester before the rest of the class caught up to me when they learned about imaginary numbers for the first time. Of course, that smug sense of superiority vanished overnight when I hit Trigonometry. It was a humbling experience.

GB

[jiggeryqua]

Some people just like to feel superior to their peers (it's a rather common failing here on the JREF forums, ;) and I plead guilty to that as well). I felt that way for a whole semester before the rest of the class caught up to me when they learned about imaginary numbers for the first time. Of course, that smug sense of superiority vanished overnight when I hit Trigonometry. It was a humbling experience.

GB

I was a tad concerned that your teacher had 'smirked' at you, I don't think that's generally an acceptable expression for educators to adopt, but since it turned out you were smug I'll let the smirking go... :p

[Gandalfs Beard]

I was a tad concerned that your teacher had 'smirked' at you, I don't think that's generally an acceptable expression for educators to adopt, but since it turned out you were smug I'll let the smirking go... :p

Maybe bemusement would be a better word. She actually seemed more than a bit impressed; the smirk bit was more at my audacity for thinking I had invented imaginary numbers. :D

GB

[roger]

You're not trying not to be rude either, given that you've acknowledged that it is rude and said it anyway.

I don't believe myself to be 'math illiterate' any more than I consider math graduates to be drooling gibbons because they don't write poetry, even if they can spell and form sentences. At no point in my life has anything but the ego of some mathemiticians and one particular poor question setter hung on whether I knew some arbitrary rule from the math club. My mathematical literacy suffices for real life. 'You're not a mathematician!' isn't rude, but I'd be surprised if you bothered saying it (and a tad concerned for you too). "You don't know something you don't know!" isn't rude either, but again, would you say it? Only "you're illiterate" is rude, as you acknowledge, and its rudeness seems to be the only reason to choose to say it.
"Illiterate" is not an insult. I haven't done partial differential equations for at least 10 years, and that makes me illiterate with them. In a different vein, I'm completely ignorant about Peruvian pottery, and that is not an insulting statement either. Of course, both terms can have a pejorative implication, and so I hastened to point out I was not employing the pejorative use.

You keep asking why this convention? It's been explained. The facebook example is trivial, but the equations used in science are not. They are filled with terms, and we most often really do want to do exponents first, then multiplication, then addition. Having to surround every equation with superfluous parenthesis just isn't going to fly. The rules are made for people that work in it every day.

You've also asked why not just write in the order that you want things done. That doesn't work for things like polynomials and infix notation. You would need parens. No mathematician would want to spend their days writing 2*(x2)+(4*x)-3 when they can write 2x2+4x-3. Recognize that is a very simple equation; if you got rid of operator precedence you'd end up with equations with parens stacked 6 deep, and that becomes very hard to parse.

The rules work very very well for the vast majority of equations that need to be written in engineering and physics, and that is why they are used. I've never come across a working engineer that couldn't do operator precedence in their sleep.

[roger]

The precedence rules are completely arbitrary - I do not see why I should have to Google them every time the odd occasion arises that some smart-arse wants to remind us that he or she knows operator precedence.They are not arbitrary. They are chosen based on how we most often need to do math.

Polynomials are the most common equation on earth. And, you need to do them in the order of exponents, multiplication, then addition. Exactly the same as operator precedence. That is not a coincidence.

It also follows how we speak. What is 5 plus a half? 5.5, of course. What is the equation? 5 + 1/2. What is the operation order? multiplication/division followed by addition.

Of course, not every equation works out that way, and so various grouping terms are used. The long ------ horizontal fraction bar is used to group the stuff on the top and bottom of the bar. That is easier to read than (1+2)/(3+4). Sure, just slightly, but that is of course a trivial example of what can be complex equations.

This convention goes back centuries, and was adopted because of the common form that math takes (polynomials). The rules aren't really meant for chains of arithmetic 3+4-6*78-6/4+3-5/3*4 or whatever - a few extra parens would probably help with readability there. They are meant for algebra, calculus, et al, and for these fields the rules work gloriously. But as I note, it works well for how we speak (five and a half).

[Gandalfs Beard]

Hey Roger, I'm with you on knowing the Math Rules, I really am. But in the Rules of debate, "Illiterate" is nearly ALWAYS a Pejorative (which should only be reserved for the truly imbecilic).


GB

[roger]

http://upload.wikimedia.org/math/7/e/2/7e2b91f0f01278f3be5466a98a84444e.pngin parens:

1/(2*pi) * f (1-(r^2)/(1+(r^2)-(2*r*cos(o-o'))*u(o'))do' (I'm illiterate in latex, so I can't make the latex version of this equation, sorry).

Of course the former uses text formatting to make things clearer - implied multiplication, spacing surround + and -, long division, etc. You basically go to great lengths to avoid parens because they once nested they become extremely difficult to parse - you have to start scanning left and right, counting indentation level, to figure out what ( the ) matches.

It should be noted that these groupings have meaning. It is not arbitrary that r is squared - r is a radius in the above equation, and you tend to need to square radii. It is not arbitrary to multiply pi by 2 - that the number of degrees in a circle. Again and again, it just makes sense to deal with multiplication first.

[jiggeryqua]

You keep asking why this convention? It's been explained.

No, I keep asking why the question wasn't written "10 x 0 + 10", but that's been explained too: 'to catch out the mathematically illiterate, so that math specialists can enjoy an all too infrequent moment of feeling superior'.

[roger]

Hey Roger, I'm with you on knowing the Math Rules, I really am. But in the Rules of debate, "Illiterate" is nearly ALWAYS a Pejorative (which should only be reserved for the truly imbecilic).


GBI'm open to a better term. Math unpracticed? math unaware? Math doesn't do much high level? Math only at the arithmetic level? Sure, these constructions are silly, but I can't think of a good one. To me it is exactly the right term - you need to be able to read equations to do math (as opposed to arithmetic). I certainly didn't mean it as an insult, am uncomfortable that I made somebody think I insulted them, and I tried to use 'illiterate' to refer to myself in later posts to point that out.

[roger]

No, I keep asking why the question wasn't written "10 x 0 + 10", but that's been explained too: 'to catch out the mathematically illiterate, so that math specialists can enjoy an all too infrequent moment of feeling superior'.
?? It's a fun little quiz. The world isn't as hostile as you think.

edited to add: if you want to test if somebody knows the precedence rules, you need to order the equation to test if they are using them correctly or not. Your order allows the person to get it right if they use left-right or the precedence ordering. It's not a test to see if you can perform arithmetic.

[jiggeryqua]

"Illiterate" is not an insult.

Here, and in the wider world, we are not protected from all offence, not all insults are actionable, but it is the convention in human interaction (recognised in UK law at least) that an insult occurs when the person feels insulted. It's conventional in polite society to make an apology, albeit insincerely. But it's no surprise you're ignorant of those conventions, as a mathematician... :p

[roger]

Here, and in the wider world, we are not protected from all offence, not all insults are actionable, but it is the convention in human interaction (recognised in UK law at least) that an insult occurs when the person feels insulted. It's conventional in polite society to make an apology, albeit insincerely. But it's no surprise you're ignorant of those conventions, as a mathematician... :pI sincerely apologize.

