Pipe organs measure pitch in "feet". Bigger number = lower pitch. The 
number is not /directly/ related to the physical size of the pipes, 
although generally bigger numbers mean bigger pipes.

A "normal" organ stop has 8' pitch. The pipes controlled by the peddles 
are normally 16' pitch (i.e., one octave lower). Most organs will also 
have 4' and 2' pitches, and unless it's a really small organ, there's 
usually at least one 16' stop.

Now, a *cathedral* pipe organ will have at least one 32' stop, and a 
really powerful one might have several of them.

There are exactly two pipe organs in the entire world which have a 64' 
stop. And here's why:

http://www.sydneyorgan.com/STH64.mp3 [Sydney Town Hall]
http://www.die-orgelseite.de/audio/atlanticcity_64ft.mp3 [Broadwalk Hall 
Auditorium Organ, New Jersey]

(Many organs have a 64' stop which actually generates /harmonics of/ a 
64' pitch, but only these two actually have true 64' pitch pipes.)

Worth it... :-P

Then again, the organ at Liverpool Cathedral has a 32' Double Open Bass 
which the organ's designer referred to as "the expensive draft". When 
played, it makes a vague fluttering sound. The louder 32' stops make a 
more definite sort of noise. (As best as I can tell, from video 
recordings made with professional equipment...) If 32' isn't that 
useful, why bother with 64'?

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Le 2011-04-23 11:59, Orchid XP v8 a écrit :
> Then again, the organ at Liverpool Cathedral has a 32' Double Open Bass
> which the organ's designer referred to as "the expensive draft". When
> played, it makes a vague fluttering sound. The louder 32' stops make a
> more definite sort of noise. (As best as I can tell, from video
> recordings made with professional equipment...) If 32' isn't that
> useful, why bother with 64'?
>

Nigel Tufnel: The numbers all go to eleven. Look, right across the 
board, eleven, eleven, eleven and...
Marty DiBergi: Oh, I see. And most amps go up to ten?
Nigel Tufnel: Exactly.
Marty DiBergi: Does that mean it's louder? Is it any louder?
Nigel Tufnel: Well, it's one louder, isn't it? It's not ten. You see, 
most blokes, you know, will be playing at ten. You're on ten here, all 
the way up, all the way up, all the way up, you're on ten on your 
guitar. Where can you go from there? Where?
Marty DiBergi: I don't know.
Nigel Tufnel: Nowhere. Exactly. What we do is, if we need that extra 
push over the cliff, you know what we do?
Marty DiBergi: Put it up to eleven.
Nigel Tufnel: Eleven. Exactly. One louder.
Marty DiBergi: Why don't you just make ten louder and make ten be the 
top number and make that a little louder?
Nigel Tufnel: [pause] These go to eleven.


-- 
/*Francois Labreque*/#local a=x+y;#local b=x+a;#local c=a+b;#macro P(F//
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/*   gmail.com     */}camera{orthographic location<6,1.25,-6>look_at a }

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Le 2011/04/23 11:59, Orchid XP v8 a écrit :

> (Many organs have a 64' stop which actually generates /harmonics of/ a
> 64' pitch, but only these two actually have true 64' pitch pipes.)
>

And then, the harmonics of 64 are:
32, 21 1/3, 16, 12 4/5, 10 2/3, 9 1/7, 8, 7 1/9, 6 4/10,....

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On 25/04/2011 20:23, Alain wrote:

> And then, the harmonics of 64 are:
> 32, 21 1/3, 16, 12 4/5, 10 2/3, 9 1/7, 8, 7 1/9, 6 4/10,....

I love how the harmonics look like completely randomly chosen numbers, 
with no obvious pattern at all.

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Le 2011-05-03 04:45, Invisible a écrit :
> On 25/04/2011 20:23, Alain wrote:
>
>> And then, the harmonics of 64 are:
>> 32, 21 1/3, 16, 12 4/5, 10 2/3, 9 1/7, 8, 7 1/9, 6 4/10,....
>
> I love how the harmonics look like completely randomly chosen numbers,
> with no obvious pattern at all.

64/1 = 64
64/2 = 32
64/3 = 21 1/3
64/4 = 16
64/5 = 12 4/5
64/6 = 10 2/3
64/7 = 9 1/7
64/8 = 8
64/9 = 7 1/9
64/10 = 6 4/10
...

