Re: Help with Newton quote
- From: "Der alte Hexenmeister" <vanquish@xxxxxxxxxxxx>
- Date: Tue, 03 Jan 2006 12:37:16 GMT
"DMF" <me@xxxxxxxxxxxxx> wrote in message
news:Y8Odnff7Et8UpCfeRVn-rw@xxxxxxxxxxxxxx
> All,
>
> I am reading "Infinite Ascent: A Short History of Mathematics"
> by David Berlinski. In the chapter on Calculus page 47 he is
> discussing objections raised against Newton's conception of
> instantaneous speed. One objection raised is that the concept
> gives rise to the mathematically meaningless term 0/0.
>
> Berlinski writes....
>> In a section of the Principia Mathematica titled The Nature
>> of the First and Last Ratios, Newton addressed this
>> objection. His argument has all the force of his implacable
>> genius. If an object in motion has no discernable speed at
>> any given time, then "by the same argument," Newton
>> observed, "it may be alleged that a body arriving at a certain
>> place, and then stopping, has no ultimate velocity; because
>> the velocity, before the object comes to the place, is not its
>> ultimate velocity; when it has arrived, there is none." This
>> Newton remarks, is absurd. And so it is.
>
> I don't see the absurdity... can someone explain or help me to
> understand Newton's point?
>
> Regards,
> David
What Newton actually said was:
"Of the method of first and last ratios of quantities, by the help whereof
we demonstrate the propositions that follow.
LEMMA I.
Quantities, and the ratios of quantities, which in any finite time converge
continually to equality, and before the end of that time approach nearer the
one to the other than by any given difference, become ultimately equal.
If you deny it, suppose them to be ultimately unequal, and let D be their
ultimate difference. Therefore they cannot approach nearer to equality than
by that given difference D; which is against the supposition." -- Principia.
Thus "absurd" was not the proof Newton gave, he gave a proof by
contradiction.
Having first constructed a lemma, it is then permissible to make use of it
without further reference. So Berlinski is correct, but has put Newton's
meaning (or intent) into his own word, "absurd". It means "already proven".
Reductio-ad-absurdum is never a truly valid proof or disproof, but is often
used as a shortcut in the belief that the reader will instantly recognise
the obvious, which you did by stating "mathematically meaningless term 0/0".
When writing about the work of another, it is of course essential to quote
accurately least the reader finds ambiguity, as you have done.
Incidentally, the buffoon Einstein makes these statements:
[quote]
we establish by definition that the "time" required by light to travel
from A to B equals the "time" it requires to travel from B to A.
[end quote]
[quote]
In agreement with experience we further assume the quantity
2AB/(t'A-tA) = c,
to be a universal constant--the velocity of light in empty space.
[end quote]
Ref: http://www.fourmilab.ch/etexts/einstein/specrel/www/
In agreement with experience, Einstein's suppositions are against Newton's
definition of velocity.
AB /(tB-tA) = c,
BA/(t'A-tB) = -c,
c+ (-c) = 0.
http://www.androcles01.pwp.blueyonder.co.uk/Sagnac.JPG
100 years of misleading garbage have ensued, Einstein was never a
mathematician. He is not permitted to dictate to Nature His own definition
of time unless He is God, as some imagine Him to be. He was a Huckster, a
latter day astrologer and fortune teller, holding out his palm to be crossed
with silver by the gullible.
The most recent accusations of forgery made against Ptolemy came from Newton
in [12]. He begins this book by stating clearly his views:-
This is the story of a scientific crime. ... I mean a crime committed by a
scientist against fellow scientists and scholars, a betrayal of the ethics
and integrity of his profession that has forever deprived mankind of
fundamental information about an important area of astronomy and history.
Towards the end Newton, having claimed to prove every observation claimed by
Ptolemy in the Almagest was fabricated, writes [12]:-
[Ptolemy] developed certain astronomical theories and discovered that they
were not consistent with observation. Instead of abandoning the theories, he
deliberately fabricated observations from the theories so that he could
claim that the observations prove the validity of his theories. In every
scientific or scholarly setting known, this practice is called fraud, and it
is a crime against science and scholarship.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Ptolemy.html
The most recent accusations of forgery made against Einstein came from
Androcles. He begins this accusation by stating clearly his views:-
This is the story of a scientific crime. ... I mean a crime committed by a
scientist against fellow scientists and scholars, a betrayal of the ethics
and integrity of his profession that has forever deprived mankind of
fundamental information about an important area of astronomy and history.
Androcles, having claimed to prove every observation claimed by Einstein in
the theory of relativity was fabricated, writes:-
Einstein developed certain physical theories and discovered that they were
not consistent with observation. Instead of abandoning the theories, he
deliberately fabricated observations from the theories so that he could
claim that the observations prove the validity of his theories. In every
scientific or scholarly setting known, this practice is called fraud, and it
is a crime against science and scholarship.
Androcles Dumbledore, Headmaster, hogwarts.physics, der alte Hexenmeister.
.
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- From: DMF
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