Message #2730

From: Melinda Green <>
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.


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, 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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