Nope, no discernable pattern at all
;)


-- 
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/*   gmail.com     */}camera{orthographic location<6,1.25,-6>look_at a }

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>> I love how the harmonics look like completely randomly chosen numbers,
>> with no obvious pattern at all.
>
> 64/1 = 64
> 64/2 = 32
> 64/3 = 21 1/3
> 64/4 = 16
> 64/5 = 12 4/5
> 64/6 = 10 2/3
> 64/7 = 9 1/7
> 64/8 = 8
> 64/9 = 7 1/9
> 64/10 = 6 4/10
> ...
>
> Nope, no discernable pattern at all ;)

Exactly. I mean, unless you happen to be able to compute 64/7 mentally, 
which normal humans can't.

If it was notated some other way, the pattern might be more obvious. But 
as it is...

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Le 2011/05/03 04:45, Invisible a écrit :
> On 25/04/2011 20:23, Alain wrote:
>
>> And then, the harmonics of 64 are:
>> 32, 21 1/3, 16, 12 4/5, 10 2/3, 9 1/7, 8, 7 1/9, 6 4/10,....
>
> I love how the harmonics look like completely randomly chosen numbers,
> with no obvious pattern at all.

Harmonics are integer multiple of the base frequency, or integer 
quotients of the base wave length having integer quotient of the power.

Armonic 1 is the base signal.
Armonic 2 have twice the frequency, or half the wave length, and half 
the amplitude. For 64, it gives 32.

Nothing random here, not even a bad pseudo-random. It's totaly 
deterministic.



Alain

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On 04/05/2011 00:21, Alain wrote:

> Nothing random here, not even a bad pseudo-random. It's totaly
> deterministic.

So is a psuedo-random number generator, and yet it still *looks* random.

Post a reply to this message

Le 2011-05-03 08:47, Invisible a écrit :
>>> I love how the harmonics look like completely randomly chosen numbers,
>>> with no obvious pattern at all.
>>
>> 64/1 = 64
>> 64/2 = 32
>> 64/3 = 21 1/3
>> 64/4 = 16
>> 64/5 = 12 4/5
>> 64/6 = 10 2/3
>> 64/7 = 9 1/7
>> 64/8 = 8
>> 64/9 = 7 1/9
>> 64/10 = 6 4/10
>> ...
>>
>> Nope, no discernable pattern at all ;)
>
> Exactly. I mean, unless you happen to be able to compute 64/7 mentally,
> which normal humans can't.

You're not that much younger than me, so maybe there's something 
fundamentally different between the school system in the UK vs. Canada, 
but in the 2nd or 3rd grade, we had to learn our multiplication tables 
by heart.

Normal humans should remember that 7 * 9 = 63.

Or if they don't, they should be able to guestimate that since 64 is 
rather close to 70, there's a good chance that 64/7 would be just a bit 
less than 70/7, which is easy to compute.

If not, I weep for humanity.

-- 
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>> Exactly. I mean, unless you happen to be able to compute 64/7 mentally,
>> which normal humans can't.
>
> You're not that much younger than me, so maybe there's something
> fundamentally different between the school system in the UK vs. Canada,
> but in the 2nd or 3rd grade, we had to learn our multiplication tables
> by heart.

This is almost universally regarded as one of the most useless things 
you learn in school. I haven't studied this statistically, but I suspect 
the majority of adults long since forgot all this stuff.

> Or if they don't, they should be able to guestimate that since 64 is
> rather close to 70, there's a good chance that 64/7 would be just a bit
> less than 70/7, which is easy to compute.
>
> If not, I weep for humanity.

Start weeping. This kind of reasoning is apparently far beyond the 
ability of most average people.

Even if it wasn't, standing there for five minutes computing tables 
isn't very immediate. If, instead of notating note pitches as 
wavelengths, they were noticed as, say "K * 7" or something, it would be 
far more instantly obvious what the relationship is, without having to 
perform complex mental arithmetic.

Post a reply to this message

On 04/05/2011 1:34 PM, Invisible wrote:
> This is almost universally regarded as one of the most useless things
> you learn in school. I haven't studied this statistically, but I suspect
> the majority of adults long since forgot all this stuff.

Rubbish! Maybe young adults can't remember them as they are over reliant 
on calculators.

-- 
Regards
     Stephen

Post a reply to this message

On 04/05/2011 06:05 PM, Stephen wrote:
> On 04/05/2011 1:34 PM, Invisible wrote:
>> This is almost universally regarded as one of the most useless things
>> you learn in school. I haven't studied this statistically, but I suspect
>> the majority of adults long since forgot all this stuff.
>
> Rubbish! Maybe young adults can't remember them as they are over reliant
> on calculators.