I feel rather insulted that you basically called me a liar, btw. I think I'll get over it, though.

[Gandalfs Beard]

I'm open to a better term. Math unpracticed? math unaware? Math doesn't do much high level? Math only at the arithmetic level? Sure, these constructions are silly, but I can't think of a good one. To me it is exactly the right term - you need to be able to read equations to do math (as opposed to arithmetic). I certainly didn't mean it as an insult, am uncomfortable that I made somebody think I insulted them, and I tried to use 'illiterate' to refer to myself in later posts to point that out.

I do comprehend your dilemma. And it's kind of you to use the term on yourself to demonstrate that you didn't mean it unkindly. I almost thought of "Arithmetically Challenged" but that sounded worse, and it would most certainly apply to me at this point in my life (well not if I really put my mind to it, but I'm definitely rusty).

How about just sticking to: "Well these are the math rules, and they've taken centuries to create, and it would be inconvenient to change that all now. And I suppose we could have put parentheses around the right bits in the poll question for those that don't remember which are the right bits, but we were curious to see who would actually remember the right bits so we didn't."

It's a lot less to write than you've had to write to say the same thing, and it doesn't make the otherwise intelligent people here feel insulted. :)

GB

[Ladewig]

I'm open to a better term. Math unpracticed? math unaware? Math doesn't do much high level? Math only at the arithmetic level?

I going to guess that suggesting "innumerate" won't help the matter.

[jiggeryqua]

?? It's a fun little quiz. The world isn't as hostile as you think.

If you could recognise for a moment that the question I keep repeating is not the one you ascribed to me, we might be a step closer to agreeing on an answer. Why was the question presented to a lay audience when the only way to get the 'right' answer is to be 'literate' (and no, the lack of some specific convention does not equal illiteracy - I have an enduring mental block on several (sp?) common words but I am a succesful performance poet. I am neither illiterate with words nor maths. I'm just not a mathematician.)

As presented, the question's only function is to separate (sp?) those who chose a particular route in education. How those elevated to the superior group by the question choose to respond to it may not have been planned or foreseen by the setter.

'Fun', by the way, is another of those words I'll define by myself. It's not universal - in this case, I'm sure mathematicians enjoyed the question. I didn't have fun, but I didn't regard it as 'hostile', just rather trivial, like those adventure games with death-dealing doors ("There are exits East and West"; GO EAST; "You died!"). I didn't see it in its original setting, maybe if it told you you were wrong Ripley's-style I'd be mildly interested in some quirk that the boffins work by. Here, the result was accompanied by a threadful of 'What?? You didn't know this? You're illiterate', though I accept your apology inability to apologise.

How 'hostile' do I think the world is (I ask you since you seem to know)? Is there a recognised scale? Let's say 1 - 11, with 11 being 'one more hostille than 10' (as is the convention). How hostile is the world actually (using the same scale)? How far should I carry this before you realise that your unfounded claim is itself 'hostile'?

[SOdhner]

In case anyone is curious, this was my thought process:

1. Okay, so it says (10 + 10) * 0. No problem, that's zero.

2. Wait, wait. That's too easy. They wouldn't have asked if they didn't think there was a good chance you would get it wrong. Read it again.

3. Sigh. Fine. Oh! Huh, I could have sworn there were parentheses there a second ago.

4. What, you think they're magical disappearing parentheses?

5. Shut up. Anyway, so this is probably an Order of Operations thing. Wasn't there a pneumonic device for that?

6. You mean a mnemonic device, and yes... but I don't remember it. Anyway, I'm positive that multiplication and division go first so it's ten, not zero.

7. I'm going to look it up.

8. You don't need to look it up. Multiplication is before addition unless there's parentheses.

9. The internet is right here, though. Hmm. Okay, so it looks like multiplication is before addition unless there's parentheses - so it's ten, not zero.

10. I hate you.

So I got it right, but if I had been just answering it casually I might have very well said zero. It's not that I wasn't educated properly, it's that I rarely do multi-step math without it being something where the order is obvious because it relates to actual physical objects, or it's written with the parentheses. I agree that it's important to have rules about what order to apply things so that everyone (in theory) gets the same answer, but I don't think people getting this wrong says anything dire about humanity.

[not daSkeptic]

Here, and in the wider world, we are not protected from all offence, not all insults are actionable, but it is the convention in human interaction (recognised in UK law at least) that an insult occurs when the person feels insulted. It's conventional in polite society to make an apology, albeit insincerely. But it's no surprise you're ignorant of those conventions, as a mathematician... :p

You felt insulted because someone you've probably never met and probably never will pointed out your lack of ability to read a certain language?

[roger]

I agree that it's important to have rules about what order to apply things so that everyone (in theory) gets the same answer, but I don't think people getting this wrong says anything dire about humanity.
No, that's true. I mean, I forgot tons of stuff that I learned in 4th and 5th grade, about when you'd learn this rule. It does speak to mathematical literacy (too bad if somebody get torqued off by that term, it's used all over education websites, in published papers, etc). Of course opinions vary, but in general to claim that you are educating somebody to basic mathematical literacy they are expected to be able to do simple graphs, solve linear equations, solve word problems requiring linear equations, etc. You generally aren't expected to be able to do quadratic equations or generalized polynomials. We could bicker endlessly about it, but generally those constraints allow a person to tackle problems that they may face - figuring out how to build a closet or put in stairs, calculate the most efficient purchase options, mortgages, stuff like that. Sure, you can work out a lot of stuff like that without simple algebra, but linear equations make a lot of stuff easier.

And, I would say that our nation (the US, don't know where any individual poster lives) has pretty low math literacy (example source (http://abcnews.go.com/US/story?id=319129), another (http://web.mit.edu/newsoffice/2006/hockfield-educate.html)), and I do consider that a problem. Not that every person needs it - I believe in specialization - but a lot of countries have a higher level of literacy than we do, and that has enormous consequences for people's ability to do science, understand news reports, etc. There's a lot of math in understanding things like risk assessment, for example (which has nothing to do with operator precedence, of course), and people get it very, very wrong. OH NOES, my risk is doubled. Not a big deal if your risk factor was 1 in 12 million.

So, I speculate without any proof whatsoever that you would find a higher proportion of correct answers to that problem in countries that beat us (the US) in math and science education, because it is just a pretty low level piece of knowledge required to do all the rest. That any one person misses the question does not bother me - I'd miss questions about many things historical and political that people would consider part of a base education. That a country as a whole misses it by large percentage is worrisome to me.

[Madalch]

Everyone (who speaks English) uses plain English every day and is therefore well practised in its grammar. Most people have no need to know or practice the rules of mathematical operators precedence on a regular basis.

