On 12/10/2023 11:50 AM, Volney wrote:
> On 12/9/2023 7:31 PM, Laurence Clark Crossen wrote:

> You're ineducable.

Kudos to Uncle Al.

On Sunday, December 10, 2023 at 11:12:39 AM UTC-8, whodat wrote:
> On 12/10/2023 11:50 AM, Volney wrote:
> > On 12/9/2023 7:31 PM, Laurence Clark Crossen wrote:
>
> > You're ineducable.
>
> Kudos to Uncle Al.
Long time no see! That's what they say in Soviet education camps!

On 12/10/2023 2:09 PM, whodat wrote:
> On 12/10/2023 11:39 AM, Volney wrote:
>> On 12/8/2023 6:21 PM, Richard Hertz wrote:
>>> On Friday, December 8, 2023 at 5:31:28 PM UTC-3, Chris M. Thomasson
>>> wrote:
>>>
>>> <snip>
>>>
>>>> Everywhere and nowhere? ;^) Let me throw out a point wrt unit sphere
>>>> centered at (0, 0, 0):
>>>>
>>>> (1, 0, 0) this is on the surface, however is it the center? What
>>>> about point (-1, 0, 0)? lol.
>>>>
>>>> :^)
>>>
>>> Be an arbitrary sphere, having a radius "1" be centered at (x₁,y₁,z₁)
>>> in a Euclidean 3D space.
>>>
>>> It's mathematically TRUE that the infinite collection of (x,y,z)
>>> points that verify (x-x₁)² + (y-y₁)² + (z-z₁)² = 1
>>> form part of a surface equidistant to the center (x₁,y₁,z₁).
>>>
>>> The volume of the sphere is centered in (x₁,y₁,z₁), as well as THE
>>> SHELL OF THE SPHERE (outer layer of infinitesimal thickness) is
>>> centered in (x₁,y₁,z₁).
>>>
>>> Think of the Earth, or the Sun.
>>>
>>> Can't believe how deranged people have become. So ignorant, so
>>> clueless, without any visualization power at all.
>>>
>>> I blame relativism, which has converted their adherents into drooling
>>> mutant cretins!
>>>
>>> For instance, the points
>>>
>>> x₁ ± 1, y₁, z₁
>>> x₁, y₁ ± 1, z₁
>>> x₁, y₁, z₁ ± 1
>>>
>>> are three points contained in such surface, out of an infinite number
>>> of 3D points.
>>>
>>> I have to ask myself: 1) Did you take your medications? ; 2) Did you
>>> really go to HS?; 3) Have you procreated?
>>>
>>>
>> 1) It certainly appears you didn't take your medicine, at least not
>> the antipsychotics.
>> 2) I can't be sure but you didn't manage to get a high school
>> education in sciences.
>> 3) I hope you didn't!
>
> The problem concerning a high school science education has to do with
> those who think the only aspects worthy of learning are the ones that
> directly impact the narrow subdiscipline that interests them. They take
> up space in the room and more or less pay attention where the topic of
> the day sounds as though it may have something to do with their
> interest (these days usually some subdiscipline of electronics.)
>
This sounds like a variant of what Odd Bodkin and others noted: Why are
so many cranks electrical engineers?

On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
>> On 12/9/2023 9:33 AM, Volney wrote:
>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
>> [...]
>>>> The fun part is that any observer on the surface of a sphere might
>>>> think its at the center. Or, well, think about the great attractor,
>>>> in space...
>>>
>>> Exactly. No matter where you are on the surface of a sphere, it LOOKS
>>> like you are at the center.
>>>
>>> Same with the 3D universe. No matter where you are, it LOOKS like
>>> you're at the center.
>>
>> Another point... Think of a 3d point in a 4d system where any "true"
>> 3d point has a w component of zero, ala:
>>
>> (x, y, z, w), fine... vec4, okay:
>>
>> vec4 point_4d = { 1, 1, 1, 0 };
>>
>> Is a "pure" 3d point. However:
>>
>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
>>
>> is not a "pure" 3d point at all, not in any way shape or form! A 4d
>> observer at that point with a non-zero w component, would be able to
>> look at the 3d world as a sort of alpha blend, in a sense. It could
>> see right through things, and walk right through walls... Eve ones
>> made of lead. ;^)
>>
>> Too much pondering here? lol. :^)
>
> In a land far far away... The 4d observer, with a non-zero w point in
> its 4-ary vector, would be able to stand on the surface of a planet,
> look down and see right through said planet into space on the other
> side... Everything looks like an alpha channel/blend of sorts, it would
> be able to see things akin to a 3d person drawing 2d plans. It would be
> able to walk right through walls that exist in points that have zero for
> a 4d component, w = 0... It would be able to see in every room, see
> inside of people, look down and see space look up and see more space...
> Sorry, I wrote that for fun. Try not to call me a 100% kook? ;^) lol.

I like the description of what it would look like if a 1 meter diameter
4D hypersphere with its x,y,z coordinates of its center were in the room
you are and its w coordinate going from negative to zero to positive.
First you'd see a point which rapidly would grow into a sphere, continue
growing but slower until it was 1 meter diameter, then it would shrink
to a point and wink out of existence.

On 12/10/2023 2:12 PM, whodat wrote:
> On 12/10/2023 11:50 AM, Volney wrote:
>> On 12/9/2023 7:31 PM, Laurence Clark Crossen wrote:
>
>> You're ineducable.
>
> Kudos to Uncle Al.
>
Maybe his famous rant about Archie Plutonium needs to be modified to be
about Laurence. He would post a rant about him if he was here to do so.

Am 11.12.2023 um 04:21 schrieb Volney:

>>>> I have to ask myself: 1) Did you take your medications? ; 2) Did you
>>>> really go to HS?; 3) Have you procreated?
>>>>
>>>>
>>> 1) It certainly appears you didn't take your medicine, at least not
>>> the antipsychotics.
>>> 2) I can't be sure but you didn't manage to get a high school
>>> education in sciences.
>>> 3) I hope you didn't!
>>
>> The problem concerning a high school science education has to do with
>> those who think the only aspects worthy of learning are the ones that
>> directly impact the narrow subdiscipline that interests them. They
>> take up space in the room and more or less pay attention where the
>> topic of
>> the day sounds as though it may have something to do with their
>> interest (these days usually some subdiscipline of electronics.)
>>
> This sounds like a variant of what Odd Bodkin and others noted: Why are
> so many cranks electrical engineers?

This is so, because electrical engineers have a MUCH better
understanding of magnetism and electricity than usual physicists.

Since everybody who dares to criticise mainstream physics is called
'crank' (or: psycho, Nazi, crackpot, nutcase...), physicists call all
electrical enigineers 'crank'.

But much worse than the electrical cranks are the other variants of
engineers (like e.g. myself), who simply refuse to accept illogic nonsense.

TH

On 12/10/2023 9:42 PM, Volney wrote:
> On 12/10/2023 2:12 PM, whodat wrote:
>> On 12/10/2023 11:50 AM, Volney wrote:
>>> On 12/9/2023 7:31 PM, Laurence Clark Crossen wrote:
>>
>>> You're ineducable.
>>
>> Kudos to Uncle Al.
>>
> Maybe his famous rant about Archie Plutonium needs to be modified to be
> about Laurence. He would post a rant about him if he was here to do so.

