Discussion:
Dark Numbers (8)
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WM
2020-11-20 12:24:12 UTC
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What Caused this Acceptance?

How did the belief emerge that there were actually infinitely many natural numbers following upon every natural number, all of them were definable, but between all these natural numbers and ω nothing was existing?

First, it is clear that in potential infinity infinitely many natural numbers are following upon every defined natural number. Alas there is no ω. But set theorists are eagerly concerned with blurring the difference between potential and actual infinity. Many even deny that there were any difference.

On the other hand, many students of mathematics are attracted by counter intuitive statements and may be even quite a bit proud of being able to "understand" that stuff. Further the gateway drug is not that strong: For the moment they are taught harmlessly that every natural number is followed by a larger natural number, but that no natural number is larger than all others. And with the plausible explanation that everybody has a mother, but there is no mother of everybody, the argument appears not problematic.

If in the gapless sequence of ordinal numbers, on the "ordinal axis", one ordinal is missing before ω, then this gap is not standing out. It occurs in the infinite and its position cannot be verified anyway.

After this little gap has been swallowed, the dose can be increased. Then ℵo gaps of missing numbers will soon be accepted. And the recognition that in any case there are more numbers missing between n and ω than are existing before n enters an immunized brain that considers every sceptic simply as incapable of receiving the higher ordinations of infinity.

Yet the understanding of the potentially infinite class of definable numbers should appear counter intuitive enough. This class can be arbitrarily increased without end whereas the class of dark numbers can be decreased infinitely but without losing its actually infinite size.

A lecture about this topic will be given on Saturday, 21 Nov, 6 PM c.t. here:
https://hs-augsburg.zoom.us/j/92096767073?pwd=aG1DUzJOdnFqTzNTYk1FU0RFQUZ0QT09

Regards, WM
Gus Gassmann
2020-11-20 14:40:13 UTC
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Post by WM
What Caused this Acceptance?
How did the belief emerge that there were actually infinitely many natural numbers following upon every natural number, all of them were definable, but between all these natural numbers and ω nothing was existing?
First, it is clear that in potential infinity infinitely many natural numbers are following upon every defined natural number. Alas there is no ω. But set theorists are eagerly concerned with blurring the difference between potential and actual infinity. Many even deny that there were any difference.
On the other hand, many students of mathematics are attracted by counter intuitive statements and may be even quite a bit proud of being able to "understand" that stuff. Further the gateway drug is not that strong: For the moment they are taught harmlessly that every natural number is followed by a larger natural number, but that no natural number is larger than all others. And with the plausible explanation that everybody has a mother, but there is no mother of everybody, the argument appears not problematic.
If in the gapless sequence of ordinal numbers, on the "ordinal axis", one ordinal is missing before ω, then this gap is not standing out. It occurs in the infinite and its position cannot be verified anyway.
After this little gap has been swallowed, the dose can be increased. Then ℵo gaps of missing numbers will soon be accepted. And the recognition that in any case there are more numbers missing between n and ω than are existing before n enters an immunized brain that considers every sceptic simply as incapable of receiving the higher ordinations of infinity.
Yet the understanding of the potentially infinite class of definable numbers should appear counter intuitive enough. This class can be arbitrarily increased without end whereas the class of dark numbers can be decreased infinitely but without losing its actually infinite size.
And at the end of this entire diatribe it once again comes down to what has been clear all along: Infinity leads to results that are perfectly logical, yet seem counter-intuitive. Intuition that works well for finite things cannot necessarily be extended to infinite things. In particular, there is no intuitive answer to Galileo's question: Are there more natural numbers than there are squares of natural numbers, or not? Set theory explains this perfectly, GroeMAZ has no clue how to do it.
Sergio
2020-11-20 14:53:03 UTC
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Post by WM
What Caused this Acceptance?
How did the belief emerge that there were actually infinitely many natural numbers following upon every natural number, all of them were definable, but between all these natural numbers and ω nothing was existing?
not a "belief", but a proven technology, it came from the early Hittites
who used it to count their goats.
Post by WM
First, it is clear that in potential infinity infinitely many natural numbers are following upon every defined natural number. Alas there is no ω. But set theorists are eagerly concerned with blurring the difference between potential and actual infinity. Many even deny that there were any difference.
you need to prove there is a "potential infinity" first.
Post by WM
On the other hand, many students of mathematics are attracted by counter intuitive statements and may be even quite a bit proud of being able to "understand" that stuff. Further the gateway drug is not that strong: For the moment they are taught harmlessly that every natural number is followed by a larger natural number, but that no natural number is larger than all others. And with the plausible explanation that everybody has a mother, but there is no mother of everybody, the argument appears not problematic.
Sheep Counters are not druggies, and love their mothers.
Post by WM
If in the gapless sequence of ordinal numbers, on the "ordinal axis", one ordinal is missing before ω, then this gap is not standing out. It occurs in the infinite and its position cannot be verified anyway.
oh, you mean Gap Numbers, formally known as Dark Numbers, which are not
numbers, but a blob...
Post by WM
After this little gap has been swallowed, the dose can be increased. Then ℵo gaps of missing numbers will soon be accepted. And the recognition that in any case there are more numbers missing between n and ω than are existing before n enters an immunized brain that considers every sceptic simply as incapable of receiving the higher ordinations of infinity.
it worries you, what you call this gap, this not knowing a whole lot of
really big numbers.
Post by WM
Yet the understanding of the potentially infinite class of definable numbers should appear counter intuitive enough. This class can be arbitrarily increased without end whereas the class of dark numbers can be decreased infinitely but without losing its actually infinite size.
best if written in equations, the language of Mathematics, your are
trying to compare infinities, and who is the arbitrator who does this
increasing ?
Post by WM
https://hs-augsburg.zoom.us/j/92096767073?pwd=aG1DUzJOdnFqTzNTYk1FU0RFQUZ0QT09
Regards, WM
WM
2020-11-20 16:38:09 UTC
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Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.

