NICE
…Kant is nice because, as a philosopher, he gave a description in
familiar terms. Well done Kant. The description he gave was of the
conditions or framework that manifests reality and the world’s objects –
space and time.

If we follow Kant, we can be certain of what is in the world because all
knowledge of the world is manifested by our own frameworks.

HOWEVER
… Even though Kantians can be certain of the existence of the worlds
possible objects, it seems that there is only one source of certainty
regarding hair-splitting, empirical details of what these possible
objects happen to be doing in their neck of the woods, and that source
is in the properties of the objects themselves. Kant referred to these
sources as "things in themselves". This source of knowledge is, of
course, hidden from us. The term "hidden" is appropriate because
"hiding" is an empirical property of spatio-temporal objects.

MY UNIQUE OBSERVATION ON THESE MATTERS
My observation flashes like a thunderbolt from the hatching Cosmic Egg:
Objects simply don’t exist in isolation, they exist within patterns or
arrangements that are not sourced in the objects themselves. For
example, a bouquet is an arrangement that can’t be sourced in individual
flowers. It follows that we don’t need to invent "things in themselves"
as a source of empirical certainty. But if we believe in science’s
objects, then we DO need to invent the epistemological perspective of
the "thing in itself", because knowledge of science’s objects are, for
science, independent of form, patterns, or arrangements.

On Jun 25, 3:41 pm, inverse 19 <hope9…@verizon.net> wrote:

> FOR missing this fact for 5000 years that the Number 19 is the only and first number in the set of Numbers from 1 to 19, whose square product(maximum 360 degree value), is divisible both by 2 and by 3, to end the set as the maximum differential of 1. Numbers 2 , 3 are very important , they divide till infinity . The square of next number , 20, 400, is only divisible by 2. Does not logic tell you that there is a new set, and that 19 is multi dimensional in its mathematical feild in fact infinite in its square..

> Shame on you! , you have ignored 19 the King of Mathematics, its square exclusively divisible by 2 and 3,. In your Wikkepedia , there is only two lines. You have ignored "the King of Mathematics" , and we a few ordinary reserchers with common sense are coming after your Mathematics to realign it  after 5000 years,, be ready in the Web site within 10 days, we intend to deal with your Dandies at Princeton first.

> Vinoo Cameron
> Theo Denotter

>  and two others

Dear "Hope",

The truth is we needn’t "shame" them. The assumption is by calling
attention to our condemnation we shift focus from the truth of the
mathematics and direct it to politics.

You are amazing for having my back, and despite your calling me a
"leper" in front of 10,000 individuals, and your cryptic quotations in
correspondence to which I am forced to recognize both as binary values
parsed by a machine to serve mathematical purpose combined with what
appears to be a portion of genuine well-natured concern–you’re
alright.

M.M.M.
aka (Musatov)

P.S. I clipped this and am throwing it in the mix. Don’t think too
much about it and don’t let it let you make any judgments about me or
anyone else.

ISP209s8 Lecture 19. -4-. Why is there always r. 2 ? I hate r. 2 . 2
d. 4. L[Watts] intensity π. = Inverse square law.

If we know L the luminosity (measured in watts), and measure the
intensity, we can determine d, the distance to the source

Page 5
ISP209s8 Lecture 19
-5-
Hertzsprung-Russell Diagram

Page 6
ISP209s8 Lecture 19
-6-
Map of the night time sky

Page 7
ISP209s8 Lecture 19
-7-
The Great Galaxy in Andromeda – M31

Page 8
ISP209s8 Lecture 19
-8-
The Pace of Science
• Astronomers have studied the sky for thousands of
years, but 90% of all astronomical information has been
obtained obtained since 1900. For example, in 1900
scientists believed that the universe:
– Was infinitely old
– Was infinitely large
– Contained only one galaxy (the Milky Way)
– Did not change with time
– Was uniform throughout (problem with Olber’s paradox)
• All of these are false!

