That’s interesting and sort of ties in with a book I’ve just started
reading. “Zen and the Art of Motorcycle Maintenance”, by Robert M. Pirsig.
One of his hypothesis is that ‘quality’, as such, cannot be defined other
than by saying, “You know it when you see it”. One can prove it’s existance
simply by observing the world around us and how we react to various things.
One can observe it’s importance simply by contemplating what the world would
be like if there were no such concept. ie. Would we have all these
varieties of food if ‘quality’ didn’t exist or would we just eat that which
provided sufficient nutrition? Would people be interested in observing
sporting events? Trying to pin it down is much more difficult though.
Dijkstra’s definition of mathematical elegance is simply, “That which is
recognized as beautiful by a mathematician”.
On Thu, 6 Jun 2002 11:24:09 -0400, “Kris Warkentin” <> kewarken@qnx.com
wrote:
In this exchange of quotations let me recall another one - on
not so elusive elegance (from EWD709):
“Later I learned that for the kind of effectiveness that I
loved, mathematicians had a perfectly adequate, technical term: they
call it ‘mathematical elegance’, or ‘elegance’ for short. I also
discovered that the term is much more ‘technical’ that most
mathematicians suspect, much more in the sense that even among
mathematicians of very different brands there exist a much greater
consensus about what is a really elegant argument than they themselves
seemed to be aware of. Show any mathematician a really elegant
argument that is new to him: at the moment it becomes his intellectual
property, he starts to laugh!”
“ed1k” <ed1k@spamerstrap.com> wrote in message
news:01c21092$abfdc5c0$106fa8c0@ED1K…
Misha Nefedov <> mnefedov@qnx.com> > wrote in article
adqcfi$4hm$> 1@inn.qnx.com> >…
That is very intrestring. In Russia the first part will be opposite. It
sounds like:
“Keep quite idiot, people will think you are smart!”
-Misha.
The following is in original language:
“??? ???, ?? ??? ???”
Misha,
Out of curiosity… What is those ???
Maybe, it was a try to imagine the look of this quite man ?
Never wrote russians letters here, just experiment:
“ðÏ ËÏÍÁÎÄÅ shutdown ÎÁÓÔÕÐÉÌÏ ÕÔÒÏ…”
On Mon, 10 Jun 2002 11:38:46 -0400, “Kris Warkentin”
<kewarken@qnx.com> wrote:
That’s interesting and sort of ties in with a book I’ve just started
reading. “Zen and the Art of Motorcycle Maintenance”, by Robert M. Pirsig.
One of his hypothesis is that ‘quality’, as such, cannot be defined other
than by saying, “You know it when you see it”. One can prove it’s existance
simply by observing the world around us and how we react to various things.
One can observe it’s importance simply by contemplating what the world would
be like if there were no such concept. ie. Would we have all these
varieties of food if ‘quality’ didn’t exist or would we just eat that which
provided sufficient nutrition? Would people be interested in observing
sporting events? Trying to pin it down is much more difficult though.
Dijkstra’s definition of mathematical elegance is simply, “That which is
recognized as beautiful by a mathematician”.
Kris
Actually, what EWD describes is more a litmus than a
definition. As for the rest… that’s too broad a subject to dig into,
regrettably enough. We’d have to talk the whole eternity.
But Zen and motorcycles? Good Heavens!
I guess my config in Outlook doesn’t allow me to send Russian. I’ll try to
put that saying in latin alphabet ( for those who cares
“Molchi durak, za umnogo sojdesh.”
-Misha.
P.S.:
those question marks looked really good, though ).
“ed1k” <ed1k@spamerstrap.com> wrote in message
news:01c21092$abfdc5c0$106fa8c0@ED1K…
Misha Nefedov <> mnefedov@qnx.com> > wrote in article
adqcfi$4hm$> 1@inn.qnx.com> >…
That is very intrestring. In Russia the first part will be opposite. It
sounds like:
“Keep quite idiot, people will think you are smart!”
-Misha.
