Banach–Tarski paradox

[peteolcott]

---
The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together
in a different way to yield two identical copies of the original ball.

Any idiot knowing any geometry would know that spheres are comprised on an infinite number of points, thus making the above claim silly.

Copyright 2018 Pete Olcott // just in case no one noticed this silly mistake before.

[Rupert]

No, the claim is fine, the ball is partitioned into finitely many sets some of which are infinite.

[Ross A. Finlayson]

On Friday, August 17, 2018 at 8:05:28 PM UTC-7, Rupert wrote:
> No, the claim is fine, the ball is partitioned into finitely many sets some of which are infinite.

They each are, except one of the 5 might be
just a point while the other 4 equidecomposable
"subsets" of the "points" are each "non-measurable"
(or so the story goes).

Much like Vitali's construction, about what would
be "measure-preserving" transformations that result
in doubling (neatly), one way to look at it is that
those sets are non-measurable, and another that the
properties of the points is finding 1 or 2 sides "in"
or "on" the line, and then about moving to the plane
that "sides" or "directions" as converging to the point
the gap in abscence is skipped over and that the resulting
"doubling" in measure is as the "equidecomposable"
duplicates are quite so completely split apart this way.


There are some apocryphal situations in physics where
something like this pops up so they insert this sort
of explanation. This is usually stopping exactly and
only at "doubling", though.

https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

[peteolcott]

On 8/17/2018 10:05 PM, Rupert wrote:
> No, the claim is fine, the ball is partitioned into finitely many sets some of which are infinite.
>

A (for concrete example, one inch diameter) sphere cannot possibly
be partitioned into any sets at all and remain spherical. It always
requires every single one of its infinite number of points.

[Jeff Barnett]

Once again in the breach with utter nonsense! Let's take another thing
comprised of an infinite number of things - the integers. Consider: both
the odds and evens are infinite subsets. Was that so hard. Don't you
think that you ought to think before writing your drivel? If you had
tried to read the proof (much much too hard for a novice at your level)
you might have gained enough insight to not post this foolishness. You
still wouldn't understand the theorem but at least you wouldn't have
soiled your pants in public. Again.

You are defective in so many elementary ways that you should take a
break: give your mind a rest and see if you can crawl back to non brain
dead. Give these news groups a break from the sound of breaking wind.
--
Jeff Barnett

[peteolcott]

If you remove a single point of a 1 inch diameter sphere having
its center point anchored in the 3D space (relative to 10,000
miles straight north of the center of the Earth) it is no longer
a sphere at all.

I anchor this in a specific geographic location so you cannot fool
yourself into using the same point twice.

[Jeff Barnett]

So you can't understand what the theorem says is true can you. You
decompose the sphere in to several parts each of which has a possibly
infinite number of points - the cardinailty and topological properties
of each piece being specified. Then you use some of those pieces to
construct one sphere then the rest to construct another. It's a mind
bending and beautiful result that can only be understood by someone who
appreciates the mathematics involved. We know that's not you. If you
want to remove your ignorance, grab books on real analysis aka point set
topology and measure theory (a math topic, not engineering) and crawl in
a hole for a few months and study. It seems that you have about the same
level of understanding here as in logic: damn little.

Question for you: How do you always and I do mean always claim unique
insight when near total ignorance and your lack of ability to read and
understand are the obvious reality?
--
Jeff Barnett

[Rupert]

We're not saying the sets in the partition are spherical. Their union is a ball, and the union of their images under a bunch of rotational isometries is two balls. The pieces are made using the axiom of Choice, they are not Boreland sets.

[peteolcott]

On 8/18/2018 1:20 AM, Jeff Barnett wrote:
> peteolcott wrote on 8/17/2018 11:32 PM:
>> On 8/17/2018 11:40 PM, Jeff Barnett wrote:
>>> peteolcott wrote on 8/17/2018 8:15 PM:
>>>> ---
>>>> The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back
>>>> together in a different way to yield two identical copies of the original ball.
>>>>
>>>> Any idiot knowing any geometry would know that spheres are comprised on an infinite number of points, thus making the above claim silly.
>>>>
>>>> Copyright 2018 Pete Olcott // just in case no one noticed this silly mistake before.
>>>
>>> Once again in the breach with utter nonsense! Let's take another thing comprised of an infinite number of things - the integers. Consider: both the odds and evens are infinite subsets. Was that so hard. Don't you think that you ought to think before
>>> writing your drivel? If you had tried to read the proof (much much too hard for a novice at your level) you might have gained enough insight to not post this foolishness. You still wouldn't understand the theorem but at least you wouldn't have soiled
>>> your pants in public. Again.
>>>
>>> You are defective in so many elementary ways that you should take a break: give your mind a rest and see if you can crawl back to non brain dead. Give these news groups a break from the sound of breaking wind.
>>
>> If you remove a single point of a 1 inch diameter sphere having
>> its center point anchored in the 3D space (relative to 10,000
>> miles straight north of the center of the Earth) it is no longer
>> a sphere at all.
>>
>> I anchor this in a specific geographic location so you cannot fool
>> yourself into using the same point twice.
>
> So you can't understand what the theorem says is true can you. You decompose the sphere in to several parts each of which has a possibly infinite number of points - the cardinailty and topological properties of each piece being specified. Then you use some
> of those pieces to construct one sphere then the rest to construct another.

When these points are georeferenced as I specified, then they cannot
actually be moved at all. One could copy an infinite set of points
to create an different set of points, yet these would not be the
original points at all.

If one removes even a single point to begin to create another different
georeferenced sphere, this original object would no longer be a sphere.

If you take the points away and don't put them all back in the same
place then they are not the same points. If you take all of the points
away put one set back in the same place and put another set somewhere
else then these points in the other place are copies of (thus not the
same as) the original points.

Copyright 2018 Pete Olcott

[peteolcott]

On 8/18/2018 3:03 AM, Rupert wrote:
> We're not saying the sets in the partition are spherical. Their union is a ball, and the union of their images under a bunch of rotational isometries is two balls. The pieces are made using the axiom of Choice, they are not Boreland sets.
>

Ah so so are trying to get away with fudging the meaning of the words.
If by ball you mean a physically existing object then we are not dealing
with points we are dealing with atoms. If you take away all of the atoms
and divide them into two balls of the same size and shape they now have
half as much mass.

Talking about points on a physically exiting ball is incongruous thus
incoherent. It is either atoms of a ball or points on a sphere. Either
way Banach–Tarski is simply a silly mistake.

Copyright 2018 Pete Olcott

[Rupert]

No, I made no reference to physical reality at all, and there was no fudging of the meanings of words. The Banach-Tarski paradox is provable in ZFC. It says that there exists a partition of the solid ball in 3-space into five subsets, four of which have infinitely many points and which are not Borel sets. What you are saying is rubbish.

[Peter Percival]

What has that got to do with the Banach–Tarski paradox?

[Peter Percival]

peteolcott wrote:

> When these points are georeferenced as I specified, then they cannot
> actually be moved

The proof makes reference to isometries. What has your "geo" got to do
with anything?

[Peter Percival]

peteolcott wrote:
> On 8/18/2018 3:03 AM, Rupert wrote:
>> We're not saying the sets in the partition are spherical. Their union
>> is a ball, and the union of their images under a bunch of rotational
>> isometries is two balls. The pieces are made using the axiom of
>> Choice, they are not Boreland sets.
>>
>
> Ah so so are trying to get away with fudging the meaning of the words.
> If by ball

Obviously the ball isn't physical, you dribbling half-wit.

[peteolcott]

You would have to point out an actual error of my reasoning for your
assertion that it is rubbish to have any basis what-so-ever.

The fact that two different sets of reasoning derive contradictory
conclusions unequivocally proves that at least one of these sets
must be incorrect. I assert that any reasoning contradicting the
reasoning that I provided has hidden gaps.

I have spent almost no time examining Banach–Tarski, yet see no error
in my current reasoning. If it actually is impossible to show any error
in my reasoning then concluding that it is incorrect would be a logical
error.

http://mathworld.wolfram.com/Banach-TarskiParadox.html

I have made at least one serious mistake in this forum that Jim Burn's
corrected. I did apparently go off half cocked about the ordinality of
sets. From what I recall I accepted Jim's correction the same day.

[Peter Percival]

peteolcott wrote:
> ---
> The Banach–Tarski paradox is a theorem in set-theoretic geometry, which
> states the following: Given a solid ball in 3‑dimensional space, there
> exists a decomposition of the ball into a finite number of disjoint
> subsets, which can then be put back together in a different way to yield
> two identical copies of the original ball.
>
> Any idiot knowing any geometry would know that spheres are comprised on
> an infinite number of points, thus making the above claim silly.

(i) You are posting to the wrong newsgroups.

(ii) The pieces (five will do!) into which the original sphere is
decomposed are not themselves spheres.

Is there any hope that you will find out about the Banach–Tarski paradox
before commenting on it further (maybe by reading Stan Wagon's book)?
No, there isn't, is there?

[Peter Percival]

peteolcott wrote:
> On 8/18/2018 9:47 AM, Rupert wrote:
>> On Saturday, August 18, 2018 at 4:03:32 PM UTC+2, peteolcott wrote:
>>> On 8/18/2018 3:03 AM, Rupert wrote:
>>>> We're not saying the sets in the partition are spherical. Their
>>>> union is a ball, and the union of their images under a bunch of
>>>> rotational isometries is two balls. The pieces are made using the
>>>> axiom of Choice, they are not Boreland sets.
>>>>
>>>
>>> Ah so so are trying to get away with fudging the meaning of the words.
>>> If by ball you mean a physically existing object then we are not dealing
>>> with points we are dealing with atoms. If you take away all of the atoms
>>> and divide them into two balls of the same size and shape they now have
>>> half as much mass.
>>>
>>> Talking about points on a physically exiting ball is incongruous thus
>>> incoherent. It is either atoms of a ball or points on a sphere. Either
>>> way Banach–Tarski is simply a silly mistake.
>>>
>>> Copyright 2018 Pete Olcott
>>
>> No, I made no reference to physical reality at all, and there was no
>> fudging of the meanings of words. The Banach-Tarski paradox is
>> provable in ZFC. It says that there exists a partition of the solid
>> ball in 3-space into five subsets, four of which have infinitely many
>> points and which are not Borel sets. What you are saying is rubbish.
>>
>
> You would have to point out an actual error of my reasoning

And do you feel any obligation to point out the "actual error" in Banach
and Tarski's paper (Sur la décomposition des ensembles de points en
parties respectivement congruentes, /Fundamenta Mathematicae/, vol 6,
pages 244–277 (on-line copies may be found))?

