On 1/1/25 6:29 AM, Farley Flud wrote:
> We all know that the volume of a cube with each side = 1
> is equal to 1. That's because volume = 1^3 = 1.
>
> In fact, the volume of any higher dimensional hypercube
> is also 1 because in any dimension n the volume = 1^n = 1.
>
> Example, the volume of a hypercube of 100 dimensions is
> 1^100 = 1.
>
> But what is the volume of a 100D hypersphere of radius = 1
> that is inscribed within this 100D hypercube?
>
> Answer: π^50/30414093201713378043612608166064768844377641568960512000000000000
>
> = 2.3682021018828293*10^-40
>
> = 0.00000000000000000000000000000000000000023682021018828293
>
> Why so fucking small, when the volume of the containing hypercube
> is 1.0?
>
> In fact, as the dimensions increase further, a hypersphere of radius=1
> has a volume that approaches zero.
>
> How can this be?
>
> Consider a hypersphere of radius = 1 mile. As the dimensions increase
> the volume will approach 0 cubic miles (i.e. nothing, zip, nada).
>
> But the containing hypercube will always have a volume of 1 cubic mile.
>
>
> Oblinux:
>
> Maxima CAS was used to do the exact calculations.
>
>

Sounds like something one gets tempted to ask AI about it.

On Thu, 2 Jan 2025 16:55:28 -0600, Physfitfreak wrote:

>
> Sounds like something one gets tempted to ask AI about it.
>

IMO, that's a very bad attitude to take. One should not
always immediately run to AI as if it is a panacea.

But that's just what the commercial vendors want you to do.

--
Systemd: solving all the problems that you never knew you had.

On Thu, 02 Jan 2025 16:55:28 -0600, Physfitfreak wrote:

>
> Sounds like something one gets tempted to ask AI about it.
>

There's no need for AI (even it could give an answer).

The answer is in the "corners."

A hypercube of n dimensions has 2^n corners, and it is these corners
that contain most of the volume.

An inscribed hypersphere will always touch each face of the cube but
it always curves away from the corners.

Furthermore, the distance from the center of the hypercube (and its
inscribed hypersphere) to each corner is sqrt(n) * r, where n is the
number of dimensions and r is the radius of the hypersphere and also
the length of 1/2 side of the hypercube.

Thus as n increases, so too does the distance to each corner from
the center of the hypersphere.

N-D spaces are fascinating places.

For n=100, the cube has 2^100 corners with each corner located
10 units from the center of a hypersphere of radius = 1 unit.

That's LOT of hypervolume outside of the hypersphere but still
inside the hypercube.

--
Hail Linux! Hail FOSS! Hail Stallman!

On 1/3/25 8:20 AM, Farley Flud wrote:
> On Thu, 02 Jan 2025 16:55:28 -0600, Physfitfreak wrote:
>
>
>>
>> Sounds like something one gets tempted to ask AI about it.
>>
>
> There's no need for AI (even it could give an answer).
>
> The answer is in the "corners."
>
> A hypercube of n dimensions has 2^n corners, and it is these corners
> that contain most of the volume.
>
> An inscribed hypersphere will always touch each face of the cube but
> it always curves away from the corners.
>
> Furthermore, the distance from the center of the hypercube (and its
> inscribed hypersphere) to each corner is sqrt(n) * r, where n is the
> number of dimensions and r is the radius of the hypersphere and also
> the length of 1/2 side of the hypercube.
>
> Thus as n increases, so too does the distance to each corner from
> the center of the hypersphere.
>
> N-D spaces are fascinating places.
>
> For n=100, the cube has 2^100 corners with each corner located
> 10 units from the center of a hypersphere of radius = 1 unit.
>
> That's LOT of hypervolume outside of the hypersphere but still
> inside the hypercube.
>
>

Yes, makes sense. There'll be more corners and therefore a smaller
volume for the hypersphere. Interesting. But for some reason I feel I've
got other, much more down to earth, facts of life entangled with me.

For instance, when I boot and out of blue, nothing comes up on the
screen, but computer lights indicate normal activities, is it the fault of:

1. Dell OptiPlex 7050 micro computer's GPU?
2. its displayport receptacle?
3. the displayport plug of the display cable?
4. the wire part of the display cable?
5. the DVI plug at the other end of the display cable?
6. the DVI receptacle at the back of the monitor?
7. Something inside the monitor burnt perhaps?
8. Something inside the 7050 burnt perhaps?

The only suggestion Relf ever had in his life for _any_ computer issue
was, "Get a new display cable." So ...

