FC/OT: This is why LionJim stays off Twitter....

[LionJim]

In each case, you've argued that you should not correct people today because eventually the truth will become obvious.

I have never argued that I should not correct people on this issue. if you ask me, I'll say that mathematics is objective, not subjective. But for the bigger picture outside this board, it's being taken care of by competent people. "The cost is too high to wait." Who's waiting? Like I said, the mathematical community is addressing this. Maybe I should be more vocal on this board, but whatever impact I have on this board doesn't carry over outside this board and outside this board my impact is nonexistent anyway.

 

[KanePoster]

I have never argued that I should not correct people on this issue. if you ask me, I'll say that mathematics is objective, not subjective. But for the bigger picture outside this board, it's being taken care of by competent people. "The cost is too high to wait." Who's waiting? Like I said, the mathematical community is addressing this. Maybe I should be more vocal on this board, but whatever impact I have on this board doesn't carry over outside this board and outside this board my impact is nonexistent anyway.

Fair enough.

 

[LionJim]

Fair enough.

Good discussion. Appreciate it.

 

[Fac]

So what is the correct answer?

 

[PSU Mike]

China is laughing their asses off.

Anyone who believes that math is subjective should never vote again.

Idiots. Morons.

A lot of these “riddles” exist in a vacuum without practical application, but there is a lesson in many of them. I work with some 50 PhD decision scientists (math, compsci, OR), the majority whose early schooling came in China. Every month I reveal something wrong in what they’re doing because of a basic breakdown in analytical skills in translating a real world objective into its mathematical framing. They can laugh at us for not being trained on some fundamentals. I’ll keep my snickers to myself as I pick away at the “we out-credential you” notion a little at a time.

 

[LionDeNittany]

Apparently this problem has been going around on FB and Twitter lately because Herbie and I had a discussion about this the other week. What follows is an old riddle which I’d like to try on youse. LHS= Left Hand Side.

1. Suppose that a=b.
2. Add a to both sides: a+a=b+a
3. Simplify LHS: 2a=b+a
4. Subtract 2b from both sides: 2a-2b=(b+a)-2b
5. Factor LHS, simplify RHS: 2(a-b)=a-b
6. Divide out a-b from both sides:
2(a-b)/(a-b)=(a-b)/(a-b)
7. Simplify to get 2=1.

Okay, obviously there’s a mistake. Where’s the mistake?

5

 

[Erial_Lion]

So what is the correct answer?

9

 

[BobPSU92]

So what is the correct answer?

It depends. There is the irrefutable LionJim proof, and then there’s everything else.

LionJim sez 9.

 

[NatLion]

Pemdas, schmendas - best rule is to use parentheses to avoid all possible ambiguities.

 

[LionJim]

Not to prolong the discussion but I believe statistics illiteracy is a much, much more serious problem than mathematical illiteracy.

 

[BobPSU92]

Not to prolong the discussion but I believe statistics illiteracy is a much, much more serious problem than mathematical illiteracy.

Is it statistically significant?

 

[psu_1294]

Can't avoid it. How else can we keep score in our games?

Or polls!

 

[KanePoster]

A lot of these “riddles” exist in a vacuum without practical application, but there is a lesson in many of them. I work with some 50 PhD decision scientists (math, compsci, OR), the majority whose early schooling came in China. Every month I reveal something wrong in what they’re doing because of a basic breakdown in analytical skills in translating a real world objective into its mathematical framing. They can laugh at us for not being trained on some fundamentals. I’ll keep my snickers to myself as I pick away at the “we out-credential you” notion a little at a time.

Translating the physics of a problem into the proper mathematics is always difficult. Really, being able to do this at a high level is what separates "OK" from "awesome".

But I'm not sure what you're saying or trying to get at.

I know a few Chinese born scientists and engineers - one of whom is tremendous. It's the same with American scientists. Most adequate - some brilliant.

I'm only saying that it can't be good when we have a significant group of people in education/activism who are saying "Math is subjective" and pushing that as a new way to educate people. It really gets us closer to the point where people think that "everything is an opinion, and nothing is a provable fact/theory".

What are you saying?

 

[KanePoster]

Funny you say this... I presented the problem to my dad who got the correct answer.

He then googled it and said:
"The thing that I saw disturbing was the written discussion gave credence to 9 since that is what a calculator gave."