Regards, WM
FromTheRafters
2020-11-20 16:51:04 UTC
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Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
The rubber WMclass which can stretch or shrink as needed but is
*always* finite?
FredJeffries
2020-11-20 17:07:12 UTC
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Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
There is no such class
Sergio
2020-11-20 18:40:31 UTC
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Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
Regards, WM
so no proof, but a topic change.


there is no class of "known" primes. Again you insert the "observer
dependency" into a math definition. there is no list of known primes either.
FredJeffries
2020-11-20 19:02:26 UTC
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Post by Sergio
Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
Regards, WM
so no proof, but a topic change.
there is no class of "known" primes. Again you insert the "observer
dependency" into a math definition. there is no list of known primes either.
Ah, but in the magic kingdom our Great and Powerful Professor has access to an ALL known primes with attendant magical powers (principle of extensionality need not apply).

It is unfortunate that a person with a higher degree in physics is unfamiliar with the issues involved with the principle of 'simultaneity'.
Sergio
2020-11-20 19:12:40 UTC
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Post by FredJeffries
Post by Sergio
Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
Regards, WM
so no proof, but a topic change.
there is no class of "known" primes. Again you insert the "observer
dependency" into a math definition. there is no list of known primes either.
Ah, but in the magic kingdom our Great and Powerful Professor has access to an ALL known primes with attendant magical powers (principle of extensionality need not apply).
It is unfortunate that a person with a higher degree in physics is unfamiliar with the issues involved with the principle of 'simultaneity'.
WM could be using the advanced skill of 'remote viewing' to see

1. all primes "known"
2. all dark numbers are not there.
FromTheRafters
2020-11-20 22:01:50 UTC
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Post by Sergio
Post by FredJeffries
Post by Sergio
Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
Regards, WM
so no proof, but a topic change.
there is no class of "known" primes. Again you insert the "observer
dependency" into a math definition. there is no list of known primes either.
Ah, but in the magic kingdom our Great and Powerful Professor has access to
an ALL known primes with attendant magical powers (principle of
extensionality need not apply).
It is unfortunate that a person with a higher degree in physics is
unfamiliar with the issues involved with the principle of 'simultaneity'.
WM could be using the advanced skill of 'remote viewing' to see
1. all primes "known"
2. all dark numbers are not there.
Any resemblance to persons living or dead or any principle of
simultaneity is purely coincidental.
FredJeffries
2020-11-20 22:08:53 UTC
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Post by FromTheRafters
Post by Sergio
Post by FredJeffries
Post by Sergio
Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
Regards, WM
so no proof, but a topic change.
there is no class of "known" primes. Again you insert the "observer
dependency" into a math definition. there is no list of known primes either.
Ah, but in the magic kingdom our Great and Powerful Professor has access to
an ALL known primes with attendant magical powers (principle of
extensionality need not apply).
It is unfortunate that a person with a higher degree in physics is
unfamiliar with the issues involved with the principle of 'simultaneity'.
WM could be using the advanced skill of 'remote viewing' to see
1. all primes "known"
2. all dark numbers are not there.
Any resemblance to persons living or dead or any principle of
simultaneity is purely coincidental.
If out-of-the-body experiences are possible, a person could be simultaneously living AND dead
Python
2020-11-20 19:24:16 UTC
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Post by FredJeffries
Post by Sergio
Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
Regards, WM
so no proof, but a topic change.
there is no class of "known" primes. Again you insert the "observer
dependency" into a math definition. there is no list of known primes either.
Ah, but in the magic kingdom our Great and Powerful Professor has access to an ALL known primes with attendant magical powers (principle of extensionality need not apply).
It is unfortunate that a person with a higher degree in physics is unfamiliar with the issues involved with the principle of 'simultaneity'.
Crank Professor Wolfgang Mueckenheim, from Hochschule Augsburg has
repeatedly supported Special Relativity deniers during the recent years,
especially the ones who deny Cantor's diagonal argument as well.
Me
2020-11-20 19:33:26 UTC
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Post by Python
Crank Professor Wolfgang Mueckenheim, from Hochschule Augsburg has
repeatedly supported Special Relativity deniers during the recent years,
especially the ones who deny Cantor's diagonal argument as well.
Sounds familiar.

