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James Fingas
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 Re: what we do   « Reply #25 on: Aug 22nd, 2003, 7:20am » Quote Modify

I agree ... adding trailing zeros is a very sloppy way to show accuracy. Besides, even when I want a value to be +/- 0.05, I can still put something in the hundredths spot:

1.23 mm +/- 0.05 mm

The rule of thumb they taught us in physics lab was to only give one digit in the tolerance, and never give digits in the answer that could be completely obliterated by the tolerance. For instance, these are just silly:

1.23 mm +/- 0.0512 mm
1.23501 mm +/- 0.05 mm

Although mathematically the extra digits are meaningful, practically they're not.
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Sir Col
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 Re: what we do   « Reply #26 on: Aug 22nd, 2003, 7:47am » Quote Modify

on Aug 22nd, 2003, 4:57am, wowbagger wrote:
 Are you serious about that last part?

Only in the context of rounding errors. An answer written as 5.60 implies that it is correct to 2 decimal places. However, as I demonstrated, 1.32+4.28 could be anything from 5.59 to 5.61 (using lower and upper bounds). Therefore, I can only say that the answer is 5.6 with confidence. The general rule of thumb is that combining two rounded values can at best produce an answer to one degree of accuracy less. You add two numbers, both correct to 3 d.p., and your answer can only be given accuractely to 2 d.p.

However, as we've said, unless you're asked specifically to take this into account, you would not do it. If I present two numbers, given to 3 d.p., you would assume that they are exact (not rounded), unless stated otherwise.

I believe the unique convention (of leaving trailing zeroes) arises from approximately equal signs vs. equality with qualifying statements of accuracy. For example, we can write sqr(2)[approx]1.41 or sqr(2)=1.41 (2 d.p.). As the use of trailing zeroes would normally be redundant, writing x=5.60, implies that it is correct to 2 d.p.; in other words, it is closer to 5.60 than 5.59 or 5.61. However, it is a sloppy convention, as sqr(2)=1.41 would be invalid.

I detest the whole realm of rounding and bounds. I especially object to the standards now of stating that the least and greatest values that are equal to the integer 10 are 9.5 and 10.5 respectively. In examinations, in England, candidates are expected to state that 10.5 (the lower bound of 11 to the nearest whole number) is the greatest value that 10 can be. The question will actually state: "A number, given to the nearest whole number, is 10. Write down the greatest value that this number could be." Not upper bound, but greatest value. It all stems from the general lack of understanding of bounds and limits. You will even hear examiners saying, "Well how about allowing 10.4999... then?" Argh!
 « Last Edit: Aug 22nd, 2003, 7:51am by Sir Col » IP Logged

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 Re: what we do   « Reply #27 on: Aug 22nd, 2003, 8:37am » Quote Modify

on Aug 22nd, 2003, 7:20am, James Fingas wrote:
 The rule of thumb they taught us in physics lab was to only give one digit in the tolerance, and never give digits in the answer that could be completely obliterated by the tolerance.

That's what they teach here, too. Although it wasn't strictly only one digit in the tolerance, because you shouldn't round down. So either keep +/- 0.053, or use +/- 0.06.

on Aug 22nd, 2003, 7:47am, Sir Col wrote:
 Only in the context of rounding errors.

I thought (and hoped) so.

Quote:
 In examinations, in England, candidates are expected to state that 10.5 (the lower bound of 11 to the nearest whole number) is the greatest value that 10 can be. The question will actually state: "A number, given to the nearest whole number, is 10. Write down the greatest value that this number could be." Not upper bound, but greatest value.

Shocking!

Quote:
 You will even hear examiners saying, "Well how about allowing 10.4999... then?" Argh!

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James Fingas
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 Re: what we do   « Reply #28 on: Aug 22nd, 2003, 10:18am » Quote Modify

on Aug 22nd, 2003, 8:37am, wowbagger wrote:
 That's what they teach here, too. Although it wasn't strictly only one digit in the tolerance, because you shouldn't round down. So either keep +/- 0.053, or use +/- 0.06.

Seems a little pedantic. What I find apalling is how they teach you precisely how to do something, and demand that you get precisely the right answer using just the right method, but don't care a whit whether or not you understand why you're doing it. The best example of this I've seen is multiple-choice exams in first-year Calculus! Fortunately the final exam was only allowed to be up to 60% multiple choice...

