Who first invented calculus - Newton or Leibniz?
Immortalist
The quarrel was a retrospective affair. In 1696, already some years
later than the events that became the subject of the quarrel, the
position still looked potentially peaceful: Newton and Leibniz had
each made limited acknowledgements of the other's work, and
L'Hospital's 1696 book about the calculus from a Leibnizian point of
view had also acknowledged Newton's published work of the 1680s as
'nearly all about this calculus' ('presque tout de ce calcul'), while
expressing preference for the convenience of Leibniz's notation.
At first, there was no reason to suspect Leibniz's good faith. In 1699
Nicolas Fatio de Duillier had accused Leibniz of plagiarizing Newton,
but Fatio was not a person of consequence. It was not until the 1704
publication of an anonymous review of Newton's tract on quadrature, a
review implying that Newton had borrowed the idea of the fluxional
calculus from Leibniz, that any responsible mathematician doubted that
Leibniz had invented the calculus independently of Newton. With
respect to the review of Newton's quadrature work, all admit that
there was no justification or authority for the statements made
therein, which were rightly attributed to Leibniz. But the subsequent
discussion led to a critical examination of the whole question, and
doubts emerged. Had Leibniz derived the fundamental idea of the
calculus from Newton? The case against Leibniz, as it appeared to
Newton's friends, was summed up in the Commercium Epistolicum of 1712,
which referenced all allegations. That document was thoroughly
machined by Newton.
No such summary (with facts, dates, and references) of the case for
Leibniz was issued by his friends; but Johann Bernoulli attempted to
indirectly weaken the evidence by attacking the personal character of
Newton in a letter dated 7 June 1713. When pressed for an explanation,
Bernoulli most solemnly denied having written the letter. In accepting
the denial, Newton added in a private letter to Bernoulli the
following remarks, Newton's claimed reasons for why he took part in
the controversy. "I have never," he said, "grasped at fame among
foreign nations, but I am very desirous to preserve my character for
honesty, which the author of that epistle, as if by the authority of a
great judge, had endeavoured to wrest from me. Now that I am old, I
have little pleasure in mathematical studies, and I have never tried
to propagate my opinions over the world, but I have rather taken care
not to involve myself in disputes on account of them."
Leibniz explained his silence as follows, in a letter to Conti dated 9
April 1716:
Pour répondre de point en point à l'ouvrage publié contre moi, il
falloit entrer dans un grand détail de quantité de minutiés passées il
y a trente à quarante ans, dont je ne me souvenois guère: il me
falloit chercher mes vieilles lettres, dont plusiers se sont perdus,
outre que le plus souvent je n'ai point gardé les minutes des miennes:
et les autres sont ensevelies dans un grand tas de papiers, que je ne
pouvois débrouiller qu'avec du temps et de la patience; mais je n'en
avois guère le loisir, étant chargé présentement d'occupations d'une
toute autre nature."
["In order to respond point by point to all the work published
against me, I would have to go into much minutiae that occurred
thirty, forty years ago, of which I remember little: I would have to
search my old letters, of which many are lost. Moreover, in most cases
I did not keep a copy, and when I did, the copy is buried in a great
heap of papers, which I could sort through only with time and
patience. I have enjoyed little leisure, being so weighted down of
late with occupations of a totally different nature."]
While Leibniz's death put a temporary stop to the controversy, the
debate persisted for many years.
To Newton's staunch supporters this was a case of Leibniz's word
against a number of contrary, suspicious details. His unacknowledged
possession of a copy of part of one of Newton's manuscripts may be
explicable; but it appears that on more than one occasion, Leibniz
deliberately altered or added to important documents (e.g., the letter
of June 7 1713, in the Charta Volans, and that of April 8 1716, in the
Acta Eruditorum), before publishing them, and falsified a date on a
manuscript (1675 being altered to 1673). All this casts doubt on his
testimony.
Several points should be noted. Considering Leibniz's intellectual
prowess, as demonstrated by his other accomplishments, he had more
than the requisite ability to invent the calculus (which was more than
ready to be invented in any case). What he is alleged to have received
was a number of suggestions rather than an account of the calculus; it
is possible that since he did not publish his results of 1677 until
1684 and since the differential notation was his invention, Leibniz
may have minimized, 30 years later, any benefit he may have enjoyed
from reading Newton's work in manuscript. Moreover, he may have seen
the question of who originated the calculus as immaterial when set
against the expressive power of his notation.
In any event, a bias favoring Newton tainted the whole affair from the
outset. The Royal Society set up a committee to pronounce on the
priority dispute, in response to a letter it had received from
Leibniz. That committee never asked Leibniz to give his version of the
events. The report of the committee, finding in favor of Newton, was
written by Newton himself and published as "Commercium
Epistolicum" (mentioned above) early in 1713. But Leibniz did not see
it until the autumn of 1714.
The prevailing opinion in the eighteenth century was against Leibniz
(in Britain, not in the German-speaking world). Today the consensus is
that Leibniz and Newton independently invented and described the
calculus in Europe in the 17th century.
