…as i ask "why do u think logically", the answer could be so long…

I am guessing it was Fermat who came up with the chord concept to
obtain the slope of a arbitrary point on a smooth curve. Anyway, most
textbooks of Calculus omit the Chord concept and that is bad news
because the Chord concept is better than any algebraic concept to
understanding the derivative and how it is linked to the integral.

The old thread was getting too long and so this new thread.

I been meaning to ask a historical question about Newton and Leibniz
concerning the discovery of the Calculus. In Newton’s Principia, if my
memory serves me, Newton made a mistake by calling energy as m*v, not
m*v^2. The v^2 is area and the integral is an area. And it was Leibniz
who claimed energy is m*v^2. So my question is, does this historical
facts indicate that Leibniz had a better grasp of the Calculus rather
than Newton’s fluxions. Did Leibniz get the energy correct because of
Calculus?

So, now, what about 3rd dimension where a summation of cross-sections
of a object in 3rd dimension would be the volume of the object and so
the integral in 3rd dimension should be easy and strong, but now what
about derivative in 3rd dimension? If the integral is summation of
cross-sections what is the derivative? What is the generalization of a
chord in 3rd dimension.

So we seem to see Calculus falling apart in 3rd dimension. So why is
Calculus so weak as an enterprise that it is not able to generalize
into the 3rd dimension, and we only piecewise compute integration and
differentiation in 3rd dimension?

Is it because in Physics, velocity is linked to energy, but volume is
not linked to anything of physical forces. Can we say a Force is a
volume measure? So when we have F = m*a that the integral in 3rd
dimension is m*a and the derivative is acceleration?

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies

Another SD Rodrian Prediction True:
Cosmological Constant (i.e. "Dark Energy") is BOGUS

Slowly but surely all of the nonsense which is nowadays
plaguing cosmology and physics are, one by one, being
exposed for the nonsense they all are… exactly as I have
time and again predicted:  http://physics.sdrodrian.com

>A Challenge to Evolution of Universe
>’Dark Energy’ Finding Casts Doubt
>on Einstein’s ‘Cosmological Constant’
>By Guy Gugliotta Washington Post Staff Writer
> Thursday, January 12, 2006; Page A02
>In the quest to decipher
>the evolution of the cosmos,
>no topic generates greater
>interest among scientists than
>"dark energy," the mysterious
>force that appears to be
>causing the universe to expand
>at an ever-accelerating rate.

The "proposal" for dark energy is not as a result
of any particular requirement in the Big Bang model;
rather, the real world (the universe) was unexpectedly
discovered to be working in the exact opposite manner
that model says it ought to be working… but rather than
acknowledge the observed facts have invalidated the
model, BB theorists merely now said they thought some
"dark energy" MUST exist which is making the model
work in the exact opposite way the BB model should work.

The original requirement for a "Big Bang" were effectively
nullified by the discovery that the universe is "expanding"
NOT from some primordial "explosion" (Big Bang) but due
to some "other" reason NOT YET UNDERSTOOD. (The
proposal that it MUST BE some "dark force" is somewhat
like people who do not understand how/why planes fly
suggesting that it MUST BE because of some "dark force"
invisibly holding planes up in the air: It is nonsense which
not everyone has yet realized what utter nonsense it is.
And it is utter nonsense because it violates any number of
physical laws, not least of which is that its WORKING needs
LOADS of energy consumption/conversion which no one
has either observed or proposed how it is taking place. The
proposal of a pushing force acting in the same place and at
the same time as the "pull" of gravity simply insults logic.)

Where did the Big Bang model come from? Einstein asked:
"If there is gravity, why hasn’t the universe collapsed?"
He thought "there MUST be" some force keeping the
universe from collapsing (i.e. counter-balancing the "pull"
of gravity). He called his "MUST-BE pushing force" the
Cosmological Constant. But then Hubble discovered that
the galaxies "appeared" to be moving away from each
other, and Einstein immediately realized the folly of his
Cosmological Constant proposal. Instead another down-
to-earth bit of nonsense was proposed: Wasn’t it the case
here on earth that whenever things expanded from a
common point there had been an explosion at that point?
Ergo, since the universe’ galaxies were seen to be moving
away from each other… they MUST be moving away from
some super-ancient explosion (some really Big Bang).

