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The problem is the discontinuity in the number system being used. Creating a continuous wrap around number system representing the compass as 0 to 179 180 -179 to -1 makes all of the averaging problems go away. Conversion of negative numbers requires a

w..

Dave VanHorn wrote:
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Walter,

On Thu, 16 Sep 2004 08:56:46 -0400, Walter Banks wrote:

> The problem is the discontinuity in the number system being used. Creating a continuous wrap around number
system representing the compass as 0 to 179 180 -179 to -1 makes all of the averaging problems go away.
Conversion of negative numbers requires a simple add of 360.

I think you've just shifted the problem 180 degrees:  average of -1 and 1 is 0, which is correct.  But the
average of -179 and 179 is also 0, which is wrong (should be 180 or -180).

Cheers,

Howard Winter
St.Albans, England

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If I understand what you are proposing, this would remove the problem at
zero deg and shift the error to 180 deg.  For example if you have
(179, -179) this averages to 0, which of course, is wrong.

Regards,

Gordon Williams

{Original Message removed}
> The problem is the discontinuity in the number system being
> used. Creating a continuous wrap around number system
> representing the compass as 0 to 179 180 -179 to -1 makes all
> of the averaging problems go away. Conversion of negative
> numbers requires a simple add of 360.

So which formula would you use to calculate the average? Simple
sum(Xi)/N does not work: take 170 and -170, sum = 0, average would be 0,

Wouter van Ooijen

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>-----Original Message-----
>From: piclist-bouncesmit.edu [piclist-bouncesmit.edu]
>On Behalf Of Wouter van Ooijen
>Sent: 16 September 2004 15:00
>To: 'Microcontroller discussion list - Public.'
>Subject: RE: [OT] cyclic average.
>
>
>> The problem is the discontinuity in the number system being
>> used. Creating a continuous wrap around number system
>> representing the compass as 0 to 179 180 -179 to -1 makes all
>> of the averaging problems go away. Conversion of negative
>> numbers requires a simple add of 360.
>
>So which formula would you use to calculate the average?
>Simple sum(Xi)/N does not work: take 170 and -170, sum = 0,
>average would be 0, correct answer is 180.

Actually, 180 is one correct answer, 0 is the other.  Given two arbitrary
points to average between and no other inforamtion, you do not know how the
heading is varying between samples.  One would naturaly assume that it would
be the smaller angle, but there are no guarantees.

Regards

Mike

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Good point I have rotated the problem. This doesn't cleanly solve the -1,0,1 problem.
The circular number system will solve the two number average if the negative number(s)
are always normalized positive (((-179 + 360) +179) / 2) MOD 360 . This will not work
for averaging three angles.

w..

Howard Winter wrote:
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At 10:11 AM 9/16/2004, Walter Banks wrote:

>Good point I have rotated the problem. This doesn't cleanly solve the -1,0,1 problem.
>The circular number system will solve the two number average if the negative number(s) are always normalized positive (((-179 + 360) +179) / 2) MOD 360 . This will not work for averaging three angles.

It's not that hard, even in assembler. The toughest thing was the square root.
For simplicity, I calculated my angles in "Dilberts". (I've defined a Dilbert as any unit that is chosen because it fits well into binary math.)
There are 265 Dilberts in a circle.

In the end, I convert the Dilberts to degrees.
The overall accuracy of this sort of device, is only a few degrees anyway, so I don't really loose anything, and I gain tons of processing time, over trying to do it in degrees.

This is a pretty good example of how working in assembler (or at least having that mindset) pushes you twoard solutions that are much easier on the machine.
I'm sure it would be dead easy to code in C, but I'd hate to see the execution time.

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> >So which formula would you use to calculate the average?
> >Simple sum(Xi)/N does not work: take 170 and -170, sum = 0,
> >average would be 0, correct answer is 180.
>
> Actually, 180 is one correct answer, 0 is the other.  Given
> two arbitrary
> points to average between and no other inforamtion, you do
> not know how the
> heading is varying between samples.  One would naturaly
> assume that it would
> be the smaller angle, but there are no guarantees.

I don't understand that. Your encoding uses -180 ... + 180 for the full
circle, so 170 and -170 are pretty close, just 20 degrees apart, so
there is only one average (south, if 0 is north).

Wouter van Ooijen

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But the math result of 170 and -170 would be zero, since -170 + 170 = 0.
If zero is north, and 170 and -170 are just east and west of south, the

I think in the end, one just has to figure out what the end result of the
data has to be and tailor the system to fit.

