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devel / comp.arch / Re: The purpose of our universe simulation was just made clear to me through communication with time.

SubjectAuthor
* Re: The purpose of our universe simulation was just made clear to meMitchAlsup
`* Re: The purpose of our universe simulation was just made clear to meQuadibloc
 +* Re: The purpose of our universe simulation was just made clear to meMitchAlsup
 |+* Re: The purpose of our universe simulation was just made clear to meIvan Godard
 ||`* Re: The purpose of our universe simulation was just made clear to me through comAndreas Eder
 || `* Re: The purpose of our universe simulation was just made clear to meQuadibloc
 ||  +- Re: The purpose of our universe simulation was just made clear to meDavid Brown
 ||  `* Re: The purpose of our universe simulation was just made clear to me through comAndreas Eder
 ||   `* Re: The purpose of our universe simulation was just made clear to meQuadibloc
 ||    `* Re: The purpose of our universe simulation was just made clear to meDavid Brown
 ||     +- Re: The purpose of our universe simulation was just made clear to meIvan Godard
 ||     `* Re: The purpose of our universe simulation was just made clear to meTerje Mathisen
 ||      `* Re: The purpose of our universe simulation was just made clear to meDavid Brown
 ||       +* Re: The purpose of our universe simulation was just made clear to meStephen Fuld
 ||       |+- Re: The purpose of our universe simulation was just made clear to me through comStefan Monnier
 ||       |`- Re: The purpose of our universe simulation was just made clear to meTerje Mathisen
 ||       `* Re: The purpose of our universe simulation was just made clear to meTerje Mathisen
 ||        `* Re: The purpose of our universe simulation was just made clear to meDavid Brown
 ||         `* Re: The purpose of our universe simulation was just made clear to me through comAnton Ertl
 ||          `- Re: The purpose of our universe simulation was just made clear to meJimBrakefield
 |+- Re: The purpose of our universe simulation was just made clear to meQuadibloc
 |+- Re: The purpose of our universe simulation was just made clear to meDavid Brown
 |`* Re: The purpose of our universe simulation was just made clear to meTerje Mathisen
 | `* Re: The purpose of our universe simulation was just made clear to meJimBrakefield
 |  `* Re: The purpose of our universe simulation was just made clear to me through comStefan Monnier
 |   +* Re: The purpose of our universe simulation was just made clear to meMitchAlsup
 |   |`* Re: The purpose of our universe simulation was just made clear to meJimBrakefield
 |   | `* Re: The purpose of our universe simulation was just made clear to meQuadibloc
 |   |  `* Re: The purpose of our universe simulation was just made clear to me through comAndreas Eder
 |   |   `* Re: The purpose of our universe simulation was just made clear to meDavid Brown
 |   |    `* Re: The purpose of our universe simulation was just made clear to meJimBrakefield
 |   |     `- Re: The purpose of our universe simulation was just made clear to meMichael S
 |   `* Re: The purpose of our universe simulation was just made clear to meDavid Brown
 |    `- Re: The purpose of our universe simulation was just made clear to me through comStefan Monnier
 `* Re: The purpose of our universe simulation was just made clear to meQuadibloc
  `- Re: The purpose of our universe simulation was just made clear to meDavid Brown

Pages:12
Re: The purpose of our universe simulation was just made clear to me through communication with time.

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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
From: MitchAl...@aol.com (MitchAlsup)
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 by: MitchAlsup - Mon, 2 May 2022 21:08 UTC

On Sunday, May 1, 2022 at 10:13:40 PM UTC-5, Skybuck Flying wrote:
> Hahahaha this is a bit of a scratch but bare with me =D
>
> I will re-cap shortly:
> Now I have this hypothesis that "externals" are communicating with me/us through time. By coincidentally concidencing our thoughts with time itself.
>
> For example:
>
> I just came to the conclusion that math itself has a problem:
>
> Dividing by zero is undefined.
> Multiplieing by infinity is also undefined.
<
Neither of these is true in a mathematical sense.
Both of these are true in a computer arithmetic sense.
<
So, it is not math that has the problem, but computer arithmetics.
>
> and when I came to this conclusion I looked at the clock on my microwave and it read:
>
> 5:05
>
> which can also be interpreted as S.O.S.
<
Off your lithium again ?
>
> which is a term out of shipping... basically a ship in trouble.
>
> and then it occured to me:
>
> IF THE UNIVERSE IS INFINITY
<
Universe is finite but unbounded.
>
> AND HERE COMES THE BIG ONE:
>
> THEN HOW DO YOU NAVIGATE IT....
<
Same way that you could an infinite set.
>
> IF YOU CAN'T PROPERLY COMPUTE WITH INFINITY HAHAHAHAHAHAHAHAHA
<
You need to use real math, There is an infinite sequence of (ahem) infinities
ℌ₀ being the first ℌ₁ being the second,...
>
> HOLY FUCKING SHIT.
<
Yes there is math that extends beyond 8th grade algebra.
>
> SO BASICALLY THESE EXTERNALS/CREATURES HAVE CREATED THIS UNIVERSE/SIMULATION IN THE HOPE THAT WE WILL FIND A MATHEMATHETICAL SOLUTION FOR THEM.
<
We already know the answer is 42, you just have not produced the result yet..
>
> SO THAT THEY CAN FINALLY NAVIGATE INFINITY SPACE/UNIVERSE.
>
> PERHAPS THEY ARE EVEN LOST...
>
> OR PERHAPS THEY STILL ON THEIR HOME PLANET... SCARED OF BEING LOST.
>
> HAHAHAHAHA
>
> I WILL LEAVE YOU WITH THIS THOUGHT FOR NOW.
>
> BYE,
> SKYBUCK.

