The accuracy of the Calculus
BURT
There is a zero point derivative. But in real world problems(physics)
there is not complete exactness. To find a slope you hone in on a
infinitely small part of the real world curve but you cannot make it
infinitely small. That would require infinite calculations so you
cannot reach it.
Mitch Raemsch
rabid_fan
I don't follow this gibberish, but the subject of accuracy
is an interesting and important one.
Currently, accuracy in physical computation is dependent
on the digital floating point representation of numbers
and currently this is determined by the IEEE 754/854
standard which has been in effect for twenty years or
so. This standard sets the precision at roughly 16-bits
of decimal or 53-bits of binary.
This standard is already severely outdated, but amazingly
there is little impetus for change. Hardware makers such
as Intel are taking the multi-core processor concept to
higher and higher levels but the floating point registers
remain fixed at a paltry 64-bits. These should be bumped to
at least 128-bits or even 256 bits. 512-bits would not be
an unreasonable requirement.
The current workaround is multi-precision FP software,
but, as expected, the software routines are S-L-O-W.
How long will it take for this IEEE bureaucracy to begin
to demand higher precision for FP computation? It is
certainly feasible so let's get moving now.
Huang
Ever heard of a thing called the Limit ?
Androcles
"rabid_fan" <r...@righthere.net> wrote in message
news:pan.2009.11...@righthere.net...
why 512 bits would be a "reasonable" requirement.
The paltry 64-bit registers that Intel provides for most users
is paralleled by Ford's Model T. If you want 512-bit precision
then buy a Cray or Rolls Royce. It may be feasible but I don't
need it and neither do MOST people. In fact, MOST people
don't use FP at all. If you had a million dollars win on a lottery
you would not quibble about it being $1,000,000 and 1 cent,
for which 64-bit fixed point is more than adequate.
The subject of accuracy is an uninteresting and unimportant
one to MOST people. Buy yourself a Cray.
BURT
You can't hone in on the curve by the unlimited calculation.
Mitch Raemsch
purple
Burt thinks arithmetical absolute precision is perfection.
Androcles
"purple" <pur...@colorme.com> wrote in message
news:7mpaavF...@mid.individual.net...
1+1 = 2 absolutely perfectly when I went to school.
BURT
How do you know that one plus one equals two?
Who told you?
Mitch Raemsch
Benj
> > > Burt thinks arithmetical absolute precision is perfection.
>
> > 1+1 = 2 absolutely perfectly when I went to school.
>
> How do you know that one plus one equals two?
> Who told you?
Hey "Mitch" got those two Nobel prizes yet? Algore and Obama have
theirs! Bigmouth idiot!
Who says 1 + 1 = 2? Since mathematics is abstract 1+ 1 can equal
ANYTHING you say it is! Of course, whatever you say, thus defines a
mathematical system which you must then demonstrate to be consistent
or it isn't mathematics.
Sorry for feeding the trolls. Forgive me.
jmfbahciv
Did you test it on a one's-complement, two's-complement and
three's-complement machine? Did you add 1 and -1 and
get a negative or positive zero?
/BAH
Raghar
> On Fri, 20 Nov 2009 18:09:24 -0800, BURT wrote:
>
> I don't follow this gibberish, but the subject of accuracy
> is an interesting and important one.
>
> Currently, accuracy in physical computation is dependent
> on the digital floating point representation of numbers
> and currently this is determined by the IEEE 754/854
> standard which has been in effect for twenty years or
> so. This standard sets the precision at roughly 16-bits
> of decimal or 53-bits of binary.
>
bits, but accurate to at most to n bit. In certain rare cases a number
which is precise to 53 bits has 0 bits of accuracy.
> This standard is already severely outdated, but amazingly
> there is little impetus for change.
You can't change it. You need exact errors in calculation that are
guaranteed by said standard.
> Hardware makers such
> as Intel are taking the multi-core processor concept to
> higher and higher levels but the floating point registers
> remain fixed at a paltry 64-bits.
That's nice, but multiplication is O(n^2) algorithm, and the simplest
division algorithm which is working is a subtraction algorithm, which
requires as many steps as bits of accuracy. While there are also
higher radix algorithms, doubling register size means doubling CPU
speed requirements for one operation.
> These should be bumped to
> at least 128-bits or even 256 bits. 512-bits would not be
> an unreasonable requirement.
I do have library for high accuracy computing that doesn't need stuff
like NaN or something absurd like that. However when n-body simulation
with 100 objects is slow on Doubles, the same simulation would be even
slower in SW mode. There is a cut off where higher precession doesn't
help much.
FP is basically something which is supposed to help mathematicians to
use programming without much hassle, as long as they don't require too
accurate results. Real programmers are using i64, or i32 because
addition of two whole numbers is an exact modulo 2^n operation, which
is extremely efficient for a real world algorithms.
Frederick Williams
>
> In the abstract realm of polynomial functions there is exactitude.
> There is a zero point derivative. But in real world problems(physics)
> there is not complete exactness.
Maybe, but does it matter?
--
Which of the seven heavens / Was responsible her smile /
Wouldn't be sure but attested / That, whoever it was, a god /
Worth kneeling-to for a while / Had tabernacled and rested.
rabid_fan
>
> That's nice, but multiplication is O(n^2) algorithm, and the simplest
> division algorithm which is working is a subtraction algorithm, which
> requires as many steps as bits of accuracy. While there are also higher
> radix algorithms, doubling register size means doubling CPU speed
> requirements for one operation.
>
Ordinary multiplication is O(n^2) but multiplication using
FFT methods is O(nlogn). Already hardware-based FFT methods
(implemented in FPGA) are being used on 4096-bit operands.
It is not far-fetched at all to expect this kind of performance
to appear on desktops.
>
> FP is basically something which is supposed to help mathematicians to
> use programming without much hassle, as long as they don't require too
> accurate results. Real programmers are using i64, or i32 because
> addition of two whole numbers is an exact modulo 2^n operation, which is
> extremely efficient for a real world algorithms.
Integer arithmetic would also benefit from larger registers.
The IEEE standard was drafted over a generation ago when hardware
was much more limited than it is today. It's time to move
forward with the future.
rabid_fan
I suppose the gist of this question (or whatever it is)
concerns the impossibility of attaining the infinitely
small in real world problems.
But physics makes no attempt to deal with the infinitely
small. The models of the real world are based on the
idea of a differential, which is not an infinitely small
quantity but rather a quantity that is small enough to
allow the derivative to be approximated by the difference
quotient.
How small is "small enough?" The answer depends on
the particular experiment or investigation but it
is never infinitely small.
For more info on this often overlooked but
essential concept, just do a search for
"differential."
Aside: When doing a search, try to avoid using
Google. Google is not the only search engine
but somehow it has become a de facto monopoly.
A new verb, "google," a synonym for search, has
even arisen in the language. This is not good.