The following is in original language:
“??? ???, ?? ??? ???”
Misha,
Out of curiosity… What is those ???
Never wrote russians letters here, just experiment:
“ðÏ ËÏÍÁÎÄÅ shutdown ÎÁÓÔÕÐÉÌÏ ÕÔÒÏ…”
I guess my config in Outlook doesn’t allow me to send Russian. I’ll try to
put that saying in latin alphabet ( for those who cares >
“Molchi durak, za umnogo sojdesh.”
-Misha.
P.S.:
those question marks looked really good, though > > ).
I guess my config in Outlook doesn’t allow me to send Russian. I’ll try to
put that saying in latin alphabet ( for those who cares >
“Molchi durak, za umnogo sojdesh.”
“Keep quite idiot, people will think you are smart!”
Hm…
I guess it was
“Keep quiet, idiot, people will think you are smart!”
Only two letters was swaped… or does it was improved by Outlook ?
Eduard.
ed1k at ukr dot net
“ä×ÉÖÅÎÉÅ ÒÁÄÕÅÔ, ÒÅÚÕÌØÔÁÔ ÏÇÏÒÞÁÅÔ.”
On Mon, 10 Jun 2002 11:38:46 -0400, “Kris Warkentin” kewarken@qnx.com> > wrote:
That’s interesting and sort of ties in with a book I’ve just started
reading. “Zen and the Art of Motorcycle Maintenance”, by Robert M. Pirsig.
[snip]
But Zen and motorcycles? Good Heavens!
Actually, it’s not particularily about Zen or motorcycles, although they do
enter into the story. It’s more like a philosophical road trip.
Kris
It’s a book that I think would appeal to many engineers or designers.
Don’t let the title put you off. It reads like a novel but is, among
other things, about how we might see our interface with the world
in a different light. Enlightening.
Richard
Thanks, I’m reassured a little. But there’s something telling
in picking up titles like that. Buddha and stock investments. Another
slippery ground - oriental ideas in the western civilisation.
To clarify: I don’t assert that 0.999… doesn’t exist.
You just can’t start a proof of its existence (and equivalence to 1)
by asserting that it exists.
Limits can exist. However, they do not necessarily exist. It does
depend on your system of reference. We were talking about the set of
real numbers before, and “infinity” is not included in that set.
“Angela Lin” <> alin@qnx.com> > wrote in message
news:adqghi$bjj$> 1@nntp.qnx.com> …
I think you’re treading on dangerous territory when you treat limits
like a number. You can’t subtract 0.999… from anything if it doesn’t
exist. Just because we can represent it doesn’t mean it exists.
I think I disagree with your assertion that 0.9999… doesn’t exist. It’s
just a different way of writing ‘1’. All the ‘proof’ did was illustrate
that equivalence of the two values by substituting that value for 1 and
showing how it drops out in the end.
Chris Wiebe <> cwiebe@qnx.com> > wrote:
: Nah, he’s just ripping off Michelangelo… >
:> Geez Kris, I’ve never heard something so ‘elegant’ come out of your
mouth.
:> In fact, I still haven’t. But your fingers–wow–they’ve got something
to
:> say to the world!
On Mon, 10 Jun 2002 11:38:46 -0400, “Kris Warkentin” kewarken@qnx.com> > wrote:
That’s interesting and sort of ties in with a book I’ve just started
reading. “Zen and the Art of Motorcycle Maintenance”, by Robert M. Pirsig.
[snip]
But Zen and motorcycles? Good Heavens!
It’s a book that I think would appeal to many engineers or designers.
Don’t let the title put you off. It reads like a novel but is, among
other things, about how we might see our interface with the world
in a different light. Enlightening.
Something I thought of this morning - a circle of infinite diameter exists,
just not in reality. These are all mathematical concepts, just like in
It doesn’t exist in math, eiter. At least not in Euclidean gemoetry.
By definition, a circle is the set of all those points on a plane, whose
distance from the centre equals to the radius. The centre is a point on
the plane, and the radius is a number, not “infinity”.