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
From: jsav...@ecn.ab.ca (Quadibloc)
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 by: Quadibloc - Wed, 4 May 2022 19:20 UTC

On Monday, May 2, 2022 at 3:08:49 PM UTC-6, MitchAlsup wrote:

> You need to use real math, There is an infinite sequence of (ahem) infinities
> ℌ₀ being the first ℌ₁ being the second,....

Of course, we know what ℵ₀ is, the number of years in forever - the cardinality of
the natural numbers. While we also have a definition for ℵ₁ - which is the number of
well-orderings of the natural numbers - we don't know if the cardinality of the continuum
(the number of real numbers) is equal to aleph-one, or if it is much greater.

John Savard

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
From: MitchAl...@aol.com (MitchAlsup)
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 by: MitchAlsup - Wed, 4 May 2022 20:10 UTC

On Wednesday, May 4, 2022 at 2:20:50 PM UTC-5, Quadibloc wrote:
> On Monday, May 2, 2022 at 3:08:49 PM UTC-6, MitchAlsup wrote:
>
> > You need to use real math, There is an infinite sequence of (ahem) infinities
> > ℌ₀ being the first ℌ₁ being the second,....

> Of course, we know what ℵ₀ is, the number of years in forever - the cardinality of
> the natural numbers. While we also have a definition for ℵ₁ - which is the number of
> well-orderings of the natural numbers - we don't know if the cardinality of the continuum
> (the number of real numbers) is equal to aleph-one, or if it is much greater.
<
I was taught (1974) that the number of integers and the number of reals is the same
both ℌ₀. You have to find a counting problem that causes k×ℌ₀×ℌ₀ = ℌ₁ (for any
K > 0)
>
> John Savard

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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From: iva...@millcomputing.com (Ivan Godard)
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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
Date: Wed, 4 May 2022 13:27:16 -0700
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 by: Ivan Godard - Wed, 4 May 2022 20:27 UTC

On 5/4/2022 1:10 PM, MitchAlsup wrote:
> On Wednesday, May 4, 2022 at 2:20:50 PM UTC-5, Quadibloc wrote:
>> On Monday, May 2, 2022 at 3:08:49 PM UTC-6, MitchAlsup wrote:
>>
>>> You need to use real math, There is an infinite sequence of (ahem) infinities
>>> ℌ₀ being the first ℌ₁ being the second,...
>
>> Of course, we know what ℵ₀ is, the number of years in forever - the cardinality of
>> the natural numbers. While we also have a definition for ℵ₁ - which is the number of
>> well-orderings of the natural numbers - we don't know if the cardinality of the continuum
>> (the number of real numbers) is equal to aleph-one, or if it is much greater.
> <
> I was taught (1974) that the number of integers and the number of reals is the same
> both ℌ₀. You have to find a counting problem that causes k×ℌ₀×ℌ₀ = ℌ₁ (for any
> K > 0)

You are mis-remembering. The number of integers is the same as the
number of *rationals*, but less than the number of reals, and it is
unknown whether there is a number between that of integers and that of
reals.

For any set S, the powerset of S has more elements than S does, which
leads to the hierarchy of infinities. It is unknown whether there are
any sets whose cardinality is not that of one of the members of the
hierarchy, but no one has found one yet either.

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
From: jsav...@ecn.ab.ca (Quadibloc)
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 by: Quadibloc - Thu, 5 May 2022 04:03 UTC

On Wednesday, May 4, 2022 at 2:10:15 PM UTC-6, MitchAlsup wrote:

> I was taught (1974) that the number of integers and the number of reals is the same
> both ℌ₀. You have to find a counting problem that causes k×ℌ₀×ℌ₀ = ℌ₁ (for any
> K > 0)

Visit my page at:

http://www.quadibloc.com/math/infint.htm

Cantor's diagonal proof is shown there.

