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From: Noons on 21 Nov 2009 06:00 Elliott Roper wrote,on my timestamp of 21/11/2009 11:22 AM: > Middle Ages are generally supposed to be from 5th to 16th C. Yes. > Slide rule is 17th century invention after John Napier's work on > logarithms. The mathematical work on vernier scales was done by a guy called Pedro Nunes and was used by the Portuguese to calculate deviations, declinations and navigation tables since the 14th century, smack bang in the middle ages. It's how they managed to work their way around the world without a single map to guide them. > That's a bit curmudgeonly. Nevertheless, it's reality. You can of course chose to hide it.
From: Elliott Roper on 21 Nov 2009 07:03 In article <La2dnRcFo9UW3prWnZ2dnUVZ_gOdnZ2d (a)giganews.com>, Bill Graham<weg9 (a)comcast.net> wrote:> "Elliott Roper" <nospam (a)yrl.co.uk> wrote in message > news:211120090022284678%nospam (a)yrl.co.uk...> >> Yes. When slide rules disappeared, knowledge of their principal of > >> operation > >> disappeared with them. > > > It took a bit longer to explain enough about logs for > > her to get how it works. > > When she's 15, ask her again how they work......Unless she's a math major, > she won't even know what logs are...... Er no. Not if her mum and grandad have anything to do with it, she'll be fine. Also, here in UK, nobody majors in anything at 15, except perhaps soccer. Looking at maths syllabuses for primary and junior high school would support your position. Of course nobody will be taught log table use - except for curiosity value - but there may be enough in there to get/retain a basic understanding. They do powers and scientific notation f'rinstance. Not great, but at least something close. It is pretty fashionable to rubbish school maths teaching; us old curmudgeons blather on about declining standards, but there is good stuff replacing square roots by long division and 4 figure log tables. They are doing much better on more fundamental stuff like sets and number theory and logic and 'patterns' than what was dealt out to me when I were a young 'un. I was taught logs by rote at about 12 or 13. Nobody ever bothered to teach us much about /why/ it worked. I don't look back at that with any fondness at all. -- To de-mung my e-mail address:- fsnospam$elliott$$ PGP Fingerprint: 1A96 3CF7 637F 896B C810 E199 7E5C A9E4 8E59 E248
From: J. Clarke on 21 Nov 2009 07:56 Elliott Roper wrote: > In article <La2dnRcFo9UW3prWnZ2dnUVZ_gOdnZ2d (a)giganews.com>, Bill> Graham <weg9 (a)comcast.net> wrote:> >> "Elliott Roper" <nospam (a)yrl.co.uk> wrote in message>> news:211120090022284678%nospam (a)yrl.co.uk...>>>> Yes. When slide rules disappeared, knowledge of their principal of >>>> operation >>>> disappeared with them. >>> >> It took a bit longer to explain enough about logs for >>> her to get how it works. >> >> When she's 15, ask her again how they work......Unless she's a math >> major, she won't even know what logs are...... > > Er no. Not if her mum and grandad have anything to do with it, she'll > be fine. > Also, here in UK, nobody majors in anything at 15, except perhaps > soccer. > > Looking at maths syllabuses for primary and junior high school would > support your position. Of course nobody will be taught log table use - > except for curiosity value - but there may be enough in there to > get/retain a basic understanding. They do powers and scientific > notation f'rinstance. Not great, but at least something close. > > It is pretty fashionable to rubbish school maths teaching; us old > curmudgeons blather on about declining standards, but there is good > stuff replacing square roots by long division and 4 figure log tables. > They are doing much better on more fundamental stuff like sets and > number theory and logic and 'patterns' than what was dealt out to me > when I were a young 'un. I was taught logs by rote at about 12 or 13. > Nobody ever bothered to teach us much about /why/ it worked. I don't > look back at that with any fondness at all. Most college bound high school students in the US who don't get calculus in high school will get a course called "Precalculus Mathematics" that hits exponentials and logs pretty heavily. You need logs to handle any "Integral of 1/u du" type problem so they're important in calculus even if you don't use them anymore for multiplication and division. And anybody who has completed a three-semester calculus course will have had more. No need to be a math major--engineering, physics, and chemistry curricula require it too--Calculus is the _beginning_ of learning math, not the _end_. I'm surprised that biology doesn't require it given how heavily it has become dependent on chemistry these days. While there should be a development of the theory of logs and exponentials in precalculus and expanded on a bit in calculus, to _really_ learn how it all works with rigorous proofs of everything you need to take a course that used to be called "Advanced Calculus" and is now usually called "Real Analysis".
