[Zelandakh]

Interesting problem gwnn - is the answer 50? 1 x 3 (27) + 7 x 2 (56) + 42 x 1 (42) is the smallest I got it in my head.

[kenberg]

 gwnn, on 2014-May-26, 03:30, said:

Linguists* describe how people use language in their day-to-day lives, logicians describe how people ought to think and speak in an ideal world that is nowhere to be found in our galaxy. Why is it unfortunate that lawyers (who work with real people in real life, not robots from outer space) use language as other people do? I agree, though, that sloppy wording is in no one's best interest.

*-descriptive linguists, at any rate.

This reminds me of a math problem we had in high school, something like "We cut a 5x5x5 cube in cubes that have whole numbers as their edge length. What is the minimum number of cubes that we can obtain?" And there was an obnoxious guy somewhere in the front who said, thinking he's very clever, "one!! we cut the cube in one!" and would not sway when we repeated the first two words of the problem many times: we cut the cube. If you leave something intact, it means you do not cut it, and if you cut something, it means you do not not cut it.

A favorite story along these lines:
I was part of a group that created a statewide mathematics competition. One year, after we had completed it and carefully checked it, someone, maybe it was even me, I forget, thought of a way of "improving" one of the questions We all agreed this was a great improvement and we adopted it. Oops. As far as I know, this is the only question we ever asked that escaped our careful review. One of the answers came back like this: "As this question is formulated, the answer is trivial. However I assume this is the question that you meant to ask." And then he went on to restate and correctly answer out original question. He came in first and went on to a successful career in mathematics.


With the cube questron, you say "went something like this" If it began "made some number of cuts" then I guess 0 is some number. But even if that was what happened it should be easy to deal with, just say "Charlie, I know I said some number, for you I will correct that to some positive number, now let's get on with the problem."

[gwnn]

 Zelandakh, on 2014-May-26, 04:05, said:

Interesting problem gwnn - is the answer 50? 1 x 3 (27) + 7 x 2 (56) + 42 x 1 (42) is the smallest I got it in my head.

I think so. As long as you don't have a 4x4x4 cube (or 8 adjacent 2x2x2's), you can't go wrong.

[Cyberyeti]

 kenberg, on 2014-May-26, 04:33, said:

A favorite story along these lines:
I was part of a group that created a statewide mathematics competition. One year, after we had completed it and carefully checked it, someone, maybe it was even me, I forget, thought of a way of "improving" one of the questions We all agreed this was a great improvement and we adopted it. Oops. As far as I know, this is the only question we ever asked that escaped our careful review. One of the answers came back like this: "As this question is formulated, the answer is trivial. However I assume this is the question that you meant to ask." And then he went on to restate and correctly answer out original question. He came in first and went on to a successful career in mathematics.


With the cube questron, you say "went something like this" If it began "made some number of cuts" then I guess 0 is some number. But even if that was what happened it should be easy to deal with, just say "Charlie, I know I said some number, for you I will correct that to some positive number, now let's get on with the problem."

It's terribly easy to get this wrong, what's half of 2 + 2 ?

And as far as I can tell Zel's solution is right.

[gwnn]

 Cyberyeti, on 2014-May-26, 05:55, said:

It's terribly easy to get this wrong, what's half of 2 + 2 ?

Normally, 2. Depends on the intonation. No one would say "half of twoplustwo" if they wanted to say "0.5*2+2." I definitely don't think the answer is clearly 3.

[kenberg]

Fairly early on a student learns that (1/2)X2+2 means ((1/2)X2)+2 rather than (1/2)X(2+2). But really that is a conventional agreement, meaning that we could just as well have decided otherwise. . i see no reason to assume that the written phrase "half of 2+2" means (half if 2) plus 2. A person who want to avoid ambiguity could say 2plus half of 2 if that is what he intended. The meaning of "half of 2+2" might be clear by intonation if spoken. When written, I would call it ambiguous.

