Subject: Re: Plus and minus infinity
From: steffend@lamar.colostate.edu (Dave Steffen)
Date: 29 Oct 1996 23:56:08 GMT
Asger Tornquist (Tornquist@dk-online.dk) wrote:
> Alfonso Martinez Vicente wrote:
> >Do plus infinity and minus infinity meet at the infinity? I mean, if I
> >go towards the infinity along the real line, will I somehow get to the
> >the minus infinity?
> I see no logical reason that + and - inf. should meet. If it were so
> the result of finding lim(x->+inf.) and lim(x->-inf.) for any real
> function would give the same result, which it doesn't.
It does in the complex plane. If one extends to complex
numbers, you can go to infinity along the positive real axis ("plus
infinity") or along the negative real axis ("minus infinity")... or
along the positive imaginary axis ("plus imaginary infinity?!"), or in
any one of an infinite number of directions.
> If the real number line were placed on an infinately big sphere on
> the other hand, maybe plus/minus-inf would be the same.
This is, in fact, exactly what's done in complex analysis; the
complex plane is mapped to a sphere.
/\
\/
Dave Steffen Wave after wave will flow with the tide
Dept. of Physics And bury the world as it does
Colorado State University Tide after tide will flow and recede
steffend@lamar.colostate.edu Leaving life to go on as it was...
- Peart / RUSH
"If you live in interesting times, I pray the fact causes you no alarm"
- Frank Herbert
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Subject: Re: A review of Infinite Energy, No. 9
From: johmann@atlantic.net (Kurt Johmann)
Date: Wed, 30 Oct 1996 04:42:51 GMT
jac@ibms48.scri.fsu.edu (Jim Carr) wrote:
>johmann@atlantic.net (Kurt Johmann) writes:
>>
>> ... Miley's paper (the coauthor is James Patterson who
>>is the CETI inventor) is titled "Nuclear Transmutations in Thin-Film
>>Nickel Coatings Undergoing Electrolysis." This paper is very solid, in my
>>opinion.
> Then enlighten us. What specific reactions are taking place?
> Are they all aneutronic, and are the rates what would be expected
> from any of the theories propounded here? For that matter, are
> they consistent with any pattern at all when one looks at the Q
> values and Coulomb barriers? The posted tables have some really
> weird patterns, or lack thereof.
I have lent the magazine to another person and no longer have it
to refer to; without reference to the original article I don't
feel qualified to answer any of your questions. Instead of
asking me or whoever these questions, I suggest you get the IE
issue in question for yourself and read the article yourself and
then reach your own conclusions yourself. All I did was report
what was in that issue and mention my own reaction to it.
The IE phone number is 603-228-4516. Perhaps you can order just
that issue.
Subject: Re: Plus and minus infinity
From: David Kastrup
Date: 30 Oct 1996 13:47:13 +0100
steffend@lamar.colostate.edu (Dave Steffen) writes:
> Asger Tornquist (Tornquist@dk-online.dk) wrote:
>
> > I see no logical reason that + and - inf. should meet. If it were so
> > the result of finding lim(x->+inf.) and lim(x->-inf.) for any real
> > function would give the same result, which it doesn't.
>
> It does in the complex plane. If one extends to complex
> numbers, you can go to infinity along the positive real axis ("plus
> infinity") or along the negative real axis ("minus infinity")... or
> along the positive imaginary axis ("plus imaginary infinity?!"), or in
> any one of an infinite number of directions.
Of course, this is wrong. Just view the limits of the function
exp(z). They are quite different for different directions of
infinity. Rational functions, though, have the "same" limits for each
kind of infinity if you consider all of them alike. The Riemann
sphere is a mapping of the complex plane onto a sphere and happens to
map values of arbitrary magnitude to an arbitrarily small area.
Note that the function x^2 maps +x and -x to the same value, yet
nobody would claim that this would make +x and -x the same.
> > If the real number line were placed on an infinately big sphere on
> > the other hand, maybe plus/minus-inf would be the same.
If we find a mapping where some things get mapped onto each other, it
proves nothing whatsoever about the proximity of those points before
the mapping.
> This is, in fact, exactly what's done in complex analysis; the
> complex plane is mapped to a sphere.
Not at all. That a mapping of the complex plane onto a sphere exists,
and that for purposes of rational functions one can still form
consistent limiting expressions on this sphere does not imply that the
sphere is always used for complex analysis.