If course, it’s possible that you can find or invent a non-Euclidean
geometry where circles of infinite diameter exist; but if that’s the
context you had in mind, you’ll have to give us more details…
calculus when you take the limit as some value approaches zero (or infinity
as in the case of the many nines). So, a segment of a circle is still a
straight line if you let the diameter approach infinity. If you had a
formula which described the curvature of a line taken from a circle, I would
bet that the diameter would exist somewhere in the denominator causing the
curvature to approach zero as the diameter approached infinity. Either way,
it’s not an approximation. If we were still in school, some professor would
probably make us come up with a proof of this…good thing we don’t have to
do those type of things anymore. >
In calculus, there is a definition of what it means that a series or a
function does have a limit. I don’t remember ever coming across such a
concept in geometry. I think your professor would have to define it
before he could come up with a proof.
And I doubt it would be easy to define it in a way that would make a
proof possible. Notice that no matter how big you make the circle,
only a finite section of the line is actually near the circle. The part
of the line that’t near the circle grows as you grow the circle, but the
part that’s far away from the circle doesn’t shrink!
“Angela Lin” <> alin@qnx.com> > wrote in message
news:adqghi$bjj$> 1@nntp.qnx.com> …
I think you’re treading on dangerous territory when you treat limits
like a number. You can’t subtract 0.999… from anything if it doesn’t
exist. Just because we can represent it doesn’t mean it exists.
I think I disagree with your assertion that 0.9999… doesn’t exist. It’s
just a different way of writing ‘1’. All the ‘proof’ did was illustrate
that equivalence of the two values by substituting that value for 1 and
showing how it drops out in the end.
Kris,
Are you seriously about that “proof”? Why you use identity
10x - x == 9x?
I tell you, because it’s easy for you to multiply to 10 just by moving the point in written form
of number to one place right. But this way just sometimes work, but not always. Your case is
exactly an example. Let me to remind the 10x is
x + x + x + x + x + x + x + x + x + x
Isn’t? I don’t see any monkeying with decimal point.
What will with the “proof” if say I want to use another identity
123x - x == 122x?
It’s bad proof if you have no words for me
Well, here is another ‘proof’:
Let me to suppose 0.9999(9) = 1 - alpha, where alpha is infinitly small value. Then, by using your
identity,
10 * (1 - alpha) - (1 - alpha) == 9 * x
10 - 10 * alpha - 1 - alpha == 9 * x
9 - 9 * alpha == 9 * x
x = (9 - 9x) / 9 = [9*(1 - alpha)] / 9 = 1- alpha,
So, x is still (1 - alpha) = 0.9999(9)
It’s true for any true identity, as homework could play around 123x - x == 122x
What is infinity in your CPU? Just exeption interrupt “dev by 0”? I’m working with DSP now, it very
smoothly calculate the division when divisor is 0 Without any exeptions I just get 0 in
accumulator if dividend was 0 (according the doc dividend should be positive, I’m not sure 0 is
positive, but it work ) and, if divident was really positive number, I get MAX_VAL in accumulator
and OVerflow flag is setted - it’s infinity in my case.
Cheers.
Eduard.
ed1k at ukr dot net
“If you want to f…k the sky you must teach your p…s fly”
Unknown author wrote this on the table in the class room when I was studend. Stupid say, but I
still remember it.
In calculus, there is a definition of what it means that a series or a
function does have a limit. I don’t remember ever coming across such a
concept in geometry. I think your professor would have to define it
before he could come up with a proof.
And I doubt it would be easy to define it in a way that would make a
proof possible. Notice that no matter how big you make the circle,
only a finite section of the line is actually near the circle. The part
of the line that’t near the circle grows as you grow the circle, but the
part that’s far away from the circle doesn’t shrink!
It’s entirely possible that I’m just being silly but it’s fun to speculate.
