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 Posted: Fri Jul 11, 2008 7:46 am Post subject: #571 Prime numbers-- are they illusionary concepts in math o |
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I am beginning to recall how I departed the condition of this book
last Sept, in that I had made considerable
progress on many fronts. One of those fronts was the idea that only
multiply, divide, add, subtract are
fundamental features of numbers and that features or characteristics
of numbers such as rational versus
irrational or prime versus composite were not really features of
importance or even of meaning.
Let me describe a situation in physics, where we consider a feature of
matter as its smell or its taste
or its color or its sound. Now many of those features sort of make
sense, especially to nonscientists.
But when it comes right down to it, none of those are fundamental
features of matter. Fundamental
features of matter are things such as mass, or atomic number, or
electron configuration.
So, now, let us ask a question. Is primeness a fundamental feature of
the Natural Numbers or is it
a secondary feature that eventually makes no sense in Infinite
Integers.
Whilst doing the first edition of this book, I slowly became aware
that the feature of Rational versus
Irrational is not fundamental to the Reals, for I began to find
numbers that are neither rational nor
irrational. The Real Number 1.0000....000001 is neither rational or
irrational. So when you find something
like that, you begin to realize that all this time spent on these
concepts of Rational versus Irrational
or Prime versus Composite were simply forays into fetish fascinations,
and not something deep and
meaningful about mathematics.
Now what about prime numbers? I cannot give you an example of a
Counting Number that is neither
prime nor composite (other than 1 as unit). But the longer I spend
time on Infinite Integers, I feel someday
soon I will hand over a Counting Number that is neither prime nor
composite and just like
1.000000.....000001 is neither rational nor irrational.
What I am driving at here, is that our concept of rational,
irrational, prime and composite are not really
concepts of mathematics but are human fascinations of perceived traits
and characteristics but have
no basis in reality.
We can dream that atoms have smell and believe they have smell, but
smell is not a characteristic
of atoms.
One example shatters the concept of Rational versus Irrational in
Reals. One example is all it takes
to shatter the concept of "prime" in mathematics. What about this
number ....1413121110987654321
is it prime or composite? Can it be neither?
What about this number 100000.......0000001? Looks prime and
composite. Or take the example
of square root of negative 1 in 5-adics, that number is neither prime
nor composite.
What I am saying is that we never stood back and looked at the big
picture of math as to whether
concepts such as prime are really meaningful, or are they more of a
human fetish fascination
of some minor trivial aspect of math that is not even an intrinsic
feature of math.
This much is certain, all numbers are interesting and no numbers are
more interesting than others.
So that 4 is just as interesting as 3 or 5.
I have the hunch that primeness is not a fundamental feature of
mathematics.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies |
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Raphanus
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| Posted: Fri Jul 11, 2008 8:11 pm Post subject: Re: #573 Primeness and Rational/Irrational are subjective fe |
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On Jul 11, 1:07 pm, plutonium.archime...@gmail.com wrote:
| Quote: |
Raphanus wrote:
On Jul 11, 3:46 am, plutonium.archime...@gmail.com wrote:
(snipped)
Thanks for your comments. Not too long ago I held the same beliefs as
you about
primeness and about rational versus irrational. But when one examines
mathematics
with the Reals as "all possible digit arrangements" of rightward
strings and the
Natural-Numbers as "all possible digit arrangements" of leftward
strings.
Or, alternatively, examines all of mathematics as either Euclidean
versus Elliptic + Hyperbolic
Then many to most of our old beliefs vanish as what can be called a
fanatical fetish. Our
attached importance of "primeness" or of rational versus irrational
are akin to attaching
importance to the color of white fur to a cat. A white furred cat
means almost nothing compared
to the whole of the science of biology. And for mathematics and
mathematicians spending so much
time on questions of prime or irrational is like a person breeding for
white cats and then calling themselves
some great biologist.
I was very much surprized that "primeness" held up so well as it did.