Use AltaVista or something else once in a while.
rabid_fan
>
> Did you test it on a one's-complement, two's-complement and
> three's-complement machine? Did you add 1 and -1 and get a negative or
> positive zero?
>
There are 10 kinds of people that post to sci.physics.
We must all ask ourselves: "Which one am I?"
1 + 1 = Overflow and carry out flagged
Tim Little
> Currently, accuracy in physical computation is dependent on the
> digital floating point representation of numbers and currently this
> is determined by the IEEE 754/854 standard which has been in effect
> for twenty years or so. This standard sets the precision at roughly
> 16-bits of decimal or 53-bits of binary.
IEEE 754 already defines a 128-bit floating point type as a basic
format. There are some CPUs that have worked with 128-bit floating
point types for quite a while, though not many as it is not very
useful. Note that "128-bit floating point pipeline" in modern
graphics cards actually refers to operations on 4x 32-bit floating
point operands.
> This standard is already severely outdated, but amazingly there is
> little impetus for change.
That is because there are real costs to increasing the native width of
operands, which can be much larger than you might expect. Meanwhile,
the benefits are minor: old FPUs had 80-bit operands for intermediate
results, but the extra precision over 64 bits was almost never useful.
Any serious algorithm design with floating point numbers addresses
error propagation to reduce the effects of finite precision. Moving
to even 512-bit numbers cannot remove the need for this analysis: a
good algorithm can bound the accuracy to within a few units in the
last place. A poor one will often produce useless output with _any_
fixed intermediate precision, 512 bits or not.
So in practice the need for intermediate precision is usually
determined by the required final accuracy, which seldom exceeds 15
decimal places. The exceptions tend to be in specialized fields, for
which specialized software or hardware can be employed.
When the choice in a mass-market CPU design is between 128-bit FPU
pathways vs twice as many 64-bit pathways, the usefulness of the
latter overwhelmingly dominates. That's actually conservative in
favour of the 128-bit path: complexity of higher-precision operations
scales much worse than linearly.
What's more, someone who needs more than 64-bit precision often needs
more than 128-bit as well, so designing a 128-bit path may well be in
vain. Similar considerations apply to 256 bits or greater.
- Tim
Tim Little
> methods is O(nlogn). Already hardware-based FFT methods
> (implemented in FPGA) are being used on 4096-bit operands.
Specialized hardware for specialized tasks. If you need it, you can
easily get it. If you don't need it, it's a useless waste of silicon
and power across billions of CPUs.
It would be sheer lunacy to fix into mass-market CPUs the designs for
everything that has ever been done in FPGAs. That's why they (and
ASICs) exist.
> Integer arithmetic would also benefit from larger registers.
Not much. Integer arithmetic would benefit much much more from being
able to do more of it per clock cycle. And hey, guess what? That's
exactly the direction taken by CPU designers.
64-bit integer registers only became common when a significant
fraction of practical operations (such as calculating offsets in large
files or memory blocks) needed it. It's an optimization, and you
don't optimize the least common cases at the expense of the more
common ones. Silicon real estate is a finite resource, so widening
registers and all their data paths comes at the expense of other
things.
> The IEEE standard was drafted over a generation ago when hardware
> was much more limited than it is today. It's time to move forward
> with the future.
The current IEEE 754 standard is IEEE 754-2008. Last year, not a
generation ago.
- Tim
spudnik
which latter I'd seen mentioned, somewhere on the IEEE website, but
I wasn't a member. anyway, 754 is an article in Computer (magazine),
from 1980; its implimentation is quite variable, I think.
anyone got a reference to link?
> The current IEEE 754 standard is IEEE 754-2008. Last year, not a
--l'Ouvre: www.wlym.com
stop the second cap & trade rip-off;
install a tariff on imported oil!
zzbu...@netscape.net
> In the abstract realm of polynomial functions there is exactitude.
> There is a zero point derivative. But in real world problems(physics)
> there is not complete exactness.
Well, that's mostly because Physics cranks are about
the only people who have ever proclaimed the real number systems
the unique exemplar of exactness.
The educable people, some time started working on DSP,
rather than whip antennas. And today they have HDTV,
Home Broadband, Laser Disks, mp3, mpeg, Blue Ray,
USB, non AT&T PCM, Multiplexed Fiber Optics Systems,
Digital Books, Post ACME Fastener Systems, Self-Assembling Robots,
Cyber Batteries, Self-Replicating Machines, Deconvolution
Algorithms,
Desktop Publishing, All-In-Printers, Mini External Computer
Hardisks, Flash Memory,
4D Holographics Research Programs, On-Line Publishing, Reverse
Compilers,
GPS and Post US Steel Welding Robots, Rapid Prototyping, Digital
Terrain Mapping,
Weather Satellites, Pv Cell Energy, Data Fusion, Atomic Clock
Wristwatches,
Light Sticks, Post Watt Turbines and Biodiesel and Hybrid-Electric
Energy.
Rather than just Newton Apples.
spudnik
I never googol anything that I am dyscussing online,
particualry when using the googol front-end for Usenet
at some public terminal. I recently saw who owned altavista.com, but
I forgot, though I've used it, when needed.
> A new verb, "google," a synonym for search, has
> even arisen in the language. This is not good.
thus:
the original poster had mentioned 754 and 854,
which latter I'd seen mentioned, somewhere on the IEEE website, but
I wasn't a member. anyway, 754 is an article in Computer (magazine),
from 1980; its implimentation is quite variable, I think.
anyone got a reference to link?
> The current IEEE 754 standard is IEEE 754-2008. Last year, not a
--l'Ouvre: www.wlym.com
Stop the second cap & trade rip-off;
install a tariff on imported oil -- dumb-*** "republicans R Them!"
spudnik
the engineers didn't get stuck on Stevin's "real" odometer.
> Light Sticks, Post Watt Turbines and Biodiesel and Hybrid-Electric
> Energy.
--l'Ouvre: www.wlym.com
Mahipal7638
not questionable from even before Liebniz&|Newton, without the need of
any -- advanced or otherwise -- computational limitations, discovered
it.
Enjo(y)...
--
Mahipal
spudnik
demonstrated at the Royal Society, where Clarke
made a rather obsequious comment, about having
to convert-by-hand to obtain negative numbers
(ten's compliment .-)
thus:
the problem with Podolsky, Rosen and Einstein,
as refuted by the Aspect experiment & so forth, is that
they require the "gedanken" part of it to be a photon;
Young conclusively proved, a hundred years
after Newton-the-quackologist squeezed-out a corpuscular "theory"
of light, that *all* of lights essential properties are those
of waves, with the sole exception of the photo-eclectical effect,
when Moon hits your eye *like* banana-cream pie. and, all
of the important work, by Huyghens, Fresnel, Fizzeau etc. etc. has
only improved this comprehension, perhaps best *formulated*
by Schroedinger (and, anyway, let us recall, that
Newton merely algebraized Kepler's orbital constraints -- if
he didn't steal it from Hooke, which he did).