Most "young adults" apparently cannot compute that 4 x £2.99 is 
approximately £12, but there we are...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 4-5-2011 14:34, Invisible wrote:
>>> Exactly. I mean, unless you happen to be able to compute 64/7 mentally,
>>> which normal humans can't.
>>
>> You're not that much younger than me, so maybe there's something
>> fundamentally different between the school system in the UK vs. Canada,
>> but in the 2nd or 3rd grade, we had to learn our multiplication tables
>> by heart.
>
> This is almost universally regarded as one of the most useless things
> you learn in school. I haven't studied this statistically, but I suspect
> the majority of adults long since forgot all this stuff.

The whole point of learning multiplication tables by heart is that you 
need them to do all other computations in base 10.
If you don't know them by heart a large part of our culture is 
inaccessible to you.

>
>> Or if they don't, they should be able to guestimate that since 64 is
>> rather close to 70, there's a good chance that 64/7 would be just a bit
>> less than 70/7, which is easy to compute.
>>
>> If not, I weep for humanity.

I'll join you.

-- 
Apparently you can afford your own dictator for less than 10 cents per 
citizen per day.

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On 24/05/2011 21:40, andrel wrote:

> The whole point of learning multiplication tables by heart is that you
> need them to do all other computations in base 10.

Most people would consider that you need a calculator to do any 
computations in base 10, beyond really trivial ones.

> If you don't know them by heart a large part of our culture is
> inaccessible to you.

Such as?

>>> If not, I weep for humanity.
>
> I'll join you.

I fear for the future of society, but for many reasons in addition to 
this...

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Le 2011/05/25 03:48, Invisible a écrit :
> On 24/05/2011 21:40, andrel wrote:
>
>> The whole point of learning multiplication tables by heart is that you
>> need them to do all other computations in base 10.
>
> Most people would consider that you need a calculator to do any
> computations in base 10, beyond really trivial ones.

Trivial, like multiplying 2 random phone numbers in your head? :P
I've done that several times, just for the /fun/...
Take some random 10 digits number, then another random 7 digit number. 
OK. Now, without paper, what is the product? Hint, it's 17 digit long, 
possibly 18. Your pocket calculator can't give you the exact result.

>
>> If you don't know them by heart a large part of our culture is
>> inaccessible to you.
>
> Such as?
>
>>>> If not, I weep for humanity.
>>
>> I'll join you.
>
> I fear for the future of society, but for many reasons in addition to
> this...

:P Alain

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>> Most people would consider that you need a calculator to do any
>> computations in base 10, beyond really trivial ones.
>
> Trivial, like multiplying 2 random phone numbers in your head? :P
> I've done that several times, just for the /fun/...
> Take some random 10 digits number, then another random 7 digit number.
> OK. Now, without paper, what is the product? Hint, it's 17 digit long,
> possibly 18. Your pocket calculator can't give you the exact result.

Now, personally, I can't even *remember* a 17 digit number without 
pencil and paper, never mind *compute* it. :-P

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Le 2011/05/25 16:31, Orchid XP v8 a écrit :
>>> Most people would consider that you need a calculator to do any
>>> computations in base 10, beyond really trivial ones.
>>
>> Trivial, like multiplying 2 random phone numbers in your head? :P
>> I've done that several times, just for the /fun/...
>> Take some random 10 digits number, then another random 7 digit number.
>> OK. Now, without paper, what is the product? Hint, it's 17 digit long,
>> possibly 18. Your pocket calculator can't give you the exact result.
>
> Now, personally, I can't even *remember* a 17 digit number without
> pencil and paper, never mind *compute* it. :-P
>

Remember the 10 digit number and the 7 digit number.
Multiply the first one by the first digit of the 7 digit one.
Remember that.
Repeat for all other 6 digits.
Shift and add the 7 intermediate results.
DONE!

It's a king of mental jogging :)

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Le 2011/05/25 16:31, Orchid XP v8 a écrit :
>>> Most people would consider that you need a calculator to do any
>>> computations in base 10, beyond really trivial ones.
>>
>> Trivial, like multiplying 2 random phone numbers in your head? :P
>> I've done that several times, just for the /fun/...
>> Take some random 10 digits number, then another random 7 digit number.
>> OK. Now, without paper, what is the product? Hint, it's 17 digit long,
>> possibly 18. Your pocket calculator can't give you the exact result.
>
> Now, personally, I can't even *remember* a 17 digit number without
> pencil and paper, never mind *compute* it. :-P
>

I forgot to tel that you should do it while walking in the city. Please 
use secondary streets.