If I was a scientist, and went through the trouble of measuring some quanity that was generally accepted to be equal to 10.0, and I got an answer of 9.6 +/- 0.5, I wouldn't be happy and publish. I'd go and check my apparatus and methods until I got a clear answer one way or another. The whole point of having bounds on your answers is that it lets you know what you do and do not know, so you can tell when your agreement is as good as you'll get, versus when you really ought to check your numbers and method.
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wowbagger
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 Re: what we do   « Reply #29 on: Aug 22nd, 2003, 10:48am » Quote Modify

on Aug 22nd, 2003, 10:18am, James Fingas wrote:
 Seems a little pedantic.

You're probably right.

Quote:
 If I was a scientist, and went through the trouble of measuring some quanity that was generally accepted to be equal to 10.0, and I got an answer of 9.6 +/- 0.5, I wouldn't be happy and publish. I'd go and check my apparatus and methods until I got a clear answer one way or another. The whole point of having bounds on your answers is that it lets you know what you do and do not know, so you can tell when your agreement is as good as you'll get, versus when you really ought to check your numbers and method.

As far as I know (from computer "experiments" mostly), it often isn't feasible to improve your answer due to limitations like computation time. In the case of lab experiments, it is often just too costly to do more precise measurements because you need better equipment or whatever.

Whether I'd publish in your example scenario depends on where the knowledge of the "correct" value of 10.0 comes from. If it's a value predicted by theory which hasn't been measured more precisely before - or not with your new ingenious method -, it's ok to get 9.6 +/- 0.5. If it has already been measured with an accuracy of, say, less than 1%, I wouldn't boast of my results.
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James Fingas
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 Re: what we do   « Reply #30 on: Aug 22nd, 2003, 1:32pm » Quote Modify

on Aug 22nd, 2003, 10:48am, wowbagger wrote:
 As far as I know (from computer "experiments" mostly), it often isn't feasible to improve your answer due to limitations like computation time. In the case of lab experiments, it is often just too costly to do more precise measurements because you need better equipment or whatever.

Good point. I don't think there's anybody who has enough money to do a good job of anything. Sniff... But we do a good job of answering puzzles! That I can feel good about!

Except that it contributes to my whole slacking off at work/procrastination/general laziness problem. The best thing about having that particular problem is that I'm not motivated enough to do anything about it ... or maybe that's the worst thing?

<WARNING: imminent mind shutdown in T-2 minutes. WARNING: weekend approaching>

Aaaah. That feels better!
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Icarus
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 Re: what we do   « Reply #31 on: Aug 23rd, 2003, 8:47pm » Quote Modify

on Aug 22nd, 2003, 4:57am, wowbagger wrote:
 (I guess Icarus would refer you to the definition of decimal numbers to show that adding 0 hundredths doesn't change the value of 5.6. )

Sorry - but you forgot that Icarus is not only a mathematician, but also a physicist and engineer. When working in a strictly mathematical arena, this is true. But when inaccuracy is included, it no longer holds (not even mathematically - the concept of number here is slightly different than the normal one in mathematics).

I'm sorry to hear that some of you have been told to abandon the rule that the number of decimal places in the sum or difference should be the same as least number of places in any term, and that the number of significant digits in a product or quotient is the same as the least number for a factor.

While not completely accurate, these rules have a solid mathematical basis, and are a very useful guide. I sincerely wish I could convince my coworkers of the need for them. Some of them regularly report weights in such a way that if they had weighed 7 units on a scale whose base measuring unit is 0.02 Lbs, and read off a value of 1.00, they would report the unit weight as being 0.142857 (they only stop there because they are limited to 6 decimal places).

Yes - the planes we fly in all the time are designed and built by people with so little understanding of measurement.
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 Re: what we do   « Reply #32 on: Aug 24th, 2003, 7:53am » Quote Modify

on Aug 22nd, 2003, 4:57am, wowbagger wrote:
 However, 1m is one metre if you don't give the specific context of a measurement.
Personally I would assume the opposite unless it was a mathematical context. As far as I'm concerned exact numbers only exist in math, and not even all math at that.
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 Re: what we do   « Reply #33 on: Aug 24th, 2003, 7:54am » Quote Modify

on Aug 23rd, 2003, 8:47pm, Icarus wrote:
 Sorry - but you forgot that Icarus is not only a mathematician, but also a physicist and engineer.

