From: Elliott Roper on
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.

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From: Tzortzakakis Dimitrios on

? "Elliott Roper" <nospam(a)yrl.co.uk> ?????? ??? ??????
news:211120091203428012%nospam(a)yrl.co.uk...
> 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.
>
In my college, here in Iraklion, www.teiher.gr , we did complex numbers,
hyperbolic sin and cos, tables 2X 2 etc, calculus and double integral
calculus. Never mind I ended up as an electrician;we are in a no-man's land
between the scientists (university graduates) and technicians (trade school
graduates). We did all this with our sci calculators; everyone has to have
one. I got mine for 10 euros, Philips, compete with a rule, eraser, pencil
sharpener and head scarf. I got my first one, sci calc from my godfather
which was a present to him but like my father was a complete doofus in math
so he gave it to me. It was solar.



--
Tzortzakakis Dimitrios
major in electrical engineering
mechanized infantry reservist
hordad AT otenet DOT gr


From: Noons on
Elliott Roper wrote,on my timestamp of 22/11/2009 12:03 AM:
>
> 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?

So what? Did anyone create a mark post in history saying this is middle ages,
that is renaissance, all around the world? Renaissance might have started in
the 16th century somewhere in Europe. Hardly everywhere in the world. Even
today there are places where it hasn't started...

> 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.

Just like the ones to Newfoundland, and the ones that pre-dated Brazil's
discovery two years later? I'm sure South America and Africa have drifted away
since but I don't think even then, it was quite exactly a coast-hugging
navigation exercise... Remember Tordesillas? Do you think they'd know the
correct distance to set the meridian if they had no clue what was there?

But the most interesting period started after Vasco, until about 1600 and the
cretin "Spanish Armada" exercise. It's the kind of thing that led to the 1580
bronze sphere that is in the Vienna museum of art, with the coast of Australia
clearly delineated. Cook would "discover and map" it, but only 200 years later...


> 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.

Of course. Hey: you brought Vasco da Gama into this, not me. I said "Portuguese
navigators", I didn't say Vasco da Gama. There were quite a lot more than Vasco,
get informed.


> 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.

Remarkably, it's a 0-9 to 0-10 ratio scale that allows a slide rule to work...

> Nunes work was with putting vernier-precursors on astrolabes,

and in inventing the principle of operation of the vernier. Which was refined
later but that is totally irrelevant.

>>> 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?

Quite frankly, I couldn't care less. Like I said, choose or chose whatever you
want. It's totally irrelevant. Would you prefer me to write in any of 3 other
languages? Can you?


> What am I supposed to be hiding?

That kids nowadays are incapable of using a slide rule, much less understand its
principle of operation. And that their education system is failing to teach what
are essential principles and knowledge.


> 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.

Sure. Why is it then so few even know how to load a calculator at all? Assuming
a cell phone capable of a serious one, the iPhone is in vast minority. At least
here.
I checked in a few schools a while ago what calculators kids were using.
Surprise: most were of the +-/*M+M-RM variety and little else. Oh yes: some had
%: like, that one is soooooo hard to work out, it needs its own key...

One would think today's "educated" kids would have worked out the basic 4
operations and would be using calculators for the really hard stuff. They
aren't. That, is a serious situation.

I can understand calculators being used as replacements for a slide rule: more
powerful, faster to operate. But when the work possible with a slide rule is
not even in scope and the challenge is how to divide 2 numbers, I don't think we
have progressed that much, if at all.


> 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.

I see no such evidence either. The reason is that we are talking about the
education provided to kids, not their intelligence. They are not dumber, just
not educated properly. Ignorance is not proof of lack of intelligence.


> Now do you understand why I used 'curmudgeonly' as a semi-serious joke?

I don't see why a joke was called for. Are you training to be a clown?
From: Elliott Roper on
In article <hea0md$sn6$1(a)news.eternal-september.org>, Noons
<wizofoz2k(a)yahoo.com.au> wrote:

> Elliott Roper wrote,on my timestamp of 22/11/2009 12:03 AM:
> >
> > 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?
>
> So what? Did anyone create a mark post in history saying this is middle
> ages,
> that is renaissance, all around the world? Renaissance might have started in
> the 16th century somewhere in Europe. Hardly everywhere in the world. Even
> today there are places where it hasn't started...

You originally said
"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."

The bit I found puzzling was how a man born in 1502 was able to produce
the theory behind instruments used in the 1300's.

I was using the marker post *you* defined there. "14th century, smack
bang in the middle ages"
I'm not a historian, but it is generally accepted that the late Middle
Ages ended with the 15th Century. It is a date convention for the
convenience of historians and schoolteachers I suspect. You are free to
redefine it any time you like, but don't expect anyone to take you
seriously when you later use your private definition to win an
argument.
>
> > 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.
>
> Just like the ones to Newfoundland, and the ones that pre-dated
> Brazil's discovery two years later? I'm sure South America and
> Africa have drifted away since but I don't think even then, it was
> quite exactly a coast-hugging navigation exercise...