That would prove irresistible!

On 12/10/2023 9:21 PM, Volney wrote:
> On 12/10/2023 2:09 PM, whodat wrote:
>> On 12/10/2023 11:39 AM, Volney wrote:
>>> On 12/8/2023 6:21 PM, Richard Hertz wrote:
>>>> On Friday, December 8, 2023 at 5:31:28 PM UTC-3, Chris M. Thomasson
>>>> wrote:
>>>>
>>>> <snip>
>>>>
>>>>> Everywhere and nowhere? ;^) Let me throw out a point wrt unit
>>>>> sphere centered at (0, 0, 0):
>>>>>
>>>>> (1, 0, 0) this is on the surface, however is it the center? What
>>>>> about point (-1, 0, 0)? lol.
>>>>>
>>>>> :^)
>>>>
>>>> Be an arbitrary sphere, having a radius "1" be centered at
>>>> (x₁,y₁,z₁) in a Euclidean 3D space.
>>>>
>>>> It's mathematically TRUE that the infinite collection of (x,y,z)
>>>> points that verify (x-x₁)² + (y-y₁)² + (z-z₁)² = 1
>>>> form part of a surface equidistant to the center (x₁,y₁,z₁).
>>>>
>>>> The volume of the sphere is centered in (x₁,y₁,z₁), as well as THE
>>>> SHELL OF THE SPHERE (outer layer of infinitesimal thickness) is
>>>> centered in (x₁,y₁,z₁).
>>>>
>>>> Think of the Earth, or the Sun.
>>>>
>>>> Can't believe how deranged people have become. So ignorant, so
>>>> clueless, without any visualization power at all.
>>>>
>>>> I blame relativism, which has converted their adherents into
>>>> drooling mutant cretins!
>>>>
>>>> For instance, the points
>>>>
>>>> x₁ ± 1, y₁, z₁
>>>> x₁, y₁ ± 1, z₁
>>>> x₁, y₁, z₁ ± 1
>>>>
>>>> are three points contained in such surface, out of an infinite
>>>> number of 3D points.
>>>>
>>>> I have to ask myself: 1) Did you take your medications? ; 2) Did you
>>>> really go to HS?; 3) Have you procreated?
>>>>
>>>>
>>> 1) It certainly appears you didn't take your medicine, at least not
>>> the antipsychotics.
>>> 2) I can't be sure but you didn't manage to get a high school
>>> education in sciences.
>>> 3) I hope you didn't!
>>
>> The problem concerning a high school science education has to do with
>> those who think the only aspects worthy of learning are the ones that
>> directly impact the narrow subdiscipline that interests them. They
>> take up space in the room and more or less pay attention where the
>> topic of
>> the day sounds as though it may have something to do with their
>> interest (these days usually some subdiscipline of electronics.)
>>
> This sounds like a variant of what Odd Bodkin and others noted: Why are
> so many cranks electrical engineers?

In my father's day (early 20th century) The most popular discipline was
mechanical engineering. I predict that rocket science will be next, of
course I won't be around to see it.

Am 11.12.2023 um 15:18 schrieb whodat:

>> This sounds like a variant of what Odd Bodkin and others noted: Why
>> are so many cranks electrical engineers?
>
> In my father's day (early 20th century) The most popular discipline was
> mechanical engineering. I predict that rocket science will be next, of
> course I won't be around to see it.
>

No, the 'Next Big Thing' will be 'Flying Saucers'.

Rockets are a thing from the past.

TH

Am 05.12.2023 um 00:22 schrieb Tom Roberts:
> On 12/4/23 3:10 PM, Laurence Clark Crossen wrote:
>> The Big Bang and the Center of the Universe The velocity-distance
>> relationship interprets the redshift-distance relationship as caused
>> by the Doppler shift of starlight. This relationship is the same in
>> every direction from Earth. This requires we are at the center of
>> the universe.
>
> Nope! In a homogeneous and isotropic universe this would hold at any
> location, and THERE IS NO "CENTER".

The center is me (or you).

The reason: as we see 'the universe' this universe is not universal, but
identical to what relativity calls 'past light cone'.

This past light cone is always the past light cone of the observer in
question and that is me (or you or whoever else).

'The universe' is actually a picture we receive from the past.

And what we see is a set of events, which didn't happen at the same
time, but the longer ago the further away.

That IS (!!!!) the set of of events located on our own past light cone.

This is actually a picture and does not reflect any kind of reality.

So our picture from the past has a center, which we call 'big bang'. And
from there it does expand in all directions (and so forth).

But that's no big deal, because it is not real anyhow.

....

TH

On 12/10/2023 7:40 PM, Volney wrote:
> On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
>> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
>>> On 12/9/2023 9:33 AM, Volney wrote:
>>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
>>> [...]
>>>>> The fun part is that any observer on the surface of a sphere might
>>>>> think its at the center. Or, well, think about the great attractor,
>>>>> in space...
>>>>
>>>> Exactly. No matter where you are on the surface of a sphere, it
>>>> LOOKS like you are at the center.
>>>>
>>>> Same with the 3D universe. No matter where you are, it LOOKS like
>>>> you're at the center.
>>>
>>> Another point... Think of a 3d point in a 4d system where any "true"
>>> 3d point has a w component of zero, ala:
>>>
>>> (x, y, z, w), fine... vec4, okay:
>>>
>>> vec4 point_4d = { 1, 1, 1, 0 };
>>>
>>> Is a "pure" 3d point. However:
>>>
>>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
>>>
>>> is not a "pure" 3d point at all, not in any way shape or form! A 4d
>>> observer at that point with a non-zero w component, would be able to
>>> look at the 3d world as a sort of alpha blend, in a sense. It could
>>> see right through things, and walk right through walls... Eve ones
>>> made of lead. ;^)
>>>
>>> Too much pondering here? lol. :^)
>>
>> In a land far far away... The 4d observer, with a non-zero w point in
>> its 4-ary vector, would be able to stand on the surface of a planet,
>> look down and see right through said planet into space on the other
>> side... Everything looks like an alpha channel/blend of sorts, it
>> would be able to see things akin to a 3d person drawing 2d plans. It
>> would be able to walk right through walls that exist in points that
>> have zero for a 4d component, w = 0... It would be able to see in
>> every room, see inside of people, look down and see space look up and
>> see more space... Sorry, I wrote that for fun. Try not to call me a
>> 100% kook? ;^) lol.
>
> I like the description of what it would look like if a 1 meter diameter
> 4D hypersphere with its x,y,z coordinates of its center were in the room
> you are and its w coordinate going from negative to zero to positive.
> First you'd see a point which rapidly would grow into a sphere, continue
> growing but slower until it was 1 meter diameter, then it would shrink
> to a point and wink out of existence.

Well, so far, that is how some of my 4-ary vector field experiments
actually look/act like! The problem is that I am having trouble
visualizing points that have a w component that is non-zero. My n-ary
vector field helps! But its still strange. I can see how a "ghost" point
with a non-zero w component effect points in the 3d world, but its still
odd to me. I actually have no idea where to plot a 4d point that has
zero x, y, z components, and a non-zero w! Say,

(0, 0, 0, 1) ? Where do I plot that sucker!