But now that I am trying to
make sense of the last primes in the 99999....999999 series, I am
slowly realizing that "primeness" was
a homomorphism. You know how we humans love to look at rock cliffs and
try to make out a face
in the rocks, where a gap is an eyeball and a protrusion is a nose,
that sort of thing. Well, primeness
in mathematics is almost just as shallow of a reality as the face in
the rock cliff.
When your numbers for Natural Numbers are 0000.....00000 then
0000....00001 then 0000....00002
etc etc and never any number such as 2222....222221 those zeroes
easily can hide the fakeness
that is primeness. But when you bring together all the Natural-Numbers
such as 9999...99999
then 9999....999998, then 99999.....99997 all the way down to
0000....00001 then 0000...0000
you begin to realize that primeness was this homomorphic fascination
over something that
was never intrinsic in mathematics. Primeness was like the face in the
rock cliff.
"1.000000.....000001 is neither rational nor irrational."
Well I should have elaborated on that. When we have "all possible
digit arrangements"
for Reals and the same thing for Natural-Numbers, where the only
difference is that Reals
are strings infinite rightward and Natural-Numbers the opposite
direction, well, then, both
sets are equinumerous and comparable.
And since 99999.....9999999 is not equal to 1, we must have
0.99999....9999999 is not equal
to 1.0 Thus we must have 0.9999....99999 + 0.0000....00001 = 1.0
Since there exists this number in the Reals of 0.0000....000001 and is
the counterpart to
the number 00000.....000001 (commonly called 1) in Natural Numbers.
Then there is a
Natural Number of 10 which has a counterpart in Reals as
0.00000.....0000010
This number in Reals of 0.00000.....0000010 is neither rational nor is
it irrational. It breaks
apart the definition of rational and irrational. It is only one
example of a Real Number that
breaks the definition of rational, irrational.
What mathematics never had previously for Reals was the concept of
Frontview versus
Rearview or endview. When you have Frontview, the concept of rational
versus irrational
dissolves away.
When mathematicians ignore Frontview, what they really are doing is
sweeping their dirt
under a carpet.
because the dots aren't filled in and thus it is undefined. If one
fills in the dots as in
The dots in my arguments or discussion have no bearing on the
substance of the ideas.
What destroys rational versus irrational is that the Natural Numbers
are equinumerous
with Reals and there is a Frontview to both.
1.000001 = 1000001/1000000 ( a rational number)
Well that is all fine and dandy because your Real of 1.000001 is
actually
1.00000100000......00000 and where you chose to ignore all of those
zero
digits righwards of the "1" digit.
But, there is a Real Number 1.0000......000000010 just as there is a
Natural
Number 100000......0000010. Both exist, because they are one amoung
All Possible Digit Arrangements. And the Real example is neither
rational
nor irrational.
or one could say that (to be indefinite)
1.00....001 = 100....001/100....000 ( a rational number)
If one knows how many dots there are one can give the rational
equivalent.
The dots are not the problem. The problem of the past was to say "we
define things
only if we make them finite" and anything that is infinite in expanse
we simply ignore,
sweep under the rug or call it nonmath.
Color and smell are subjective - there are those of us who are color
blind. (How do I know my "blue" is the same as your "blue?" (we could
quantitize a color as a frequency of EM wave - and then have a basis
for comparison - but I stray.) One could communicate the definition
of "primeness" to an alien intelligent life form and they would agree
with us that 7, for example, is prime. Primeness is fundamental.
Yes, and calling a face in a rock cliff is also subjective. And the
mathematics of
Prime and Rational versus Irrational is not mathematics but an
exercise in subjectivity.
Archimedes Plutoniumwww.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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"But when one examines mathematics with the Reals as "all possible
digit arrangements" of rightward
strings and the Natural-Numbers as "all possible digit arrangements"
of leftward strings."
And why would we do that? Progress is made by agreeing to common
definitions so that communication can take place. If I call "1," "2"
we couldn't communicate. We must work with definitions that we agree
on. It is no act of genius to redefine something and then claim great
insight. |
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Guest
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| Posted: Sat Jul 12, 2008 6:14 am Post subject: #575 the great new tool of mathematics-- FrontView; new text |
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Raphanus wrote:
| Quote: |
"But when one examines mathematics with the Reals as "all possible
digit arrangements" of rightward
strings and the Natural-Numbers as "all possible digit arrangements"
of leftward strings."