For what it is worth, VIkings beat the Portuguese official navigators
16th Century arrival to Newfoundland by 500 years. Brazil was 16th
Century.
> Remember Tordesillas? Do you think they'd know the
> correct distance to set the meridian if they had no clue what was there?
The treaty of Tordesillas *was* signed without anyone knowing much
about what was there. It was to artificially settle a squabble between
Spain and Portugal and was defined as a meridian 370 leagues west of
Cape Verde Islands, which as you doubtless know are off the coast of
*Africa*. It specifically did *not* include a meridian of Longitude as
we know it today.

> But the most interesting period started after Vasco, until about 1600
> and the cretin "Spanish Armada" exercise. It's the kind of thing
> that led to the 1580 bronze sphere that is in the Vienna museum of
> art, with the coast of Australia clearly delineated. Cook would
> "discover and map" it, but only 200 years later...
Your "interesting period" starts after the end of the Middle Ages.
> > 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.
>
> Of course. Hey: you brought Vasco da Gama into this, not me. I said
> "Portuguese navigators", I didn't say Vasco da Gama. There were quite
> a lot more than Vasco, get informed.
I chose Vasco da Gama's route to India as a possible first for open
ocean Portuguese navigation to give your line of argument the best
possible chance of success. Henry the Navigator's voyages were pretty
much coast-huggers, and Vasco da Gama's voyage more or less marks the
end of the Middle Ages, especially for Portugal, which I freely admit
was one of the most technologically advanced countries.

> > 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.
>
> Remarkably, it's a 0-9 to 0-10 ratio scale that allows a slide rule to work...
Oh my dear God! Remarkably? You are living proof that inability to deal
with mathematical concepts predates the current crop of schoolkids.
Verniers have nothing whatever to do with slide rules or logarithms.
There is nothing 0-9 and nothing 0-10 on a slide rule. Go and look. If
you want me to descend to your level of magical numerological
mythology, you might say it is 1-10 that makes a slide rule work. i.e
the CD scales go from 10^0 to 10^1.

<snip>

> > 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.
>
> Sure. Why is it then so few even know how to load a calculator at
> all? Assuming a cell phone capable of a serious one, the iPhone is in
> vast minority. At least here. I checked in a few schools a while ago
> what calculators kids were using. Surprise: most were of the
> +-/*M+M-RM variety and little else. Oh yes: some had %: like, that
> one is soooooo hard to work out, it needs its own key...
>
> One would think today's "educated" kids would have worked out the
> basic 4 operations and would be using calculators for the really hard
> stuff. They aren't. That, is a serious situation.
>
> I can understand calculators being used as replacements for a slide
> rule: more powerful, faster to operate. But when the work possible
> with a slide rule is not even in scope and the challenge is how to
> divide 2 numbers, I don't think we have progressed that much, if at
> all.
I can't refute your assertion that kids in your unspecified bit of the
backwoods are incapable of using a slide rule, and that they can
operate, and have been exposed to, only the most primitive feature-free
calculators known to mankind. All I can do is repeat that my own
experience in a little piece of backwoods UK is wildly different. Any
high school kid bright enough to work a slide rule can and does learn
enough about the log and exponential functions that explain a slide
rule's principle of operation. I'd say only a small fraction of all
kids would be unable to use a slide rule after a few minutes tuition.
Many would work it out for themselves after being told it multiplies
and divides and the scales are logarithmic. Kids are a lot smarter than
they let on. Always have been.

> > 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.
>
> I see no such evidence either. The reason is that we are talking
> about the education provided to kids, not their intelligence. They
> are not dumber, just not educated properly. Ignorance is not proof
> of lack of intelligence.

Once again, I can't comment on how bad the schools and the parents are
in your bit of the Boondocks. It's not my experience.

PS You might think I'm bigging up UK schools and kids, but we too are
rednecks compared to the school Tzortzakakis Dimitrios went to.

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From: Robert Coe on
On Fri, 20 Nov 2009 23:58:51 -0500, tony cooper <tony_cooper213(a)earthlink.net>
wrote:
: On Fri, 20 Nov 2009 20:27:54 -0800, Savageduck
: <savageduck1@{REMOVESPAM}me.com> wrote:
:
: >On 2009-11-20 19:09:55 -0800, tony cooper <tony_cooper213(a)earthlink.net> said:
: >
: >> On Fri, 20 Nov 2009 17:31:09 -0800, Savageduck
: >> <savageduck1@{REMOVESPAM}me.com> wrote:
: >>
: >>> Along with 2 Faber Castell slide rules, I still have my old book of
: >>> log/antilog and trig tables. Use the word "mantissa" today, and see
: >>> what sort of baffled looks you will get from kids.
: >>
: >> What? Spanish ladies don't wear veils today?
: >
: >Forget Spanish ladies and veils, think in terms of significand.
: >Traditional usage of "mantissa" regarding logarithms refers to the
: >fractional part of a logarithm.
:
: You think I didn't know that? A mantilla is a (usually) lace scarf
: worn by Spanish women as a veil. Just a word-play joke. I probably
: shouldn't joke in this group.

Don't give up, Tony. Some of us did get it! :^)

Bob