The precedence rules are completely arbitrary - I do not see why I should have to Google them every time the odd occasion arises that some smart-arse wants to remind us that he or she knows operator precedence.

Use parenthesis.
Sure, we'll just change all of math to comfort those who can't be bothered to remember things they should have been taught in grade 4. The effort required to re-write thousands of math texts is trivial compared the amount of work you'd have to do to learn a concept like BEDMAS (BODMAS, Please Excuse My Dear Aunt Sally, whatever), since that effort wouldn't be on your part.

I had a student (in a first-year university math class) hand in an assignment which required the use of long division. She wrote "We haven't covered long division!" on her paper and handed it in, fully expecting to not be penalized for this answer. For some reason, I'm reminded of her.

[Gandalfs Beard]

No, that's true. I mean, I forgot tons of stuff that I learned in 4th and 5th grade, about when you'd learn this rule. It does speak to mathematical literacy (too bad if somebody get torqued off by that term, it's used all over education websites, in published papers, etc). Of course opinions vary, but in general to claim that you are educating somebody to basic mathematical literacy they are expected to be able to do simple graphs, solve linear equations, solve word problems requiring linear equations, etc. You generally aren't expected to be able to do quadratic equations or generalized polynomials. We could bicker endlessly about it, but generally those constraints allow a person to tackle problems that they may face - figuring out how to build a closet or put in stairs, calculate the most efficient purchase options, mortgages, stuff like that. Sure, you can work out a lot of stuff like that without simple algebra, but linear equations make a lot of stuff easier.

And, I would say that our nation (the US, don't know where any individual poster lives) has pretty low math literacy (example source (http://abcnews.go.com/US/story?id=319129), another (http://web.mit.edu/newsoffice/2006/hockfield-educate.html)), and I do consider that a problem. Not that every person needs it - I believe in specialization - but a lot of countries have a higher level of literacy than we do, and that has enormous consequences for people's ability to do science, understand news reports, etc. There's a lot of math in understanding things like risk assessment, for example (which has nothing to do with operator precedence, of course), and people get it very, very wrong. OH NOES, my risk is doubled. Not a big deal if your risk factor was 1 in 12 million.

So, I speculate without any proof whatsoever that you would find a higher proportion of correct answers to that problem in countries that beat us (the US) in math and science education, because it is just a pretty low level piece of knowledge required to do all the rest. That any one person misses the question does not bother me - I'd miss questions about many things historical and political that people would consider part of a base education. That a country as a whole misses it by large percentage is worrisome to me.

I'm not really sure it's due to my being born in the UK; we moved here to the US when I was 7. Part of it may have to do with the fact that family members on both of my parents' sides were themselves were good enough at math to make a living using it.

But I think the biggest problem in the US in particular, is that education isn't valued very highly. There's a sort of cultural attitude that knowing a lot of stuff is a sissy nerdy thing to do, and the US does foster a certain level of machismo among its populace that seems to outstrip that of other nations (it may have something to do with John Wayne and the Marlboro Man ;) ).

It's often claimed that US Americans (by other US Americans) don't like electing people to office that are smarter than them. I don't think that's really true of the majority of people in the US. But it does seem to often be true of the people that actually end up in the voting booth.

I'm really not sure that the above is quantifiable enough to be testable.

GB

[jiggeryqua]

You felt insulted because someone you've probably never met and probably never will pointed out your lack of ability to read a certain language?

No, I felt insulted because of the way he expressed it, and insulting me for it won't change that.

[jiggeryqua]

It does speak to mathematical literacy (too bad if somebody get torqued off by that term, it's used all over education websites, in published papers, etc).

Well I'm not alone in getting 'torqued off', apparantly. To call someone 'illiterate' is to say that they cannot read or write. At all. To call someone 'mathematically illiterate' is to suggest they can't count, when what you mean is they haven't specialised in maths. If that's a common use of the term it's a debasement of language...and I care about language. Less so about maths, as we've established, if the precedence matters those to whom it matters know, and if you're addressing non-specialists you pose the question better.

10 x 0 + 10 gets the result you wanted from specialists and non-specialists alike, unless the result you want is to identify the non-specialists so the remainder can feel superior for a change.

I wasn't even that worked up about it, it's the frantic refusal to admit having given offence that has dragged this out.

[sol invictus]

They are not arbitrary. They are chosen based on how we most often need to do math.

That might be true for some conventions, although you're going to have a tough time making the case. But it's plainly not true for some others. For example, simply invert (left<-->right) the order in which things are written, and that will obviously work just as well.

Of course it might not be convenient to do that for written languages that go left to right - but there are plenty that go right to left, and that ordering in itself is obviously arbitrary.

Polynomials are the most common equation on earth.

Polynomials aren't an equation. And if your goal is (for some reason) to write down polynomials in the most efficient way possible, I assure you our notation isn't it (I can think of another of the top of my head that is better).

[Lukraak_Sisser]

Maybe a bit off topic, but isn't the point to pretty much any mathematical, scientific question an attempt to 'catch out' those who do know the answer and those who don't?
Especially one that appears to come straight out of some low grade math textbook, where the whole idea would be to get an indication of how many students get it wrong so they can be taught the right way before leaving school?

[Gandalfs Beard]

Maybe a bit off topic, but isn't the point to pretty much any mathematical, scientific question an attempt to 'catch out' those who do know the answer and those who don't?
Especially one that appears to come straight out of some low grade math textbook, where the whole idea would be to get an indication of how many students get it wrong so they can be taught the right way before leaving school?

It's not off topic at all. It was a quiz to see how many people would come up with the right answer given the information they had at hand. No problem there.

I think the main problem is that calling someone "Illiterate" on a forum dedicated to intellectual pursuits is clearly insulting. Which is alright when you are on a particularly controversial topic and are engaged in verbal combat (take no prisoners is my attitude). But it wasn't really necessary to wind people up on a thread like this.

GB

[SOdhner]

Just to put this out there: If this question had been asked out loud, I absolutely would have said zero rather than ten and would have felt perfectly justified doing so unless the pacing and inflection clearly indicated that the multiplication should happen first. In conversational settings (as opposed to reciting selected portions of a math textbook like some sort of nerdy poetry reading), I would expect most rational people to say "What is ten times zero plus ten?" rather than "what is ten plus ten times zero?" just because of unwritten rules of conversation (as observed by an American living in Arizona).

[roger]

That might be true for some conventions, although you're going to have a tough time making the case. But it's plainly not true for some others. For example, simply invert (left<-->right) the order in which things are written, and that will obviously work just as well.

Of course it might not be convenient to do that for written languages that go left to right - but there are plenty that go right to left, and that ordering in itself is obviously arbitrary.I'm sorry, I do not understand your point here.

edit: went back and reread and got it this time. I'm not claiming the rules are perfect or the best available, just that they are usually better than the alternative being suggested.