[Zelandakh]

When you say "What is half of <some calculation>" you are implicitly drawing a bracket around the calculation unless you add an obvious pause.

As for the cube problem I think it would be interesting to hear how others visualised this. I mentally split the cube into a 5 x 5 x 3 and a 5 x 5 x 2 and then used the volumes to work out the number of 1 x 1 x 1 cubes to add in at the end. An engineer would probably visualise the entire cube as a single entity. A topologist might come up with some useful transformation. An architect would probably just draw it. Or there is the apple approach of removing the accounted-for sections until only the single areas are leftover. What is great is that a bunch of 6 year olds with building blocks will probably come up with the answer just as fast as some mathematicians!

[gwnn]

The written version "half of 2+2" points very much to "0.5*(2+2)" since there is a clear barrier between the part with natural language and the part of math stuff. On the other hand, no one would ever write or say "half of two plus two" in any real-life scenario other than as a "tricky" math trap (the numbers are too low), so there.

[gwnn]

 Zelandakh, on 2014-May-26, 06:25, said:

As for the cube problem I think it would be interesting to hear how others visualised this. I mentally split the cube into a 5 x 5 x 3 and a 5 x 5 x 2 and then used the volumes to work out the number of 1 x 1 x 1 cubes to add in at the end. An engineer would probably visualise the entire cube as a single entity. A topologist might come up with some useful transformation. An architect would probably just draw it. Or there is the apple approach of removing the accounted-for sections until only the single areas are leftover. What is great is that a bunch of 6 year olds with building blocks will probably come up with the answer just as fast as some mathematicians!

I have a transparent 5x5x5 cube in my head, which gets filled up by smaller, opaque cubes. 4x4x4 is clearly too big, so you start by putting a 3x3x3 in one of the corners and then putting as many 2x2x2 as possible, then add up the volumes and see how many little guys we need.

[kenberg]

 gwnn, on 2014-May-26, 06:33, said:

The written version "half of 2+2" points very much to "0.5*(2+2)" since there is a clear barrier between the part with natural language and the part of math stuff. On the other hand, no one would ever write or say "half of two plus two" in any real-life scenario other than as a "tricky" math trap (the numbers are too low), so there.

I agree with this. Although I do not have an example handy, I have seen advertisements, warranties, etc where the exact meaning simply is not clear. Sometimes I think this is intentional, sometimes probably just bad wording.

[Cyberyeti]

 kenberg, on 2014-May-26, 06:58, said:

I agree with tis. Although I do not have an example handy, I have seen advertisements, warranties, etc where the exact meaning simply is not clear. Sometimes I think this is intentional, sometimes probably just bad wording.

I was just putting it out there to show how easy it was to put up an ambiguous question. Where I came across it the answer wanted was 3 and it was written down (so no intonation). This was in a MMO and there was no particular consequence for getting it wrong.

[kenberg]

In some ways this all still is addressing the original subject. Gotcha questions may have their place, but in a sixth grade assessment they should not happen. They definitely should not happen intentionally, and care should be taken that they do not happen inadvertently. In the real world we do in fact have to do our best when we encounter badly written stuff. But a sixth grade test, one with substantial consequences, should not test whether the kid can make sense out of carelessly worded questions. There will be planty of opportunity for error when everything is played straight up.

[Cyberyeti]

 kenberg, on 2014-May-26, 10:10, said:

In some ways this all still is addressing the original subject. Gotcha questions may have their place, but in a sixth grade assessment they should not happen. They definitely should not happen intentionally, and care should be taken that they do not happen inadvertently. In the real world we do in fact have to do our best when we encounter badly written stuff. But a sixth grade test, one with substantial consequences, should not test whether the kid can make sense out of carelessly worded questions. There will be planty of opportunity for error when everything is played straight up.

True but it happens. In my university final maths exams, one of the questions (one I didn't answer thankfully, it was an "answer 5 of 7" type paper) was either unanswerable, or took 20 minutes instead of 3 (I forget which) because a plus sign was printed as a minus or vice versa. It was the chaos theory paper so I suppose it was somehow appropriate.