Remember, this sort of thing is why creative problem solvers with a good
grip on the underlying concepts will have jobs for a good long time to come.
So be grateful these problems exist!

Mike H.

> I don't understand that. Your encoding uses -180 ... + 180 for the full
> circle, so 170 and -170 are pretty close, just 20 degrees apart, so
> there is only one average (south, if 0 is north).
>
>
>
> Wouter van Ooijen
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> I think in the end, one just has to figure out what the end
> result of the data has to be and tailor the system to fit.
>
> Remember, this sort of thing is why creative problem solvers
> with a good
> grip on the underlying concepts will have jobs for a good
> long time to come.
> So be grateful these problems exist!

Hmmm...

I would say that a real problem solver would 'simply' find a (the?)
correct way to solve the problem. Vectorial addition is such a correct
way, I think it is the only way. Everything else (tayloring the system
depending on the result - juk!) is just fiddleing with a wrong solution
until it happens to give the correct anwer for the particular test data
set you use.

Wouter van Ooijen

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I'm not sure I understand the distinction here:  isn't tailoring a
system to fit the need the same thing as solving a problem?

For example, Dave's system of using "Dilberts" to measure the
angle is just an example of him making a system which nicely
fits the need at hand.

I suppose "tailor" may not be the best word.  Perhaps "fabricate"
or "create" fits better?

I do agree that "tweaking" until your test works is NOT the best
way to go.  Unfortunately, though, that seems
to be the "preferred" (read: most common) method of system
development which was taught at least at my university.  :-(

Mike H.

On Thu, 16 Sep 2004 19:51:39 +0200, Wouter van Ooijen <woutervoti.nl> wrote:
{Quote hidden}

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At 02:14 PM 9/16/2004, Mike Hord wrote:

>I'm not sure I understand the distinction here:  isn't tailoring a
>system to fit the need the same thing as solving a problem?
>
>For example, Dave's system of using "Dilberts" to measure the
>angle is just an example of him making a system which nicely
>fits the need at hand.

I just thought it was much more elegant than trying to do 16 bit math to handle 360 degrees, and since I couldn't achieve that precision anyway, there was no point in trying to preserve it.

>I suppose "tailor" may not be the best word.  Perhaps "fabricate"
>or "create" fits better?
>
>I do agree that "tweaking" until your test works is NOT the best
>way to go.  Unfortunately, though, that seems
>to be the "preferred" (read: most common) method of system
>development which was taught at least at my university.  :-(

Very dangerous.  When things don't act as you expect, you'd best find out why.
Designs where this is done, routinely fall apart on the production floor.

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Hi,

maybe I'm missing something but I am not surprised reading the result
here, because of south is ambiguous in that way there is no natural value
for it. One must arbitrarly assign either -180 or 180 to it, but it is a
DECISION and math does not know nothing about decisions, at least in this
case. It is like a function with a non-contiguous point.

Imre

On Thu, 16 Sep 2004, Mike Hord wrote:

{Quote hidden}

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does not know nothing?

dr. Imre Bartfai wrote:

{Quote hidden}

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dr. Imre Bartfai wrote:

> but it is a DECISION and math does not know nothing about
> decisions

and Engineering Info <piclistmit.edu> replied:

> does not know nothing?

Engineering Info (if that is your true name):

Was that a comment on Dr. Bartfai's command of English grammar?

-Andy

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> does not know nothing?

Given the fact that it's manifestly obvious that the people whose comments
appeared below this comment know a vast amount about many things, I deduce
that you are referring to yourself/
No? :-)

This subject is rather more complex than meets the eye. Reading the thread
from the start would be a good idea if one wanted to get a feel for the
reason for the comments. Appreciating that English may not be the first
language of some of the posters would also be wise.

Russell McMahon

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On Thu, 16 Sep 2004, Wouter van Ooijen wrote:

> I don't understand that. Your encoding uses -180 ... + 180 for the full
> circle, so 170 and -170 are pretty close, just 20 degrees apart, so
> there is only one average (south, if 0 is north).

'apart' is the key. Average and 'apart' are two different things.

Peter
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On Thu, 16 Sep 2004, Walter Banks wrote:

> Good point I have rotated the problem. This doesn't cleanly solve the -1,0,1
> problem. The circular number system will solve the two number average if the
> negative number(s) are always normalized positive (((-179 + 360) +179) / 2)
> MOD 360 . This will not work for averaging three angles.