> for your
> assertion that it is rubbish to have any basis what-so-ever.
>
> The fact that two different sets of reasoning derive contradictory
> conclusions unequivocally proves that at least one of these sets
> must be incorrect. I assert that any reasoning contradicting the
> reasoning that I provided has hidden gaps.
>
> I have spent almost no time examining Banach–Tarski

Obviously. Will you spend any time "examining" it? No.

[Rupert]

On Saturday, August 18, 2018 at 6:54:18 PM UTC+2, peteolcott wrote:
> On 8/18/2018 9:47 AM, Rupert wrote:
> > On Saturday, August 18, 2018 at 4:03:32 PM UTC+2, peteolcott wrote:
> >> On 8/18/2018 3:03 AM, Rupert wrote:
> >>> We're not saying the sets in the partition are spherical. Their union is a ball, and the union of their images under a bunch of rotational isometries is two balls. The pieces are made using the axiom of Choice, they are not Boreland sets.
> >>>
> >>
> >> Ah so so are trying to get away with fudging the meaning of the words.
> >> If by ball you mean a physically existing object then we are not dealing
> >> with points we are dealing with atoms. If you take away all of the atoms
> >> and divide them into two balls of the same size and shape they now have
> >> half as much mass.
> >>
> >> Talking about points on a physically exiting ball is incongruous thus
> >> incoherent. It is either atoms of a ball or points on a sphere. Either
> >> way Banach–Tarski is simply a silly mistake.
> >>
> >> Copyright 2018 Pete Olcott
> >
> > No, I made no reference to physical reality at all, and there was no fudging of the meanings of words. The Banach-Tarski paradox is provable in ZFC. It says that there exists a partition of the solid ball in 3-space into five subsets, four of which have infinitely many points and which are not Borel sets. What you are saying is rubbish.
> >
>
> You would have to point out an actual error of my reasoning for your
> assertion that it is rubbish to have any basis what-so-ever.

So you're putting forward a claim to having engaged in reasoning?

[Shobe, Martin]

On 8/18/2018 9:03 AM, peteolcott wrote:
> On 8/18/2018 3:03 AM, Rupert wrote:
>> We're not saying the sets in the partition are spherical. Their union
>> is a ball, and the union of their images under a bunch of rotational
>> isometries is two balls. The pieces are made using the axiom of
>> Choice, they are not Boreland sets.
>>
>
> Ah so so are trying to get away with fudging the meaning of the words.

No. That's your shtick.

> If by ball you mean a physically existing object then we are not dealing
> with points we are dealing with atoms. If you take away all of the atoms
> and divide them into two balls of the same size and shape they now have
> half as much mass.
>
> Talking about points on a physically exiting ball is incongruous thus
> incoherent. It is either atoms of a ball or points on a sphere. Either
> way Banach–Tarski is simply a silly mistake.

Stop fudging with the meaning of words. We don't mean a physically
existing object.

Martin Shobe

[Shobe, Martin]

On 8/18/2018 11:54 AM, peteolcott wrote:
> On 8/18/2018 9:47 AM, Rupert wrote:
>> On Saturday, August 18, 2018 at 4:03:32 PM UTC+2, peteolcott wrote:
>>> On 8/18/2018 3:03 AM, Rupert wrote:
>>>> We're not saying the sets in the partition are spherical. Their
>>>> union is a ball, and the union of their images under a bunch of
>>>> rotational isometries is two balls. The pieces are made using the
>>>> axiom of Choice, they are not Boreland sets.
>>>>
>>>
>>> Ah so so are trying to get away with fudging the meaning of the words.
>>> If by ball you mean a physically existing object then we are not dealing
>>> with points we are dealing with atoms. If you take away all of the atoms
>>> and divide them into two balls of the same size and shape they now have
>>> half as much mass.
>>>
>>> Talking about points on a physically exiting ball is incongruous thus
>>> incoherent. It is either atoms of a ball or points on a sphere. Either
>>> way Banach–Tarski is simply a silly mistake.
>>>
>>> Copyright 2018 Pete Olcott
>>
>> No, I made no reference to physical reality at all, and there was no
>> fudging of the meanings of words. The Banach-Tarski paradox is
>> provable in ZFC. It says that there exists a partition of the solid
>> ball in 3-space into five subsets, four of which have infinitely many
>> points and which are not Borel sets. What you are saying is rubbish.
>>
>
> You would have to point out an actual error of my reasoning for your
> assertion that it is rubbish to have any basis what-so-ever.

Like pointing out that your presupposition was wrong?

Martin Shobe

[George Greene]

On Friday, August 17, 2018 at 11:05:28 PM UTC-4, Rupert wrote:
> No, the claim is fine, the ball
> is partitioned into finitely many sets some of which are infinite.

But the OP, PO, dared to call the claim silly.

Even though literally thousands of math professors have been agreeing with it
for decades.

What does THAT mean?

Aren't you sort of ignoring the OP's having publicly professed his mental
illness here? Do you really think that is legitimately tolerable?

[George Greene]

On Saturday, August 18, 2018 at 12:01:17 AM UTC-4, peteolcott wrote:
> A (for concrete example, one inch diameter) sphere cannot possibly
> be partitioned into any sets at all and remain spherical. It always
> requires every single one of its infinite number of points.

Damn, you're stupid.
A parition doesn't "remove" any points. It just assigns each point -- each AND EVERY point -- to one (and only one -- no more, no less) of the parts.

The fact that you did NOT ALREADY know this
is deplorable.

How can you expect anybody to listen to anything you say
about anything COMPLICATED when you have just PUBLICLY PROVEN
that you are too stupid to even know what "partition" means??

[George Greene]

On Saturday, August 18, 2018 at 12:54:18 PM UTC-4, peteolcott wrote:
> You would have to point out an actual error of my reasoning

Everybody pointed out that your dumb ass didn't know what a partition was.
Everybody pointed out that you claimed that an infinite set couldn't have
a finite partition. That was erroneous. So WE DID that.

> for your
> assertion that it is rubbish to have any basis what-so-ever.

And we did that. "Finite partition" means partitioned into a finite
NUMBER OF parts, NOT that all the parts have a finite number of points.
You made the error and we DID point it out.

> The fact that two different sets of reasoning derive contradictory
> conclusions unequivocally proves that at least one of these sets
> must be incorrect.

No, it doesn't, because you don't know what "correct" means.
Reasoning can be "correct" without being sound.
The chain of reasoning from "if the weather is sunny" to "the clothes on the
clothesline will dry out" is every bit as correct as the chain from
"if the weather is rainy" to "the clothes on the clothesline will be wet".
Yet they lead to opposite conclusions. One of them may be sound one
day and unsound the next -- equally so the other. Whether P does or
doesn't (tauto-)logically imply Q has NOTHING WHATSOEVER TO DO with
whether P is true or false. Unforutunately, you also didn't know THAT,
yet here you sit trying to sound authoritative among experts, when
you don't even know basic simple stuff.

The only reason we engage is to study modes of mental illness, I fear.

[peteolcott]

On 8/18/2018 11:47 AM, Peter Percival wrote:
> peteolcott wrote:
>
>> When these points are georeferenced as I specified, then they cannot
>> actually be moved
>
> The proof makes reference to isometries.  What has your "geo" got to do with anything?
>

It prevents idiots from getting confused and using the same point twice.

[Ross A. Finlayson]

Why, they're idiots?

[peteolcott]

Banach-Tarski Paradox
First stated in 1924, the Banach-Tarski paradox states that it is
possible to decompose a ball into six pieces which can be reassembled
by rigid motions to form two balls of the same size as the original.
The number of pieces was subsequently reduced to five by Robinson
(1947), although the pieces are extremely complicated.

I contend that it is impossible to decompose any sphere into any
subsets and recompose two identical spheres from these same points.

My proof of that is that when these points are georeferenced
(to eliminate the possibility of inadvertently using the same
points twice) it is self-evident that no method for achieving
the desired end-result can possibly exist.

On the other hand, not having these points georeferenced would
allow the possibility of using the same points twice to go
undetected.

Copyright 2018 Pete Olcott

[Jim Burns]

On 8/20/2018 1:51 PM, peteolcott wrote:
> On 8/18/2018 12:59 PM, Rupert wrote:
>> On Saturday, August 18, 2018 at 6:54:18 PM UTC+2,
>> peteolcott wrote:

>>> You would have to point out an actual error of my reasoning
>>> for your assertion that it is rubbish to have any basis
>>> what-so-ever.
>>
>> So you're putting forward a claim to having engaged in
>> reasoning?
>
> Banach-Tarski Paradox
> First stated in 1924, the Banach-Tarski paradox states
> that it is possible to decompose a ball into six pieces
> which can be reassembled by rigid motions to form two
> balls of the same size as the original. The number of
> pieces was subsequently reduced to five by Robinson (1947),
> although the pieces are extremely complicated.
>
> I contend that it is impossible to decompose any sphere
> into any subsets and recompose two identical spheres from
> these same points.
>

> My *proof* of that is that when these points are georeferenced

> (to eliminate the possibility of inadvertently using the same

> points twice) *it is self-evident* that no method for achieving

> the desired end-result can possibly exist.

*emphasis added*

"It is self-evident" is not a proof of your claim.

Your attempt to use the phrase as a proof does prove that
you have not the faintest idea what a proof is, but that's all.

> On the other hand, not having these points georeferenced
> would allow the possibility of using the same points twice
> to go undetected.