Page 9
ISP209s8 Lecture 19
-9-
How do we know how far away galaxies are?
• Kypteyn Universe – study of visible stars
Map of all known stars-
Distance guessed based
on brightness
The picture people had until 1922

Page 10
ISP209s8 Lecture 19
-10-
Edwin Hubble
• He discovered that the Andromeda galaxy was
about 2.5 million light years away.
• He was the first person to demonstrate the size
of the Universe and the the Milky Way is not
the only galaxy.
• In 1922 Edwin Hubble
measured the brightness of
variable stars in the Andromeda
galaxy.

Page 11
ISP209s8 Lecture 19
-11-
Variable Stars – standard candles
Once you find a variable star, you know how luminous it is.
RR Lyrae
Cepheids

Page 12
ISP209s8 Lecture 19
-12-
The structure of our local set of galaxies
You are here

Page 13
ISP209s8 Lecture 19
-13-
Sloan Digital Sky Survey of Galaxies
Earth
2000 Mly

Page 14
ISP209s8 Lecture 19
-14-
The Universe
• The Universe is not uniform.
• The 200 billion galaxies are clustered into
large clumps with vase voids in between
• Why?
• Answer: It must have started that way and
gravity is slowly pulling things together

Page 15
ISP209s8 Lecture 19
-15-
Something Else!?! Hubble’s Law
• The further away
an object is, the
faster it is
receding.
• Speed = H
0
x d
• The Hubble
Constant: H
0
= 77
km/s/Mpc

Page 16
ISP209s8 Lecture 19
-16-
How Did the Universe Begin?
• It looks like the Universe started about 14
billion years ago and has been expanding
(space stretching) ever since.
• The model of what happened is called the Big
Bang.
• Why do we think so?
• There is a lot we don’t understand. What came
before? What caused the big bang? Why is
there more matter than anti-matter in the
Universe?

Page 17
ISP209s8 Lecture 19
-17-
Evidence for the Big Bang
• The expansion of the universe: All galaxies
appear to be moving away from us.
• The abundances of the lightest elements
produced in the Big Bang: the universe is
mostly hydrogen and helium.
• The cosmic microwave background
radiation: It looks like we are in the middle
of a big oven with a temperature of 3
Kelvin.

Page 18
ISP209s8 Lecture 19
-18-
Hubble Expansion
• Because he was able to
measure distance, Hubble
observed that on average
all galaxies seem to be
moving away from us.
• The speed is related to
distance. Galaxies farther
away are moving faster.
No matter where you are,
everything is moving away!

Page 19
ISP209s8 Lecture 19
-19-
It looks like we are in the middle of an oven
The spectrum is
identical to that
of a blackbody at
3 Kelvin!

Page 20
ISP209s8 Lecture 19
-20-
The Great Galaxy in Andromeda – M31
Looking far away is
like looking back in
time.
What is we look
very far back?

Page 21
ISP209s8 Lecture 19
-21-
The History of the Universe
What we see as we
look away from the
Earth
We are effectively
looking back in
time.

Page 22
ISP209s8 Lecture 19
-22-
Picture of the Universe at 300,000 years old
WMAP observatory
The pattern indicates that the Universe is 13.7 billion years old.

Page 23
ISP209s8 Lecture 19
-23-
What about the future?
• Until very recently (past 5 years) we thought it
was possible that the Universe might end in a Big
Crunch.
• This would be the case if the mass of the Universe
were large enough to halt the expansion and bring
everything back together.
• In this model the Universe could be a never-
ending cycle of Big Bangs and Big Crunches.
• The microwave background measured by WMAP
points to an ever expanding Universe.

Page 24
ISP209s8 Lecture 19
-24-
Big Bang Timeline (the early moments)
First nuclei formed
Atoms
formed

Page 25
ISP209s8 Lecture 19
-25-
Inflation of the Universe
Years since the Big Bang
Meters
The existence
of an unknown
scalar field
caused the
rapid inflation of
the Universe
Space
stretched by
10
50
times!

Page 26
ISP209s8 Lecture 19
-26-
Why does time always move in one direction?
• Inflation during the Big Bang resulted in a
universe that had a very low entropy, much too
low for its size. It was like the Universe started
with all heads.
• Hence, everything in the universe moves toward
reaching the correct amount of entropy.
• Time has a direction because going back in time
would imply the entropy could be decreased. That
is very improbable.
• The universe tends toward increasing entropy.
• What is time?