And why would we do that?
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Because the two sets of numbers are then related. So if infinite
rightward
strings gives Euclidean geometry, then infinite leftward strings
should give
Elliptic + Hyperbolic geom yielding again Euclidean geometry.
When a mind is satisfied with status quo, progress is never made.
| Quote: |
Progress is made by agreeing to common
definitions so that communication can take place.
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Not really, progress is made more from the introduction of new tools
to use in
a science. One of the new tools I introduced is "Frontview". Frontview
is such
a powerful new tool that it has already questioned the validity of
primeness
and rational versus irrational.
Agreement in science is not what makes science advance but rather
mostly
serves the function of bringing aboard the dumber scientists (like
you) in the field.
| Quote: |
If I call "1," "2"
we couldn't communicate.
|
Your problem is that you understood little of what I wrote. You come
to my threads out
of curiosity but come to them with a feverish pitch of closed
mindedness, not wanting
to understand anything that I write. And as usual, in your second
post, you show your
lack of understanding and also your low opinion of me comes to the
fore. People like you
are predictable in your replies to me. Your first post asks a question
with no signs of your
acid hatred of me, but your second post shows your acidity.
The number 1 in my scheme is 0000....00001 which is the number 1 all
along as per the
old math. It is that you and the old math never recognized the zeroes.
So try understanding what I write before you lambast.
| Quote: |
We must work with definitions that we agree
on. It is no act of genius to redefine something and then claim great
insight.
|
It is an act of genius to discover a new tool. The new tool of
"Frontview". This is a new and
great tool because it questions old concepts such as primeness,
irrational/rational. Frontview
questions the validity of many old math theorems.
Frontview is simple and obviously true. Just because something is
infinite, does not mean we can
only talk or view it from one of its ends. We can talk and view it and
make conclusions about the
entity from both ends of the entity. So, Raphanus, are you like the
other hatemongers of Archimedes
Plutonium that can only spew hatred and never congratulate me over a
accomplishment. Are you
as blind of hatemongers as them?
Frontview is so powerful that it will revolutionize and re-energize
mathematics. It takes a genius
to discover Frontview and to recognize that a infinite number or
infinite object can have both a
Frontview and a Rearview. Something that you, with your low opinion of
me, could never do.
And something that you could never accept nor understand.
Your problem is the problem of the majority of scientists around the
world. That anything new
and true, is never acknowledged by any one of your types because you
lack the science ability
to judge. And only after my work is judged true and printed in some
journal fifty years later can obtuse scientists like yourself come to
say "he had it right".
Sad to say that most scientists "truth scheme of the reality of the
world" sadly hinges on
whether the idea is in print in some newspaper or magazine. If not in
print saying "this is true"
then these rumdummy scientists cannot accept the new idea.
So do not tell me how science works for you are a poor and lousy
practitioner of science.
So, Raphanus, if you had any science brains, why did you not discover
"Frontview"? Judging
from your post, I would dare say you have no discoveries in science at
all. Funny, how a man
with zero discoveries (in my opinion) would dare judge me who has
over 100 new discoveries.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies |
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David R Tribble
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| Posted: Sat Jul 12, 2008 7:08 pm Post subject: Re: #573 Primeness and Rational/Irrational are subjective fe |
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Archimedes Plutonium wrote:
| Quote: |
"1.000000.....000001 is neither rational nor irrational."
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Raphanus wrote:
| Quote: |
because the dots aren't filled in and thus it is undefined. If one
fills in the dots as in
1.000001 = 1000001/1000000 ( a rational number)
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Archimedes Plutonium wrote:
| Quote: |
Well that is all fine and dandy because your Real of 1.000001 is
actually
1.00000100000......00000 and where you chose to ignore all of those
zero digits righwards of the "1" digit.
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It's not from clear your posts if all those zeros actually make
a difference or not.
