Re: Mystery of High Dimensions [NOT OT]

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.