I responded:
"China is eating our lunch"

The key is to ask: What could possibly be the motivation for PRETENDING that math is subjective?

I'd love to hear an answer to that - in general, I find that people want to avoid that question by simply saying, "Well, obviously that's wrong. Now I'm done talking about it."

But that's NOT the question: The question is: "Why would a significant percentage of people push for it?"

 

[JBott]

In general, acronyms in mathematics aren’t a good idea as they’re limiting. Everyone has heard of FOIL, right, for multiplying binomials. Once you get a problem like, say,
(2x+5)(3x^2+4x+3), what do you do?

After teaching mathematics at the HS level for 31 years, I agree that the “acronyms” at the very least have limitations and can lead to confusion!

 

[sluggo72]

After teaching mathematics at the HS level for 31 years, I agree that the “acronyms” at the very least have limitations and can lead to confusion!

you telling me Oscar doesnt have a heap of Apples?

 

[KanePoster]

Not to prolong the discussion but I believe statistics illiteracy is a much, much more serious problem than mathematical illiteracy.

A specific example would be helpful.

 

[sluggo72]

Apparently this problem has been going around on FB and Twitter lately because Herbie and I had a discussion about this the other week. What follows is an old riddle which I’d like to try on youse. LHS= Left Hand Side.

1. Suppose that a=b.
2. Add a to both sides: a+a=b+a
3. Simplify LHS: 2a=b+a
4. Subtract 2b from both sides: 2a-2b=(b+a)-2b
5. Factor LHS, simplify RHS: 2(a-b)=a-b
6. Divide out a-b from both sides:
2(a-b)/(a-b)=(a-b)/(a-b)
7. Simplify to get 2=1.

Okay, obviously there’s a mistake. Where’s the mistake?

maybe this is a duh, but
if a=b, line 5 then 2*0=0 which is correct, correct?

 

[interrobang]

Apparently this problem has been going around on FB and Twitter lately because Herbie and I had a discussion about this the other week. What follows is an old riddle which I’d like to try on youse. LHS= Left Hand Side.

1. Suppose that a=b.
2. Add a to both sides: a+a=b+a
3. Simplify LHS: 2a=b+a
4. Subtract 2b from both sides: 2a-2b=(b+a)-2b
5. Factor LHS, simplify RHS: 2(a-b)=a-b
6. Divide out a-b from both sides:
2(a-b)/(a-b)=(a-b)/(a-b)
7. Simplify to get 2=1.

Okay, obviously there’s a mistake. Where’s the mistake?

Not enough dutchie passed on the LHS?

 

[LionJim]

maybe this is a duh, but

if a=b, line 5 then 2*0=0 which is correct, correct?

yes.

 

[LionJim]

A specific example would be helpful.

I’ll do what I can.

 

[LionJim]

Scientific method: Statistical errors - Nature

P values, the 'gold standard' of statistical validity, are not as reliable as many scientists assume.

www.nature.com

I understand that this is a good for-example. "For many scientists, this is especially worrying in light of the reproducibility concerns. In 2005, epidemiologist John Ioannidis of Stanford University in California suggested that most published findings are false; since then, a string of high-profile replication problems has forced scientists to rethink how they evaluate results."

 

[KanePoster]

Scientific method: Statistical errors - Nature

P values, the 'gold standard' of statistical validity, are not as reliable as many scientists assume.

www.nature.com

I understand that this is a good for-example. "For many scientists, this is especially worrying in light of the reproducibility concerns. In 2005, epidemiologist John Ioannidis of Stanford University in California suggested that most published findings are false; since then, a string of high-profile replication problems has forced scientists to rethink how they evaluate results."

OK, yes. It's absolutely a problem, especially in the soft sciences where statistics must be used (and the scientists are not the very cream of the crop).

But the problem isn't so much with the statistics, it's with a lack of understanding of how science really works.

The first question that should be asked of a presenter who is about to unveil his statistics is: "What's your underlying physical model? Why do you think, based on first principles, that the model is correct?"

If the presenter is unable to answer both of those questions satisfactorily, then you can assume they are essentially just throwing data at the problem and hoping it sticks (with a good P-value).

If the presenter can answer those questions adequately, then you can expect some good stuff to follow.

Seldom is the issue that the statistics themselves are shoddy.