John Savard

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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From: a_eder_...@web.de (Andreas Eder)
Newsgroups: comp.arch
Subject: Re: The purpose of our universe simulation was just made clear to me through communication with time.
Date: Thu, 05 May 2022 09:09:23 +0200
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 by: Andreas Eder - Thu, 5 May 2022 07:09 UTC

On Mi 04 Mai 2022 at 13:27, Ivan Godard <ivan@millcomputing.com> wrote:

> On 5/4/2022 1:10 PM, MitchAlsup wrote:
>> On Wednesday, May 4, 2022 at 2:20:50 PM UTC-5, Quadibloc wrote:
>>> On Monday, May 2, 2022 at 3:08:49 PM UTC-6, MitchAlsup wrote:
>>>
>>>> You need to use real math, There is an infinite sequence of (ahem) infinities
>>>> ℌ₀ being the first ℌ₁ being the second,...
>>
>>> Of course, we know what ℵ₀ is, the number of years in forever - the cardinality of
>>> the natural numbers. While we also have a definition for ℵ₁ - which is the number of
>>> well-orderings of the natural numbers - we don't know if the cardinality of the continuum
>>> (the number of real numbers) is equal to aleph-one, or if it is much greater.
>> <
>> I was taught (1974) that the number of integers and the number of reals is the same
>> both ℌ₀. You have to find a counting problem that causes k×ℌ₀×ℌ₀ = ℌ₁ (for any
>> K > 0)
>
> You are mis-remembering. The number of integers is the same as the
> number of *rationals*, but less than the number of reals, and it is
> unknown whether there is a number between that of integers and that of
> reals.
>
> For any set S, the powerset of S has more elements than S does, which
> leads to the hierarchy of infinities. It is unknown whether there are
> any sets whose cardinality is not that of one of the members of the
> hierarchy, but no one has found one yet either.

That is the continuum problem of Cantor.
It was solved (in a way) by Gödel and Cohen who proved that of os
independent of the axioms of set theory (ZF). So you can have it both
ways, whichever you prefer.

'Andreas

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
From: jsav...@ecn.ab.ca (Quadibloc)
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 by: Quadibloc - Thu, 5 May 2022 08:18 UTC

On Thursday, May 5, 2022 at 1:15:06 AM UTC-6, Andreas Eder wrote:

> It was solved (in a way) by Gödel and Cohen who proved that of os
> independent of the axioms of set theory (ZF). So you can have it both
> ways, whichever you prefer.

That just shows that our understanding of set theory is incomplete.

What we need is something that makes absolutely clear the exact relationship
between the cardinality of the continuum and aleph-one, in the same way that
Cantor's diagonal proof makes it clear that the cardinality of the continuum is
greater than aleph-null.

So list all the well-orderings of the natural numbers, and pair them off with
all the real numbers. That hasn't been done since the list of those well-orderings
is maddeningly complex.

John Savard

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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From: david.br...@hesbynett.no (David Brown)
Newsgroups: comp.arch
Subject: Re: The purpose of our universe simulation was just made clear to me
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 by: David Brown - Thu, 5 May 2022 08:20 UTC

On 04/05/2022 22:10, MitchAlsup wrote:
> On Wednesday, May 4, 2022 at 2:20:50 PM UTC-5, Quadibloc wrote:
>> On Monday, May 2, 2022 at 3:08:49 PM UTC-6, MitchAlsup wrote:
>>
>>> You need to use real math, There is an infinite sequence of (ahem) infinities
>>> ℌ₀ being the first ℌ₁ being the second,...
>
>> Of course, we know what ℵ₀ is, the number of years in forever - the cardinality of
>> the natural numbers. While we also have a definition for ℵ₁ - which is the number of
>> well-orderings of the natural numbers - we don't know if the cardinality of the continuum
>> (the number of real numbers) is equal to aleph-one, or if it is much greater.
> <
> I was taught (1974) that the number of integers and the number of reals is the same
> both ℌ₀. You have to find a counting problem that causes k×ℌ₀×ℌ₀ = ℌ₁ (for any
> K > 0)

Aleph 0, ℵ₀, is the cardinality of the integers. It is the smallest
transfinite cardinality, and has the same size as the smallest
transfinite ordinal 𝜔. Aleph 1, ℵ₁, is the smallest cardinal bigger
than ℵ₀.

Beth 0, ℶ₀, is identical to ℵ₀.

Beth 1, ℶ₁, is defined as 2 ^ ℶ₀. It is the number of sets of integers.
This is also the number of real numbers - the cardinality of the
reals. It is very different, and much bigger, than the cardinality of
the integers ℶ₀.

We don't know if ℵ₁ equals ℶ₁ - i.e., if there is a cardinality greater
than that of the integers but smaller than that of the reals. (The
non-existence of such a cardinality is the aforementioned continuum
hypothesis.)