Never mind that all "explosions" require energy. Never
mind that the creation of matter/energy from nothingness
revives the ancient paradox of a First Cause Uncaused (God).
Never mind thinking/reasoning at all. The Big Bang model
satisfied men’s thirst for a quick, slick answer. And since
people are lazy at everything, but especially about exercising
their brains… the nonsense’s stuck (it’s easier to shout down
objections than to think them through seriously).

- Hide quoted text — Show quoted text -

>Yesterday, Louisiana State
>University astronomer Bradley
>E. Schaefer tossed a grenade
>into this debate, presenting
>new research to suggest that
>the force dark energy exerts
>may have varied over time.
>That casts new doubt on the
>validity of Albert Einstein’s
>"cosmological constant" only
>a few years after astronomers
>rescued the concept from
>scientific oblivion.
>"I’m not pushing this as a proof,"
>Schaefer said in an
>interview at this week’s
>meeting of the American
>Astronomical Society in
>the District, where he presented
>his research. "It’s pointing
>against the cosmological
>constant, but it’s a first result
>describing how dark energy
>changes with time. We need
>more people to test the
>results and get more information."

Well, I for one am glad that it’s so darn hard
for so many to let go of their most cherished prejudices
(they were taught to us all by the fools we love so much,
after all), and to actually see what’s right in front of
their eyes … because that way the joy of being able
to keep telling people that I told them so is multiplied
by the number of dense brains there are out there.

- Hide quoted text — Show quoted text -

>Schaefer based his findings
>on analysis of ultra-bright
>cosmic explosions called
>gamma-ray bursts, detected as
>far as 12.8 billion light-years
>away. He found that the
>most distant explosions
>appeared brighter than they
>should have been if the universe
>were accelerating at
>a constant rate.
>"As you go back in time, the
>universe is pushing [outward]
>less and less," he said. "At
>some point, the pressure of dark
>energy is zero and is exerting
>no force on the universe.
>There is no explanation for it."

NOT in the Big Bang model, certainly. But
consider what the case would be in an imploding
universe: The further back in time you go, the
larger the universe is (i.e. the slower it is imploding).
Now the observation makes sense. And we can
remove all the nonsense about "dark matter."

What "pushing [outward] less and less," in the
paragraph above means is that the acceleration of
the universe’s expansion is "less and less" as we go
"more and more" back in time. At "zero point" there
is no "dark force" at all, and ONLY the pull of gravity
is acting on the universe (so we are effectively back
at the point where Hubble discovered the galaxies
appear to be moving away from each other AGAINST
the pull of gravity … devoid of any reason why/how).
However, now any quick/slick "Big Bang" suggestion
becomes more problematic because most explosions
tend to make things move faster at first and then slower
with time… NOT the other way around, certainly!

My, my…! Wonder how long Big Bangers will hold out.

- Hide quoted text — Show quoted text -

>Schaefer’s findings, the first
>attempt to use gamma-ray
>bursts to study dark energy,
>produced a result that
>disagreed with accumulating
>evidence gleaned from
>observing a different kind of
>blast — the exploding stars
>called supernovae. That work
>suggested that the expansion
>of the universe is accelerating
>in accordance with Einstein’s
>cosmological constant.
>"The idea of using a gamma-ray
>burst as a distance
>indicator is a very exciting one,"
>said California Institute
>of Technology astronomer
>Richard Ellis, a supernova
>cosmologist. "The trouble is
>there are no ways to check
>the techniques. I’m not saying
>it’s no good, but I can’t
>believe it’s as precise as supernovae."
>The concept of dark energy
>emerged in 1999 as a way to
>explain the fact that the
>expansion of the universe, once
>thought to be slowing ever
>since the big bang about 13.7
>billion years ago, was accelerating.
>That resurrected the
>idea of a cosmological constant,
>introduced by Einstein
>more than 80 years ago as a
>"fudge factor" to explain why
>the universe then appeared to
>be in equilibrium, rather
>than being pulled together
>by gravity.
>A few years later, however,
>astronomer Edwin Hubble
>discovered that the universe
>was not in stasis, after all,
>but was expanding. There
>was no "constant." Einstein
>condemned his own idea
>as "my greatest blunder."

Actually, what Hubble discovered was that the galaxies
"appeared" to be moving away from each other.