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On 5/25/2011 4:10 PM, Alain wrote:

>
> Remember the 10 digit number and the 7 digit number.
> Multiply the first one by the first digit of the 7 digit one.
> Remember that.
> Repeat for all other 6 digits.
> Shift and add the 7 intermediate results.
> DONE!
>
> It's a king of mental jogging :)

Crap! no way I could do that, my working memory does not have enough 
capacity!

-- 
~Mike

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On 25-5-2011 9:48, Invisible wrote:
> On 24/05/2011 21:40, andrel wrote:
>
>> If you don't know them by heart a large part of our culture is
>> inaccessible to you.
>
> Such as?

basically most of the mathematical knowledge.


-- 
Apparently you can afford your own dictator for less than 10 cents per 
citizen per day.

Post a reply to this message

>>> If you don't know them by heart a large part of our culture is
>>> inaccessible to you.
>>
>> Such as?
>
> basically most of the mathematical knowledge.

I don't see why you need to memorise multiplication tables to understand 
mathematics.

Indeed, one of the most important things I learned at college is that 
mathematics is *not* just about memorising multiplication tables. 
There's actually far more to it than that. The fact that my school 
education completely failed to mention this is... rather worrying.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 28-5-2011 14:36, Orchid XP v8 wrote:
>>>> If you don't know them by heart a large part of our culture is
>>>> inaccessible to you.
>>>
>>> Such as?
>>
>> basically most of the mathematical knowledge.
>
> I don't see why you need to memorise multiplication tables to understand
> mathematics.

You can not understand long division or long multiplication without 
those tables. That means that e.g. the whole concept of prime number 
becomes void. As will be most things in number theories. Not that you 
actually need them, but not having a feeling for numbers will reduce it 
to a collection of unrelated facts.
How to understand how to do long division with polynomials or binary 
numbers without knowing how to do it with base 10 infinite precision 
numbers?

What I am trying to say is not that the multiplication tables are 
important, but that they are needed for the next steps. Long 
multiplication and long division are among the first algorithms kids 
learn. Skip them and everything in maths and physics (and ...) that uses 
algorithms will suffer greatly.

> Indeed, one of the most important things I learned at college is that
> mathematics is *not* just about memorising multiplication tables.
> There's actually far more to it than that. The fact that my school
> education completely failed to mention this is... rather worrying.

And that relates to the other thing I want to get across: maths is part 
of our Culture. As a teacher your task is to get across how beautiful it 
can be.
ATM the problem is that some decades ago a process was started by which 
the teachers teachers were selected on other grounds than knowledge of 
the subject. Being taught by people who equated maths with boring sums 
and stupid tables, the next generation was even worse. With time the old 
teachers resigned and the young generation took over. In short: we are 
in a downward spiral.
At the same time also politicians were recruited more and more from the 
humanities departments (IIRC none of the politicians of our ruling 
parties have a degree in any science of technology subject. In the 
largest opposition party we have one real scientist (was professor in 
biology, became minister of education and lost the election). In total 
we have 150 members of parliament.) Culture is redefined as anything but 
science by these incompetents. Not understanding maths is now considered 
something to be proud of by those who think of themselves as the elite 
of this society. That spiral will make have to make a few more turns 
before it goes up again.
I hope Asia will be the guardian of this piece of human culture this 
time, like the Arabs in mediaeval times. In the western world science is 
on it's way to become extinct with very few changes of stopping the process.



-- 
Apparently you can afford your own dictator for less than 10 cents per 
citizen per day.

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andrel wrote:

> On 28-5-2011 14:36, Orchid XP v8 wrote:
> > > > > If you don't know them by heart a large part of our culture is
> > > > > inaccessible to you.
> > > > 
> > > > Such as?
> > > 
> > > basically most of the mathematical knowledge.
> > 
> > I don't see why you need to memorise multiplication tables to
> > understand mathematics.
> 
> You can not understand long division or long multiplication without
> those tables.

One note: I think people should know them by heart and also be able to
do simple calculations in their head, simply because it is not very
pragmatic not to know them. You can't and shouldn't, IMO, always revert
to a calculator for that. It keeps you fit, up there.

But knowing these tables by heart does not help in *understanding*
anything. The knowledge only helps in applying that understanding a
little more pragmatically.

I can understand long division and multiplication, prime numbers and
number theory principles very well without knowing the multiplication
tables by heart.
-- 
Rudy Velthuis

"Go away...I'm alright." -- H.G.Wells, dying words

Post a reply to this message

>> I don't see why you need to memorise multiplication tables to understand
>> mathematics.
>
> You can not understand long division or long multiplication without
> those tables.