What we /do/ know is that the number of integers and the number of reals
is different. This was figured out by the early 20th century - if you
were taught something different in 1974 then your teacher was hugely out
of date. A simple diagonalisation argument lets you take any countably
infinite subset of the reals and construct a new real number that is not
in that set, showing that there are more reals than integers.

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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From: david.br...@hesbynett.no (David Brown)
Newsgroups: comp.arch
Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
Date: Thu, 5 May 2022 13:20:09 +0200
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 by: David Brown - Thu, 5 May 2022 11:20 UTC

On 05/05/2022 10:18, Quadibloc wrote:
> On Thursday, May 5, 2022 at 1:15:06 AM UTC-6, Andreas Eder wrote:
>
>> It was solved (in a way) by Gödel and Cohen who proved that of os
>> independent of the axioms of set theory (ZF). So you can have it both
>> ways, whichever you prefer.
>
> That just shows that our understanding of set theory is incomplete.
>

Gödel's incompleteness theorem shows that mathematics will /always/ be
incomplete.

> What we need is something that makes absolutely clear the exact relationship
> between the cardinality of the continuum and aleph-one, in the same way that
> Cantor's diagonal proof makes it clear that the cardinality of the continuum is
> greater than aleph-null.
>

Why?

You can do some interesting maths assuming the continuum hypothesis is
true. You can do some assuming it is /not/ true. You can do some
interesting things without assuming either way.

There are many hypotheses in maths that are in a similar situation,
though some might be resolvable eventually.

> So list all the well-orderings of the natural numbers, and pair them off with
> all the real numbers. That hasn't been done since the list of those well-orderings
> is maddeningly complex.
>

Mathematicians do maddeningly complex things all the time. That's not
the problem here.

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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
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 by: Terje Mathisen - Thu, 5 May 2022 11:59 UTC

MitchAlsup wrote:
> On Wednesday, May 4, 2022 at 2:20:50 PM UTC-5, Quadibloc wrote:
>> On Monday, May 2, 2022 at 3:08:49 PM UTC-6, MitchAlsup wrote:
>>
>>> You need to use real math, There is an infinite sequence of (ahem) infinities
>>> ℌ₀ being the first ℌ₁ being the second,...
>
>> Of course, we know what ℵ₀ is, the number of years in forever - the cardinality of
>> the natural numbers. While we also have a definition for ℵ₁ - which is the number of
>> well-orderings of the natural numbers - we don't know if the cardinality of the continuum
>> (the number of real numbers) is equal to aleph-one, or if it is much greater.
> <
> I was taught (1974) that the number of integers and the number of reals is the same
> both ℌ₀. You have to find a counting problem that causes k×ℌ₀×ℌ₀ = ℌ₁ (for any
> K > 0)

Mitch, you are wrong here: The proof that the cardinality of real
numbers is greater than Aleph-0, the number of integers (as well as
rationals by the triangle countability proof) was on of the first
findings of Cantor afaik. (I did read a/his book many decades ago.)

I.e. real numbers are not countable.

Terje

--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"

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 by: Andreas Eder - Thu, 5 May 2022 14:17 UTC

On Do 05 Mai 2022 at 01:18, Quadibloc <jsavard@ecn.ab.ca> wrote:

> On Thursday, May 5, 2022 at 1:15:06 AM UTC-6, Andreas Eder wrote:
>
>> It was solved (in a way) by Gödel and Cohen who proved that of os
>> independent of the axioms of set theory (ZF). So you can have it both
>> ways, whichever you prefer.
>
> That just shows that our understanding of set theory is incomplete.

Well, it shows that the continuum hypthesis is independent of the other
axioms of ZF.
If you are a platonist you may think this shows a deficiency in our
understanding of set theory.
I would say it shows that there is a wide landscape if set theories,
just like in geometry, where you have euclidean, hyperbolic and elliptic
geometries - and a whole bunch of others. (even finite ones).

'Andreas

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 by: Quadibloc - Thu, 5 May 2022 16:52 UTC

On Thursday, May 5, 2022 at 8:35:04 AM UTC-6, Andreas Eder wrote:

> Well, it shows that the continuum hypthesis is independent of the other
> axioms of ZF.

> If you are a platonist you may think this shows a deficiency in our
> understanding of set theory.

> I would say it shows that there is a wide landscape if set theories,
> just like in geometry, where you have euclidean, hyperbolic and elliptic
> geometries - and a whole bunch of others. (even finite ones).

It's true that there are surfaces in Euclidean geometry which follow the
laws of Riemannian/spherical or Lobatchevskian/hyperbolic geometry.

However, it would _seem_ that questions like _how many well-orderings
of the integers are there_ and _how many real numbers are there_ have only
one answer. We might be able to construct mathematical entities analogous
to sets which obey different laws, but we should also be able to fully flesh out
what the things we think of as sets are like.

