Cubes & Spheres (2001/08/07)

Cubes & Spheres

Posted by Philip Ayres on 2001/08/07 11:24

I believe that Borg technology is Scalable - IE not all Cubes and Spheres
are of the same size. Witness in First Contact the Sphere that
effectively is an Escape Vessel from the Cube.

The Cube in Best of Both was far larger than the Enterprise D. Voyager is
considerably smaller than the D, yet was proportionately bigger than the D
against that Cube. Therefore there are Cubes of diffrent sizes.

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Cubes & Spheres

Posted by Chris Turner on 2001/08/07 11:43

On Tue, 7 Aug 2001, Philip.Ayres@ wrote:

I believe that Borg technology is Scalable - IE not all Cubes and Spheres
are of the same size. Witness in First Contact the Sphere that
effectively is an Escape Vessel from the Cube.

Given the Borg's arrogance - why would they have such a device onboard a
Cube? I wonder if they built it once they realised they were in trouble.

The Cube in Best of Both was far larger than the Enterprise D. Voyager is
considerably smaller than the D, yet was proportionately bigger than the D
against that Cube. Therefore there are Cubes of diffrent sizes.

I'm assuming you meant Voyager was proportionately smaller? It makes
perfect sense if you think about it. What happens to all the space ships
they "assimilate"? All the Cubes you've seen so far have looked like junk
from the outside, so it seems feasible that they dismantle the ship and
expand the craft. Otherwise - it'd get very crowded.

I think we've even see new Cubes & Spheres being built in Dark Frontier, but
it's been ages since I've seen it. I can't think where else they'd build
them otherwise, apart from Borg HQ.

Chris

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Cubes & Spheres

Posted by George Proctor on 2001/08/07 14:01

Chris Turner <christ@> 08/07 11:43 am >>>

On Tue, 7 Aug 2001, Philip.Ayres@ wrote:

I believe that Borg technology is Scalable - IE not all Cubes and Spheres
are of the same size. Witness in First Contact the Sphere that
effectively is an Escape Vessel from the Cube.

Given the Borg's arrogance - why would they have such a device onboard a
Cube? I wonder if they built it once they realised they were in trouble.

Was the Sphere really an escape vessel? I figured it was part of the Borg's=
original plan - Cube strides into Federation space, destroys Starfleet arm=
ada, launches Sphere into past, Sphere stops first contact, assimilates Ear=
th. A plan which would have worked nicely if not for the Enterprise, plus t=
he fact that the Borg's shields apparently weren't working that day.

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Cubes & Spheres

Posted by Philip Ayres on 2001/08/07 17:04

On Tue, 7 Aug 2001, Philip.Ayres@ wrote:

I believe that Borg technology is Scalable - IE not all Cubes and Spheres
are of the same size. Witness in First Contact the Sphere that
effectively is an Escape Vessel from the Cube.

Given the Borg's arrogance - why would they have such a device onboard a
Cube? I wonder if they built it once they realised they were in trouble.

It's a good question - but there's no reason why the Borg shouldn't use shuttles, probe
vessels etc.

The existance of a Borg scout vessel is started in I Borg. (Wot was crashed at the
begining) Maybe that's what we saw in FC.

The Cube in Best of Both was far larger than the Enterprise D. Voyager is
considerably smaller than the D, yet was proportionately bigger than the D
against that Cube. Therefore there are Cubes of diffrent sizes.

I'm assuming you meant Voyager was proportionately smaller?

No.

Against the Cube they nearly hit last night Voyager looked to be a significant proportion
of the Cube's length.
Against the BoBW Cube the Enterprise D looked to be much smaller.

The Intrepid Class Voyager is smaller than the Galaxy Class Enterprise D

Therefore there is more than one size of Cube since the Cube last night has to be smaller
than the BoBW.

It makes
perfect sense if you think about it. What happens to all the space ships
they "assimilate"? All the Cubes you've seen so far have looked like junk
from the outside, so it seems feasible that they dismantle the ship and
expand the craft. Otherwise - it'd get very crowded.

Good point. Sounds about right.