Newton's "theory" was probably about as important
as Descartes ridiculous ad hoc explanation
for the law of refraction (see l'Ouvre, below .-)
> > By the way, I think I heard that John Bell himself
> > expected his theorem to prove EPR /right/. If the
thus:
dood said, Numbertheory;
if you don't want to know that, you don't want to know any thing
in science, vis-a-vu *mathematica* --
not the God-am programme of the Wolframites / KNU Kinda Science;
see l'Ouvre, below!
> You have a point of view Marxist, mine is Platonist. What is the
thus:
Lord Berty was quite an evil pacifist (see larouchepub.com), but
he also made me realize that "silly" must be derived from syllogism;
apparently, he was completely fried by Godel's thing, although
Whitehead would not have been.
> Gorgias lived 2400 years ago. Maybe Russel borrowed from him :)
thus:
I have always meant to study difference equations, alas. anyway,
I never googol anything that I am dyscussing online,
particualry when using the googol front-end for Usenet
at some public terminal. I recently saw who owned altavista.com, but
I forgot, though I've used it, when needed.
> A new verb, "google," a synonym for search, has
thus:
jmfbahciv
> On Sat, 21 Nov 2009 07:32:32 -0500, jmfbahciv wrote:
>
>> Did you test it on a one's-complement, two's-complement and
>> three's-complement machine? Did you add 1 and -1 and get a negative or
>> positive zero?
>>
>
> There are 10 kinds of people that post to sci.physics.
>
> We must all ask ourselves: "Which one am I?"
I haven't been able to answer that question yet.
>
> 1 + 1 = Overflow and carry out flagged
>
<grin> Whenever I had to deal with computer arithmetic, my hair
hurt (as you probably could tell from my post). I simply
intended to whet the curiosity of the poster. If s/he/it had
done any investigation of the terms, s/he/it would have had
found piles of docs and specs to munch on. We had a math
PhD who would teach us how to make the computer add better;
it took a lot of research.
/BAH
zzbu...@netscape.net
wrote:
Well, the subject of computer registers, of any kind,
is unintering to many people, so that's how distributed
processing software came to be.
>
> - Show quoted text -
Huang
Zeno's paradoxes are pretty lame thing to argue about.
I can now understand why teachers and professors can become so burned
out, trying to teach things to people who refuse to comprehend
anything. I'd rather dig ditches for a living.
If I was a teacher and I had one person like Burt in my classroom I
think my head would explode.
This is what happens when tax dollars are used to educate people. When
they are required to pay their own money out of pocket things become a
bit less silly and the person who is responsible to learn something
probably has greater motivation to actually absorb something of value
instead of simply being disruptive.
zzbu...@netscape.net
> in other words,
> the engineers didn't get stuck on Stevin's "real" odometer.
More to the point, they didn't get stuck on functional analysis.
rabid_fan
>
> I can now understand why teachers and professors can become so burned
> out, trying to teach things to people who refuse to comprehend anything.
> I'd rather dig ditches for a living.
>
> If I was a teacher and I had one person like Burt in my classroom I
> think my head would explode.
>
Yes! You got it!
Recently, I was offered a position as an Adjunct Instructor
at a local community college. It would have been an easy
way to pick up a few grand without doing too much work (very
little work actually).
But I refused to accept the offer. I know exactly what teaching
is like when confronted with a class full of people that do not
want to learn. Within two days I would have gone ballistic.
> This is what happens when tax dollars are used to educate people. When
> they are required to pay their own money out of pocket things become a
> bit less silly and the person who is responsible to learn something
> probably has greater motivation to actually absorb something of value
> instead of simply being disruptive.
The problem is not wholly one of money. The problem is
the idea of intellectual equality wherein everybody is
lumped together irrespective of their desire or their
talent. What is required is a strict segregation to
separate the good students from the bad and to keep
them separate.
My university had the option of an honors program that
was designed to attract a different brand of student.
An honors program is a weak form of segregation but it
is better that no segregation at all. Unfortunately,
when I was enrolled there, not many people were attracted
to the honors program and so it was canceled.
I would propose completely separate institutions,
one kind for disinterested job seekers and the other
kind for devoted tyros of higher learning.
It would never happen.
rabid_fan
>>
>>
> <grin> Whenever I had to deal with computer arithmetic, my hair hurt
> (as you probably could tell from my post). I simply intended to whet
> the curiosity of the poster. If s/he/it had done any investigation of
> the terms, s/he/it would have had found piles of docs and specs to munch
> on. We had a math PhD who would teach us how to make the computer add
> better; it took a lot of research.
>
That's the problem with our educational system. The methods
of computer arithmetic should be introduced very early.
Our official curriculum, still essentially based in the
Medieval Quadrivium, has been left far behind by the
new ways of the digital revolution.
The confused are left only to trust in Microsoft.
spudnik
with functional analysis?
Raghar
> On Sat, 21 Nov 2009 04:46:32 -0800, Raghar wrote:
>
> > That's nice, but multiplication is O(n^2) algorithm, and the simplest
> > division algorithm which is working is a subtraction algorithm, which
> > requires as many steps as bits of accuracy. While there are also higher
> > radix algorithms, doubling register size means doubling CPU speed
> > requirements for one operation.
>
> Ordinary multiplication is O(n^2) but multiplication using
> FFT methods is O(nlogn). Already hardware-based FFT methods
> (implemented in FPGA) are being used on 4096-bit operands.
> It is not far-fetched at all to expect this kind of performance
> to appear on desktops.
>
also
a + (b*128)^2 < c + (d*128)*log(d*128)
FFT multiplication is usable only for large numbers. BTW what about a
division? Intel CPUs have three different division algorithms. One of
C2D advantages was speeding up 64 bit division to 16-24 CPU cycles,
register increase would slow things again. AFAIK SQRT stayed at the
same speed.
> > FP is basically something which is supposed to help mathematicians to
> > use programming without much hassle, as long as they don't require too
> > accurate results. Real programmers are using i64, or i32 because
> > addition of two whole numbers is an exact modulo 2^n operation, which is
> > extremely efficient for a real world algorithms.
>
> Integer arithmetic would also benefit from larger registers.
When I do programming, I try to choose data types to have the correct
size. Two 32 bit operations can be merged by 64 bit CPU into one
operation (behind the scene). The other benefit is a smaller memory
footprint. 4GB instead of 8GB is fairly noticeable.
Integer addition can be well, and fast, emulated without large
registers. The problems are with multiplication, division, and sqrt.
Bacle
>
> >
> > I can now understand why teachers and professors
> can become so burned
> > out, trying to teach things to people who refuse to
> comprehend anything.
> > I'd rather dig ditches for a living.
