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On April 08 2011 10:49 Zeke50100 wrote:Show nested quote +On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text).
Rules exist for a reason you say. The reason is of course to make communication from the writer to the reader as easy as possible. My point is, however, that this is sometimes better achieved with less strictness.
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On April 08 2011 11:01 MadVillain wrote:Show nested quote +On April 08 2011 10:56 space_yes wrote:
People think the question is ambiguous b/c they don't understand the order of operations. If you do it isn't ambiguous at all.
1/xy = y/x
True or false? What!?! Did you even see the results of the second poll... Obviously people understand the order of operations. However in a setting (such as the University that I'm at) more times than not if you wrote that expression people would assume 2(9+3) as a single unit, that is just how people write it and expect it to be interpreted many times. The wikipedia article for ambiguity starts with: "Ambiguity is a term used in writing and math, and under conditions where information can be understood or interpreted in more than one way..." The second poll is EVIDENCE that people can interpret 1/2x as (1/2)x and 1/(2x), which by definition makes it AMBIGUOUS. Get it?
It's evidence people applied different order of operations to each question. Getting the second question wrong doesn't make it ambiguous.
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On April 08 2011 11:02 space_yes wrote:
You'll never see 1/(2x) written as 1/2x in any published mathematical text b/c 1) formatting and 2) order of operations. I agree the question is tricky but that doesn't make it ambiguous. If you got the first question right and you apply the same rules to the second question you should also get it right. If you got it wrong you used different rules for each question.
And you wouldn't see (48/2)(9+3) written as 48/2(9+3) with the exception of trick questions in the exercises.
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On April 08 2011 11:03 jtan wrote:Show nested quote +On April 08 2011 10:49 Zeke50100 wrote:On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text). Rules exist for a reason you say. The reason is of course to make communication from the writer to the reader as easy as possible. My point is, however, that this is sometimes better achieved with less strictness.
Obviously not, otherwise nobody beyond the necessary level of math (which would be almost everybody) would get all of the questions correct.
"Easier" doesn't mean "better".
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There also seems to be some different use of the word ambigous.
The expression 1/x*y is unambigious in the strict computer-sience sense, but like I said, it's ambigious in the sense that a lot of people interpret it differently, you can't really argue against that.
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On April 08 2011 11:06 jtan wrote:
There also seems to be some different use of the word ambigous.
The expression 1/x*y is unambigious in the strict computer-sience sense, but like I said, it's ambigious in the sense that a lot of people interpret it differently, you can't really argue against that.
Lack of knowledge does not mean ambiguous.
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On April 08 2011 11:04 space_yes wrote:Show nested quote +On April 08 2011 11:01 MadVillain wrote:On April 08 2011 10:56 space_yes wrote:
People think the question is ambiguous b/c they don't understand the order of operations. If you do it isn't ambiguous at all.
1/xy = y/x
True or false? What!?! Did you even see the results of the second poll... Obviously people understand the order of operations. However in a setting (such as the University that I'm at) more times than not if you wrote that expression people would assume 2(9+3) as a single unit, that is just how people write it and expect it to be interpreted many times. The wikipedia article for ambiguity starts with: "Ambiguity is a term used in writing and math, and under conditions where information can be understood or interpreted in more than one way..." The second poll is EVIDENCE that people can interpret 1/2x as (1/2)x and 1/(2x), which by definition makes it AMBIGUOUS. Get it? It's evidence people applied different order of operations to each question. Getting the second question wrong doesn't make it ambiguous.
Yes and the fact that people applied different order of operations to each question means that people interpreted them differently so you can say there were two different interpretations of the problem therefore, given what the word "ambiguity" means...
"Ambiguity is a term used in writing and math, and under conditions where information can be understood or interpreted in more than one way..."
I don't think you know what the word ambiguity means.
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On April 08 2011 11:05 Zeke50100 wrote:Show nested quote +On April 08 2011 11:03 jtan wrote:On April 08 2011 10:49 Zeke50100 wrote:On April 08 2011 10:45 jtan wrote:
It is an ambigous expression in the sense that people in fact interpret it differently, as witnessed by the poll.
Having extremely strict rules of "math-grammar" might be good for some purposes, such as teaching high school students how a calculator works, but when communicating mathematical ideas it is often more convenient to use less strict notation and rely on the mutual understanding of the people involved.
For example, if I got an email from a professor containing the expression 1/2x I would be sure he meant 1/(2x) because otherwise he would have written x/2.
In any case, calling people stupid just because they get this wrong is ridiculous. It is a test of grammar-nazism, not of mathematical ability. And if you had the question on a test, you would get it wrong. Rules exist for a reason. It doesn't matter if you rely on "informal" meanings, because you should never assume everybody will follow them, because they are technically wrong (at least when you're limited to single lines of text). Rules exist for a reason you say. The reason is of course to make communication from the writer to the reader as easy as possible. My point is, however, that this is sometimes better achieved with less strictness. Obviously not, otherwise nobody beyond the necessary level of math (which would be almost everybody) would get all of the questions correct. "Easier" doesn't mean " better".
In the case of writing code to be read and interpreted by others, "easier" sure as fuck means "better". How is this different?