--
David Kastrup Phone: +49-234-700-5570
Email: dak@neuroinformatik.ruhr-uni-bochum.de Fax: +49-234-709-4209
Institut fuer Neuroinformatik, Universitaetsstr. 150, 44780 Bochum, Germany
Subject: Re: Miley and the curve of binding energy
From: blue@pilot.msu.edu (Richard A Blue)
Date: Wed, 30 Oct 1996 16:00:21 GMT
John Logajan indicates that he looked at the nuclear energy
balance to see whether Miley et al. were suggesting a violation
of energy conservation by their transmutation claims. He seems
to attach some significance to his discovery that they are not
claiming "over unity."
Has this topic degenerated to the point were we can't even assume
that a man of George Miley's expericnce and reputation does not play it
fast and loose with fundamental conservation laws? I would give
him credit for having checked to see whether his claimed transmutations
do conform to basic thermodynamics.
However, while we are on the topic of conservation laws I wish to
point out that Miley is perhaps not paying attention to another
conservation law that I would deem equally important. Need I remind
you all that nuclear states are states of definite angular momentum
and that angular momentum is also a conserved quantity?
So before anyone goes rushing wildly about claiming that nucleus X
can be easily transmuted into nucleus Y just by ripping off a
few nucleons they really out to consider the angular momentum. If
the system is already constrained by the requirement that all final
states are ground states of stable isotopes it may just turn out
that you can't get there from here.
Now I do not understand John's comment that, "We wouldn't necessarily
expect contaminants to yield such a nice result, but it certainly
is possible."
What nice result? The calorimetry stinks, and Miley as much as admits
that right up front. The assortment of mass numbers found on the beads
following electrolysis isn't particularly "nice." It's just gunk.
There would be absolutely nothing remarkable about the Miley mass spectra
except for the fact that, I believe, he got the mass scale wrong!
Dick Blue
Subject: FS: 2 Texts on Nuclear Fusion
From: dcleaves@mitretek.org
Date: 30 Oct 1996 08:22:01 -0800
I currently have for sale two texts in the area of nuclear fusion.
The books are:
"Fusion Energy Conversion," by Dr. George Miley, published in 1976
by the Am. Nuclear Soc. The 454 page hardback book is in very good
condition, with no page tears or pen marks, suffering only
from a hole in the dust jacket from a price sticker being
carelessly removed. Available for $10 plus $2 postage (within
the US, postage at cost elsewhere).
"Plasma Physics for Nuclear Fusion," by Kenro Miyamoto, published
by the MIT Press in 1980. The 610 page hardbound book is very clean,
with no page tears or pen marks. Dust jacket still in good condition.
Available for $12 plus $3 postage (within the US).
If interested, please email to "dcleaves@mitretek.org" for additional
info. Thanks, and best regards.
Dave
Subject: Re: Plus and minus infinity
From: "Spencer M. Simpson, Jr."
Date: Wed, 30 Oct 1996 00:38:44 -0500
> > Asger Tornquist (Tornquist@dk-online.dk) wrote:
> >
> > > I see no logical reason that + and - inf. should meet. If it were so
> > > the result of finding lim(x->+inf.) and lim(x->-inf.) for any real
> > > function would give the same result, which it doesn't.
steffend@lamar.colostate.edu (Dave Steffen) replied:
steffen> It does in the complex plane. If one extends to complex
steffen> numbers, you can go to infinity along the positive real axis ("plus
steffen> infinity") or along the negative real axis ("minus infinity")... or
steffen> along the positive imaginary axis ("plus imaginary infinity?!"), or in
steffen> any one of an infinite number of directions.
David Kastrup replied:
David > Of course, this is wrong. Just view the limits of the function
David > exp(z). They are quite different for different directions of
David > infinity. Rational functions, though, have the "same" limits for each
David > kind of infinity if you consider all of them alike. The Riemann
David > sphere is a mapping of the complex plane onto a sphere and happens to
David > map values of arbitrary magnitude to an arbitrarily small area.
David > Note that the function x^2 maps +x and -x to the same value, yet
David > nobody would claim that this would make +x and -x the same.
steffen> If the real number line were placed on an infinately big sphere on
steffen> the other hand, maybe plus/minus-inf would be the same.
David > If we find a mapping where some things get mapped onto each other, it
David > proves nothing whatsoever about the proximity of those points before
David > the mapping.
steffen> This is, in fact, exactly what's done in complex analysis; the
steffen> complex plane is mapped to a sphere.
David > Not at all. That a mapping of the complex plane onto a sphere exists,
David > and that for purposes of rational functions one can still form
David > consistent limiting expressions on this sphere does not imply that the
David > sphere is always used for complex analysis.
I think that both respondents are missing the point (rim-shot-with-cymbals).
"infinity" is _not_ a real number, so in the _real_ number line, the infinities
do _not_ meet, but schemes do exist where you add extra points representing infinity
to a space and both infinities have to use the same point (i.e. projective spaces).
Best Regards
Spencer