In my experience, if students see that you are motivated and interested in doing real teaching, they will eventually become motivated themselves. But some are farther gone into the world of over-commercial vulgarity and stupidity out there, and takes much more time and effort to reach them. Or maybe it takes someone with more teaching talent than me.
> >
> > If I was a teacher and I had one person like Burt
> in my classroom I
> > think my head would explode.
> >
>
> Yes! You got it!
>
> Recently, I was offered a position as an Adjunct
> Instructor
> at a local community college. It would have been an
> easy
> way to pick up a few grand without doing too much
> work (very
> little work actually).
>
> But I refused to accept the offer. I know exactly
> what teaching
> is like when confronted with a class full of people
> that do not
> want to learn. Within two days I would have gone
> ballistic.
Why not try reaching at least a few. I have been able to, and it is satisfying, tho pretty hard.
>
>
> > This is what happens when tax dollars are used to
> educate people. When
> > they are required to pay their own money out of
> pocket things become a
> > bit less silly and the person who is responsible to
> learn something
> > probably has greater motivation to actually absorb
> something of value
> > instead of simply being disruptive.
>
> The problem is not wholly one of money. The problem
> is
> the idea of intellectual equality wherein everybody
> is
> lumped together irrespective of their desire or their
> talent.
Agree. I study at a state school, and students, including myself, are extremely motivated , even during the first few years when we get funding.
What is required is a strict segregation to
> separate the good students from the bad and to keep
> them separate.
Yes, something like that. I was put , in undergrad., in a Calc class together with nursing students and with
people who were part-timers. Class was watered down to try to serve all groups. I have nothing against either group, by it may be a better idea to put non-math students not interested in rigor , in a separate class from math majors.
That is the flip side of popularizing knowledge to make it available to every one.
mike3
And those whose families do not HAVE the money in the first place...?
mike3
> On Sun, 22 Nov 2009 08:48:00 -0800, Huang wrote:
>
> > I can now understand why teachers and professors can become so burned
> > out, trying to teach things to people who refuse to comprehend anything.
> > I'd rather dig ditches for a living.
>
> > If I was a teacher and I had one person like Burt in my classroom I
> > think my head would explode.
>
> Yes! You got it!
>
> Recently, I was offered a position as an Adjunct Instructor
> at a local community college. It would have been an easy
> way to pick up a few grand without doing too much work (very
> little work actually).
>
> But I refused to accept the offer. I know exactly what teaching
> is like when confronted with a class full of people that do not
> want to learn. Within two days I would have gone ballistic.
>
How many do you think though "don't want" as opposed to "don't
have the talent"?
mike3
For example, I wasn't born into wealth. Though I don't go around and
do the
stuff like "BURT" if by that you mean that poster that posts really
nonsensical
stuff here and I have wanted to really learn more stuff than I already
know,
but have been stumbled up by the lack of money (e.g. can't buy lots
of text books, etc.).
Is there some sort of work or something I could do to make enough
money
_myself_ while also being able to do (i.e. leaving enough _time_) that
learning
of something at a school that isn't funded by "tax dollars" and so
"bad"?
jmfbahciv
> On Sun, 22 Nov 2009 08:47:46 -0500, jmfbahciv wrote:
>
>>>
>> <grin> Whenever I had to deal with computer arithmetic, my hair hurt
>> (as you probably could tell from my post). I simply intended to whet
>> the curiosity of the poster. If s/he/it had done any investigation of
>> the terms, s/he/it would have had found piles of docs and specs to munch
>> on. We had a math PhD who would teach us how to make the computer add
>> better; it took a lot of research.
>>
>
> That's the problem with our educational system. The methods
> of computer arithmetic should be introduced very early.
If so, then the first sentence of all materials should read,
"Computers can't add."
>
> Our official curriculum, still essentially based in the
> Medieval Quadrivium, has been left far behind by the
> new ways of the digital revolution.
Wrong. The problem IS the new ways of "digital revolution".
Calculators are used so exponentiation isn't taught. A bum
answer is never caught because rough guesstimates are
never done to double-check the calculator output.
>
> The confused are left only to trust in Microsoft.
>
Oh, these were problems before Microsoft became a buzz word.
/BAH
jmfbahciv
What do you mean "don't have the talent"? The post was about
a community college. I doubt the course was about proving
the 4 color theorem.
/BAH
rabid_fan
>>
> How many do you think though "don't want" as opposed to "don't have the
> talent"?
As unpalatable at it may seem, some people just do not have
the talent, in spite of any desire. I have, as I am sure
have many others, witnessed examples of this first hand.
Initially one may wish to disbelieve, but the force of truth
soon prevails.
But talent is still an extremely overblown concept. My
basic issue is not with the existence of talent but with
those who claim the power to determine it. My experience
has taught me that a mature individual is the best judge
and the only judge of his talent and aptitude.
I was informed once, by a fat and ugly middle-aged female
psychologist, that I did not possess the visual aptitude
to become, for example, an architect. This infuriated me
to no end. I know the human mind far better than this
two-bit hunk of failed flesh and I do not accept assessments
of my character from same.
rabid_fan
>
> What do you mean "don't have the talent"? The post was about a
> community college. I doubt the course was about proving the 4 color
> theorem.
>
The four color theorem was proved by computer.
That's the trend. The computer will make obsolete many
kinds of "talent." I don't need to prove my mettle
by being some calculating or integrating jock. Computer
algebra will do all the work while I just nod my final
approval to the result from a realm of pure thought.
zzbu...@netscape.net
> On Mon, 23 Nov 2009 07:40:25 -0500, jmfbahciv wrote:
>
> > What do you mean "don't have the talent"? The post was about a
> > community college. I doubt the course was about proving the 4 color
> > theorem.
>
> The four color theorem was proved by computer.
>
> That's the trend. The computer will make obsolete many
> kinds of "talent."
Well, since it's only the idiots who only know McDonald's about
computers
that ever say that it doesn't matter. Since the Engineers who
actually know more than shit
still work on *DSP* and *Laser Disks& and *Fiber Optics* and *mp3*
and *mpeg*,
and *External Low RPM Hardisks* and *Post 1950 Cell Phones* and
*Digital Books*
and *Desktop Publishing* and *On-Line Publishing* rather than with
stooge
mathematicians and integrals or M-Branes anyway.
And they still work on USB, non Vacuum Tube Microcomputers,
Optical computers,
Atomic Clock Watches, Flat Scrren Debuggers, 4D Holographics
Integration, Blue Ray,
Flash Memory, hdtv, home broadband,, rapid prototyping and the 21st
Century, rather than
with idiot and uneducable and imbecile computer science paper
rollers either.
rabid_fan
>
> And those whose families do not HAVE the money in the first place...?
>
If they don't have the money, then engage in self study.
Follow the steps that would otherwise be taken by going
to a university. (One could even do them faster and much
more efficiently.)
Then present yourself to an employer with your self-acquired
skills. What happens? The door will be promptly slammed
in your face.