That is, basically, we should be able to find a new set of axioms on which to
base an axiomatic set theory capable of fully replacing naive set theory.
Or, possibly, a "collections theory", since it may well be the case that excluding
things like the set of all sets is not something we want to do. (Genuinely
paradoxical sets, of course, like the set of all sets that don't include themselves,
still would have to be excluded.)

John Savard

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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 by: Quadibloc - Thu, 5 May 2022 17:19 UTC

On Wednesday, May 4, 2022 at 1:20:50 PM UTC-6, Quadibloc wrote:
> On Monday, May 2, 2022 at 3:08:49 PM UTC-6, MitchAlsup wrote:
>
> > You need to use real math, There is an infinite sequence of (ahem) infinities
> > ℌ₀ being the first ℌ₁ being the second,....

> Of course, we know what ℵ₀ is, the number of years in forever - the cardinality of
> the natural numbers. While we also have a definition for ℵ₁ - which is the number of
> well-orderings of the natural numbers - we don't know if the cardinality of the continuum
> (the number of real numbers) is equal to aleph-one, or if it is much greater.

I'm using the character U+2135, "Alef Symbol", since the Hebrew letter Alef plays tricks
with character ordering in display.

John Savard

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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 by: David Brown - Fri, 6 May 2022 08:42 UTC

On 05/05/2022 18:52, Quadibloc wrote:
> On Thursday, May 5, 2022 at 8:35:04 AM UTC-6, Andreas Eder wrote:
>
>> Well, it shows that the continuum hypthesis is independent of the other
>> axioms of ZF.
>
>> If you are a platonist you may think this shows a deficiency in our
>> understanding of set theory.
>
>> I would say it shows that there is a wide landscape if set theories,
>> just like in geometry, where you have euclidean, hyperbolic and elliptic
>> geometries - and a whole bunch of others. (even finite ones).
>
> It's true that there are surfaces in Euclidean geometry which follow the
> laws of Riemannian/spherical or Lobatchevskian/hyperbolic geometry.
>
> However, it would _seem_ that questions like _how many well-orderings
> of the integers are there_ and _how many real numbers are there_ have only
> one answer. We might be able to construct mathematical entities analogous
> to sets which obey different laws, but we should also be able to fully flesh out
> what the things we think of as sets are like.
>

We know how many real numbers there are - that's easy. It's the
cardinality of the power set of the integers.

It turns out, however, that both the continuum hypotheses and its
negation are consistent with ZF (and ZFC) set theory. It may /seem/
like you are asking a question that has a single answer, but the answer
is unknowable within the standard set theory axioms. Alternatively, you
could say that the question doesn't actually make sense within the ZF or
ZFC frameworks.

> That is, basically, we should be able to find a new set of axioms on which to
> base an axiomatic set theory capable of fully replacing naive set theory.

The whole concept of axioms are statements (ideally simple and "basic"
statements) that are independent of your existing set of axioms - that
is, both the axiom and its negation are consistent with the set you have
already. This means you can add the axiom to your set, or remove it, or
pick different axioms. (Think of them like basis vectors in a vector
space.)

That means we /can/ find a new set of axioms that answer the question of
whether aleph 1 equals beth 1 - just add the continuum hypothesis as a
new axiom to existing ZFC.

> Or, possibly, a "collections theory", since it may well be the case that excluding
> things like the set of all sets is not something we want to do. (Genuinely
> paradoxical sets, of course, like the set of all sets that don't include themselves,
> still would have to be excluded.)
>

Paradoxes are unavoidable - or at least, you can't prove that you won't
have them. You want to get a good book on Gödel's incompleteness
theorem, and read it for a bit of mind-bending. (I don't know what
would be a good choice, and of course it depends on what balance you
want between "easy reading layman explanations" and heavy, rigorous
mathematics.) It turns out that no matter how you define your
mathematics, if you've given it enough flexibility to be interesting
(i.e., enough axioms to be able to count), there will be statements that
are true but cannot be proven, and others that are false but cannot be
disproven.

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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From: david.br...@hesbynett.no (David Brown)
Newsgroups: comp.arch
Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
Date: Fri, 6 May 2022 10:53:30 +0200
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 by: David Brown - Fri, 6 May 2022 08:53 UTC

On 05/05/2022 19:19, Quadibloc wrote:
> On Wednesday, May 4, 2022 at 1:20:50 PM UTC-6, Quadibloc wrote:
>> On Monday, May 2, 2022 at 3:08:49 PM UTC-6, MitchAlsup wrote:
>>
>>> You need to use real math, There is an infinite sequence of (ahem) infinities
>>> ℌ₀ being the first ℌ₁ being the second,...
>
>> Of course, we know what ℵ₀ is, the number of years in forever - the cardinality of
>> the natural numbers. While we also have a definition for ℵ₁ - which is the number of
>> well-orderings of the natural numbers - we don't know if the cardinality of the continuum
>> (the number of real numbers) is equal to aleph-one, or if it is much greater.
>
> I'm using the character U+2135, "Alef Symbol", since the Hebrew letter Alef plays tricks
> with character ordering in display.
>
> John Savard