But it should work for averaging them if they are taken in pairs. This begins
to resemble vector addition more and more, no ? E.g. keeping a running average:

first time:
Avg = NewValue + OFFSET
every next time:
Avg = (Avg + (NewValue + OFFSET)) / 2

OFFSET must be substracted from Avg before use.

This brings back Wouter's question with the months of the year: The average
between 1 and 11 is 6 but the intuitively correct answer is 12. This is caused
by the bad definition of 'average' in the context of a circular axis of numbers
which allows two distances between the numbers for any two numbers (and
contradicts one of the arithmetic axioms on which the arithmetic operators used
in averaging depend). Solving the months average problem seems to be related to
the 'reduction to the first quadrant' problem for trigonometric functions.

So the answer seems to be find the bisecting angle between two vectors on the
unit circle. This can be solved in many ways and extended incrementally to N
vectors. The bisecting angle is always relative to the vectors, so an offset
derived from one of the input angles must be added in to get an absolute
result. Again there are several ways to do this but the result will likely be
ambiguous (two values coming out of the equation) and one will have to be
selected (probably the lower value one to match the expected human
interpretation).

Back to months if we assume they are angles then we want the bisecting angle
which we get from the difference angle like this (each month is a point on the
unit circle with associated angle A = M*30 degrees, enumerated in trig.
direction). This is still not perfect because of the ambiguity of the
definition. F.ex. the average of January and June is either March or December.
Both answers are correct unless you redefine 'average' more exactly. Here is
aprogram that illustrates the a solution to the average of two months problem
and introduces a new problem:

--snip--
/*
* 'Average of 2 months'
*
* plp 2004
* v0
*/

#include <stdio.h>

#define MOD 12

int avg( int m1, int m2 )
{
int d1, d2, avg, r;

m1 = (m1-1) % MOD; // reduce to 0-11
m2 = (m2-1) % MOD;

d1 = (MOD + m1 - m2) % MOD;
d2 = (MOD - m1 + m2) % MOD;
avg = (d1 <= d2) ? -1 * (d1 / 2) : d2 / 2;
r = (MOD + m1 + avg) % MOD;

++r;  // fix for human convention 0-11 -> 1-12

printf("average of %d, %d: %d\n", m1+1, m2+1, r);

return( r );
}

void main(void)
{
int i, t;

for(t = 1; t <= MOD/2; t += MOD/4) // try several target avg. angles
for(i = 1; i <= MOD/2; ++i) {
avg( i+t, t+MOD-i);
avg( t+MOD-i, i+t);
}

}
--snap--

running this yields:

average of 2, 12: 1
average of 12, 2: 1
average of 3, 11: 1
average of 11, 3: 1
average of 4, 10: 1 (!!)
average of 10, 4: 7 (!!)
average of 5, 9: 7
average of 9, 5: 7
average of 6, 8: 7
average of 8, 6: 7
average of 7, 7: 7
average of 7, 7: 7
average of 5, 3: 4
average of 3, 5: 4
average of 6, 2: 4
average of 2, 6: 4
average of 7, 1: 4  (!!)
average of 1, 7: 10 (!!)
average of 8, 12: 10
average of 12, 8: 10
average of 9, 11: 10
average of 11, 9: 10
average of 10, 10: 10
average of 10, 10: 10

Note the problem I was talking about at (!!). Both answers are correct. But if
the result is used as is for further averaging problems will occur (the result
of the next averaging will be off by up to 3 months under the right
circumstances).

The short answer seems to be, if you have a compass heading you know where you
are heading, if you have two or more, then you don't ;-)

Could someone with more math studies <g> clarify what rules apply in a circular
axis of (integer, for now) numbers ?

Peter
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> > I don't understand that. Your encoding uses -180 ... + 180
> for the full
> > circle, so 170 and -170 are pretty close, just 20 degrees apart, so
> > there is only one average (south, if 0 is north).
>
> 'apart' is the key. Average and 'apart' are two different things.

Two different words indeed.

Feel free to disagree, but for me averaging is a way to combine a number
of data points in such a way that (among other things) small variations
are removed. So it makes (much) more sense to average NW and NE together
to N than to S. Or think about a boat that is drifting in the wind.
After an hour of NW wind and an hour of NE wind the total effect is more
likely to resemble that of two hours N wind than of two hours S wind.