I didn't mean to give anybody the impression you were one-dimensional.

Quote:
 When working in a strictly mathematical arena, this is true. But when inaccuracy is included, it no longer holds (not even mathematically - the concept of number here is slightly different than the normal one in mathematics).

It was exactly the strictly mathematical sense I was referring to at that point.

Quote:
 I'm sorry to hear that some of you have been told to abandon the rule that the number of decimal places in the sum or difference should be the same as least number of places in any term, and that the number of significant digits in a product or quotient is the same as the least number for a factor.   While not completely accurate, these rules have a solid mathematical basis, and are a very useful guide.

I agree on them being a useful guide - much better indeed than to give ridiculously precise values. In my personal work, I don't encounter any ("real") measurements (fortunately), so I haven't used this rule for years.

Quote:
 I sincerely wish I could convince my coworkers of the need for them. Some of them regularly report weights in such a way that if they had weighed 7 units on a scale whose base measuring unit is 0.02 Lbs, and read off a value of 1.00, they would report the unit weight as being 0.142857 (they only stop there because they are limited to 6 decimal places).   Yes - the planes we fly in all the time are designed and built by people with so little understanding of measurement.

..which is another good reason why I myself don't "fly all the time".
Hm, it probably should make me wonder, however, whether the people who design our trains, cars, etc. knew any better.
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wowbagger
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 Re: what we do   « Reply #34 on: Aug 24th, 2003, 7:59am » Quote Modify

on Aug 24th, 2003, 7:53am, towr wrote:
 Personally I would assume the opposite unless it was a mathematical context. As far as I'm concerned exact numbers only exist in math, and not even all math at that.

Well, I'm a theoretician.
My interpretation of numbers is based on math as long as the context doesn't give me a good reason not to do so.
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 Re: what we do   « Reply #35 on: Aug 24th, 2003, 6:52pm » Quote Modify

on Aug 24th, 2003, 7:54am, wowbagger wrote:
 I didn't mean to give anybody the impression you were one-dimensional.

I only meant that because I also "indulge" in these areas, I also see their view.

I said in my previous post that the concept of number in physics and engineering differs from that in mathematics. This was mistated. It is not the concept of number that is different, but the concept of decimal notation.

In pure mathematics a decimal expression represents a single number. In applied mathematics, the concept has a few differences: First of all, we no longer have "infinite decimal expressions". These are purely a conceptual idea, not to be found in the real world. Second, an applied decimal does not represent a single real number, but rather a range of numbers which round to the actual decimal expression.

So 1.1 and 1.10 are not the same thing in application. 1.1 refers to the conceptual interval [1.05, 1.15), while 1.10 refers to the conceptual interval [1.095, 1.105), which is definitely a different beast. In this sense, 1.1 [ne] 1.10.

(As for the rest of the zero argument - quite frankly it seems to me to be nothing more than semantic haggling, which I find is almost always a waste of time.)
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hiv
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 Re: what we do   « Reply #36 on: Sep 18th, 2003, 9:13am » Quote Modify

I think you should have student on there, because what if someone is a student? I chose the career I want to be when I 'grow up' but now I am just learning.
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 Re: what we do   « Reply #37 on: Sep 18th, 2003, 10:35am » Quote Modify

it says "field of work or study",
I don't think student is generally a field of study or work
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James Fingas
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 Re: what we do   « Reply #38 on: Sep 18th, 2003, 10:49am » Quote Modify

Quote:
 I don't think student is generally a field of study or work

I don't know about that! I have heard stories about "perma-students" who live off TA money and grad study grants and take post-graduate degrees until they're well past middle age.

And don't forget those students permanently enrolled in the school of hard knocks...
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 Re: what we do   « Reply #39 on: Sep 18th, 2003, 1:33pm » Quote Modify

That's hardly "generally"
Even then it's what they study that is the field of their study, and that's rarely if ever them being a student. I'd dare say there are only very few people that really study themselves in an academic way (and in doing so making themselves the field of their studies).
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James Fingas
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 Re: what we do   « Reply #40 on: Sep 18th, 2003, 1:41pm » Quote Modify

If a man learns something, but never uses it, has he really learned anything but how to be a student?
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 Re: what we do   « Reply #41 on: Sep 18th, 2003, 2:40pm » Quote Modify

If a man goes to university to study physics, and in doing so learns to find his way to the university, is finding his way to university his field of study?
I'd say not.