That is the correct Unicode symbol to use, and is the one I have been
using too. (Unicode mathematics symbols are not always the same as the
normal language letters they are based on.) Mitch has been using the
symbol "ℌ", which is "U+210C BLACK-LETTER CAPITAL H = Hilbert space". I
don't know why - I'm guessing that he misremembered the symbol as he did
some of the properties of the different infinities. This is not the
kind of stuff most people use every day, and we can't remember
/everything/ we learned nearly 50 years ago.

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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From: iva...@millcomputing.com (Ivan Godard)
Newsgroups: comp.arch
Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
Date: Fri, 6 May 2022 08:14:58 -0700
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 by: Ivan Godard - Fri, 6 May 2022 15:14 UTC

On 5/6/2022 1:42 AM, David Brown wrote:
> On 05/05/2022 18:52, Quadibloc wrote:
>> On Thursday, May 5, 2022 at 8:35:04 AM UTC-6, Andreas Eder wrote:
>>
>>> Well, it shows that the continuum hypthesis is independent of the other
>>> axioms of ZF.
>>
>>> If you are a platonist you may think this shows a deficiency in our
>>> understanding of set theory.
>>
>>> I would say it shows that there is a wide landscape if set theories,
>>> just like in geometry, where you have euclidean, hyperbolic and elliptic
>>> geometries - and a whole bunch of others. (even finite ones).
>>
>> It's true that there are surfaces in Euclidean geometry which follow the
>> laws of Riemannian/spherical or Lobatchevskian/hyperbolic geometry.
>>
>> However, it would _seem_ that questions like _how many well-orderings
>> of the integers are there_ and _how many real numbers are there_ have
>> only
>> one answer. We might be able to construct mathematical entities analogous
>> to sets which obey different laws, but we should also be able to fully
>> flesh out
>> what the things we think of as sets are like.
>>
>
> We know how many real numbers there are - that's easy.  It's the
> cardinality of the power set of the integers.
>
> It turns out, however, that both the continuum hypotheses and its
> negation are consistent with ZF (and ZFC) set theory.  It may /seem/
> like you are asking a question that has a single answer, but the answer
> is unknowable within the standard set theory axioms.  Alternatively, you
> could say that the question doesn't actually make sense within the ZF or
> ZFC frameworks.
>
>> That is, basically, we should be able to find a new set of axioms on
>> which to
>> base an axiomatic set theory capable of fully replacing naive set theory.
>
> The whole concept of axioms are statements (ideally simple and "basic"
> statements) that are independent of your existing set of axioms - that
> is, both the axiom and its negation are consistent with the set you have
> already.  This means you can add the axiom to your set, or remove it, or
> pick different axioms.  (Think of them like basis vectors in a vector
> space.)
>
> That means we /can/ find a new set of axioms that answer the question of
> whether aleph 1 equals beth 1 - just add the continuum hypothesis as a
> new axiom to existing ZFC.
>
>> Or, possibly, a "collections theory", since it may well be the case
>> that excluding
>> things like the set of all sets is not something we want to do.
>> (Genuinely
>> paradoxical sets, of course, like the set of all sets that don't
>> include themselves,
>> still would have to be excluded.)
>>
>
> Paradoxes are unavoidable - or at least, you can't prove that you won't
> have them.  You want to get a good book on Gödel's incompleteness
> theorem, and read it for a bit of mind-bending.  (I don't know what
> would be a good choice, and of course it depends on what balance you
> want between "easy reading layman explanations" and heavy, rigorous
> mathematics.)  It turns out that no matter how you define your
> mathematics, if you've given it enough flexibility to be interesting
> (i.e., enough axioms to be able to count), there will be statements that
> are true but cannot be proven, and others that are false but cannot be
> disproven.

"Godel, Escher, Bach" - Hofstadter

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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
From: jim.brak...@ieee.org (JimBrakefield)
Injection-Date: Fri, 06 May 2022 22:03:09 +0000
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 by: JimBrakefield - Fri, 6 May 2022 22:03 UTC