Polynomials aren't an equation. And if your goal is (for some reason) to write down polynomials in the most efficient way possible, I assure you our notation isn't it (I can think of another of the top of my head that is better).Ya, they're an expression, I think you know what I mean (polynomial equations).

The goal is not the most efficient expression possible, not sure where you got that. I'm responding to a very specific suggestion of replacing operator precedence with full use of parens instead. The current scheme works very well for our math needs, and full parens becomes quite unreadable (to me, YMMV).

[Gandalfs Beard]

Just to put this out there: If this question had been asked out loud, I absolutely would have said zero rather than ten and would have felt perfectly justified doing so unless the pacing and inflection clearly indicated that the multiplication should happen first. In conversational settings (as opposed to reciting selected portions of a math textbook like some sort of nerdy poetry reading), I would expect most rational people to say "What is ten times zero plus ten?" rather than "what is ten plus ten times zero?" just because of unwritten rules of conversation (as observed by an American living in Arizona).

Except that it wasn't asked out loud.

GB

[SOdhner]

Except that it wasn't asked out loud.

Oh my gosh, that completely invalidates my entire point! How could I have missed that? Oh, no, wait. I did notice that and it changes nothing at all about what I was saying. Look, the word "if" is there in my post and everything!

The point is: while it's super important to have rules about how to calculate stuff, this kind of thing doesn't mesh well with the way we think (even about math) in other contexts, the same way it's harder to recognize someone from work if you bump into them at the supermarket.

Because of this, I would expect a fair number of people to get this kind of question wrong in ambiguous contexts like facebook not because they don't know the rules but because they weren't in the correct mindset. (Although yes, some people will also get it wrong because they forget (or are unaware) that the rule exists.)

[Gandalfs Beard]

Oh my gosh, that completely invalidates my entire point! How could I have missed that? Oh, no, wait. I did notice that and it changes nothing at all about what I was saying. Look, the word "if" is there in my post and everything!

The point is: while it's super important to have rules about how to calculate stuff, this kind of thing doesn't mesh well with the way we think (even about math) in other contexts, the same way it's harder to recognize someone from work if you bump into them at the supermarket.

Because of this, I would expect a fair number of people to get this kind of question wrong in ambiguous contexts like facebook not because they don't know the rules but because they weren't in the correct mindset. (Although yes, some people will also get it wrong because they forget (or are unaware) that the rule exists.)

No, no! I get that. I saw the word "if", that's why I used the word "except." ;)

GB

[not daSkeptic]

The amount of whining and justifying in this thread is crazy. So you didn't know something and got a question wrong. Oh noes, the world is ending!! Learn from it and move on already.

[CaveDave]

See above, since you've also leapt into the middle of something and taken it out of context. :rolleyes: You've compounded your error, of course, by tossing out (it seems the most appropriate verb) some banal conspiracy strawman slurs masquerading as comedy. There are rules of writing too, for the specialist, but since you can at least spell and construct a sentence I'll refrain from you calling you illiterate.

I sincerely apologize: I must have not been transparent enough, for my intent was not to ridicule honest lack of knowledge; I was in a funky mood and wanted to try my hand at creative parody/humor writing, the phrase I had highlighted caught my attention, and I cut loose at the Conspiracy Theory kooks I have seen far too many of lately. I was not wanting to personally attack YOU, but the attitude some others had hinted at upthread, and your phrase exemplified, that I see throughout this forum and the interwebz in general.

I believe that ignorance is a correctable oversight, - not a character flaw -, but that willful stupidity - a refusal to even WANT to learn - deserves all the scorn we can heap on it's owner.
I imagine you are in the former category, and therefore blameless.:)

I, along with many others, come here for the "E" in JREF.:)

... but since you can at least spell and construct a sentence...
Thank you for noticing:). I sometimes wonder if it is worth the effort to hold on to the old ways in light of society's apparent apathetic disregard for politeness and formality, but I think it helps moderate my brain's decay from advancing age and youthful indiscretions.:)


-----------------------
[!Tang ]
I make an ill-advised foray into humor, I neglect to consider that the anonymous nature of the medium, an internet forum, has been amply demonstrated in the past to be highly prone to misunderstandings, but I willfully charge on, my scattershot pathetic attempt at parody brings collateral damage to innocent victims, I die, the disgusting vapors from my purifying corpse spreads across the land, all living things experience terminal seizures of vomiting, all die, O the Embarrassment!![/!Tang ]


-----------------------

Cheers,

Dave

ETA: I posted this without having read the ~50 post PAGE that came in before I hit "submit post". I have NOW read that batch, marked those I wanted to respond to (many, MANY), and now I will respond to those BEFORE I read any that arrived after this one, and continue in the same fashion. That is just how I do things, and will continue to.
I say this because I do not want any ambiguity to creep in, as far as possible.

[CaveDave]

It was a trivial question on Facebook, which is itself trivial.

True.

As you said earlier, people don't actually need to know this stuff unless they're in a position where it matters, in which case they will. Can you explain why the question wasn't written 10 x 0 + 10, which would have enabled the 'math illiterate' to get the right answer too? That doesn't even need parentheses. The sole purpose of the question is to identify non-math-specialists - and then, apparantly, to insult them. :rolleyes:

Sigh.:confused:

I am not one who assumes others' motives are automatically evil, and they are out to get me. Am I a "Polyanna[sp?]" because of that? Perhaps, but I don't think so. I assume innocence until the preponderance of evidence tips the scales.

To assume someone is malevolent without evidence feels wrong to me.

But that may only be me.:o

[Gandalfs Beard]

True.



Sigh.:confused:

I am not one who assumes others' motives are automatically evil, and they are out to get me. Am I a "Polyanna[sp?]" because of that? Perhaps, but I don't think so. I assume innocence until the preponderance of evidence tips the scales.

To assume someone is malevolent without evidence feels wrong to me.

But that may only be me.:o

No matter how you slice it, calling someone "Illiterate" is an insult. I should know. I just called someone illiterate on another thread. :p

GB

[roger]

No matter how you slice it, calling someone "Illiterate" is an insult. I should know. I just called someone illiterate on another thread. :p

GBStop *********** lying about me. I did not intend it as an insult, I said in the post it was not intended as an insult, and I explained afterward it was meant as an insult.

It is insulting to suggest I lied. I note that while I apologized for the hurt feeling you and the other fellow have just kept the nastiness up. Classy.

I suggest contacting John Allen Paulos (http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its-Consequences/dp/0809058405/ref=ntt_at_ep_dpt_1), MIT (http://web.mit.edu/newsoffice/2006/hockfield-educate.html), the National Mathematics Advisory Panel (http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf), et. al., and tell them they are all being insulting for using the term.

[Gandalfs Beard]

Stop *********** lying about me. I did not intend it as an insult, I said in the post it was not intended as an insult, and I explained afterward it was meant as an insult.

It is insulting to suggest I lied. I note that while I apologized for the hurt feeling you and the other fellow have just kept the nastiness up. Classy.

