The Grail in Camelot Castle

The Grail in Camelot Castle

In the last vignette, The Grail in Camelot College, we saw how the Grail works. In this one, we explore how to use it to restore the land to its new fertility.

Let’s call our system of creativity from the previous vignette the Da Vinci System. Right now, you can generate the necessary tables to create mathematical structures using a word processor. It works, but it’s clumsy: you must type in each component and structure by hand and organize everything yourself.

But what if there were dedicated software?

Enter STEAM CAD—short for Conceptual Aided Design. With it, the process becomes streamlined, efficient, and scalable to include more tables and levels.

Still, even this doesn’t yet restore fertility to the land.

The steam engine alone didn’t change the world; it needed a factory.

So, what kind of factory could we build for Da Vinci CAD?

Surprisingly, the answer is simple. All we need is to combine three types of software with a 3D printer, and we create a new kind of fully integrated manufacturing system, one that turns mathematical ideas into physical objects:

Da Vinci CAD becomes our creativity engine, where ideas are formed and structured.

Those ideas inspire designs using a graphic design engine like Great Stella by Robert Webb.

The designs are exported to a slicing program, like Bambu Studio, which prepares them for the printer.

Finally, the 3D printer brings them into the world.

Table 1 illustrates the 3-step process from mathematical design, graphic design to 3D print. 

With this, we have a system that transforms abstract thought into tangible reality. Examples of 3D printed mathematics that have created with this system can be found here: Albert P. Carpenter - 3D Printed Sculptures 

Moreover, since there are atomic and molecular analogues for geometric components like points, lines, polygons, and polyhedra, the entire system can, in principle, be adapted for molecular printing—simply by replacing Great Stella with Crystal Maker software and using molecular printers instead of FDM 3D printers.

As it stands: Great Stella, Bambu Studio, and 3D printers already exist.
The only thing missing is Da Vinci CAD. (Appendix 1 includes a possible user interface.) There is no software program currently available that has the capability to bridge the gap between mathematics and graphic design.

Returning to the mirror metaphor from the vignette Occam’s Chalice:
Science is that mirror.
It holds up the reflection of reality, and Occam’s sword and Occam’s chalice tell us what can and cannot appear within it. The laws of matter and energy explain why.

Taken together, they describe a reflection of the world in which language plays only a passive role as a mirror of the world.

But with the integrated manufacturing system described above, the situation changes, and language becomes a dynamic agent in the world where linguistic structures become the physical structures of the world.

Allow me to explain.

Since geometric structures have molecular analogues, it means the two languages of mathematics and science—structural geometry and structural chemistry—can be converted from one into the other.

This, in turn, means we can build mathematical or molecular ideas using Da Vinci CAD and use a molecular printer to create them.
In this way, scientific ideas expressed as words become physical realities, but only with technology: computers, software, and printers.

As science (literally, "knowledge") becomes matter,
the King and the Land become one—
in the languages of both science and myth.

And so to extend the language of myth:

This is how the Grail returns, how my journey comes full circle —

and the Wasteland blooms again.