 

[STPGopherfan]

Here is where a lot of elementary and middle school teachers get it wrong. They use things like Please Excuse Me Dear Aunt Sally or PEMDAS which gives the impression that operations are done in the following order:

1. Parentheses
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Subtraction

While actually it should be :

1. Work inside parentheses if any
2. Do exponents from right to left
3. Do multiplication and divisions from left to right
4. Do addition and subtraction from left to right

Obviously I suck at math...

 

[Agoodnap]

In the original post, If the expression 2(1+2) is implied to be divided into 6, than the answer is 1. The equation should have been 6 /(2(1+2)) However, if you believe that it implies 6/2 x (1+2) than the answer is 9.

@KanePoster see how subjective maths can be?

 

[PSU Mike]

Translating the physics of a problem into the proper mathematics is always difficult. Really, being able to do this at a high level is what separates "OK" from "awesome".

But I'm not sure what you're saying or trying to get at.

I know a few Chinese born scientists and engineers - one of whom is tremendous. It's the same with American scientists. Most adequate - some brilliant.

I'm only saying that it can't be good when we have a significant group of people in education/activism who are saying "Math is subjective" and pushing that as a new way to educate people. It really gets us closer to the point where people think that "everything is an opinion, and nothing is a provable fact/theory".

What are you saying?

I’m saying that many higher credentialed people that can do a lot of math properly still miss the part where you make the math do the exact work you want it to do. And this group includes many that came through the education system in China. The poster I responded to implied the Chinese would be laughing at “us.” I contend that they while they may laugh in one regard, they have no advantage in this one critical skill.

 

[IANit]

Funny you say this... I presented the problem to my dad who got the correct answer.

He then googled it and said:
"The thing that I saw disturbing was the written discussion gave credence to 9 since that is what a calculator gave."

I responded:
"China is eating our lunch"

Your dad answered 9, right? Because on first read I thought you were indicating he said something other than 9, which made your answer face-palm worthy. I think you're saying he got 9 and was disturbed that people on Twitter with enough time on their hands to get into such a debate (almost assuredly not math wizards) were pointing to the fact that the calculator came up with 9 as their reason. I would only be worried if that was coming from an audience made up of math educators/practitioners.

 

[Ski]

PEMDAS is currently tending in the U.S.:

View embedded media

I tried to put the formula into a cell in Excel to see what it gave as the answer and it said the formula has a typo, as it was entered. It suggested correcting it to 6/2*(1+2) to fix it. I think the lack of an operator between the 2 and the ( throws a lot of people, but it also throws Excel, so I don't feel bad about it. It is a trick question.

 

[udsig91]

That is flat out stupid!!! No wonder we lag so far behind the rest of the educated world in math and science...the education system in this country is ridiculous!!!

 

[2PBC22]

Your dad answered 9, right? Because on first read I thought you were indicating he said something other than 9, which made your answer face-palm worthy. I think you're saying he got 9 and was disturbed that people on Twitter with enough time on their hands to get into such a debate (almost assuredly not math wizards) were pointing to the fact that the calculator came up with 9 as their reason. I would only be worried if that was coming from an audience made up of math educators/practitioners.

Exactly. He got 9 and was disturbed that the only reason people online could validate their answer was by stating that their calculator said 9 was the answer.

 

[psuaxe70]

That is flat out stupid!!! No wonder we lag so far behind the rest of the educated world in math and science...the education system in this country is ridiculous!!!

We lead the world in science and technology, have won more Nobels in science than the rest of the world combined, send kids to college at one of the highest rates in the world, send women to college at the highest rate in the world, and have the most productive workforce in the world. But if you are in a hurry to blurt out something stupid, you are spot on.

 

[BobPSU92]

That is flat out stupid!!! No wonder we lag so far behind the rest of the educated world in math and science...the education system in this country is ridiculous!!!

I hate U.S.

 

[IANit]

We lead the world in science and technology, have won more Nobels in science than the rest of the world combined, send kids to college at one of the highest rates in the world, send women to college at the highest rate in the world, and have the most productive workforce in the world. But if you are in a hurry to blurt out something stupid, you are spot on.

The main difference here is that almost anyone can go to school and anyone can voice their opinion, no matter how ill-informed it is. So you probably hear from more of the dummies here than in other places.

 

[KanePoster]

In the original post, If the expression 2(1+2) is implied to be divided into 6, than the answer is 1. The equation should have been 6 /(2(1+2)) However, if you believe that it implies 6/2 x (1+2) than the answer is 9.