I think we've even see new Cubes & Spheres being built in Dark Frontier, but
it's been ages since I've seen it. I can't think where else they'd build
them otherwise, apart from Borg HQ.

I wonder if it's possible to dock 8 of the same size Borg Cube together and form a larger
Cube vessel ?

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Cubes & Spheres

Posted by Rey Blewitt on 2001/08/07 17:30

you could always stack 3 cubes on top of each other, put them in a line and
then roll a sphere at them.

-----Original Message-----
From:Philip Ayres [SMTP:payres@]
Sent:07 August 2001 16:04
To:chat
Subject:Re: Cubes & Spheres

On Tue, 7 Aug 2001, Philip.Ayres@ wrote:

I believe that Borg technology is Scalable - IE not all Cubes and

Spheres

are of the same size. Witness in First Contact the Sphere that
effectively is an Escape Vessel from the Cube.

Given the Borg's arrogance - why would they have such a device onboard a
Cube? I wonder if they built it once they realised they were in

trouble.

It's a good question - but there's no reason why the Borg shouldn't use
shuttles, probe
vessels etc.

The existance of a Borg scout vessel is started in I Borg. (Wot was
crashed at the
begining) Maybe that's what we saw in FC.

The Cube in Best of Both was far larger than the Enterprise D.

Voyager is

considerably smaller than the D, yet was proportionately bigger than

the D

against that Cube. Therefore there are Cubes of diffrent sizes.

I'm assuming you meant Voyager was proportionately smaller?

No.

Against the Cube they nearly hit last night Voyager looked to be a
significant proportion
of the Cube's length.
Against the BoBW Cube the Enterprise D looked to be much smaller.

The Intrepid Class Voyager is smaller than the Galaxy Class Enterprise D

Therefore there is more than one size of Cube since the Cube last night
has to be smaller
than the BoBW.

It makes
perfect sense if you think about it. What happens to all the space

ships

they "assimilate"? All the Cubes you've seen so far have looked like

junk

from the outside, so it seems feasible that they dismantle the ship and
expand the craft. Otherwise - it'd get very crowded.

Good point. Sounds about right.

I think we've even see new Cubes & Spheres being built in Dark Frontier,

but

it's been ages since I've seen it. I can't think where else they'd

build

them otherwise, apart from Borg HQ.

I wonder if it's possible to dock 8 of the same size Borg Cube together
and form a larger
Cube vessel ?

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Philip Ayres
payres@
www.netcomuk.co.uk/~payres
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Cubes & Spheres

Posted by Philip Ayres on 2001/08/07 18:35

you could always stack 3 cubes on top of each other, put them in a line and
then roll a sphere at them.

<Brief Terrahawks Flashback>

Ummm.. Maybe.

Philip - who got his Space 1999 DVDs today.

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www.netcomuk.co.uk/~payres
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Cubes & Spheres

Posted by Mark L. on 2001/08/07 21:34

You could stack 7 of them into the shape of an unfolded hypercube and see if
it collapsed into a real hypercube when you shot them (who wrote that story
with the hypercube house - I can't remember?). Then you could shoot them a
bit more while all the drones were trying to make sense of the new geometry.

Mark

I wonder if it's possible to dock 8 of the same size Borg Cube
together and form a larger
Cube vessel ?

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Philip Ayres
payres@
www.netcomuk.co.uk/~payres
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Cubes & Spheres

Posted by Ron W. on 2001/08/07 21:39

Wot's a Hypercube?

Some of us don't have the benefits of obscure mathematical backgrounds to
draw on, thank you.

Now, if you want to know how Borg nanotechnology probably works (short
answer, it doesn't), then perhaps I can help...

=$-)

You could stack 7 of them into the shape of an unfolded hypercube and see
if
it collapsed into a real hypercube when you shot them (who wrote that
story
with the hypercube house - I can't remember?). Then you could shoot them a
bit more while all the drones were trying to make sense of the new
geometry.

Mark

Cubes & Spheres

Posted by Simon Richardson on 2001/08/08 12:13

Wot's a Hypercube?

Some of us don't have the benefits of obscure mathematical backgrounds to
draw on, thank you.

Take a box of matches and some plastique.