Does ignoring all those rightmost digits change the meaning
of the number? Does adding a whole bunch of zero digits to
a number change its value?
Is 1.000...000 equal to 1, or not?
Is 000...0001 equal to 1, or not? |
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| Posted: Sat Jul 12, 2008 11:56 pm Post subject: #578 clarity on a Real Number that is neither rational nor |
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David R Tribble wrote:
| Quote: |
Is 1.000...000 equal to 1, or not?
Is 000...0001 equal to 1, or not?
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Yes.
Now let us look at two different numbers
Real: 0.00000.....0000010
and
Natural-Number 00000.....00000010
The Natural Number is your normal everyday 10. That Real number
however is a strange one.
It is no Real Number that mathematicians have ever tackled before I
discovered FrontView.
The smallest Real Number that exists is this Real Number:
0.00000.....000001 and is only
one metric distance away from the Real Number 0. The smallest Natural-
Number is one metric
unit away from 0 and is the number 1.
So, now the question arises is this Real Number 0.0000....000010 a
rational or irrational Real
number? It is neither rational nor irrational. The definition of
rational and irrational break down
when mathematics defines the Reals as All Possible Digit Arrangements
of infinite rightward strings.
The Real Number 0.99999.... is no longer the bogus belief that it is
equal to 1. This is true, however,
0.9999....999999 + 0.0000....000001 = 1.0
So, David, when Reals are taken as the set of all possible digit
arrangements of infinite rightward strings
what happens is that the concept of Rational Reals versus Irrational
Reals no longer holds up, it dissolves.
There are many Reals which no longer obey the definition of Rational/
Irrational.
Now for Natural Numbers and we start them off as All Possible Digit
Arrangements of Infinite Leftward
strings. We get a new result, that was denied by the old math with
their old fogey mathematicians. We no
longer have heirarchies of infinity by Cantor. There is only one type
of infinity where the cardinality of
Reals is the same as the Natural Numbers. But we lose something which
before we thought was
intrinsic in the Natural Numbers. We lose the concept of prime. Just
as Reals dissolves the concept of
Rational versus Irrational, the Natural Numbers loses primeness.
Now a few days ago I ranted a spiel about irrational-Natural Numbers
such as ....1413121110987654321
saying that I could manufacture an infinite supply of Twin Primes
using that as the rootstock and grafting
twin-primes onto its base of irrational string. And later on you piped
into the conversation with the
irrational Natural Number of 39000039000390039 saying that you thought
it looked divisible by 3. So we
have a example of an Irrational-Natural-Number that is composite. So,
now, we have to ask is this
Irrational-Natural-Number prime or composite .....1413121110987654321.
I thought it was prime, without a doubt.
But if you examine the p-adics, of the old fogey mathematics, what you
find is that there are no primes
in p-adics except for the base prime of 5 in 5-adics. So you have
irrational-p-adics such as square root
of -1 but even that is not a prime in 5-adics.
So what this tells me, is that the notion or definition or concept of
prime breaks apart and is no longer
of any meaning in Natural Numbers. It breaks apart because of infinite
length of digits. We can have
rational/irrational Reals if we give up the notion that a Real number
is infinite in length, likewise for
prime in Natural Numbers.
For Reals to be infinite, you must abandon rational/irrational.
I am not yet sure, but suspect the number ....1413121110987654321 is
neither prime nor is it
composite. It is what is called Champernownes number as a Real
designated number, and here I
represent it as a Natural Number. Possible way of proving it is
neither prime nor composite is to see
how the various p-adics handle it.
Another way of proving that primeness has no meaning in mathematics,
is the route of geometry in
that the surface of a sphere hold both prime numbers and composite
numbers to make up the surface.