On 12/11/2023 10:20 PM, Chris M. Thomasson wrote:
> On 12/10/2023 7:40 PM, Volney wrote:
>> On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
>>> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
>>>> On 12/9/2023 9:33 AM, Volney wrote:
>>>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
>>>> [...]
>>>>>> The fun part is that any observer on the surface of a sphere might
>>>>>> think its at the center. Or, well, think about the great
>>>>>> attractor, in space...
>>>>>
>>>>> Exactly. No matter where you are on the surface of a sphere, it
>>>>> LOOKS like you are at the center.
>>>>>
>>>>> Same with the 3D universe. No matter where you are, it LOOKS like
>>>>> you're at the center.
>>>>
>>>> Another point... Think of a 3d point in a 4d system where any "true"
>>>> 3d point has a w component of zero, ala:
>>>>
>>>> (x, y, z, w), fine... vec4, okay:
>>>>
>>>> vec4 point_4d = { 1, 1, 1, 0 };
>>>>
>>>> Is a "pure" 3d point. However:
>>>>
>>>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
>>>>
>>>> is not a "pure" 3d point at all, not in any way shape or form! A 4d
>>>> observer at that point with a non-zero w component, would be able to
>>>> look at the 3d world as a sort of alpha blend, in a sense. It could
>>>> see right through things, and walk right through walls... Eve ones
>>>> made of lead. ;^)
>>>>
>>>> Too much pondering here? lol. :^)
>>>
>>> In a land far far away... The 4d observer, with a non-zero w point in
>>> its 4-ary vector, would be able to stand on the surface of a planet,
>>> look down and see right through said planet into space on the other
>>> side... Everything looks like an alpha channel/blend of sorts, it
>>> would be able to see things akin to a 3d person drawing 2d plans. It
>>> would be able to walk right through walls that exist in points that
>>> have zero for a 4d component, w = 0... It would be able to see in
>>> every room, see inside of people, look down and see space look up and
>>> see more space... Sorry, I wrote that for fun. Try not to call me a
>>> 100% kook? ;^) lol.
>>
>> I like the description of what it would look like if a 1 meter
>> diameter 4D hypersphere with its x,y,z coordinates of its center were
>> in the room you are and its w coordinate going from negative to zero
>> to positive. First you'd see a point which rapidly would grow into a
>> sphere, continue growing but slower until it was 1 meter diameter,
>> then it would shrink to a point and wink out of existence.
>
> Well, so far, that is how some of my 4-ary vector field experiments
> actually look/act like! The problem is that I am having trouble
> visualizing points that have a w component that is non-zero. My n-ary
> vector field helps! But its still strange. I can see how a "ghost" point
> with a non-zero w component effect points in the 3d world, but its still
> odd to me. I actually have no idea where to plot a 4d point that has
> zero x, y, z components, and a non-zero w! Say,
>
> (0, 0, 0, 1) ? Where do I plot that sucker!

Thinking of that type of plotting makes me want to listen to strange music:

https://youtu.be/OCjGzFBckIw?t=8587

;^)

On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:
> On 12/10/2023 7:40 PM, Volney wrote:
>> On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
>>> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
>>>> On 12/9/2023 9:33 AM, Volney wrote:
>>>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
>>>> [...]
>>>>>> The fun part is that any observer on the surface of a sphere might
>>>>>> think its at the center. Or, well, think about the great
>>>>>> attractor, in space...
>>>>>
>>>>> Exactly. No matter where you are on the surface of a sphere, it
>>>>> LOOKS like you are at the center.
>>>>>
>>>>> Same with the 3D universe. No matter where you are, it LOOKS like
>>>>> you're at the center.
>>>>
>>>> Another point... Think of a 3d point in a 4d system where any "true"
>>>> 3d point has a w component of zero, ala:
>>>>
>>>> (x, y, z, w), fine... vec4, okay:
>>>>
>>>> vec4 point_4d = { 1, 1, 1, 0 };
>>>>
>>>> Is a "pure" 3d point. However:
>>>>
>>>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
>>>>
>>>> is not a "pure" 3d point at all, not in any way shape or form! A 4d
>>>> observer at that point with a non-zero w component, would be able to
>>>> look at the 3d world as a sort of alpha blend, in a sense. It could
>>>> see right through things, and walk right through walls... Eve ones
>>>> made of lead. ;^)
>>>>
>>>> Too much pondering here? lol. :^)
>>>
>>> In a land far far away... The 4d observer, with a non-zero w point in
>>> its 4-ary vector, would be able to stand on the surface of a planet,
>>> look down and see right through said planet into space on the other
>>> side... Everything looks like an alpha channel/blend of sorts, it
>>> would be able to see things akin to a 3d person drawing 2d plans. It
>>> would be able to walk right through walls that exist in points that
>>> have zero for a 4d component, w = 0... It would be able to see in
>>> every room, see inside of people, look down and see space look up and
>>> see more space... Sorry, I wrote that for fun. Try not to call me a
>>> 100% kook? ;^) lol.
>>
>> I like the description of what it would look like if a 1 meter
>> diameter 4D hypersphere with its x,y,z coordinates of its center were
>> in the room you are and its w coordinate going from negative to zero
>> to positive. First you'd see a point which rapidly would grow into a
>> sphere, continue growing but slower until it was 1 meter diameter,
>> then it would shrink to a point and wink out of existence.
>
> Well, so far, that is how some of my 4-ary vector field experiments
> actually look/act like! The problem is that I am having trouble
> visualizing points that have a w component that is non-zero. My n-ary
> vector field helps! But its still strange. I can see how a "ghost" point
> with a non-zero w component effect points in the 3d world, but its still
> odd to me. I actually have no idea where to plot a 4d point that has
> zero x, y, z components, and a non-zero w! Say,
>
> (0, 0, 0, 1) ? Where do I plot that sucker!

Only points with w=0 can be observed by 3D beings. In my example, the
hypersphere with a diameter of 1 will be nonexistent until its center
coordinate becomes w = -1. At that time a single point (with w=0)
hypersurface appears. As w of the center increases, the number of points
with w=0 and thus "real" increases. When the center is at w=0, the
hypersurface is at a maximum and appears as a sphere with diameter 1. As
w increases the sphere shrinks and when w=1 it is a point and then vanishes.