See:

https://en.wikipedia.org/wiki/Deutsche_Physik
https://en.wikipedia.org/wiki/Deutsche_Mathematik

Of course, there's no place for Einsteins Theory or Cantor's Theory in Deutsche Physik or Deutsche Mathematik, resp.
Sergio
2020-11-20 22:15:30 UTC
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Post by Me
Post by Python
Crank Professor Wolfgang Mueckenheim, from Hochschule Augsburg has
repeatedly supported Special Relativity deniers during the recent years,
especially the ones who deny Cantor's diagonal argument as well.
Sounds familiar.
https://en.wikipedia.org/wiki/Deutsche_Physik
https://en.wikipedia.org/wiki/Deutsche_Mathematik
Of course, there's no place for Einsteins Theory or Cantor's Theory in Deutsche Physik or Deutsche Mathematik, resp.
Deutsche_Physik A pseudoscientific movement,"Aryan Physics" vs "Jewish
science"

Deutsche Mathematik [Nazi Math] promote "German mathematics" and
eliminate "Jewish influence" in mathematics, similar to the Deutsche
Physik movement.

interesting,

but the Jews invented the laser, defibrillators, Genetic engineering,
stanless steel, E= mc^2, vaccinens for cholera and bubonic plage, etc
Me
2020-11-20 22:52:54 UTC
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Post by Sergio
but the Jews invented the laser, defibrillators, Genetic engineering,
stanless steel, E = mc^2, vaccinens for cholera and bubonic plage, etc
Well, what can I say? Maybe "they" (=some of them) invented even more.

But I've never looked at scientific endeavors this way. Who the hell cares?
Sergio
2020-11-21 01:49:16 UTC
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Post by Me
Post by Sergio
but the Jews invented the laser, defibrillators, Genetic engineering,
stanless steel, E = mc^2, vaccinens for cholera and bubonic plage, etc
Well, what can I say? Maybe "they" (=some of them) invented even more.
But I've never looked at scientific endeavors this way. Who the hell cares?
totally agree, race/religion/sex/etc they are not factors at all.

rather; it is how intelligent one is in a field, and the opportunity for
them to create/invent something (have the right job at the right time,
with a need, some companies love patents, others dont.)

I knew a phd physicist brilliant in small slice of electro optics, but a
complete nutter otherwise.

Another dude I worked with had 47 patents in microwave, his huge ego he
could not work with others.

one other factor is it may take a staff of people to get something
invented now days, but only a few names make it on the patent.
WM
2020-11-21 16:13:37 UTC
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Post by FredJeffries
Post by Sergio
Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
there is no class of "known" primes.
There is.
Post by FredJeffries
Ah, but in the magic kingdom our Great and Powerful Professor has access to an ALL known primes with attendant magical powers (principle of extensionality need not apply).
There is the class of known prime numbers for every system, for instance human mathematicians or the members of some foreign civilization.
Post by FredJeffries
It is unfortunate that a person with a higher degree in physics is unfamiliar with the issues involved with the principle of 'simultaneity'.
No simultaneity required. Every system has its own class of known prime numbers.

Regards, WM
Sergio
2020-11-21 16:36:05 UTC
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Post by WM
Post by FredJeffries
Post by Sergio
Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
there is no class of "known" primes.
There is.
Post by FredJeffries
Ah, but in the magic kingdom our Great and Powerful Professor has access to an ALL known primes with attendant magical powers (principle of extensionality need not apply).
There is the class of known prime numbers for every system, for instance human mathematicians or the members of some foreign civilization.
Post by FredJeffries
It is unfortunate that a person with a higher degree in physics is unfamiliar with the issues involved with the principle of 'simultaneity'.
No simultaneity required. Every system has its own class of known prime numbers.
Regards, WM
each entity in the universe, each separate bug, each separate person,
schools, each different aliens, each seperate microbes has a different
list of known prime numbers.

so, the list of known primes is unknown by anyone. Because they all
disagree, as the lists are different.
Me
2020-11-21 17:32:18 UTC
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Post by Sergio
each entity in the universe, each separate bug, each separate person,
schools, each different aliens, each seperate microbes has a different
list of known prime numbers.
so, the list of known primes is unknown by anyone. Because they all
disagree, as the lists are different.
We might consider the union of all these classes. :-P

.... at a certai
Sergio
2020-11-21 17:52:44 UTC
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Post by Me
Post by Sergio
each entity in the universe, each separate bug, each separate person,
schools, each different aliens, each seperate microbes has a different
list of known prime numbers.
so, the list of known primes is unknown by anyone. Because they all
disagree, as the lists are different.
We might consider the union of all these classes. :-P
.... at a certai
How about selling a standard list of all known primes to all entities,
"List A" and get them to throw their list away ? (they would have to
cover postage) ... then offer a subscription service for updates ?
WM
2020-11-22 18:00:54 UTC
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Post by Sergio
Post by WM
No simultaneity required. Every system has its own class of known prime numbers.
each entity in the universe, each separate bug, each separate person,
schools, each different aliens, each seperate microbes has a different
list of known prime numbers.
Could be defined this way.
Post by Sergio
so, the list of known primes is unknown by anyone. Because they all
disagree, as the lists are different.
They are intelligent and know that the lists are different. But if there is communication, the lists can be compared and updated. That is no problem. What is important is that the class of dark prime numbers is actually infinite and will remain so forever. THAT is observer-independent-

