Math and my ignorant vaporings!

[Peter Lissaman]

First, the title refers to mine own "ignorant vaporings"!  I have been
following the discussion about the putative non-existence of a point and
its spatial and temporal derivatives with great interest, but I must be too
stupid to understand the issue.

I have a smattering of mathematics; that I studied as a  scholar in grad
school at Cambridge University and Caltech, and wangled a Ph. D. , but
consider  myself very ignorant on  deep Mathematics -  the Queen of the
Sciences.  There's a lot  t'know there!!   One was reminded by the austere
statement in the Cambridge catalog, that being granted a Ph.D  only
"PREPARED" students for research in the subject.   But we, and LaGrange,
allus considered  bodies as assemblages of mass points, elastically
connected.  Jes like Marilyn Monroe!  And those points had numerous
derivatives in space and time, in many reference systems (some
non-inertial) and usually, quel horreur, did not even conserve mass - think
any propellant and oxidizer.  And so, "prepared" or not, I spent half a
century on four continents gainfully predicting the future state of
vehicles plying their way through space, sky, sea or land.  Usually Nature
opposed, and the Gods of Vacuum, Wind, Wave and Rock oftentimes took out  a
vehicle, and occasionally a good pilot, too.  But I was surprised at how
often approximations that we knew to be pretty horrible worked well enough
to get home in one piece.

Consequently, I was deelited when my acquaintance, Dick Feynman (bless his
quantum soul) told me that Newtonian Calculus was "just" a method of
predicting the future, and much more successfully than astrologers, fortune
tellers or the Biblical prophets.  Given the inputs to system one can
predict its future state.    Magick!!!!   But that's all it is.  He also
stated that one should not discuss physics or mathematics until one had
worked professionally at it for a long time .  Same reason Catholic Priests
are piss poor advisors on matters sexual, or should be!    Also don't
discuss puzzlements in words until one has made numerical calculation that
can be corroborated by test.  

Thirty years of brilliant orbital mechanics in the space programs have
proven a solid validation of Newtonian Calculus.  And, Yes, Virginia, there
is a Saint Isaac, and those simple laws hold here, on the moon and
everywhere else we've been able to check.  So it doesn't seem to me there's
no such thing as a point with various state derivatives!!!

I do not suggest that other writers are wrong, and do not expect I am
correct here, experience has demonstrated that being right is indeed a rare
event for me.    But, but, but, I wanted to express my personal
professional experience through the better part of the 20th century, as
simply another point of view on this arcane subject.  If someone will
express their puzzlement in the form of an equation, or better yet ,
numerical results, I will be able much more clearly to see the problem.


Peter Lissaman, Da Vinci Ventures

Expertise is not knowing everything, but knowing what to look for.

1454 Miracerros Loop South, Santa Fe, New Mexico 87505
TEL: [phone] FAX: [phone]

 



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[Russell Standish]

On Tue, Jul 15, 2008 at 05:31:11PM -0600, Peter Lissaman wrote:
>
> Thirty years of brilliant orbital mechanics in the space programs have
> proven a solid validation of Newtonian Calculus.  And, Yes, Virginia, there
> is a Saint Isaac, and those simple laws hold here, on the moon and
> everywhere else we've been able to check.  So it doesn't seem to me there's
> no such thing as a point with various state derivatives!!!
>

I don't think it is a point that has a derivative in Newtonian
mechanics, but rather the trajectory of a point particle through phase
space.

I haven't been following this thread closely, so I may be way
off-base, of course.

--

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