9. Should I order a new display cable?

I've thrown away all damaged monitors which worked but the display was
messy. So I have nothing to change the present monitor with to see if
problem is with monitor's end of the system. All my other computers are
nicely stowed away after hours of work, as of last night. So ...

10. Should I go fuck it up again and get them into a mess like they were
before I carefully carried them away and placed them there away from
cats, nice and neat, just to see monitor works with them correctly?

Things of this nature. Hehe :)

Doesn't go well with n-dimensional hyperstuff.

On 1/3/25 2:32 AM, Farley Flud wrote:
> On Thu, 2 Jan 2025 16:55:28 -0600, Physfitfreak wrote:
>
>>
>> Sounds like something one gets tempted to ask AI about it.
>>
>
> IMO, that's a very bad attitude to take. One should not
> always immediately run to AI as if it is a panacea.
>
> But that's just what the commercial vendors want you to do.
>
>
>
>
>

People do that with Wikipedia all the time. And AI is much much better
than Wikipedia for certain stuff. Wikipedia cannot tell you what the
name of some movie you saw in 1972 was. Give a few clues you remember
from the movie and AI places the name right in front of you :)

I forget little from good movies, but I always forget the name of it.
Even right after seeing it the name is history as far as my mind is
concerned.

On 2025-01-03, Farley Flud <fsquared@fsquared.linux> wrote:
> On Thu, 02 Jan 2025 16:55:28 -0600, Physfitfreak wrote:
>
>
>>
>> Sounds like something one gets tempted to ask AI about it.
>>
>
> There's no need for AI (even it could give an answer).
>
> The answer is in the "corners."
>
> A hypercube of n dimensions has 2^n corners, and it is these corners
> that contain most of the volume.
>
> An inscribed hypersphere will always touch each face of the cube but
> it always curves away from the corners.
>
> Furthermore, the distance from the center of the hypercube (and its
> inscribed hypersphere) to each corner is sqrt(n) * r, where n is the
> number of dimensions and r is the radius of the hypersphere and also
> the length of 1/2 side of the hypercube.
>
> Thus as n increases, so too does the distance to each corner from
> the center of the hypersphere.
>
> N-D spaces are fascinating places.
>
> For n=100, the cube has 2^100 corners with each corner located
> 10 units from the center of a hypersphere of radius = 1 unit.
>
> That's LOT of hypervolume outside of the hypersphere but still
> inside the hypercube.

What part of this is NOT off topic?

--
“Evil is not able to create anything new, it can only distort and destroy
what has been invented or made by the forces of good.” —J.R.R. Tolkien

On Fri, 3 Jan 2025 20:21:12 -0600, Physfitfreak wrote:

>
> Yes, makes sense. There'll be more corners and therefore a smaller
> volume for the hypersphere. Interesting. But for some reason I feel I've
> got other, much more down to earth, facts of life entangled with me.
>

The space in which we exist is 4-D.

But for some idiotic reason, the educational system still instructs
students that we exist in 3-D space. Only those choose to become
scientific specialists later in life actually learn the truth.

>
> For instance, when I boot and out of blue, nothing comes up on the
> screen, but computer lights indicate normal activities, is it the fault of:
>

Monitors don't need input to be diagnosed. Monitors have
buttons or switches located somewhere to allow configuration.
If the monitor is functional, those buttons should produce
a display on the screen.

Maybe it is just that the wrong input has been selected,
e.g. VGA instead of HDMI.

Get a copy of the monitor manual and find out how to enter
the configuration.

>
> Things of this nature. Hehe :)
>
> Doesn't go well with n-dimensional hyperstuff.
>

There is more to life and living than laboring for
immediate practical ends -- or at least there should
be. Otherwise we are no more than slaves.

Recreational mathematics is a fantastic pastime, and
GNU/Linux provides the tools for glorious exploration.

--
Systemd: solving all the problems that you never knew you had.

On Sat, 4 Jan 2025 07:39:32 -0000 (UTC), RonB wrote:

>
> What part of this is NOT off topic?
>

The part in which you inserted your boorish, ignoramus ass.

That's what part.

--
Systemd: solving all the problems that you never knew you had.

On 1/4/2025 4:31 AM, Lameass Larry wrote:

> Recreational mathematics is a fantastic pastime

booorrrriiiinnnnggggg!