On 12/13/2023 1:03 AM, Volney wrote:
> On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:
>> On 12/10/2023 7:40 PM, Volney wrote:
>>> On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
>>>> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
>>>>> On 12/9/2023 9:33 AM, Volney wrote:
>>>>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
>>>>> [...]
>>>>>>> The fun part is that any observer on the surface of a sphere
>>>>>>> might think its at the center. Or, well, think about the great
>>>>>>> attractor, in space...
>>>>>>
>>>>>> Exactly. No matter where you are on the surface of a sphere, it
>>>>>> LOOKS like you are at the center.
>>>>>>
>>>>>> Same with the 3D universe. No matter where you are, it LOOKS like
>>>>>> you're at the center.
>>>>>
>>>>> Another point... Think of a 3d point in a 4d system where any
>>>>> "true" 3d point has a w component of zero, ala:
>>>>>
>>>>> (x, y, z, w), fine... vec4, okay:
>>>>>
>>>>> vec4 point_4d = { 1, 1, 1, 0 };
>>>>>
>>>>> Is a "pure" 3d point. However:
>>>>>
>>>>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
>>>>>
>>>>> is not a "pure" 3d point at all, not in any way shape or form! A 4d
>>>>> observer at that point with a non-zero w component, would be able
>>>>> to look at the 3d world as a sort of alpha blend, in a sense. It
>>>>> could see right through things, and walk right through walls... Eve
>>>>> ones made of lead. ;^)
>>>>>
>>>>> Too much pondering here? lol. :^)
>>>>
>>>> In a land far far away... The 4d observer, with a non-zero w point
>>>> in its 4-ary vector, would be able to stand on the surface of a
>>>> planet, look down and see right through said planet into space on
>>>> the other side... Everything looks like an alpha channel/blend of
>>>> sorts, it would be able to see things akin to a 3d person drawing 2d
>>>> plans. It would be able to walk right through walls that exist in
>>>> points that have zero for a 4d component, w = 0... It would be able
>>>> to see in every room, see inside of people, look down and see space
>>>> look up and see more space... Sorry, I wrote that for fun. Try not
>>>> to call me a 100% kook? ;^) lol.
>>>
>>> I like the description of what it would look like if a 1 meter
>>> diameter 4D hypersphere with its x,y,z coordinates of its center were
>>> in the room you are and its w coordinate going from negative to zero
>>> to positive. First you'd see a point which rapidly would grow into a
>>> sphere, continue growing but slower until it was 1 meter diameter,
>>> then it would shrink to a point and wink out of existence.
>>
>> Well, so far, that is how some of my 4-ary vector field experiments
>> actually look/act like! The problem is that I am having trouble
>> visualizing points that have a w component that is non-zero. My n-ary
>> vector field helps! But its still strange. I can see how a "ghost"
>> point with a non-zero w component effect points in the 3d world, but
>> its still odd to me. I actually have no idea where to plot a 4d point
>> that has zero x, y, z components, and a non-zero w! Say,
>>
>> (0, 0, 0, 1) ? Where do I plot that sucker!
>
> Only points with w=0 can be observed by 3D beings. In my example, the
> hypersphere with a diameter of 1 will be nonexistent until its center
> coordinate becomes w = -1. At that time a single point (with w=0)
> hypersurface appears. As w of the center increases, the number of points
> with w=0 and thus "real" increases. When the center is at w=0, the
> hypersurface is at a maximum and appears as a sphere with diameter 1. As
> w increases the sphere shrinks and when w=1 it is a point and then
> vanishes.

I see I was inconsistent. In my replies replace "diameter" with "radius"
everywhere.

On Wednesday 13 December 2023 at 07:03:14 UTC+1, Volney wrote:
> On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:
> > On 12/10/2023 7:40 PM, Volney wrote:
> >> On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
> >>> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
> >>>> On 12/9/2023 9:33 AM, Volney wrote:
> >>>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
> >>>> [...]
> >>>>>> The fun part is that any observer on the surface of a sphere might
> >>>>>> think its at the center. Or, well, think about the great
> >>>>>> attractor, in space...
> >>>>>
> >>>>> Exactly. No matter where you are on the surface of a sphere, it
> >>>>> LOOKS like you are at the center.
> >>>>>
> >>>>> Same with the 3D universe. No matter where you are, it LOOKS like
> >>>>> you're at the center.
> >>>>
> >>>> Another point... Think of a 3d point in a 4d system where any "true"
> >>>> 3d point has a w component of zero, ala:
> >>>>
> >>>> (x, y, z, w), fine... vec4, okay:
> >>>>
> >>>> vec4 point_4d = { 1, 1, 1, 0 };
> >>>>
> >>>> Is a "pure" 3d point. However:
> >>>>
> >>>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
> >>>>
> >>>> is not a "pure" 3d point at all, not in any way shape or form! A 4d
> >>>> observer at that point with a non-zero w component, would be able to
> >>>> look at the 3d world as a sort of alpha blend, in a sense. It could
> >>>> see right through things, and walk right through walls... Eve ones
> >>>> made of lead. ;^)
> >>>>
> >>>> Too much pondering here? lol. :^)
> >>>
> >>> In a land far far away... The 4d observer, with a non-zero w point in
> >>> its 4-ary vector, would be able to stand on the surface of a planet,
> >>> look down and see right through said planet into space on the other
> >>> side... Everything looks like an alpha channel/blend of sorts, it
> >>> would be able to see things akin to a 3d person drawing 2d plans. It
> >>> would be able to walk right through walls that exist in points that
> >>> have zero for a 4d component, w = 0... It would be able to see in
> >>> every room, see inside of people, look down and see space look up and
> >>> see more space... Sorry, I wrote that for fun. Try not to call me a
> >>> 100% kook? ;^) lol.
> >>
> >> I like the description of what it would look like if a 1 meter
> >> diameter 4D hypersphere with its x,y,z coordinates of its center were
> >> in the room you are and its w coordinate going from negative to zero
> >> to positive. First you'd see a point which rapidly would grow into a
> >> sphere, continue growing but slower until it was 1 meter diameter,
> >> then it would shrink to a point and wink out of existence.
> >
> > Well, so far, that is how some of my 4-ary vector field experiments
> > actually look/act like! The problem is that I am having trouble
> > visualizing points that have a w component that is non-zero. My n-ary
> > vector field helps! But its still strange. I can see how a "ghost" point
> > with a non-zero w component effect points in the 3d world, but its still
> > odd to me. I actually have no idea where to plot a 4d point that has
> > zero x, y, z components, and a non-zero w! Say,
> >
> > (0, 0, 0, 1) ? Where do I plot that sucker!
> Only points with w=0 can be observed by 3D beings. In my example, the

Stop fucking, stupid Mike, and tell us how many
observers on Earth have observed/concluded
that Earth has no center. Have you?

Volney wrote:

>> hypersurface is at a maximum and appears as a sphere with diameter 1.
>> As w increases the sphere shrinks and when w=1 it is a point and then
>> vanishes.
> I see I was inconsistent. In my replies replace "diameter" with "radius"
> everywhere.

so true indeed. The 𝗸𝗵𝗮𝘇𝗮𝗿_𝗴𝗼𝘆𝘀 of america and the 𝗸𝗵𝗮𝘇𝗮𝗿_𝗴𝗼𝘆𝘀 of ukurina
killed people and destroyed countries, just 𝗯𝗲𝗰𝗮𝘂𝘀𝗲_"𝗮_𝘀𝗲𝗹𝗹𝗶𝗻𝗴_𝗽𝗼𝗶𝗻𝘁". I'm not
trying to convince 𝘆𝗼𝘂, I'm not trying to convince anybody.

𝗨𝗸𝗿𝗮𝗶𝗻𝗲_𝘄𝗮𝘀_𝗻𝗲𝘃𝗲𝗿_𝗴𝗼𝗶𝗻𝗴_𝘁𝗼_𝘄𝗶𝗻_–_𝗨𝗦_𝘀𝗲𝗻𝗮𝘁𝗼𝗿
Tommy Tuberville has also dismissed the notion that Russia would invade
Europe, suggesting it was just 𝗮_“𝘀𝗲𝗹𝗹𝗶𝗻𝗴_𝗽𝗼𝗶𝗻𝘁”
https://r%74.com/news/588986-ukraine-never-win-senator/

moreover, these corrupt guys of europe were thinking they remain prime
ministers the rest of their fucking life. Not they are taken out, for
treason, by their own people.