I suggest contacting John Allen Paulos (http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its-Consequences/dp/0809058405/ref=ntt_at_ep_dpt_1), MIT (http://web.mit.edu/newsoffice/2006/hockfield-educate.html), the National Mathematics Advisory Panel (http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf), et. al., and tell them they are all being insulting for using the term.

I never called you a liar. I have been very nice to you because I agree with everything you say...except for the part where you (unintentionally) insulted everyone not as good at math as you and me.

Pointing out that an insult is an insult (intended or not) is not the same as calling you a liar (which I didn't) or being nasty myself (which I wasn't).

GB

EDIT: PS: By the way, talking about Illiteracy in society generally, is not the same as calling an individual Illiterate.

[CaveDave]

For the Language Award?? :rolleyes: We can tell you're a mathematician...

Thank you for the compliment, but actually not. I was an EXTREMELY poor student, at least in "formal" environments. I HATED school - it was years of unending torment for me. I COULD NOT be forced to conform, "pay attention", follow orders, turn in work, "practice", or any of the putative "virtues" of "good students".

When tests were given, unless they required massive writing (which I also refused), I had high scores, ant officials were baffled.

Cheating? No.
Osmosis? How would THAT work?
Magic? Hell No!
What?

Turns out I was absorbing the information all along without looking like I was. I was BORED but I still heard it all.

I tend to learn quickly, and if I am particularly interested, I can get completely absorbed to the point of shutting out all else. If it doesn't interest me, I still get the gist, but don't appear to care.

Genius? Moron? You tell me.
Autism Spectrum? I don't know.
ADD/ADHD? In the 1960s these were unknown and I was never diagnosed - some people have speculated so, but never certified.
Organic brain defect? Perhaps: I am a bit Bipolar, and have had my full share of problems.

Bottom line: I learn what catches my eye, ignore what doesn't. I try to be aware of enough things that I can recognize what people are discussing, and am often able to add to the conversation, and usually know what "bin" to file new nuggets in if I hear new data; when I stumble across something "new", I ask or research enough to decide if I want to pursue it or not.

I adopt the stance of Rikki-Tikki-Tavi, Kipling's mythical Mongoose: When I want to know something, I run and find out.

My personal motto is: "If there comes a day where I don't learn something new, Dig a hole, toss me, and replace the dirt, before I attract flies.;)

Iam a Jack of Many Trades, but a Master of none.

Cheers,

Dave

P.S. I just now see the rolleyes emoticon, so you may have intended sarcasm: If so, I hope taking advantage of my good nature and naivete gave you a rush, but you didn't get my "cherry", that was lost 50 years and millions of times ago. Enjoy it.

[Gandalfs Beard]

When tests were given, unless they required massive writing (which I also refused), I had high scores, ant officials were baffled.

Cheating? No.
Osmosis? How would THAT work?
Magic? Hell No!
What?


Well I wasn't as poor a student as you apparently (I actually liked school). But I got through math (until Trig) pretty much as you described. I barely did any of my homework and still aced my tests.

GB

[CaveDave]

I want to comment on so many posts that 1 at a time is impractical, so here they in one whack.:)
Some people just like to feel superior to their peers (it's a rather common failing here on the JREF forums, ;) and I plead guilty to that as well). I felt that way for a whole semester before the rest of the class caught up to me when they learned about imaginary numbers for the first time. Of course, that smug sense of superiority vanished overnight when I hit Trigonometry. It was a humbling experience.

GB

Indeed.

Maybe bemusement would be a better word. She actually seemed more than a bit impressed; the smirk bit was more at my audacity for thinking I had invented imaginary numbers. :D

GB

;)

"Illiterate" is not an insult. I haven't done partial differential equations for at least 10 years, and that makes me illiterate with them. In a different vein, I'm completely ignorant about Peruvian pottery, and that is not an insulting statement either. Of course, both terms can have a pejorative implication, and so I hastened to point out I was not employing the pejorative use.

You keep asking why this convention? It's been explained. The facebook example is trivial, but the equations used in science are not. They are filled with terms, and we most often really do want to do exponents first, then multiplication, then addition. Having to surround every equation with superfluous parenthesis just isn't going to fly. The rules are made for people that work in it every day.

You've also asked why not just write in the order that you want things done. That doesn't work for things like polynomials and infix notation. You would need parens. No mathematician would want to spend their days writing 2*(x2)+(4*x)-3 when they can write 2x2+4x-3. Recognize that is a very simple equation; if you got rid of operator precedence you'd end up with equations with parens stacked 6 deep, and that becomes very hard to parse.

The rules work very very well for the vast majority of equations that need to be written in engineering and physics, and that is why they are used. I've never come across a working engineer that couldn't do operator precedence in their sleep.

Beautifully crafted and informative.

They are not arbitrary. They are chosen based on how we most often need to do math.

Polynomials are the most common equation on earth. And, you need to do them in the order of exponents, multiplication, then addition. Exactly the same as operator precedence. That is not a coincidence.

It also follows how we speak. What is 5 plus a half? 5.5, of course. What is the equation? 5 + 1/2. What is the operation order? multiplication/division followed by addition.

Of course, not every equation works out that way, and so various grouping terms are used. The long ------ horizontal fraction bar is used to group the stuff on the top and bottom of the bar. That is easier to read than (1+2)/(3+4). Sure, just slightly, but that is of course a trivial example of what can be complex equations.

This convention goes back centuries, and was adopted because of the common form that math takes (polynomials). The rules aren't really meant for chains of arithmetic 3+4-6*78-6/4+3-5/3*4 or whatever - a few extra parens would probably help with readability there. They are meant for algebra, calculus, et al, and for these fields the rules work gloriously. But as I note, it works well for how we speak (five and a half).

YES.

No, I keep asking why the question wasn't written "10 x 0 + 10", but that's been explained too: 'to catch out the mathematically illiterate, so that math specialists can enjoy an all too infrequent moment of feeling superior'.

Does anyone catch a whiff of Delusions of Persecution?
It's NOT all about you...

I'm open to a better term. Math unpracticed? math unaware? Math doesn't do much high level? Math only at the arithmetic level? Sure, these constructions are silly, but I can't think of a good one. To me it is exactly the right term - you need to be able to read equations to do math (as opposed to arithmetic). I certainly didn't mean it as an insult, am uncomfortable that I made somebody think I insulted them, and I tried to use 'illiterate' to refer to myself in later posts to point that out.

I don't think it matters: when a person carries their feelings on their sleeve, daring any and all to bruise them, They will bump a wall and claim you whacked them.;)

?? It's a fun little quiz. The world isn't as hostile as you think.

edited to add: if you want to test if somebody knows the precedence rules, you need to order the equation to test if they are using them correctly or not. Your order allows the person to get it right if they use left-right or the precedence ordering. It's not a test to see if you can perform arithmetic.

Good.