No, actually it doesn't need to be matches and plastique,
cocktail sticks and blu-tack will do. Now, consider one
stick. Think of your cocktail stick as a representation of
a one dimensional line segment. Peer at it from one end,
and see how it is just a dot.

Now grab some blu-tack and three more cocktail sticks.
Join them together and you have a square. This is a
representation of a plane segment. Look at it from one
side, and it looks like a couple of lines, one of which
looks bigger than the other. If you remove one blob
of blu-tack you have a line with three joins in it, which
can be folded into a square, if you use a second dimension.

So put it on the table, and add four uprights and another
square on top. Your twelve sticks now should be approximately
a cube.

If you wanted to represent your cube with cardboard, cut
a crucifix shape, four cubes in a row with two hanging out
the sides. You can fold it up into a cube if you use the
third dimension.

Now take some more blu-tack and another sixteen cocktail
sticks, and add another seven cubes around your cube to
make a ... no wait, you're not following me, are you?
Or if you are, I don't want to see what's on your table now,
because I've already lost enough SAN. But if you look along
the edge of it, it should look like a couple of cubes, one bigger
than the other. They are actually the same size, but one
is further away than the other But you can represent
it with cubes, like the cardboard. You need four cubes in
a row, and four around the second cube along, one on either
face. Think of this as the equivalend of that cardboard
cross. But don't think too hard, it'll make your brain ache.

Now, if you want to know how Borg nanotechnology probably works (short
answer, it doesn't), then perhaps I can help...

=$-)

You could stack 7 of them into the shape of an unfolded hypercube and see
if
it collapsed into a real hypercube when you shot them (who wrote that
story
with the hypercube house - I can't remember?). Then you could shoot them a
bit more while all the drones were trying to make sense of the new
geometry.

The short story is called "And he Built a Crooked House" and
is by Robert Heinlein.

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Cubes & Spheres

Posted by Andy W. on 2001/08/08 13:05

<snip>

Now take some more blu-tack and another sixteen cocktail
sticks, and add another seven cubes around your cube to
make a ... no wait, you're not following me, are you?
Or if you are, I don't want to see what's on your table now,
because I've already lost enough SAN. But if you look along
the edge of it, it should look like a couple of cubes, one bigger
than the other. They are actually the same size, but one
is further away than the other But you can represent
it with cubes, like the cardboard. You need four cubes in
a row, and four around the second cube along, one on either
face. Think of this as the equivalend of that cardboard
cross. But don't think too hard, it'll make your brain ache.

Too late. I'm trying to figure out how what you've just described can look
like two cubes, and it just doesn't. I think I'll go and buy a book on
higher dimensions and see if I can get my head round it. Any
recommendations?

Andy
_____________________
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www.knightsofni.freeserve.co.uk
07968 357 854

Cubes & Spheres

Posted by Asan Tu on 2001/08/08 13:32

<snip>

Now take some more blu-tack and another sixteen cocktail
sticks, and add another seven cubes around your cube to
make a ... no wait, you're not following me, are you?
Or if you are, I don't want to see what's on your table now,
because I've already lost enough SAN. But if you look along
the edge of it, it should look like a couple of cubes, one bigger
than the other. They are actually the same size, but one
is further away than the other But you can represent
it with cubes, like the cardboard. You need four cubes in
a row, and four around the second cube along, one on either
face. Think of this as the equivalend of that cardboard
cross. But don't think too hard, it'll make your brain ache.

Too late. I'm trying to figure out how what you've just described can look
like two cubes, and it just doesn't. I think I'll go and buy a book on
higher dimensions and see if I can get my head round it. Any
recommendations?

have a look at

http://torina.fe.uni-lj.si/~zlobec/cube/Cube.html

instead

Cubes & Spheres

Posted by Andy W. on 2001/08/08 13:38

Too late. I'm trying to figure out how what you've just described can

look

like two cubes, and it just doesn't. I think I'll go and buy a book on
higher dimensions and see if I can get my head round it. Any
recommendations?

have a look at

http://torina.fe.uni-lj.si/~zlobec/cube/Cube.html

instead

Very pretty, but it doesn't look much like a cube to me.