Another irrational human automaton rears his ugly and
abysmally stupid head.
While at school I studied many things that did not fall
under the rubric of my official degree. As one example,
I acquired skills in electrical engineering. I was able
to design from scratch many sophisticated electronic instruments
and computer interfaces. My self-acquired skills rival
those of any official engineering graduate. But none of
this has gone down on my "official" record. If I were to
approach an engineering firm they would slam the door in
my face. (My former adviser could testify on my behalf but,
sadly, he has passed away.)
This makes no real difference to me. I introduce it as an
example that talent is not the issue. No one is recognized
on the basis of talent. Credentials are all that matter.
Caveat emptor. At the university I had a few friends that
studied medicine and are now licensed, credentialed physicians.
However, if I ever become sick I would never seek out these
doctors. I knew them personally and I knew their talent.
I had little respect for their intelligence (although they
were tolerable drinking companions). I do not doubt that,
in spite of their official credentials, their expertise is
only marginal.
Former chief justice Warren Burger (SCOTUS) once publicly
stated that half the trial lawyers in the US are flat out
incompetence. It isn't only lawyers. It is reasonable to
assume that at least half of all professions are composed
of incompetent practitioners. The job of weeding out
incompetents should fall on the schools but the job would be
enormous and practically impossible.
As long as no one notices -- and they won't -- the charade
will continue.
rabid_fan
>
> Wrong.
Wrong? That's impossible. I cannot be wrong. It is a law
of the universe.
> The problem IS the new ways of "digital revolution".
> Calculators are used so exponentiation isn't taught. A bum answer is
> never caught because rough guesstimates are never done to double-check
> the calculator output.
>
Instruction should not be based on performing calculations.
Instruction should deal exclusively with concepts. Calculation
is incidental and even superfluous.
"Don't make a calculation until you know the answer."
That is a very old truism, and it demonstrates the bold new
direction of education based on digital technologies.
I go even further: "Don't calculate; just know the answer."
Only the stupid calculate. Talented men just realize the answer
and then hand the computation task to their subordinates. In this
case the subordinates are any of the computer algebra and
computer mathematics packages that are available.
When I was in school I would always refuse to perform the
trivial arithmetic steps that conclude the solution to,
for example, a definite integral. The instructors would
usually comment in red ink: "Why didn't you solve this?"
"What the f*** for?" The integral is correct. The
rest is superfluous bullsh**. Pay some wino $2.00 to
go through the useless arithmetic motions.
Computer algebra has the potential to lift education
beyond the state of useless motions.
We need, however, to first eliminate these decrepit
dinosaurs.
There is a grave danger in this approach. Many, many
more people would flunk if they had to deal with concepts
rather than rote calculations. The colleges would lose
a lot of tuition.
jmfbahciv
/BAH
jmfbahciv
> On Sun, 22 Nov 2009 22:23:42 -0800, mike3 wrote:
>
>> And those whose families do not HAVE the money in the first place...?
>>
>
> If they don't have the money, then engage in self study.
> Follow the steps that would otherwise be taken by going
> to a university. (One could even do them faster and much
> more efficiently.)
>
> Then present yourself to an employer with your self-acquired
> skills. What happens? The door will be promptly slammed
> in your face.
>
> Another irrational human automaton rears his ugly and
> abysmally stupid head.
>
> While at school I studied many things that did not fall
> under the rubric of my official degree. As one example,
> I acquired skills in electrical engineering. I was able
> to design from scratch many sophisticated electronic instruments
> and computer interfaces. My self-acquired skills rival
> those of any official engineering graduate. But none of
> this has gone down on my "official" record. If I were to
> approach an engineering firm they would slam the door in
> my face. (My former adviser could testify on my behalf but,
> sadly, he has passed away.)
The purpose of getting that engineering degree is to be able
to document, using terms others will be able to comprehend,
what you build. If cannot produce a spec that others are
able to read, all your work will be useless because others
won't use it.
/BAH
jmfbahciv
> On Mon, 23 Nov 2009 07:37:18 -0500, jmfbahciv wrote:
>
>> Wrong.
>
> Wrong? That's impossible. I cannot be wrong. It is a law
> of the universe.
Which is why you refuse to be trained.
>
>
>> The problem IS the new ways of "digital revolution".
>> Calculators are used so exponentiation isn't taught. A bum answer is
>> never caught because rough guesstimates are never done to double-check
>> the calculator output.
>>
>
> Instruction should not be based on performing calculations.
> Instruction should deal exclusively with concepts. Calculation
> is incidental and even superfluous.
How does one check that a concept is useful? Do you burn
incense and kill a chicken or do you collect data?
>
> "Don't make a calculation until you know the answer."
>
> That is a very old truism, and it demonstrates the bold new
> direction of education based on digital technologies.
>
I don't know where you got the idea that's a truism. You
should learn how the real work gets done.
> I go even further: "Don't calculate; just know the answer."
>
> Only the stupid calculate. Talented men just realize the answer
> and then hand the computation task to their subordinates. In this
> case the subordinates are any of the computer algebra and
> computer mathematics packages that are available.
And who wrote those math packages? Who tested them and verified
that the code produced consistent results? The stupid?
>
> When I was in school I would always refuse to perform the
> trivial arithmetic steps that conclude the solution to,
> for example, a definite integral. The instructors would
> usually comment in red ink: "Why didn't you solve this?"
>
> "What the f*** for?" The integral is correct. The
> rest is superfluous bullsh**. Pay some wino $2.00 to
> go through the useless arithmetic motions.
IOW, you never finished a job. You don't know how to work.
>
> Computer algebra has the potential to lift education
> beyond the state of useless motions.
>
> We need, however, to first eliminate these decrepit
> dinosaurs.
Those so-called decrepit dinosaurs were the people who
did the work so you could set on your hieny and
write this kind of ASCII bullshit and ship it all over
the world.
>
> There is a grave danger in this approach. Many, many
> more people would flunk if they had to deal with concepts
> rather than rote calculations. The colleges would lose
> a lot of tuition.
First learn, if you are able, how work gets done. Then
reread your post and see if you can find the bugs.
/BAH
rabid_fan
>
> How does one check that a concept is useful? Do you burn incense and
> kill a chicken or do you collect data?
>
>
> And who wrote those math packages? Who tested them and verified that
> the code produced consistent results? The stupid?
>
I am speaking of concepts versus blind calculation within
an educational context. The conventional educator regards
the ability to perform rote calculations to be more important
than a deep conceptual understanding. This is true because
the fundamental structure of our schools does not readily permit
anything beyond stupid rote calculations.
>
>
>
> IOW, you never finished a job. You don't know how to work.
>
You got it! Laziness is the mother of invention, baby!
You can laboriously dig that ditch with a pick and
shovel, the rivers of sweat pouring from your brow serving
as penance for all of the invented sins of the anally
neurotic Western world.
