Dali and the Fourth Dimension: "Impossible" Objects, Part II

Robert Heinlein's short story "And He Built a Crooked House" is sort of a guided tour of a tesseract.

There is a fantastic museum dedicated just to Salvador Dali right on the waterfront in downtown St. Petersburg, Florida. It's an interesting building at a very scenic location. Worth a visit if you're ever in the Tampa - Clearwater - St. Petersburg area.

The Dali

Went there recently. When I got to the parking lot and stepped out of the car my first thought was the building was designed by cubists!

My favorite work of his is "The Discovery of America by Christopher Columbus".

I went there years ago, long before the new building was built. I always liked the variations on the 'Persistence of Memory' with the melted clocks. I also liked the digital Abraham Lincoln one, though I can't remember if I saw it there or in a book about his work.

The thing you can't pull out of the pictures you see in the text books and magazines is the extraordinary minute detail in his paintings.

Even his large works have very fine resolution in the details.

I had the fortune to see "The Artist's Eye" at the Henry Gallery in Seattle. The detail was indeed extraordinary. I don't recall this painting being reproduced in a few books I have about Dali's work, so it was a most delightful surprise.

I recall having pondered on these sort of 4th dimensional approximations years ago in high school. (I had lots of free time in study hall.)

Just adding more 3D boxes to the original box at odd angles is a rather poor representation of the 4th dimension in my opinion.

To me adding the 4th dimension of time does not change the shape of an item it only adds that concept of when to it. The X,Y,Z reference points, and distances relative to each other if any, stay the same but given the T dimension they are only going to be potentially offset relative to all common reference points by the distance changes, if any, that occurred over the additional dimensional unit T.

X,Y,Z +- XT,YT,ZT sort of.

Well it make sense to me better that a bunch of additional oddly angled and positioned cubes does any way.

I'm with you. I would say viewing a slow-motion video of a cube falling or maybe a water droplet would suit me better. But here are a couple of videos I pulled up to check out all the same. They might give you a different perspective on the subject. Then again, they might not

http://www.youtube.com/watch?v=uDaKzQNlMFw

http://www.youtube.com/watch?v=MN4KC_zlW4g

I guess it all comes down to what the fourth dimension is going be defined as. To me its based on time which is something we can perceive yet is not one the three primary dimensions we interpret as our reality but has an observable effect and influence on everything associated with the other three as we perceive them.

To me adding extra theoretical to us physical dimensions fits into the 5th 6th and so on dimensional aspects since they would be extend parts of our primary three physical ones but not necessarily moved through the fourth that we can perceive being ethereal the point in time dimension.

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My wife just asked me what I am doing and I told her I am studying up on the fourth dimension of time.

She then asked why would you want to learn about that?

I said, because I want to finish my time machine.

She then asked, well do you have it working yet?

I said, Well you're still here aren't you? So the answer is obviously no!

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I find that joke relatively funny!

Hi Usbport. Good presentation about the "hyper-cube" issue (you call it "tessaract", I prefer to call it "hyper-cube", as it is a geometrical object located in the 4D hyper-space). However, I'd like to add a comment-correction.

What you have shown as a hyper-cube presentation on a 3D space -i.e. the "cube inside the cube"- is not the geometrical presentation -i.e. the geometrical projection- of a hyper-cube on a 3D space, but actually it is the optical projection of a hyper-cube on a 3D space. I made some drawings to show you that.

Consider a cube located above a plane as shown in the Figure1 (i.e. a cube's face is parallel to the plane). Consider this cube as a "construction made of wires". Above this cube there is a light source. As the light falls on this cube, you'll see the cube's shadow on the plane. This shadow is shown in Figure2 -i.e. a "square inside a square"- and this is, actually, the optical projection of the cube on the plane. In the same way, what you have shown as a "cube inside a cube", is actually the optical projection of the Hyper-cube on a 3D space.

So, in order to be precise, as the actual geometrical projection of a cube on a plane (i.e. an image on a plane) is like that:

then the respective, actual geometrical projection of a hyper-cube on a 3D space (i.e. imagine it as a construction on a 3D space) is like in Figure3:

Figure4 shows the way to design such a shape. There are two cubes located on the 3D space, shifted to each other, with their respective edges connected. The Hyper-cube is combined by 8 cubes, although most of them are distorted due to the geometrical projection (in the same way that most squares in the geometrical projection of a cube on a plane are distorted due to the geometrical projection.)

A 'rotating' tesseract...

Yes, I have already seen such animations in the past. It's fun to "chose" one of the cubes and watch it changing its position and be distorted, as the Hyper-cube is rotating.

#6 didn't show up on my page... here is a different version.