@KanePoster see how subjective maths can be?

That is not evidence that math is subjective. That's evidence that there's a conflicting view about what the symbols we use to communicate mathematics mean.

I can't actually see the original post, but I can see the replies enough to know that it is simply left intentionally confusing to make a point. Anyone that's any good would just throw in a few extra parenthesis to clarify.

 

[KanePoster]

I’m saying that many higher credentialed people that can do a lot of math properly still miss the part where you make the math do the exact work you want it to do. And this group includes many that came through the education system in China. The poster I responded to implied the Chinese would be laughing at “us.” I contend that they while they may laugh in one regard, they have no advantage in this one critical skill.

I think the Chinese are going to be laughing at us. Hell, I'm laughing at us.

There is ample evidence to conclude that the average US citizen has an IQ almost exactly equal to the average Chinese citizen. Now the real breakthroughs are typically made by the right hand side of the bell curve. I mean the far right side. About that, the statistics aren't so clear.

And of course, when we're talking about math and physics, we're really talking IQ. In any event, there's no reason we need to be at a disadvantage to China.

But this perversion with dumbing down everything (and what else would you call a nation that has a serious contingent of people trying to make math "subjective") is ridiculous.

The average Chinese scientist has nothing over the average American scientist.

The average Chinese leader/politician is a thousand times more focused and more sensible than the average American "leader/politician".

I will also note something else - we had the same average IQ back in 1870-1960 when we were absolutely kicking the crap out of every nation on earth in terms of development. What was different?

 

[gamblepsu]

Dividing in this sense is the same as multiplying fractions. Hence the person who wrote this was stirring up trouble because if you are already writing your multiplication like that then you wouldn’t be using the stupid division symbol.

The real solution: the person who made this problem should rewrite it without the division symbol to remove ambiguity.

 

[OhioLion]

Here is where a lot of elementary and middle school teachers get it wrong. They use things like Please Excuse Me Dear Aunt Sally or PEMDAS which gives the impression that operations are done in the following order:

1. Parentheses
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Subtraction

While actually it should be :

1. Work inside parentheses if any
2. Do exponents from right to left
3. Do multiplication and divisions from left to right
4. Do addition and subtraction from left to right

This is the way I taught it for years. Use the dear aunt sally reminder, but heavy emphasis was always on My Dear and Aunt Sally if together in the expression, is left to right.

OL

 

[Agoodnap]

I think the Chinese are going to be laughing at us. Hell, I'm laughing at us.

There is ample evidence to conclude that the average US citizen has an IQ almost exactly equal to the average Chinese citizen. Now the real breakthroughs are typically made by the right hand side of the bell curve. I mean the far right side. About that, the statistics aren't so clear.

And of course, when we're talking about math and physics, we're really talking IQ. In any event, there's no reason we need to be at a disadvantage to China.

But this perversion with dumbing down everything (and what else would you call a nation that has a serious contingent of people trying to make math "subjective") is ridiculous.

The average Chinese scientist has nothing over the average American scientist.

The average Chinese leader/politician is a thousand times more focused and more sensible than the average American "leader/politician".

I will also note something else - we had the same average IQ back in 1870-1960 when we were absolutely kicking the crap out of every nation on earth in terms of development. What was different?

The Chinese are laughing because the World Bank has barely budged the exchange rate in almost 20 years. Right now about 6.5 RMB to the Dollar. Should be about 2 RMB to the Dollar.

 

[BW Lion]

No. Multiply and divide are on the same level ... but work from left to right. SO OhioLion got it right!

Left to right is fine, but I was always taught that whatever function is inside the parentheses takes priority.

The answer completely depends on the assumed mathematical operator between the "2" and the left parenth.

The correct answer is "1" if one assumes there is a multiplication sign.

As written, the equation is mathematically incorrect based on missing operation information despite what the person incapable of removing wallpaper in a timely fashion claims

 

[sluggo72]

Left to right is fine, but I was always taught that whatever function is insider the parentheses takes priority.

The answer completely depends on the assumed mathematical operator between the "2" and the left parenth.

The correct answer is "1" if one assumes there is a multiplication sign.

As written, the equation is mathematically incorrect based on missing operation information despite what the person incapable of removing wallpaper in a timely fashion claims

I am curious about how old you are. Or how old your algebra teacher was when you learned that. It was taught that way at one time, but was changed at some point