I'll use explosives while sipping a can of illicit beer.
Kaboom! The work is finished. I'll allow you, the lackey subordinate,
to smooth over the rough edges.
You'd make an excellent Human Resources director. That whole
"profession" is characterized as spaced-out and demented "pussy."
>
> Those so-called decrepit dinosaurs were the people who did the work so
>
No. Those decrepit dinosaurs work within the paradigms
that were established, at tremendous risk, by men of a
unique and courageous genius. They (the dinosaurs) only
wield a set of tools which most of them do not fully
comprehend.
> you could set on your hieny and write this kind of ASCII bullshit and
> ship it all over the world.
>
You bet! But I suppose that you would prefer that I used
a pen and paper to laboriously compose "hard copy" and
then physically disseminate it across the globe using cargo
aircraft and trucks.
After all, in the anal West, we all must labor as dogs
to prove that we are worthy and free of sin.
>
> First learn, if you are able, how work gets done. Then reread your post
> and see if you can find the bugs.
>
I have long ago discovered the "bugs," and they are the
ignoramuses such as you.
I have no counter advice to offer. You are beyond enlightenment
and redemption.
jmfbahciv
> On Tue, 24 Nov 2009 09:46:37 -0500, jmfbahciv wrote:
>
>> How does one check that a concept is useful? Do you burn incense and
>> kill a chicken or do you collect data?
>>
>>
>> And who wrote those math packages? Who tested them and verified that
>> the code produced consistent results? The stupid?
>>
>
> I am speaking of concepts versus blind calculation within
> an educational context. The conventional educator regards
> the ability to perform rote calculations to be more important
> than a deep conceptual understanding. This is true because
> the fundamental structure of our schools does not readily permit
> anything beyond stupid rote calculations.
However, having the student finish the problem also trains him
to finish a job. If you don't do the final step or two in the
real world, somebody else will have to pick up the job and
do that work. This will require more time and a huge cost
overrun compared to you just finishing the job.
>
>>
>>
>> IOW, you never finished a job. You don't know how to work.
>>
>
> You got it! Laziness is the mother of invention, baby!
This is not laziness. This kind of not-working is abject stupidity.
>
> You can laboriously dig that ditch with a pick and
> shovel, the rivers of sweat pouring from your brow serving
> as penance for all of the invented sins of the anally
> neurotic Western world.
>
> I'll use explosives while sipping a can of illicit beer.
>
> Kaboom! The work is finished. I'll allow you, the lackey subordinate,
> to smooth over the rough edges.
The work isn't finished. That ditch has to be a precise size at a
specified depth going in a particular direction. Your approach simply
made a big hole which has to be fixed before the real job can
continue.
>
> You'd make an excellent Human Resources director. That whole
> "profession" is characterized as spaced-out and demented "pussy."
Useless straw.
>
>
>> Those so-called decrepit dinosaurs were the people who did the work so
>>
>
> No. Those decrepit dinosaurs work within the paradigms
> that were established, at tremendous risk, by men of a
> unique and courageous genius. They (the dinosaurs) only
> wield a set of tools which most of them do not fully
> comprehend.
You do not know what you are talking about.
>
>> you could set on your hieny and write this kind of ASCII bullshit and
>> ship it all over the world.
>>
>
> You bet! But I suppose that you would prefer that I used
> a pen and paper to laboriously compose "hard copy" and
> then physically disseminate it across the globe using cargo
> aircraft and trucks.
My point is that you denigrate the "dinosaurs" whose work made
it possible for you to be able to set at home with a complete
computer system on your lap using house power and transmit
your ignorance all over the net.
>
> After all, in the anal West, we all must labor as dogs
> to prove that we are worthy and free of sin.
I knew computer types who were very glad to get out of Russia
and finally do the work they had to get done. You've been
spoiled rotten and still don't know anything about the work,
that was required for you to use that system of yours.
>
>
>> First learn, if you are able, how work gets done. Then reread your post
>> and see if you can find the bugs.
>>
>
> I have long ago discovered the "bugs," and they are the
> ignoramuses such as you.
>
> I have no counter advice to offer. You are beyond enlightenment
> and redemption.
That's too bad. You might have learned something.
/BAH
BURT
Calculations cannot reach the unlimited.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
> On Nov 20, 7:09 pm, Huang <huangxienc...@yahoo.com> wrote:
>
> > On Nov 20, 8:09 pm, BURT <macromi...@yahoo.com> wrote:
>
> > > In the abstract realm of polynomial functions there is exactitude.
> > > There is a zero point derivative. But in real world problems(physics)
> > > there is not complete exactness. To find a slope you hone in on a
> > > infinitely small part of the real world curve but you cannot make it
> > > infinitely small. That would require infinite calculations so you
> > > cannot reach it.
>
> > > Mitch Raemsch
>
> > Ever heard of a thing called the Limit ?
>
> You can't hone in on the curve by the unlimited calculation.
>
What is a "real world curve"? Can you give me an example of a REAL
WORLD curve which is truly differentiable or even continuous? Is the
real-world Dow-Jones Index graph continuous? Is your pencil drawing
continuous? How does a drawn curve look under a microscope?
BURT
>
> - Show quoted text -
You know nothing about real world curves?
John Nash has said that every real world curve slope cannnot be
exactly determined as opposed to the polynomial.
The expansion rate of the universe is an example of a curve over time
since the beginning.
Part of calculus is not exact and that is for real world problems.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
> On Nov 29, 2:46 am, "Ostap S. B. M. Bender Jr."
>
>
>
> <ostap_bender_1...@hotmail.com> wrote:
> > On Nov 20, 8:15 pm, BURT <macromi...@yahoo.com> wrote:
>
> > > On Nov 20, 7:09 pm, Huang <huangxienc...@yahoo.com> wrote:
>
> > > > On Nov 20, 8:09 pm, BURT <macromi...@yahoo.com> wrote:
>
> > > > > In the abstract realm of polynomial functions there is exactitude.
> > > > > There is a zero point derivative. But in real world problems(physics)
> > > > > there is not complete exactness. To find a slope you hone in on a
> > > > > infinitely small part of the real world curve but you cannot make it
> > > > > infinitely small. That would require infinite calculations so you
> > > > > cannot reach it.
>
> > > > > Mitch Raemsch
>
> > > > Ever heard of a thing called the Limit ?
>
> > > You can't hone in on the curve by the unlimited calculation.
>
> > What is a "real world curve"? Can you give me an example of a REAL
> > WORLD curve which is truly differentiable or even continuous? Is the
> > real-world Dow-Jones Index graph continuous? Is your pencil drawing
> > continuous? How does a drawn curve look under a microscope?- Hide quoted text -
>
> > - Show quoted text -
>
> You know nothing about real world curves?
>
I do as much as the next guy. For example, I love curvy women.
>
> John Nash has said
>
Is this "proof by name-dropping"?