The idea that this discovery suggested that the universe
is expanding is both reasonable and idiotic, since while
in a very simple way it resembles the way an explosion
here on earth works… it also presents impossible hurdles
to explaining where all that energy came from. [Recently
someone who must have gotten the idea from watching
bedsheets hung out for drying in a yard fluttering in the
wind... suggested the nonsense of "branes" flapping in
the Mind of God or something, which when they touch
create a rupture through which pour all the energy in the
Big Bang--I must say I had to laugh like a mule when I
read it. But that's me, other people actually take this non-
sense quite seriously, I swear to God. Naturally, people
who suggest a God as The Origin "forget" to tell us about
the origin of God, and it's no different here, where they
are happy to explain the origin of our "dimensions" from
some other "dimensions" but they never ever quite get
around to explaining the origins of those other dimensions
--which I assume did not originate from ours.]

>But in the 1990s, astronomers
>found ways to use
>supernovae as cosmic "standard
>candles" whose luminosity
>could be analyzed to track
>the history of the universe’s
>expansion as far back as
>9.8 billion light-years.
>That led to the 1999 discovery
>that the expansion of the
>universe was accelerating
>rather than slowing. There had
>to be some "repulsive force"

THERE JUST HAD TO BE, right?
It just couldn’t be something OTHER THAN
what they were imagining/proposing!

>overcoming the gravity that
>should have been causing
>the universe to come together.
>Astronomers called the force
>dark energy, and "it mimics
>the cosmological constant,"
>said Michigan Technological
>University astronomer Robert
>J. Nemiroff. Einstein may
>have been right after all.

Wonder how many times in all people will repeat
the same error before they finally acknowledge it
as an error and move on to something else…!

>Astronomers estimate that
>dark energy makes up 70 percent
>of the universe, but they do not
>know what it is.

Is it some "invisible hand" holding the plane
up in the air?

>Solving the
>mystery is as all-consuming
>as any passion in physics. "It’s
>so spooky," said Astronomical
>Society President Robert B.
>Kirshner, a cosmology expert
>at the Harvard-Smithsonian
>Center for Astrophysics.
>"Everybody is looking for ways to
>get at it."

If all the seekers are searching
…

read more »

Instead of spending two years by the Europeans to convince Iran to stop
its nuclear program, how much easier it would have been for a M.A.D.
Fleet to have parked off of Iran and even perhaps posed a blockade and
if the Fleet had been fired upon by the Iranians would be mandatory for
the Fleet to regime change Iran.

You see the beauty in this is that if the Fleet were in existence in
the 1990s, that it would have parked off of Iraq and when SH had fired
on any of its airplanes meant mandatory regime change of Iraq, where no
country had to worry and fret about intelligence data or reasons of
going to war and noone had to worry about Iraq after it was regime
changed because the UN has responsibility for that. There is an easy
way of doing any politics and a M.A.D. Fleet would be the easiest,
whereas Bush’s method in Iraq is the most blithering difficult and
costly way.

Same with North Korea, where we park a second M.A.D. Fleet off its
coast and if it is fired upon by the NorthKoreans means we must regime
change there also.

Unless the world installs and trains and practices and promulgates the
tenets of a M.A.D. Fleet, then this planet is going to learn the hard
way about nuclear weapons. Where a nuclear war is virtually inevitable
with about 2 to 3 per century. Where the entire Pakistan and India is
bathed in nuclear warfare and the pollination is spread over the entire
globe.

Remember, it was a M.A.D. Fleet that saved the day for Kennedy in the
Cuban Missile Crisis of the 1960s.

We should have had a M.A.D. Fleet in operation before the year 2000, in
order to stand down Pakistan and India when they were on the verge of a
nuclear war circa 2001 over Kashmir.

There is nothing more urgent, more pressing, more priority for this
planet, than to build and form and practice several M.A.D. Fleets to
hinder and to put the incentive into every country that it is a
liability to ever own or want to build nuclear weapons.

For you see, the M.A.D. Fleet number one tenet is that if a country
launches nuclear weapons the Fleet is mandated to annihilate that
country. That is what prevented the USA and USSR in the 1960s to not
launch. With that Fleet surrounding Cuba, it was likely that WW3 would
have taken place in the 20th century.