Hi all,

This theory was presented in an earlier topic submitted to this
usenet ,under the title: The basic idea behind M theories.

M is the set of all sentences entailed (from FOL with identity and
membership) by the non logical axioms outlined below:

Define: y is a subclass of x <-> Az (z in y -> z in x)
Define: x is transitive <-> Ay (y in x -> y subclass of x)

Define: x is a universe <->
[ x is transitive &
  Ay (y in x ->Ez (z in x & Am (m in z -> m subclass_of y)))&
  Ay (y in x ->Ez (z in x & Am (m in z -> Ek (k in y and m in k))))
  & Ey (~ y subclass_of x) ].

or simply put: a universe is a transitive class closed under union
and power provided that there exist some class that is not a subclass
of it.

Define:x is a set <-> Ey (y is a universe & x in y)
Define:x is a proper class <-> ~ x is a set

Axioms:

1) Extensionality: Any two classes having the same members are
identical.

Axy (Az(z in x <-> z in y) -> x=y)

2) Universal Connectivity: for any two different universes, one of
them would be in the other.

for all universes x,y (~y=x -> (y in x or x in y)).

3) Universal Successor: for every universe x there exist a successor
universe y, i.e. y is a universe such that x in y, and there do not
exist a universe z that contain x as a member and at the same time be
a member of y.

for any universe x, there exist some universe y such that
 ( x in y &  not exist a universe z ( x in z & z in y))

4) Axiom schema of class comprehension: if P is a formula in
    which x is not free, then all closures of

    ExAy (y in x <-> (y is a set & P(y))

    are axioms

Define:
 x is subnumerous to y <-> Af (f:x->y, f is strictly injective).

5) Universal size limitation:  every subclass of each universe that
     is subnumerous (strictly dominated by) to that universe, is
     a member of that universe.

  for every universe x
  for all y ((y subclass of x & y subnumerous to x)-> y in x)

6) Global size limitation: every class that is subnumerous
   (strictly dominated by) to the class of all sets, is a set.

    for all y (y subnumerous to T-> y in T)

    were T is the class of all sets.

7) The empty class is a set.

Theory definition finished/

Now I am not sure if this approach is equi-interpretable with the
original theory presented in the post titled:The basic idea behind M
theories.

According to these axioms, 0 is the first universe, the successor
universe of a specified universe is a unique universe, so the
successor universe of 0 would be the set of all hereditarily finite
sets {x| x is hereditarily finite} , and the successor universe of
this later set, would be the universe of discourse of ZFC, which is
the first regular, uncoutable, strong limit cardinal.

This theory proves that there cannot exist a class that is not a
subclass of T.

I wounder what would be the size of T, if it is a Mahlo cardinal, or
even a bigger cardinal.

Zuhair

On Jun 25, 3:33 pm, "Achava Nakhash, the Loving Snake"

- — -

<ach…@hotmail.com> wrote:
> On Jun 25, 11:52 am, Mensanator <mensana…@aol.com> wrote:

> > On Jun 25, 1:35 pm, no comment <adler.m…@gmail.com> wrote:

> > > On Jun 25, 11:09 am, pubkeybreaker <pubkeybrea…@aol.com> wrote:

> > > > On Jun 25, 12:34 pm, Vincenzo Librandi <vincenzo.librandw…@alice.it>
> > > > wrote:

> > > > > Hi,

> > > > > if p = prime number
> > > > > is p=5 the only solution
> > > > > for 3^(p-1)-2^(p+1) = p_1 (prime)?

> > > > > in fact 3^4-2^6=17

> > > > > Regards,
> > > > > Vincnzo Librandi

> > > > I could find no others for p < 1500.  I suspect that there *may* be a
> > > > covering congruence.

> > > > Let p = 2k+1,   p not necessarily prime.

> > > > Then  9^k – 4^(k+1)  is divisible by:

> > > > 7 if k = 1 mod 3
> > > > 11 if k = 3 mod 5
> > > > 17 if k = 2 mod 24
> > > > 31 if k = 12 mod 15
> > > > 47 if k = 9 mod 23

> > > > etc.