I would suggest that you (PO) go look at the proof in order to
see that points are not being referenced twice, except that
(1) I know you won't do that, and (2) even if you ever did,
you wouldn't understand what you're looking at.

This isn't much different from your argument for the
invalidity of Godel's and Tarski's results on formal
incompleteness and undefinability of truth: You don't
know what is being said, so you make something up.
At that point, it is "self-evident" to you that the thing
you made up is wrong.

I'm not sure I've ever seen you make an argument that is
different from this in any important way:
"I (PO) don't know what you're saying, so I'll pretend this
other thing is what you're saying, and show that the
other thing is wrong."

https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

[peteolcott]

AKA axiomatic. The point is totally proven entirely on the basis
of the meaning of its words.

>
> Your attempt to use the phrase as a proof does prove that
> you have not the faintest idea what a proof is, but that's all.

Mutually interlocking semantic specifications. Not the sort of
thing that you would have much knowledge of or experience with.

>
>> On the other hand, not having these points georeferenced
>> would allow the possibility of using the same points twice
>> to go undetected.
>
> I would suggest that you (PO) go look at the proof in order to
> see that points are not being referenced twice, except that
> (1) I know you won't do that, and (2) even if you ever did,
> you wouldn't understand what you're looking at.
>

When points are uniquely identified by georeferencing it
is obvious that only a single sphere can possibly exist
with these uniquely identified points.

When-so-ever these points are not uniquely identified then
using a point more than once is indiscernible.

Do you have some other way besides georeferencing that makes
using the same point more than once unequivocally discernible?

I contend that no such system exists, provide a counter-example
proving me wrong on this point.

This whole (Banach–Tarski paradox) only arises because people
are not using my solution (derived in 15 minutes) to totally
abolish the whole issue of: [The Identity of Indiscernibles]
https://plato.stanford.edu/entries/identity-indiscernible/

When the identity of a thing also includes its precise point
in space-time, then two different things are always discernible
and have unique identities.

An imaginary sphere may not have a location in time, yet when
anchored in space has a unique identity. When it is not anchored
in space it lacks a unique identity. Thus the whole idea of
decomposing and recomposing a specific sphere that is not anchored
in space is incorrect because it is impossible to actually
identify any such sphere.

Copyright 2016, 2017, 2018 Pete Olcott

[wugi]

Op 20/08/2018 om 19:51 schreef peteolcott:

> Banach-Tarski Paradox
> First stated in 1924, the Banach-Tarski paradox states that it is
> possible to decompose a ball into six pieces which can be reassembled
> by rigid motions to form two balls of the same size as the original.
> The number of pieces was subsequently reduced to five by Robinson
> (1947), although the pieces are extremely complicated.
>
> I contend that it is impossible to decompose any sphere into any
> subsets and recompose two identical spheres from these same points.
>
> My proof of that is that when these points are georeferenced
> (to eliminate the possibility of inadvertently using the same
> points twice) it is self-evident that no method for achieving
> the desired end-result can possibly exist.
>
> On the other hand, not having these points georeferenced would
> allow the possibility of using the same points twice to go
> undetected.

Even if formulated in a more challenging way than the following
examples, I see hardly a difference with the fact that any line segment
is equipotent (or what's it called) to any other line segment, yes to
any surface, to any volume, and so on: R ~ R^n.

So let's take two concentric circles with radii r and 2r. Circle r can
self-evidently be transformed onto circle 2r. Each point of circle r
finds its own place on circle 2r by a simple radial transfer (and vice
versa). Afterwards, from the circle 2r curve you can make two new
circles with radius r.

QED

--
"copywrite" guido wugi

[peteolcott]

[Mike Terry]

True, but here you're partitioning the cirlce into infinitely many
partitions, which is missing a key point.

Try again, but dividing the circle into only a finite number of pieces!

Regards,
Mike.

[FredJeffries]

But those aren't rigid motions

http://mathworld.wolfram.com/RigidMotion.html

https://en.wikipedia.org/wiki/Motion_(geometry)

https://www.cut-the-knot.org/do_you_know/banach.shtml

[Jim Burns]

On 8/20/2018 3:39 PM, peteolcott wrote:

> When the identity of a thing also includes its precise point
> in space-time, then two different things are always discernible
> and have unique identities.

Your mention of space-time must mean that you're referring
to the actual world. In the actual world, some objects
(fundamental particles, for example) can be different and
also indiscernible.

It's a quantum thing. Suppose we want to know how many
states W the electrons in a piece of silicon crystal _could_
be in, if the total energy of the electrons were U.
(W is essentially the entropy S of the electrons,
S = k log W, a very important physical measurement.)

If we count the possible states while assuming that the
electrons are all discernible from each other, _we get_
_the wrong number_ as revealed by our measurements. If we
count while assuming electrons are _not_ discernible,
_we get the right number_ .

For example, suppose we have three orbitals that _could_
accept an electron, and two electrons -- discernible,
we assume, so e1 and e2. How many states are possible?

[e1][e2][ ], [e1][ ][e2], [ ][e1][e2],
[e2][e1][ ], [e2][ ][e1], [ ][e2][e1]

So, six states.
How many states if the electrons are indiscernible?

[e][e][ ], [e][ ][e], [ ][e][e],
[e][e][ ], [e][ ][e], [ ][e][e]

This time, *three states*, because swapping the positions
of indiscernible electrons leaves the state unaltered.

It's an odd thing to be correcting the Creator of the
Universe about, but there you have it. It would be an
understandable mistake to come from one of us non-Creators.

----
Of course, the Banach-Tarski paradox is not about the
actual physical universe, so both your comment and my
rejoinder are irrelevant to that. I just mean to correct
that one mistake in this post, and leave your others
for later.

[Jim Burns]

On 8/20/2018 3:39 PM, peteolcott wrote:

> On 8/20/2018 1:22 PM, Jim Burns wrote:
>> On 8/20/2018 1:51 PM, peteolcott wrote:
>>> On 8/18/2018 12:59 PM, Rupert wrote:
>>>> On Saturday, August 18, 2018 at 6:54:18 PM UTC+2,
>>>> peteolcott wrote:

>>>>> You would have to point out an actual error of my
>>>>> reasoning for your assertion that it is rubbish to
>>>>> have any basis what-so-ever.
>>>>
>>>> So you're putting forward a claim to having engaged in
>>>> reasoning?
>>>
>>> Banach-Tarski Paradox
>>> First stated in 1924, the Banach-Tarski paradox states
>>> that it is possible to decompose a ball into six pieces
>>> which can be reassembled by rigid motions to form two
>>> balls of the same size as the original. The number of
>>> pieces was subsequently reduced to five by Robinson
>>> (1947), although the pieces are extremely complicated.
>>>
>>> I contend that it is impossible to decompose any sphere
>>> into any subsets and recompose two identical spheres from
>>> these same points.
>>>
>>> My *proof* of that is that when these points are
>>> georeferenced (to eliminate the possibility of

>>> inadvertently using the same points twice) *it is*
>>> *self-evident* that no method for achieving the desired

>>> end-result can possibly exist.
>> *emphasis added*
>>
>> "It is self-evident" is not a proof of your claim.
>
> AKA axiomatic. The point is totally proven entirely on
> the basis of the meaning of its words.

(1) A proposition being provable on the basis of the meaning
of its words _is not_ the same as that proposition being
self-evident. There are many examples of long and intricate
lines of reasoning, definitely not self-evident, which are
based on the meanings of the words. Godel's and Tarski's
works are probably examples. Do you claim their results are
self-evident?

I think that by "self-evident" you don't mean anything more
than that we should be able to work it out for ourselves --
which would be fine, I suppose, if there were something to
work out. Except, you don't know of any such proof that
"My proof" refers to. "My proof" promised us a proof, but
all you gave us was "Go prove my proof for me" (which is
how I translate "self-evident").

(2) _You (PO) don't know_ what the meanings of the words used
in the Banach-Tarski paradox _are_ . For you to call upon
them as support for your claim is dishonest. To substitute
_your own_ meanings for what others mean is also dishonest.
I can't tell which is worse, but both are very bad.

>> Your attempt to use the phrase as a proof does prove
>> that you have not the faintest idea what a proof is,
>> but that's all.
>
> Mutually interlocking semantic specifications. Not the
> sort of thing that you would have much knowledge of or
> experience with.

Sigh. You prove my point. You don't have a clue.

Also, if I weren't used to it by now, I would consider
taking offense at your apparent attempt to dazzle me
with polysyllabic bloviation -- offense taken because
"mutually interlocking semantic specifications" is such
very low-grade, un-dazzling polysyllabic bloviation.

The phrase "mutually interlocking semantic specifications"
describes any dictionary. It does not describe any proof,
I think. It seems that what you mean by "proof" is
"Peter Olcott says this is so". That's not a proof.
I'm pretty sure I've mentioned this to you before.

[peteolcott]

Which cannot possibly be recomposed into two identical spheres if every point of these original two pieces has been georeferenced.

If every point in the original sphere had not been georeferenced then the original sphere would have never been uniquely identified thus even talking about it would be incorrect.

[Peter Percival]

What do you mean by "georeferenced"? It is not a word I have come
across before.

[Peter Percival]

peteolcott wrote:


> Banach-Tarski Paradox
> First stated in 1924, the Banach-Tarski paradox states that it is
> possible to decompose a ball into six pieces which can be reassembled
> by rigid motions to form two balls of the same size as the original.
> The number of pieces was subsequently reduced to five by Robinson
> (1947), although the pieces are extremely complicated.
>
> I contend that it is impossible to decompose any sphere into any
> subsets and recompose two identical spheres from these same points.
>
> My proof of that is

What?

Also, are you posting to appropriate newsgroups?

[Peter Percival]

What have points in space-time got to do with the Banach–Tarski paradox?
It seems that you do not know what mathematicians mean by "sphere".

[peteolcott]

I already explained that:

The center of a one inch diameter sphere is exactly ten miles above
the center of the north pole.

Without this degree of specificity the sphere is never uniquely
identified thus indiscernible from other spheres.

When we decompose this sphere into any parts and recompose them it is
impossible to create two spheres, thus Banach–Tarski has been fully refuted.