Ever since the Berlin Wall came down, we have dropped our guard on the
defence that saved us from nuclear war in the 20th century– the
working concept of Mutual Assured Destruction.

What will convince Iran, convince NorthKorea, convince any tin-pot
despot country from building a nuclear weapon is the threat by a M.A.D.
Fleet that will regime change or annihilate the violators.

Not this 2 years spent by Europeans to talkity talk Iran. Not the
revolving door of talkity talk diplomats and secretaries of state. To
prevent nuclear proliferation requires M.A.D. concept in action.

Time is a wasting, and the further out in time we do not install a
M.A.D. Fleet is virtual guarantee that we will suffer a nuclear war and
the continents polluted with radioative waste.

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies

Hello,
Are _all concepts of set theory expressible / eliminable entirely by
means of quantifiers (I hope that they are, and there are no choices
and trade offs, i.e. "nothing is left to guesswork")?

I am trying to express:

1. 1 a A
2. x e A
3. {x: p(x)}  (as well as)
4. {1, 2, 3}
(5. I know that 1, 2, and 3 will be defined later as the cardinalities
of sets, and that this circularity is most _possibly unavoidable)

by means of quantifiers and variables alone.

And a side question, if some person kindly will, I assume that a
_proper theory of variables can only be expressed in ST (i.e. a proper
theory of variables is set theory). Is that right?

(I am sorry. I seem to be a lousy student, but I do have a hard will.
The TM, i.e. an x86, I produced cost me years, but it was well worth
every second of it. Morever, I would have never built it without this
fine NG.)

Thank you very much indeed for your time.
Tom

Is the following a valid inductive argument, or is it a fallacy?

—————————————————————————-
Premise 1:

Person P once made a shoot-’em-up computer game containing a cheat: one of
the weapons, "The Annihilator", had a hidden secondary function that made
it overly powerful. Only P and P’s friends knew how to activate this
secondary function. Everyone else could still use the weapon, but only with
its primary, legitimate function. It wasn’t easy to tell whether or not a
person using this weapon was doing so legitimately.

Premise 2:

P recently made another computer game, containing a weapon called "The
Annihilator".

Conclusion:

P’s new computer game has a hidden cheat.
—————————————————————————-

Both premises are true, but the verity of the conclusion cannot be
determined.

I’m reading Set Theory from Kunen, and I have some troubles to do following
exercise. Any help will be appreciated!

Assume Con(ZFC), and show the consistency of ZFC- (which is ZFC minus
Foundation) plus the following modified Mostowki Collapsing Theorem: If R is
an extensional relation on a set A, then <A,R> is isomorphic to <M, \in> for
some transitive set M. Note: R is not assumed to be well-founded

Does anyone else blow fuse when ordering caffe latte at Starbucks because at
Starbucks tall = small?

Bryan

A professor walked into class on Monday and stated, "We
will have a suprise exam sometime this week. On the morning
of the exam you will not know that the exam will be that day."

A logic student reasoned with himself like this: "We can’t have
the exam on Friday, since, knowing that the exam must be this
week, we’d know that it would have to be that day. Since we
know it can’t be Friday, then we know it also can’t be Thursday,
since it we’d know on Thursday that it must be on that day because
it can’t be on Friday." This reasoning was extended all the way to
Tuesday. (The exam was not given on Monday.)

What’s wrong with this reasoning?

I believe I saw this in Raymond Smullyan’s "Forever Undecided," but
I don’t know if he created it. I’ve never seen a solution to this,
and would be interested to know if one exists.
—
%  Randy Yates                  % "Rollin’ and riding and slippin’ and
%% Fuquay-Varina, NC            %  sliding, it’s magic."
%%% 919-577-9882                %  
%%%% <ya…@ieee.org>           % ‘Living’ Thing’, *A New World Record*, ELO
http://home.earthlink.net/~yatescr

Hi ,
Can anyone here help me to solve one task from my study. I tried to
find a solution for it by myself but hanged up.
I have a logic function F(A,B,C). After a simplification I received a
simple function as following:
 F(A,B,C)= A XOR C.
I was said to implemented the function with 4*1  MUX and 2*1 MUX. And
it is OK, I did it.
Now I have to implemetent it with  2-to-4 decoder and NAND gate. The
decoder is 74LS139 .
(This decoder has Enable pin) How can I do it ?

Thank you in advance.