Regards, WM
Sergio
2020-11-22 18:38:14 UTC
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Post by WM
Post by Sergio
Post by WM
No simultaneity required. Every system has its own class of known prime numbers.
each entity in the universe, each separate bug, each separate person,
schools, each different aliens, each seperate microbes has a different
list of known prime numbers.
Could be defined this way.
Post by Sergio
so, the list of known primes is unknown by anyone. Because they all
disagree, as the lists are different.
They are intelligent and know that the lists are different. But if there is communication, the lists can be compared and updated.
wrong-o

IF there are 2 lists there is 1 compairson
if there are 3 lists there are 2 compairisons
if there are 4 lists there are 6 compairisons

# of compairisons = n*(n-1)/2 = (n^2-n)/2 where n is the number of lists.

so with the population on earth, 7.8 *10^9, each has their own list,
leads to 6.084 * 10^19 compairisons

And that does not include translations, nor does it include how fast
each list changes.

and if the lists are 10^16 long, how long does it take to compair two
lists? or put the list into a computer readable form ?

that is an *unsolvable problem*
Post by WM
That is no problem. What is important is that the class of dark prime numbers is actually infinite and will remain so forever. THAT is observer-independent-
then show it is infinite. Remember your dark numbers are not countable
because they have no attributes, they cannot be distinguished from each
other...
Post by WM
Regards, WM
This also raises the question of what it means that a prime is "known".
If I generate a dozen hundred-digit primes and they are forgotten after
I close the window showing them, are these primes still "known"? If
instead I print out one of them and save the copy in a safe without
showing it to anybody, is that prime "known"? What if I cast it into the
concrete foundation for my new house?




In order to get a rough estimate, I checked performance of PrimeQ
function in Mathematica on my computer. It appears, that in order to
calculate all primes up to 10^n
using this function, I need ≈11^(n−6)seconds on my single core of amd
athlon 7750. Then it would take me for example ≈1500 years to calculate
all primes up to 10^16, and as a result I would get 10^14 primes.
WM
2020-11-23 20:53:08 UTC
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Post by Sergio
Post by WM
They are intelligent and know that the lists are different. But if there is communication, the lists can be compared and updated.
wrong-o
IF there are 2 lists there is 1 compairson
if there are 3 lists there are 2 compairisons
if there are 4 lists there are 6 compairisons
No, there are 3 comparisons because they have arranged a limear order.
Post by Sergio
Post by WM
That is no problem. What is important is that the class of dark prime numbers is actually infinite and will remain so forever. THAT is observer-independent-
It may be harder to prove the existence of infinitely many dark primes. But the existence of aleph_0 different natnumbers is our point of departure.
Post by Sergio
This also raises the question of what it means that a prime is "known".
If I generate a dozen hundred-digit primes and they are forgotten after
I close the window showing them, are these primes still "known"?
Not by you but by the system comprising you and your computer. You can repeat the procedure.
Post by Sergio
If
instead I print out one of them and save the copy in a safe without
showing it to anybody, is that prime "known"? What if I cast it into the
concrete foundation for my new house?
These are justified questions which may be scrutinized in depth. But they are irrelevant for the existence of aleph_0 dark natural numbers.

Regards, WM
Sergio
2020-11-24 00:20:59 UTC
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Post by WM
Post by Sergio
Post by WM
They are intelligent and know that the lists are different. But if there is communication, the lists can be compared and updated.
wrong-o
IF there are 2 lists there is 1 compairson
if there are 3 lists there are 2 compairisons
if there are 4 lists there are 6 compairisons
No, there are 3 comparisons because they have arranged a limear order.
study up,
4 different lists, A, B, C, D

one must compare each list to each other list (because none of the lists
are known to be complete)

A to B
A to C
A to D
B to C
B to D
C to D

it is simple combination problem taken 2 at a time.
Post by WM
Post by Sergio
Post by WM
That is no problem. What is important is that the class of dark prime numbers is actually infinite and will remain so forever. THAT is observer-independent-
if it is "observer dependent", it is not math.
Post by WM
It may be harder to prove the existence of infinitely many dark primes. But the existence of aleph_0 different natnumbers is our point of departure.
"Prime" numbers is a red herring.
Post by WM
Post by Sergio
This also raises the question of what it means that a prime is "known".
If I generate a dozen hundred-digit primes and they are forgotten after
I close the window showing them, are these primes still "known"?
Not by you but by the system comprising you and your computer. You can repeat the procedure.
but no one else has access to the computer.

and saying the existence of a number is dependent upon someone looking
at it is... how do you say....

the old tree falling in the forest makes no noise, but since no one saw
it, it did not fall either.

conflict.
Post by WM
Post by Sergio
If
instead I print out one of them and save the copy in a safe without
showing it to anybody, is that prime "known"? What if I cast it into the
concrete foundation for my new house?
These are justified questions which may be scrutinized in depth. But they are irrelevant for the existence of aleph_0 dark natural numbers.
your "dark numbers" depend upon someone observing them or not.