Here, and in the wider world, we are not protected from all offence, not all insults are actionable, but it is the convention in human interaction (recognised in UK law at least) that an insult occurs when the person feels insulted. It's conventional in polite society to make an apology, albeit insincerely. But it's no surprise you're ignorant of those conventions, as a mathematician... :p

Liberal Marxist, much?:rolleyes:

Men need to stand on their own hind legs, not expect to NEVER be injured, or else.

I sincerely apologize.

I feel rather insulted that you basically called me a liar, btw. I think I'll get over it, though.

I did too, but when this was posted, I was still composing mine. If the reception is the same, I will be disappointed. But I too, will get over it. Some folks are never satisfied.

I do comprehend your dilemma. And it's kind of you to use the term on yourself to demonstrate that you didn't mean it unkindly. I almost thought of "Arithmetically Challenged" but that sounded worse, and it would most certainly apply to me at this point in my life (well not if I really put my mind to it, but I'm definitely rusty).

How about just sticking to: "Well these are the math rules, and they've taken centuries to create, and it would be inconvenient to change that all now. And I suppose we could have put parentheses around the right bits in the poll question for those that don't remember which are the right bits, but we were curious to see who would actually remember the right bits so we didn't."

It's a lot less to write than you've had to write to say the same thing, and it doesn't make the otherwise intelligent people here feel insulted. :)

GB

Yep.

I going to guess that suggesting "innumerate" won't help the matter.

:)

If you could recognise for a moment that the question I keep repeating is not the one you ascribed to me, we might be a step closer to agreeing on an answer. Why was the question presented to a lay audience when the only way to get the 'right' answer is to be 'literate' (and no, the lack of some specific convention does not equal illiteracy - I have an enduring mental block on several (sp?) common words but I am a succesful performance poet. I am neither illiterate with words nor maths. I'm just not a mathematician.)

The point, as I understand it, is entertainment, at the participant's free choice. No one can be forced to "play", and it is trivially obvious that there two possible outcomes; the player is ""right" or s/he is "wrong". No other way to go. The rules are also obvious: look at the problem, evaluate it's structure, look at possible answers, pick the best fit, check to see if you were right or wrong. No ones life, liberty, or ability to persue happiness is ever in jeopardy.

Real life IS NOT Pee Wee league baseball (the new "style with no winners, no losers, everybody gets a trophy... Yuccch. :p:boggled:) Everyone can make themselves aware of the rules, and to or to not particiipate or not.

So what is your point - "where's the Beef"?

As presented, the question's only function is to separate (sp?) those who chose a particular route in education. How those elevated to the superior group by the question choose to respond to it may not have been planned or foreseen by the setter.

Absolutely Wrong. What "Illuminatum" could have such low self-esteem and be stupid enough to believe that his own stature would be elevated by pointlessly humiliating helpless commoners.

Man, what a twisted world view would THAT be?:rolleyes::jaw-dropp

'Fun', by the way, is another of those words I'll define by myself. It's not universal - in this case, I'm sure mathematicians enjoyed the question. I didn't have fun, but I didn't regard it as 'hostile', just rather trivial, like those adventure games with death-dealing doors ("There are exits East and West"; GO EAST; "You died!"). I didn't see it in its original setting, maybe if it told you you were wrong Ripley's-style I'd be mildly interested in some quirk that the boffins work by. Here, the result was accompanied by a threadful of 'What?? You didn't know this? You're illiterate', though I accept your apology inability to apologise.



How 'hostile' do I think the world is (I ask you since you seem to know)? Is there a recognised scale? Let's say 1 - 11, with 11 being 'one more hostille than 10' (as is the convention). How hostile is the world actually (using the same scale)? How far should I carry this before you realise that your unfounded claim is itself 'hostile'?

Whatever... :rolleyes: I am beginning to tire of this game.

I wish you peace and a happy life, but I fear you won't, what the massive baggage you evidently insist on hauling around.:(:confused:

In case anyone is curious, this was my thought process:

1. Okay, so it says (10 + 10) * 0. No problem, that's zero.

2. Wait, wait. That's too easy. They wouldn't have asked if they didn't think there was a good chance you would get it wrong. Read it again.

3. Sigh. Fine. Oh! Huh, I could have sworn there were parentheses there a second ago.

4. What, you think they're magical disappearing parentheses?

5. Shut up. Anyway, so this is probably an Order of Operations thing. Wasn't there a pneumonic device for that?

6. You mean a mnemonic device, and yes... but I don't remember it. Anyway, I'm positive that multiplication and division go first so it's ten, not zero.

7. I'm going to look it up.

8. You don't need to look it up. Multiplication is before addition unless there's parentheses.

9. The internet is right here, though. Hmm. Okay, so it looks like multiplication is before addition unless there's parentheses - so it's ten, not zero.

10. I hate you.

So I got it right, but if I had been just answering it casually I might have very well said zero. It's not that I wasn't educated properly, it's that I rarely do multi-step math without it being something where the order is obvious because it relates to actual physical objects, or it's written with the parentheses. I agree that it's important to have rules about what order to apply things so that everyone (in theory) gets the same answer, but I don't think people getting this wrong says anything dire about humanity.

Good.

You felt insulted because someone you've probably never met and probably never will pointed out your lack of ability to read a certain language?

Sadly, It looks that to me, too.

No, that's true. I mean, I forgot tons of stuff that I learned in 4th and 5th grade, about when you'd learn this rule. It does speak to mathematical literacy (too bad if somebody get torqued off by that term, it's used all over education websites, in published papers, etc). Of course opinions vary, but in general to claim that you are educating somebody to basic mathematical literacy they are expected to be able to do simple graphs, solve linear equations, solve word problems requiring linear equations, etc. You generally aren't expected to be able to do quadratic equations or generalized polynomials. We could bicker endlessly about it, but generally those constraints allow a person to tackle problems that they may face - figuring out how to build a closet or put in stairs, calculate the most efficient purchase options, mortgages, stuff like that. Sure, you can work out a lot of stuff like that without simple algebra, but linear equations make a lot of stuff easier.

And, I would say that our nation (the US, don't know where any individual poster lives) has pretty low math literacy (example source (http://abcnews.go.com/US/story?id=319129), another (http://web.mit.edu/newsoffice/2006/hockfield-educate.html)), and I do consider that a problem. Not that every person needs it - I believe in specialization - but a lot of countries have a higher level of literacy than we do, and that has enormous consequences for people's ability to do science, understand news reports, etc. There's a lot of math in understanding things like risk assessment, for example (which has nothing to do with operator precedence, of course), and people get it very, very wrong. OH NOES, my risk is doubled. Not a big deal if your risk factor was 1 in 12 million.

So, I speculate without any proof whatsoever that you would find a higher proportion of correct answers to that problem in countries that beat us (the US) in math and science education, because it is just a pretty low level piece of knowledge required to do all the rest. That any one person misses the question does not bother me - I'd miss questions about many things historical and political that people would consider part of a base education. That a country as a whole misses it by large percentage is worrisome to me.

Ditto.