You need to know what a multiplication table *is* in order to understand 
long multiplication and long division. However, you absolutely do *not* 
need to memorise the contents of said table to comprehend mathematics.

I have no idea what the corresponding tables are for octal. But I still 
understand how long division works in octal - i.e., THE EXACT SAME WAY 
AS IN DECIMAL!

The rest of your argument seems to follow from this flawed premis.

>> Indeed, one of the most important things I learned at college is that
>> mathematics is *not* just about memorising multiplication tables.
>> There's actually far more to it than that. The fact that my school
>> education completely failed to mention this is... rather worrying.
>
> And that relates to the other thing I want to get across: maths is part
> of our Culture. As a teacher your task is to get across how beautiful it
> can be.

Agreed.

FWIW, my teachers also utterly failed to demonstrate that literature can 
be enjoyable. The only literature we did was Shakespear and some dope 
addict named Coleridge...

> Not understanding maths is now considered
> something to be proud of by those who think of themselves as the elite
> of this society. That spiral will make have to make a few more turns
> before it goes up again.

I've often wondered how the hell we ended up in a society where being 
stupid is considered a virtue. Apparently a few centuries back, 
everybody who was anybody had to know and be able to debate the finer 
points of (say) Lord Kelvin's new theories about thermodynamics...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 29-5-2011 13:12, Rudy Velthuis wrote:
> andrel wrote:
>
>> On 28-5-2011 14:36, Orchid XP v8 wrote:
>>>>>> If you don't know them by heart a large part of our culture is
>>>>>> inaccessible to you.
>>>>>
>>>>> Such as?
>>>>
>>>> basically most of the mathematical knowledge.
>>>
>>> I don't see why you need to memorise multiplication tables to
>>> understand mathematics.
>>
>> You can not understand long division or long multiplication without
>> those tables.
>
> One note: I think people should know them by heart and also be able to
> do simple calculations in their head, simply because it is not very
> pragmatic not to know them. You can't and shouldn't, IMO, always revert
> to a calculator for that. It keeps you fit, up there.
>
> But knowing these tables by heart does not help in *understanding*
> anything. The knowledge only helps in applying that understanding a
> little more pragmatically.
>
> I can understand long division and multiplication, prime numbers and
> number theory principles very well without knowing the multiplication
> tables by heart.

You can in theory, but I am pretty sure you won't in practice. Or at 
least the vast majority of people won't. At the age you are normally 
learning it you need practical examples. Only much later on when you 
have mastered abstract thinking you can understand the process without 
being able to perform the process yourself.
That leaves open the question how much mastering abstract thinking is 
hampered by not learning long division at the appropriate age. Then 
again, I don't know what kind of games kids play nowadays, so abstract 
reasoning and the concept of algorithms may come in a totally different 
way than in my time. (Though my time as a teacher does not suggest that 
other way was very effective).


-- 
Apparently you can afford your own dictator for less than 10 cents per 
citizen per day.

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On 29-5-2011 15:51, Orchid XP v8 wrote:
>>> I don't see why you need to memorise multiplication tables to understand
>>> mathematics.
>>
>> You can not understand long division or long multiplication without
>> those tables.
>
> You need to know what a multiplication table *is* in order to understand
> long multiplication and long division. However, you absolutely do *not*
> need to memorise the contents of said table to comprehend mathematics.
>
> I have no idea what the corresponding tables are for octal. But I still
> understand how long division works in octal - i.e., THE EXACT SAME WAY
> AS IN DECIMAL!

My point exactly. Having learned it in one situation carries over to 
another. Proves how vital it was for you to learn at that point ;) See 
also my response to Rudy.

> The rest of your argument seems to follow from this flawed premis.

That you didn't think it through does not make it flawed ;)

>>> Indeed, one of the most important things I learned at college is that
>>> mathematics is *not* just about memorising multiplication tables.
>>> There's actually far more to it than that. The fact that my school
>>> education completely failed to mention this is... rather worrying.
>>
>> And that relates to the other thing I want to get across: maths is part
>> of our Culture. As a teacher your task is to get across how beautiful it
>> can be.
>
> Agreed.
>
> FWIW, my teachers also utterly failed to demonstrate that literature can
> be enjoyable. The only literature we did was Shakespeare and some dope
> addict named Coleridge...

Any relation with http://www.youtube.com/watch?v=JTD1QW3SM60 ?