Math does not change due to an outside observer.

How would the math know if something was looking at it ?
Post by WM
Regards, WM
Chris M. Thomasson
2020-11-24 07:09:33 UTC
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Post by Sergio
Post by WM
Post by Sergio
Post by WM
They are intelligent and know that the lists are different. But if there is communication, the lists can be compared and updated.
wrong-o
IF there are 2 lists there is 1 compairson
if there are 3 lists there are 2 compairisons
if there are 4 lists there are 6 compairisons
No, there are 3 comparisons because they have arranged a limear order.
study up,
4 different lists, A, B, C, D
one must compare each list to each other list (because none of the lists
are known to be complete)
A to B
A to C
A to D
B to C
B to D
C to D
it is simple combination problem taken 2 at a time.
Post by WM
Post by Sergio
Post by WM
That is no problem. What is important is that the class of dark prime numbers is actually infinite and will remain so forever. THAT is observer-independent-
if it is "observer dependent", it is not math.
Post by WM
It may be harder to prove the existence of infinitely many dark primes. But the existence of aleph_0 different natnumbers is our point of departure.
"Prime" numbers is a red herring.
Post by WM
Post by Sergio
This also raises the question of what it means that a prime is "known".
If I generate a dozen hundred-digit primes and they are forgotten after
I close the window showing them, are these primes still "known"?
Not by you but by the system comprising you and your computer. You can repeat the procedure.
but no one else has access to the computer.
and saying the existence of a number is dependent upon someone looking
at it is... how do you say....
the old tree falling in the forest makes no noise, but since no one saw
it, it did not fall either.
conflict.
Post by WM
Post by Sergio
If
instead I print out one of them and save the copy in a safe without
showing it to anybody, is that prime "known"? What if I cast it into the
concrete foundation for my new house?
These are justified questions which may be scrutinized in depth. But they are irrelevant for the existence of aleph_0 dark natural numbers.
your "dark numbers" depend upon someone observing them or not.
Math does not change due to an outside observer.
How would the math know if something was looking at it ?
But wait, we have the book!



This still cracks me up.
Me
2020-11-24 08:34:38 UTC
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Post by Chris M. Thomasson
But wait, we have the book!
http://youtu.be/rVtHrgdcvZA
Seems to be inspired by Mückenheims "dark numbers". After all NO number in this encyclopedia is DARK!!! This helps a lot!
Chris M. Thomasson
2020-11-24 09:33:56 UTC
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Post by Me
Post by Chris M. Thomasson
But wait, we have the book!
http://youtu.be/rVtHrgdcvZA
Seems to be inspired by Mückenheims "dark numbers". After all NO number in this encyclopedia is DARK!!! This helps a lot!
ROFL! Too funny.

I can imagine WM using the following phone:



It only has one button.
Sergio
2020-11-24 12:26:08 UTC
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Post by Chris M. Thomasson
Post by Me
Post by Chris M. Thomasson
But wait, we have the book!
http://youtu.be/rVtHrgdcvZA
Seems to be inspired by Mückenheims "dark numbers". After all NO
number in this encyclopedia is DARK!!! This helps a lot!
ROFL! Too funny.
http://youtu.be/ZG8ZKwaC1jY
It only has one button.
I need that phone, no confusing dial with too many buttons, and no
incoming calls!!

its like an old rotary phone, without the rotor, no dialing instead a
pure serial digital stream for addressing, simpler than Morse code.
Chris M. Thomasson
2020-11-25 03:42:09 UTC
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Post by Sergio
Post by Chris M. Thomasson
Post by Me
Post by Chris M. Thomasson
But wait, we have the book!
http://youtu.be/rVtHrgdcvZA
Seems to be inspired by Mückenheims "dark numbers". After all NO
number in this encyclopedia is DARK!!! This helps a lot!
ROFL! Too funny.
http://youtu.be/ZG8ZKwaC1jY
It only has one button.
I need that phone, no confusing dial with too many buttons, and no
incoming calls!!
Indeed! I love the cooling gel they provide... ;^)
Post by Sergio
its like an old rotary phone, without the rotor, no dialing instead a
pure serial digital stream for addressing, simpler than Morse code.
beep beep beep = 3

pause for two seconds = 0

beep beep beep = 3

pause for one second = delimiter

beep beep beep = 3

pause for two seconds = 0

pause for three seconds, it finally makes the call...