Sure, we'll just change all of math to comfort those who can't be bothered to remember things they should have been taught in grade 4. The effort required to re-write thousands of math texts is trivial compared the amount of work you'd have to do to learn a concept like BEDMAS (BODMAS, Please Excuse My Dear Aunt Sally, whatever), since that effort wouldn't be on your part.

I had a student (in a first-year university math class) hand in an assignment which required the use of long division. She wrote "We haven't covered long division!" on her paper and handed it in, fully expecting to not be penalized for this answer. For some reason, I'm reminded of her.

Sad tale.:(

I'm not really sure it's due to my being born in the UK; we moved here to the US when I was 7. Part of it may have to do with the fact that family members on both of my parents' sides were themselves were good enough at math to make a living using it.

But I think the biggest problem in the US in particular, is that education isn't valued very highly. There's a sort of cultural attitude that knowing a lot of stuff is a sissy nerdy thing to do, and the US does foster a certain level of machismo among its populace that seems to outstrip that of other nations (it may have something to do with John Wayne and the Marlboro Man ;) ).

It's often claimed that US Americans (by other US Americans) don't like electing people to office that are smarter than them. I don't think that's really true of the majority of people in the US. But it does seem to often be true of the people that actually end up in the voting booth.

I'm really not sure that the above is quantifiable enough to be testable.

GB

RA-MEN, brother;)
Well I'm not alone in getting 'torqued off', apparantly. To call someone 'illiterate' is to say that they cannot read or write. At all. To call someone 'mathematically illiterate' is to suggest they can't count, when what you mean is they haven't specialised in maths. If that's a common use of the term it's a debasement of language...and I care about language. Less so about maths, as we've established, if the precedence matters those to whom it matters know, and if you're addressing non-specialists you pose the question better.

10 x 0 + 10 gets the result you wanted from specialists and non-specialists alike, unless the result you want is to identify the non-specialists so the remainder can feel superior for a change.

I wasn't even that worked up about it, it's the frantic refusal to admit having given offence that has dragged this out.

Please STOP.

That might be true for some conventions, although you're going to have a tough time making the case. But it's plainly not true for some others. For example, simply invert (left<-->right) the order in which things are written, and that will obviously work just as well.

Of course it might not be convenient to do that for written languages that go left to right - but there are plenty that go right to left, and that ordering in itself is obviously arbitrary.



Polynomials aren't an equation. And if your goal is (for some reason) to write down polynomials in the most efficient way possible, I assure you our notation isn't it (I can think of another of the top of my head that is better).

The reason, as I see it, is not so much that one is better than any others, but that reliable exchange of information possible, repeatable, reproducibly, falsfiably, universally understandably, across language, cultural, physical and temporal.

without "standards", Chaos would ensue. Think of the Legend of the tower of Babylon - each worker had his own language/dialect, none could communicate, Chaos reigns supreme.

Maybe a bit off topic, but isn't the point to pretty much any mathematical, scientific question an attempt to 'catch out' those who do know the answer and those who don't?
Especially one that appears to come straight out of some low grade math textbook, where the whole idea would be to get an indication of how many students get it wrong so they can be taught the right way before leaving school?

If you look at it that way, yeah.

It's not off topic at all. It was a quiz to see how many people would come up with the right answer given the information they had at hand. No problem there.

I think the main problem is that calling someone "Illiterate" on a forum dedicated to intellectual pursuits is clearly insulting. Which is alright when you are on a particularly controversial topic and are engaged in verbal combat (take no prisoners is my attitude). But it wasn't really necessary to wind people up on a thread like this.

GB

Evidently.

Just to put this out there: If this question had been asked out loud, I absolutely would have said zero rather than ten and would have felt perfectly justified doing so unless the pacing and inflection clearly indicated that the multiplication should happen first. In conversational settings (as opposed to reciting selected portions of a math textbook like some sort of nerdy poetry reading), I would expect most rational people to say "What is ten times zero plus ten?" rather than "what is ten plus ten times zero?" just because of unwritten rules of conversation (as observed by an American living in Arizona).

True. The grammar to express complex information must be (or be able to be used in a way that makes it ) sufficiently unambiguous that there is little doubt that the interpretation of the receiver matches the intention of the sender - sort of the whole PURPOSE of language, eh?

Without that ---- Chaos!!

I'm sorry, I do not understand your point here.

edit: went back and reread and got it this time. I'm not claiming the rules are perfect or the best available, just that they are usually better than the alternative being suggested.

Ya, they're an expression, I think you know what I mean (polynomial equations).

The goal is not the most efficient expression possible, not sure where you got that. I'm responding to a very specific suggestion of replacing operator precedence with full use of parens instead. The current scheme works very well for our math needs, and full parens becomes quite unreadable (to me, YMMV).

Therefore, you were able to self -detect-and-correct the confusion, without any additional information. I believe that supports my earlier point.;):)

Oh my gosh, that completely invalidates my entire point! How could I have missed that? Oh, no, wait. I did notice that and it changes nothing at all about what I was saying. Look, the word "if" is there in my post and everything!

The point is: while it's super important to have rules about how to calculate stuff, this kind of thing doesn't mesh well with the way we think (even about math) in other contexts, the same way it's harder to recognize someone from work if you bump into them at the supermarket.

Because of this, I would expect a fair number of people to get this kind of question wrong in ambiguous contexts like facebook not because they don't know the rules but because they weren't in the correct mindset. (Although yes, some people will also get it wrong because they forget (or are unaware) that the rule exists.)

Clever, that.

The amount of whining and justifying in this thread is crazy. So you didn't know something and got a question wrong. Oh noes, the world is ending!! Learn from it and move on already.

Bravo!!

Cheers,

Dave

[CaveDave]

No matter how you slice it, calling someone "Illiterate" is an insult. I should know. I just called someone illiterate on another thread. :p

GB

I invite you to trace-back and read the post that I was responding to. I believe you will find that it was S/HE who used the term before me, and simply bounced off of that.:confused:

Please, come back and tell me if I am wrong.:)

ETA: wait - were you [1], referring specifically to the post by me that you quoted:

Originally Posted by CaveDave

Sigh.

I am not one who assumes others' motives are automatically evil, and they are out to get me. Am I a "Polyanna[sp?]" because of that? Perhaps, but I don't think so. I assume innocence until the preponderance of evidence tips the scales.

To assume someone is malevolent without evidence feels wrong to me.

But that may only be me.


In which I was addressing {jiggeryqua}'s arguement:

Quote:
As you said earlier, people don't actually need to know this stuff unless they're in a position where it matters, in which case they will. Can you explain why the question wasn't written 10 x 0 + 10, which would have enabled the 'math illiterate' to get the right answer too? That doesn't even need parentheses. The sole purpose of the question is to identify non-math-specialists - and then, apparantly, to insult them.

Which I believe is encroaching hard into paranoid territory?

Or [2], were you meaning the one that seemed to start this entire Melee in the first place?

