[Hogman]

It's nice to be able to argue about something I understand. The debates that go on at Three Pound Brain might as well be in a foreign language for all the sense they make to me. I do sometimes wonder whether they're making it all up as they go along...

[Callan S.]

Let me turn the question around: how would you rephrase it to make it more precise? I say it's impossible, because it's already as precise as it could be.

It's not really a question when you insist it is DEFINITELY as precise as it could be.

I'd be interested to see a test run with the 'more' version and a 'the bats cost is one dollar greater in value than the ball's cost is in value' version. I suspect the correct answer turning up more often in the latter.

I think the initial idea that maybe the hubris of people self identifying as smarter makes them think they've got the answer before they actually have - that's a fair moral to the story. But using approximation words to trick without identifying the means of the trick will lead to another kind of hubris.

[Wilshire]

I'd be interested to see a test run with the 'more' version and a 'the bats cost is one dollar greater in value than the ball's cost is in value' version. I suspect the correct answer turning up more often in the latter.

More words do not mean more precise and/or easier to understand. This new way seems more confusing to me than the original, and I don't think its any more or less precise. Granted, without a test that won't ever happen, its just my opinion over yours.

I'm curious, how are you measuring how precise a phrase is, and how is this way more precise than the original? What additional clarity did you intend to provide with the rephrasing?

[Callan S.]

To stop using a singular approximation word for what is not an approximation. Of course it would be 'more confusing' - when you stop using approximations/broad heuristics the world is more complicated and confusing.

[Wilshire]

So if I understand you correctly, you're saying that by intentionally making it more confusing people are more likely to select the correct answer more often? I suppose that could work, but that seems like an odd way to go about it.

If your goal is to stop people from getting the question wrong, then using words is the wrong way to go. Just give them the partially solved equation:

x = (1.1-1)/2. Solve for x.

Or to make it an actual question:

2x+1 = 1.1. Solve for x.

One step up again, though now its really getting confusing but more analogous to the original question:

(x+1)+x=1.1

Either way, I'd imagine you would be far more likely to get the correct answer.

To stop using a singular approximation word for what is not an approximation.

Can you explain how "greater in value" is a better choice than "more"? Or somehow less approximate?

Do you expect that someone capable of reading this question and doing the math is likely to get tripped up on the word "more" because they don't know its definition or meaning? If so, then do you expect a person who doesn't know the definition of "more" to know the definition of "greater"?

Does adding "in value" somehow fundamentally change how someone understands the question? What other thing is being referred to by "more" in the his question, if not "value"?

If you can't understand "more" on some fundamental level, why isn't "greater" just as confusing?

Why is "value" not confusing? Do you mean dollar amount? Personal value? Weight in gold?


I just don't get how a person who understands the question to begin with would be lead to the answer by your rephrase more often than the original.

edit
For the sake of completion:
You need a series of equations to make it precisely what the question originally asks with words:
y=x+1
y+x=1.1

[Callan S.]

Can you explain how "greater in value" is a better choice than "more"? Or somehow less approximate?

Yes, by running the test.

Otherwise you're blending together A: Merely asking me about my hypothesis/speculation and B: Proving the hypothesis to be the case.

If you want to know more about my hypothesis feel free to ask. But you're phrasing it in a 'IS a better choice?' way right now. It's an old conversational pattern - either it gives the impression I'm wrong (without having run a test) if I don't engage it, but if I do engage we've hit the happy hunting ground of asserting reeeeal hard that we're right rather than testing. Kind of like 'When did you stop beating your wife?', there is no good answer when A and B are blended.

[Wilshire]

Can you explain how "greater in value" is a better choice than "more"? Or somehow less approximate?

Yes, by running the test.

Otherwise you're blending together A: Merely asking me about my hypothesis/speculation and B: Proving the hypothesis to be the case.

If you want to know more about my hypothesis feel free to ask. But you're phrasing it in a 'IS a better choice?' way right now

I'll never understand why the specific phrasing is so important to you. I feel like you assume I'm trying to trick you somehow, which I'm not. Wouldn't a generous reading here assume "A" - that I'm merely asking you about your hypothesis? If not, or if I don't deserve a generous reading, could you explain why?

. It's an old conversational pattern - either it gives the impression I'm wrong (without having run a test) if I don't engage it

Again, not trying to trick you. I'm not trying to 'win' a debate. I simply don't understand your position is better (which, is a given, else you wouldn't have proposed it, yeah?), so I asked some follow up questions to try and ferret that out.

asserting reeeeal hard

lol, yes, agreed.


Really, I'm more interested in understanding your proposition than I am trying to defend (assert?) anything I've put forth. I've got nothing invested here other than an interest to understand. Granted, I don't agree with you, but I'm not opposed to changing my mind.

Maybe you could point out where I communicatively went wrong here so I can avoid such foibles in the future, should you be interested.

[Callan S.]

I'll never understand why the specific phrasing is so important to you.

How do you know you'll never understand?

I feel like you assume I'm trying to trick you somehow, which I'm not. Wouldn't a generous reading here assume "A" - that I'm merely asking you about your hypothesis?

Could you see the A/B distinction before?

I'm just making the conversation clarified and explicit. If we're talking about charitable reading, why take me as seeing a trick? To me, at least, language is a train wreck with difficult ground to pick over. I'm not walking awkwardly trying to avoid traps you've laid down, I'm walking awkwardly because of the traps the wreckage makes all by itself. Indeed, the riddle itself is an example of laying down traps without even intending to.

Anyway, have you ever done programming? You can often describe in a single sentence what it takes a page or several pages of code to do in a program. Why would that be so if shorter versions describe things in a better way?

