I have a very long history of studying, constructing and playing with higher dimensional objects and since they are naturally of an intangible nature it seemed to me that NFTs are perhaps a perfect medium to actually possess one.
Not sure what a Non Fungible Token (NFT) is? Look into it and come back!
To understand the description to come, let’s start with discussing shadows and 3 dimensional objects. When you consider a three dimensional object it is no doubt obvious that it’s shadow on a flat surface will be two dimensional. A shadow is fundamentally the simultaneous projection of every 3d point in an object to a 2d point on a surface; it effectively converts a 3d object to a 2d object by discarding one of its dimensions.
What may not be so obvious though, but for the same reasons as above for 3d objects, is that the shadow of a four dimensional object actually has three dimensions, not two! So to be clear, if I could somehow posses a 4d object and a 4d flashlight to shine at it I would be able to cast a 3d shadow; I have always absolutely loved this concept 🙂
My piece of art is based on a play of shadows and dimensions and starts with a painstakingly constructed 4 dimensional hypercube. This hypercube was developed using excel, a custom C# program to build (and test) the hypercube that I designed and various voxel software to visualize the 3d projections. And while there isn’t a good way for me to actually *show* you this hypercube I can, as we discussed above, show you the four 3d shadows it would cast from each direction in 4 dimensions, and that is just the start!
Here is one of the 3d shadows with some slight transparency and animation to give a better sense of the complexity of each cube:
As you can see, each of the cubes is perforated in a very unusual way; any guesses why?!
Well now that we have four 3d shadows of our hypercube, we can now cast shadows of those 3d shadow cubes themselves to get plain-old 2d shadows! If we do so for each of the three dimensions of the cube we will get these twelve 2d shadows (three shadows from each shadow cube):
Now if for each cube we arrange its three shadows in a row like above and then we stack all four sets of those shadows on top of one another, we will find that all the holes will cancel out leaving only a couple distinct points of light left that light could pass through as you can see below:
If you look closely you will find that this final shadow composited from those 2d shadows of those 3d shadows of the 4d hypercube is in fact Morse code!
I thought long and hard on what this message should contain. This is such a terrific opportunity for a message that speaks over the backdrop of the transcendence of the simple from the complex, from 1 dimensional data to 4 dimensional data, a secret, a profound statement worthy of such elaborate obfuscation… but ultimately I came up with nothing I felt worthy.
So I studied Samuel Morse more in search of inspiration and came to find that when he was set to send the first message on May 24th 1844 across a United States experimental telegraph line stretching from Washington DC to Baltimore he was not sure what to send to mark the momentous occasion either. What he ultimately transmitted was the suggestion of the young daughter of a friend, Annie Ellworth, and I think it was the perfect choice to express the hope, opportunity, danger and unknown consequence of advances in technology. The message:
“What hath God wrought?”
.– …. .- – …. .- – …. –. — -.. .– .-. — ..- –. …. – ..–..
The accepted digital formats of the major NFT marketplaces are constrained to images, videos and audio so a data file containing 4D coordinates was not possible. With that in mind I decided I would encode the actual 4d hypercube data as an image. Each coordinate of the 4d object that occupies space is mapped to 2d space as a black pixel and each 4d-hole as a white pixel. This algorithm is fully reversible so that the image produced can be converted back into the data; it is not an interpretation or result of the data, it IS the data!
While I anticipated the output to be effectively static, it is just binary data after all, I was very pleased to see that the image is actually quite dark and beautiful. It is reminiscent of a tapestry, recurrent patterns of the cube faces are throughout and as much as I think about it I am frankly still not certain as to why I see the emergence of asymmetrical patterns come through. You can really appreciate the nuances by zooming in as on some displays it can appear like a black box.
I am very happy with the product and I think as an NFT it is engaging, unique, beautiful, mysterious and compelling on multiple levels; and for me, that is what good art is about. As my first NFT I am very curious to see if others out there can share the same appreciation for both the final product as well as the effort required to create it.
Update: I have since expanded my collection of hyperdimensional NFTs and dedicated a separate page to cataloging them here: Four Shadows NFT Collection
Here is the final algorithmic image output and a link to purchase this NFT:
How lucky I am to love and be loved by a true genius?! Good job baby.