Wouter van Ooijen

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>
>Feel free to disagree, but for me averaging is a way to combine a number
>of data points in such a way that (among other things) small variations
>are removed. So it makes (much) more sense to average NW and NE together
>to N than to S. Or think about a boat that is drifting in the wind.
>After an hour of NW wind and an hour of NE wind the total effect is more
>likely to resemble that of two hours N wind than of two hours S wind.

Two hours of less potent north wind, though not really.
When I've been out storm spotting, I've had winds from both sides, strong enough to roll a lesser vehicle, and that wouldn't average out to "sitting upright" :)

The vector method solves the averaging for circles, and automatically resolves the inside angle, but it still comes down to wether the thing you're looking at is primarily a cycle, like a heading, or a line, like time (in the absolute sense) or a calendar in the cyclic sense of seasons..

I can see time represented as a grid (calendar), a line, a circle, or a spiral, and there are probably other ways..

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Dave,

On Sat, 18 Sep 2004 08:41:29 -0500, Dave VanHorn wrote:

> I can see time represented as a grid (calendar), a line, a circle, or a spiral, and there are probably other
ways..

I find it's an increasingly-steep downhill slope!  :-)

Cheers,

Howard Winter
St.Albans, England

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On Sat, 18 Sep 2004, Wouter van Ooijen wrote:

>>> I don't understand that. Your encoding uses -180 ... + 180
>> for the full
>>> circle, so 170 and -170 are pretty close, just 20 degrees apart, so
>>> there is only one average (south, if 0 is north).
>>
>> 'apart' is the key. Average and 'apart' are two different things.
>
> Two different words indeed.
>
> Feel free to disagree, but for me averaging is a way to combine a number
> of data points in such a way that (among other things) small variations
> are removed. So it makes (much) more sense to average NW and NE together
> to N than to S. Or think about a boat that is drifting in the wind.
> After an hour of NW wind and an hour of NE wind the total effect is more
> likely to resemble that of two hours N wind than of two hours S wind.

The word averaging is precisely defined as the arithmetic average of
values (D1+..+Dn)/N by default or as the geometric average (and some other
rarer forms of averaging). What you really want is a form of filtering I
think. F.ex. I believe that you can achieve your 'averaging' (in the sense
yuo understand it) by running some sort of low pass filter on the input
data, after you take care of the 'jumps'.

Peter
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Hi,

would you so kind please to explain me what is wrong with the statement in
context? Or it was really not to be understand what I wanted to express? I
rechecked the statement and found nothing strange. Maybe I have translated
something word-by-word from my native language (which is Hungarian).

Regards,
Imre

On Fri, 17 Sep 2004, Andrew Warren wrote:

{Quote hidden}

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At 01:24 AM 9/21/2004, dr. Imre Bartfai wrote:

>Hi,
>
>would you so kind please to explain me what is wrong with the statement in
>context? Or it was really not to be understand what I wanted to express? I
>rechecked the statement and found nothing strange. Maybe I have translated
>something word-by-word from my native language (which is Hungarian).

We'd all better be careful now! THEY are watching us. :)

From The Curve of Binding Energy:

Not all Los Alamos theories could be tested. Long popular within the Theoretical Division was, for example, a theory that the people of Hungary are Martians. The reasoning went like this: The Martians left their own planet several aeons ago and came to Earth; they landed in what is now Hungary; the tribes of Europe were so primitive and barbarian that it was necessary for the Martians to conceal their evolutionary difference or be hacked to pieces. Through the years, the concealment had on the whole been successful, but the Martians had three characteristics too strong to hide: their wanderlust, which found its outlet in the Hungarian <http://www.ufomind.com/area51/desertrat/1995/dr29/rat_29_fnote.html#gypsy>gypsy; their language (Hungarian is not related to any of the languages spoken in surrounding countries); and their unearthly intelligence. One had only to look around to see the evidence: Teller, <http://www.ufomind.com/area51/desertrat/1995/dr29/rat_29_wigner.txt>Wigne!
r, <http://www.ufomind.com/area51/desertrat/1995/dr29/rat_29_szilard.txt>Szilard, von Neumann-- Hungarians all. Szilard had been among the first to suggest that fission could be used to make a bomb. Von Neumann had developed the digital computer. Teller--moody, tireless, and given to fits of laughter, bursts of anger--worked long hours and was impatient with what he felt to be the excessively slow advancement of Project Panda, as the hydrogen-bomb development was known. Kindly to juniors, he had done much to encourage Ted Taylor in his work. His impatience with his peers, however, eventually caused him to leave Los Alamos and establish a rival laboratory at Livermore in California. Teller had a thick Martian accent. He also had a sense of humor that could penetrate bone. Dark-haired, heavy-browed, he limped pronouncedly. In Europe, one of his feet had been mangled by a streetcar.