>
> that every real world curve slope cannnot be
> exactly determined as opposed to the polynomial.
>
Is a polynomial a "real world curve"?
If so - it is an example of a curve with a known derivative.
If not - what is an example of a "real world curve"?
How about exponential, logarithm, sine, cosine, etc?
>
> The expansion rate of the universe is an example of a curve over time
> since the beginning.
>
Is Expansion a curve, and a real world curve to boot? Where can I see
this curve?
>
> Part of calculus is not exact
>
Of course not. Like all human knowledge and models, calculus and the
"derivative" are abstractions. But so is the concept of a "curve".
They are all products of the human mind.
>
> and that is for real world problems.
>
Whatever that means....
Name me a "real world problem" that requires (or even allows) infinite
precision.
jmfbahciv
/BAH
Ostap S. B. M. Bender Jr.
Well, shouldn't we give him a 0.638234567 in IQ points for knowing the
name of John Nash? Or do I need to provide more precision?
BURT
>
> - Show quoted text -
It is simple. You cannot have unlitmited calculation to hone in on the
curve. Thus in this application of calculus there is no exactitude.
John Nash has said that this is for all real world problems.
Mitch Raemsch - The aether
Ostap S. B. M. Bender Jr.
But which particular "curve" do you want to "hone in" on? Or are you
just sharing with us Nash's alleged words for the sake of name-
dropping? If so - would you care to give us a reference to his exact
words, so that we can see them and the context?
jmfbahciv
You're way off. :-) There are so many zeroes between the decimal point
and the one that you need an infinite number of memory locations to
describe it. Before you suggest using exponents, think about what I
wrote.
/BAH
Ostap S. B. M. Bender Jr.
I am trying to, but the only number that seems to satisfy your
condition that there are infinitely many 0's up front is 0, but it
takes exactly one register. So, no number does. In any case, the
difference between IQ of 1 and IQ of 0 is negligible to all of us,
except to Burt.
Let us be objective. It doesn't take much brain to achieve an IQ of 1
or even 30, so Burt may very well be as smart as 50 on a good day.
BURT
>
> - Show quoted text -
This principle applies to the derivative of all curves that exist as
real soley world problems. The polynomial derivative though is exact.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
Mitch, as much as I would like to try to help you, I still don't
understand what your problem is and which "real world curves" and
their slopes you need to measure with infinite precision. Could you
please explain in more concrete terms what really bothers you on this
topic? And please give me some example of such "real world curve".
BURT
>
> - Show quoted text -
Only polynomial curves have exact derivates. Our calculations of
curves in real world problems cannot come to an exact answer. We
cannot do the unlimited calculations required. Thus we can never reach
an infinitely small arc of a curve. And thus the derivative remains
inexact.
I have already given an example. John Nash concures with me on this
subject. He has said it himself.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
That's stupidly false. What about exponentials and trigonometric
functions, for example?
>
> Our calculations of
> curves in real world problems cannot come to an exact answer. We
> cannot do the unlimited calculations required. Thus we can never reach
> an infinitely small arc of a curve. And thus the derivative remains
> inexact.
>
Are you saying that curves in "real world problems" don't have exact
derivatives? But the "real world" curves (i.e., curves based on human
measurements of the real-world) are based on finitely many
measurements, and these measurements themselves are inexact. So, how
can you eve expect "exact" derivatives from inexact curves?
>
> I have already given an example.
>
Could you please humour the stupid and inferior me with repeating this
example? Do you mean this:
>
> > > > > > > >> The expansion rate of the universe is an example of a curve over time
> > > > > > > >> since the beginning.
>
Well, where can I see this "real world curve" curve?
>
John Nash concures with me on this
> subject.
>
He does? Is he even aware of your existence?
>
> He has said it himself.
>
Where did he say it? You keep on making this claim without giving us
the link and/or the exact quote. Where is your reference?
BURT
>
> - Show quoted text -
He said it to me. I have talked with him. He noticed my work.
It is simple. Polynomial curves have exact derivatives while the
curves that come from real world problems can never have exact
derivatives by the Calculus.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
Good for Nash. It's high time that somebody else heard his voices in
their head.
>
> It is simple. Polynomial curves have exact derivatives while the
> curves that come from real world problems can never have exact
> derivatives by the Calculus.
>
How about the curves that describe planets' motion in Space? Or how
about the radioactive decay? Can't you derive differentiable formulas
for those? Try. You may be able to do so. My 11 year old son sure
can.
purple
> On Dec 1, 7:38 pm, BURT <macromi...@yahoo.com> wrote:
[...]
>> It is simple. Polynomial curves have exact derivatives while the
>> curves that come from real world problems can never have exact
>> derivatives by the Calculus.
>>
>
> How about the curves that describe planets' motion in Space? Or how
> about the radioactive decay? Can't you derive differentiable formulas
> for those? Try. You may be able to do so. My 11 year old son sure
> can.
Every few years another kook rediscovers this and all the
other troll issues by reading the archives, then posts it
as newly invented by them. For all I know it is the same
troll. I haven't done so myself but I'll take a wild guess
the BURT is accurately repeating the arguments used in the
past in similar threads, having recently (re)read them.
The only original things in BURT's play book are the names
he uses for this troll. An "obvious sincerity" is at the
core of his success. I have to wonder about some of the
people playing with him.
BURT
No. A planetary orbit is effected by the curve of space and the slow
of time at every point. And there are an infinity of points in every
finite quanitity along the the elliptical curve that swivels by time.
We need to look at orbits this way.
Radio active decay?
Half life is dependent on the quantity of the element that is found
together. But how does it know how many atoms it contains? Decay rate
depends on an amount. But how?
MItch Raemsch
Ostap S. B. M. Bender Jr.
Why? Didn't even Kepler in old times compute the planet trajectories/
orbits/curves with high precision?
Are you saying that you yourself are incapable of deriving/exhibiting
these real-world curves?
>
> Radio active decay?
>
> Half life is dependent on the quantity of the element that is found
> together. But how does it know how many atoms it contains?
>
Have you tried weighing? Try to derive the formula how to compute the
number of atoms of a pure chemical substance from its weight. My
little son can.
>
> Decay rate
> depends on an amount. But how?
>
Try to figure it out. My little son can. You, being a genius, should
be able as well.
Are you saying that you are unable to produce/compute the radioactive
decay curve or the planet trajectory curve? So, which real world
curves **can** you produce with exactitude? None? Surely, you, being a
genius, must be able to do better than that, right?
Ostap S. B. M. Bender Jr.
I apologise for this little mind game. I need some silliness in my
life, plus I have a psychological/tutorial question in mind that I
want answered.
purple
Enjoy yourself.
BURT
>
> - Show quoted text -
The derivative of a real world curve can never be calculated exacttly.
You cannot hone in on it an unlimited amount of times.
Mitch RFaemsch
Ostap S. B. M. Bender Jr.