so it dials: 30330


;^)
Sergio
2020-11-24 12:20:34 UTC
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Post by Chris M. Thomasson
Post by Sergio
Post by WM
Post by Sergio
Post by WM
They are intelligent and know that the lists are different. But if
there is communication, the lists can be compared and updated.
wrong-o
IF there are 2 lists there is 1 compairson
if there are 3 lists there are 2 compairisons
if there are 4 lists there are 6 compairisons
No, there are 3 comparisons because they have arranged a limear order.
study up,
4 different lists, A, B, C, D
one must compare each list to each other list (because none of the lists
are known to be complete)
A to B
A to C
A to D
B to C
B to D
C to D
it is simple combination problem taken 2 at a time.
Post by WM
Post by Sergio
Post by WM
That is no problem. What is important is that the class of dark
prime numbers is actually infinite and will remain so forever. THAT
is observer-independent-
if it is "observer dependent", it is not math.
Post by WM
It may be harder to prove the existence of infinitely many dark
primes. But the existence of aleph_0 different natnumbers is our
point of departure.
"Prime" numbers is a red herring.
Post by WM
Post by Sergio
This also raises the question of what it means that a prime is "known".
If I generate a dozen hundred-digit primes and they are forgotten after
I close the window showing them, are these primes still "known"?
Not by you but by the system comprising you and your computer. You
can repeat the procedure.
but no one else has access to the computer.
and saying the existence of a number is dependent upon someone looking
at it is...   how do you say....
the old tree falling in the forest makes no noise, but since no one saw
it, it did not fall either.
conflict.
Post by WM
Post by Sergio
If
instead I print out one of them and save the copy in a safe without
showing it to anybody, is that prime "known"? What if I cast it into the
concrete foundation for my new house?
These are justified questions which may be scrutinized in depth. But
they are irrelevant for the existence of aleph_0 dark natural numbers.
your "dark numbers" depend upon someone observing them or not.
Math does not change due to an outside observer.
     How would the math know if something was looking at it ?
But wait, we have the book!
http://youtu.be/rVtHrgdcvZA
This still cracks me up.
great video, even better books!
I wonder if I can buy a book of just even numbers, so I can check if
someone asks ?
WM
2020-11-24 11:10:31 UTC
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Post by Sergio
Post by WM
Post by Sergio
Post by WM
They are intelligent and know that the lists are different. But if there is communication, the lists can be compared and updated.
wrong-o
IF there are 2 lists there is 1 compairson
if there are 3 lists there are 2 compairisons
if there are 4 lists there are 6 compairisons
No, there are 3 comparisons because they have arranged a limear order.
study up,
4 different lists, A, B, C, D
one must compare each list to each other list (because none of the lists
are known to be complete)
The lists go from A to D and are complete at D.
Post by Sergio
the old tree falling in the forest makes no noise, but since no one saw
it, it did not fall either.
Mathematics is part of physics.
Post by Sergio
Math does not change due to an outside observer.
But the knowledge of the observer does. Anyhow, this cannot be denied:

For the *defined* natural numbers we have

|∩{E(k) : k ∈ ℕ_def}| = ℵo

They are not enough to yield

|∩{E(k) : k ∈ ℕ}| = 0 .

Regards, WM
Sergio
2020-11-24 12:32:55 UTC
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Post by WM
Post by Sergio
Post by WM
Post by Sergio
Post by WM
They are intelligent and know that the lists are different. But if there is communication, the lists can be compared and updated.
wrong-o
IF there are 2 lists there is 1 compairson
if there are 3 lists there are 2 compairisons
if there are 4 lists there are 6 compairisons
No, there are 3 comparisons because they have arranged a limear order.
study up,
4 different lists, A, B, C, D
one must compare each list to each other list (because none of the lists
are known to be complete)
The lists go from A to D and are complete at D.
wont work. You have to line up people single file, millions of them,
and compare each of them to a master one at a time. by the 10th person
the lists are changing again.
Post by WM
Post by Sergio
the old tree falling in the forest makes no noise, but since no one saw
it, it did not fall either.
Mathematics is part of physics.
Fail. physics uses math for modeling. Math is stand alone set of languages
Post by WM
Post by Sergio
Math does not change due to an outside observer.
But the knowledge of the observer does.
so you agree that an observer cannot change math, and the math can only
change the observer.