Andy
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www.knightsofni.freeserve.co.uk
07968 357 854

Cubes & Spheres

Posted by Charlotte R on 2001/08/08 14:42

Too late. I'm trying to figure out how what

you've just described can
look

like two cubes, and it just doesn't. I think

I'll go and buy a book on

higher dimensions and see if I can get my head

round it. Any

recommendations?

I would recommend a book called Hyperspace, by Michio
Kaku, (ISBN 0-19-286189-1) it explains all the strange
multi-dimension stuff really well. Even I understood
it so it must be good! It has hypercubes, black
holes, wormholes, time travel and two dimensional
ostriches (really it does)!

Charlotte

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Cubes & Spheres

Posted by Andy W. on 2001/08/08 15:10

----- Original Message -----
From: "Charlotte Ruddick" <andromeda_explorer@>
To: <chat@>
Sent: Wednesday, August 08, 2001 2:42 PM
Subject: Re: Cubes & Spheres

Too late. I'm trying to figure out how what

you've just described can
look

like two cubes, and it just doesn't. I think

I'll go and buy a book on

higher dimensions and see if I can get my head

round it. Any

recommendations?

I would recommend a book called Hyperspace, by Michio
Kaku, (ISBN 0-19-286189-1) it explains all the strange
multi-dimension stuff really well. Even I understood
it so it must be good! It has hypercubes, black
holes, wormholes, time travel and two dimensional
ostriches (really it does)!

Charlotte

You know I would probably have bought it even if hadn't mentioned the
Ostriches, but I'm going to have to now...

Andy
_____________________
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www.knightsofni.freeserve.co.uk
07968 357 854

Cubes & Spheres

Posted by Philip Ayres on 2001/08/08 14:31

Now take some more blu-tack and another sixteen cocktail
sticks, and add another seven cubes around your cube to
make a ... no wait, you're not following me, are you?
Or if you are, I don't want to see what's on your table now,
because I've already lost enough SAN. But if you look along
the edge of it, it should look like a couple of cubes, one bigger
than the other. They are actually the same size, but one
is further away than the other But you can represent
it with cubes, like the cardboard. You need four cubes in
a row, and four around the second cube along, one on either
face. Think of this as the equivalend of that cardboard
cross. But don't think too hard, it'll make your brain ache.

Too late. I'm trying to figure out how what you've just described can look
like two cubes, and it just doesn't. I think I'll go and buy a book on
higher dimensions and see if I can get my head round it. Any
recommendations?

I think what your proposing looks like a Plus symbol in all direction -
you've got a cube at the center, and each of it's faces is against the face
of another cube. All of the other 6 cubes have 5 exposed faces, and one
face against one of the faces of the other cube. It might be worth getting
7 identical D6. Take one and bluetack each face. Onto each bit of
blutack stick another D6. I think that's what we mean....

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Cubes & Spheres

Posted by Andy W. on 2001/08/08 13:43

Now take some more blu-tack and another sixteen cocktail
sticks, and add another seven cubes around your cube to
make a ... no wait, you're not following me, are you?
Or if you are, I don't want to see what's on your table now,
because I've already lost enough SAN. But if you look along
the edge of it, it should look like a couple of cubes, one bigger
than the other. They are actually the same size, but one
is further away than the other But you can represent
it with cubes, like the cardboard. You need four cubes in
a row, and four around the second cube along, one on either
face. Think of this as the equivalend of that cardboard
cross. But don't think too hard, it'll make your brain ache.

Too late. I'm trying to figure out how what you've just described can

look

like two cubes, and it just doesn't. I think I'll go and buy a book on
higher dimensions and see if I can get my head round it. Any
recommendations?

I think what your proposing looks like a Plus symbol in all direction -
you've got a cube at the center, and each of it's faces is against the

face

of another cube. All of the other 6 cubes have 5 exposed faces, and one
face against one of the faces of the other cube. It might be worth

getting

7 identical D6. Take one and bluetack each face. Onto each bit of
blutack stick another D6. I think that's what we mean....

Not quite. What you need to do is take the shape you've just described and
stick another D6 onto it to create a sort of crucifix with another cross-bar
sticking out at right angles. Where you take it from there though is
completely out of my league.