[blackshoe]

 gwnn, on 2014-May-26, 03:30, said:

…nowhere to be found in our galaxy…

Assumption. Where's your evidence?

[blackshoe]

 kenberg, on 2014-May-25, 07:07, said:

The main thing for young people to learn about credit cards is that they are the invention of the devil.

No. Credit cards are the invention of bankers. Bankers are the invention of the devil - with apologies to my Uncle Rep, who at one time owned two banks.

[blackshoe]

 gwnn, on 2014-May-26, 06:33, said:

The written version "half of 2+2" points very much to "0.5*(2+2)" since there is a clear barrier between the part with natural language and the part of math stuff. On the other hand, no one would ever write or say "half of two plus two" in any real-life scenario other than as a "tricky" math trap (the numbers are too low), so there.

A comma might be useful here (as opposed to the many times I see them where they don't belong).

[chasetb]

 blackshoe, on 2014-May-26, 13:08, said:

No. Credit cards are the invention of bankers. Bankers are the invention of the devil - with apologies to my Uncle Rep, who at one time owned two banks.

No, you have that wrong. LAWYERS are the invention of the devil, bankers just lie down with them.

[gwnn]

 blackshoe, on 2014-May-26, 13:05, said:

Assumption. Where's your evidence?

Do you refer to extraterrestrial or terrestrial logic? In any case, it was not an assumption, it was an assertion exaggerated on purpose for comedic purposes. And my evidence to back it up is only my own experience and that of others that I have come across and discussed with. You are free to disagree with my opinion, I did not put a QED at the end of it (except the Carlin quote at the bottom, I guess). I do not think pure logic is the overriding concern in the lives of most people. I do use it from time to time but much too often only as a post mortem measuring stick to assess how badly I failed to use it.

[blackshoe]

 gwnn, on 2014-May-26, 14:01, said:

Do you refer to extraterrestrial or terrestrial logic? In any case, it was not an assumption, it was an assertion exaggerated on purpose for comedic purposes. And my evidence to back it up is only my own experience and that of others that I have come across and discussed with. You are free to disagree with my opinion, I did not put a QED at the end of it (except the Carlin quote at the bottom, I guess). I do not think pure logic is the overriding concern in the lives of most people. I do use it from time to time but much too often only as a post mortem measuring stick to assess how badly I failed to use it.

Neither. I asked for evidence, not logic — although logic in these discussions is always welcome.

Quote

Hyperbole: exaggerated statements or claims not meant to be taken literally.

I suppose that's fair enough — and I did recognize it as such, but it seemed an unnecessary exaggeration, so I wondered if you were serious.

[gwnn]

Quote

Neither. I asked for evidence, not logic — although logic in these discussions is always welcome.

I can read. I know that you asked for evidence, I was asking only what you asked the evidence for... OK, for you, here is my question in a correct, logical wording:

Quote

I find your question slightly unclear. You are asking for evidence to support my assertion, but which assertion exactly?

a) People on Earth rarely follow rigid logical rules in their day-to-day communication and thought processes. (this was the point I was trying to make)
b) No form of life in this galaxy could ever conceivably follow rigid logical rules. (this was the over-the-top restatement)

Anyway, moving on, I was very much serious in that in my opinion, linguists are better equipped to interpret day-to-day communication than logicians. (I am unable to provide evidence for this and your opinion may well differ. I don't think it's a kind of statement that is easy to (dis)prove with concrete evidence, anyway) For example, there is no logical difference between saying "more than 50 people" and "more than 500 people" if the actual number was 10,000 (say, people at a concert), but a linguist will immediately recognise how both of these statements are misleading in a likely malicious way, if the speaker knows the correct figure. At the same time, I admit that a lot of illogical expressions irk the logician in me. For example, "Do you mind helping me?" "Sure."