On Thursday, May 5, 2022 at 6:59:16 AM UTC-5, Terje Mathisen wrote:
> MitchAlsup wrote:
> > On Wednesday, May 4, 2022 at 2:20:50 PM UTC-5, Quadibloc wrote:
> >> On Monday, May 2, 2022 at 3:08:49 PM UTC-6, MitchAlsup wrote:
> >>
> >>> You need to use real math, There is an infinite sequence of (ahem) infinities
> >>> ℌ₀ being the first ℌ₁ being the second,...
> >
> >> Of course, we know what ℵ₀ is, the number of years in forever - the cardinality of
> >> the natural numbers. While we also have a definition for ℵ₁ - which is the number of
> >> well-orderings of the natural numbers - we don't know if the cardinality of the continuum
> >> (the number of real numbers) is equal to aleph-one, or if it is much greater.
> > <
> > I was taught (1974) that the number of integers and the number of reals is the same
> > both ℌ₀. You have to find a counting problem that causes k×ℌ₀×ℌ₀ = ℌ₁ (for any
> > K > 0)
> Mitch, you are wrong here: The proof that the cardinality of real
> numbers is greater than Aleph-0, the number of integers (as well as
> rationals by the triangle countability proof) was on of the first
> findings of Cantor afaik. (I did read a/his book many decades ago.)
>
> I.e. real numbers are not countable.
>
> Terje
>
> --
> - <Terje.Mathisen at tmsw.no>
> "almost all programming can be viewed as an exercise in caching"

It has been said that almost all integers are large, as opposed to almost
all numbers humans encounter are small.
The same can not be said for reals as they are uncountable?

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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From: monn...@iro.umontreal.ca (Stefan Monnier)
Newsgroups: comp.arch
Subject: Re: The purpose of our universe simulation was just made clear to me through communication with time.
Date: Fri, 06 May 2022 19:07:07 -0400
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 by: Stefan Monnier - Fri, 6 May 2022 23:07 UTC

JimBrakefield [2022-05-06 15:03:08] wrote:
> It has been said that almost all integers are large, as opposed to almost
> all numbers humans encounter are small.
> The same can not be said for reals as they are uncountable?

The numbers that human will encounter are pretty much all among the
computable numbers (of which there are aleph0 "only") anyway.
The rest is a bit like dark matter: the theory says it's there but we
can't see it.

Stefan

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
From: MitchAl...@aol.com (MitchAlsup)
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 by: MitchAlsup - Sat, 7 May 2022 00:23 UTC

On Friday, May 6, 2022 at 6:07:11 PM UTC-5, Stefan Monnier wrote:
> JimBrakefield [2022-05-06 15:03:08] wrote:
> > It has been said that almost all integers are large, as opposed to almost
> > all numbers humans encounter are small.
> > The same can not be said for reals as they are uncountable?
> The numbers that human will encounter are pretty much all among the
> computable numbers (of which there are aleph0 "only") anyway.
> The rest is a bit like dark matter: the theory says it's there but we
> can't see it.
<
Plank data shows that something like dark mater is really there.
We just don't know how to detect it (other than by watching galactic
clusters magnify background galaxies.)
>
>
> Stefan

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
From: jim.brak...@ieee.org (JimBrakefield)
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 by: JimBrakefield - Sat, 7 May 2022 01:49 UTC

On Friday, May 6, 2022 at 7:23:49 PM UTC-5, MitchAlsup wrote:
> On Friday, May 6, 2022 at 6:07:11 PM UTC-5, Stefan Monnier wrote:
> > JimBrakefield [2022-05-06 15:03:08] wrote:
> > > It has been said that almost all integers are large, as opposed to almost
> > > all numbers humans encounter are small.
> > > The same can not be said for reals as they are uncountable?
> > The numbers that human will encounter are pretty much all among the
> > computable numbers (of which there are aleph0 "only") anyway.
> > The rest is a bit like dark matter: the theory says it's there but we
> > can't see it.
> <
> Plank data shows that something like dark mater is really there.
> We just don't know how to detect it (other than by watching galactic
> clusters magnify background galaxies.)
> >
> >
> > Stefan

Flash news: Dark reals magnify mathematical ignorance.
Actually it is worse than that. There are dark natural numbers:
https://www.hs-augsburg.de/~mueckenh/Transfinity/Dark%20Numbers.pdf
Delving further into the subject leads to politics/arguments?

To put it another way: There be dragons inhabiting infinite time and infinite machines.

Re: The purpose of our universe simulation was just made clear to me through communication with time.

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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
From: jsav...@ecn.ab.ca (Quadibloc)
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 by: Quadibloc - Sat, 7 May 2022 06:10 UTC

On Friday, May 6, 2022 at 7:49:47 PM UTC-6, JimBrakefield wrote:

> Flash news: Dark reals magnify mathematical ignorance.
> Actually it is worse than that. There are dark natural numbers:
> https://www.hs-augsburg.de/~mueckenh/Transfinity/Dark%20Numbers.pdf
> Delving further into the subject leads to politics/arguments?

The paper claims to prove that there exist natural numbers that can't
be identified by a finite string of characters.

That is simply false. Every natural number, no matter how large, can be identified
by a string of digits. The fact that the string of digits is so long that it could never
be written out by mortal man or any machine of his devising is neither here nor
there - the string of digits is finite, even as the number *itself* is finite.