𝘁𝗵𝗲_"𝘆𝗼𝘂𝗻𝗴_𝗴𝗹𝗼𝗯𝗮𝗹_𝗹𝗲𝗮𝗱𝗲𝗿𝘀"_𝗼𝗳_𝗪𝗘𝗙
Emmanuel Macron President of France,
Volodoymr Zelensky President of Ukraine,
Jacinda Ardern, former Prime Minister of New Zealand,
Sanna Marin Prime Minister of Finland,
Alexander De Croo Prime Minister of Belgium,
Leo Varadkar Tánaiste of Ireland,
Annalena Baerbock Foreign Minister of Germany,
Rishi Sunak, Prime Minister of the United Kingdom,
Mark Rutte, Prime Minister of the Netherlands,
Sebastian Kurz, former Chancellor of Austria

On 12/12/2023 10:03 PM, Volney wrote:
> On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:
>> On 12/10/2023 7:40 PM, Volney wrote:
>>> On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
>>>> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
>>>>> On 12/9/2023 9:33 AM, Volney wrote:
>>>>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
>>>>> [...]
>>>>>>> The fun part is that any observer on the surface of a sphere
>>>>>>> might think its at the center. Or, well, think about the great
>>>>>>> attractor, in space...
>>>>>>
>>>>>> Exactly. No matter where you are on the surface of a sphere, it
>>>>>> LOOKS like you are at the center.
>>>>>>
>>>>>> Same with the 3D universe. No matter where you are, it LOOKS like
>>>>>> you're at the center.
>>>>>
>>>>> Another point... Think of a 3d point in a 4d system where any
>>>>> "true" 3d point has a w component of zero, ala:
>>>>>
>>>>> (x, y, z, w), fine... vec4, okay:
>>>>>
>>>>> vec4 point_4d = { 1, 1, 1, 0 };
>>>>>
>>>>> Is a "pure" 3d point. However:
>>>>>
>>>>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
>>>>>
>>>>> is not a "pure" 3d point at all, not in any way shape or form! A 4d
>>>>> observer at that point with a non-zero w component, would be able
>>>>> to look at the 3d world as a sort of alpha blend, in a sense. It
>>>>> could see right through things, and walk right through walls... Eve
>>>>> ones made of lead. ;^)
>>>>>
>>>>> Too much pondering here? lol. :^)
>>>>
>>>> In a land far far away... The 4d observer, with a non-zero w point
>>>> in its 4-ary vector, would be able to stand on the surface of a
>>>> planet, look down and see right through said planet into space on
>>>> the other side... Everything looks like an alpha channel/blend of
>>>> sorts, it would be able to see things akin to a 3d person drawing 2d
>>>> plans. It would be able to walk right through walls that exist in
>>>> points that have zero for a 4d component, w = 0... It would be able
>>>> to see in every room, see inside of people, look down and see space
>>>> look up and see more space... Sorry, I wrote that for fun. Try not
>>>> to call me a 100% kook? ;^) lol.
>>>
>>> I like the description of what it would look like if a 1 meter
>>> diameter 4D hypersphere with its x,y,z coordinates of its center were
>>> in the room you are and its w coordinate going from negative to zero
>>> to positive. First you'd see a point which rapidly would grow into a
>>> sphere, continue growing but slower until it was 1 meter diameter,
>>> then it would shrink to a point and wink out of existence.
>>
>> Well, so far, that is how some of my 4-ary vector field experiments
>> actually look/act like! The problem is that I am having trouble
>> visualizing points that have a w component that is non-zero. My n-ary
>> vector field helps! But its still strange. I can see how a "ghost"
>> point with a non-zero w component effect points in the 3d world, but
>> its still odd to me. I actually have no idea where to plot a 4d point
>> that has zero x, y, z components, and a non-zero w! Say,
>>
>> (0, 0, 0, 1) ? Where do I plot that sucker!
>
> Only points with w=0 can be observed by 3D beings. In my example, the
> hypersphere with a diameter of 1 will be nonexistent until its center
> coordinate becomes w = -1. At that time a single point (with w=0)
> hypersurface appears. As w of the center increases, the number of points
> with w=0 and thus "real" increases. When the center is at w=0, the
> hypersurface is at a maximum and appears as a sphere with diameter 1. As
> w increases the sphere shrinks and when w=1 it is a point and then
> vanishes.

Still not sure if an 3d observer could see a 4d object with a non-zero
w. Afaict, it seems like you are taking w on a range of -1...1. Say:

x = 0
y = 0
z = 0
w = -1...0...1

When w is at the center and is actually equal to zero, 3d observers can
finally see it. A fun part is that a 4d observer would be able to see
the 4d object moving, and it would be able to see completely inside the
3d realm (aka alpha blend) its moving through wrt its (x, y, z) components.

I sometimes wonder if the w component can be very small yet non-zero to
a point where a 3d object might be able to notice something, akin to
paranormal activity wrt the 3d object. That is a fun one to ponder on... :^)