Banach–Tarski only exists because no one ever bothered to uniquely
identify the specific sphere in question, thus got confused and made a
copy of the sphere without realizing that it was only a copy and not
the original sphere at all.

The identity of otherwise indiscernibles is always uniquely established
if anchored in points in space and/or a point in time as appropriate.
In Banach–Tarski we anchor the sphere in points in space.

Copyright 2016, 2017, 2018 Pete Olcott

>

[peteolcott]

I augmented the conception of a sphere such that an individual
sphere can be uniquely identified and thus not inadvertently
conflated with other different spheres having the exact same size.

When I add this required extra degree of discernment, Banach–Tarski
cannot slip through the cracks of vagueness, thus ceases to exist.

Copyright 2018 Pete Olcott

[Peter Percival]

These physical things have nothing to do with the Banach–Tarski paradox.
Do you even know what a sphere is to a mathematician? It's not a
rhetorical question, I'd really like to know if you know.

> Without this degree of specificity the sphere is never uniquely
> identified thus indiscernible from other spheres.
>
> When we decompose this sphere into any parts and recompose them it is
> impossible to create two spheres, thus Banach–Tarski has been fully
> refuted.

Read Banach and Tarski's paper. Where is the first error?

> Banach–Tarski only exists because no one ever bothered to uniquely
> identify the specific sphere in question, thus got confused and made a

Because there is no "the" sphere. The theorem is true of all
mathematical spheres.

> copy of the sphere without realizing that it was only a copy and not
> the original sphere at all.
>
> The identity of otherwise indiscernibles is always uniquely established
> if anchored in points in space and/or a point in time as appropriate.
> In Banach–Tarski we anchor the sphere in points in space.

Time and space are irrelevant.

You're a bit of an idiot, aren't you? And you have no sense of shame.

[Peter Percival]

That's very obliging of you. The Banach–Tarski paradox is about
mathematical spheres, it is not about your augmentation.

[Jim Burns]

On 8/21/2018 10:06 AM, peteolcott wrote:
> On 8/21/2018 7:40 AM, Peter Percival wrote:

>> What do you mean by "georeferenced"?  It is not a word
>> I have come across before.
>
> I already explained that:
>
> The center of a one inch diameter sphere is exactly ten
> miles above the center of the north pole.
>
> Without this degree of specificity the sphere is never
> uniquely identified thus indiscernible from other spheres.

Let the center of a one-inch-diameter sphere S be ten miles
above the north pole. _Rigidly translate_ the points in
sphere S to another location such that the new center of S
is ten miles above the _south_ pole.

Is that impossible to do? Is that what you're claiming?
Because that is the sort of thing that the Banach-Tarski
theorem asks us to do, only instead of rigidly translating
a whole sphere, pieces are rigidly translated, to two
different locations, and there assembled -- rigidly --
into two spheres each the same size as the original sphere.

Go ahead and give the centers of the spheres whatever
latitude, longitude, and altitude you like. That's utterly
irrelevant.

> When we decompose this sphere into any parts and recompose
> them it is impossible to create two spheres,

You don't say _why_ it is impossible.
You don't seem to be aware that you are not saying _why_
it is impossible.

> thus Banach–Tarski has been fully refuted.
>
> Banach–Tarski only exists because no one ever bothered to
> uniquely identify the specific sphere in question, thus
> got confused and made a copy of the sphere without realizing
> that it was only a copy and not the original sphere at all.
>
> The identity of otherwise indiscernibles is always uniquely
> established if anchored in points in space and/or a point in
> time as appropriate. In Banach–Tarski we anchor the sphere
> in points in space.

https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
<wiki>
The reason the Banach-Tarski theorem is called a paradox is
that it contradicts basic geometric intuition. "Doubling the
ball" by dividing it into parts and moving them around by
rotations and translations, without any stretching, bending,
or adding new points, seems to be impossible, since all these
operations ought, intuitively speaking, to preserve the volume.
The intuition that such operations preserve volumes is not
mathematically absurd and it is even included in the formal
definition of volumes. However, this is not applicable here
because in this case it is impossible to define the volumes
of the considered subsets. Reassembling them reproduces a
volume, which happens to be different from the volume at
the start.
</wiki>

[Peter Percival]

Peter Percival wrote:
> peteolcott wrote:
>
>
>> Banach-Tarski Paradox
>> First stated in 1924, the Banach-Tarski paradox states that it is
>> possible to decompose a ball into six pieces which can be reassembled
>> by rigid motions to form two balls of the same size as the original.
>> The number of pieces was subsequently reduced to five by Robinson
>> (1947), although the pieces are extremely complicated.
>>
>> I contend that it is impossible to decompose any sphere into any
>> subsets and recompose two identical spheres from these same points.
>>
>> My proof of that is
>
> What?
>
> Also, are you posting to appropriate newsgroups?

Meant inappropriate.

[peteolcott]

This is related to sci.lang in that it further elaborates the mathematics
of semantics which is the broader subject of the mathematics of the
meaning of words, AKA formal semantics of linguistics.

When we imagine Banach-Tarski and do not provide some way or another
of uniquely identifying the sphere in question (such as georeferencing)
then we inadvertently conflate one sphere with another and through this
conflation confuse ourselves into thinking that one sphere can
be decomposed into pieces and then subsequently recomposed into two
different spheres.

Yes it is quite unconventional to apply georeferencing to mathematical
objects, new knowledge always tends to be quite unconventional. The
only possible way to eliminate the issue of the identity of (otherwise)
indiscernibles is to specify some set of properties such that a distinction
can always be made between two otherwise indiscernible objects.

It occurred to me less then 15 minutes after first encountering the identity
of indiscernibles through Mitch that otherwise indiscernible objects might
always be made discernible when one considers the property of their point in
time and their points in space.

The whole subject of quantum mechanics as illustrated by Schrödinger's cat
has its ultimate ground of being in the actual true nature of reality as
opposed to common misconceptions of this nature of reality.

Since these answers delve into religion they are off-topic here because none
of you has a sufficient basis to begin to understand them. Only the first-hand
direct experience of Buddhist enlightenment adequately provides these answers
in a way accessible to the human mind.

[Peter Percival]

peteolcott wrote:
> ---
> The Banach–Tarski paradox is a theorem in set-theoretic geometry, which
> states the following: Given a solid ball in 3‑dimensional space, there
> exists a decomposition of the ball into a finite number of disjoint
> subsets, which can then be put back together in a different way to yield
> two identical copies of the original ball.
>
> Any idiot knowing any geometry would know that spheres are comprised on
> an infinite number of points, thus making the above claim silly.
>
> Copyright 2018 Pete Olcott // just in case no one noticed this silly
> mistake before.

It seems that your objection to the Banach–Tarski paradox is that no
physical sphere can behave as required.

When you were at school and you were taught what the surface area and
volume of a sphere are, did you object that the reasoning could not
apply to physical spheres?

[Peter Percival]

peteolcott wrote:

>
> The whole subject of quantum mechanics as illustrated by Schrödinger's cat
> has its ultimate ground of being in the actual true nature of reality as
> opposed to common misconceptions of this nature of reality.

Schrödinger with his cat intended to refute the Copenhagen
interpretation of qm. It does not illustrate the whole subject.

[peteolcott]

On 8/21/2018 10:43 AM, Peter Percival wrote:
> peteolcott wrote:
>> ---
>> The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back
>> together in a different way to yield two identical copies of the original ball.
>>
>> Any idiot knowing any geometry would know that spheres are comprised on an infinite number of points, thus making the above claim silly.
>>
>> Copyright 2018 Pete Olcott // just in case no one noticed this silly mistake before.
>
> It seems that your objection to the Banach–Tarski paradox is that no physical sphere can behave as required.
>

Not really. Within the identity of indiscernibles when-so-ever
any sphere is by what-so-ever means uniquely identified then
the Banach–Tarski paradox ceases to be possible.

Copyright 2018 Pete Olcott

[peteolcott]

By what possible means could a cat actually be simultaneously
alive and dead?

[Ross A. Finlayson]

What cat?

[peteolcott]

On 8/21/2018 10:24 AM, Jim Burns wrote:
> On 8/21/2018 10:06 AM, peteolcott wrote:
>> On 8/21/2018 7:40 AM, Peter Percival wrote:
>
>>> What do you mean by "georeferenced"?  It is not a word
>>> I have come across before.
>>
>> I already explained that:
>>
>> The center of a one inch diameter sphere is exactly ten
>> miles above the center of the north pole.
>>
>> Without this degree of specificity the sphere is never
>> uniquely identified thus indiscernible from other spheres.
>
> Let the center of a one-inch-diameter sphere S be ten miles
> above the north pole. _Rigidly translate_ the points in
> sphere S to another location such that the new center of S
> is ten miles above the _south_ pole.
>

It thus ceases to be the original sphere at all.
If by what-so-ever means you end up with more than
one sphere, you simply duplicated the original sphere.

As soon as the sphere is moved from its original location
it loses its identity and is no longer the original sphere
at all.

Think of it as the same idea as the Cantor's cardinality proof.
We have an original sphere that has its own set of unique
points. A set of points that was previously not mapped to
any other points after decomposition and recomposition becomes
mapped to a whole new set of points that did not previously
exist. This proves that we really only just copied the sphere
without realizing it.

Copyright 2018 Pete Olcott

[peteolcott]

https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat

[peteolcott]

On 8/21/2018 1:08 PM, Peter T. Daniels wrote:

> On Tuesday, August 21, 2018 at 11:37:53 AM UTC-4, peteolcott wrote:
>
>> This is related to sci.lang in that it further elaborates the mathematics
>> of semantics which is the broader subject of the mathematics of the
>> meaning of words, AKA formal semantics of linguistics.
>

> Nothing to do with human language. There's no such thing as "formal semantics
> of linguistics."
>

https://academic.oup.com/jos
About the journal
Journal of Semantics covers all areas in the study
of meaning, with a focus on formal and experimental
methods. It welcomes submissions on semantics,
pragmatics, the syntax/semantics interface,
cross-linguistic semantics, experimental studies of
meaning, and semantically informed philosophy of language.