Poof! their goes your dark numbers.
Post by WM
For the *defined* natural numbers we have
the issue here is your "defined" which is an observer looking at a number.
Post by WM
|∩{E(k) : k ∈ ℕ_def}| = ℵo
They are not enough to yield
|∩{E(k) : k ∈ ℕ}| = 0 .
Regards, WM
zelos...@gmail.com
2020-11-25 06:32:48 UTC
Reply
Permalink
Post by WM
Post by Sergio
Post by WM
Post by Sergio
Post by WM
They are intelligent and know that the lists are different. But if there is communication, the lists can be compared and updated.
wrong-o
IF there are 2 lists there is 1 compairson
if there are 3 lists there are 2 compairisons
if there are 4 lists there are 6 compairisons
No, there are 3 comparisons because they have arranged a limear order.
study up,
4 different lists, A, B, C, D
one must compare each list to each other list (because none of the lists
are known to be complete)
The lists go from A to D and are complete at D.
Post by Sergio
the old tree falling in the forest makes no noise, but since no one saw
it, it did not fall either.
Mathematics is part of physics.
Post by Sergio
Math does not change due to an outside observer.
For the *defined* natural numbers we have
|∩{E(k) : k ∈ ℕ_def}| = ℵo
They are not enough to yield
|∩{E(k) : k ∈ ℕ}| = 0 .
Regards, WM
|∩{E(k) : k ∈ ℕ_def}| = ℵo
Given your N_def=|N, this is false
Gus Gassmann
2020-11-25 11:13:17 UTC
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Post by ***@gmail.com
Given your N_def=|N, this is false
IN_def must be different from IN, since IN_def, if it exists, is finite. However, since its defining relation implies that for every n in IN_def there is a larger one (namely n+1) also in IN_def, IN_def cannot be finite. Ergo, it is not a set, or it does not exist. Either way, WM's approach is crackpottery.
Me
2020-11-25 11:35:46 UTC
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Post by Gus Gassmann
Either way, WM's approach is crackpottery.
You think?!
Gus Gassmann
2020-11-25 15:38:07 UTC
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Post by Me
Post by Gus Gassmann
Either way, WM's approach is crackpottery.
You think?!
Do I think? Yes. Every Saturday, need it or not. :)
zelos...@gmail.com
2020-11-25 13:33:19 UTC
Reply
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Post by Gus Gassmann
Post by ***@gmail.com
Given your N_def=|N, this is false
IN_def must be different from IN, since IN_def, if it exists, is finite. However, since its defining relation implies that for every n in IN_def there is a larger one (namely n+1) also in IN_def, IN_def cannot be finite. Ergo, it is not a set, or it does not exist. Either way, WM's approach is crackpottery.
Given what he has said, it is equal, but then again he has no issue contradicting himself
Gus Gassmann
2020-11-25 15:36:56 UTC
Reply
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Post by ***@gmail.com
Post by Gus Gassmann
Post by ***@gmail.com
Given your N_def=|N, this is false
IN_def must be different from IN, since IN_def, if it exists, is finite. However, since its defining relation implies that for every n in IN_def there is a larger one (namely n+1) also in IN_def, IN_def cannot be finite. Ergo, it is not a set, or it does not exist. Either way, WM's approach is crackpottery.
Given what he has said, it is equal, but then again he has no issue contradicting himself
Actually, he insists on the intersection of all end segments over elements of IN_def having infinite cardinality. This means that IN_def is finite. Unfortunately, that leads to a quick contradiction, so I maintain that IN_def does not exist. (WM of course has no clue about any of these issues.)
FredJeffries
2020-11-25 16:52:42 UTC
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Post by ***@gmail.com
Post by Gus Gassmann
Post by ***@gmail.com
Given your N_def=|N, this is false
IN_def must be different from IN, since IN_def, if it exists, is finite. However, since its defining relation implies that for every n in IN_def there is a larger one (namely n+1) also in IN_def, IN_def cannot be finite. Ergo, it is not a set, or it does not exist. Either way, WM's approach is crackpottery.
Given what he has said, it is equal, but then again he has no issue contradicting himself
Actually, he insists on the intersection of all end segments over elements of IN_def having infinite cardinality. This means that IN_def is finite. Unfortunately, that leads to a quick contradiction, so I maintain that IN_def does not exist. (WM of course has no clue about any of these issues.)
With respect, you are being silly. First of all (pun intended), |N_def is NOT A SET. It is nonsense to attempt to determine its cardinality or whether it is finite or infinite because those concepts are (only) (well-)defined for SETS.

It is even more nonsense to speak of 'the intersection of ALL end segments over elements of IN_def'. An ALL (whatever it may be in the magic kingdom) is NOT A SET. It makes no sense to speak of an intersection of an ALL.

Also, |N_def, not being a SET, cannot legitimately be used to index operations like union and intersection and ...

And, since |N_def is not a SET, the notion of it's 'elements' is not (well-)defined.
Me
2020-11-25 18:46:19 UTC
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Permalink
Wait a second, man. As far as I can tell Gus is well aware of (some of) the points you mentioned below.
Post by FredJeffries
[WM] insists on the intersection of all end segments over elements of IN_def having infinite cardinality.
This means that IN_def is finite. Unfortunately, that leads to a quick contradiction, so I maintain that IN_def
does not exist.
With respect, you are being silly.
I don't think so.
Post by FredJeffries
First of all (pun intended), |N_def is NOT A SET.
How would you know? Do you know of a proper definition of IN_def?