If you're looking for some scientific computing code to plagiarize:

Professor John Burkardt of Florida State and Univ South Carolina

https://people.sc.fsu.edu/~jburkardt/
https://people.math.sc.edu/Burkardt/

On 1/4/25 3:33 AM, Farley Flud wrote:
> On Sat, 4 Jan 2025 07:39:32 -0000 (UTC), RonB wrote:
>
>>
>> What part of this is NOT off topic?
>>
>
> The part in which you inserted your boorish, ignoramus ass.
>
> That's what part.
>
>
>

I was going to suggest telling him, "If my dick is what's doing it, it
is on topic." :)

On 1/4/25 3:31 AM, Farley Flud wrote:
> On Fri, 3 Jan 2025 20:21:12 -0600, Physfitfreak wrote:
>
>>
>> Yes, makes sense. There'll be more corners and therefore a smaller
>> volume for the hypersphere. Interesting. But for some reason I feel I've
>> got other, much more down to earth, facts of life entangled with me.
>>
>
> The space in which we exist is 4-D.
>
> But for some idiotic reason, the educational system still instructs
> students that we exist in 3-D space. Only those choose to become
> scientific specialists later in life actually learn the truth.
>
>
>>
>> For instance, when I boot and out of blue, nothing comes up on the
>> screen, but computer lights indicate normal activities, is it the fault of:
>>
>
> Monitors don't need input to be diagnosed. Monitors have
> buttons or switches located somewhere to allow configuration.
> If the monitor is functional, those buttons should produce
> a display on the screen.
>
> Maybe it is just that the wrong input has been selected,
> e.g. VGA instead of HDMI.
>
> Get a copy of the monitor manual and find out how to enter
> the configuration.
>
>>
>> Things of this nature. Hehe :)
>>
>> Doesn't go well with n-dimensional hyperstuff.
>>
>
> There is more to life and living than laboring for
> immediate practical ends -- or at least there should
> be. Otherwise we are no more than slaves.
>
> Recreational mathematics is a fantastic pastime, and
> GNU/Linux provides the tools for glorious exploration.
>
>
>
>
>

Monitor's buttons themselves?.. Hehhehh :-) You sure live in fairyland.

Let's see. I have five tomcats. Each urinates on it about five times a
day, really each time they see me spending my time in front of it they
must join in the effort. It's a social matter for them. That makes it 25
layers of urine per _one_ day, that all slide down and gather where the
"buttons" of the monitor are, and get semi dried slowly turning into a
sticky paste.

My monitors last 3, max 4 weeks before screen goes bad viaother routs
that urine takes, but the buttons underneath it will much earlier than
that become glued with 300 or 400 solidified layers of urine, and even
hammering the buttons won't make them move. The buttons will get crushed
by hammer, but crushed _in_place_ without moving!

That's my monitor's buttons, dude :)

This is still my older monitor I'm using, cause the new one I got on
31st Dec, when I proceeded to install it I found that it required a
power adapter .. Hehe :) I guess that's why it was $5 less than other
ones. It didn't come with its power adapter. The other ones which I
didn't buy (and will perhaps, tomorrow) used a simple computer power
cable. I have a box full of various power adapters in the attic and one
might work with this new monitor. But that's another project.

But last night after having a nice hot tea, no sugar, I went and fetched
the $12 9020 thing back out of the taped boxes (it's not just tomcats
that urinate on them, it is the baby roaches also that go inside them -
hence taping them). Looked at its back, it does have displayport
receptacles. I connected it to monitor and powered it up (uses same
power adapter that 7050 does) and screen does not come up. But 9020 also
has a VGA port. So this time I went to the attic with a flash light (its
own light is turned off - there's a short somewhere) and after plowing
through a half ton of dust I got the box that I had VGA cables in it.
The monitor also, of course, is old enough to have a VGA receptacle on
its back.

And what do you know, the monitor works. So, loosely speaking, I've so
far reduced the problem to either the monitor cable, or to my 7050 GPU.
The latter doesn't have a VGA receptacle, only displayport and HDMI. The
monitor does not have an HDMI receptacle.

But I can't still order a cable like Relf would. Cause the problem might
be just the DVI port of the monitor and not the cable. So this matter is
still open.

I'm writing this, right now, using the $12 thingy, but with the 7050's
SSD instead of the HD that it came with, and after messing with "set up"
when booting. For some reason 9020 changes the set up to "legacy" while
this SSD does not want that. So each time I boot, I have to also
manually remove the legacy support for it to boot up.

So what would you suggest? I'm sure it is too soon to order a new
monitor cable.

But the point is, as I said, with such messes to deal with, who needs
n-dimensional figures to think about :)