>> Not understanding maths is now considered
>> something to be proud of by those who think of themselves as the elite
>> of this society. That spiral will make have to make a few more turns
>> before it goes up again.
>
> I've often wondered how the hell we ended up in a society where being
> stupid is considered a virtue.

It is not stupidity, they appreciate other things, like... like... whatever.

> Apparently a few centuries back,
> everybody who was anybody had to know and be able to debate the finer
> points of (say) Lord Kelvin's new theories about thermodynamics...

Yes. Interesting isn't it.

-- 
Apparently you can afford your own dictator for less than 10 cents per 
citizen per day.

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andrel wrote:

> On 29-5-2011 13:12, Rudy Velthuis wrote:
> > andrel wrote:
> > 
> > > On 28-5-2011 14:36, Orchid XP v8 wrote:
> > > > > > > If you don't know them by heart a large part of our
> > > > > > > culture is inaccessible to you.
> > > > > > 
> > > > > > Such as?
> > > > > 
> > > > > basically most of the mathematical knowledge.
> > > > 
> > > > I don't see why you need to memorise multiplication tables to
> > > > understand mathematics.
> > > 
> > > You can not understand long division or long multiplication
> > > without those tables.
> > 
> > One note: I think people should know them by heart and also be able
> > to do simple calculations in their head, simply because it is not
> > very pragmatic not to know them. You can't and shouldn't, IMO,
> > always revert to a calculator for that. It keeps you fit, up there.
> > 
> > But knowing these tables by heart does not help in understanding
> > anything. The knowledge only helps in applying that understanding a
> > little more pragmatically.
> > 
> > I can understand long division and multiplication, prime numbers and
> > number theory principles very well without knowing the
> > multiplication tables by heart.
> 
> You can in theory, but I am pretty sure you won't in practice. Or at
> least the vast majority of people won't.

I'm not so sure. OK, I know lots of people who don't understand
fractions (I'm a dentist and most of my - especially younger -
assistants don't), and these usually don't know the tables very well
either, but I think that is because of a common cause: they hate maths.

I don't think knowing the tables is a prerequisite. It is just
correlated with an interest in maths, and that is probably a
prerequisite for the understanding (or vice versa).

-- 
Rudy Velthuis

"Computers make it easier to do a lot of things, but most of the 
 things they make it easier to do don't need to be done." 
 -- Andy Rooney.

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>> You need to know what a multiplication table *is* in order to understand
>> long multiplication and long division. However, you absolutely do *not*
>> need to memorise the contents of said table to comprehend mathematics.
>>
>> I have no idea what the corresponding tables are for octal. But I still
>> understand how long division works in octal - i.e., THE EXACT SAME WAY
>> AS IN DECIMAL!
>
> My point exactly. Having learned it in one situation carries over to
> another. Proves how vital it was for you to learn at that point ;) See
> also my response to Rudy.
>
>> The rest of your argument seems to follow from this flawed premis.
>
> That you didn't think it through does not make it flawed ;)

You don't need to know the numerical value of pi to 40 decimal places in 
order to know how to use it. Similarly, you do not need to memorise 50 
figures of a multiplication table to understand how long division works.

>> I've often wondered how the hell we ended up in a society where being
>> stupid is considered a virtue.
>
> It is not stupidity, they appreciate other things, like... like...
> whatever.

 From what I can tell, "being rich enough to be able to afford stylists 
and makeup artists and photo editing staff to give you immaculate looks".

Either that or "being on TV".

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 29-5-2011 22:58, Orchid XP v8 wrote:
>>> You need to know what a multiplication table *is* in order to understand
>>> long multiplication and long division. However, you absolutely do *not*
>>> need to memorise the contents of said table to comprehend mathematics.
>>>
>>> I have no idea what the corresponding tables are for octal. But I still
>>> understand how long division works in octal - i.e., THE EXACT SAME WAY
>>> AS IN DECIMAL!
>>
>> My point exactly. Having learned it in one situation carries over to
>> another. Proves how vital it was for you to learn at that point ;) See
>> also my response to Rudy.
>>
>>> The rest of your argument seems to follow from this flawed premis.
>>
>> That you didn't think it through does not make it flawed ;)
>
> You don't need to know the numerical value of pi to 40 decimal places in
> order to know how to use it. Similarly, you do not need to memorise 50
> figures of a multiplication table to understand how long division works.

You do at the age you (or actually we, the old men in this group) 
learned long division.


-- 
Apparently you can afford your own dictator for less than 10 cents per 
citizen per day.

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On 29/05/2011 10:03 PM, andrel wrote:
> You do at the age you (or actually we, the old men in this group)
> learned long division.