When anyone repeats the same false claim after
being repeatedly corrected it must be dishonestly.

[Ross A. Finlayson]

So, you might presume we follow the link
and read the entire article.

But, is that Schroedinger's cat?

"Schrödinger's cat is a thought experiment,
sometimes described as a paradox,...".

So: what cat?

Parastatistics and Bose and Fermi statistics
are various classification of statistics about
particles in probabilistic models of particle
behavior in particle research grounded and
founded with various (or usually, "the Bayesian
for the Bohmian") probability theory.

https://en.wikipedia.org/wiki/David_Bohm
https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory

"In addition to a wavefunction on the space of
all possible configurations, it also postulates
an actual configuration that exists even when
unobserved. The evolution over time of the
configuration (that is, the positions of all
particles or the configuration of all fields)
is defined by the wave function by a guiding
equation. The evolution of the wave function
over time is given by the Schrödinger equation."

So, what cat?

Also, what wave?

[peteolcott]

On 8/21/2018 1:27 PM, DKleinecke wrote:

> On Tuesday, August 21, 2018 at 11:08:18 AM UTC-7, Peter T. Daniels wrote:
>> On Tuesday, August 21, 2018 at 11:37:53 AM UTC-4, peteolcott wrote:
>>

>>> This is related to sci.lang in that it further elaborates the mathematics
>>> of semantics which is the broader subject of the mathematics of the
>>> meaning of words, AKA formal semantics of linguistics.
>>

>> Nothing to do with human language. There's no such thing as "formal semantics
>> of linguistics."
>

> There does seem to be a group of people who try to add
> semantics to Chomskian formalism and call the result
> "formal semantics". Montague started it and it doesn't
> seem to have died out yet.
>

http://www.cyc.com/documentation/ontologists-handbook/writing-efficient-cycl/cycl-representation-choices/
Since you already acknowledged the validity of the above why are you contradicting yourself now?

[Jim Burns]

On 8/21/2018 4:41 PM, peteolcott wrote:
> On 8/21/2018 10:24 AM, Jim Burns wrote:
>> On 8/21/2018 10:06 AM, peteolcott wrote:
>>> On 8/21/2018 7:40 AM, Peter Percival wrote:

>>>> What do you mean by "georeferenced"?  It is not a word
>>>> I have come across before.
>>>
>>> I already explained that:
>>>
>>> The center of a one inch diameter sphere is exactly ten
>>> miles above the center of the north pole.
>>>
>>> Without this degree of specificity the sphere is never
>>> uniquely identified thus indiscernible from other spheres.
>>
>> Let the center of a one-inch-diameter sphere S be ten miles
>> above the north pole. _Rigidly translate_ the points in
>> sphere S to another location such that the new center of S
>> is ten miles above the _south_ pole.
>
> It thus ceases to be the original sphere at all.

Apparently you got the idea from somewhere that
Banach-Tarski claim is that the two resulting spheres are
in the same location as the one original sphere.

Have you considered finding out what the Banach-Tarski
theorem is? (BIG spoiler: It's not what you think it is.)

[Jim Burns]

On 8/21/2018 5:12 PM, Ross A. Finlayson wrote:

>> https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat
>
> So, you might presume we follow the link
> and read the entire article.
>
> But, is that Schroedinger's cat?
>
> "Schrödinger's cat is a thought experiment,
> sometimes described as a paradox,...".
>
> So: what cat?

Schrödinger's cat was originally a thought experiment,
and much too technically difficult to be actually performed.
An essential part of the experiment was Schrödinger's box
which, when closed, sealed the cat off from observation
_by anyone or anything even in principle_ , sealed off from
the rest of the universe. This was not your cheap-o cardboard
box, nor a box of any other kind of material.

_Decades later_ the art of experimenting around and about
uncollapsed quantum states advanced to the point that
the Schrödinger "thought" experiment could be performed
in real life -- not with a cat, but with other real-world
objects.

The first example I heard of was a superposition of two
electron states in a beryllium atom, floating in a very
well-shielded vacuum. Your wiki-link points to other examples.

What I found fascinating and enlightening about the
beryllium-atom-cat was that the experimenters could "open
the lid" of the box a little at a time, and, for each
increment of box-opening, the mixed cat-state resolved
a little more into one or the other pure states. This is
what was _observed_ .

For one experiment, at least, "opening the box" was allowing
the beryllium atom to interact with increasing numbers of
photons near the frequency of the mixed state. Zero photons and
the lid was fully closed. Ten photons (if I remember correctly)
and the lid was fully open.

It seems that quantum wave collapse is not so much a spooky
consciousness-dependent effect, but more a result of
interacting with The Universe, or maybe just a small part of
said Universe, like a ten-photon part. Quantum collapse appears
to be a falling-into-incoherence between different parts of a
quantum state, which gets triggered when the quantum state
gets screwed around with by (essentially) anything else.

(WARNING: this is not _precisely_ a layman's version of
an updated version of quantum wave collapse. I've studied
me enough physics for a bachelor's degree. _But_ the distance
between me and a layman is much shorter than the distance
between me and your random physicist-in-the-street. Add
grains of salt as needed.)

----
A reference from your link:
http://www.quantumsciencephilippines.com/seminar/seminar-topics/SchrodingerCatAtom.pdf

[peteolcott]

[Ross A. Finlayson]

A wave is usually a very-well-understood
classical formula as about periodic motion
that is very well explored analytically about
all sorts of usual systems of conservation of
momentum or the pendulum (or spring).

Here light's (or, particles') "wave" as about
wave optics and geometric optics is that
there is a very well understood "wave model"
of the distribution more than less of the event(s).

This is similiar to that electrical current has a
"fluid model".

These metaphors or models as from the study
of water waves are a representation, but not
all the usual assumptions of the media or material
of the water wave apply. For example, electricity
has the "skin effect" not the "core effect", this is
basically the _opposite_ as about what surface tension
in the universal (chemical) solvent's, water's,
theory is.

Then, this "wave" of the particle physics can be
much different, or basically, with some opposite
assumptions. Here there's basically a usual assumption
that the waveform collapse is like the bursting of a
bubble. But, it might be fruitful to consider that
unlike a balloon being popped at a point, this wave
or "pilot wave" or "ghost wave" breaks everywhere
at once except the point, that its "tensions" are
basically the opposite, while that it as well falls
out of the equations that it is the same.

The idea of these "supermodels" or wave supermodels
or fluid supermodels or color supermodels is that they
fall out as the classical for solutions in terms, but that
there's a bit more to the picture than applying some
classical (and perfect) assumptions to these non-classical
regimes.

Then effects like the measurement effect, the observer
effect, the sampling effect, here there are ideas that
the mathematical models have features directly on the
supermodels of the numbers themselves to so facilitate
the automatic equippal of the physical theories.

Vocabulary: not just for scrabble any-more.

[Jim Burns]

On 8/21/2018 6:47 PM, peteolcott wrote:
> On 8/21/2018 4:31 PM, Jim Burns wrote:
>> On 8/21/2018 4:41 PM, peteolcott wrote:
>>> On 8/21/2018 10:24 AM, Jim Burns wrote:
>>>> On 8/21/2018 10:06 AM, peteolcott wrote:
>>>>> On 8/21/2018 7:40 AM, Peter Percival wrote:

>>>>>> What do you mean by "georeferenced"?  It is not a word
>>>>>> I have come across before.
>>>>>
>>>>> I already explained that:
>>>>>
>>>>> The center of a one inch diameter sphere is exactly ten
>>>>> miles above the center of the north pole.
>>>>>
>>>>> Without this degree of specificity the sphere is never
>>>>> uniquely identified thus indiscernible from other spheres.
>>>>
>>>> Let the center of a one-inch-diameter sphere S be ten miles
>>>> above the north pole. _Rigidly translate_ the points in
>>>> sphere S to another location such that the new center of S
>>>> is ten miles above the _south_ pole.
>>>
>>> It thus ceases to be the original sphere at all.
>>
>> Apparently you got the idea from somewhere that
>> Banach-Tarski claim is that the two resulting spheres are
>> in the same location as the one original sphere.
>>

>> *Have you considered finding out what the Banach-Tarski*
>> *theorem is* ? (BIG spoiler: It's not what you think it is.)

>
> Think of it as the same idea as the Cantor's cardinality
> proof. We have an original sphere that has its own set of
> unique points. A set of points that was previously not
> mapped to any other points after decomposition and
> recomposition becomes mapped to a whole new set of points
> that did not previously exist. This proves that we really
> only just copied the sphere without realizing it.

No. Just no.

I point out one misconception, and you respond with six
more misconceptions. I point out one of the new
misconceptions, and you return another six misconceptions.
With each of my answers, you diverge further and further
from reality. So, just no.

*Have you considered finding out what the Cantor's*
*cardinality proof is* ?

[Ross A. Finlayson]

And if you don't know, now you know?

(
https://www.youtube.com/watch?v=InGtiEXQyF0
https://www.youtube.com/watch?v=6-WMbP1RcC4
https://www.youtube.com/watch?v=_95UuA93k18

https://www.youtube.com/watch?v=An2a1_Do_fc
https://www.youtube.com/watch?v=CpSdePGgVyQ
https://www.youtube.com/watch?v=LTrk4X9ACtw
)

[peteolcott]

On 8/21/2018 4:12 PM, Ross A. Finlayson wrote:
> On Tuesday, August 21, 2018 at 2:00:05 PM UTC-7, peteolcott wrote:
>> On 8/21/2018 2:33 PM, Ross A. Finlayson wrote:
>>> On Tuesday, August 21, 2018 at 12:30:10 PM UTC-7, peteolcott wrote:
>>>> On 8/21/2018 12:03 PM, Peter Percival wrote:
>>>>> peteolcott wrote:
>>>>>
>>>>>>
>>>>>> The whole subject of quantum mechanics as illustrated by Schrödinger's cat
>>>>>> has its ultimate ground of being in the actual true nature of reality as
>>>>>> opposed to common misconceptions of this nature of reality.
>>>>>
>>>>> Schrödinger with his cat intended to refute the Copenhagen interpretation of qm.  It does not illustrate the whole subject.
>>>>
>>>> By what possible means could a cat actually be simultaneously
>>>> alive and dead?
>>>
>>> What cat?
>>>
>>
>> https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat
>
> So, you might presume we follow the link
> and read the entire article.
>
> But, is that Schroedinger's cat?
>
> "Schrödinger's cat is a thought experiment,
> sometimes described as a paradox,...".