On 12/13/2023 4:04 PM, Chris M. Thomasson wrote:
> On 12/12/2023 10:03 PM, Volney wrote:
>> On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:
>>> On 12/10/2023 7:40 PM, Volney wrote:
>>>> On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
>>>>> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
>>>>>> On 12/9/2023 9:33 AM, Volney wrote:
>>>>>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
>>>>>> [...]
>>>>>>>> The fun part is that any observer on the surface of a sphere
>>>>>>>> might think its at the center. Or, well, think about the great
>>>>>>>> attractor, in space...
>>>>>>>
>>>>>>> Exactly. No matter where you are on the surface of a sphere, it
>>>>>>> LOOKS like you are at the center.
>>>>>>>
>>>>>>> Same with the 3D universe. No matter where you are, it LOOKS like
>>>>>>> you're at the center.
>>>>>>
>>>>>> Another point... Think of a 3d point in a 4d system where any
>>>>>> "true" 3d point has a w component of zero, ala:
>>>>>>
>>>>>> (x, y, z, w), fine... vec4, okay:
>>>>>>
>>>>>> vec4 point_4d = { 1, 1, 1, 0 };
>>>>>>
>>>>>> Is a "pure" 3d point. However:
>>>>>>
>>>>>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
>>>>>>
>>>>>> is not a "pure" 3d point at all, not in any way shape or form! A
>>>>>> 4d observer at that point with a non-zero w component, would be
>>>>>> able to look at the 3d world as a sort of alpha blend, in a sense.
>>>>>> It could see right through things, and walk right through walls...
>>>>>> Eve ones made of lead. ;^)
>>>>>>
>>>>>> Too much pondering here? lol. :^)
>>>>>
>>>>> In a land far far away... The 4d observer, with a non-zero w point
>>>>> in its 4-ary vector, would be able to stand on the surface of a
>>>>> planet, look down and see right through said planet into space on
>>>>> the other side... Everything looks like an alpha channel/blend of
>>>>> sorts, it would be able to see things akin to a 3d person drawing
>>>>> 2d plans. It would be able to walk right through walls that exist
>>>>> in points that have zero for a 4d component, w = 0... It would be
>>>>> able to see in every room, see inside of people, look down and see
>>>>> space look up and see more space... Sorry, I wrote that for fun.
>>>>> Try not to call me a 100% kook? ;^) lol.
>>>>
>>>> I like the description of what it would look like if a 1 meter
>>>> diameter 4D hypersphere with its x,y,z coordinates of its center
>>>> were in the room you are and its w coordinate going from negative to
>>>> zero to positive. First you'd see a point which rapidly would grow
>>>> into a sphere, continue growing but slower until it was 1 meter
>>>> diameter, then it would shrink to a point and wink out of existence.
>>>
>>> Well, so far, that is how some of my 4-ary vector field experiments
>>> actually look/act like! The problem is that I am having trouble
>>> visualizing points that have a w component that is non-zero. My n-ary
>>> vector field helps! But its still strange. I can see how a "ghost"
>>> point with a non-zero w component effect points in the 3d world, but
>>> its still odd to me. I actually have no idea where to plot a 4d point
>>> that has zero x, y, z components, and a non-zero w! Say,
>>>
>>> (0, 0, 0, 1) ? Where do I plot that sucker!
>>
>> Only points with w=0 can be observed by 3D beings. In my example, the
>> hypersphere with a diameter of 1 will be nonexistent until its center
>> coordinate becomes w = -1. At that time a single point (with w=0)
>> hypersurface appears. As w of the center increases, the number of
>> points with w=0 and thus "real" increases. When the center is at w=0,
>> the hypersurface is at a maximum and appears as a sphere with diameter
>> 1. As w increases the sphere shrinks and when w=1 it is a point and
>> then vanishes.
>
> Still not sure if an 3d observer could see a 4d object with a non-zero
> w. Afaict, it seems like you are taking w on a range of -1...1. Say:
>
> x = 0
> y = 0
> z = 0
> w = -1...0...1
>
> When w is at the center and is actually equal to zero, 3d observers can
> finally see it. A fun part is that a 4d observer would be able to see
> the 4d object moving, and it would be able to see completely inside the
> 3d realm (aka alpha blend) its moving through wrt its (x, y, z) components.
>
> I sometimes wonder if the w component can be very small yet non-zero to
> a point where a 3d object might be able to notice something, akin to
> paranormal activity wrt the 3d object. That is a fun one to ponder on...
> :^)

The hypersphere is moving in the w dimension and has a finite radius in
all dimensions including w, of 1. When its center is at w= -1, a single
point at w=1 (relative to the center) is visible. As w of the center
increases but is still negative, parts of the hypersphere have w=0 and
become visible as a sphere. For example, when the center is at w= -0.5,
parts of the hypersphere with w=0.5 (total w=0) are visible. When the
center is at w=0, a sphere with radius 1 is visible. As w becomes
positive the reverse happens. At w=1 only a single point (w = -1
relative to the center) is possible, after which (w>1) it vanishes.

On 12/13/2023 9:30 PM, Volney wrote:
> On 12/13/2023 4:04 PM, Chris M. Thomasson wrote:
>> On 12/12/2023 10:03 PM, Volney wrote:
>>> On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:
>>>> On 12/10/2023 7:40 PM, Volney wrote:
>>>>> On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
>>>>>> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
>>>>>>> On 12/9/2023 9:33 AM, Volney wrote:
>>>>>>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
>>>>>>> [...]
>>>>>>>>> The fun part is that any observer on the surface of a sphere
>>>>>>>>> might think its at the center. Or, well, think about the great
>>>>>>>>> attractor, in space...
>>>>>>>>
>>>>>>>> Exactly. No matter where you are on the surface of a sphere, it
>>>>>>>> LOOKS like you are at the center.
>>>>>>>>
>>>>>>>> Same with the 3D universe. No matter where you are, it LOOKS
>>>>>>>> like you're at the center.
>>>>>>>
>>>>>>> Another point... Think of a 3d point in a 4d system where any
>>>>>>> "true" 3d point has a w component of zero, ala:
>>>>>>>
>>>>>>> (x, y, z, w), fine... vec4, okay:
>>>>>>>
>>>>>>> vec4 point_4d = { 1, 1, 1, 0 };
>>>>>>>
>>>>>>> Is a "pure" 3d point. However:
>>>>>>>
>>>>>>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
>>>>>>>
>>>>>>> is not a "pure" 3d point at all, not in any way shape or form! A
>>>>>>> 4d observer at that point with a non-zero w component, would be
>>>>>>> able to look at the 3d world as a sort of alpha blend, in a
>>>>>>> sense. It could see right through things, and walk right through
>>>>>>> walls... Eve ones made of lead. ;^)
>>>>>>>
>>>>>>> Too much pondering here? lol. :^)
>>>>>>
>>>>>> In a land far far away... The 4d observer, with a non-zero w point
>>>>>> in its 4-ary vector, would be able to stand on the surface of a
>>>>>> planet, look down and see right through said planet into space on
>>>>>> the other side... Everything looks like an alpha channel/blend of
>>>>>> sorts, it would be able to see things akin to a 3d person drawing
>>>>>> 2d plans. It would be able to walk right through walls that exist
>>>>>> in points that have zero for a 4d component, w = 0... It would be
>>>>>> able to see in every room, see inside of people, look down and see
>>>>>> space look up and see more space... Sorry, I wrote that for fun.
>>>>>> Try not to call me a 100% kook? ;^) lol.
>>>>>
>>>>> I like the description of what it would look like if a 1 meter
>>>>> diameter 4D hypersphere with its x,y,z coordinates of its center
>>>>> were in the room you are and its w coordinate going from negative
>>>>> to zero to positive. First you'd see a point which rapidly would
>>>>> grow into a sphere, continue growing but slower until it was 1
>>>>> meter diameter, then it would shrink to a point and wink out of
>>>>> existence.
>>>>
>>>> Well, so far, that is how some of my 4-ary vector field experiments
>>>> actually look/act like! The problem is that I am having trouble
>>>> visualizing points that have a w component that is non-zero. My
>>>> n-ary vector field helps! But its still strange. I can see how a
>>>> "ghost" point with a non-zero w component effect points in the 3d
>>>> world, but its still odd to me. I actually have no idea where to
>>>> plot a 4d point that has zero x, y, z components, and a non-zero w!
>>>> Say,
>>>>
>>>> (0, 0, 0, 1) ? Where do I plot that sucker!
>>>
>>> Only points with w=0 can be observed by 3D beings. In my example, the
>>> hypersphere with a diameter of 1 will be nonexistent until its center
>>> coordinate becomes w = -1. At that time a single point (with w=0)
>>> hypersurface appears. As w of the center increases, the number of
>>> points with w=0 and thus "real" increases. When the center is at w=0,
>>> the hypersurface is at a maximum and appears as a sphere with
>>> diameter 1. As w increases the sphere shrinks and when w=1 it is a
>>> point and then vanishes.
>>
>> Still not sure if an 3d observer could see a 4d object with a non-zero
>> w. Afaict, it seems like you are taking w on a range of -1...1. Say:
>>
>> x = 0
>> y = 0
>> z = 0
>> w = -1...0...1
>>
>> When w is at the center and is actually equal to zero, 3d observers
>> can finally see it. A fun part is that a 4d observer would be able to
>> see the 4d object moving, and it would be able to see completely
>> inside the 3d realm (aka alpha blend) its moving through wrt its (x,
>> y, z) components.
>>
>> I sometimes wonder if the w component can be very small yet non-zero
>> to a point where a 3d object might be able to notice something, akin
>> to paranormal activity wrt the 3d object. That is a fun one to ponder
>> on... :^)
>
> The hypersphere is moving in the w dimension and has a finite radius in
> all dimensions including w, of 1. When its center is at w= -1, a single
> point at w=1 (relative to the center) is visible. As w of the center
> increases but is still negative, parts of the hypersphere have w=0 and
> become visible as a sphere. For example, when the center is at w= -0.5,
> parts of the hypersphere with w=0.5 (total w=0) are visible. When the
> center is at w=0, a sphere with radius 1 is visible. As w becomes
> positive the reverse happens. At w=1 only a single point (w = -1
> relative to the center) is possible, after which (w>1) it vanishes.