So if some numbers are special than other numbers means that primes
should show themselves
as something special compared to the numbers around them. But every
point on a sphere is important
and no more special than any other point.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies |
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| Posted: Sun Jul 13, 2008 12:45 am Post subject: #579 some history of Frontview on the Internet; new textbook |
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--- quoting #299 post in the series ---
Newsgroups: sci.math
From: a_plutonium <a_pluton...@hotmail.com>
Date: Wed, 14 Nov 2007 22:11:13 -0800 (PST)
Local: Thurs, Nov 15 2007 12:11 am
Subject: #299 All Possible Digit Arrangements gives order and pattern
to the Reals and makes them Countable; new textbook: Mathematical
Physics (Reals & Counting Numbers/AP-adics Primer) for age 6 years
onward
Jesse F. Hughes wrote:
| Quote: |
David R Tribble <da...@tribble.com> writes:
David R Tribble writes:
I guess you're right - I don't understand what all that is
supposed to mean. I can see what those rightmost digits
mean:
...00054321 =
1x10^0 + 2x10^1 + 3x10^2 + 4x10^3 + 5x10^4
+ 0x10^5 + 0x10^6 + 0x10^7 + ...
But I can't make any sense out of the leftmost digits.
Could you express the number 9876000...00054321 in
the form of a sum of digits and powers of 10?
Otherwise I can't make any sense of where those leftmost
digits are supposed to mean mathematically.
Jesse F. Hughes wrote:
Golly, are you just slow or what?
|
He is more concerned about finding me wrong on something than the
pursuit of
mathematics.
| Quote: |
The number is
1x10^0 + 2x10^1 + 3x10^2 + 4x10^3 + 5x10^4
+ 0x10^5 + 0x10^6 + 0x10^7 + ... + 5x10^{oo - 4}
+ 4x10^{oo - 3} + 3x10^{oo - 2} + 2x10^{oo - 1}
+ 1x10^oo
Duh.
|
Pretty good, but we can replace the infinity symbol with the world's
largest integer 999....99999
| Quote: |
I guess I'm just not up to big thinking like AP.
I guess it's that magical "..." part in the middle that bothers me.
|
My vote is that you remain in the conversation for although it is very
negative towards me, I still seem to thrive better in a negative
environment
than a yes-man environment of praise.
| Quote: |
I know you and me and a lot of others went through all this
some time ago with Tony Orlow over his infinite "T-riffic"
numbers, and it's all starting to sound like the same monotonous
tune, like deja vu all over again.
Except that AP discovered FrontView.
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Well that is one nice feature of the Internet newsgroups is that it
can validate and
sort out priority of discovery and I knew that I had discovered
frontview first.
--- end quoting last years post in this book ---
So the Internet can sort out priority of discovery. I had discovered
FrontView sometime
in the early 1990s when I posted the largest Natural Number of
9999...99999 and although
I did not state FrontView, the mere fact that I posted 9999....99999
instead of ...999999
signifies that FrontView was borne when I posted 9999....9999. I did
not realize its
vast importance as a tool of mathematics until 2007
The logic is quite simple. Any given infinite entity can be said to
have a front section, a middle section
and a rear section. Think of a cat as a infinite number. Are we going
to spend all our time on cats talking
only about the hind quarters and tail. Or would it make more sense to
focus on the head region. To think
that in mathematics, because a number is infinite, that you can only
talk and work on the hind quarter
region of the number is rather ludicrous. Although it is infinite, we
can shift focus on the frontview of the
number.
A number like this ....999999 we can easily focus on its frontview as
9999.....9999. But a number
like this .....151413121110987654321 well, we have a hard time of
focusing on its frontview even though
we suspect it has alot of 9s digits.
What makes it very exciting is that FrontView has alot to say about
Reals. If I divide 3 into 1, is the
answer really 0.33333..... which implies 0.3333.....333333 Well,no,
because 3 divided into 1 constantly
leaves a remainder of a 1 carryover.
3 divided into 0.9999..... is precisely 0.3333....33333
but 3 divided into 1.000....... is not 0.33333..... and is not
0.333....33333
it is actually 0.333....33333r where the r signifies a residue
carryover of 1.
And that is the crux of the flaw of so called proofs that claim to
prove 0.9999.... is equal to 1.
that is a false proof.
So these two concepts open up brand new vistas into mathematics
(1) All Possible Digit Arrangements
(2) FrontView
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies |
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