Is is enormously more than that from the frame-of-reference of Buddhist enlightenment.

[peteolcott]

It is a mathematical mapping between set of points
on a number line.

I have proven that the sphere has been duplicated
by copying its points to another sphere, thus
refuting Banach-Tarski.

It is not merely decomposing a single sphere and
recomposing this same sphere into two identical
spheres.

It is copying the points from one sphere to another
in such a way that it is not apparent that it is
copying anything.

Olcott's KEY hypothesis (to be progressively proven)
Every paradox has a hidden error somewhere.

Copyright 2018 Pete Olcott

Copyright 2018 Pete Olcott

[exflaso....@gmail.com]

On Tuesday, August 21, 2018 at 10:18:55 PM UTC-4, peteolcott wrote:
> I have proven that the sphere has been duplicated
> by copying its points to another sphere, thus
> refuting Banach-Tarski.

No you haven't. Try watching this: https://www.youtube.com/watch?v=s86-Z-CbaHA

Maybe even you can understand it if you don't have to read.

EFQ

[peteolcott]

if Banach-Tarski asserts it decomposes a sphere into
parts and then recompose two spheres from these same
parts then I have proven that Banach-Tarski is asserting
a falsehood.

The first two minutes of the video confirm that my
understanding of the Banach-Tarski assertion is correct.

The details after this assertion are moot as long as
I prove that the assertion itself is impossible.

I take exactly this same approach on the 1931 GIT. I do
not need to understand any detail of the 1931 GIT to
utterly refute it as long as I prove that its conclusion
is impossible.

Olcott's KEY hypothesis (to be progressively proven)
Every paradox has a hidden error somewhere.

[peteolcott]

On 8/21/2018 9:54 PM, peteolcott wrote:
> On 8/21/2018 9:24 PM, exflaso....@gmail.com wrote:
>> On Tuesday, August 21, 2018 at 10:18:55 PM UTC-4, peteolcott wrote:
>>> I have proven that the sphere has been duplicated
>>> by copying its points to another sphere, thus
>>> refuting Banach-Tarski.
>>
>> No you haven't.  Try watching this: https://www.youtube.com/watch?v=s86-Z-CbaHA
>>
>> Maybe even you can understand it if you don't have to read.
>>
>> EFQ
>>
>
> if Banach-Tarski asserts it decomposes a sphere into
> parts and then recompose two spheres

each identical to the original

[Jeff Barnett]

By the un-Copenhagen interpretation of QM! Since you don't know logic,
mathematics, linguistics, or programing (I read your silly patent) we
are sure you don't understand physics either: according to the first
sentence, you can't reason, you can't model, you can't communicate, and
you can't express complex processes. All you can do is try to impress -
"Please notice me. Please. Please." We've noticed and the verdict is in:
dunce!

Now please let these newsgroups go back to being semi-useful and you
take a long rest. Please. Please.
--
Jeff Barnett

[exflaso....@gmail.com]

On Tuesday, August 21, 2018 at 10:58:31 PM UTC-4, peteolcott wrote:
> On 8/21/2018 9:54 PM, peteolcott wrote:
> > On 8/21/2018 9:24 PM, exflaso....@gmail.com wrote:
> >> On Tuesday, August 21, 2018 at 10:18:55 PM UTC-4, peteolcott wrote:
> >>> I have proven that the sphere has been duplicated
> >>> by copying its points to another sphere, thus
> >>> refuting Banach-Tarski.
> >>
> >> No you haven't.  Try watching this: https://www.youtube.com/watch?v=s86-Z-CbaHA
> >>
> >> Maybe even you can understand it if you don't have to read.
> >

> > if Banach-Tarski asserts it decomposes a sphere into
> > parts and then recompose two spheres
>
> each identical to the original

They are "identical" in that they have the same number of points, the same volume, the same surface area, etc. "Equivalent" is a less loaded term than "identical".

EFQ

[peteolcott]

On 8/21/2018 10:43 PM, Jeff Barnett wrote:
> peteolcott wrote on 8/21/2018 1:30 PM:
>> On 8/21/2018 12:03 PM, Peter Percival wrote:
>>> peteolcott wrote:
>>>
>>>>
>>>> The whole subject of quantum mechanics as illustrated by Schrödinger's cat
>>>> has its ultimate ground of being in the actual true nature of reality as
>>>> opposed to common misconceptions of this nature of reality.
>>>
>>> Schrödinger with his cat intended to refute the Copenhagen interpretation of qm.  It does not illustrate the whole subject.
>>
>> By what possible means could a cat actually be simultaneously
>> alive and dead?
> By the un-Copenhagen interpretation of QM!

According to the Copenhagen interpretation, physical
systems generally do not have definite properties prior
to being measured, and quantum mechanics can only
predict the probabilities that measurements will produce
certain results. The act of measurement affects the system,
causing the set of probabilities to reduce to only
one of the possible values immediately after the
measurement. This feature is known as wave function collapse.

Most people do not realize that this "answer" only dodges the question.

What assumptions regarding the fundamental nature of reality
would support the above behavior of physical systems?

Ah that never occurred to you, as I would have guessed.
All questions that do not have answers that can be looked
up do not count as worthy questions?

[peteolcott]

What you are not getting is the inherent impossibility
of creating a bijective mapping from a set of points
that did not previously exist to the original set of
points by merely rearranging the original set of points.

You and up with a bijective mapping between two spheres
whereas only the set of points of one of these spheres
originally existed.

Copyright Pete Olcott 2018

[exflaso....@gmail.com]

On Wednesday, August 22, 2018 at 1:26:14 AM UTC-4, peteolcott wrote:
> On 8/21/2018 11:46 PM, exflaso....@gmail.com wrote:
> > On Tuesday, August 21, 2018 at 10:58:31 PM UTC-4, peteolcott wrote:
> >>> if Banach-Tarski asserts it decomposes a sphere into
> >>> parts and then recompose two spheres
> >>
> >> each identical to the original
> >
> > They are "identical" in that they have the same number of points, the same volume, the same surface area, etc. "Equivalent" is a less loaded term than "identical".
>

> What you are not getting is the inherent impossibility

It's not impossible, so why would I want to "get" that it's impossible? That would be stupid.

I bet you think that the set of integers is twice as large as the set of even integers.

EFQ

[Ross A. Finlayson]

Euh, the asymptotic density of the even integers
(in the integers) is one half.

https://en.wikipedia.org/wiki/Schnirelmann_density

This asymptotic or Schnirelmann density is a usual
fact about the numbers and in terms of "measures"
as it were, of the "size" of things.

We can point to F. Katz and OUTPACING also as about
how proper subsets of a set are "smaller".

https://arxiv.org/abs/math/0106100

Of course everyone here knows about trans-finite
cardinals as about "infinite counting", and about
how Galileo showed the integers biject, for example,
with the squares.

[exflaso....@gmail.com]

On Wednesday, August 22, 2018 at 2:22:31 AM UTC-4, Ross A. Finlayson wrote:
> On Tuesday, August 21, 2018 at 11:01:05 PM UTC-7, exflaso....@gmail.com wrote:
> > On Wednesday, August 22, 2018 at 1:26:14 AM UTC-4, peteolcott wrote:
> > > On 8/21/2018 11:46 PM, exflaso....@gmail.com wrote:
> > > > On Tuesday, August 21, 2018 at 10:58:31 PM UTC-4, peteolcott wrote:
> > > >>> if Banach-Tarski asserts it decomposes a sphere into
> > > >>> parts and then recompose two spheres
> > > >>
> > > >> each identical to the original
> > > >
> > > > They are "identical" in that they have the same number of points, the same volume, the same surface area, etc. "Equivalent" is a less loaded term than "identical".
> > >
> > > What you are not getting is the inherent impossibility
> >
> > It's not impossible, so why would I want to "get" that it's impossible? That would be stupid.
> >
> > I bet you think that the set of integers is twice as large as the set of even integers.
>

> Euh, the asymptotic density of the even integers
> (in the integers) is one half.

And a 1 gram ice cube will float in 1 gram of liquid water, but they both have the same number of molecules.

Spreading things out doesn't change how many there are.

EFQ

[Ross A. Finlayson]

I'd mostly agree and thank you chemistry class
for teaching me about stoichiometry and Avogadro's
number and pretty modern and faultless models of
the atom, orbitals, and fundamental principles,
but those are the same fraction of Avogadro's
number amount of molecules: identical (up to
the limits of precision), because of the definition
of 1 AMU and these days about "running constants"
or why NIST CODATA updates regularly.

Here's also a reference to the ideal gas law,
basically that removing half the molecules
(by mass) from a volume halves the pressure
(or is doubling the temperature).

Imagine a lattice and the pigeonhole principle
(aka Dirichlet or box principle) and a usual
inductive result that if every other box is empty
then only half are full, or that filling all the
boxes moves one of the pigeons infinitely far.
It's not quite clear exactly how that relates,
but number theory provides asymptotic density
and exactly half of the integers are even.

[Ross A. Finlayson]

It's also easy to formalize that exactly
half of the non-zero integers are positive
(because of symmetry).

[Peter Percival]

peteolcott wrote:

> On 8/21/2018 10:43 AM, Peter Percival wrote:
>> peteolcott wrote:

>>> ---
>>> The Banach–Tarski paradox is a theorem in set-theoretic geometry,
>>> which states the following: Given a solid ball in 3‑dimensional
>>> space, there exists a decomposition of the ball into a finite number
>>> of disjoint subsets, which can then be put back together in a
>>> different way to yield two identical copies of the original ball.
>>>
>>> Any idiot knowing any geometry would know that spheres are comprised
>>> on an infinite number of points, thus making the above claim silly.
>>>
>>> Copyright 2018 Pete Olcott // just in case no one noticed this silly
>>> mistake before.
>>
>> It seems that your objection to the Banach–Tarski paradox is that no
>> physical sphere can behave as required.
>>
>
> Not really. Within the identity of indiscernibles when-so-ever
> any sphere is by what-so-ever means uniquely identified then
> the Banach–Tarski paradox ceases to be possible.

