# Message #2730

From: Melinda Green <melinda@superliminal.com>

Subject: Re: [MC4D] Re: Puzzle in Minkowski Space?

Date: Thu, 02 May 2013 16:17:21 -0700

Certainly this is a question whose answer currently is "don’t know", but

the question itself is already a great contribution. Time is such a

funny dimension and has been one of the most difficult to deal with in

my career. Naturally people first think of mapping time to animations

over time, but I don’t find that terribly interesting. I would much

rather see iso-surfaces built from MRI data for example than to watch 2D

slices moving up and down through a 3D density field. A simple stock

chart is a better use of a time dimension when needing to understand a

given equity than something bouncing up and down during animation. We

therefore naturally roll time into a spatial dimension, which is an

improvement, but still something seems to be missing. The big question

is what exactly is missing? I think so far I may be just restating what

Roice expressed. I would like to reframe the question as "how can we

treat time in a more intrinsic way?" Whatever falls out from that

question, I would like to then ask what might be the most interesting

meanings and visualizations and puzzles that can be designed explicitly

in 0+2 or 0+3 spaces, or really any topologies involving more than one

time dimension.

-Melinda

On 5/2/2013 3:45 PM, schuma wrote:

> Thanks for the attention!

>

> OK, a 2D hyperbolic tiling lives on a 2D surface in a Minkowski 2+1 space. Here the Minkowski space is just a model that can be replaced by a disk model, say. So I think Minkowski is not essential in this application.

>

> My question is more about, can we define 3D puzzles that fill a 3D region in a Minkowski 2+1 space?

>

> Nan

>

> — In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:

>> In a sense (for 2D tilings), hyperbolic tilings are the

>> regular tessellations/polytopes of a Minkowski 2+1 space. E.g. one can

>> think of the {7,3} living on a constant radius surface in Minkowski space,

>> just as one can think of the spherical tilings living in Euclidean 3+0

>> space, and the Euclidean tilings living in Euclidean 2+0 space. (Of

>> course, one doesn’t have to think of all these objects being embedded in

>> any of these spaces - they can be looked at just from the "intrinsic

>> geometry" perspective.)

>>

>> I purposefully didn’t write Minkowski space*time* above by the way. One

>> can still think of Minkowski 2+1 space without thinking of time. The

>> "distance" between points is just calculated in a weird way, with one

>> component having a negative contribution. This makes me wonder though…

>> What would a {7,3} tiling look like as an animation, where that special

>> component was plotted along the time dimensions? Would the regular

>> heptagons even be recognizable?

>>

>> Roice

>>

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