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Anthony concerning the casting of the Galilean inclined plane experiment:
> If by "factually" you mean actual experience of endless linear motion, then
> I agree that there is no such evidence. But if "factually" can include
> observable patterns towards such a result, then there is such evidence. I
> really don't see anything about Galileo's incline plane experiment which
> depends on the conclusion, since it argues on the basis of the observable
> pattern, not from the conclusion itself. The ball rolls down one incline,
> then up the facing incline, and reaches the same height that it started at
> every time, no matter what angle the facing incline is set at. As the second
> incline is dropped closer and closer to horizontal, the point on the second
> incline at which the ball would return to the same height gets farther and
> farther away, and yet the ball still "perseveres" towards the same height
> every time, accounting for drag. Nothing about this observable pattern
> depends on the conclusion, but it does lead to a certain conclusion about
> what the ball itself "perseveres" to do if drag is taken into account.
Sorry to interrupt this fascinating struggling discourse 'tween Anthony and
MichaelE, but this paragraph sparked off something. It is the business of
limit and continuity.
The projecting of the concept of 'in the limit' (e.g., as the angle of the
plane approaches zero) has a casting of the complex concept of continuity.
Both Newton and Leibnitz formulated the infinitesimal calculus in which the
concept of continuity is brought to a conclusion, to a stand. We are, in
such
a casting, expected to assume that whatever is the state of play here and
now shall not be that different not-quite-here and not-quite-now, i.e., in
'neighbouring' space-time (or whatever dimension one fancies). Moreover, we
are expected to take on board the concept of some quantum that is neither
nothing nor quite something (it is not zero but is the smallest something,
smaller than anything we can come up with (and then some...)), the
infinitesimally small. Such a quantum guarantees continuity and generates
the power of the calculus. And it depends upon a limiting process, e.g., the
lessening of the angle of the inclined plane in the experiment of Galileo
until it becomes zero. But at the zero limit, experientially, the ball does
not move at all: only 'in the limit' does such an unobservable eternal
motion 'occur'; the limit being the infinitesimally small angle, not the
zero angle. My point being that the reasoning success of Galileo's
experiment and its conclusion depends upon the same kind of reasoning used
in the calculus of Newton and Leibnitz, and that depends upon a casting, a
prior projecting, of 'continuity' upon the 'observable' world of beings, so
that, despite the unobserved eternal motion of the ball, the 'ball' 'did'
(would?) 'move eternally' when the plane was horizontal. Isn't this
extraordinary?
I 'continually' find the basis of Newton's calculus, the infinitesimally
small, an
astonishing casting.
Michael Pennamacoor
"Nietzsche is something that must be overcome :-)"
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<TITLE>Re: Method - Axiomatic casting</TITLE>
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<FONT COLOR=3D"#0000FF">Anthony concerning the casting of the Galilean inclin=
ed plane experiment:<BR>
</FONT><BR>
> If by "factually" you mean actual experience of endless line=
ar motion, then<BR>
> I agree that there is no such evidence. But if "factually" c=
an include<BR>
> observable patterns towards such a result, then there is such evidence=
. I<BR>
> really don't see anything about Galileo's incline plane experiment whi=
ch<BR>
> depends on the conclusion, since it argues on the basis of the observa=
ble<BR>
> pattern, not from the conclusion itself. The ball rolls down one incli=
ne,<BR>
> then up the facing incline, and reaches the same height that it starte=
d at<BR>
> every time, no matter what angle the facing incline is set at. As the =
second<BR>
> incline is dropped closer and closer to horizontal, the point on the s=
econd<BR>
> incline at which the ball would return to the same height gets farther=
and<BR>
> farther away, and yet the ball still "perseveres" towards th=
e same height<BR>
> every time, accounting for drag. Nothing about this observable pattern=
<BR>
> depends on the conclusion, but it does lead to a certain conclusion ab=
out<BR>
> what the ball itself "perseveres" to do if drag is taken int=
o account.<BR>
<BR>
<FONT COLOR=3D"#0000FF">Sorry to interrupt this fascinating struggling discou=
rse 'tween Anthony and<BR>
MichaelE, but this paragraph sparked off something. It is the business of<B=
R>
limit and continuity.<BR>
<BR>
The projecting of the concept of 'in the limit' (e.g., as the angle of the<=
BR>
plane approaches zero) has a casting of the complex concept of continuity.<=
BR>
Both Newton and Leibnitz formulated the infinitesimal calculus in which the=
<BR>
concept of continuity is brought to a conclusion, to a stand. We are, in su=
ch<BR>
a casting, expected to assume that whatever is the state of play here and<B=
R>
now shall not be that different not-quite-here and not-quite-now, i.e., in<=
BR>
'neighbouring' space-time (or whatever dimension one fancies). Moreover, we=
<BR>
are expected to take on board the concept of some quantum that is neither<B=
R>
nothing nor quite something (it is not zero but is the smallest something,<=
BR>
smaller than anything we can come up with (and then some...)), the<BR>
infinitesimally small. Such a quantum guarantees continuity and generates<B=
R>
the power of the calculus. And it depends upon a limiting process, e.g., th=
e<BR>
lessening of the angle of the inclined plane in the experiment of Galileo<B=
R>
until it becomes zero. But at the zero limit, experientially, the ball does=
<BR>
not move at all: only 'in the limit' does such an unobservable eternal<BR>
motion 'occur'; the limit being the infinitesimally small angle, not the<BR=
>
zero angle. My point being that the reasoning success of Galileo's<BR>
experiment and its conclusion depends upon the same kind of reasoning used<=
BR>
in the calculus of Newton and Leibnitz, and that depends upon a casting, a<=
BR>
prior projecting, of 'continuity' upon the 'observable' world of beings, so=
<BR>
that, despite the unobserved eternal motion of the ball, the 'ball' 'did'<B=
R>
(would?) 'move eternally' when the plane was horizontal. Isn't this extraor=
dinary?<BR>
<BR>
I 'continually' find the basis of Newton's calculus, the infinitesimally sm=
all, an<BR>
astonishing casting.<BR>
<BR>
<BR>
</FONT>
<P ALIGN=3DCENTER>
<FONT COLOR=3D"#FF0000"><FONT SIZE=3D"2">Michael Pennamacoor<BR>
"Nietzsche is something that must be overcome :-)"<BR>
</FONT></FONT>
<P>
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