Re: Geometry: No four vectors can be pairwise at an right angle to each other

very funny, I think, that
you consructed a graph with a right-elbow in it;
taht is *exactly* the thing:
we are simply dealing with time in a phase-space, and
one could just as well use an axis of time,
that was oblique to your other one (in your case,
it was just (another?) scalar !-)

all of these other well-known orthogonalities do not really matter,
even if they can ultimately be treated geometerically,
as they can mathematically.

here is a related question:
did Lagrangians and Hamiltonians come before, or
after Riemannian manifolds?

Do you agree or disagree: There is no such thing as vectors
in R^n which are orthogonal under the dot product and which

following 2 hours and 15 minutes = ( 2.25 h, - 3 d). Do You claim, that
there is an right angle between a certain rise in temperature and a
certain fall of temperature?
Friendly greetings
Hero
PS. Maths is also about ,,spaces", which are sets with a structure.
And Cantor defined ,,Eine Menge ist eine Zusammenfassung bestimmter,
wohlunterschiedlicher Dinge unserer Anschauung oder unseres Denkens,
welche Elemente der Menge genannt werden, zu einem Ganzen. ,, A set is
a collection of specified, proper differentiated things of our
reception or reasoning (thinking), which are called elements of the
set, into a whole. (my translation). So in math we can talk about sets
of numbers as well as sets of dogs, sets of temperature changes,...

thus:
have you read Bernoulli's brachistochrone paper?...
there is another book on it, out, called _The Calculus Wars_,
which at least (as I recall) shows how to use both
of the notations (ask Conway, what the dots are good for;
I forgot what he wrote, when I asked him on Geometry.pre-college,
or whatever it was on Swarthmore's site)....
anyway, this book doesn't have any notion that
there was a political reason for the attacks
of the "Newton circle" (in other word, conspiracy). as for Hooke's
role,
I'll see if I can find the text of the keynoter
of the Ninth Annual Nonlinear Science confab,
which was at the faculty center, here.

thus:
I think this is easy to guess at, since
it is approximately my own situation....
I took a two-year course in electronics engineering,
doing passably well as they say, but have never entered
into the field. it only gives me some insight
into the use of complex numbers, "period."

thus:
the brachistocrhone problem actually helped Leibniz and Bernoulli
to establish "the" calculus. I'm sure, Newton had to weigh-in
with his cannonballs, but, Who cares?... I mean,
all he did was algebraize Kepler's orbital constraints
-- didn't cite his contemporary ... I mean, Galileo didn't, either --
although evidence points to his stealing the 2nd-power law
from what's-his-face (no-one knows, since Sir Duh destroyed all
of his pics at the Society, which wrote a whole Philosophic Tract,
to obfuscate the basic idea....
Bernoulli's paper is fairly elementary,
even in French.

thus:
to be featured in the next movie,
"Harry Potter's New Crusades and
the 'Public' Charter Schools: Faith-based Initiatives
in the New Millennium CCE: Come the Rapture,
No Child Left Behind!:"
http://larouchepub.com/other/2006/3333uk_scoop_soc.html

--it takes some to jitterbug!
http://members.tripod.com/~american_almanac
http://www.21stcenturysciencetech.com/2006_articles/Amplitude.W05.pdf
http://www.rwgrayprojects.com/synergetics/plates/figs/plate01.html
http://larouchepub.com/other/2006/3322_ethanol_no_science.html
http://www.wlym.com/pdf/iclc/howthenation.pdf

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