Another thing I was thinking about was taking an arc of a certain width from
a circle. Say I take a line of length 2. Then I make an arc on that line
that is part of a circle of some radius r. Now, if I start moving the
center of the circle away from me, the distance from the center of the line
to edge of the arc decreases. The angle of the arc also decreases so I have
a triangle (based on my original line) where the angle at the tip is
decreasing towards zero. Didn’t someone say that parallel lines are lines
that cross infinitely far away? So using this method we can also construct
a triangle where two corners are 90 degrees each. Yeehaw!
You saw the original “proof” didn’t you? The one with the 10 and the 9 was
just to show that it’s kind of silly. It isn’t a proof but rather an
illustration. I think that a lot of background work is required to show
that 0.9999… is exactly equal to one and given that background, Angela’s
proof is sufficient. Your demonstration is just as silly as mine since
alpha being an infinitesemly [sp?] small value means that it is exactly
equivalent to zero right?
RK had cleverly pointed out that using different numerical bases can
demonstrate these things too. In base 3, 0.1 = 1/3 and 0.1 + 0.1 + 0.1 = 1.
Anyway, I’m afraid that the ‘proof’ I clipped from Slashdot was not
mathematically rigorous enough for this audience. (Wow! Tough crowd…take
my wife, please… but I think it did serve it’s original purpose of
satisfying RK.
Kris
“ed1k” <ed1k@spamerstrap.com> wrote in message
news:01c211eb$d97c8b80$106fa8c0@ED1K…
ed1k <> ed1k@spamerstrap.com> > wrote in article
01c211eb$15493060$106fa8c0@ED1K>…
x = (9 - 9x) / 9 = [9(1 - alpha)] / 9 = 1- alpha,
^^^^^^^^
sorry, it should be
OMG! That takes me back. Wasn’t there an argument about quality being
subjective as opposed to objective or something like that. I can remember
talking about that crap for months back when I was in school.
That’s interesting and sort of ties in with a book I’ve just started
reading. “Zen and the Art of Motorcycle Maintenance”, by Robert M.
Pirsig.
One of his hypothesis is that ‘quality’, as such, cannot be defined other
than by saying, “You know it when you see it”. One can prove it’s
existance
simply by observing the world around us and how we react to various
things.
One can observe it’s importance simply by contemplating what the world
would
be like if there were no such concept. ie. Would we have all these
varieties of food if ‘quality’ didn’t exist or would we just eat that
which
provided sufficient nutrition? Would people be interested in observing
sporting events? Trying to pin it down is much more difficult though.
Dijkstra’s definition of mathematical elegance is simply, “That which is
recognized as beautiful by a mathematician”.
Actually, Quality (with a capital Q) is neither objective nor subjective,
but comes before…
The first time I read ZAMM it was a truly mind-blowing experience (ok I was
young and impressionable). Read it again a few years ago. It’s still
fascinating to read. There is also a sequel “Lila” that came out a few
years ago - but it IMHO it just didn’t live up to the spirit of the
original. I’d highly recommend reading ZAMM if you’re looking for a way to
break out of your cartesian mindset…
OMG! That takes me back. Wasn’t there an argument about quality being
subjective as opposed to objective or something like that. I can remember
talking about that crap for months back when I was in school.
“Kris Warkentin” <> kewarken@qnx.com> > wrote in message
news:ae2gof$9ar$> 1@nntp.qnx.com> …
That’s interesting and sort of ties in with a book I’ve just started
reading. “Zen and the Art of Motorcycle Maintenance”, by Robert M.
Pirsig.
One of his hypothesis is that ‘quality’, as such, cannot be defined
other
than by saying, “You know it when you see it”. One can prove it’s
existance
simply by observing the world around us and how we react to various
things.
One can observe it’s importance simply by contemplating what the world
would
be like if there were no such concept. ie. Would we have all these
varieties of food if ‘quality’ didn’t exist or would we just eat that
which
provided sufficient nutrition? Would people be interested in observing
sporting events? Trying to pin it down is much more difficult though.
Dijkstra’s definition of mathematical elegance is simply, “That which is
recognized as beautiful by a mathematician”.