If a man learns anything, has he learned to be a student?
Not necessarily imo. In so much as learning implies being a student it needn't be learned in the first place. And in so much as being a student implies more than simply learning, one might well not learn it from all sorts of learning.

Anyway, while one can certainly study being a student, that is part of the field of psychology, not a field on its own.
Also I don't think studying and learning are equal, studying imo implies a greater commitment and activity, while learning can also be quite passive.
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 Re: what we do   « Reply #42 on: Sep 18th, 2003, 5:23pm » Quote Modify

on Sep 18th, 2003, 9:13am, hiv wrote:
 I think you should have student on there, because what if someone is a student? I chose the career I want to be when I 'grow up' but now I am just learning.

Welcome to the boards, hiv. For your sake, I added the "Primary-High School student". (My apologies for messing with your poll, William! ) My fellow moderators have failed to notice the implications of your "when I grow up" statement. Either that, or they've forgotten that specialization of study does not begin until the latter stage of your education. "Undeclared" might be an appropriate choice for you - it means you haven't settled into any specializations yet, but this gives you a more specific choice.
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 Re: what we do   « Reply #43 on: Sep 19th, 2003, 1:23am » Quote Modify

If don't have a field of work and study shouldn't the answer simply be 'none'?

Besides, around here you're not called 'student' untill you go to university.
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 Re: what we do   « Reply #44 on: Sep 19th, 2003, 4:05pm » Quote Modify

So what do you call your Pre-college school attendees? Student is the acceptable English term for anyone who studies. And "none" implies considerably more (or less) than "student" does.

The object of this poll is to find out what sort of people are visiting this forum. I see no reason to pigeon-hole the younger members in this fashion.
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 Re: what we do   « Reply #45 on: Sep 20th, 2003, 4:59am » Quote Modify

on Sep 19th, 2003, 4:05pm, Icarus wrote:
 So what do you call your Pre-college school attendees? Student is the acceptable English term for anyone who studies.
Yes, I know, but since we here in the Netherlands aren't English (yet), we call pre-college school attendees "scholieren" (not to be confuced with scholars ), or "leerlingen" (depending on context). And university students are "studenten" ("student" in singular).
So since we have different names for both, I only associate 'student' with the university group, even in English (unless the context makes it clear that that's the wrong association).

Quote:
 And "none" implies considerably more (or less) than "student" does.
Yes, but it's not a field of work or study, it's an occupation. Which frankly is what I first thought the poll was, untill I noticed it asked for something else.

Quote:
 The object of this poll is to find out what sort of people are visiting this forum. I see no reason to pigeon-hole the younger members in this fashion.
Probably true, but it should reflect it better in the poll-question.
It might just as well have asked where our intrests ly. That's probably more the intend than what we do for a living, or what we study (which hopefully is inculded in the field where our intrest lies, but is usually much more limited)
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 Re: what we do   « Reply #46 on: Sep 20th, 2003, 6:18pm » Quote Modify

on Sep 20th, 2003, 4:59am, towr wrote:
 Yes, I know, but since we here in the Netherlands aren't English (yet), we call pre-college school attendees "scholieren" (not to be confuced with scholars ), or "leerlingen" (depending on context). And university students are "studenten" ("student" in singular). So since we have different names for both, I only associate 'student' with the university group, even in English (unless the context makes it clear that that's the wrong association).

I'm glad to hear you aren't English, and may any such change be long in coming. A world with one language would be considerably less interesting than ours. Keep this up and I might actually pick up something of other languages myself! (I've studied French and Greek, but have an appalling retention level of either. I also learned barely enough German to pass my language requirements for my degree. Since all I had to do was translate a written mathematical paper with the aid of a lexicon, this wasn't much.) Alas, 2nd languages are not something wherein I possess any native talents.

But, since we are speaking English here, I'm afraid you'll have to get used to "students" being applied to everyone from preschool to postdoctoral.