It's certainly true that all but an infinitesimal fraction of the natural numbers
will never by named or uttered by Man or any of his works. But this paper seems
to have a definition of 'dark' that is too broad.

John Savard

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From: a_eder_...@web.de (Andreas Eder)
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Subject: Re: The purpose of our universe simulation was just made clear to me through communication with time.
Date: Sat, 07 May 2022 09:53:43 +0200
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 by: Andreas Eder - Sat, 7 May 2022 07:53 UTC

On Fr 06 Mai 2022 at 23:10, Quadibloc <jsavard@ecn.ab.ca> wrote:

> On Friday, May 6, 2022 at 7:49:47 PM UTC-6, JimBrakefield wrote:
>
>> Flash news: Dark reals magnify mathematical ignorance.
>> Actually it is worse than that. There are dark natural numbers:
>> https://www.hs-augsburg.de/~mueckenh/Transfinity/Dark%20Numbers.pdf
>> Delving further into the subject leads to politics/arguments?
>
> The paper claims to prove that there exist natural numbers that can't
> be identified by a finite string of characters.
>
> That is simply false. Every natural number, no matter how large, can be identified
> by a string of digits. The fact that the string of digits is so long that it could never
> be written out by mortal man or any machine of his devising is neither here nor
> there - the string of digits is finite, even as the number *itself* is finite.
>
> It's certainly true that all but an infinitesimal fraction of the natural numbers
> will never by named or uttered by Man or any of his works. But this paper seems
> to have a definition of 'dark' that is too broad.
>
> John Savard

That paper is by Wolfgang Mückenheim. He is a well known crank.

'Andreas

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From: david.br...@hesbynett.no (David Brown)
Newsgroups: comp.arch
Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
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 by: David Brown - Sat, 7 May 2022 12:31 UTC

On 07/05/2022 01:07, Stefan Monnier wrote:
> JimBrakefield [2022-05-06 15:03:08] wrote:
>> It has been said that almost all integers are large, as opposed to almost
>> all numbers humans encounter are small.
>> The same can not be said for reals as they are uncountable?
>
> The numbers that human will encounter are pretty much all among the
> computable numbers (of which there are aleph0 "only") anyway.
> The rest is a bit like dark matter: the theory says it's there but we
> can't see it.
>

The fun thing is that we can identify and describe some non-computable
real numbers without ever having a way to actually compute them!

<https://en.wikipedia.org/wiki/Chaitin%27s_constant>

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From: terje.ma...@tmsw.no (Terje Mathisen)
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Subject: Re: The purpose of our universe simulation was just made clear to me
through communication with time.
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 by: Terje Mathisen - Sat, 7 May 2022 13:02 UTC

David Brown wrote:
> Paradoxes are unavoidable - or at least, you can't prove that you won't
> have them.  You want to get a good book on Gödel's incompleteness
> theorem, and read it for a bit of mind-bending.  (I don't know what
> would be a good choice, and of course it depends on what balance you
> want between "easy reading layman explanations" and heavy, rigorous
> mathematics.)  It turns out that no matter how you define your
> mathematics, if you've given it enough flexibility to be interesting
> (i.e., enough axioms to be able to count), there will be statements that
> are true but cannot be proven, and others that are false but cannot be
> disproven.

Id doesn't matter if you care about the details or not, everyone should
read Hofstadter's GEB - An Eternal Golden Braid! The book won a Pulitzer
Price as well afair?

Terje

--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"

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From: monn...@iro.umontreal.ca (Stefan Monnier)
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Subject: Re: The purpose of our universe simulation was just made clear to me through communication with time.
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 by: Stefan Monnier - Sat, 7 May 2022 16:21 UTC

David Brown [2022-05-07 14:31:56] wrote:
> On 07/05/2022 01:07, Stefan Monnier wrote:
>> JimBrakefield [2022-05-06 15:03:08] wrote:
>>> It has been said that almost all integers are large, as opposed to almost
>>> all numbers humans encounter are small.
>>> The same can not be said for reals as they are uncountable?
>>
>> The numbers that human will encounter are pretty much all among the
>> computable numbers (of which there are aleph0 "only") anyway.
>> The rest is a bit like dark matter: the theory says it's there but we
>> can't see it.
> The fun thing is that we can identify and describe some non-computable
> real numbers without ever having a way to actually compute them!
> <https://en.wikipedia.org/wiki/Chaitin%27s_constant>

Indeed, we humans can occasionally encounter non-computable numbers that
we can describe (another example is for some some (bounded) increasing
sequences, where the least upper bound is not computable even though
each of the numbers in the sequence is), but I still think it's a good
analog of the dark matter (whose effect we can also occasionally
witness) :-)

Stefan

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