Do you expect that someone capable of reading this question and doing the math is likely to get tripped up on the word "more" because they don't know its definition or meaning? If so, then do you expect a person who doesn't know the definition of "more" to know the definition of "greater"?

Why read it that way? It's simply that 'more value' isn't really accepted English while 'greater value' is.

[Wilshire]

I feel like you assume I'm trying to trick you somehow, which I'm not. Wouldn't a generous reading here assume "A" - that I'm merely asking you about your hypothesis?

Could you see the A/B distinction before?

I didn't see it until after you pointed it out, and I still don't really grasp what you're getting at.

I'm just making the conversation clarified and explicit. If we're talking about charitable reading, why take me as seeing a trick?

Ah, 'charitable' was the word I was looking for.
Your responses seemed to indicate this? Go ahead and correct me if I'm wrong, but it seems you weren't giving me a charitable reading.

To me, at least, language is a train wreck with difficult ground to pick over. I'm not walking awkwardly trying to avoid traps you've laid down, I'm walking awkwardly because of the traps the wreckage makes all by itself. Indeed, the riddle itself is an example of laying down traps without even intending to.

Good to know.

Anyway, have you ever done programming? You can often describe in a single sentence what it takes a page or several pages of code to do in a program. Why would that be so if shorter versions describe things in a better way?

A small amount. I'm aware of the phenomenon you describe.
I imagine that's a product of the language itself. Some languages take longer to say certain things, while others take far less. Bringing in other languages complicates things more.
Indeed, someone's mastery of a language, lets say english, allows them to say the same thing in more than one way. Shorter isn't necessarily better, but its not necessarily worse. I'm asking you why you think your rephrase was better.

Unless we're talking about SAT/ACT english questions, were statistically the shortest answers is more likely to be correct. That's the only factoid I have on the subject.

Do you expect that someone capable of reading this question and doing the math is likely to get tripped up on the word "more" because they don't know its definition or meaning? If so, then do you expect a person who doesn't know the definition of "more" to know the definition of "greater"?

Why read it that way? It's simply that 'more value' isn't really accepted English while 'greater value' is.

That might be the case (I don't know), but we aren't trying to make the sentence more grammatically correct, we are trying to make it "more precise" - which I interpreted as more easily leads the reader to the answer.

[Hogman]

Anyway, have you ever done programming? You can often describe in a single sentence what it takes a page or several pages of code to do in a program. Why would that be so if shorter versions describe things in a better way?

Agreed. It works the other way as well - sometimes writing something in code is far more illuminating than writing it in text. So one can't judge the worth of an explanation on length alone.

we are trying to make it "more precise" - which I interpreted as more easily leads the reader to the answer.

I would define "more precise" as "less open to misinterpretation by somebody knowledgeable about the subject". For example, jargon usually makes things more precise, but only for the people who know what it means. This leads to a difficulty with a question like this, where in my opinion the most precise way of presenting it is in simultaneous equation form, which would make it harder to understand for some people. So my conclusion is that precision is not necessarily desirable when you're describing something to a general audience.

Anyway, to freshen this thread up a bit, here's the next puzzle in the series:

At 12 o'clock, the two hands of an analogue clock are pointing at the same place. Question: excluding noon and midnight themselves, how many times between noon and midnight do the two hands point to the same place?

[Wilshire]

(click to show/hide)

Once every hour, the minute hand must cross the hour hand on its way back to the top of the hour. That time is 12:00 between noon and 1, so we won't count it.

So, between the hours of 
1) 1 and 2
2) 2 and 3
3) 3 and 4
4) 4 and 5
5) 5 and 6
6) 6 and 7
7) 7 and 8
8 ) 8 and 9
9 ) 9 and 10
10) 10 and 11
11) 11 and 12

Answer: 11 times. 10 times.

More irritating to figure out would be exactly what times those are, since, for example, at 3:15 the hour hand is slightly past the 15, so the cross time will be around 3:18. This would also depend on the clock itself as different clocks have different gears and the crossing time might appear slightly differently for each one.

I'll go ahead and assume I missed something as this seemed like an obvious question? Maybe I've spent too much time in my life thinking about clocks.

[Hogman]

I believe you have done yourself a disservice, Wilshire. I checked this earlier and you had the correct answer, but now you've edited it to be incorrect.

The point is that although it seems obvious, there's an easy trap to fall into. You avoided the trap but then jumped right back in it! One of your proposed options is bogus.

The precise time at which the hands cross is a more interesting question, mathematically. I believe the answer is

(click to show/hide)

that they cross at x hours and 5x + 5x/11 minutes, as x ranges from 1 to 10. To get this answer you have to work out the limit of a convergent sequence. More details available if anyone so desires. And since this is a mathematical question, I think we can assume the clock works perfectly!

[Wilshire]

Added between 1 and 2 which I intended to include previously but missed it.  So maybe I got the right answer for the wrong reason.

Assuming a perfect clock, I guess they wouldn't cross between 11 and 12, rather exactly at 12 again. So the answer was what I originally put down. However, like I said, right answer but wrong work, so no points for me .

I was thinking 11:59.59, or some such crossing just before midnight. I don't know what a perfect clock is. Does that mean that the gears are independent and the gears are infinitely small so that the hand swings perfectly without pause? I ask because if the hour ticks are dependant on the miniute ticks, then wouldn't the minute hand have to arrive at 12:00 before the hour hand to force it to tick to 12:00?

[Callan S.]

I was thinking zero at first as if it meant pointing to the same number - but it says place, I guess.

[H]

Well, I don't do math, but shouldn't this be solvable by graphing the fiction of degrees of the hour hand versus time and the degrees of the minute hand by time?

(click to show/hide)

It seems it is, although I can't be bothered to do the actual math.  Luckily someone else already did:
[/spoler]