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dr. Imre Bartfai wrote:

> but it is a DECISION and math does not know nothing about decisions

and then:

> would you so kind please to explain me what is wrong with the statement
> in context? Or it was really not to be understand what I wanted to
> express?

Imre:

Your meaning was perfectly clear.  The only error -- and it's a small
one which would hardly warrant a comment if it had been made by a
native English speaker, let alone by someone who thinks in another
language -- was the use of the word "nothing" instead of "anything".

"Math does not know anything about decisions" means that math has no
knowledge of decisions; on the other hand, the two negatives in "math
does not know nothing about decisions" cancel each other, so the
meaning is that math DOES have knowledge of decisions.

This "doube negative" is a very common mistake heard all the time
here in America; in fact, it's usually accompanied by ANOTHER
mistake, misconjugation of the verb: "Math don't know nothing."

I think that most English-speakers here would agree with me that the
contributions made by the non-English-speakers on the list are
valuable and appreciated.  Minor -- or, hell, even major --
grammatical or spelling errors are easily overlooked; I hope you and
others who aren't native English speakers will continue to post
freely without worrying that you'll be flamed for imperfect English.

After all... As is often pointed out, your English is WAY better than
our Hungarian, or Spanish, or Dutch or German or whatever.

-Andrew

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===
=== Principal Design Engineer
=== Cypress Semiconductor Corporation

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>-----Original Message-----
>From: piclist-bouncesmit.edu [piclist-bouncesmit.edu]
>On Behalf Of Andrew Warren
>Sent: 21 September 2004 10:17
>To: Microcontroller discussion list - Public.
>Subject: Re: [OT] cyclic average.
>
>After all... As is often pointed out, your English is WAY better than
>our Hungarian, or Spanish, or Dutch or German or whatever.
>
>-Andrew

Agreed, and I'd just like to add that Imre's English is considerably better
than many native English speaking people.

Regards

Mike

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>This "doube negative" is a very common mistake heard all the time
>here in America;

As a colleague of mine is fond of saying when corrected on such
errors:

"I aint never gonna use no double negatives no more, and that's no word of a
lie!"

:-)

Cheers,
Robin.

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Andrew,

On Tue, 21 Sep 2004 02:16:32 -0700, Andrew Warren wrote:

> This "doube negative" is a very common mistake heard all the time
> here in America;

Indeed, in fact using a double negative is sadly common here in England too.  It may be a result of
"inaccurate thinking" as some people have said, but I think it may also be related to inverse snobbery, where
to speak "posh" is seen as a weakness - I encountered that at school, where my accent and standard of speaking
deteriorated as a self-defence mechanism.  My posh accent was beaten out of me!

Incidentally (sorry for fraying the thread) I never understand why Americans, expressing "I don't care" say "I
could care less", when clearly they don't mean that.  Brits say "I couldn't care less".  I wonder when it got
reversed, Stateside?

> I think that most English-speakers here would agree with me that the
> contributions made by the non-English-speakers on the list are
> valuable and appreciated.  Minor -- or, hell, even major --
> grammatical or spelling errors are easily overlooked; I hope you and
> others who aren't native English speakers will continue to post
> freely without worrying that you'll be flamed for imperfect English.

I agree completely.  Almost nobody speaks perfect English, and in my opinion it is counterproductive to point
out grammatical errors when the context makes it clear what was meant.  And for anyone it's easy enough to
make a slip which reverses the intended meaning (by saying "inaccessible" instead of "accessible" for example)
just by typing too fast and having your fingers out of step with your thoughts.  Funny how you spot your own
mistakes when reading-back from the list  :-)

> After all... As is often pointed out, your English is WAY better than
> our Hungarian, or Spanish, or Dutch or German or whatever.

Absolutely!  I always feel somewhat humbled when I speak to a Dutchman that they switch into English without a
pause, and although it sometimes has some quaint characteristics (I can often tell from a typed message that
the sender is Dutch) it is certainly not worthy of any criticism.  I attended a meeting in Arnhem in the
Netherlands last year, and there were people from most Western European countries present.  I noticed that
whenever a mixed-nation group was talking to each other, they would use English, even if they were, for
example, Dutch and German with no Englishmen involved!