From: Elliott Roper on 21 Nov 2009 08:03 In article <he8h85$nt3$1 (a)news.eternal-september.org>, Noons<wizofoz2k (a)yahoo.com.au> wrote:> Elliott Roper wrote,on my timestamp of 21/11/2009 11:22 AM: > > > Middle Ages are generally supposed to be from 5th to 16th C. > > Yes. > > > Slide rule is 17th century invention after John Napier's work on > > logarithms. > > The mathematical work on vernier scales was done by a guy called Pedro Nunes > and > was used by the Portuguese to calculate deviations, declinations and > navigation > tables since the 14th century, smack bang in the middle ages. It's how they > managed to work their way around the world without a single map to guide them. Pedro Nunes 1502-1578. That is, he was *born* 2 years into the 16th C. Perhaps his great-great-great-great grandad passed it on down the family? You are also wrong about the dates of Portuguese navigation primacy. Vasco da Gama made it to India in 1498 - two years before the end of the Middle Ages. Earlier Portuguese voyages of discovery were limited to hugging the coast of Africa. There is little evidence that Vasco da Gama had access to navigation tables. The open sea section of his first voyage to India was navigated by an unknown muslim pilot he took on board in Malindi. Verniers have nothing to do with logarithms or slide rules. The only similarity is a little slidy thing on modern calipers that has a totally different purpose. A vernier is nothing much more than an optical lever. It has more to do with similar triangles than with anything log-like. Nunes work was with putting vernier-precursors on astrolabes, which also have nothing to do with logs or slide rules, but of course are far more ancient than Portuguese navigation of the very late Middle Ages. Hipparchus 200 BC anyone? > > That's a bit curmudgeonly. > > Nevertheless, it's reality. You can of course chose to hide it. Huh? In addition to history of science, you are also not doing too well on grammar, logic and relevance. Chose? Is that the correct tense? What am I supposed to be hiding? The reality is that the same sort of kids who would have been comfortable with their granddad's slide rule will be comfortable with the use of log functions on their iPhone emulation of their dad's HP41 calculator. The reality is that in all generations, there are/were lots of kids who would not have been comfortable with anything like either. I see no evidence that the current crop of kids are dumber than us old goats. Now do you understand why I used 'curmudgeonly' as a semi-serious joke? -- To de-mung my e-mail address:- fsnospam$elliott$$ PGP Fingerprint: 1A96 3CF7 637F 896B C810 E199 7E5C A9E4 8E59 E248
From: Elliott Roper on 21 Nov 2009 08:12
In article <he8org02qjr (a)news6.newsguy.com>, J. Clarke<jclarke.usenet (a)cox.net> wrote:> Elliott Roper wrote: > > In article <La2dnRcFo9UW3prWnZ2dnUVZ_gOdnZ2d (a)giganews.com>, Bill> > Graham <weg9 (a)comcast.net> wrote:> > > >> "Elliott Roper" <nospam (a)yrl.co.uk> wrote in message> >> news:211120090022284678%nospam (a)yrl.co.uk...> >>>> Yes. When slide rules disappeared, knowledge of their principal of > >>>> operation > >>>> disappeared with them. > >>> > >> It took a bit longer to explain enough about logs for > >>> her to get how it works. > >> > >> When she's 15, ask her again how they work......Unless she's a math > >> major, she won't even know what logs are...... > > > > Er no. Not if her mum and grandad have anything to do with it, she'll > > be fine. > > Also, here in UK, nobody majors in anything at 15, except perhaps > > soccer. > > > > Looking at maths syllabuses for primary and junior high school would > > support your position. Of course nobody will be taught log table use - > > except for curiosity value - but there may be enough in there to > > get/retain a basic understanding. They do powers and scientific > > notation f'rinstance. Not great, but at least something close. > > > > It is pretty fashionable to rubbish school maths teaching; us old > > curmudgeons blather on about declining standards, but there is good > > stuff replacing square roots by long division and 4 figure log tables. > > They are doing much better on more fundamental stuff like sets and > > number theory and logic and 'patterns' than what was dealt out to me > > when I were a young 'un. I was taught logs by rote at about 12 or 13. > > Nobody ever bothered to teach us much about /why/ it worked. I don't > > look back at that with any fondness at all. > > Most college bound high school students in the US who don't get calculus in > high school will get a course called "Precalculus Mathematics" that hits > exponentials and logs pretty heavily. You need logs to handle any "Integral > of 1/u du" type problem so they're important in calculus even if you don't > use them anymore for multiplication and division. And anybody who has > completed a three-semester calculus course will have had more. No need to > be a math major--engineering, physics, and chemistry curricula require it > too--Calculus is the _beginning_ of learning math, not the _end_. I'm > surprised that biology doesn't require it given how heavily it has become > dependent on chemistry these days. While there should be a development of > the theory of logs and exponentials in precalculus and expanded on a bit in > calculus, to _really_ learn how it all works with rigorous proofs of > everything you need to take a course that used to be called "Advanced > Calculus" and is now usually called "Real Analysis". I'm in violent agreement with all of that. However, the original part of that discussion was about 15 year-olds and logs. Only a few will have started calculus at that age in high school. Few of those will be integrating 1/u du by then. A bit of a shame really, since that is where it starts getting to be fun. -- To de-mung my e-mail address:- fsnospam$elliott$$ PGP Fingerprint: 1A96 3CF7 637F 896B C810 E199 7E5C A9E4 8E59 E248 |