I never memorised the tables, as in being able to say 3 X 4 = 12. I had 
to recite them and stop at the right place.
Three nothings are nothing.
Three ones are three.
Three twos are six.
Three threes are nine.
Three fours are twelve.
Three fives are, oops!
Three fours are twelve.

But then as I’ve said before, I had problems at school.


-- 
Regards
     Stephen

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On 29-5-2011 23:18, Stephen wrote:
> On 29/05/2011 10:03 PM, andrel wrote:
>> You do at the age you (or actually we, the old men in this group)
>> learned long division.
>
> I never memorised the tables, as in being able to say 3 X 4 = 12. I had
> to recite them and stop at the right place.
> Three nothings are nothing.
> Three ones are three.
> Three twos are six.
> Three threes are nine.
> Three fours are twelve.
> Three fives are, oops!
> Three fours are twelve.
>
> But then as I’ve said before, I had problems at school.

Interesting, someone between old school and the calculator generation.
I think the most relevant question in this context is: Do you understand 
long division and if so at what age did you learn it?


-- 
Apparently you can afford your own dictator for less than 10 cents per 
citizen per day.

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On 30/05/2011 11:49 PM, andrel wrote:
> Interesting, someone between old school and the calculator generation.
> I think the most relevant question in this context is: Do you understand
> long division and if so at what age did you learn it?

It depends what you mean by "Old" school. When I was at school, 
calculators were mechanical and you turned a handle to power them.

Yes I understand long division and I can generally divide by two digits 
in my head if the dividend is not too big. I really can't remember when 
I was taught it, at a guess I would say, about 9 years of age.

-- 
Regards
     Stephen

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On 5/25/2011 14:10, Alain wrote:
> It's a king of mental jogging :)

I used to be able to do 4 and 5 digit long division in my head, back in 
grade school.

-- 
Darren New, San Diego CA, USA (PST)
   "Coding without comments is like
    driving without turn signals."

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On 5/29/2011 4:12, Rudy Velthuis wrote:
> simply because it is not very pragmatic not to know them.

Indeed. Actually, there was one event that eventually convinced my very 
smart wife that there are *actually* people in the world who are not very 
smart. She'd never actually encountered it as a gut feeling before.

We're in a store. We're buying something that's $20, but 60% off. The clerk 
is taking *minutes* to try to figure out the price. She finally digs out a 
calculator, figures out the answer is 12, and then hopelessly says "But is 
that the discount, or the price?" My wife finally snaps and goes "It's 60%! 
It's more than half!"

So, yeah, I think you must have at some point memorized the multiplication 
tables and used them a bit to get a feeling for such things.

Nowadays, I like to torture people when I buy $10.20 worth of stuff by 
giving the person a $20, waiting until they've rung it up, then handing them 
another $0.25 coin, and watch them struggle helplessly trying to figure out 
what the change should be on their own. (Actually, there's a dilbert about 
that that's pretty funny.)

-- 
Darren New, San Diego CA, USA (PST)
   "Coding without comments is like
    driving without turn signals."

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On 5/29/2011 6:51, Orchid XP v8 wrote:
> FWIW, my teachers also utterly failed to demonstrate that literature can be
> enjoyable.

My problem with many of those subjects is that nobody ever said why we'd 
need to know that stuff. Why in the world do I need to read The Great 
Gatsby? Or Macbeth?  Now I know, and I regret not having actually read them 
properly when I had the time to do so.

-- 
Darren New, San Diego CA, USA (PST)
   "Coding without comments is like
    driving without turn signals."

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On 06/06/2011 04:27 PM, Darren New wrote:

> We're in a store. We're buying something that's $20, but 60% off. The
> clerk is taking *minutes* to try to figure out the price. She finally
> digs out a calculator, figures out the answer is 12, and then hopelessly
> says "But is that the discount, or the price?" My wife finally snaps and
> goes "It's 60%! It's more than half!"

Three words: Verizon math fail.

> So, yeah, I think you must have at some point memorized the
> multiplication tables and used them a bit to get a feeling for such things.

You don't need to memorise anything to be able to solve basic estimation 
problems. You just need to *have* a frigging clue.

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On 06/06/2011 04:29 PM, Darren New wrote:
> On 5/29/2011 6:51, Orchid XP v8 wrote:
>> FWIW, my teachers also utterly failed to demonstrate that literature
>> can be
>> enjoyable.
>
> My problem with many of those subjects is that nobody ever said why we'd
> need to know that stuff. Why in the world do I need to read The Great
> Gatsby? Or Macbeth? Now I know, and I regret not having actually read
> them properly when I had the time to do so.

