How are René Descartes sleeping habits and what I do at CeorfanWorks connected?

Descartes (1596 – 1650), the French mathematician (scientist and philosopher), apparently did not like to get up early. Allegedly, while Monsieur Descartes was enjoying one of his frequent morning lie-ins he was watching a fly on his ceiling. Being the curious type of fellow he was rather than thinking about what he was going to eat for breakfast (or lunch depending what time he decided to get up), he was trying to work out how he could describe the position of the fly mathematically. He realised that if you use the corner of the ceiling as a point of reference you could locate the fly by measuring the distance along each straight edge going from that corner of the ceiling.

Nowadays we typically use this way of indicating a point as horizontal and vertical positions on a graph and they are called Cartesian coordinates, so named after our favourite late-rising French polymath. These values are described as X values for the horizontal axis and Y for the vertical axis. They can be used to describe individual positions and even shapes (using algebraic equations) on any flat plane.

If you now imagine laying our flat piece of graph paper on a table and then adding another straight axis coming up from the surface of it, we can locate any position above or below our grid by giving the 3rd dimension which is indicated as the Z-axis. This means that based on a given reference point to measure from we can describe any point in space by giving the X, Y and Z measurements (positive or negative) from that point – for more technical info see Wikipedia - https://en.wikipedia.org/wiki/Cartesian_coordinate_system.

This way of indicating positions is critical to how the CNC-machine we use at CeorfanWorks operates. The CNC (Computer Numerically Controlled) machine is essentially a robot with a spindle (like a powerful drill) attached to it that can be programmed to cut out parts using rapidly rotating, shaped, cutting-tools. Each time you use the machine you provide it with a reference point for the end of the tool, typically on the corner or middle of your piece of material. This is X-zero, Y-zero and Z-zero. Now based on moving from that position we can send it to any point within its work-space using our Cartesian coordinate system described earlier.

Positions are fed to the machine many times per second by computer files that may contain thousands and potentially millions of coordinates. While it is possible to program these values as a manually written list, that would not allow you to cut anything very complex in a timely fashion. This is where the Computer Numerically Controlled part comes in. Complex cutting-programs are generated using specialist software to first draw either the 2D or 3D shapes you want to carve. Then either the same or different software can be used to create the list of coordinates, derived from what we have drawn, that we can feed to machine to get it to move our tool and cut the parts. These lists of Cartesian coordinates are typically known in the CNC world as “toolpaths”.

The design part of this type of software is called CAD (Computer Aided Design) and the part that generates the paths for the CNC-machine is known as CAM (Computer Aided Manufacturing). This of course is where Descartes involvement goes full circle as using this technology for making things you can literally say “I think therefore I CAM”…