I think the problem with languages as they are taught here (I learned Latin, French and German at school) is
that it is targetted at passing an exam, and not speaking/understanding it in conversation.  There is a huge
difference between being able to read French and being able to understand directions when you ask someone on
the streets of Paris!  (A quick hint: "Toujour droite" translates directly as "always right".  Keep turning
right?  No, it means "go straight on"! :-)

Cheers,

Howard Winter
St.Albans, England

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Robin,

On Tue, 21 Sep 2004 11:37:12 +0100, Robin.Bussellaxa-sunlife.co.uk wrote:

> As a colleague of mine is fond of saying when corrected on such errors:
>
> "I aint never gonna use no double negatives no more, and that's no word of a lie!"
>
> :-)

I couldn't possibly fail to disagree with him less!

:-)))

Cheers,

Howard Winter
St.Albans, England

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Love you!

PerL

----- Original Message -----
From: "Andrew Warren" <aiwcypress.com>
To: "Microcontroller discussion list - Public." <piclistmit.edu>
Sent: Tuesday, September 21, 2004 11:16 AM
Subject: Re: [OT] cyclic average.

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>
>I think that most English-speakers here would agree with me that the
>contributions made by the non-English-speakers on the list are
>valuable and appreciated.  Minor -- or, hell, even major --
>grammatical or spelling errors are easily overlooked; I hope you and
>others who aren't native English speakers will continue to post
>freely without worrying that you'll be flamed for imperfect English.

Absofreakinlutely.
:)

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Hi,

thank you for your insight-bearing comment. Really, Hungarian language
uses the double-negation almost exclusively and in such a hidden form I
used I disregarded this. It WAS really a direct translation of a Hungarian
sentence. An other example would clarify this: as I learned English, the
following sentence was completely rubbish for me:

"I like all fruits but apples" because of a Hungarian would think and say
" ... but NOT apples."

I recall " ... does not ... anything " is the correct form.

Thank you.

Imre

On Tue, 21 Sep 2004, Andrew Warren wrote:

{Quote hidden}

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At 09:08 AM 9/21/2004, dr. Imre Bartfai wrote:

>Hi,
>
>thank you for your insight-bearing comment. Really, Hungarian language
>uses the double-negation almost exclusively and in such a hidden form I
>used I disregarded this. It WAS really a direct translation of a Hungarian
>sentence. An other example would clarify this: as I learned English, the
>following sentence was completely rubbish for me:
>
>"I like all fruits but apples" because of a Hungarian would think and say
>" ... but NOT apples."

English is such fun.. Spelling, grammar, we just made it all up as we went along, and we "borrowed" heavily from other languages.  In some ways, I think it's a pity that English is becoming the worldwide language through the internet.  Still, I'm glad it's happening, it's too easy to demonize someone who speaks another language.

"I like all fruits but not apples" makes sense to me, but I agree it's not the right construct for english.. "I like any fruits but apples" would work.

The double-negative form would be "but not no apples."

The intended meaning would be "but not apples", with the "no" added for emphasis, I guess.

You hear this a lot in the midwest and south, a bit of "redneck" dialogue.

"I ain't not goin' over there"
"Don't give me none of that!"
"Don't give me no apples!", as my brother in law would say. (his given name is William Robert, you do the math)

http://www.humorsphere.com/you_might_be_3.htm  Jeff foxworthy "you might be a redneck"

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>>thank you for your insight-bearing comment. Really, Hungarian language
>>uses the double-negation almost exclusively and in such a hidden form I
>>used I disregarded this. It WAS really a direct translation of a Hungarian
>>sentence. An other example would clarify this: as I learned English, the
>>following sentence was completely rubbish for me:
>>
>>"I like all fruits but apples" because of a Hungarian would think and say
>>" ... but NOT apples."

I think this is because of a very fine variation of the meaning of "but"
here.
It corresponds to "except" all by itself.

Old motto

"Touch not the Cat Bot a glove"

VERY olde english - but has the same sense for 'but" as above.

Russell McMahon

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> I think the problem with languages as they are taught here (I learned
> Latin, French and German at school) is  that it is targetted at passing
> an exam, and not speaking/understanding it in conversation.

I don't think that thing with teaching language at school so much different
in Germany, or probably other places. After all, most at this age /are/ in
school to pass exams and not for much else :)

But English has become the de-facto international communication standard,
almost world-wide accepted, and that of course makes it easier (and
provides more motivation) to learn English (mostly after getting out of
school :) than, say, French or German -- unless you are in a country where
that language is spoken.

Gerhard
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