Afaict, its as if you are using the w component as the radii of the
sphere where the radius goes from 0...1...0? Where the middle has a w =
0? Think of a 4d unit sphere moving from p0 to p1, all x, y, z
components are zero, so it is a "pure" 4d object:

p0 = (0, 0, 0, -1)
p1 = (0, 0, 0, 1)

dif = p1 - p0

mid = p0 + dif / 2

At the mid point it should be at point (0, 0, 0, 0) Which should be
visible to the 3d world as a unit sphere. Say the unit is one meter,
just for now... ;^)

I think as soon as the w component of the origin of the sphere is zero,
it can be visually observed by 3d observers, aka their w = 0.

On 12/14/2023 6:22 PM, Chris M. Thomasson wrote:
> On 12/13/2023 9:30 PM, Volney wrote:
>> On 12/13/2023 4:04 PM, Chris M. Thomasson wrote:
>>> On 12/12/2023 10:03 PM, Volney wrote:
>>>> On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:
>>>>> On 12/10/2023 7:40 PM, Volney wrote:
>>>>>> On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
>>>>>>> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
>>>>>>>> On 12/9/2023 9:33 AM, Volney wrote:
>>>>>>>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
>>>>>>>> [...]
>>>>>>>>>> The fun part is that any observer on the surface of a sphere
>>>>>>>>>> might think its at the center. Or, well, think about the great
>>>>>>>>>> attractor, in space...
>>>>>>>>>
>>>>>>>>> Exactly. No matter where you are on the surface of a sphere, it
>>>>>>>>> LOOKS like you are at the center.
>>>>>>>>>
>>>>>>>>> Same with the 3D universe. No matter where you are, it LOOKS
>>>>>>>>> like you're at the center.
>>>>>>>>
>>>>>>>> Another point... Think of a 3d point in a 4d system where any
>>>>>>>> "true" 3d point has a w component of zero, ala:
>>>>>>>>
>>>>>>>> (x, y, z, w), fine... vec4, okay:
>>>>>>>>
>>>>>>>> vec4 point_4d = { 1, 1, 1, 0 };
>>>>>>>>
>>>>>>>> Is a "pure" 3d point. However:
>>>>>>>>
>>>>>>>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
>>>>>>>>
>>>>>>>> is not a "pure" 3d point at all, not in any way shape or form! A
>>>>>>>> 4d observer at that point with a non-zero w component, would be
>>>>>>>> able to look at the 3d world as a sort of alpha blend, in a
>>>>>>>> sense. It could see right through things, and walk right through
>>>>>>>> walls... Eve ones made of lead. ;^)
>>>>>>>>
>>>>>>>> Too much pondering here? lol. :^)
>>>>>>>
>>>>>>> In a land far far away... The 4d observer, with a non-zero w
>>>>>>> point in its 4-ary vector, would be able to stand on the surface
>>>>>>> of a planet, look down and see right through said planet into
>>>>>>> space on the other side... Everything looks like an alpha
>>>>>>> channel/blend of sorts, it would be able to see things akin to a
>>>>>>> 3d person drawing 2d plans. It would be able to walk right
>>>>>>> through walls that exist in points that have zero for a 4d
>>>>>>> component, w = 0... It would be able to see in every room, see
>>>>>>> inside of people, look down and see space look up and see more
>>>>>>> space... Sorry, I wrote that for fun. Try not to call me a 100%
>>>>>>> kook? ;^) lol.
>>>>>>
>>>>>> I like the description of what it would look like if a 1 meter
>>>>>> diameter 4D hypersphere with its x,y,z coordinates of its center
>>>>>> were in the room you are and its w coordinate going from negative
>>>>>> to zero to positive. First you'd see a point which rapidly would
>>>>>> grow into a sphere, continue growing but slower until it was 1
>>>>>> meter diameter, then it would shrink to a point and wink out of
>>>>>> existence.
>>>>>
>>>>> Well, so far, that is how some of my 4-ary vector field experiments
>>>>> actually look/act like! The problem is that I am having trouble
>>>>> visualizing points that have a w component that is non-zero. My
>>>>> n-ary vector field helps! But its still strange. I can see how a
>>>>> "ghost" point with a non-zero w component effect points in the 3d
>>>>> world, but its still odd to me. I actually have no idea where to
>>>>> plot a 4d point that has zero x, y, z components, and a non-zero w!
>>>>> Say,
>>>>>
>>>>> (0, 0, 0, 1) ? Where do I plot that sucker!
>>>>
>>>> Only points with w=0 can be observed by 3D beings. In my example,
>>>> the hypersphere with a diameter of 1 will be nonexistent until its
>>>> center coordinate becomes w = -1. At that time a single point (with
>>>> w=0) hypersurface appears. As w of the center increases, the number
>>>> of points with w=0 and thus "real" increases. When the center is at
>>>> w=0, the hypersurface is at a maximum and appears as a sphere with
>>>> diameter 1. As w increases the sphere shrinks and when w=1 it is a
>>>> point and then vanishes.
>>>
>>> Still not sure if an 3d observer could see a 4d object with a
>>> non-zero w. Afaict, it seems like you are taking w on a range of
>>> -1...1. Say:
>>>
>>> x = 0
>>> y = 0
>>> z = 0
>>> w = -1...0...1
>>>
>>> When w is at the center and is actually equal to zero, 3d observers
>>> can finally see it. A fun part is that a 4d observer would be able to
>>> see the 4d object moving, and it would be able to see completely
>>> inside the 3d realm (aka alpha blend) its moving through wrt its (x,
>>> y, z) components.
>>>
>>> I sometimes wonder if the w component can be very small yet non-zero
>>> to a point where a 3d object might be able to notice something, akin
>>> to paranormal activity wrt the 3d object. That is a fun one to ponder
>>> on... :^)
>>
>> The hypersphere is moving in the w dimension and has a finite radius
>> in all dimensions including w, of 1. When its center is at w= -1, a
>> single point at w=1 (relative to the center) is visible. As w of the
>> center increases but is still negative, parts of the hypersphere have
>> w=0 and become visible as a sphere. For example, when the center is at
>> w= -0.5, parts of the hypersphere with w=0.5 (total w=0) are visible.
>> When the center is at w=0, a sphere with radius 1 is visible. As w
>> becomes positive the reverse happens. At w=1 only a single point (w =
>> -1 relative to the center) is possible, after which (w>1) it vanishes.
>
> Afaict, its as if you are using the w component as the radii of the
> sphere where the radius goes from 0...1...0? Where the middle has a w =
> 0?