> You cannot hone in on it an unlimited amount of times.
>
You don't seem to respond to questions in a human way. Instead of
answering my concrete questions, you repeat the same mantra over and
over gain. Are you a robot or an AI program or a scientologist or a
member of some other religious cult?
purple
> On Dec 3, 11:33 am, BURT <macromi...@yahoo.com> wrote:
>> On Dec 2, 6:00 pm, "Ostap S. B. M. Bender Jr."
>>> Are you saying that you are unable to produce/compute the radioactive
>>> decay curve or the planet trajectory curve? So, which real world
>>> curves **can** you produce with exactitude? None? Surely, you, being a
>>> genius, must be able to do better than that, right?
>> The derivative of a real world curve can never be calculated exacttly.
>> You cannot hone in on it an unlimited amount of times.
> You don't seem to respond to questions in a human way. Instead of
> answering my concrete questions, you repeat the same mantra over and
> over gain. Are you a robot or an AI program or a scientologist or a
> member of some other religious cult?
He's only a stupid troll. What else would you expect. I would
think any AI program, or even a robot, would return some
variability in an attempt to emulate humans.
Ostap S. B. M. Bender Jr.
Yes. I tried to see if he can be tutored into understanding this issue
a bit better, but I failed. Seems that the thesis, that anybody can be
tutored if patience is applied, doesn't work. He is either unable or
unwilling to engage in a meaningful dialogue.
BURT
>
> - Show quoted text -
Only the polynomial derivates of the calculus can be exact. This is
the abstract realm of math.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
What about exponential derivatives? Logarithmic derivatives?
Trigonometric derivatives? Didn't Nash tell you about them?
BURT
>
> - Show quoted text -
He told me about real world problem. All the curves you have
domenstrated are abstract math and are exact.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
> domenstrated are abstract math and are exact.
>
He told me that exponentials are as real as polynomials. When did YOU
talk to him last?
BURT
>
> - Show quoted text -
He has told me he considered me a fellow genius and that we have
similar ideas. I talked to him today. He said that people will deny
what I am saying because they are dumb. He backs me up all of the way.
We are on the same page.
All he said is that in real world problems the curves have derivatives
that can never be made exact because you cannot do an unlimited amount
calculations that would be required.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
Did he tell you that in real world problems, the curves have VALUES
that can be made exact?
BURT
>
> - Show quoted text -
No. That is not true.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
>
Well, if you/we can't even compute the VALUES of your "real world"
curves exactly, why are you upset that you/we can't compute their
slopes? How can you expect to compute the exact derivative of a
function if you don't exactly know its values?
BURT
>
> - Show quoted text -
Derivatives are slopes. For real world problems they never can become
exact.
Mitch Raemsch
jmfbahciv
There exist people who take pride in remaining ignorant and will do
pots of extra work to remain that way. Unfortunately, the current
PCistis makes this mindset mandatory.
/BAH
jmfbahciv
if you're designing a container which will have a minimum of surface
area with a maximum volume.
/BAH
BURT
>
> - Show quoted text -
Still calculus cannot hone in on the curve an unlimited amount of
times and therefore the derivative remains an approximation and is
never exact.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
> exact.
>
Damn! I was thinking I was getting close to explaining something to
you. I could almost feel it. I was anticipating that joyous moment of
having actually successfully explained something to somebody. Alas....
Raghar
> rabid_fan wrote:
>
> > 1 + 1 = Overflow and carry out flagged
>
> <grin> Whenever I had to deal with computer arithmetic, my hair
> hurt (as you probably could tell from my post). I simply
> intended to whet the curiosity of the poster. If s/he/it had
> done any investigation of the terms, s/he/it would have had
> found piles of docs and specs to munch on. We had a math
> PhD who would teach us how to make the computer add better;
> it took a lot of research.
What's difficult on?:
00110010 (50)
00101010 (40)
0010001
01011100 (90)
That's interesting I wrote whole decimal numbers in binary by accident.
jmfbahciv
for finding areas under a meandering curve than algebra. You can
spend your whole lifetime calculating an area using algebra.
/BAH
jmfbahciv
I was talking about the operation we call arithmetic, not the
way we stored numbers in core. [There, that should date me.]
Looks like your hair should be hurting, too, if you think
the list above is arithmetic.
/BAH
BURT
Not at all. It is just the reverse. Calculus requires unlimited
calculation for intergration and differentiation.
Intergration is counting alot of boxes but never goes exact because it
requires an infinity of them to find the area. Finding the slope of a
real world curve requires unlimited calculation to hone in on the
infinitely small arc.
And please give an example where algebra is inexact and Calculus is.
Mitch Raemsch
>I much rather use calculus
> for finding areas under a meandering curve than algebra. You can
> spend your whole lifetime calculating an area using algebra.
>
Ostap S. B. M. Bender Jr.
Algebra is inexact. How much is 2 - 3?
BURT
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
What do you mean?
Mitch Raemsch
jmfbahciv
Do you use algebra to do trig calculations?
/BAH
BURT
So which one is more accurate for area under the curve? Algebra or
calculus?
jmfbahciv
> On Dec 8, 6:08 am, jmfbahciv <jmfbahciv@aol> wrote:
>> BURT wrote:
>>> On Dec 5, 6:14 am, jmfbahciv <jmfbahciv@aol> wrote:
>>>> BURT wrote:
>>>>> Still calculus cannot hone in on the curve an unlimited amount of
>>>>> times and therefore the derivative remains an approximation and is
>>>>> never exact.
>>>> Huh? It's more "exact" than algebra.
>>> Not at all. It is just the reverse. Calculus requires unlimited
>>> calculation for intergration and differentiation.
>>> Intergration is counting alot of boxes but never goes exact because it
>>> requires an infinity of them to find the area. Finding the slope of a
>>> real world curve requires unlimited calculation to hone in on the
>>> infinitely small arc.
>>> And please give an example where algebra is inexact and Calculus is.
>> I gave you an example: area under a curve.
>>
>> Do you use algebra to do trig calculations?
>>
>> /BAH- Hide quoted text -
>>
>> - Show quoted text -
>
> So which one is more accurate for area under the curve? Algebra or
> calculus?
>
Answer the fucking question.
I'll ask another. What do you use to graph an equation?
Algebra or calculus?
/BAH
Ostap S. B. M. Bender Jr.
An algebraic equation or a differential equation?
BURT
>
> - Show quoted text -
The point is the Calculus is never exact except in the realm of
polynomial functions.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
And this brilliant observation that calculus is "never exact" with
trigonometry and exponentials, is dear to you why?
jmfbahciv
algebraic equation. It was so much less work using
calculus.
/BAH
BURT
>
> - Show quoted text -
It is not exact for real world problems. And is exact for the abstract
realm of math.
Mitch Raemsch
Ostap S. B. M. Bender Jr.
You are not much of a conversationalist, are you?