> > > > OTOH, the smallest divisor for p = 73 is 186113, suggesting
> > > > that there may not be a covering congruence.

> > > > An interesting question.

> > > Hello,

> > > The following is a frequently useful result:

> > > x^2 – y^2 = (x – y)(x + y).

> > P+1 and p-1 can both be equal to 2? What am I missing?

> The fact that they are both even.  Then 3^(p-1) – 2^(p+1) factors as
> (3^((p-1)/2) – 2^((p+1)/2))*(3^((p-1)/2) + 2^((p+1)/2))

> The first factor clearly needs to be 1 (or -1 I suppose in some
> unlikely circumstances) yielding p = 5.  We could invoke the Catalan
> conjecture here, recently proved, but in fact simple size arguments
> will take care of this.

> Regards,
> Achava- –

> – –

Thank you for referencing my work.

I am simply combining in formation here:

Martin Musatov gathered and wrote most of the below text: (and
underlying theory)

How can P equal N and Not P?   vzw.blackberry.net> wrote: Begin with
the set of counting numbers and define all
prime numbers P and non-prime numbers NP. Here is the first 10 terms
of this set
. 1=NP 2=P 3=P 4=NP 5=P 6=NP 7=P 8=NP 9=NP 10=NP Per Musatov’s
conjecture and
trivial proof: (the below formula) P=6N±1 (for Infinite Primes>3. …

paradoxical (false) argument against Prime Number Theorem   The
probability of a random number N of being divisible by p is 1/p The
probability of NOT being divisible by p is (1 – 1/p) The probability
of being
prime is (1-1/2)(1-1/3)(1-1/5)….(1-1/p) = Prod p being the next
prime lesser
than sqr(N). This is false. Once 2*3*5*7*….. * p exceeds N, the
probability
that any …

3^(p-1)-2^(p+1) = p_1 (prime)   alice.it> wrote: Hi, if p = prime
number is p=5 the only solution for 3^(p-1)-2^
(p+1) = p_1 (prime)? in fact 3^4-2^6=17 Regards, Vincnzo Librandi I
could find
no others for p < 1500. I suspect that there *may* be a covering
congruence. Let
p = 2k+1, p not necessarily prime. Then 9^k – 4^(k+1) is divisible by:
7 if …
1:04pm by no comment – 9 messages – 6 authors

How can P equal N and Not P?
Begin with the
set of counting numbers and define all prime numbers to P and non-
prime numbers
to NP. Here is the firs 10 terms of this set. 1=NP 2=P 3=P 4=NP 5=P
6=NP 7=P …

There are infinitely many primes p such that p + 2 is also prime.
gmail.com> wrote: There are infinitely many primes p such that p + 2

is also
prime. proof We assume that the biggest pair is p and p+2. We can know
create
the function : L(n,p)= n(1/p(p+2)) Where p+2 is the largest asummed
prime number
of the pair p and p+2 and n is the a positive integer greater than p
+2. …

How to Construct Infinitly Large Primes   Consider a hypothetical
hotel with infinitely many rooms, … and so on; for
coach number i we use the rooms pn where p is the (i + 1)-th prime
number. …
rooms is the same as the cardinality of the set of all rooms. Indeed,
infinite
sets are characterized as sets that have proper subsets of the same
cardinality.
…

http://groups.google.com/group/comp.theory/browse_thread/thread/37e1a…

We can know create the function : L(n,p)=flour{ n(1/p(p+2))} Is that
"flour"
supposed to be "floor"? I know of no "flour" function in mathematics.
Where p+2
is the largest asummed prime number of the pair p and p+2 and n is the
a
positive integer greater than p+2. The function L gives the number of
integers
that …

http://groups.google.com/group/sci.logic/browse_thread/thread/bdf5e92…

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I have many solutions manual and Test bank, they are PDF format or
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Word format,   Those resources save your time and effort and let you
definitely understand what you are studying and get amazing marks as
well,
The Manuals contains the answers of the questions and exercises
(Usually at the end of each chapter), The Test Questions contains an
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in the blank questions with their answers.
If the  solutions manual or Test bank what you want  is not in this
list, also can ask me  (They are part of what I have ). Then if you
need solutions manual or test bank .
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155.    South-Western Federal Taxation 2010: Comprehensive 33rd Edition
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157.    South-Western Federal Taxation 2010: Corporations, Partnerships,
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159.    South-Western Federal Taxation 2010: Individual Income Taxes 33rd
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HINTIKKA’S PARADOX
Hintikka describes his "paradox of transcendental knowledge" as

