Message #1095

From: Jonathan Mecias <jonathan.mecias001@mymdc.net>
Subject: Re: [MC4D] New: Questions thread…
Date: Tue, 27 Jul 2010 21:13:06 -0400

wow! I understand it perfectly now. Thanks Cris and Roice! now.. lemme ask
a crazy question. whats a 4D twist like is it just a combination of
"elementary 3D twists "? I think i know what a rotation in 4D is ie like on
the MC5D like the Y-U button . So, a 5D rotation would be U-V ? i was
always curious about this, but i never was too sure on the subject.

Jonathan

On Tue, Jul 27, 2010 at 11:52 AM, Roice Nelson <roice3@gmail.com> wrote:

>
>
> Chris covered everything well, but I figured I’d still mention that I’ve
> always liked the MC4D FAQ answer to the question of what it means to twist<http://superliminal.com/cube/faq.html#Q8>.
> I think it helps in understanding differences like this between the 3D and
> 4D puzzles.
>
>
>> Q8: So what does it mean to "twist" on a 4D magic cube?
>> A: People generally think of twists in 3D as turning something about an
>> axis. It’s just a quirk of three dimensions that that makes any sense,
>> and is no help in the general case. It’s better to think about a twist on
>> the 4D cube as follows: Take the face you want to twist and remove it from
>> the larger object. Turn it around any way you like without flipping it over,
>> and then put it back so that it fits exactly like it did before. On a 3D
>> magic cube, there are therefore only four possible ways to put the face back
>> on. With a "face" of a 4D cube, it’s like taking a cube out of a box,
>> turning it any which way (but not turning it inside-out), and putting it
>> back in its box. There are 24 different ways to do this.
>
>
> Roice
>
>
> On Tue, Jul 27, 2010 at 9:40 AM, Chris Locke <project.eutopia@gmail.com>wrote:
>
>>
>>
>> It’s more of a shortcut than anything really. For each face in 4D, there
>> are 24 possible twists (that includes the identity twist - i.e. the
>> do-nothing twist). There are three axis through each face, and if you label
>> a quarter-twist of the axes X, Y, Z respectively, then it turns out all the
>> possible twists can be built from a combination of these elementary twists.
>> The corner and edge twists are basically a combination of these fundamental
>> twists and are not necessary. They were added because we can use our 3D
>> intuition to see that it should be possible to twist along an axis that is
>> not the x, y, or z axis. Such rotation axes go through edge and corner
>> pieces, so it is added as an possible twist.
>>
>> In 5D there are most definitely many ways of twisting a given face that
>> are simply defined by just 2c pieces, but there are basically 3 reasons why
>> only these are available. One, it is much harder for us to visualize a 4D
>> face to ‘see’ what possible ways you can twist it that are not the 2c
>> fundamental twists. Two, how one would allow the user to execute these
>> twists in the given interface is a difficult problem. Three, since all
>> twists can be built up by those fundamental 2c twists anyway, it is already
>> a completely operational 5D puzzle, and the additional twists would just
>> make it possible to push twist counts to lower values.
>>
>> So yes, while it would be possible to implement such a feature, I imagine
>> it would have little pay-off and a lot of headache to implement. Besides,
>> extra overhead could possibly just end up cluttering the interface.
>>
>> Hope what I’ve said is accurate. Let me know if I’ve made a mistake in my
>> observations.
>>
>> Chris
>>
>> 2010/7/27 Jonathan Mecias <jonathan.mecias001@mymdc.net>
>>
>>
>>>
>>> Hmm good question. i want to know the answer too because im not 100% sure
>>> why you can rotate by clicking on corners and edges. Can any one elaborate
>>> on this?
>>>
>>>
>>> On Mon, Jul 26, 2010 at 5:23 PM, deustfrr <deustfrr@yahoo.ca> wrote:
>>>
>>>>
>>>>
>>>> Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you
>>>> can rotate by clicking on corners and edges (corner&edge turns). Why is that
>>>> possible?
>>>> I think I asked over 9000 questions so I just made this thread
>>>>
>>>>
>>>
>>
>>
>>
>
>