"It was certainly Isaac Newton who first devised a new
infinitesimal calculus and elaborated it into a widely extensible
algorithm, whose potentialities he fully understood; of equal
certainty, the differential and integral calculus, the fount of great
developments flowing continuously from 1684 to the present day, was
created independently by Gottfried Leibniz." (Hall 1980: 1)
One author has identified the dispute as being about 'profoundly
different' methods:
"Despite... points of resemblance, the methods [of Newton and
Leibniz] are profoundly different, so making the priority row a
nonsense." (Grattan-Guinness 1997: 247)
On the other hand, other authors have emphasized the equivalences and
mutual translatability of the methods: here N Guicciardini (2003)
appears to confirm L'Hospital (1696) (already cited):
"... the Newtonian and Leibnizian schools shared a common
mathematical method. They adopted two algorithms, the analytical
method of fluxions, and the differential and integral calculus, which
were translatable one into the other." (Guicciardini 2003, at page 250)
[5]
http://en.wikipedia.org/wiki/Leibniz_and_Newton_calculus_controversy
John Stafford
quite recently. Regardless, it was perfectly useful until then, and
remains useful today.
For the obsessive of the 'Inductive Reasoning' thread - eat your hearts
out.
Back to the subnect, it was found that Leibniz's approach was more
useful, fewer hacks, more direct. Leibniz wins.
spudnik
As Bernoulli pointed out, the problem posed could not be solved, even
by the method of maxima and minima of Fermat. For in those cases,
Fermat sought the maximum and minimum from among a given set of
quantities or loci, such as the point of maximum curvature of a conic
section. Instead, Bernoulli's problem was to find a minimum curve,
among an infinity of possible paths. Every position on this sought
after curve, was determined by a principle of change. So, what had to
be discovered was, from a given a principle of change, i.e., least-
time, how are the positions of the body determined. This is the
equivalent of finding the correct orbit of a planet, not merely a
possible one. Or to put it in metaphysical terms, "How can we know,
how a falling body knows, to find the path of least descent?"
As you will see, Bernouilli was not posing an abstract mathematical
puzzle, for the mere sake of befuddling others, the solution to this
problem led to important discoveries in mechanics, as well as
metaphysics.
Bernoulli's attack on this problem began with what he called "Fermat's
metaphysical principle", that light always seeks out the path of least
time. It was a discovery of the ancient Greeks, that when light was
reflected from a mirror, the path it took was the shortest length.
However, when light was refracted by traveling through different
media, such as water and air, the path of the light was not the
shortest length. Fermat, discovering that the velocity of light was
slower in denser media, demonstrated that the light changed its
direction at the boundary between the two media, so as to follow the
path of least time. This, of course, was consistent with the Greek
discovery. In reflection, since the light travels through only one
medium and therefore doesn't change velocity, the shortest path, is
also the path of least time. But, when there's a change in medium, the
light travels the shortest path in space-time, or the path of least-
time.
Bernoulli's approach was to follow the light, so to speak, to the path
of least time. If the path of a ray of light traveling through a
medium, whose density is continuously changing, according the same
principle as that of a body falling under gravity, the the least time
path of the light, will be the same as the least time path of the
body.
But, how to discover the path, when we only know the principle of
change, and have no positions to which to orient? At each moment along
the light's path, the light would be changing its speed and direction,
such that its overall travel took the least time. Thus, similar to the
motion of a planet, at each such moment, the light was ceasing to be
what it was, and becoming what it will be. At each moment, the
position of the light was a function of the principle of maintaining
the least-time path.
Fermat had shown, that as light moved from a rarer to a denser medium,
it slowed down, and its path became more vertical. For example, if
light were traveling through air to water, the angle its path made
with a vertical line, changed at the boundary between the air and
water. If the angle its path made with the vertical in the air
changed, the angle it made with the vertical under the water changed
accordingly. However, the two angles did not change proportionally.
Rather, they changed such that the sines of the angles were always in
the same proportion.
So, at each "moment of becoming" along the light's path, the light's
velocity and trajectory were changing, such the sine of the angle the
light's path made at that moment, was always proportional to the sines
of the angles at all such "moment's of becoming."
To find the brachistichrone, Bernoulli thought of the medium in the
following way:
"If we now consider a medium which is not uniformly dense but is as if
separated by an infinite number of sheets lying horizontally one
beneath another, whose interstices are filled with transparent
material of rarity increasing or decreasing according to a certain
law; then it is clear that a ray which may be considered as a tiny
sphere travels not in a straight but instead in a certain curved path.
This path is such that a particle traversing it with velocity
continuously increasing or diminishing in proportion to the rarity,
passes from point to point in the shortest time."
Under this idea, at each horizontal sheet, the speed and direction of
the light changes. The principle under which its speed and direction
changes at each horizontal sheet, Leibniz called, the differential.
The totality of all such differentials, (what Leibniz called the
integral), is the sought after brachistichrone curve.
From one "moment of becoming" to the next, the position of the light
changes, as it passes vertically from one density to the next. Each
such vertical change in position is accompanied by a horizontal change
in position, that corresponds to the sine of the angle of inclination
at each "moment of becoming". (Bernoulli's geometrical construction of
the above can be found on p. 652 of Smith.) Bernoulli adopted Leibniz'
notation for these ideas, calling the vertical change, dy, the
horizontal change, dx, and the resulting change in the path of the
light, dz. The proportion between the vertical and the horizontal,
dy:dx, and the resulting change in the path, dz, is a function of the
rate at which the density of the medium is changing.
Bernoulli shows, that if the density of the medium is changing
according to the rate at which a body falls under its own weight,
(specifically, that the velocity changes according to the square root
of the vertical distance) then the resulting curve is a cycloid.