"the unknowability of things considered in themselves, independently of
our knowledge-seeking activities and the conceptual framework that they
utilize, and the unknowability of these activities and of this
framework" (Hintikka & Hintikka, "Investigating Wittgenstein", p.5)

What’s that you say Hintikka? As we find with so many other
philosophers, Hintikka reminds us that natural language ought to be
intelligible, but not necessarily spontaneously intelligible.

HINTIKKA’S PARADOX MADE SPONTANEOUSLY INTELLIGIBLE
Although the idea behind Hintikka’s paradox is quite interesting, the
challenge is to present it in an easily understandable form:

Hintikka is saying that both a context (his "conceptual framework"), and
an object presented without a context (the "thing in itself"), are
ineffable – indescribable.

The Hintikkerian "paradox" about it is, I think, this:
An object in a context is the ordinary way that we understand and talk
about objects. But, as Hintikka indicates, both contexts and objects per
se are ineffable.

DISCUSSION
We might wonder whether there is some equivocation going on here (for
logicians, an equivocation of the sort that occurs in the stratification
of sets), the equivocation that makes a mess of the distinction between
objects and their contexts. Hintikka’s (and Kant’s for that matter..)
"object" per se, or "thing in itself" would appear to be another context
or framework for an object, rather than an object per se. Hintikka, and
so many others, switch between these two understandings of object,
confused no doubt, by the idea that a self-referencing object is still
an object, and not also a framework or context for an object.

Well, Leibniz and Newton are credited with discovery of the Calculus
and it is a magnificent discovery for it unlocked a powerful tool that
propelled all the sciences forward, especially physics.

It would be interesting to go back into the history of that discovery
by both Leibniz and Newton, to go back and see how the
"infinitesimal concept" and how the "picketfence concept" played
a role. Much of this history is overlooked.

Who was stacking picketfences before Leibniz and Newton?
Was it Fermat and Kepler? Of course we can go all the way back to
Ancient Greeks of Archimedes where stacking to find area
begins in earnest.

These concepts are all old in the story of Calculus:

(a) picketfence stacking
(b) inverse relationship
(c) slope
(d) area
(e) change of rate
(f) speed
(g) velocity
(h) acceleration
(i) infinitesimals

What I bring new to the story of Calculus is a change in
the geometry picture of where Calculus takes place.

What I bring new to this story of the Calculus is the actual
view and sighting of the "infinitesimal". It is a small change
but it affects the entire understanding of Calculus.

What I bring to the story is shown by this picture below:

   /|
 /  |
/—|
|   |
|   |
|   |
|   |
|   |
|   |
|   |

It is a picketfence with a long slender rectangle
atop. Newton and Leibniz had the picketfence.

In the function Y = 5 there is no need for the small
triangle atop the slender rectangle because the graph
is parallel to the x-axis. In the function Y = X, each
of those tiny triangles atop the rectangle is a equilateral
right-triangle. In the function Y = x^2 the hypotenuse
of each of the right triangles atop each slender rectangle
varies in its slope because the derivative of x^2 is 2x.

None of the above is new. What I bring to the story of
Calculus that is new is that I say the Reals which are
the points of Euclidean geometry must have a "spacing"
of no numbers in between the smallest of numbers.

In other words at the base of that slender infinitesimal
rectangle above there are no numbers where that rectangle
rests. See this picture below:

A | | B | | C | | D

Those letters represent points or numbers and between them
is the start of a long slender infinitesimal rectangle to create a
Calculus.