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In spanish we have what we call ''Pobre Pepe Mató Dos Sapos Raros'' when solving math problems with more than 2 operations. It english, it means literally ''Poor pepe killed two weird frogs''. This is nothing more that the priority of the operations, where:
Pobre -> Paréntesis (Parenthesis)
Pepe -> Potencia (Elevation)
Mató -> Multiplicación (Multiplication)
Dos -> División (Division)
Sapos -> Suma (Addition)
Raros -> Resta (Subtraction)
I learnt it that way in fourth grade 
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i think people are misunderstanding the definition of ambiguous.
if someone asked me "am i right?" and i said "maybe" that is ambiguous.
if someone told me that their cpu takes too much space in their room, i would say their definition of cpu is wrong, after which they would tell me the definition of cpu is ambiguous, after which i would be like O_O wat.
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On April 08 2011 11:07 Zeke50100 wrote:Show nested quote +On April 08 2011 11:06 jtan wrote:
There also seems to be some different use of the word ambigous.
The expression 1/x*y is unambigious in the strict computer-sience sense, but like I said, it's ambigious in the sense that a lot of people interpret it differently, you can't really argue against that. Lack of knowledge does not mean ambiguous.
Are you really trying to argue that hundreds of people don't know order of operations, or am I missing something?
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Cayman Islands24199 Posts
anyways this is not a maths problem. it is discussed extensively as the problem of rule following.
see here
http://plato.stanford.edu/entries/wittgenstein/#Rul
the original problem has to do with the natural tendency to give priority to closely linked particle words within a larger sentence.
i walked on the grassland
i walked on the grass-land
i walked on the grass
natural language usually evolve conventions that merge such words to eliminate ambiguity, which here is a distinct concept from vagueness. ambiguity is different interpretations of rules with discrete outcomes. maths builds symbolic convention in the same, pragmatic way.
tldr stop trying to trick people by writing bad formula
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Hmm. I got it wrong, but I'm not really bothered by it. My calculus book never had such poor notation. Parenthesis are your friend. I think this thread really just amounts to people being annoyed by bad notation (not necessarily wrong, but bad nonetheless). In the math classes that I took, using parenthesis to make your work clear and concise was mandatory.
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On April 08 2011 11:08 jalstar wrote:Show nested quote +On April 08 2011 11:07 Zeke50100 wrote:On April 08 2011 11:06 jtan wrote:
There also seems to be some different use of the word ambigous.
The expression 1/x*y is unambigious in the strict computer-sience sense, but like I said, it's ambigious in the sense that a lot of people interpret it differently, you can't really argue against that. Lack of knowledge does not mean ambiguous. Are you really trying to argue that hundreds of people don't know order of operations, or am I missing something?
Yes. Hundreds of people (those who have bothered to reply, anyway, which is indicative of response bias in the first place) just don't know their stuff.
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Hmm, reading through the thread I've picked up a few things:
A parallel to the strategy forums:
Mathematicians saying it is ambiguous, high schoolers saying it is obviously 288. (not saying everyone stating 288 is a high schooler or even "wrong")
High masters saying a strategy is good, bronze leaguers saying it is bad.
Lots of people posting without reading the thread.
Also appears to be a difference between different disciplines at university level. Engineers/Computer Scientists seem to think more in terms of syntax executed by a computer, making a straight application of the order of operations logical.
Pure mathematicians/physicists seem to think more in terms of mathematical structure where it is ambiguous as to what is meant. Having done abstract maths, thinking of it as a grouped structure is natural to me, rather than as a linear list of operations.
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This is just simple mathematics... Maybe its because I was a comp sci major.. I am not sure, but order of operations will not change.
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On April 08 2011 11:10 Zeke50100 wrote:Show nested quote +On April 08 2011 11:08 jalstar wrote:On April 08 2011 11:07 Zeke50100 wrote:On April 08 2011 11:06 jtan wrote:
There also seems to be some different use of the word ambigous.
The expression 1/x*y is unambigious in the strict computer-sience sense, but like I said, it's ambigious in the sense that a lot of people interpret it differently, you can't really argue against that. Lack of knowledge does not mean ambiguous. Are you really trying to argue that hundreds of people don't know order of operations, or am I missing something? Yes. Hundreds of people (those who have bothered to reply, anyway, which is indicative of response bias in the first place) just don't know their stuff.
You can't be serious. I just refuse to believe you're serious. You really can't see how the problem is a trick without assuming complete lack of order of operations knowledge? What the fuck?
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i loled
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Lmao. Even google adds parentheses to add clarity.
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On April 08 2011 11:11 jalstar wrote:Show nested quote +On April 08 2011 11:10 Zeke50100 wrote:On April 08 2011 11:08 jalstar wrote:On April 08 2011 11:07 Zeke50100 wrote:On April 08 2011 11:06 jtan wrote:
There also seems to be some different use of the word ambigous.
The expression 1/x*y is unambigious in the strict computer-sience sense, but like I said, it's ambigious in the sense that a lot of people interpret it differently, you can't really argue against that. Lack of knowledge does not mean ambiguous. Are you really trying to argue that hundreds of people don't know order of operations, or am I missing something? Yes. Hundreds of people (those who have bothered to reply, anyway, which is indicative of response bias in the first place) just don't know their stuff. You can't be serious. I just refuse to believe you're serious. You really can't see how the problem is a trick without assuming complete lack of order of operations knowledge? What the fuck?
I never said a complete lack of knowledge. You might want to look up what knowledge means.
Somebody's ignorance of the fact that you do not, indeed, multiply 2 by 9+3 before proceeding with the rest of the simplification is a lack of knowledge.
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EPT