"...you will be petrified with astonishment when I say that this
cycloid, the tautochrone of Huygens is our required
brachistochrone..." he declared.
But, Bernoulli noted that this was not a discovery of a particular
physical phenomenon, but a metaphysical discovery of a universal
principle:
"Before I conclude, I cannot refrain from again expressing the
amazement which I experienced over the unexpected identity of Huygen's
tautochrone and our brachistochrone. Furthermore, I think it is
noteworthy that this identity is found only under the hypothesis of
Galileo so that even from this we may conjecture that nature wanted it
to be thus. For, as nature is accustomed to proceed always in the
simplest fashion, so here she accomplishes two different services
through one and the same curve, while under every other hypothesis two
curves would be necessary the one for oscillations of equal duration
the other for quickest descent. If, for example, the velocity of a
falling body varied not as the square root but as the cube root of the
height falalen through, then the brachistochrone would be algebraic,
then tautochrone on the other hand transcendental; but if the velocity
varied as the height fallen through then the curves would be
algebraic, the one a circle, the other a straight line."
http://www.wlym.com/drupal/node/286
thus:
on the wayside, I am not "top-posting;"
I am self-publishing on an infinitessimal scale. and,
I certainly did know that it was not you,
who was whining about to top-post or not to -- and
I am rather set, for decades, in making fun
of this so-called nettiquette-cum-obsessive-repulsive-
strain-dysorder.
so, you've "solved" the problem of quantum gravity, but
you have yet to coin a proper name for de entrain!... really,
not a bad stab at it (whoosh,
goes the dysplaced and/or entrained aether-shockwave,
in front of the blade & behind it .-)
> You can't distinguish between my posts and the other poster who is
> asking you not to top post? Unless you post something relevant, I'm
> done replying to your posts. Take care.
thus:
incidentally, Oberon, husband of Titanya and
King of the Fairies, is twirling around Uranus!
> Not sure what is going on with the heliopause. Haven't had a chance to
> think about it much yet.
thus:
doctor Einstein's essay seems quite confuzed
about the electromegnetic properties of matter, but
that was a while before our standard textbookoid concepts
were put out from the Texas Schoolbook Suppository.
thus:
he is giving a lot of credit to Lorentz, who may
be more responsible, after all, for the time-space crack-up
than doctor Minkowski; can you say,
Most useless formalism of Century 20.1?
however, the real problem is your persistent use
-- with whomever else from the past & future --
of the the concept of vacuum, as Pascal first thought of it,
which is really, strictly relative or active (as in,
That giant sucking sound, you hear, when you're trying
to read this ****).
> http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html
--Brit's hate Shakespeare, Why?
http://wlym.com/campaigner/8011.pdf
--Madame Rice is a Riceist, How?
http://larouchepub.com/other/2009/3650rice_racist.html
--The Riemannian Space of the Nucleus, What?
http://www.21stcenturysciencetech.com/Articles_2009/Relativistic_Moon.pdf
--In perpetuity clause in healthcare bill, Where?
spudnik
Intelligence Review.
FIRST ENGLISH TRANSLATION OF WEBER 1846 TREATISE
The Ampère Angular Force and the Newton Hoax
by Laurence Hecht
http://www.larouchepub.com/other/2007/sci_techs/3415weber.html
Peter Webb
What was Newton's - the f '(x) notation, or something else?
Androcles
"Peter Webb" <webbf...@DIESPAMDIEoptusnet.com.au> wrote in message
news:4b434c27$0$31487$afc3...@news.optusnet.com.au...
> Liebniz basically invented the dy/dx notation, right?
>
> What was Newton's - the f '(x) notation, or something else?
>
>
contrariorum 17-1 et 18-2 semper erunt paartium sexdecim..." -- Principia.
"And so the sums of the conspiring motions 15+1, or 16+0, and the
differences of the contrary motions 17-1 and 18-2, will always be equal to
16 parts..."
Notice that 16 is written as sexdecim.
You wanna work in Latin?
M Purcell
> It matters not. The Calculus was not philosophically rationalized until
> quite recently. Regardless, it was perfectly useful until then, and
> remains useful today.
How was calculus recently philosophically rationalized?
> For the obsessive of the 'Inductive Reasoning' thread - eat your hearts
> out.
I hope you realize mathematical induction is deductive.
> Back to the subnect, it was found that Leibniz's approach was more
> useful, fewer hacks, more direct. Leibniz wins.
Leibniz also published first, Newton's delay is suspect.
John Stafford
<80022c43-5c39-46ea...@q4g2000yqm.googlegroups.com>,
M Purcell <sacs...@aol.com> wrote:
> On Jan 4, 7:36�pm, John Stafford <n...@droffats.ten> wrote:
> > It matters not. The Calculus was not philosophically rationalized until
> > quite recently. Regardless, it was perfectly useful until then, and
> > remains useful today.
>
> How was calculus recently philosophically rationalized?
By recent, I mean after most philosophers were over dithering on the
meaning of infinitesimals. The philosophers could not 'rationalize' the
process, it seemed unnatural (another problem for the philosophers), but
somehow calculus all worked very well regardless of objections. The
first rationalization was when the Calculus turned to limits instead. I
think it was the late 1800's. More recently, the 1960s's, Abraham
Robinson returned to the interpretation of infinitesimal numbers apart
from the philosophical, to mathematical theory - a stunning bit of
reasoning, IMHO.