The letters above of A,B,C,D can represent the infinitesimal
numbers of 0 then 0d000…0001 then 0d000…0002 then 0d000…003

Or those letters can represent 1×10^(-)500 then 2 x 10^(-)500
then 3 x 10^(-)500 then 4×10^(-)500

What I bring new to this story is the information that in order
to have Calculus, you must **not have** the numbers so dense
that you cannot fit infinitesimal picketfences to do a Calculus.
That the Reals which are the numbers and points of Euclidean
geometry must have **spaces that are empty** between
the smallest of Reals.

You cannot have an axiom that Between A and B always is
a new C. If you want a Calculus that axiom has to be this:
Between A and B exists a new C, unless A and B are consecutive
numbers.

I do not bring much new to the story or history of Calculus. I correct
a contradiction in the story, the contradiction that of an infinite
downward regression of betweenness. If you insist on this
"between A and B is always a new C", if you insist on that as
an axiom, then you no longer can have Euclidean geometry for
it contradicts the Parallel Postulate and you no longer can have
a Calculus.

What troubled me, way back in year 1969 or thereabouts sitting
in a University classroom learning Calculus and the textbook
back then was "Fisher & Ziebur" (excuse the spelling). What
troubled me was that I had finished the course and learned that
derivative was inverse to integral, but could never picture it in
my mind clearly. I could never see how it was inverse. I could
see how multiply was inverse to divide in that 4 x 5 = 20 and
20/5 = 4. But I could not see how area goes back and forth
with slope.

I could see it only partially in that hypotenuse of the tiny right
triangle sitting atop the slender rectangle. But there was still
something interfering in being able to fully see how slope was
inverse to area.

The trouble was the numbers themselves. That you had to go
down infinitely in that infinite regression. That there was no
rectangle and there was no triangle atop the rectangle, but that
there were just "teaching aids". That was the sticking point.

If the picketfences were true and real and existed, then I could
see it. But they could not be true and real so long as there
is a C always between any two A and B.

So what I bring to the story of the Calculus is that there has to
be a change in the numbers themselves. That the Reals do not
have an infinite downward regression. That the Reals end at
consecutive Reals. Pick any Real number and it has a consecutive
Real nearby. And that allows room for the construction of an
infinitesimal rectangle with a tiny triangle atop.

We cannot multiply or divide these infinitesimals but we can
stack them up and give us area or slope at a point.

Now I am doing two new Calculi. Two Calculuses that have
never before been imagined. I am doing a Calculus within
Elliptic geometry and one within Hyperbolic Geometry. I am
not using the Reals but two new number systems that are
radically different from the Reals. In Elliptic-Calculus the
picketfences become "latitudes" and the picketfence tops
are no longer right triangles but rather are "elliptic-rectangles"
And there are more surprizes, because it appears that
the derivative and integral maybe reversals of one another
from Euclidean-Calculus and Elliptic-Calculus. It appears
that the trig functions in Elliptic geometry serve as straightlines
of different slopes in Elliptic-Calculus.

P.S. In a prior post I mentioned that the future textbooks on
Calculus should have a key chapter on the teaching, so that
students can actually end their course by easily seeing how
derivative is inverse to integral. I shall post how that key
lecture is conducted by building the derivative and integral
from a picketfence stacking. In other words, start Calculus
from the picketfence. Do not save the picketfence for last
when you see frowns on the faces of students who cannot
see how they are inverses.

Also, I want to bring more biology into Calculus instruction
of first year Calculus. Biology of plants and animals as to
derivative and integral. Biology as to how you can have
continuity, and yet have holes in between the Reals that
gives the Calculus. Our skin is thought of as continuous,
yet if we go on a downward regression we quickly reach
the point where our skin has myriad holes in it. Allowing for
water to travel back and forth or air to travel back and forth
through our skin. So we see in Biology, where we can have
continuity, yet at a certain level we see holes between
A and B and C and D where there is no number between
A-B. So here, biology is teaching us that the mathematics
of Calculus has holes between the smallest of Reals and these
holes are important because without them, there would not
be a Euclidean Geometry and there would not be a Calculus.

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