If #1, then my answer above is to be ignored and my response is "I agree", otherwise, if #2, then my response above stands.

Cheers,

Dave

[CaveDave]

Stop *********** lying about me. I did not intend it as an insult, I said in the post it was not intended as an insult, and I explained afterward it was meant as an insult.

It is insulting to suggest I lied. I note that while I apologized for the hurt feeling you and the other fellow have just kept the nastiness up. Classy.

I suggest contacting John Allen Paulos (http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its-Consequences/dp/0809058405/ref=ntt_at_ep_dpt_1), MIT (http://web.mit.edu/newsoffice/2006/hockfield-educate.html), the National Mathematics Advisory Panel (http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf), et. al., and tell them they are all being insulting for using the term.

Roger:

It appears you and I are on parallel roads, if not walking in the same footprints.:eek:

Strange, indeed.:D

Cheers,

Dave

[CaveDave]

Well I wasn't as poor a student as you apparently (I actually liked school). But I got through math (until Trig) pretty much as you described. I barely did any of my homework and still aced my tests.

GB

Perhaps I am not as abnormal as I thought.

Naaaaah!, I'm so abnormal the word almost looses meaning.;)

Cheers,

Dave

[Wolverine]

Somewhere, the trolls who helped spread this meme (http://knowyourmeme.com/memes/48293) are smiling, knowing that it continues to achieve the desired results.

The Facebook variant mentioned in the OP appears to be the latest in the series, which features other smash hits such as 48÷2(9+3) = ? and 6÷2(1+2)= ?

Carry on.

[SomeGuy]

Well I understood your sentence, so it perhaps wasn't the best example to make your point, but more to the point, you missed my point...which was your point: that labelling those of us who got the 'wrong' answer to a poorly-presented question as 'math illiterate' is a little harsh, when it doesn't matter except to mathematicians.

You seem to have missed the post I was responding to - I'm not complaining about pawns or the arcane practises of mathematicians. I was responding to someone who called me (and LibraryLady among others) 'math illiterate' for not having specialist knowledge.

The "specialist knowledge" in question being something that (at least in the Netherlands) is taught in the final classes of primary school.

I would say that if you can't perform arithmetic at the entrance level of highschool, you shouldn't get overly irrate if someone calls you a "math illiterate".

I'm getting a bit tired of the "I don't need math in real life, so I can be all dismissive about it..... but don't you dare call me out on that".

Don't answer math test questions, if you can't handle finding out you're bad at math.

[Gandalfs Beard]

I invite you to trace-back and read the post that I was responding to. I believe you will find that it was S/HE who used the term before me, and simply bounced off of that.:confused:

Please, come back and tell me if I am wrong.:)

ETA: wait - were you [1], referring specifically to the post by me that you quoted:



In which I was addressing {jiggeryqua}'s arguement:


Which I believe is encroaching hard into paranoid territory?

Or [2], were you meaning the one that seemed to start this entire Melee in the first place?

If #1, then my answer above is to be ignored and my response is "I agree", otherwise, if #2, then my response above stands.

Cheers,

Dave

It was #1. :)



GB

ETA: I really never thought this thread would become so controversial.

I happen to agree with the Math people that the test was perfectly fair.

I also happen to agree with the people who have hurt feelings that (especially on a forum like this) calling someone "illiterate" is nearly always intended to wind people up (i.e. insult them) and throw them off their game.

Yet I also happen to agree that on internet forums people need to develop a pretty thick hide. I almost wish most forums would allow Flame Wars (they are so entertaining).

[CaveDave]

The "specialist knowledge" in question being something that (at least in the Netherlands) is taught in the final classes of primary school.

I would say that if you can't perform arithmetic at the entrance level of highschool, you shouldn't get overly irrate if someone calls you a "math illiterate".

I'm getting a bit tired of the "I don't need math in real life, so I can be all dismissive about it..... but don't you dare call me out on that".

Don't answer math test questions, if you can't handle finding out you're bad at math.

Indeed.:)

It was #1. :)



GB

I was afraid I might have been off-base (before editing to find out!:D)

I hereby apologize.

ETA: I really never thought this thread would become so controversial.

I happen to agree with the Math people that the test was perfectly fair.

Me too.:)

I also happen to agree with the people who have hurt feelings that (especially on a forum like this) calling someone "illiterate" is nearly always intended to wind people up (i.e. insult them) and throw them off their game.

Yet I also happen to agree that on internet forums people need to develop a pretty thick hide. I almost wish most forums would allow Flame Wars (they are so entertaining).

Only if you forget That "labels"'s FUNCTION in language is to provide shorthand word picture, to convey meaning, to save time, etc. Words MEAN things..

Perhaps "innumerate" would be more accurate and less prone to misunderstanding.

Dave

[not daSkeptic]

Don't answer math test questions, if you can't handle finding out you're bad at math.

It's interesting to generalize this ...


A person is tested.
The person fails the test.
The person complains and attempts to justify their failure.

Where else have we seen this exact behavior?

[rjh01]

Can I vent my frustration here? I have an Excel spreadsheet. I want to add up several cells and then multiply the total by another number. Either I need
1. Use the sum function
2. Use two cells. One for the addition, one for the multiplication.
3. Use brackets.

If the order was left to right then I could just put the operations in the order in which I wanted them to be carried out.

Maybe next version of Excel they will change it and invalidate everyone else's calculations that depend on this stupid rule. Such things happen.

[SOdhner]

The "specialist knowledge" in question being something that (at least in the Netherlands) is taught in the final classes of primary school.

I don't remember all the state capitals, either. There are a lot of things that I was taught, didn't use, and forgot about. I use math every day in one way or another, but that doesn't mean I use all aspects of it. The Order of Operations is a simple thing, and a fundamental one, and yet I almost never come across a situation where I would need to refer to it.

I'm getting a bit tired of the "I don't need math in real life, so I can be all dismissive about it..... but don't you dare call me out on that".

I think it's fair to be dismissive of this particular quiz. It's mildly interesting to realize there's a rule that is commonly forgotten, but that's it. Getting this wrong doesn't really indicate much about your intelligence or your level of education.

Don't answer math test questions, if you can't handle finding out you're bad at math.

I got it right, and I still think this is stupid.

[Gandalfs Beard]

Only if you forget That "labels"'s FUNCTION in language is to provide shorthand word picture, to convey meaning, to save time, etc. Words MEAN things.

Yes, you're absolutely right. I'm quite a stickler myself (to the point of being anal) about word definitions. Which is why I felt perfectly comfortable calling someone else (and the Oxford educated Authority they were buttressing their argument with) Illiterate on another thread.

But I also used the word because I knew it would be taken as an insult :D (which it basically is when you say it to someone's face...or in this case Avatar).


Perhaps "innumerate" would be more accurate and less prone to misunderstanding.

Dave

Good Point. Though the irony is that most people would have to look up the word "innumerate," which is why it would be less prone to misunderstanding. ;)

GB