I can't make sense of that.

[Peter Percival]

peteolcott wrote:

> On 8/21/2018 12:03 PM, Peter Percival wrote:
>> peteolcott wrote:
>>
>>>

[Peter Percival]

peteolcott wrote:
> On 8/21/2018 4:31 PM, Jim Burns wrote:
>> On 8/21/2018 4:41 PM, peteolcott wrote:
>>> On 8/21/2018 10:24 AM, Jim Burns wrote:
>>>> On 8/21/2018 10:06 AM, peteolcott wrote:
>>>>> On 8/21/2018 7:40 AM, Peter Percival wrote:
>>
>>>>>> What do you mean by "georeferenced"?  It is not a word
>>>>>> I have come across before.
>>>>>
>>>>> I already explained that:
>>>>>
>>>>> The center of a one inch diameter sphere is exactly ten
>>>>> miles above the center of the north pole.
>>>>>
>>>>> Without this degree of specificity the sphere is never
>>>>> uniquely identified thus indiscernible from other spheres.
>>>>
>>>> Let the center of a one-inch-diameter sphere S be ten miles
>>>> above the north pole. _Rigidly translate_ the points in
>>>> sphere S to another location such that the new center of S
>>>> is ten miles above the _south_ pole.
>>>
>>> It thus ceases to be the original sphere at all.
>>
>> Apparently you got the idea from somewhere that
>> Banach-Tarski claim is that the two resulting spheres are
>> in the same location as the one original sphere.
>>
>> Have you considered finding out what the Banach-Tarski
>> theorem is? (BIG spoiler: It's not what you think it is.)
>>
>
> Think of it as the same idea as the Cantor's cardinality proof.

Why would one think of it as something that it is not? No wonder you
have spent 30 years learning nothing. Can you multiply 2 by 3? Olcott:
'think of it as adding 2 and 3'.

[Peter Percival]

peteolcott wrote:

>
> Olcott's KEY hypothesis (to be progressively proven)
> Every paradox has a hidden error somewhere.

I know you think that every word should have just one meaning, but
"paradox" has more than one. One of those meanings is "contrary to the
man in the street's expectations"; and it is that kind of paradox that
Banach–Tarski's is. But the man in the street (like the Olcott in his
box) cannot be expected to be familiar with the farther reaches of
mathematics.

[Peter Percival]

peteolcott wrote:


> I take exactly this same approach on the 1931 GIT. I do
> not need to understand any detail of the 1931 GIT to

Cranks have no sense of shame, do they?

[Peter Percival]

peteolcott wrote:
> On 8/21/2018 9:54 PM, peteolcott wrote:
>> On 8/21/2018 9:24 PM, exflaso....@gmail.com wrote:
>>> On Tuesday, August 21, 2018 at 10:18:55 PM UTC-4, peteolcott wrote:
>>>> I have proven that the sphere has been duplicated
>>>> by copying its points to another sphere, thus
>>>> refuting Banach-Tarski.
>>>
>>> No you haven't.  Try watching this:
>>> https://www.youtube.com/watch?v=s86-Z-CbaHA
>>>
>>> Maybe even you can understand it if you don't have to read.
>>>
>>> EFQ
>>>
>>
>> if Banach-Tarski asserts it decomposes a sphere into
>> parts and then recompose two spheres
>
> each identical to the original

Not identical, rather of equal volume.

[peteolcott]

Here it is at a higher level of abstraction:
Olcott's KEY hypothesis:
All paradox necessarily has hidden error at its core.
You may not have the capacity to understand this.

[peteolcott]

OK then the Banach–Tarski paradox doubles the number of points
by simply rearranging them without copying them. Since this would
be impossible therefore Banach–Tarski is impossible.

[peteolcott]

Two identical spheres have twice as much volume
as one of these spheres.

[peteolcott]

The only system that I found that would uniquely
identify a single sphere is georeferencing.

If we do not uniquely identify a single sphere
then when we decompose a sphere and recompose
it into two spheres we can get confused about
the specific details of which sphere we are
talking about.

It is like talking about some guy and then
later referring to some other guy simply as
some guy. There is no discernible difference
between the two guys so people are confused
into thinking that there has always only been
one guy.

Copyright 2018 Pete Olcott

[peteolcott]

"physical systems generally do not have
definite properties prior to being measured"

What definition of reality makes that work?

[peteolcott]

Even a very stupid computer program can be a mere naysayer.
I proved my point in the part you ignored.

[peteolcott]

On 8/22/2018 7:00 AM, Peter Percival wrote:
> peteolcott wrote:
>
>>
>> Olcott's KEY hypothesis (to be progressively proven)
>> Every paradox has a hidden error somewhere.
>
> I know you think that every word should have just one meaning,

There exists a set of unique semantic meanings.
That very many of these meanings are tied to the same word
greatly hinders the effectiveness of the communication process.

Any formalized system of this unique set of meanings
would have a unique integer value for each meaning.

> but "paradox" has more than one.  One of those meanings is "contrary to the man in the street's expectations"; and it is that kind of paradox that Banach–Tarski's is.  But the man in the street
> (like the Olcott in his box) cannot be expected to be familiar with the farther reaches of mathematics.
>
>

Here is my first draft of a definition:

A paradox is the application of what seems to be correct
reasoning to any set of seemingly true premises such that
a contradiction is derived.

Copyright 2018 Pete Olcott

// Olcott's Truth schema
∀L ∈ Formal_Systems True(L, C) ↔ ∃Γ ⊆ Axioms(L) (Γ ⊢ C)

// Olcott's Truth predicate for L
True(C) ↔ ∃Γ ⊆ Axioms(L) (Γ ⊢ C)

// Formalized Liar Paradox for L
LP ↔ ~∃Γ ⊆ Axioms(L) (Γ ⊢ LP) // ~(LP ∨ ~LP)

<begin quoted material>
Page 254 Chapter 10 The Relation of Prolog to Logic
Programming in Prolog Using the ISO Standard Fifth Edition by Clocksin and Mellish
?- equal(foo(Y), Y).

...match a term against an uninstantiated subterm of itself...
...So Y ends up standing for some kind of infinite structure...
<end quoted material>

?- ↔(True(LP), LP).
So LP ends up standing for some kind of infinite structure.

[peteolcott]

On 8/22/2018 7:01 AM, Peter Percival wrote:
> peteolcott wrote:
>
>
>> I take exactly this same approach on the 1931 GIT. I do
>> not need to understand any detail of the 1931 GIT to
>
> Cranks have no sense of shame, do they?
>
>> utterly refute it as long as I prove that its conclusion
>> is impossible.

This truism may be over your head:
As long as any conclusion has been shown to be impossible
the reasoning leading to this impossible conclusion is
proven to be necessarily incorrect without even looking at it.

Are you aware that personal insults are not any correct
form of rebuttal? Some otherwise intelligent people seem
to be quite stupid on this key point.

[peteolcott]

On 8/22/2018 7:02 AM, Peter Percival wrote:
> peteolcott wrote:
>> On 8/21/2018 9:54 PM, peteolcott wrote:
>>> On 8/21/2018 9:24 PM, exflaso....@gmail.com wrote:
>>>> On Tuesday, August 21, 2018 at 10:18:55 PM UTC-4, peteolcott wrote:
>>>>> I have proven that the sphere has been duplicated
>>>>> by copying its points to another sphere, thus
>>>>> refuting Banach-Tarski.
>>>>
>>>> No you haven't.  Try watching this: https://www.youtube.com/watch?v=s86-Z-CbaHA
>>>>
>>>> Maybe even you can understand it if you don't have to read.
>>>>
>>>> EFQ
>>>>
>>>
>>> if Banach-Tarski asserts it decomposes a sphere into
>>> parts and then recompose two spheres
>>
>> each identical to the original
>
> Not identical, rather of equal volume.

If we were to do Banach-Tarski with physical matter
instead of geometric spheres it would be much more
obvious that a mistake has been made because each
ball would have half the mass of the original ball.

[Peter Percival]

Find a proof of the Banach–Tarski paradox and read it. You won't
because you won't understand it. Can you learn something from your not
understanding it?

You are one of those people who is so stupid that you don't know how
stupid you are. I'm not saying you're stupid because you don't
understand the Banach–Tarski paradox, most intelligent people have never
heard of it. The reason I say you're stupid is because you think it is
reasonable to comment on the Banach–Tarski paradox (and Gödel's
incompleteness theorem and ...) from a position of ignorance, what is
more a position of ignorance that you are determined to maintain.

You people have no sense of shame.

[Peter Percival]

peteolcott wrote:
> On 8/22/2018 6:41 AM, Peter Percival wrote:
>> peteolcott wrote:
>>> On 8/21/2018 10:43 AM, Peter Percival wrote:
>>>> peteolcott wrote:
>>>>> ---
>>>>> The Banach–Tarski paradox is a theorem in set-theoretic geometry,
>>>>> which states the following: Given a solid ball in 3‑dimensional
>>>>> space, there exists a decomposition of the ball into a finite
>>>>> number of disjoint subsets, which can then be put back together in
>>>>> a different way to yield two identical copies of the original ball.
>>>>>
>>>>> Any idiot knowing any geometry would know that spheres are
>>>>> comprised on an infinite number of points, thus making the above
>>>>> claim silly.
>>>>>
>>>>> Copyright 2018 Pete Olcott // just in case no one noticed this
>>>>> silly mistake before.
>>>>
>>>> It seems that your objection to the Banach–Tarski paradox is that no
>>>> physical sphere can behave as required.
>>>>
>>>
>>> Not really. Within the identity of indiscernibles when-so-ever
>>> any sphere is by what-so-ever means uniquely identified then
>>> the Banach–Tarski paradox ceases to be possible.
>>
>> I can't make sense of that.
>>
>
> The only system that I found that would uniquely
> identify a single sphere is georeferencing.