I'm at a bit of a loss for precise description of the history - I no
longer work at the university library (real bummer, but better pay here.)
> > For the obsessive of the 'Inductive Reasoning' thread - eat your hearts
> > out.
>
> I hope you realize mathematical induction is deductive.
We may be hung on a technicality here. I agree that the vast majority of
mathematics is inductive, but during the formulation of a thesis the
mathematician might use induction to create a case to test for a proof,
or as I hope I once wrote, once induction is complete then one moves to
deductive reasoning.
>
> > Back to the subnect, it was found that Leibniz's approach was more
> > useful, fewer hacks, more direct. Leibniz wins.
>
> Leibniz also published first, Newton's delay is suspect.
I'm not as familiar with that history as I should be. Thanks for the
nudge.
Oh! I saw the new Sherlock Holmes movie. No deductions that I could
find! I can explain but it might split the subject.
John Stafford
"Androcles" <Headm...@Hogwarts.physics_r> wrote:
ego operor non disco latin
Gawd, that's probably pathetic but I really wanted to get ego and disco
into the same expression.
M Purcell
> In article
> <80022c43-5c39-46ea-ab95-6ed4e668e...@q4g2000yqm.googlegroups.com>,
> M Purcell <sacsca...@aol.com> wrote:
>
> > On Jan 4, 7:36 pm, John Stafford <n...@droffats.ten> wrote:
> > > It matters not. The Calculus was not philosophically rationalized until
> > > quite recently. Regardless, it was perfectly useful until then, and
> > > remains useful today.
>
> > How was calculus recently philosophically rationalized?
>
> By recent, I mean after most philosophers were over dithering on the
> meaning of infinitesimals. The philosophers could not 'rationalize' the
> process, it seemed unnatural (another problem for the philosophers), but
> somehow calculus all worked very well regardless of objections. The
> first rationalization was when the Calculus turned to limits instead. I
> think it was the late 1800's. More recently, the 1960s's, Abraham
> Robinson returned to the interpretation of infinitesimal numbers apart
> from the philosophical, to mathematical theory - a stunning bit of
> reasoning, IMHO.
The use of limits does make calculus more understandable but physics
still uses infinitesimal differences.
> I'm at a bit of a loss for precise description of the history - I no
> longer work at the university library (real bummer, but better pay here.)
>
> > > For the obsessive of the 'Inductive Reasoning' thread - eat your hearts
> > > out.
>
> > I hope you realize mathematical induction is deductive.
>
> We may be hung on a technicality here. I agree that the vast majority of
> mathematics is inductive, but during the formulation of a thesis the
> mathematician might use induction to create a case to test for a proof,
> or as I hope I once wrote, once induction is complete then one moves to
> deductive reasoning.
The argument:
Statement S(1) is true.
Statement S(n) implies Statement S(n+1).
Therefore, S(n) is true for all n.
has the form of a deductive argument; if the premises are true then
the conclusion is true.
> > > Back to the subnect, it was found that Leibniz's approach was more
> > > useful, fewer hacks, more direct. Leibniz wins.
>
> > Leibniz also published first, Newton's delay is suspect.
>
> I'm not as familiar with that history as I should be. Thanks for the
> nudge.
>
> Oh! I saw the new Sherlock Holmes movie. No deductions that I could
> find! I can explain but it might split the subject.
Haven't seem the movie but it is my understanding that kind of
deduction is more a process of elimination, trying to find premises to
fit the conclusion.
Androcles
"John Stafford" <nh...@droffats.net> wrote in message
news:nhoj-20D3C9.1...@news.supernews.com...
With Gawd getting in the way it's small wonder the Xtian Romans
produced no mathematicians of the earlier Greek calibre. :-)
Androcles
> In article
> <80022c43-5c39-46ea...@q4g2000yqm.googlegroups.com>,
> M Purcell <sacs...@aol.com> wrote:
>
>> On Jan 4, 7:36 pm, John Stafford <n...@droffats.ten> wrote:
>> > It matters not. The Calculus was not philosophically rationalized until
>> > quite recently. Regardless, it was perfectly useful until then, and
>> > remains useful today.
>>
>> How was calculus recently philosophically rationalized?
>
> By recent, I mean after most philosophers were over dithering on the
> meaning of infinitesimals. The philosophers could not 'rationalize' the
> process, it seemed unnatural (another problem for the philosophers), but
> somehow calculus all worked very well regardless of objections. The
> first rationalization was when the Calculus turned to limits instead. I
> think it was the late 1800's. More recently, the 1960s's, Abraham
> Robinson returned to the interpretation of infinitesimal numbers apart
> from the philosophical, to mathematical theory - a stunning bit of
> reasoning, IMHO.
>
Given f'(x) = [f(x+h)-f(x)]/h, it naturally follows that h is
the smallest number greater than zero and cannot be divided.
This statement deeply upset Bonehead Green who insisted h
was divisible by 2 simply by writing h/2. Yet at the other end
of the scale he'd be perfectly happy to turn an 8 on its side
and call it infinity.
John Stafford
<d780e1ad-fd18-4a44...@m25g2000yqc.googlegroups.com>,
M Purcell <sacs...@aol.com> wrote:
> On Jan 5, 10:13�am, John Stafford <n...@droffats.net> wrote:
> > We may be hung on a technicality here. I agree that the vast majority of
> > mathematics is inductive, but during the formulation of a thesis the
> > mathematician might use induction to create a case to test for a proof,
> > or as I hope I once wrote, once induction is complete then one moves to
> > deductive reasoning.