OK, I'll bite: Why the hell should anybody, anywhere, *ever* read Macbeth?

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On 06/06/2011 4:51 PM, Invisible wrote:
>
> OK, I'll bite: Why the hell should anybody, anywhere, *ever* read Macbeth?

So that they can memorise their lines to put on the play.

-- 
Regards
     Stephen

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On 6/6/2011 8:51, Invisible wrote:
> OK, I'll bite: Why the hell should anybody, anywhere, *ever* read Macbeth?

Because it's full of words and expressions that are shortcut references to 
entire sets of memes in educated society. Just like if someone truly ugly 
walks past and I whistle the Wicked Witch of the West theme music, it brings 
in a whole packet of memes and concepts which are incomprehensible if you 
haven't watched the movie. If you hear something referred to as a "red shirt 
assignment" in a military context, you'll have no idea what that means if 
you're not familiar with Star Trek. If someone is complaining, and I tell 
you "that's just sour grapes", you'll have no idea I'm telling you the same 
thing as an "Ar Du" unless you were familiar with the literature of both 
Grimm and China.

It's the same thing with shakespear and all those sorts of things. If I told 
you he's got a scarlet letter on his chest, you wouldn't know what that 
means different from having a scarlet letter on his mantelpiece unless 
you're familiar with both those novels. It's just the educated man's way of 
saying "African or European Swallow?"

-- 
Darren New, San Diego CA, USA (PST)
   "Coding without comments is like
    driving without turn signals."

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>> OK, I'll bite: Why the hell should anybody, anywhere, *ever* read
>> Macbeth?
>
> So that they can memorise their lines to put on the play.

Well, that's why *I* read Macbeth. But that's a pretty stupid 
justification...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 06/06/2011 05:54 PM, Darren New wrote:
> On 6/6/2011 8:51, Invisible wrote:
>> OK, I'll bite: Why the hell should anybody, anywhere, *ever* read
>> Macbeth?
>
> Because it's full of words and expressions that are shortcut references
> to entire sets of memes in educated society.

So you need to read the entire play just to comprehend the one or two 
vague references that anybody could explain to you in five seconds flat?

> Just like if someone truly
> ugly walks past and I whistle the Wicked Witch of the West theme music,
> it brings in a whole packet of memes and concepts which are
> incomprehensible if you haven't watched the movie.

I've watched that movie, and I wasn't even aware the Wicked Witch of the 
West *had* a theme tune!

> It's just the educated man's way of saying "African or European Swallow?"

Required XKCD quote: http://xkcd.com/16/

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 6/6/2011 11:33, Orchid XP v8 wrote:
> So you need to read the entire play just to comprehend the one or two vague
> references that anybody could explain to you in five seconds flat?

Yes. Because that's not really understanding.

> I've watched that movie, and I wasn't even aware the Wicked Witch of the
> West *had* a theme tune!

http://www.youtube.com/watch?v=r4kiXh8YOzk

Hint: So does Darth Vadar.

-- 
Darren New, San Diego CA, USA (PST)
   "Coding without comments is like
    driving without turn signals."

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On 06/06/2011 08:54 PM, Darren New wrote:
> On 6/6/2011 11:33, Orchid XP v8 wrote:
>> So you need to read the entire play just to comprehend the one or two
>> vague
>> references that anybody could explain to you in five seconds flat?
>
> Yes. Because that's not really understanding.

Riiight. Because reading several hundred pages of dense prose written in 
a language so archaic that you need an interpreter just to explain 
what's actually happening is *so* much more enlightening than having 
somebody actually explain to you what a specific phrase means?

>> I've watched that movie, and I wasn't even aware the Wicked Witch of the
>> West *had* a theme tune!
>
> http://www.youtube.com/watch?v=r4kiXh8YOzk

I'm not denying that one exists, I'm saying it's not very memorable.

> Hint: So does Darth Vadar.

Well yes, /obviously/. The Imperial March, by John Williams. One of his 
masterpieces. Everybody knows that...

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On 6/7/2011 1:00, Invisible wrote:
> Riiight. Because reading several hundred pages of dense prose written in a
> language so archaic that you need an interpreter just to explain what's
> actually happening is *so* much more enlightening than having somebody
> actually explain to you what a specific phrase means?

Yes.

> I'm not denying that one exists, I'm saying it's not very memorable.

i think opinions will differ on that.

-- 
Darren New, San Diego CA, USA (PST)
   "Coding without comments is like
    driving without turn signals."

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