But of course, if there is no /N_def/ "it" certainly cannot be a set. Agree. :-)
Post by FredJeffries
It is nonsense to attempt to determine its cardinality or whether it is finite or infinite because those concepts are (only)
(well-)defined for SETS.
I beg to differ. I'm quite sure that we may safely claim that proper classes are infinite (at least in the context of certain set theories which allow for proper classs)? No?
Post by FredJeffries
And, since |N_def is not a SET, the notion of its 'elements' is not (well-)defined.
Huh?! Proper classes do not have elements in YOUR magic kingdom?
FredJeffries
2020-11-25 21:26:16 UTC
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Post by Me
Wait a second, man. As far as I can tell Gus is well aware of (some of) the points you mentioned below.
Curses! Hoisted on my own hyperbole!
Even more simply can we argue: Assume that |N_def is a set. But |N_def is not a set. Contradiction.
Post by Me
Post by FredJeffries
[WM] insists on the intersection of all end segments over elements of IN_def having infinite cardinality.
This means that IN_def is finite. Unfortunately, that leads to a quick contradiction, so I maintain that IN_def
does not exist.
With respect, you are being silly.
I don't think so.
Post by FredJeffries
First of all (pun intended), |N_def is NOT A SET.
How would you know? Do you know of a proper definition of IN_def?
Of course not. But, whatever it is (or isn't) it is obvious that it does not obey the axioms of set theory, most particularly the axiom of extensionality.

You don't have to know WHAT six is or what the natural numbers REALLY are to know that six is not a prime number. You just have to know how natural numbers operate and how six is related to other natural numbers.
Post by Me
But of course, if there is no /N_def/ "it" certainly cannot be a set. Agree. :-)
Post by FredJeffries
It is nonsense to attempt to determine its cardinality or whether it is finite or infinite because those concepts are (only)
(well-)defined for SETS.
I beg to differ. I'm quite sure that we may safely claim that proper classes are infinite (at least in the context of certain set theories which allow for proper classs)? No?
Aha! Caught me!

Of course, |N_def is not a proper class either.
Post by Me
Post by FredJeffries
And, since |N_def is not a SET, the notion of its 'elements' is not (well-)defined.
Huh?! Proper classes do not have elements in YOUR magic kingdom?
I concede.
Me
2020-11-25 21:43:46 UTC
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Post by FredJeffries
I concede.
No harm no foul. (But I HAD TO speak up.)

WM
2020-11-21 16:08:26 UTC
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Post by Sergio
Post by WM
Post by Sergio
you need to prove there is a "potential infinity" first.
See the class of known prime numbers.
there is no class of "known" primes.
There is.

Regards, WM
Dan Christensen
2020-11-20 18:00:38 UTC
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Post by WM
What Caused this Acceptance?
How did the belief emerge that there were actually infinitely many natural numbers following upon every natural number, all of them were definable, but between all these natural numbers and ω nothing was existing?
Yup, no matter how large a natural number you pick, there are infinitely may natural numbers greater than it. Basic elementary-school math, Mucke. Deal with it. None of your mysterious "dark" numbers are required to understand this.

And perhaps you didn't know, but ω is NOT a natural number. It has no immediate predecessor in N. There is simply no need to concoct a set of mysterious "undefinable" or "dark" numbers that are somehow "between" the natural numbers and ω.

It really is time to time to take that high-school refresher course, Mucke. You would save yourself MUCH embarrassment here.


Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
FredJeffries
2020-11-20 18:06:15 UTC
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Post by WM
How did the belief emerge that there were actually infinitely many natural numbers following upon every natural number, all of them were definable, but between all these natural numbers and ω nothing was existing?
Your 'all' is gibberish

eod
zelos...@gmail.com
2020-11-23 06:44:51 UTC
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Post by WM
What Caused this Acceptance?
How did the belief emerge that there were actually infinitely many natural numbers following upon every natural number, all of them were definable, but between all these natural numbers and ω nothing was existing?
First, it is clear that in potential infinity infinitely many natural numbers are following upon every defined natural number. Alas there is no ω. But set theorists are eagerly concerned with blurring the difference between potential and actual infinity. Many even deny that there were any difference.
On the other hand, many students of mathematics are attracted by counter intuitive statements and may be even quite a bit proud of being able to "understand" that stuff. Further the gateway drug is not that strong: For the moment they are taught harmlessly that every natural number is followed by a larger natural number, but that no natural number is larger than all others. And with the plausible explanation that everybody has a mother, but there is no mother of everybody, the argument appears not problematic.
If in the gapless sequence of ordinal numbers, on the "ordinal axis", one ordinal is missing before ω, then this gap is not standing out. It occurs in the infinite and its position cannot be verified anyway.
After this little gap has been swallowed, the dose can be increased. Then ℵo gaps of missing numbers will soon be accepted. And the recognition that in any case there are more numbers missing between n and ω than are existing before n enters an immunized brain that considers every sceptic simply as incapable of receiving the higher ordinations of infinity.
Yet the understanding of the potentially infinite class of definable numbers should appear counter intuitive enough. This class can be arbitrarily increased without end whereas the class of dark numbers can be decreased infinitely but without losing its actually infinite size.
https://hs-augsburg.zoom.us/j/92096767073?pwd=aG1DUzJOdnFqTzNTYk1FU0RFQUZ0QT09
Regards, WM
no one cares about your "potential" "actual" crap, we defined it into existence and thats that.
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