>
> The argument:
>
> Statement S(1) is true.
> Statement S(n) implies Statement S(n+1).
> Therefore, S(n) is true for all n.
For natural numbers. Inductive in mathematics involves proofs. Not so in
philosophy where it is about inductive _reasoning_.
> > Oh! I saw the new Sherlock Holmes movie. No deductions that I could
> > find! I can explain but it might split the subject.
>
> Haven't seem the movie but it is my understanding that kind of
> deduction is more a process of elimination, trying to find premises to
> fit the conclusion.
He used _abductive_ reasoning. Arg! I think I just blew-up my speel
checker. Really, abductive.
M Purcell
> In article
> <d780e1ad-fd18-4a44-a183-9b4c408bc...@m25g2000yqc.googlegroups.com>,
> M Purcell <sacsca...@aol.com> wrote:
>
> > On Jan 5, 10:13 am, John Stafford <n...@droffats.net> wrote:
> > > We may be hung on a technicality here. I agree that the vast majority of
> > > mathematics is inductive, but during the formulation of a thesis the
> > > mathematician might use induction to create a case to test for a proof,
> > > or as I hope I once wrote, once induction is complete then one moves to
> > > deductive reasoning.
>
> > The argument:
>
> > Statement S(1) is true.
> > Statement S(n) implies Statement S(n+1).
> > Therefore, S(n) is true for all n.
>
> For natural numbers. Inductive in mathematics involves proofs. Not so in
> philosophy where it is about inductive _reasoning_.
Indeed, anything for which natual numbers can not be assigned.
> > > Oh! I saw the new Sherlock Holmes movie. No deductions that I could
> > > find! I can explain but it might split the subject.
>
> > Haven't seem the movie but it is my understanding that kind of
> > deduction is more a process of elimination, trying to find premises to
> > fit the conclusion.
>
> He used _abductive_ reasoning. Arg! I think I just blew-up my speel
> checker. Really, abductive.
The truth of improbability, actually I was just reading than Holmes
used modus ponens, an inferential deduction.
John Stafford
<715cf711-3b9e-4d89...@h9g2000yqa.googlegroups.com>,
M Purcell <sacs...@aol.com> wrote:
modus ponens?
Oh, thought that mons pubis.
Androcles
> <80022c43-5c39-46ea...@q4g2000yqm.googlegroups.com>,
> M Purcell <sacs...@aol.com> wrote:
>
>> On Jan 4, 7:36 pm, John Stafford <n...@droffats.ten> wrote:
>> > It matters not. The Calculus was not philosophically rationalized until
>> > quite recently. Regardless, it was perfectly useful until then, and
>> > remains useful today.
>>
>> How was calculus recently philosophically rationalized?
>
> By recent, I mean after most philosophers were over dithering on the
> meaning of infinitesimals. The philosophers could not 'rationalize' the
> process, it seemed unnatural (another problem for the philosophers), but
> somehow calculus all worked very well regardless of objections. The
> first rationalization was when the Calculus turned to limits instead. I
> think it was the late 1800's. More recently, the 1960s's, Abraham
> Robinson returned to the interpretation of infinitesimal numbers apart
> from the philosophical, to mathematical theory - a stunning bit of
> reasoning, IMHO.
>
Given f'(x) = [f(x+h)-f(x)]/h, it naturally follows that h is
the smallest number greater than zero and cannot be divided.
This statement deeply upset Bonehead Green who insisted h
was divisible by 2 simply by writing h/2. Yet at the other end
of the scale he'd be perfectly happy to turn an 8 on its side
and call it infinity.
> I'm at a bit of a loss for precise description of the history - I no
bvcv...@yahoo.com
of [Cardinal] Nicholas of Cusa; of course, since
you are apparently British, you've probably been indoctrinated
with the secular church of Newton, and/or the Harry Potter PS
curriculum
of the "Venetian Party" of England.
also, I keep on referring to the 2.5-page article
in *Math.Mag.* (MAA.org), that proves the isometry
of inductive & deductive proofs,
also giving a formula to convert from one to the other.
the Royal Society attack on Leibniz was political;
he was actively being considered to be the PM,
by Queen Anne. (deny that, if you care to .-)
> With Gawd getting in the way it's small wonder the Xtian Romans
> produced no mathematicians of the earlier Greek calibre. :-)- Hide quoted text -
thus:
doctor Einstein's essay seems quite confuzed
about the electromegnetic properties of matter, but
that was a while before our standard textbookoid concepts
were put out from the Texas Schoolbook Suppository.
thus:
he is giving a lot of credit to Lorentz, who may
be more responsible, after all, for the time-space crack-up
than doctor Minkowski; can you say,
Most useless formalism of Century 20.1?
however, the real problem is your persistent use
-- with whomever else from the past & future --
of the the concept of vacuum, as Pascal first thought of it,
which is really, strictly relative or active (as in,
That giant sucking sound, you hear, when you're trying
to read this ****).
> http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html
--Brit's hate Shakespeare, Why?
http://wlym.com/campaigner/8011.pdf
--Madame Rice is a Riceist, How?
http://larouchepub.com/other/2009/3650rice_racist.html
--The Riemannian Space of the Nucleus, What?
http://www.21stcenturysciencetech.com/Articles_2009/Relativistic_Moon...