Quote:
 Yes, but it's not a field of work or study, it's an occupation. Which frankly is what I first thought the poll was, untill I noticed it asked for something else. ... It might just as well have asked where our intrests ly. That's probably more the intend than what we do for a living, or what we study (which hopefully is inculded in the field where our intrest lies, but is usually much more limited)

I had the impression that William was looking for both. Thats' why I chose 3 answers myself. One is my occupation, the other two are my education and interests. Engineering per se is not of great interest to me, even if it is my job. (That does not mean I find my work uninteresting - but that my interests in it tend to differ from those of my coworkers.) Math and Physics are of considerable interest, but they are not (directly) my occupation. By asking the question he has, I pick up on all three.
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 Re: what we do   « Reply #47 on: Sep 21st, 2003, 8:34am » Quote Modify

on Sep 20th, 2003, 6:18pm, Icarus wrote:
 I'm glad to hear you aren't English, and may any such change be long in coming. A world with one language would be considerably less interesting than ours.
Well, there are many other things that make it interesting. And the world would probably become more united. In many respects things would be easier, and we wouldn't have anymore bad dubs from (or to) English

Anyway, I don't think all other languages would disappear even if English were to become the main language of every country on earth. Klingon would still be very popular among trekkies Besides, a lot of small languages are surviving quite admirably next to much larger languages. Welsh in Brittain, Frisian (my second first language) in the Netherlands, Breton in France etc. Dispite having been repressed in former times (though there's now EU-funding to preserve and promote them, because they were slowly going downhill).

Quote:
 Keep this up and I might actually pick up something of other languages myself! (I've studied French and Greek, but have an appalling retention level of either. I also learned barely enough German to pass my language requirements for my degree. Since all I had to do was translate a written mathematical paper with the aid of a lexicon, this wasn't much.) Alas, 2nd languages are not something wherein I possess any native talents.

I've never been good at languages myself.. I just had the luck of growing up bilingual, and watching a lot English cartoons on TV.
Nowadays though, there's dozens of dubbed cartoons (which are also pretty crappy aside from the bad translation, but that's besides the point). So there's little chance of kids learning to speak/understand English (or any other language) this way anymore. Despite the fact that it's the ideal time and method to learn a language.
(For some insane and unfunded reason parents seem to think children wouldn't be able to understand or like cartoons in another language.)

Quote:
 But, since we are speaking English here, I'm afraid you'll have to get used to "students" being applied to everyone from preschool to postdoctoral.
Well, it's just something I have to give second thought. I don't think I'll ever get used to it in the sense that it'll be my first association.
I also pretty much associate everyone on the internet with my age (actually with the age 23, since I was 17 or so, it's just a coincidence I'm now actually 23). Only when I get any clue as to what someone's real age is will I adjust my mental representation of them.
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 Re: what we do   « Reply #48 on: Sep 22nd, 2003, 7:29am » Quote Modify

on Sep 20th, 2003, 6:18pm, Icarus wrote:
 I also learned barely enough German to pass my language requirements for my degree. Since all I had to do was translate a written mathematical paper with the aid of a lexicon, this wasn't much.

I didn't know there are such language requirements. Is that common in the USA?

on Sep 21st, 2003, 8:34am, towr wrote:
 I just had the luck of growing up bilingual, and watching a lot English cartoons on TV.   Nowadays though, there's dozens of dubbed cartoons (which are also pretty crappy aside from the bad translation, but that's besides the point). So there's little chance of kids learning to speak/understand English (or any other language) this way anymore. Despite the fact that it's the ideal time and method to learn a language.

I can't remember any cartoons in English on German TV when I was a child. When I was first confronted with English at school I was already nine. Apart from the grounding I learned there, I think most of the progress I made was because of reading books and newspapers, not due to watching TV or films. But that may be just a matter of personal disposition. And with many teenage students it seems to be difficult enough to get them reading in their native language, let alone a foreign one...
O tempora! O mores!
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 Re: what we do   « Reply #49 on: Sep 22nd, 2003, 8:19am » Quote Modify

I simply watched BBC, and Sky Channel. We didn't have any cartoons on Dutch tv then afaik.
The problem with books/newspapers, is that you have to understand some of the language to read it (or a dictionary), moreso you have to be able to read. For some reason kids aren't taught to read anything untill their language-learning-peak has passed. And of course you can't hear how to pronounce words from newspapers and books :p (espescially not in english). I do think books help more to broaden your vocabulary, once you can speak(/read/write) a language.
Cartoons and reallife have the advantage that you can see what people are talking about. Cartoons probably moreso, since their world is simpler (less detail, less elements that distract from the story).

I allways thought it a shame that they seem to dub everything in Germany. Moreso that it used to be done so badly (and maybe still, I avoid the German channels these days). I like subtitles, and the original script and voices.
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