Ummm, the middle of 0...1...0 would be w = 1, sorry for that damn typo!!!

YIKES! ;^o

Think of a 4d unit sphere moving from p0 to p1, all x, y, z
> components are zero, so it is a "pure" 4d object:
>
> p0 = (0, 0, 0, -1)
> p1 = (0, 0, 0, 1)
>
> dif = p1 - p0
>
> mid = p0 + dif / 2
>
> At the mid point it should be at point (0, 0, 0, 0) Which should be
> visible to the 3d world as a unit sphere. Say the unit is one meter,
> just for now... ;^)
>
> I think as soon as the w component of the origin of the sphere is zero,
> it can be visually observed by 3d observers, aka their w = 0.
>
>
>

On 12/13/2023 9:30 PM, Volney wrote:
> On 12/13/2023 4:04 PM, Chris M. Thomasson wrote:
>> On 12/12/2023 10:03 PM, Volney wrote:
>>> On 12/12/2023 1:20 AM, Chris M. Thomasson wrote:
>>>> On 12/10/2023 7:40 PM, Volney wrote:
>>>>> On 12/10/2023 2:28 AM, Chris M. Thomasson wrote:
>>>>>> On 12/9/2023 10:45 PM, Chris M. Thomasson wrote:
>>>>>>> On 12/9/2023 9:33 AM, Volney wrote:
>>>>>>>> On 12/8/2023 11:05 PM, Chris M. Thomasson wrote:
>>>>>>> [...]
>>>>>>>>> The fun part is that any observer on the surface of a sphere
>>>>>>>>> might think its at the center. Or, well, think about the great
>>>>>>>>> attractor, in space...
>>>>>>>>
>>>>>>>> Exactly. No matter where you are on the surface of a sphere, it
>>>>>>>> LOOKS like you are at the center.
>>>>>>>>
>>>>>>>> Same with the 3D universe. No matter where you are, it LOOKS
>>>>>>>> like you're at the center.
>>>>>>>
>>>>>>> Another point... Think of a 3d point in a 4d system where any
>>>>>>> "true" 3d point has a w component of zero, ala:
>>>>>>>
>>>>>>> (x, y, z, w), fine... vec4, okay:
>>>>>>>
>>>>>>> vec4 point_4d = { 1, 1, 1, 0 };
>>>>>>>
>>>>>>> Is a "pure" 3d point. However:
>>>>>>>
>>>>>>> vec4 point_4d_oddball = { 1, 1, 1, 0.000000001 };
>>>>>>>
>>>>>>> is not a "pure" 3d point at all, not in any way shape or form! A
>>>>>>> 4d observer at that point with a non-zero w component, would be
>>>>>>> able to look at the 3d world as a sort of alpha blend, in a
>>>>>>> sense. It could see right through things, and walk right through
>>>>>>> walls... Eve ones made of lead. ;^)
>>>>>>>
>>>>>>> Too much pondering here? lol. :^)
>>>>>>
>>>>>> In a land far far away... The 4d observer, with a non-zero w point
>>>>>> in its 4-ary vector, would be able to stand on the surface of a
>>>>>> planet, look down and see right through said planet into space on
>>>>>> the other side... Everything looks like an alpha channel/blend of
>>>>>> sorts, it would be able to see things akin to a 3d person drawing
>>>>>> 2d plans. It would be able to walk right through walls that exist
>>>>>> in points that have zero for a 4d component, w = 0... It would be
>>>>>> able to see in every room, see inside of people, look down and see
>>>>>> space look up and see more space... Sorry, I wrote that for fun.
>>>>>> Try not to call me a 100% kook? ;^) lol.
>>>>>
>>>>> I like the description of what it would look like if a 1 meter
>>>>> diameter 4D hypersphere with its x,y,z coordinates of its center
>>>>> were in the room you are and its w coordinate going from negative
>>>>> to zero to positive. First you'd see a point which rapidly would
>>>>> grow into a sphere, continue growing but slower until it was 1
>>>>> meter diameter, then it would shrink to a point and wink out of
>>>>> existence.
>>>>
>>>> Well, so far, that is how some of my 4-ary vector field experiments
>>>> actually look/act like! The problem is that I am having trouble
>>>> visualizing points that have a w component that is non-zero. My
>>>> n-ary vector field helps! But its still strange. I can see how a
>>>> "ghost" point with a non-zero w component effect points in the 3d
>>>> world, but its still odd to me. I actually have no idea where to
>>>> plot a 4d point that has zero x, y, z components, and a non-zero w!
>>>> Say,
>>>>
>>>> (0, 0, 0, 1) ? Where do I plot that sucker!
>>>
>>> Only points with w=0 can be observed by 3D beings. In my example, the
>>> hypersphere with a diameter of 1 will be nonexistent until its center
>>> coordinate becomes w = -1. At that time a single point (with w=0)
>>> hypersurface appears. As w of the center increases, the number of
>>> points with w=0 and thus "real" increases. When the center is at w=0,
>>> the hypersurface is at a maximum and appears as a sphere with
>>> diameter 1. As w increases the sphere shrinks and when w=1 it is a
>>> point and then vanishes.
>>
>> Still not sure if an 3d observer could see a 4d object with a non-zero
>> w. Afaict, it seems like you are taking w on a range of -1...1. Say:
>>
>> x = 0
>> y = 0
>> z = 0
>> w = -1...0...1
>>
>> When w is at the center and is actually equal to zero, 3d observers
>> can finally see it. A fun part is that a 4d observer would be able to
>> see the 4d object moving, and it would be able to see completely
>> inside the 3d realm (aka alpha blend) its moving through wrt its (x,
>> y, z) components.
>>
>> I sometimes wonder if the w component can be very small yet non-zero
>> to a point where a 3d object might be able to notice something, akin
>> to paranormal activity wrt the 3d object. That is a fun one to ponder
>> on... :^)
>
> The hypersphere is moving in the w dimension and has a finite radius in
> all dimensions including w, of 1. When its center is at w= -1, a single
> point at w=1 (relative to the center) is visible. As w of the center
> increases but is still negative, parts of the hypersphere have w=0 and
> become visible as a sphere. For example, when the center is at w= -0.5,
> parts of the hypersphere with w=0.5 (total w=0) are visible. When the
> center is at w=0, a sphere with radius 1 is visible. As w becomes
> positive the reverse happens. At w=1 only a single point (w = -1
> relative to the center) is possible, after which (w>1) it vanishes.

You perplexed me a bit here. When a sphere has a non-zero w component it
is not visible to a 3d observer that has a w component of zero. Okay,
however, what happens if a 3d observer might be able to notice a 4d
object when its (the 4d objects) w component is _very_ close to zero,
but not exactly zero... Say, .00000000000000001, ect... The 3d object
with w at zero might be able to "notice" the 4d object and blame it on
some paranormal activity? Is is way too far out there? Deep in the heart
of kookville? It's all in good fun and interesting thoughts for sure.