Androcles
<bvcv...@yahoo.com> wrote in message
news:76aea297-f85e-437a...@z41g2000yqz.googlegroups.com...
*plonk*
Do not reply to this generic message, it was automatically generated;
you have been kill-filed, either for being boringly stupid, repetitive,
unfunny, ineducable, repeatedly posting politics, religion or off-topic
subjects to a sci. newsgroup, attempting cheapskate free advertising
for profit, because you are a troll, because you responded to George
Hammond the complete fruit cake, simply insane or any combination
or permutation of the aforementioned reasons; any reply will go unread.
Boringly stupid is the most common cause of kill-filing, but because
this message is generic the other reasons have been included. You are
left to decide which is most applicable to you.
There is no appeal, I have despotic power over whom I will electronically
admit into my home and you do not qualify as a reasonable person I would
wish to converse with or even poke fun at. Some weirdoes are not kill-
filed, they amuse me and I retain them for their entertainment value
as I would any chicken with two heads, either one of which enables the
dumb bird to scratch dirt, step back, look down, step forward to the
same spot and repeat the process eternally.
This should not trouble you, many of those plonked find it a blessing
that they are not required to think and can persist in their bigotry
or crackpot theories without challenge.
You have the right to free speech, I have the right not to listen. The
kill-file will be cleared annually with spring cleaning or whenever I
purchase a new computer or hard drive.
Update: the last clearance was 25/12/09. Some individuals have been
restored to the list.
I'm fully aware that you may be so stupid as to reply, but the purpose
of this message is to encourage others to kill-file fuckwits like you.
I hope you find this explanation is satisfactory but even if you don't,
damnly my frank, I don't give a dear. Have a nice day and fuck off.
M Purcell
Is this what you meant?
a classic syllogism:
All the beans from this bag are white.
These beans are from this bag.
Therefore, these beans are white.
Then we have inductive logic:
These beans are from this bag.
These beans are white.
Guess that all the beans from this bag are white.
Reasoning using abduction or retroduction is as follows:
All the beans from this bag are white.
These beans are white.
Guess that these beans are from this bag.
Androcles
"M Purcell" <sacs...@aol.com> wrote in message
news:83c40bb0-1a1a-4261...@f5g2000yqh.googlegroups.com...
a classic syllogism:
==============================================
Some distant galaxies are red-shifted.
All red-shift is caused by velocity.
The further away the galaxy is, the greater the red-shift.
Guess the universe is expanding.
Guess there was a big bonk.
Assert the guess.
THE UNIVERSE BEGAN WITH A BIG BONK BECAUSE HUBBLE
SAID SO!
He should know, they named a telescope after him.
Mars has canals, Lowell said so. He should know, they named
an observatory after him.
Does anyone, anywhere, know how to apply logic to more than beans
making five?
dorayme
"Androcles" <Headm...@Hogwarts.physics_r> wrote:
> Then we have inductive logic:
>
> These beans are from this bag.
> These beans are white.
>
> Guess that all the beans from this bag are white.
That is not any form of logic at all.
--
dorayme
Androcles
"dorayme" <dorayme...@optusnet.com.au> wrote in message
news:doraymeRidThis-E0B...@news.albasani.net...
> Then we have inductive logic:
>
> These beans are from this bag.
> These beans are white.
>
> Guess that all the beans from this bag are white.
>
Well done, dorayme, you guessed the bean colour.
Now all you need do is concentrate on the illogic of snipping attributions,
you pathetic imbecile.
Les Cargill
> Liebniz basically invented the dy/dx notation, right?
>
> What was Newton's - the f '(x) notation, or something else?
>
>
f'(x) is Lagrange's notation:
http://en.wikipedia.org/wiki/Leibniz's_notation
Newton's notation was dots over the function:
http://en.wikipedia.org/wiki/Newton's_notation
I recall *vaguely* that Liebniz invented
integration first, and Newton invented
derivatives first.
Neither were particularly rigorous - I think
it was Cauchy who first formalized limits.
--
Les Cargill
M Purcell
Any ideas about delta notation? A different Greek?
Rockinghorse Winner
Les Cargill
Dunno about that one.
--
Les Cargill
spudnik
who uses Leibniz's method:
he begins with the integral.
John Conway once responded,
on Swarthmore.edu mathforum,
what Newton's notation is really good for;
but, I really don't recall.
so, even a quack like Newton
-- the unofficail secular church of England,
as opposed to the official Harry Potter PS
"institutional affiliation --
has actually some use.
> Any ideas about delta notation? A different Greek?
--l'OEuvre!
http://wlym.com
M Purcell
> Apostol is the only author that I know of,
> who uses Leibniz's method:
> he begins with the integral.
>
> John Conway once responded,
> on Swarthmore.edu mathforum,
> what Newton's notation is really good for;
> but, I really don't recall.
It's a very economical shorthand generally used in mechanics.
Robert
chazwin
> It matters not. The Calculus was not philosophically rationalized until
> quite recently. Regardless, it was perfectly useful until then, and
> remains useful today.
>
> out.
>
chazwin
Leibniz was a better publicist, whilst Newton was a loner and recluse.
That is why we tend to use his notation.
There is evidence that Leibniz stole the idea on a trip to England,
and Newton accused him of that.
But as it was useless in the 17th Century it hardly matters.
