In the meantime Alistair from the office sent me a quick note that got me thinking: in the BIM community we generally talk about drafting tools that deal with drawings separately as "2D", and then the ones where all the information gets stored in a single model as "3D". All clear up to that. Then we get about 4D (time) and even 5D (money) to describe the advantages of meta-data and database capabilities in our beloved Building Information Models.

But in modern physics there is a diferentiation between "Spacetime", where time and distance measurements are combined in a single manifold, in the Relativistic approach and multi-dimensional Euclidean space (which is the geometry we are taught in school). So our "fourth dimension" is another distance, but somehow measured "inside the 3D point". Also, degrees of freedom would increase (Civil Engineers in the room correct me if I'm wrong):

In a 1D world elements can only move back and forth,

In 2D they can move up-down and rotate in 1 direction,

In 3D they can move in 3 directions and rotate around 3 axia.

In 4D...? Well I'm not sure, but I suppose they can move in 4 directions (remember the 4th is moving but staying in the same XYZ location) and rotate in 7 directions???

Consequences: if we imagine a "planar world" and a naughty 3D object trying to hide, it would just jump to another value of "Z"... becoming invisible to the fellow 2D objects... who could only see the projection or the intersection to their 2D space. Maybe UFOs and Aliens are among us, but just hiding in the 4th dimension...

Besides, all our screens (until recently at least) are a 2D surface, where the 3D space (represented by vectors and coorinates) gets projected to flat plans, sections, axonometric and perspective views. Similar abstract programming can transform the virtual 4D space into computer screens to "play with it in virtual reality" and research shows that human brain can actually interact with 4D space without too much training...

Thanks again to Alistair for the brain-teaser, hoping to have gotten you thinking just like he did with me, here's a couple of links to read further:

http://en.wikipedia.org/wiki/Fourth_dimension

http://math.eretrandre.org/4dbb/index.php

wich also reminded me of a quote from one of my favourite movies:

Neo: I know what you are doing.Back to the projects, I'm making progress on the Genetic Design, so expect a follow-up shortly.

Morpheus: I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it.

Have a nice week!

William.

Loving the new angle on the BIM / maths ;)

ReplyDeleteYou are sort of right with the degrees of freedom - they will increase if you are referring to a phase space (they might not if you are referring to a mechanical system...so watch out for the civil engineers).

In some of our models we need 2 dimensions of time - one for phasing (existing, demolitions, phase 1, etc) and one for site operation timlining. Technically I suppose they could both be wrapped up but the different scales of the dimensions are important for different presentations (e.g. phasing for planning, phasing for construction). Similarly we also can have dimensions for design options. We did actually try to use all of these as proper 'dimensions' (i.e. that they really did overlay one another) but it was painful. Maybe w ned to curl up our dimensions just like theoretical physicists ... anyone up for an 11-D attempt?