Andy
_____________________
andy@
www.knightsofni.freeserve.co.uk
07968 357 854

Cubes & Spheres

Posted by Simon Richardson on 2001/08/08 15:50

-----Original Message-----

From : Philip Ayres <payres@>

To : chat@
Date : 08 August 2001 14:31:18
Subject : Re: Cubes & Spheres

Now take some more blu-tack and another sixteen cocktail

sticks, and add another seven cubes around your cube to
make a ... no wait, you're not following me, are you?
Or if you are, I don't want to see what's on your table now,
because I've already lost enough SAN. But if you look along
the edge of it, it should look like a couple of cubes, one bigger
than the other. They are actually the same size, but one
is further away than the other But you can represent
it with cubes, like the cardboard. You need four cubes in
a row, and four around the second cube along, one on either
face. Think of this as the equivalend of that cardboard
cross. But don't think too hard, it'll make your brain ache.

Too late. I'm trying to figure out how what you've just described can look
like two cubes, and it just doesn't. I think I'll go and buy a book on
higher dimensions and see if I can get my head round it. Any
recommendations?

I think what your proposing looks like a Plus symbol in all direction -
you've got a cube at the center, and each of it's faces is against the face
of another cube. All of the other 6 cubes have 5 exposed faces, and one
face against one of the faces of the other cube. It might be worth getting
7 identical D6. Take one and bluetack each face. Onto each bit of
blutack stick another D6. I think that's what we mean....

Yes, except that you need to add the eighth one on the end of one,
so one of the six arms is longer than the others. Now you have an unfolded hypercube. To refold it, simply fold it at 90 degrees at each
place a cube touches another.

Can you see that? If you can, you're very strange. :-p

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Cubes & Spheres

Posted by Charlotte R on 2001/08/08 17:32

Yes, except that you need to add the eighth one on
the end of one,
so one of the six arms is longer than the others.
Now you have an unfolded hypercube. To refold it,
simply fold it at 90 degrees at each
place a cube touches another.

Can you see that? If you can, you're very strange.
:-p

oh no that means I'm very strange!
*grin*

Charlotte who has a very weird brain

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Cubes & Spheres

Posted by Nick Waterman on 2001/08/08 17:56

Charlotte Ruddick wrote:

Yes, except that you need to add the eighth one on
the end of one,
so one of the six arms is longer than the others.
Now you have an unfolded hypercube. To refold it,
simply fold it at 90 degrees at each
place a cube touches another.

Exaxctly. The 8-cube thing with a 3D cross of D6 plus an extra one is
just like the FLAT crucifix-shape that gets folded and attached to make
a cube, or a bit like the 4 line segments that haven't yet been folded
into a square.

Having got your D6 (which I'll call C for the Centre), attached another
D6 to each face (which I'll call N, S, E, W, U, and D), and another one
off of one of those (which I'll call O because it's the cube that'll end
up being "opposite" C) to make your 8-cube unfolded hypercube, you then
need to fold each 90 degrees through some other spare dimension, and
attach each cube to the faces of the appropriate cubes they meet up
with. You'll then find that from C, you can head N into N, N again into
O, N again into S, and N again to return to your starting point in C.
Similarly, head up into U, up again into O, then maybe west into E, west
again into C. This is exactly the same, in 4D, as walking across the
faces of your D6 in 3D from 1 to 2, 2 to 6, 6 to 5, and 5 back to 1.

Walk on your D6 in any direction for 2 faces and you're opposite where
you started. Keep walking in the same, or any other direction, for 2
more faces, and you're back where you started. The hypercube works in
exactly the same way but it's 4D instead of 3D, so your walk can go up
or down, not just N,S,E,W.

Can you see that? If you can, you're very strange.
:-p

oh no that means I'm very strange!
*grin*

Me too... I think. I can't actually visualise a hypercube, but I can
understand how it might fit together as described above. I can also
understand a bit of the "curved space" stuff - the leap from 3D to 4D is
a bit like the leap from 2D maps into 3D space.

Nick Waterman. Senior Systems Administrator, SO-NET, Sony UK
mailto:nick-sig@ http://www.nilex.co.uk/~nick/
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