J. Clarke
> In article
> <80022c43-5c39-46ea...@q4g2000yqm.googlegroups.com>,
> M Purcell <sacs...@aol.com> wrote:
>
>> On Jan 4, 7:36 pm, John Stafford <n...@droffats.ten> wrote:
>>> It matters not. The Calculus was not philosophically rationalized
>>> until quite recently. Regardless, it was perfectly useful until
>>> then, and remains useful today.
>>
>> How was calculus recently philosophically rationalized?
>
> By recent, I mean after most philosophers were over dithering on the
> meaning of infinitesimals. The philosophers could not 'rationalize'
> the process, it seemed unnatural (another problem for the
> philosophers), but somehow calculus all worked very well regardless
> of objections. The first rationalization was when the Calculus turned
> to limits instead. I think it was the late 1800's. More recently, the
> 1960s's, Abraham Robinson returned to the interpretation of
> infinitesimal numbers apart from the philosophical, to mathematical
> theory - a stunning bit of reasoning, IMHO.
>
> I'm at a bit of a loss for precise description of the history - I no
> longer work at the university library (real bummer, but better pay
> here.)
If anyone is interested, Prof. H. Jerome Keisler at the University of
Wisconsin wrote an introductory calculus text based on this formulation.
It's out of print now but he has generously made it available under a
creative commons license and you can download it from his web site at
<http://www.math.wisc.edu/~keisler/>. The epilogue has some of the history.
<remainder trimmed>
John Stafford
"J. Clarke" <jclarke...@cox.net> wrote:
That's it! I had forgotten Keisler's contribution. Wow. Thanks very much!
John Stafford
<3bb4b02f-c083-40ab...@c34g2000yqn.googlegroups.com>,
chazwin <chaz...@yahoo.com> wrote:
It certainly mattered regardless of material applications because
publishing the formalization of The Calculus brought the concept to more
of the general public, fostering understanding. In that regard, we have
Leibniz to thank.
karl
Can you provide this evidence?
Larry Hammick
news:4bf1106b-6020-4ca1...@s3g2000yqs.googlegroups.com...
[
Development of the quarrel
...
http://en.wikipedia.org/wiki/Leibniz_and_Newton_calculus_controversy
]
Look at the length of this thread. It illustrates that the history of
analysis is a long and painful and messy story.
Trivia question. Who was the first to hit on the following definition, and
when?
"A function f: R to R is continuous at a point x iff for every B>0 there
exists A>0 such that, if |y-x| < A then |f(y) - f(x)| <B".
Answer below ...
Heine in 1888, more than 200 years after the Newton-Leibniz kafuffle.
M Purcell
> "Immortalist" <reanimater_2...@yahoo.com> wrote in message
>
> news:4bf1106b-6020-4ca1...@s3g2000yqs.googlegroups.com...
> [
> Development of the quarrel
> ]
>
> Look at the length of this thread. It illustrates that the history of
> analysis is a long and painful and messy story.
This topic reminds me of my college days and I suspect we were
attempting to assign blame rather than credit. But now, what seems
relevant about this story is that Newton didn't seem eager to make his
work available to other people and resorted to political maneuvering.
Les Cargill
But Newton was an alchemist. They were like that, according
to what I've been told.
--
Les Cargill
M Purcell
Seems like the more things change the more they stay the same. I
suspect it's a human thing and still seems applicable today with the
contraversy over global warming, industrial and national secrets,
government grants, ect.
spudnik
with the minding of the mint?... the "controversy" was an operation
to defame Leibniz, in order to scuttle his appt. by Queen Anne.
> > > relevant about this story is that Newton didn't seem eager to make his
> > > work available to other people and resorted to political maneuvering.
>
> > But Newton was an alchemist. They were like that, according
--l'OEuvre!
http://wlym.com
spudnik
he really put me into his killfile.
thus:
the only evidence of a "photon" is,
when the wave goes, Splat!
for instance,
the "rods & cones" of the retina a)
do not contain three pigments (per Young's "[apparent] trichromacy
of vision" -- full phrase due to Land), and b)
are both conformed of "log-spiral antennae." so,
how do you get a "photon" to be absorbed by that?
if some body shoots a fulleren at your eyeball, duck!
> Oh yeah, that's right, I forgot your answer was, "Because it's a
> wave".
>
> In AD, the C-60 molecule always enters and exits a single slit while
> the displacement wave it creates in the aether enters and exits
> multiple slits.
also see:
http://www.21stcenturysciencetech.com/Articles_2009/Relativistic_Moon.pdf
> <http://web.jjay.cuny.edu/~acarpi/NSC/4-pertab.htm>.
--l'OEuvre!
http://wlym.com
M Purcell
> > > > relevant about this story is that Newton didn't seem eager to make his
> > > > work available to other people and resorted to political maneuvering.
>
> > > But Newton was an alchemist. They were like that, according
>
> why do you think that Sir Isaac was rewarded
> with the minding of the mint?... the "controversy" was an operation
> to defame Leibniz, in order to scuttle his appt. by Queen Anne.
Newton became warden of the Royal Mint in 1696, Leibniz was accused of
pliagerism in 1711, and was appointed Imperial Court Councillor to the
Habsburgs the following year. It also seems Newton had mercury
poisoning and predicted the end of the world in 2060, "This I mention
not to assert when the time of the end shall be, but to put a stop to
the rash conjectures of fanciful men who are frequently predicting the
time of the end, and by doing so bring the sacred prophesies into
discredit as often as their predictions fail."
karl
I ask again: Where is your evidence?
