Tuesday, February 9, 2016

Absolutely, Holes are Relative

This blog is normally about what computer programmers can/should learn from philosophers. Occasionally though, there is a posting like this about what philosophers can learn from programmers...

In An Introduction to Ontology[1], there is a discussion about whether holes “exist” (where “exist” has a technical Philosophical meaning). In laying out the pros/cons of defining a hole as a region of space, the (fatal?) flaw with the approach is claimed to be that, when the thing that had the hole in it (say a pair of jeans) moved to the next room, the hole wouldn’t/couldn’t move because it was defined as a particular region of space.

I, as a computer programmer, am left dumbfounded that anyone would make the definition of a hole be an absolute region of space, any more than they would define the geometry of each leg in the jeans as being an absolute region of space.

As modeled in typical vector drawing logic, the legs and the hole would each simply be a “part” of the jeans entity. Each part typically has attributes defining its contents (often simplified to just its color), so the left leg is denim/blue and the hole is void/transparent. Alternatively, the hole can be thought of as a “subtractive” part which simplifies the description of the geometry of things that have holes. (Beware of saying “that just simplifies the math but it isn’t real” because that's what they said when Copernicus noted that the math was simpler if planets orbited the sun rather than everything orbiting the earth).

CAD/CAM systems often model things as having parts known as features[2], which include not only subtractive “passages” (two openings, i.e. holes), but also subtractive “depressions” (one opening, i.e. dents) and subtractive “voids” (zero openings, i.e. completely enclosed). These are in addition to additive “protrusions”, “connectors” and “stand-alone volumes”. Don’t think a protrusion is an entity (or at least a part)? Don’t peninsulas exist?

So, just as no one has a problem with saying that the leg part of the jeans is a cylinder whose location is relative to the parent jeans, there should be no problem saying that the hole is passage relative to the parent left leg (just over the knee). After all, isn’t a hole always a hole in something? (yes, I know there is philosophical debate about this, like everything else).

The real head-scratcher, for me, is why it is apparently so non-obvious to the philosopher, that the textbook on this stuff simply ends the a-hole-is-a-region-of-space discussion with “this theory gets it thoroughly wrong”. There is no mention of “you know, there is a trivial rebuttal to that objection”. But that is why occasionally this blog has posts about what Philosophers can learn from Programmers.

[1] An Introduction to Ontology, Nikk Effingham, Polity Press, 2013
[2] Parametric and Feature-Based CAD/CAM, Shah/Mantyla, 1995, Section 7.3.1 Form Feature Schema