I asked you not long ago if you knew what a (mathematical) sphere is.
Do you?

[Peter Percival]

No, I read it. How about you reading a proof of the Banach–Tarski
paradox? Actually, it would be a major achievement if you just learned
what it said, never mind the proof.

[Peter Percival]

peteolcott wrote:
> On 8/22/2018 7:00 AM, Peter Percival wrote:
>> peteolcott wrote:
>>
>>>
>>> Olcott's KEY hypothesis (to be progressively proven)
>>> Every paradox has a hidden error somewhere.
>>
>> I know you think that every word should have just one meaning,
>
> There exists a set of unique semantic meanings.

No, there just doesn't, and the proof is immediate. Look in a
dictionary, a lot (most?) of the words in it have more than one meaning.

> That very many of these meanings are tied to the same word
> greatly hinders the effectiveness of the communication process.
>
> Any formalized system of this unique set of meanings
> would have a unique integer value for each meaning.
>
>> but "paradox" has more than one.  One of those meanings is "contrary
>> to the man in the street's expectations"; and it is that kind of
>> paradox that Banach–Tarski's is.  But the man in the street (like the
>> Olcott in his box) cannot be expected to be familiar with the farther
>> reaches of mathematics.

> Here is my first draft of a definition:

There is no need for you to draft a definition, we can all look it up in
a dictionary if we have any doubts about it. If your definition is one
among the dictionary definitions, then you are wasting your breath, if
it isn't, then you are wrong.

[Peter Percival]

peteolcott wrote:
> On 8/22/2018 7:01 AM, Peter Percival wrote:
>> peteolcott wrote:
>>
>>
>>> I take exactly this same approach on the 1931 GIT. I do
>>> not need to understand any detail of the 1931 GIT to
>>
>> Cranks have no sense of shame, do they?
>>
>>> utterly refute it as long as I prove that its conclusion
>>> is impossible.
>
> This truism may be over your head:
> As long as any conclusion has been shown to be impossible
> the reasoning leading to this impossible conclusion is
> proven to be necessarily incorrect without even looking at it.
>
> Are you aware that personal insults are not any correct
> form of rebuttal? Some otherwise intelligent people seem
> to be quite stupid on this key point.

I am aware that some people are so impervious to logical argumentation
that some people may well think that personal insults are all that's
left. But so what? I asked 'Cranks have no sense of shame, do they?'.
What's the answer?

>>>
>>> Olcott's KEY hypothesis (to be progressively proven)
>>> Every paradox has a hidden error somewhere.

Just suppose that the Banach–Tarski paradox was called the
Banach–Tarski theorem. Would you have felt the need to comment on it?

[Peter Percival]

peteolcott wrote:
> On 8/22/2018 7:02 AM, Peter Percival wrote:
>> peteolcott wrote:
>>> On 8/21/2018 9:54 PM, peteolcott wrote:
>>>> On 8/21/2018 9:24 PM, exflaso....@gmail.com wrote:
>>>>> On Tuesday, August 21, 2018 at 10:18:55 PM UTC-4, peteolcott wrote:
>>>>>> I have proven that the sphere has been duplicated
>>>>>> by copying its points to another sphere, thus
>>>>>> refuting Banach-Tarski.
>>>>>
>>>>> No you haven't.  Try watching this:
>>>>> https://www.youtube.com/watch?v=s86-Z-CbaHA
>>>>>
>>>>> Maybe even you can understand it if you don't have to read.
>>>>>
>>>>> EFQ
>>>>>
>>>>
>>>> if Banach-Tarski asserts it decomposes a sphere into
>>>> parts and then recompose two spheres
>>>
>>> each identical to the original
>>
>> Not identical, rather of equal volume.
>
> If we were to do Banach-Tarski with physical matter

Which we can't. You might as well begin 'if black were white...' Is
that the problem, that you think that the Banach–Tarski paradox is about
physical matter?

[exflaso....@gmail.com]

On Wednesday, August 22, 2018 at 10:29:47 AM UTC-4, peteolcott wrote:
> The only system that I found that would uniquely
> identify a single sphere is georeferencing.

If you had finished watching the video I directed you to, you'd see that that is pretty much exactly what is done. Every point on the surface is given a unique location marker. Despite that, you can still separate the points in the sphere into two spheres with equal volume.

EFQ

[Jim Burns]

On 8/22/2018 1:13 AM, peteolcott wrote:
> On 8/21/2018 10:43 PM, Jeff Barnett wrote:

>> peteolcott wrote on 8/21/2018 1:30 PM:

>>> By what possible means could a cat actually be
>>> simultaneously alive and dead?
>>

>> By the un-Copenhagen interpretation of QM!
>
> According to the Copenhagen interpretation, physical

> systems generally do not have definite properties prior

> to being measured, and quantum mechanics can only
> predict the probabilities that measurements will produce
> certain results. The act of measurement affects the system,
> causing the set of probabilities to reduce to only
> one of the possible values immediately after the
> measurement. This feature is known as wave function collapse.
>
> Most people do not realize that this "answer" only dodges
> the question.
>
> What assumptions regarding the fundamental nature of reality
> would support the above behavior of physical systems?

There are assumptions about the _classical_ view of reality
that the _quantum_ view of reality contradicts. It turns
out that, with regard to reality, the classical view is wrong.

(The classical view is _approximately_ correct for a wide
range of circumstances in which we, inhabiting our smaller-
-than-galaxies, larger-than-atoms bodies, find ourselves.
This is why we find _reality_ outside our usual experience
(eg, quantum mechanics experiments) to be counter-intuitive.)

Consider Bell's theorem.
https://en.wikipedia.org/wiki/Bell%27s_theorem#Importance
<wiki>
The title of Bell's seminal article refers to the 1935
paper by Einstein, Podolsky and Rosen that challenged the
completeness of quantum mechanics. In his paper, Bell
started from the same two assumptions as did EPR, namely
(i) reality (that microscopic objects have real properties
determining the outcomes of quantum mechanical measurements),
and (ii) locality (that reality in one location is not
influenced by measurements performed simultaneously at a
distant location). Bell was able to derive from those two
assumptions an important result, namely Bell's inequality.
The theoretical (and later experimental) violation of this
inequality implies that at least one of the two assumptions
must be false.
</wiki>

> Ah that never occurred to you, as I would have guessed.
> All questions that do not have answers that can be looked
> up do not count as worthy questions?

I think you claimed elsewhere that you spent 15 minutes
thinking about this. I doubt you spent that much time, but
even so: 15 minutes? Did you even do one Google search
on your topic?

You _guessed_ that no one has looked at these questions,
and that _guess_ became your "Truth". The same for Godel.
The same for Tarski. And for Cantor. And for every other
question you "work" on. I doubt you see anything wrong
with that.

https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

[peteolcott]

On 8/22/2018 11:11 AM, Peter Percival wrote:
> peteolcott wrote:
>> On 8/22/2018 7:00 AM, Peter Percival wrote:
>>> peteolcott wrote:
>>>
>>>>
>>>> Olcott's KEY hypothesis (to be progressively proven)
>>>> Every paradox has a hidden error somewhere.
>>>
>>> I know you think that every word should have just one meaning,
>>
>> There exists a set of unique semantic meanings.
>
> No, there just doesn't, and the proof is immediate.  Look in a dictionary, a lot (most?) of the words in it have more than one meaning.
>
>> That very many of these meanings are tied to the same word
>> greatly hinders the effectiveness of the communication process.
>>
>> Any formalized system of this unique set of meanings
>> would have a unique integer value for each meaning.
>>
>>> but "paradox" has more than one.  One of those meanings is "contrary to the man in the street's expectations"; and it is that kind of paradox that Banach–Tarski's is.  But the man in the street (like the Olcott in his box) cannot be expected to be
>>> familiar with the farther reaches of mathematics.
>
>> Here is my first draft of a definition:
>
> There is no need for you to draft a definition, we can all look it up in a dictionary if we have any doubts about it.  If your definition is one among the dictionary definitions, then you are wasting your breath, if it isn't, then you are wrong.
>

Many of the things you say are too stupid to respond to.
I am going you this feedback now so that you will know
exactly why I will not be responding to any poor quality replies.

They are not stupid because you have a low IQ or don't know better.
I would be rude of me to call you stupid for things that you cannot control.

You are very intelligent and have pretty good knowledge,
yet as in this case say very stupid things by not bothering
to think before you speak.

THIS IS THE DEFINITION OF PARADOX THAT I AM REFERRING TO:

>> A paradox is the application of what seems to be correct
>> reasoning to any set of seemingly true premises such that
>> a contradiction is derived.

EVERY OTHER DEFINITION IS TOO VAGUE.

[exflaso....@gmail.com]

On Wednesday, August 22, 2018 at 11:22:35 AM UTC-4, peteolcott wrote:
> On 8/22/2018 7:00 AM, Peter Percival wrote:
> > peteolcott wrote:
> >
> >> Olcott's KEY hypothesis (to be progressively proven)
> >> Every paradox has a hidden error somewhere.
> >
> > I know you think that every word should have just one meaning,
>
> There exists a set of unique semantic meanings.

Prove it. I'm sure the semanticists down the hall in the linguistics program would love to have access to that set!

17th century philosophers like Douet, Lodwick, Urquhart, Dalgarno, and Wilkins thought the same way, but that was pretty much a fad that died out in the 18th century, after it proved to be unworkable. It still rises up every now and again (e.g. Weilgart's aUI language), but it's mostly just cranks who do it these days.

> That very many of these meanings are tied to the same word
> greatly hinders the effectiveness of the communication process.

In fact, communication evolved for efficiency, and part of efficiency is homophony. We're really good at using context to disambiguate meaning.

> Any formalized system of this unique set of meanings
> would have a unique integer value for each meaning.

So you can only have a countably infinite number of meanings? Goodbye real number line!

EFQ