Provide it or concede that you are a nonsense talker!
Tonico
The only comment I can offer in this tasty discussion is the next two
pretty well-based historical facts: (1) Newton was a weirdo and a
rather not-so-nice person, to say the least, and (2) Leibnitz is one
of the greatest minds this poor humanity of ours has spawned in the
last 6,000 years.
From the above it seems to be a sound hypothesis that Newton did not
develop completely his idea until he heard/read that the kraut
Leibnitz already published something very similar to what he had been
working with the last years, and then he rushed to the editor's house.
Tonio
Larry Hammick
[
Les Cargill
[
But Newton was an alchemist. They were like that, according
to what I've been told.
]
Seems like the more things change the more they stay the same. I
suspect it's a human thing and still seems applicable today with the
contraversy over global warming, industrial and national secrets,
government grants, ect.
LOL. Just yesterday I was clashing with a rabbinically bearded
astrophysicist about biodiversity.
Les Cargill
> "M Purcell"
> [
> Les Cargill
> [
> But Newton was an alchemist. They were like that, according
> to what I've been told.
> ]
> Seems like the more things change the more they stay the same. I
> suspect it's a human thing and still seems applicable today with the
> contraversy over global warming, industrial and national secrets,
> government grants, ect.
Apparently, one of Micheal Crichton's final books was on
the very subject of DNA being intellectual property.
The hepatitis C virus is *owned*.
http://video.google.com/videoplay?docid=-2663847011110488414#
"History
In the mid 1970s, Harvey J. Alter, Chief of the Infectious Disease
Section in the Department of Transfusion Medicine at the National
Institutes of Health, and his research team demonstrated that most
post-transfusion hepatitis cases were not due to hepatitis A or B
viruses. Despite this discovery, international research efforts to
identify the virus, initially called non-A, non-B hepatitis (NANBH),
failed for the next decade. In 1987, Michael Houghton, Qui-Lim Choo, and
George Kuo at Chiron Corporation, collaborating with Dr. D.W. Bradley
from CDC, utilized a novel molecular cloning approach to identify the
unknown organism.[41] In 1988, the virus was confirmed by Alter by
verifying its presence in a panel of NANBH specimens. In April of 1989,
the discovery of the virus, re-named hepatitis C virus (HCV), was
published in two articles in the journal Science. [42][43]
Chiron filed for several patents on the virus and its diagnosis.[44] A
competing patent application by the CDC was dropped in 1990 after Chiron
paid $1.9 million to the CDC and $337,500 to Bradley. In 1994 Bradley
sued Chiron, seeking to invalidate the patent, have himself included as
a co-inventor, and receive damages and royalty income. He dropped the
suit in 1998 after losing before an appeals court.[45][46]"
http://en.wikipedia.org/wiki/Hepatitis_C
> ]
> LOL. Just yesterday I was clashing with a rabbinically bearded
> astrophysicist about biodiversity.
>
>
--
Les Cargill
M Purcell
> Larry Hammick wrote:
> > "M Purcell"
> > [
> > Les Cargill
> > [
> > But Newton was an alchemist. They were like that, according
> > to what I've been told.
> > ]
> > Seems like the more things change the more they stay the same. I
> > suspect it's a human thing and still seems applicable today with the
> > contraversy over global warming, industrial and national secrets,
> > government grants, ect.
>
> Apparently, one of Micheal Crichton's final books was on
> the very subject of DNA being intellectual property.
> The hepatitis C virus is *owned*.http://video.google.com/videoplay?docid=-2663847011110488414#
>
> "History
>
> In the mid 1970s, Harvey J. Alter, Chief of the Infectious Disease
> Section in the Department of Transfusion Medicine at the National
> Institutes of Health, and his research team demonstrated that most
> post-transfusion hepatitis cases were not due to hepatitis A or B
> viruses. Despite this discovery, international research efforts to
> identify the virus, initially called non-A, non-B hepatitis (NANBH),
> failed for the next decade. In 1987, Michael Houghton, Qui-Lim Choo, and
> George Kuo at Chiron Corporation, collaborating with Dr. D.W. Bradley
> from CDC, utilized a novel molecular cloning approach to identify the
> unknown organism.[41] In 1988, the virus was confirmed by Alter by
> verifying its presence in a panel of NANBH specimens. In April of 1989,
> the discovery of the virus, re-named hepatitis C virus (HCV), was
> published in two articles in the journal Science. [42][43]
>
> Chiron filed for several patents on the virus and its diagnosis.[44] A
> competing patent application by the CDC was dropped in 1990 after Chiron
> paid $1.9 million to the CDC and $337,500 to Bradley. In 1994 Bradley
> sued Chiron, seeking to invalidate the patent, have himself included as
> a co-inventor, and receive damages and royalty income. He dropped the
> suit in 1998 after losing before an appeals court.[45][46]"
>
> http://en.wikipedia.org/wiki/Hepatitis_C
> > ]
> > LOL. Just yesterday I was clashing with a rabbinically bearded
> > astrophysicist about biodiversity.
There has been a long standing contraversy over proprietories of the
Icelandic health database;
http://www.archives.is/index.php?node=174
They have information that could help in the fields of genetics,
medicine, and population studies but how do you compensate for
personal information?